Wikiversity enwikiversity https://en.wikiversity.org/wiki/Wikiversity:Main_Page MediaWiki 1.45.0-wmf.7 first-letter Media Special Talk User User talk Wikiversity Wikiversity talk File File talk MediaWiki MediaWiki talk Template Template talk Help Help talk Category Category talk School School talk Portal Portal talk Topic Topic talk Collection Collection talk Draft Draft talk TimedText TimedText talk Module Module talk 0 2130 2719938 2719845 2025-06-28T12:42:05Z Prototyperspective 2965911 rvv (2 edits by [[Special:Contributions/208.40.86.22]]) 2719938 wikitext text/x-wiki {{Using Wikiversity}} A '''wiki''' is a type of [[w:Website|website]] that allows users to easily add, remove, or otherwise [[Wikiversity:FAQ/Editing|edit]] and change the content of the webpages. The openness and ease of editing page content makes a wiki an effective tool for [[w:collaborative writing|collaborative authoring]]. Welcome to the '''Wiki''' learning project. If you are new to wikis, take a look at the [[Wikiversity:Introduction|introductory tutorial]]. ==Project description== This Wikiversity [[Portal:Learning Projects|learning project]] is devoted to learning how to use '''[[w:Wiki|wiki]]''' technology to facilitate online learning. It is amazing. You can edit and learn how to make Wikipedia better. When you edit or make any page you can feel proud that you are one of the members of the best site and you will also feel proud that you are a wiki editor. You will have fun by editing and making your own pages. [[Wikipedia]] is one of the stages on which you can show your talent and can give your [[Knowledge|knowledge]] to millions of people. ==Learning materials== Wikiversity has adopted the "learning by doing" model for education. Lessons should center on learning activities for Wikiversity participants. [[Portal:Learning Materials|Learning materials]] can be used by multiple departments. Cooperate with other departments that use the same learning resource. *[[Wikiversity:Introduction]] — New to Wikiversity? Start here! *[[Introduction to Wiki]] — Introduction to wiki editing and wiki communities which aims to function as a service project for the Wikiversity community and provide learning resources that will aid new Wikiversity editors. *[[Wiki 101]] — A supplement to the [[m:MediaWiki|MediaWiki Handbook]] geared toward Wiki editing at Wikiversity. This lesson goes into detail about Namespaces, Templates, Lists, Tables and other tools for advancing Wikiversity editors. *[[Named colors|Named Colors]] — An alternative way to add color to pages rather than dealing with Hex, octal, RGB codes and other cryptic forms. *[[Learning to learn a wiki way|Learn to learn a wiki way]] — using wiki technology to support learning. *[[Nature of wikis]] — a cultural introspective of wiki communities and their workspaces. * ... Learning materials are located in the main Wikiversity [[Wikiversity:Namespaces|namespace]]. Simply make a [[link]] to the name of the lesson (lessons are independent pages in the main namespace) and start writing! ==References== ===Wikipedia=== *[[w:Wiki|wiki]] ===Wikibooks=== Works in progress - these texts are currently at [[b:__Department Name___]]: * [[b:__Textbook Name___]] ==Active participants== The histories of Wikiversity pages indicate who the active participants are. If you are an active participant in this project, you can list your name here (this can help small projects grow and the participants communicate better; for large projects a list of active participants is not needed). * [[User:MarkMayhew]] - working on learning business applications of wikis. * [[User:Rayc]] --working on creating tests * [[User:JWSchmidt]] - I am currently interested in starting some exciting [[Portal:Learning Projects#General projects|community-wide projects]] for Wikiversity * [[User:Dionysios|<b>Dionysios</b>]] [[User_talk:Dionysios|^{<span style="color: #FF9933;">(talk)</span>}]], a Participant in the [[School:Advanced general studies|<b>Wikiversity School of Advanced General Studies</b>]], Date: [[w:2007|2007]]-[[w:July 18|07-18]] ([[w:July 18|July 18]], [[w:2007|2007]]) Time: [[w:1331|1331]] [[w:UTC|UTC]] [[Category:{{PAGENAME}}| ]] ==See also== *[[Wikipedia#Learning resources]] - list of learning resources on Wikipedia *[[Portal:Wiki]] - under construction *[[Wikiversity:Wiki as a tool for learning|Wiki learning project]] - Investigation of the implications of wiki technology for online learning. *[[Introduction to Wiki]] - this project aims to function as a service project for the Wikiversity community and provide learning resources that will aid new Wikiversity editors *[[Introduction to Wikiversity]] - learning how to participate at Wikiversity *[[Wikimedia]] - Wikiversity is a Wikimedia Foundation sister project *[[Portal:Education]] *[[Learning to learn a wiki way]] *[[Wikiversity:Be bold]] *[[Wikiversity:History of Wikiversity]] {{Web 2.0}} ==External links== * [http://www.youtube.com/watch?v=-dnL00TdmLY Wikis in Plain English] - 3 minute video. * [[b:Wiki Science|Wiki Science]] at Wikibooks. * [[w:Wiki|Wikis]], a key part of [[w:Web 2.0|Web 2.0]] - Wikipedia [[Category:Introductory articles in need of repair]] nykr3t507h7653zzr2kvq62hvtjdy1t 2 29185 2719982 1723303 2025-06-28T23:13:10Z Андрей Романенко 153209 ([[c:GR|GR]]) [[c:COM:FR|File renamed]]: [[File:Ardf 0001.jpg]] → [[File:Stephan Koeberle from Germany at the 2004 ARDF World Championship.jpg]] unspecified name 2719982 wikitext text/x-wiki [[User:CQ/THD|THD]] is an acronym for [http://ecovillage.wikia.com/wiki/Turkey_Herding_Deer Turkey Herding Deer], the name of a developing eco-farm in Southern Illinois, USA. owned by my friend Crystal. I am collecting research materials and resources for a long-term project to plan and build the eco-farm which we hope will someday turn into a full-featured [[w:ecovillage|ecovillage]]. This page is here to document our adventures. [[Image:Receding_glacier-en.svg|thumb|right|500px|The interesting terrain of THD EcoFarm was sculpted by the retreat of the [[w:Wisconsin glaciation|Wisconsin glaciation]] over 10,000 years ago]]. == Other Sites == THD EcoFarm and Agroecology online: * [http://ecovillage.wikia.com/wiki/Turkey_Herding_Deer THD at the Ecovillage Wiki] * [http://www.localharvest.org/listing.jsp?id=17675 THD at LocalHarvest] * [http://asap.sustainability.uiuc.edu/members/charleyquinton CQ at ASAP] * [http://wikieducator.org/User:CQ CQ at WikiEducator] == Learning resources == [[Renewable energy]] ===Wikipedia=== '''[[w:Portal:Agriculture|Portal:Agriculture]]''' *[[w:Agriculture|Agriculture]] *[[w:Agroecology|Agroecology]] *[[w:Agroforestry|Agroforestry]] *[[w:Cultivation|Cultivation]] *... ===Wikiversity=== '''[[Portal:Agriculture|School:Agriculture]]''' *[[Agriculture]] *[[Agroecology]] *[[Agroforestry]] *[[Cultivation]] *... '''[[School:Engineering]]''' *[[Renewable energy systems]] *... == About THD == <div class="messagebox"> {|style="width:100%;background:none" |width=110px align=center|[[Image:US EcologyFlag.gif|100px]] |From [http://www.csrees.usda.gov/nea/nre/in_focus/ecosystems_if_wrkgp.html Ecological Goods and Services Working Group]: ''Due to complex relationships and feedbacks among people, ecosystems, and the biosphere, human well-being is inextricably linked to the optimal use and management of ecosystems.'' |} </div> The purpose and mission of Turkey Herding Deer eco-farm and research center is to demonstrate how Humans can create a [[w:built environment|built environment]] that interfaces well to the [[w:natural environment|natural environment]]. The facility is to become a testbed for study, demonstration and experimentation: *[[w:Keyline Design|Keyline Design]] principles and cultivation *Discovering [[w:Wildlife|Wildlife]] and responsibly managing its [[w:habitat|habitat]] *Understanding the [[w:edge effect|edge effect]] between developed and wild environments *Demonstrating [[Green building]] and [[w:Agroecology|Agroecology]] *Developing [[Renewable energy]] resources ([[w:Renewable energy|solar, wind, hydrodynamic, geothermal]]) *[[w:Hydrology|Hydrology]] and [[w:watershed|watershed]] management *[[w:Permaculture|Permaculture]], [[w:organic farming|organic farming]], [[w:community-supported agriculture|community-supported agriculture]], etc. *''fully open to ideas'' The plan is to engage the THD land in a long-term program of soil-building, permaculture, watershed management and an array of other Earth-friendly practices that could make the place a prototype for the future of land use and community development. The vision includes a program in which interns learn about organic farming, [[w:bioneering|bioneering]], animal husbandry, conservation, ecosystem study, communal living, etc. Grid-independant housing and accomodations are to be built according to developing ecologically sustainable standards aligned with current university research programs. == Where on Earth is THD? == The THD land is located near the headwaters of a major branch of [[w:Casey Creek|Casey Creek]] near [[w:Texico, Illinois|Texico]], [[w:Illinois|Illinois]] - [[U.S. states|USA]]. *Latitude: 38.428748 *Longitute: -88.917031 == Who's who == A few people I've met or plan to meet and their organizations: *[http://asap.sustainability.uiuc.edu/members/dananderson Dan Anderson] is the director of ASAP - the '''Agroecology / Sustainable Agriculture Program''' of the Department of Natural Resources and Environmental Sciences in the College of Agricultural, Consumer and Environmental Sciences at the [[w:University of Illinois at Urbana-Champaign|University of Illinois at Urbana-Champaign]] *[http://www.centerforsustainablecommunity.org/Events/Permaculture/WeismanBio.html Wayne Weiseman] of Dayempur Farm in Southern Illinois, a land-based, self-reliant community project combining organic crop/food production, ecologically-built shelter, renewable energy, appropriate technologies and educational programs. Wayne is director of [http://www.permacultureproject.com/index.html The Permaculture Project] *[http://www.henrysfarm.com/ Henry Brockman] and his whole family began raising organic vegetables in 1993 near Evanston, Illinois. [http://www.illinoisfarmdirect.org/About/land_connection.html Terra Brockman] (Henry's sister) is the director of [http://www.thelandconnection.org/ The Land Connection] and was instrumental in forming along with ASAP and other organizations, [http://www.illinoisfarmdirect.org Illinois FarmDirect] - a [[w:Community-supported agriculture|CSA network]] for Illinois, USA *[http://www.midwestpermaculture.com/BillWilson.php Bill Wilson] is a communitarian, permaculturist, sustainability advocate/educator, life coach & mentor with about a 30-year history through [http://www.stellecommunity.com/ The Stelle Community] a remarkable [[w:intentional community|intentional community]] in the cornfields halfway between Chicago and Champaine-Urbana. He is also a founding director of the educational, non-profit organization [http://www.centerforsustainablecommunity.org/ Center for Sustainable Community] located in Stelle. (Stelle rhymes with "bell") *[http://www.soulmedicinejourney.com Aurora Farm Foundation] - Barbara M V Scott and Woody Wodraska teach about biodynamics, composting, land stewardship, seed collection and preservation and lots of other things. One of their goals is to help start the "university of the future" based upon the spiritual connection between Human communities and the Land. *... list is growing == Funding opportunities == I've joined the [[Research grant collaboration group]]. '''[http://ncr.sare.org/ North Central region SARE]''' - Funded by the USDA, the national Sustainable Agriculture Research and Education (SARE) program supports and promotes sustainable farming and ranching. ''(FY 2008 cycle begins in August 07)'' '''[http://www.csrees.usda.gov/ USDA Cooperative State Research, Education and Extension Service]:''' *[http://www.csrees.usda.gov/funding/rfas/nri_rfa.html National Research Initiative Competitive Grants Program] - ''[http://www.csrees.usda.gov/funding/rfas/pdfs/07_nri.doc doc] - [http://www.csrees.usda.gov/funding/rfas/pdfs/07_nri.pdf pdf]'' *[http://www.csrees.usda.gov/nea/nre/in_focus/ecosystems_if_wrkgp.html Ecological Goods and Services Working Group] *... == Hydrology == [[Image:THD upper reservoir.jpg|thumb|300px|left|This reservoir near the proposed Welcome Center & RV park is highest in elevation at 550 feet above sea level...]] ...Its overflow decends down a water course to the main creek at 480 feet at the back of the farm about a quarter of a mile behind us. A fishing lake is also formed below by an earthen dam with a level of about 520 feet. These reservoirs and their associated water course flow down one of five gorges that run from the front of the farm toward the back. A major tributary of [[w:Casey Creek|Casey Fork Creek]] runs West to East exiting the property at about 460 feet. Total surface deviation is thus right at 100 feet. The rolling land is ideally suited for micro-hydroelectric generation and [[w:Keyline Design|Keyline Design]]. [[Image:Wooded creek.jpg|thumb|right|[[w:Casey Creek|Casey Fork]] crosses THD EcoFarm running West to East toward the Northern boundary.]] Some people in [[w:Dix, Illinois|Dix]] (including the town's Water District) regard the watercourses as "ditches" and "drains". We hope to change this outlook by helping to form a '''watershed commission''' for the [[w:Big Muddy River|Casey Fork/Big Muddy system]]. Of all the [[w:Watersheds of Illinois|Watersheds of Illinois]], it is among the least represented, though cities and towns like [[w:Mount Vernon, Illinois|Mount Vernon]] and [[w:Kell, Illinois|Kell]] get their [[w:drinking water|drinking water]] from [[w:Rend Lake|Rend Lake]] downstream. I was standing in the place where we ford the creek facing West when I took the picture to the right. What you see is the affluent end (top) of our quarter-mile long stretch of the western fork of Casey Fork. This ford will become a combination filtration dam, bridge to the back acreage, and USGS guaging station as we procure funding from state and federal agencies that care about water quality. We hope to discharge nearly drinkable water at our Eastern effluent by carefully managing our tributary substreams and our part of the main watercourse. We hope to demonstrate good ecosystem management, releasing all of the documentation of our work and progress as [[Open educational resources|Open Educational Resources]] to raise public consciousness about water quality. [[Category:Open educational resources]] == Cartography == [[Image:Ardf_map.png|thumb|left|[[w:Amateur Radio Direction Finding|Amateur Radio Direction Finding]] is a new sport that could be hosted at THD]] I have had an interest in [[Portal:Cartography|map-making]] since I was a small child hearing of [[w:Amerigo Vespucci|Amerigo Vespucci]] and [[w:Ferdinand Magellan|Magellan]] in school. There's little that is more fun to me than romping around in the woods finding interesting topographical features, wild plant and animal species, following deer trails and other such [[Wikiversity:learning projects|learning activities]]. It would be great to use some sort of [[Openmoko|handheld device]] to record my adventures and upload them at the end of the day to a [[Geospatial Information Systems (GIS)|sofware model of the EcoFarm]]. [[Image:Ardf transmitter-2m.jpg|thumb|right|100px|[[w:Field (geography)|points of interest]] are marked with these low-cost [[Micro-Radio]]s]] [[Image:Stephan Koeberle from Germany at the 2004 ARDF World Championship.jpg|thumb|left|100px|[[Topic:Amateur radio|Guys like this]] would feel right at home romping around THD EcoFarm]] As an educational facility, THD is poised to become a fun place to explore. Besides the practical reasons for producing maps, we are also taking into account the "Edu-tainment" aspects of Ecotourism and Agritourism as we refine our mapping project. [[w:Amateur Radio Direction Finding|ARDF]] is a lowcost way to identify "[[w:Field (geography)|points of interest]]" such as the above-mentioned filtration dam and the epicenter of the planned Biodome to be build much later on in the horseshoe bend in the main creek. The [[Cheap IRLP Amateur Radio|Amateur radio group]] at Wikiversity is planning a series of [[Wikiversity:learning projects]] and resources for [[amateur radio direction finding]] that can be used anywhere on the planet. At THD EcoFarm, we havea ''plan'' for the '''''plan'''et''... == GIS Modeling == [[Image:THD map 01.jpg|thumb|right|400px|[[Topic:Cartography|Crude map]] of THD EcoFarm's 160 acres]] [[w:Geographic information system|Geographic information system]]s go far beyond simple mapping. The map to the right is a first pass at producing a full-featured topographical map for use as the substrate of a [[w:GIS and Hydrology|GIS and Hydrology]] Model. I hope to build a ''[[w:georeference|georeference]]d'' [[Portal:Databases|relational database]] that provides latitude, longitude and elevation for a set of points of interest all around the property. These points will represent all sorts of features - existing, historical and planned. Four major zones can be seen in the composite map: *Southwest (lower left) - The permaculture zone is about 55 acres of cleared land that has been fallow for nearly 25 years. The topography and soil conditions make it a ideal place for demonstrating [[w:Keyline Design|Keyline Design]] and soil building. A Welcome center and Eco-friendly RV park is planned (shown as small squares by the road). *Southeast (lower right) - A Circa 1900 interpretive farm and homestead is one idea for this zone. Interns will use technology, farming and forestry techniques from the turn of the last century. Antique steam engines, primitive electricity generation, human-powered equipment and other innovations from the period will be demonstrated in a live authentic way. *Village core (center) - The main lake and residence zone will include a large modern wood and metal working shop, recording studio, network operations center and other key facilities. *Ecological development zone (top) - The "back 40" includes Casey Fork Creek and a south-facing slope which is well-suited to building a line of solar-powered partially underground housing units - perhaps one of the US's first "Eco-tels" (Eco-hotel). [[w:Data modeling|Data modeling]] will help with wildlife and natural resource inventories, ecological impact studies, hydrological dynamics and design, facilities planning and maintenance, permaculture yeild prediction and a host of other geo-ecology applications. == Keyline design == In a ridge-valley system, a <b>keypoint</b> is generally the single point having the most hydrologic energy of all points between the highest and lowest elevations of an identified system. This point is characterized by the dynamics of the overall topography during a downpour as surface runoff collects along the two ridges forming a channel or watercourse somewhere along the valley floor. The keypoint is the precise point where a singular channel becomes evident for water exiting the valley toward it's draining watercourse, usually a creek or tributary headwater. The <b>keyline</b> is a line that tracks the elevation of the keypoint in both directions to the two ridge lines that enclose the valley. In the map above, notice the 550 foot elevation line that traverses the lower part of the map in the cleared southwest part of THD. This line is a fairly close approximation of a continuous keyline for a system of four ridges and three valleys that form. I'm working on a paper for the ASAP site that will use THD as an example and demonstration for the complete '''generic keyline design''' for planning dams, planting and grazing zones, roads, buildings and other features of the sustainable biodynamics testbed (permaculture zone). *[http://www.carbonfarmersofamerica.com/Holmes1.htm GEOGRAPHICAL AND TOPOGRAPHICAL BASIS OF KEYLINE] by the late Prof J. MacDonald-Holmes, Dean of the Faculty Geography, University of Sydney. ==Praxis - theory and practice== I, ([[User:CQ|CQ]]), have a set of theories and loose disciplines (oxymoron?) of how to test and prove the theories that I consider to be possibilities in the solution of what can be called '''[[w:wicked problem|wicked problem]]s'''. I favor the process of [[Successive approximation]] and [[incremental progress]] toward [[problem-solving and critical thinking]]. To ''accomplish'' things (in '''this''' world), you must be extremely patient. Nothing happens overnight, unless of course you are a [[w:Rock Star|Rock Star]] or a very well-known [[w:Athelete|Athlete]]. [[Portal:Agriculture|Farming]] is often a thankless set of daily tasks - toiling in the Hot [[w:Sun|Sun]] or in the bitter cold of [[w:Winter|Winter]]. But what THD is about is "saving the planet" and I (deeply within my heart) ''know'' that I (and my gf) are not alone in the quest to direct the resources on this fine land toward something that is truly sustainable, in every sense of the word, implementing a "this-century" focus on things that simply make [[Renewable energy systems|better sense]]. [[Image:THD Main lake.jpg|thumb|400px|right|A fishing lake is also formed below by an earthen dam with a level of about 520 feet above sea level...]] ''Sustainability'' as a term is already losing meaning. I don't purport to know about [[Soil science]], [[Animal husbandry]], [[Wildlife management]], [[Hydrology]] or even [[w:Mulch|pine straw mulch]], but i am '''''[[learning to learn a wiki way|learning]]'''''. I need people around me that are: *curious *disciplined *ethical *dedicated *creative *hard-working *resolved I welcome (and so does [http://ecovillage.wikia.com/wiki/User:Playaoms11 Crystal]) ''anyone'' who is willing to get some hands-on with a '''real''' piece of ground that is second-to-none as a '''Planetary Sweetspot''' which you will quickly see, if you come to [http://ecovillage.wikia.com/wiki/Turkey_Herding_Deer#Visiting visit]. Please '''''[[User talk:CQ/THD|talk to us!]]''''' 3ag7wxd14y744r32eqbplx80w0roi92 0 55801 2719936 2719849 2025-06-28T12:40:56Z Prototyperspective 2965911 rvv (Undo revision [[Special:Diff/2719849|2719849]] by [[Special:Contributions/208.40.86.22|208.40.86.22]] ([[User talk:208.40.86.22|talk]])) 2719936 wikitext text/x-wiki {{Educational Media Awareness Campaign/Nav}} __NOTOC__ {{Robelbox|theme=14|title=Greetings Fellow Humans,|width=100%|icon=Nuvola gaim.svg |iconwidth=48px}}<div style="{{Robelbox/pad}}"> == Goals == The goal of the [[Educational Media Awareness Campaign]] is twofold: # To help educators make the best use possible of the internet in terms of finding media to use in their learning resources. # To help educators integrate media into their learning resources both correctly and legally, paying attention to re-usability for others and permissions issues. The educational media awareness campaign is targeted primarily at the primary and secondary education sectors, but is also of use for the tertiary, informal and other education sectors. == The background == The greatest problem facing authors of digital educational resources is ''(il)legal use of images/graphic content''. Publishers, both electronic and paper-based, are constantly bombarded with submissions and uploads which have to be declined or accepted for image copyright reasons, and image copyright infringement is rampant in schools.<ref>[http://news.bbc.co.uk/1/hi/education/7283926.stm BBC News] (March 2008): "Schools using photo images downloaded from the internet on their websites are being warned they could face huge bills in unpaid copyright fees...." </ref> This is an absurd situation. It is absurd because in the last few years, the availability of well-documented, reusable and redistributable media resources from the internet has mushroomed. [http://commons.wikimedia.org Wikimedia Commons] offers in excess of 2500000 (two-and-half-million) legally re-usable, subject-related and excellently categorised images. [http://www.flickr.com Flickr] offers another 60,000,000 (sixty million) legally re-usable images, albeit less well categorised and not always so obviously subject-related. With resources such as these, nobody needs to be illegally using images. The [[Educational Media Awareness Campaign]] seeks to address this problem. The Campaign will combine the use of galleries of featured re-usable images, case studies on finding suitable media, lists of recommended internet media repositories, and tutorials on image licencing and documentation. In particular, the Campaign will usually seek to introduce educators to the ''educational'' use of Wikimedia Commons. == A multi-site effort == The [[Educational Media Awareness Campaign]] is a Wikiversity Outreach subproject which seeks to involve and coordinate with other educational and media sites. == The galleries and pictures of the day == The campaign's galleries currently include 104 selected and featured images, spread across 12 subjects of the typical school curriculum. The 100 images are carefully captioned and linked to sources of 1000's of related images, so that they can serve as entry points for educators. The 100 images are also divided into a number of dynamic pages so that they can feature on wikis as "pictures of the day", with a fresh picture each day. These rotating or dynamic page sections are available both for the whole collection and for each of the 11 constituent subjects. Investigation and analysis of digital educational resources With the progress of technology, digital educational resources are becoming increasingly diverse. Based on a survey of 82 undergraduates in our university, the use of digital educational resources shows the following characteristics: the students are more likely to use digital resources when their learning is self-directed; the search engines are the most commonly used when the students access digital resources; the students prefer to use the digital education resources by the traditional computer. To achieve the maximum utilization of digital educational resources, the educational providers should take into full account the characteristics of digital educational resources and the demands of the users == See also == *[https://outreach.wikimedia.org/wiki/Education/Archive/Main_page Outreach:Education] == References == <references /> </div> {{robelbox/close}} [[Category:EMAC]] mictwql90jbn58uw6ngvf8tpzl7qdun 0 151787 2720007 2474811 2025-06-29T10:57:03Z 42.110.169.180 Spelling mistake 2720007 wikitext text/x-wiki [[File:Munshi Ghat, Varanasi morning rituals.jpg|thumb|Munshi Ghat, Varanasi morning rituals]] ==Historical Outline== ===Ancient Period=== The city of Varanasi is archaeologically proven to have been continuously inhabited by humans since ca 800 BCE and is therefore described as one of the ancient most continuously living cities in the world. The leading prophet of Jainism, Parshvanatha, was born in Varanasi in the 8th century BCE. Later, Mahavira (599-527 BCE), the last in the line of Jain prophets (or Thirthankara-s as they are called) also made his imprint on the cultural arena of the city. The ancient city of Varanasi (popularly called Kashi) was spread between the Varana and the Gomati, the latter meeting the Ganga ca 20km north. The Indian epic Mahabharata has a passing reference to the city, but the Jataka tales of Buddhism, written after the Mahabharata, record vivid descriptions of the city. This is further supported by the literary description given in the Shatapatha Brahamana, dated ca 8th century BCE, which mentions the rich pastoral life and habitation in the northern part, the Rajghat area, of the city. Because of frequent use of clay and mud for building, human habitations were least resistant to the flooding of the river and as such physical and material evidence of earlier occupation appears to have vanished. Such evidence was unearthed at Kamauli village, lying 4km northeast from Rajghat across the Varana river. Here microlithic tools associated with a kind of Red Ware, datable to the 4th and 3rd millennium BCE were obtained underneath the sterile deposits of about 4m, just below the Sunga levels (200 BCE to the beginning of Christian era; Fig. 2). By the 4th century BCE, the Mauryan dynasty was ruling the city of Kashi. Ashoka (272-242 BCE), the great Mauryan king, had declared Buddhism a state religion and visited Sarnath. Under his patronage, a Buddhist township developed here with many monasteries, stupas and shrines. After the downfall of Mauryas, the prosperity of the city too fell into darkness until the rule of Kushana in the 1st century CE. A number of clay seals discovered at the Rajghat mounds testify to the prosperity of the township. The archaeological laonet of the houses, lanes and drainage channels shows a developed pattern of planning, as is visible even today in the old centre of the city. The city of Varanasi was rich in art, from the Kushana to the beginning of Gupta period, as exemplified by the images of Bodhisattvas, Yakshas, and Nagas. The Gupta period (ca 320-550 CE) was a period of great religious vitality and transformations. It is known as India’s Golden Age. Architectural fragments of this period are scattered in and around the city. The clay seals from this period give evidence of business, educational institutions and the importance of forests. Varanasi finally was established and recognised as a great sacred place (tirtha). During the first half of the 7th century the Chinese Buddhist pilgrim, Hsuan-tsang arrived in the city and described it as thickly populated, prospering and an important seat of learning. He mentions twenty important temples, and one of the Shiva lingas was about 30m high covered with copper plate. This in fact, was the Mauryan pillar, the fragment of which, called the Lat Bhairava, is presently only 1.5m tall. The arrival and preaching of Adya Sankaracharya in 8th century mark the revival of the Brahmanical thought, which finally uprooted Buddhism from this soil. ===Medieval Period=== In the early medieval period, Varanasi had been passed from one ruler to another --- from Maukharis of Kannauj to Gurjara Pratiharas (9th century). Finally in the early 11th century it went under Gangeyadeva, king of Kannauj. The greatest of the Gahadavalas, Govindachandra (1114-1154) is described by historians of the period as the greatest king and praised as an incarnation of Vishnu, who was commissioned to protect Vishnu’s favourite abode, the city of Varanasi. He had defeated the Muslim invaders two times during 1114-1118, and patronised the Hindu religion. Queen Kumar Devi, wife of Govindachandra, came of a Vajrayani (Tantric) Buddhist family. She restored several buildings at Sarnath and built a new vihara (monastery) there. His chief minister, Lakshmidhara is remembered as a great compiler of the most reputable and the most extensive digest of literature on dharma, composed in 14 volumes, known as the Krityakalpataru, “The Magical Wishing Tree of Rituals”. In one of its volumes, he narrates the scriptural references to over 350 shrines in Kashi and described his theory of Hindu tirtha, covering both sides of interiorisation (archetype and body symbolism) and exteriorisation (spatial affinity and orientation). Jayachandra, the grand son of Govindachandra, was a rival against Chahamans king Prithaviraja. Taking advantage of their internal conflict, Qutb-ud-din Aibak, slave-general of Muhammad Ghori, defeated Jayachandra in 1194 and beheaded him. His army sacked and looted the city, destroying nearly one thousand temples in Varanasi City alone and raised mosques on their foundation using the debris of the temples. The glorious century of the Govindachandra ended in catastrophe. The second invasion by Qutb-ud-din Aibak in 1197-98 that records the deafeat of King Harishachandra, son of Jayachandra, marks the end of the glorious of the Gahadavalas. ===Late Medieval=== In 1206 Aibak became the emperor at Delhi and reigned till 1210. The Delhi Sultanate was thus established. Duirng Muhammad Ghori’s attack, temples were destroyed again in 1300s under Firoz Shah Tughlaq (1351-1388). In the 1400s, the city came under the rule of Sharqi kings of Jaunpur, and temples were again destroyed, and their blocks hauled away for the construction of a mosque in Jaunpur. During the moments of calm, the Hindus rebuilt temples and lingas but they were again destroyed by the next wave of invaders. After the passage of time, the city came under the rule of Lodis (1451-1526), who seized power from the Sharqis, and again a major part of the city got destroyed by Sikander Lodi. A great sigh of relief was surely heaved in the late 16th century when Mughal Emperor Akbar (1556-1605) granted more religious freedom. The Rajputs Man Singh and Todarmal, the two senior ministers in the court of Akbar, participated actively in repairing, rebuilding and in new construction of temples and Varanasi ghats during this part of the Mughal period. During 11th to 17th centuries Muslim invaders destroyed the city at least four times. However, it survived and was repeatedly revived; the sites and holy spots were re-searched, the monuments were repaired and re-built. Traditions survived in spite of several ‘superimpositions’, or attempts to submerge it. The Kashi Khanda (35.10) says “The Ganga River, Lord Shiva, and the divine city of Kashi, make the Trinity of grace and perfect bliss”. The Trinity is symbolised by the three hillocks as the three forks of Shiva’s trident on which the city exists, viz. Omkareshvara in the north, Vishveshvara in the central part, and Kedareshvara in the south. With the passing of time, during the reign of Akbar’s grandson Shah Jahan (1628-1657), the imperial policy changed again. By his order, about seventy-six temples under construction were destroyed. By the order of his successor, Aurangzeb (1658-1707), in 1669-1673, once again around thousand temples including the city’s greatest temples like Vishveshvara, Krittivasa, and Vindu Madhava, were razed and their sites were forever sealed from Hindu access by the construction of mosques. In 1665 the French Traveler Jean Baptiste Tavernier, a dealer in jewels, paid a visit to Varanasi and described the grand temple of Vindu Madhava at the riverside, which he called a “great pagoda”. His account is notable because the temple was demolished in 1673 by the armies of Aurangzeb. Despite its reputation as stronghold of Hindu orthodoxy and conservatism, Varanasi participated in the vibrant devotional resurgence during 14th to early 17th centuries. Among the active poets and reformers the most notable were Ballabha, Ramananda, Kabir, Raidas, Tulasi, Caitanya and Guru Nanak. Kabir, indeed, was one of the greatest in all of Indian literature, whose colloquial songs are still sung today. Tulasi retold the epic story of the Ramayana in vernacular Hindi, naming it the Ramacharitamanasa and it remains today the single most popular classic, the Bible of the Hindi-speaking people. ===British Period=== It was from the 17th century that larger colonies of Maharashtrian Brahmans began to settle here, and with them came Vedic learning as well. After 1680 the Marathas replaced the Rajputs as major donors to the three holy places, Varanasi, Allahabad and Gaya. A fresh wave of cultural renaissance overtook Varanasi during the 18th century under the influence of the Marathas (1734-1785) who substantially rebuilt the city. The city, which had sheltered the rebel Maratha hero, Shivaji, in his challenge to Mughal power, now became the recipient of the gratitude, the wealth, the skill and energy of the Marathas. Writes a noted historian Altekar (1947: p. 24), “Modern Varanasi is largely a creation of the Marathas”. Bajirao Peshva I (1720-40) has patronised construction of Manikarnika and Dashashvamedha Ghats and nearby residential quarters. A number of ghats, water pools and noted temples of Vishvanatha, Trilochana, Annapurna, Sakshi Vinayaka and Kala Bhairava were rebuilt under Maratha patronage. Queen Ahilyabai of Indore built the present Vishvanatha temple in 1775-76. As one after another ghat was added, the temples rose, the city regained its gaiety, and its educational system was revitalised. With the decline of the government in Delhi in the early 18th century, Varanasi first came under the rule of the Nawabs of Oudh in 1722, and later became the seat of Mansaram (1730-1738), the founder of the present state of Baranas Raj in 1738. His successor Balwant Singh (1738-1770) gained the power cleverly from the Nawab in 1739 and established a fiefdom independent state, which for about forty years remained the centre of attention and source of trouble for the rising East India Company. In 1763 he built a fort on the other side of the Ganga river at Ramanagar. The tension between the two powers reached its acme in 1781, when Chet Singh (1770-1781), son of Balwant Singh, usurped the throne and put Lord Warren Hastings in serious trouble. However in 1775 Varanasi was ceded to the East India Company by the Nawab of Oudh, Asaf-ud-daula, and finally in 1794 Varanasi came under British administration with a limited jurisdiction known as ‘the Banaras State’. The face of the sacred city also changed considerably under the British rule. The urban area of the city continued to develop along the river southward and westward. Masonry bridges were built on the Ganga and the Varana river, many ponds like Benia, Maidagin and Macchodari and Godaulia Nala (rivulet) were drained and replaced by parks or streets, while many houses were demolished to widen the roads in the centre of the city. Broad roads were cut through the city where formerly there had been narrow lanes. The Dashashvamedha-Luxa Road was built running west from the river toward the Cantonment train station (now called Varanasi Junction). The north-south artery called Chauk was cleared through the business district. Slowly the city came to have its present shape. James Prinsep (1799-1840), who was the British Assay Master of the Mint in Varanasi from 1819 to 1830, published the first reliable census of the city, and also made the first and the most authentic map of the City in 1822. Moreover, on the map he has also given the latitudes and longitudes of 90 important temple and plotted over the map the Vishvanath Antargriha journey route and the temples and shrines along. In English for the first time James Prinsep (1831) has published a pictoral book. British rule brought a major change in the ancient pandit-student pattern of learning that had predominated in Varanasi for 2,500 years. By the approval of the British Governor-General Warren Hastings in 1791, Jonathan Duncan, a British resident in Varanasi, founded a Sanskrit College, and in 1853 the present buildings of the college were built in Gothic style. The oldest local educational initiative goes back to Jay Narayan Ghosal, a rich landlord from Bengal, who with the British support founded a school in 1814. On similar lines in 1898 Annie Besant, the founder of Theosophical Society in India started a Central Hindu College, a campus which proved to be only the nucleus of a growing university. In 1916, the Viceroy of India, Lord Hardinge, laid the foundation stone of what would become one of the largest and most beautiful universities in Asia, the Banaras Hindu University.Another aspect of the British period was the expansion of the activities of Christian missionaries. In 1816, the Baptist Society became the first Christian body to introduce a mission in the holy city. The Church Missionary Society of the Church of England had started to work in Varanasi beginning in 1817 and opened one churche at Sigra and another in the centre of the city at Godaulia crossing. The London Missionary Society was located in the British Cantonment beginning in 1820. Later in the century, the Wesleyan Missionary Society launched its Varanasi mission, and the Zenana Bible and Medical Mission started a hospital for women. These attempts of the Christian missions never had a chance of gaining momentum in Varanasi. ===Post Independence=== India received independence from the British rule on the 15th of August 1947, and declared a democratic republic state on the 26th of January 1950. Since 1947 no substantive change in the urban fabric and city morphology is recorded. On 15th October 1949 the district of Varanasi assumed its present form and area by the merger of the erstwhile Varanasi State (Kashiraj), and the city of Varanasi became the district headquarters. In 1948 The Banaras Improvement Trust was constituted for making ‘Master Plan of Varanasi’, and in 1951 the first such plan was prepared. Its revision and modification were made in 1973 and 1982 when the revised plans were prepared. Not a single one of these plans was implemented; all of them were delayed and recommendations were made for further revision. The latest plan was submitted on 26th February 1996, when for the first time the concept of heritage planning and preservation of heritage zones was proposed. This plan was approved and accepted by the State Government in July 2001. In this plan five cultural zones have been identified with the purpose of a special handling of these zones. In 1960s and 1970s, the Sarnath Institute of Tibetan Studies, and many Buddhist monasteries like the Chinese, Thai and Japanese were established. In 1990s many star hotels, mostly in the Mall area, were constructed to respond to the increasing influx of foreign tourists. Diesel Locomotive Works (DLW) was set up in 1961 with technical collaboration from USA; this is the only heavy industry unit in the district. In 1992 a new Hindu Observatory was opened in the compound of Sanskrit University. The five institutions, viz. Sampurnanand Sanskrit University, Mahatma Gandhi Kashi Vidyapith, Central Institute of Higher Tibetan Studies, the Parshvanatha Jain Institute, and Jamia Salfia Darul-Islamia have been given the official status of Deemed University by the University Grants Commission. ==Names and Tales== The city of Varanasi has been denoted by different names at different times in different contexts. Of course, the two names Kashi and Varanasi are the most common and were in use in early antiquity. The word Kashi means ‘concentration of cosmic light’. Kashi is the oldest name and was first used in the Atharva Veda (V.22.4), a ca.15th century BCE text: “Kashi shines and illumines the universe. Kashi makes moksha (liberation) dawn on everybody by giving wisdom”. In the period of the Mahabharata Kashi refers to the sacred city and its territory, which is comparable to the present area of Kashi Kshetra delineated by the Pancakroshi Yatra circuit. The name Varanasi refers to the capital city of the historical past, lying along the western bank of the Ganga river. The city lying between the Varana river in north and the Asi stream in south is known as Varanasi (Varana + Asi). According to a myth of the 15th century, the two rivers were created by the gods and placed in position to guard against the entrance of evil. In the early Puranas Varana river is called Varanavati or Varanasi, and the old city got its name as it was settled along the river. The Buddhist literature like the Jatakas frequently referred to Varanasi as Banarasi or Banaras. This is in fact a Pali version that became more popular and is still frequently used. According to the puranic literature Lord Shiva said “Because I never forsake it, nor let it go, this great place is therefore known as Avimukta (‘never forsaken’)”. This refers to the myth that the city was never abandoned, even in the cosmic dissolution and additionally suggests that the spirit of city itself is the bestower of liberation to everybody, irrespective of caste, creed, hierarchy or class. The Kashi Rahasya (14.39) mentions that Shiva himself explains: “My lingas are everywhere there, like little sprouts arisen out of sheer bliss”, called the Forest of Bliss (Anandavana). The remnants of the five old forests are now preserved as the names of the neighbourhoods. The whole of Kashi is a cremation ground (Mahasmashana). Shiva is the controller and divinity of the cremation place. The Skanda Purana (IV.30.103-104) explains the word as follows: “Maha’, the great, ‘sma’ means a corpse, and ‘shana’ means final rest; when the dissolution of the universe comes, even the great beings lie here as corpses and therefore this place is called Mahasmashana”. People from different parts of India came here to die with a view to receiving liberation from the transmigration. Here death is a festival and auspicious. The spiritual magnetism of Varanasi had attracted the Buddha here in the 6th century BCE to ‘Turn the Wheel of Law’. By the turn of 3rd century BCE, the great Buddhist king Ashoka had built a monastery township that flourished till 11th century CE. Now, the restored Sarnath has become a place of pilgrimage for Buddhists, and a place of spiritual tourism for others. The sense and spirit of holiness embedded in Varanasi has attracted people from various sects and religions like Vaishnavites, Shaivites, Tantrics, Buddhists, Jains, and even Muslim Sufis. In Varanasi alone, there are over 3000 Hindu shrines and temples, about 1400 Muslim shrines and mosques, 12 churches, 3 Jain temples, 9 Buddhist temples, 3 Sikh temples (Gurudvaras) and several other sacred sites and places. This is the only place in the world where such a huge number of Hindu and Muslim sacred places co-exist. The city is also known as the “City of Good Death & Liberation” and the place where ancestral souls could gain final release. {{go to top}} ⇒ [[The Varanasi Heritage Dossier|Index]] ===References=== {{Reflist|35em}} {{See also|w:Varanasi#History}} {{CourseCat}} onxbr7tcmadomwqks3581t7ne7efydo 0 207028 2719967 2652860 2025-06-28T13:43:36Z 184.54.161.253 /* What is Fair? */ changed "blacks" to "black firefighters" 2719967 wikitext text/x-wiki ==Introduction== [[File:Wikipedia scale of justice 2.svg|thumb|right|200px|Fairness is Subtle! ]] We naturally appeal to fairness to avoid or resolve conflict. Unfortunately when conflict emerges it is often difficult for adversaries to agree on what is actually fair. We often hear the complaint "But that's not fair!" Why is this? This course explores various concepts of fairness and helps the student become aware of the several forms that we consider fair. ==Objectives== The objectives of this course are to: *Define the concept of fairness, *Understand our inherent sense of fairness, *Demonstrate ambiguity inherent in our concepts of fairness, *Identify various forms of fairness, *Become aware of our own bias in suggesting what is fair when negotiating or resolving conflict, *Explore solutions that avoid bias when advocating for fairness. If you would like to contact the instructor, please [[Special:Emailuser/Lbeaumont | click here to send me an email]] or leave a comment or question on the [[Talk:Understanding_Fairness|discussion page]]. {{TOC right | limit|limit=1}} {{100%done}} {{Template:non-formal education}} {{By|lbeaumont}} The course contains many [[w:Hyperlink|hyperlinks]] to further information. Use your judgment and these [[What_Matters/link_following_guidelines|link following guidelines]] to decide when to follow a link, and when to skip over it. This course is part of the [[Wisdom/Curriculum|Applied Wisdom Curriculum]]. ==Origins of Fairness== Researcher Frans de Waal studies moral behavior in animals. Collaborating with Dr. Sarah Brosnan they conducted a famous experiment that demonstrated capuchin monkeys rejecting unequal pay. In the experiment two capuchins were caged side by side. The first was given the simple task of handing a small rock to the experimenter. For completing the task the first capuchin was rewarded with a slice of cucumber and seemed satisfied. The second capuchin was then given the same task, and rewarded with a grape. Capuchins find grapes much tastier than cucumber slices. When the task was repeated and the first capuchin rewarded with the cucumber slice, the capuchin immediately rejected this unfair reward by throwing it back at the researcher. You may enjoy seeing video of the experiment in the TED talk “[https://www.ted.com/talks/frans_de_waal_do_animals_have_morals Moral Behavior in Animals]”, Frans de Wall, filmed November 2011. Apparently fairness demands equal pay for equal work, at least for capuchins, and perhaps even for humans! ==What is Fair?== Dictionary definitions of “fair” highlight freedom from bias, dishonesty, or injustice.<ref>Dictionary.com entry for “fair”</ref> How is this concept applied? Is it sufficient for the rules of the game to be fair, or must the outcome of the process provide each person with their fair share? Is an unfair outcome evidence of unfair rules? The 2009 US Supreme Court case [[w:Ricci_v._DeStefano|Ricci v. DeStefano]] provides an opportunity to explore the concept of fairness. In this case eighteen New Haven Connecticut city firefighters, seventeen of whom were white and one of whom was Hispanic, brought suit under Title VII of the Civil Rights Act of 1964 after they had passed the test for promotions to management positions and the city declined to promote them. New Haven officials invalidated the test results because none of the black firefighters scored high enough to be considered for the positions. Because all of the applicants took the same test, the procedure used to identify the best candidates was fair. However, because the outcome of the process resulted in disparate impact to the black firefighters, the distribution of rewards—being chosen for the job—was unfair. It was argued that the black firefighters did not get their fair share. The case highlights a natural tension between the [[w:Disparate_treatment|disparate-treatment]] and [[w:Disparate_impact|disparate-impact]] interpretations of the law. Courts differed in their decisions on this case. The district court ruled in favor of the city, indicating the disparate-impact interpretation prevailed. The second circuit panel upheld that decision on appeal. However, the Supreme Court ruled in favor the defendants, finding there was no disparate-treatment and rejecting the disparate-impact argument in this case. Decisions on how to distribute the [[w:September_11th_Victim_Compensation_Fund|September 11th Victim Compensation Fund]] highlight difficulties in understanding the concept of a “fair share”. Attorney Kenneth Feinburg became responsible for making the decisions on how much each family of a victim would receive from the $7 billion fund created to compensate the families of the victims of the 9/11 terrorist attacks. This highlights the tension between proportional distribution and equal distribution alternatives. Distributing the same amount to each family would provide an equal distribution of the funds. However, there are good arguments for using a proportional distribution, using various bases for computing the proportions. Here are some alternatives: *larger families get the larger share because there are more people impacted and more people to divide the funds among, *Younger people get larger shares, because they will be living longer after the tragedy, *Distribute shares in proportion to the life earnings lost by person who died in the tragedy. Proportional distribution based on lost earnings was the primary alternative chosen. A stumbling block to settlements was the fact that many of the World Trade Center victims were highly compensated financial professionals. Families of these victims felt the compensation offers were too low, and, had a court considered their case on an individual basis, they would have been awarded much higher amounts. This concern had to be balanced against the time, complications, and risks of pursuing an individual case, and the real possibility that the airlines and their insurers could be bankrupted before being able to pay the claim. ==Three Forms of Fairness== These cases provide examples of what Johnathan Haidt describes as three forms of fairness.<ref>[http://democracyjournal.org/magazine/28/of-freedom-and-fairness/ Of Freedom and Fairness], Johnathan Haidt</ref><ref>[http://righteousmind.com/what-are-the-fairness-buttons/ What are the fairness buttons?], by Johanthan Haidt</ref> These are: '''Procedural Fairness'''—Playing by the same rules—are honest, open and impartial procedures used to decide who got what? and '''Distributive Fairness'''—Does everyone get what they deserve? This has two interpretations: *'''Equality'''—Equal outcomes, Equality as a result, everyone gets the same reward. *'''Proportionality'''—Fair share, based on effort expended, impact suffered, or some other criteria. The New Haven firefighters were arguing for procedural fairness over distributive fairness. The families of the 9/11 victims were arguing for various forms of distributive fairness, and various interpretations of proportionality. ==Fair Tax Levies== Politicians, tax payers, free riders, and revenue beneficiaries argue endlessly over the fairness of tax levies. Tax laws have become very complicated, and the need for and use of revenue collected is hotly debated. Here we will limit discussion to [[w:Income_tax_in_the_United_States#Federal_income_tax_rates_for_individuals|federal income tax rates for individuals]] in the United States. Marginal tax rates currently range from 10% for individuals with yearly taxable income below $9,275, to 39% for those with a single taxable income exceeding $415,051. Effective tax rates are typically lower than marginal rates due to various deductions, and range from zero for those with lower incomes to 20.1% for the top 1% of the population. Because the tax rate increases as the taxable amount increases, this is a [[w:Progressive_tax|progressive tax]]. Is this progressive tax levy fair? Since every person is subjected to the same tax laws, on the surface it appears to be ''procedurally fair''. But the tax law is very complicated, it offers many deductions for various reasons and exempts certain types of entities from paying taxes. [[w:Advocacy_group|Advocacy groups]] are able to influence the tax code, by [[w:Lobbying_in_the_United_States|lobbying]] legislators for example, to gain an advantage. Because individuals rarely have the resources required to influence tax laws, the creation of tax laws is not procedurally fair. Uniformly applying laws created under a procedurally unfair process leads to a procedurally unfair result. Is the resulting distribution of taxes fair? Because individuals who earn more income pay more taxes, the outcomes (in terms of the total taxes paid) are not equal. Because the tax is progressive, the tax paid is not proportional to the income earned; it is more than would be proportional under a flat tax. What happens if we look at the distribution of money ''retained after paying tax'' rather than the tax levy itself? Under today’s progressive tax plan the amount retained increases as the amount earned increases. Tax rates would have to become much more steeply progressive to result in equal amounts retained regardless of the amount earned. Arguing for or against any particular tax plan on the basis of fairness seems unable to provide a clear resolution of the many issues typically raised. It can be coherently argued that the system is or is not procedurally fair. It can be coherently argued that any particular plan results in unfair distributions of the tax burden, or of the retained income. Perhaps another viewpoint can provide better insight. === Assignment === #Choose some topic related to the [[w:Distribution_of_wealth|distribution of wealth]] to study for this assignment. This might be [[w:Wealth_concentration|wealth concentration]], [[w:Economic_inequality|economic inequality]], [[w:Progressive_tax|progressive tax]], [[w:Wealth_tax|wealth taxes]], inheritance and [[w:Inheritance_tax|estate taxes]], [[w:Old_money|old money]], [[w:Philanthropy|philanthropy]], [[w:Basic_income|universal basic income]], or some other related topic #Read the essay [[/Luck, Land, and Legacy/]]. #Propose a policy position related to your chosen distribution of wealth topic that you believe is fair. ==Deep Pragmatism== Eighteenth century philosopher [[w:Jeremy_Bentham|Jeremy Bentham]] and his successor [[w:John_Stuart_Mill|John Stuart Mill]] introduced the ''utilitarian'' philosophy. Jeremy Bentham's famous formulation of utilitarianism is known as the “greatest-happiness principle”. It holds that one must always act so as to produce the greatest aggregate happiness among all sentient beings, within reason. In his recently published book ''Moral Tribes: Emotion, Reason, and the Gap Between Us and Them'', Joshua Green revived interest in this archaic philosophy by addressing the many objections that have been raised over the centuries. He suggests using the name “deep pragmatism”, and as he explains, deep pragmatism provides the answers to two essential questions: What really matters? and Who really matters? After an in-depth exploration of these questions, he provides this shorthand answer: “Happiness is what matters, and everyone’s happiness counts the same.” It is important to recognize that the term “happiness” as it is used here is not a reference to cheap thrills, but is shorthand for a much deeper gratification, perhaps better called [[w:Well-being|well-being]], [[w:Flourishing|flourishing]], or [[w:Eudaimonia|eudaimonia]]. The connection between happiness and wealth is complex. The [[w:Easterlin_paradox|Easterlin Paradox]] holds that, "high incomes do correlate with happiness, but long term, increased income doesn't correlate with increased happiness." The economic law of [[w:Marginal_utility#Diminishing_marginal_utility|diminishing marginal utility]] expresses an important element of the relationship. This law recognizes that a few more dollars is more useful to a low-income person than it is to a high-income individual. For example, to a low income person a modest amount of additional money may mean the vital difference between eating a nutritious meal and going hungry, whereas the same amount of additional money may only slightly increase the opulence or convenience available to a high-income person. A consequence of the law of diminishing marginal utility is that income distributions approaching equality theoretically maximize total utility. This is one basis for [[w:Economic_inequality#Social_justice_arguments|social justice arguments]] in favor of sharply progressive tax levies. Using the principle of deep pragmatism rather than a variety of arguments based on fairness suggests that the most equitable tax would be a sharply progressive tax. Various claims of [[w:Moral_hazard|moral hazard]] and [[w:Incentive|disincentives]] can raise objections to this approach. == Inequality == Appeals to “reduce inequality” and often to “reduce [[w:Economic_inequality|income inequality]]” are often made in pursuit of fairness.<ref>See, for example materials at [http://Inequality.org Inequality.org].</ref> In his book ''On Inequality'', philosopher [[w:Harry_Frankfurt|Harry Frankfurt]] notes that income equality can be achieved by arranging that all incomes are ''equally below'' the [[w:Poverty_threshold|poverty line]]. He then states “Economic equality is not, as such, of any particular moral importance; and by the same token, economic inequality is not in itself morally objectionable.”<ref>{{cite book |last=Frankfurt |first=Harry G. |date=September 29, 2015 |title=On Inequality |publisher=Princeton University Press |pages=120 |isbn=978-0691167145}} @17 of 103.</ref> He goes on to say “What is morally important is that each should have enough” and then introduces the “doctrine of sufficiency”<ref>{{cite book |last=Frankfurt |first=Harry G. |date=September 29, 2015 |title=On Inequality |publisher=Princeton University Press |pages=120 |isbn=978-0691167145}} @18 of 103.</ref> where what is morally important is that everyone has enough money. == A Fair Price to Pay == Luck influences our lives in many ways. We often mistake chance results for outcomes due to skill or incompetence. Rich people may attribute their wealth to hard work, good character, and excellent judgement, while blaming poor people for being lazy and undeserving. The story “[[Understanding_Fairness/fair_enough|fair enough]]” suggests a [[w:Thought_experiment|thought experiment]] than can help us analyze the role luck plays in our lives, and what we might be willing to pay to ensure our ongoing good luck. === Assignment === #Read the story [[Understanding_Fairness/fair_enough|fair enough]]. #List those factors in your life that resulted from luck. Consider gender, intelligence, talents, race, birth defects, genetic traits, birthplace, parental structure, family structure, inherited wealth, and other factors. #For each of these factors, decide if you are satisfied with, dissatisfied with, or indifferent to the attributes you were born with. #What, if anything, would you like to change? #How much might you be willing to pay to keep your fortunate attributes? #How much might you regard as fair compensation for continuing to live with your unfortunate characteristics? #How would a [[w:Basic_income|basic income]] change your life? ==Steps Toward a Fair Resolution== We can begin to assemble the various arguments explored above into an outline of steps that may result in a fair [[w:Conflict_resolution|resolution]] of a dispute. #Identify the nature of the [[Transcending Conflict|conflict]]. What are the real interests of each part in the dispute?<ref>{{cite book |last1=Fisher |first1=Roger |last2=Ury |first2=William L. |date=1981 |title=[[w:Getting_to_Yes|Getting to YES: Negotiating Agreement Without Giving In]] |location=United Kingdom |publisher=Penguin Group |pages=200 |isbn=978-0140157352}} </ref> Is this about money, pride, utility, power, prestige, ideology, spite, humiliation, winning, survival, or something else? What is the real [[Problem Finding|problem that needs to be solved]]?<ref> {{cite book |last1=Gause |first1=Donald C. |last2=Weinberg |first2=Gerald M. |date=March 1, 1990 |title=Are Your Lights On?: How to Figure Out What the Problem Really Is |publisher=Dorset House Publishing Company, Incorporated |pages=176 |isbn=978-0932633163}}</ref> #Explore alternatives based on each of the three forms of fairness: procedural, equal distribution, or proportional distribution. Examine reasons for and against each approach. Be explicit about what form of fairness is being analyzed at each stage of the [[Practicing Dialogue|dialogue]]. Recognize that procedural fairness is typically necessary, but not sufficient to ensure distributive fairness. #If dialogue carried out in good faith becomes deadlocked because appeals to fairness have become circular, then a new criteria needs to be introduced. If a resolution cannot be arrived at based on appeals to some form of fairness, then use deep pragmatism to resolve the issue. Ask: What really matters? and Who really matters? #Apply the principle that “Happiness is what matters, and everyone’s happiness counts the same.” Identify each [[w:Stakeholder_analysis|stakeholder]]. Identify what happiness—understood as [[w:Well-being|well-being]] or [[w:Flourishing|flourishing]]—means to each stakeholder in this case. Explore solutions based on this understanding. #Test the fairness of various proposals being considered by offering stakeholders the hypothetical opportunity to change places with each of the other stakeholders. Ask each to describe the fairness of the resolution from this new vantage point. Assess the accuracy of these alternative viewpoint descriptions. This is an application of the [[Living the Golden Rule|golden rule]]. ==Assignment== #Choose an issue from the “[[Understanding_Fairness/struggles for fairness|struggles for fairness]]” gallery, or some other fairness issue you would like to study for this assignment. #Study the issue thoroughly enough to allow you to argue both for and against a variety of resolutions, based on various reasonable assessments of fairness. #Follow the “[[Understanding_Fairness#Steps_Toward_a_Fair_Resolution|Steps toward a fair resolution]]” described above to arrive at your proposed resolution. # If you wish, change places (i.e. assume the role of another stakeholder to the issue) and repeat the previous step to arrive at your proposed resolution from this new point of view. Does the previously proposed solution still seem fair from this new viewpoint? ==Further Reading== Students interested in learning more about fairness may be interested in the following materials. *{{Cite book|title=The bonobo and the atheist: in search of humanism among the primates|last=Waal|first=Frans B. M. de|date=2013|publisher=W.W. Norton & Company|isbn=978-0-393-07377-5|location=New York, NY}} *{{Cite book|title=The origins of virtue: human instincts and the evolution of cooperation|date=1998|publisher=Penguin Books|isbn=978-0-14-026445-6|editor-last=Ridley|editor-first=Matt|series=A Penguin book : science|location=London}} * {{cite book |last=Greene |first=Joshua |authorlink=w:Joshua_Greene_(psychologist)|date=December 30, 2014 |title=Moral Tribes: Emotion, Reason, and the Gap Between Us and Them |publisher=Penguin Books |pages=432 |isbn=978-0143126058}} * {{cite book |last1=Pickett |first1=Kate |last2=Wilkinson |first2=Richard |date=April 26, 2011 |title=The Spirit Level: Why Greater Equality Makes Societies Stronger |publisher=Bloomsbury Press |pages=400 |isbn= 978-1608193417}} * {{cite book |last1=Fisher |first1=Roger |last2=Ury |first2=William L. |date=1981 |title=[[w:Getting_to_Yes|Getting to YES: Negotiating Agreement Without Giving In]] |url= |location=United Kingdom |publisher=Penguin Group |pages=200 |isbn=978-0140157352}} * {{cite book |last1=Gause |first1=Donald C. |last2=Weinberg |first2=Gerald M. |date=March 1, 1990 |title=Are Your Lights On?: How to Figure Out What the Problem Really Is |publisher=Dorset House Publishing Company, Incorporated |pages=176 |isbn=978-0932633163}} *{{cite book |last=Frankfurt |first=Harry G. |authorlink=w:Harry_Frankfurt |date=September 29, 2015 |title=On Inequality |publisher=Princeton University Press |pages=120 |isbn=978-0691167145}} * Searching for books on the topic of "Unfair" returns a long list of titles to consider. Also consider searching on "mediation" or "negotiation". *(Evaluate the book: ''The Fairness Instinct: The Robin Hood Mentality and Our Biological Nature'', by L. Sun ) * (Evaluate the book: ''The Moral Underground: How Ordinary Americans Subvert an Unfair Economy'', by Lisa Dodson) ==References== <references/> {{Emotional Competency}} {{CourseCat}} [[Category:Philosophy]] [[Category:Life skills]] [[Category:Peace studies]] [[Category:Sociology]] [[Category:Applied Wisdom]] [[Category:Humanities courses]] 7v9227cakpk308plcq2kjxjq5mcuolv 0 218813 2719937 2719847 2025-06-28T12:41:52Z Prototyperspective 2965911 rvv (2 edits by [[Special:Contributions/208.40.86.22]]) 2719937 wikitext text/x-wiki — Embracing Reality ==Introduction== [[File:FacingFactsWordCloud4.jpg|thumb|right|250px|We use several different words to express degrees of uncertainty.]] {{TOC right | limit|limit=2}} "You're entitled to your own opinions”, Senator [[w:Daniel_Patrick_Moynihan|Daniel Patrick Moynihan]] declares, “but you're not entitled to your own facts.” OK, but what if I feel that whatever is true for you might not be true for me? My opinion is that I’m entitled to my beliefs and you are entitled to your beliefs and that’s all that really matters if we are to protect our freedom. How are we supposed to tell the difference between facts and opinions anyway? I feel this is a difficult problem. Whatever… This course advocates [[w:Reason|reason]] and is provided as a refuge and antidote to [[w:Post-truth_politics|post-truth]] trends. For the purposes of this course we will adopt these [[w:Axiom|axioms]]: *[[w:Reality|Reality]] exists<ref>There are many fascinating on-going philosophical discussions on the [https://plato.stanford.edu/entries/realism/ nature of reality]. Plato’s [[w:Allegory_of_the_Cave|Allegory of the Cave]], the [[w:Brain_in_a_vat|brain in a vat scenario]], and the popular science fiction film [[w:The_Matrix|''The Matrix'']] each explore the possibility that our experiences are only an elaborate illusion. Although these ideas are fascinating and have the possibility of uncovering profound truths, they do not help us navigate the world we seem to be living in each day. For now, for practical reasons, it seems best to accept the existence of the real world and use our perceptions of that real world to guide our actions.</ref>, *We live in the real world<ref>We all have dreams, vivid imaginations, use figures of speech, and enjoy fantasy stories. Unless we suffer from [[w:Delusion|delusions]], we also recognize the distinction between those fanciful mental constructs and the tangible real world we live in. </ref>, *We can explore, investigate, examine, observe, measure, and probe that real world, *You and I, and everyone we know or ever meet, all live in the same universe<ref>Although physicists and others continue to investigate and debate the intriguing possibilities of [[w:Multiverse|multiple universes]], there is no credible evidence that you, or I, or anyone we meet live in some universe other than the single universe we all live in. There is every practical reason for us to be confident we all live in the same universe. </ref>, *The most certain of all basic principles is that contradictory propositions are not true simultaneously.<ref>This is one of Aristotle's statements of the [[w:Law_of_noncontradiction|Law of non-contradiction]]. Aristotle says that without the principle of non-contradiction we could not know anything that we do know. See, for example [https://plato.stanford.edu/entries/aristotle-noncontradiction/ Aristotle on Non-contradiction], Stanford Encyclopedia of Philosophy and [https://plato.stanford.edu/entries/contradiction/ Contradiction], Stanford Encyclopedia of Philosophy.</ref> [[File:Facing Facts Audio Dialogue.wav|thumb|Facing Facts Audio Dialogue]] ==Objectives== {{100%done}}{{By|lbeaumont}} The objectives of this course are to: *Understand the importance of truth, *Evaluate and describe your understanding of reality, *Distinguish among fact, belief, feelings, and opinions, *Distinguish between reality and perception, objective reality, and subjective reality, *Distinguish among facts, controversy, and taste, *Examine the roles of [[Virtues/Tolerance|tolerance]] and [[Practicing Dialogue|dialogue]], *Examine the [[w:Consilience|unity of knowledge]], *Distinguish between [[w:Scientific_theory|''Scientific theory'']] and [[w:Working_hypothesis|''just a theory'']], *Understand observational error, *Examine the reliabilities of various epistemologies—ways of knowing, *Distinguish among science, paranormal events, pseudoscience, and conspiracy theory, *Whatever… The course contains many [[w:Hyperlink|hyperlinks]] to further information. Use your judgment and these [[What Matters/link following guidelines|link following guidelines]] to decide when to follow a link, and when to skip over it. This course is part of the [[Wisdom/Curriculum|Applied Wisdom curriculum]] and of the [[Deductive_Logic/Clear_Thinking_curriculum|Clear Thinking curriculum]]. If you wish to contact the instructor, please [[Special:Emailuser/Lbeaumont | click here to send me an email]] or leave a comment or question on the [[Talk:Facing_Facts|discussion page]]. The list of [[Wise Affirmations|wise affirmations]] on the topic of [[Wise Affirmations/Facing Facts|facing facts]] may help you develop habits based on the ideas in this course. OK, let’s face the facts and strengthen our grip on reality! ==The Importance of Truth== Why is truth important? Truth is useful.<ref>[[w:On_Truth|On Truth]], Chapter I</ref> Engineers, architects, and other builders need to know the true strength of materials so they can design and build structures that are safe and lasting. Health professionals need to understand the true benefits and risks of various medicines so they can safely and effectively treat illnesses. To effectively serve the public, officials need to know the true conditions existing in their jurisdictions and the true effects of various [[w:Public_policy|policy actions]] and options. These examples illustrate there is a clear difference between getting things right and getting things wrong. A concern for truth is essential to conducting efficient and effective commerce and public affairs. Subjective evaluations and judgements are ultimately based on what we accept as true.<ref>[[w:On_Truth|On Truth]], Chapter II</ref> If you judge someone to be a fine citizen your subjective judgment of their character rests on facts you hold to be true about that person. You will consider how you believe that person spends their time, how they treat family and friends, the work they do, the things they say, correspondence between what they say and what they do, the trust they have earned from you, the consistency of their behaviors, and many other factors that you believe indicate character. It is from these considerations you regard as true that you draw your subjective judgment and conclusion. Civilizations have never sustained their health and prosperity without relying on large quantities of factual information.<ref>[[w:On_Truth|On Truth]], Chapter II</ref> Individuals also require large quantities of factual information because it is the true information that allows us to navigate effectively in the real world. Because we live in the real world it is nearly always to our advantage to face the facts about our world than it is to remain ignorant of them.<ref>[[w:On_Truth|On Truth]], Chapter IV</ref> Also, self-awareness, the willingness to face facts about ourselves, especially those inconvenient truths, is important for living our lives successfully and authentically. Humans are distinctly rational animals.<ref>[[w:On_Truth|On Truth]], Chapter V</ref> Humans respond to reason, and reason relies on facts. False statements provide no rational support for anything. Truth is the essential element of reason, and reason is the essential justification for action. Truth forms the basis for trust.<ref>[[w:On_Truth|On Truth]], Chapter VI</ref> To the extent people are generally dishonest and untrustworthy, peaceful and productive social life becomes more difficult. Lying undermines the cohesion of human society. Because people regularly engage in lies we must carefully interpret all that we hear. “You submit to tyranny when you renounce the difference between what you want to hear and what is actually the case.”<ref> {{cite book |last=Snyder |first=Timothy |date=February 28, 2017 |title=On Tyranny: Twenty Lessons from the Twentieth Century |publisher=Tim Duggan Books |pages=128 |isbn= |author-link=w:Timothy_D._Snyder }}</ref> We are injured when we are betrayed.<ref>[[w:On_Truth|On Truth]], Chapter VII</ref> Lies impair our efforts to determine and understand the real state of affairs. Lies impede us from knowing what is really going on. Liars attempt to impose their will on us. Lies are designed to damage our grasp of reality. Furthermore although the statement that, “The Liar leads an existence of unutterable loneliness”<ref>“Women and Honor: Some Notes on Lying.” In Adrien Rich, ''Lies, Secrets, and Silence''.</ref> exercises a bit of poetic license, liars are isolated. They cannot reveal their loneliness without disclosing the lie. Also, “To discover that one has been lied to in a personal relationship leads one to feel a little crazy.”<ref>Adrien Rich, Lies, ''Secrets, and Silence'', Page 186</ref> Although we know people often lie, it is disappointing to be lied to unexpectedly by a trusted friend. Our natural expectation of access and intimacy among friends is damaged and trust is lost. As an example of the impact of sustaining a lie, the [[w:2021_storming_of_the_United_States_Capitol|2021 storming of the United States Capitol]] resulted from the [[w:Big_lie|big lie]] that the presidential [[w:Attempts_to_overturn_the_2020_United_States_presidential_election|election was stolen]] from Donald Trump. As we bump up against the world we live in we begin to understand the limits of our free will and the boundaries of our self.<ref>[[w:On_Truth|On Truth]], Chapter IX</ref> As we encounter the world as it truly is we learn what we can and cannot do, what we can change and what we cannot change, and the sort of efforts we must make to accomplish what is actually possible. This contributes to our understanding of our own identity by constantly clarifying what we are and what is not us. Reality is the ultimate arbiter. "On the whole, truth matters to us because it has survival value and allows us to function in our world."<ref>{{cite book |last1=Lakoff |first1=George |last2=Johnson |first2=Mark |date=April 15, 2003 |title=Metaphors We Live By |publisher=University Of Chicago Press |pages=242 |isbn=978-0226468013}} Page 160</ref> ===Assignment=== The purpose of this assignment is to assess the role that accurate and inaccurate information, along with unavailable, and unused information has had in making the important decisions in your life. '''Part 1:''' #Recall various important decisions you have made throughout your life. These may be your choice of friends, how you approached school studies, how you used your free time, the friends you choose, deciding to smoke or drink, risks you did or did not take, and participation in sports teams, clubs, or other activities. Career choice, deciding if, who, and when to get married. Deciding family planning issues. Car buying, home purchase decisions, investment decisions, or others. #Identify one of these decisions that turned out to be a good decision, and another decision that turned out to be a bad decision. #Reflect on the role that accurate, unavailable, unused, and incorrect information each had on each decision. #Did more accurate information result in better decisions? '''Part 2:''' Choose one of these historical events to study for this assignment. *The claim that “[[w:Rain_follows_the_plow|rain follows the plow]]” was used to encourage westward expansion of the United States in the late 1800’s and early 1900’s.<ref>{{cite book |last=Egan |first=Timothy |date=September 1, 2006 |title=The Worst Hard Time: The Untold Story of Those Who Survived the Great American Dust Bowl |publisher=Mariner Books |pages=340 |isbn=978-0618773473 }}</ref> The tragedy of the [[w:dust bowl|dust bowl]] proved the claim to be false. *[[w:Heaven's_Gate_(religious_group)|Heaven's Gate]] was an American UFO religious millenarian group. On March 26, 1997, police discovered the bodies of 39 members of the group who had committed mass suicide in order to reach what they believed was an extraterrestrial spacecraft following Comet Hale–Bopp. *"[[w:Jonestown|Jonestown]]" was the informal name for an American religious organization under the leadership of Jim Jones, in northwestern Guyana. It became internationally notorious when on November 18, 1978, a total of 918 people died in the remote commune. *The [[w:Niger_uranium_forgeries|Niger uranium forgeries]] were forged documents initially released by SISMI (Italian military intelligence), which seemed to depict an attempt made by Saddam Hussein in Iraq to purchase yellowcake uranium powder from Niger during the Iraq disarmament crisis. On the basis of these documents and other indicators, the governments of the United States and the United Kingdom asserted that Iraq violated United Nations Iraq sanctions by attempting to procure nuclear material for the purpose of creating weapons of mass destruction. This bolstered the case for the [[w:2003_invasion_of_Iraq|2003 invasion of Iraq]]. In what ways did a lack of factual information contribute to the tragedy you chose to study? '''Part 3:''' *Read this [[Facing_Facts/Harmful_false_beliefs|list of harmful false beliefs]]. *Abandon any of these false beliefs that you currently hold. ==Expressing Uncertainty== [[File:DegreesOfUncertainty.jpg|thumb|right|300px|Each word we use to describe a level of uncertainty has a particular relationship to reality. ]] We use many different words to express our level of [[w:Certainty|certainty]] or uncertainty about some statement, claim, fact, or opinion. It is helpful to review definitions of these words, and to compare their scope. Please refer to the [[w:Venn_diagram|Venn diagram]] on the right illustrating relationships among various words that express degrees of certainty. Each word is defined and characterized below. Links are to the corresponding Wikipedia article which discusses each concept in more depth. It may be best to ignore these links on the first reading and until you are ready to investigate the concepts more deeply. *[[w:Reality|Reality]] is the state of things as they actually exist, rather than as they may appear or might be imagined. Reality includes everything that is and has been, whether or not it is observable or comprehensible. Reality is often contrasted with what is imaginary, delusional, (only) in the mind, dreams, what is false, what is fictional, or what is abstract. The truth refers to what is real, while falsity refers to what is not. Fictions are considered not real. *A [[w:fact|fact]] is something that has really occurred or is actually true. The usual test for a statement of fact is [[w:Verifiability|verifiability]]—that is, whether it can be demonstrated to correspond to experience. *[[w:Knowledge|Knowledge]] is a familiarity, awareness or understanding of someone or something, such as facts, information, descriptions, or skills, which is acquired through experience or education by perceiving, discovering, or learning. Knowledge is often defined as a justified true belief. The essential goal of learning and discovery is to better align our knowledge with reality. This alignment would ultimately cause the green disk to exactly overlap the blue disk in the diagram. *[[w:Truth|Truth]] is most often used to mean being in accord with fact or reality, or fidelity to an original or standard. In short, truth is [[w:Correspondence_theory_of_truth|correspondence with reality]]. The commonly understood opposite of truth is [[w:Falsity|falsehood]], which, correspondingly, can also take on a logical, factual, or ethical meaning. The concept of truth is discussed and debated in several contexts, including philosophy, art, and religion. Many human activities depend upon the concept, where its nature as a concept is assumed rather than being a subject of discussion; these include the sciences, law, journalism, and everyday life. Some philosophers view the concept of truth as basic, and unable to be explained in any terms that are more easily understood than the concept of truth itself. Others hold that the distinction between true and false is well known to people in general.<ref>[[w:On_Truth|On Truth]], Introduction</ref> This course will take care to distinguish between (capital T) ''Truth'', and ordinary ''truth''. Capital T Truth generally implies a certainty, however, since it is widely held that [[w:Certainty|certainty]] about the real world is a failed historical enterprise, claims of Truth are suspect. When ''truth'' appears as the first word of a sentence, it is capitalized and should be understood as small t truth. *A [[c:Truth_claim|truth claim]] is a proposition or statement that a particular person or belief system holds to be true. Many everyday statements are truth claims, such as “today is my birthday”, or “Earth is the third planet from the Sun.” Truth claims can be contrasted with opinions, such as “I prefer chocolate ice cream to vanilla ice cream,” or “[[w:The_Beatles|The Beatles]] were the greatest rock group ever.” Truth claims are identified by use of the word "is" to describe an equivalence between two items, often in the form of ''X is Y'' or in the corresponding plural form of ''Xs are Ys''. *[[w:Belief|Belief]] is what people accept as being true. It is the state of mind in which a person thinks something to be the case, with or without there being empirical evidence to prove that something is the case with factual certainty. Another way of defining belief sees it as a mental representation of an attitude positively oriented towards the likelihood of something being true. *[[w:Doubt|Doubt]] characterizes a status in which the mind remains suspended between two contradictory propositions and unable to assent to either of them. Doubt on an emotional level is indecision between belief and disbelief. Doubt involves uncertainty, distrust or lack of sureness of an alleged fact, an action, a motive, or a decision. Doubt questions a notion of a perceived “reality”, and may involve delaying or rejecting relevant action out of concerns for mistakes or faults or appropriateness. *[[w:Opinion|Opinion]] is a judgment, viewpoint, or statement that is not conclusive. It may deal with [[w:Subjectivity|subjective]] matters in which there is no conclusive finding. What distinguishes fact from opinion is that facts are more likely to be [[w:Wikipedia:Verifiability|verifiable]], i.e. can be agreed to by the consensus of experts. An example is: "United States of America was involved in the Vietnam War" versus "United States of America was right to get involved in the Vietnam War". An opinion may be supported by facts and principles, in which case it becomes an [[w:Argument|argument]]. Different people may draw opposing conclusions (opinions) even if they agree on the same set of facts. Opinions rarely change without new arguments being presented. It can be reasoned that one opinion is better supported by the facts than another by analyzing the supporting arguments. In casual use, the term ''opinion'' may be the result of a person's perspective, understanding, particular feelings, beliefs, and desires. It may refer to unsubstantiated information, in contrast to knowledge and fact. It is helpful to distinguish between ''popular opinion'' and [[w:Expert|''expert'']] ''opinion''. *The word [[w:Feeling|''feeling'']] has many meanings. When used to describe a level of belief, it refers to a state of consciousness, such as that resulting from emotions, sentiments or desires. *[[w:Whatever_(slang)|''Whatever'']] is a slang term meaning "whatever you say”, "I don't care what you say" or "what will be will be". The term is used both to dismiss a previous statement and express indifference or in affirmation of a previous statement as "whatever will be will be". An interjection of "whatever" can be considered offensive and impolite or it can be considered affirming. In the late 20th century and early 21st century, the word became a sentence in its own right; in effect an interjection, often but not always, used as a [[w:Passive-aggressive_behavior|passive-aggressive]] conversational blocking tool, leaving the responder struggling to find a convincing retort. ===Assignment=== The purpose of this assignment is to help you pay closer attention to the words you choose to express your level of uncertainty regarding various truth claims. #Browse this [[Socratic Methods/questions to classify|list of questions to classify]], and choose 10 questions to work with for this assignment. #Recast each question into a statement, choosing the correct term to indicate your level of uncertainty. For example, if you chose to work on “Are Alien abductions real?” would you recast this as: #*a statement of ''fact'', making the statement “Alien abductions ''are'' real” or, #*a statement of ''belief'', making the statement “I ''believe'' alien abductions are real”, or #*a statement of ''opinion'': “In ''my opinion'', alien abductions are real”, or #*a statement of ''doubt'': “I ''doubt'' alien abduction are real”, or #*an expression of your ''feelings'': “I ''feel that'' alien abductions are real”, or #*a declaration of your indifference or annoyance: “Whatever.” #During conversations and other communications, take care to choose the word that most accurately expresses your level of uncertainty. Encourage others to do the same. ==Degrees of Consensus== [[File:Degrees of Consensus.jpg|thumb|right|250px|Degrees of consensus are labeled depending on their distance from facts.]] Distinguishing among: 1) matters of fact, 2) matters of preference, or 3) matters of controversy is an essential skill in describing and discussing reality and uncertainty. Refer to the diagram “degrees of consensus”. Statements can be classified as one of the following three types: '''Matters of fact.''' Facts describe reality. Statements of fact can be assessed and verified through the correct use of evidence gathering, and reasoning. A correct statement can be made with conviction. These statements declare “what is” and careful researchers agree on the answer. Examples include: The [[w:Boiling_point|boiling point]] of water is 100° Centigrade (at standard pressure), gold is denser than lead, and the movie ''Spotlight'' won Best Picture in 2016. Notice the use of “is” to convey certainty in these statements. These matters of fact are the targets of [[Knowing_How_You_Know#What_is_a_Theory_of_Knowledge.3F|your theory of knowledge]]. A reliable [[w:Epistemology|epistemology]]—way of knowing—will describe how to effectively research factual claims, how to identify and use reliable sources, and how to resolve disputed or contradictory factual claims. The principle of [[w:Consilience|consilience]] will ensure that reliably researched facts will converge toward the actual reality. The Wikiversity course [[Knowing How You Know]] can help you develop an effective process for identifying matters of fact. The Wikiversity course [[Evaluating Evidence]] can help you assess and reconcile a variety of information. However, there are also matters of fact that are [[w:Unknowability|unknowable]], and those that are not yet known.  Unknowable matters of fact include past events for which there is no surviving record. This includes many prehistoric events—such as determining the identity of the first individual to use fire or invent the wheel—and trivial events such as determining what Thomas Jefferson ate for lunch on July 5, 1776. Other unknowable matters of fact may be beyond the reach of researchers. These include questions such as what preceded the [[w:Big_Bang|big bang]], and the nature of experiences beyond death. Other matters of fact are [[w:Open_problem|open problems]] that not yet understood but may yield to on-going research sometime in the future. Examples include [[w:Lists_of_unsolved_problems|active research topics]] such as understanding the nature of free will, or the nature of consciousness in animals or robots. It is helpful to identify a topic as an unknowable matter of fact and to leave any further discussion to relevant experts. '''Matters of taste, preference, or opinion'''. Any claim is acceptable here, because the statement depends only on the preferences of the person making it. Examples include: I feel that purple is the most beautiful color, I prefer chocolate ice-cream to vanilla ice-cream, and I believe that Rembrandt was a better artist than Picasso. Notice the use of “prefer”, “feel”, and “believe” to convey a personal preference. These matters of preference fall outside any factual claims. Don’t dispute them, just enjoy them. '''Matters of controversy.''' Although these are not opinions, sincere experts often disagree on the best answer or the best course of action. These statements propose “what ought to be” or they ask about a topic that is not yet fully and carefully explored or researched. Examples include: I believe the most pressing problem facing the world today is the lack of clean safe drinking water for all people, I think the best approach to reducing gun violence is to require comprehensive background checks for all gun purchases, and I believe incarceration rates are too high in the United States. Notice the use of “believe” and “think” to convey personal positions here. Although it is instructive to learn more about matters of controversy by exploring them with [[Practicing Dialogue|dialogue]] and [[Socratic Methods]], they are statement of personal belief rather than truth claims. ===Assignment=== *Read this essay on the [[Knowing How You Know/Height of the Eiffel Tower|Height of the Eiffel Tower]]. *Read over this list of [[Socratic Methods/questions to classify|questions to classify]]. *Identify at least five of these questions in each of the following classifications: 1) matters of fact, 2) matters of preference, or 3) matters of controversy. ==Interpreting Evidence== [[w:Evidence|Evidence]], broadly construed, is anything presented in support of an assertion, or [[w:Truth_claim|''truth claim'']]. This support may range from strong to weak. The strongest type of evidence is that which provides direct proof of the truth of an assertion. At the other extreme is evidence that is merely consistent with an assertion but does not rule out other, contradictory assertions, as in circumstantial evidence. We naturally consider evidence to decide what we believe, and adjust our level of uncertainty about various truth claims. Interpreting evidence can be tricky. ===Assignment=== Interpreting evidence can be tricky. *Read this essay on the [[Knowing How You Know/Tyranny of Evidence|Tyranny of Evidence]]. *Recall and reflect on various beliefs you hold to be true. *What is the evidence for or against those beliefs? *What is your level of uncertainty regarding those beliefs? *Complete the Wikiversity course on [[Evaluating Evidence]]. ==Objective and Subjective Experience== [[File:Objectivity.jpg|thumb|right|250px|Subjective experiences emerge from objective stimuli.]] The technical term for subjective experience is [[w:Qualia|''qualia'']], which refers to individual instances of subjective, conscious experience. Examples of qualia include the pain of a headache, the taste of wine, or the perceived redness of an evening sky. Objective experiences can often be measured and observed by others. Subjective experiences are personal and can only be felt. However, subjective experiences originate with and emerge from objective stimuli. Our subjective experiences are as vivid as our objective experiences, even though subjective experiences are private and objective experiences are shared. The real difference in subjective vs. objective is that objective situations can be observed independent of personal biases and experience (i.e. they are based on objective evidence), whereas subjective situations can usually only be viewed by one person, filtered through their unique lens of personal experience, taste, emotion, and bias.<ref>[http://www.curiosityaroused.com/skepticism/subjective-vs-objective-whats-the-difference/ Subjective vs. Objective: What’s the Difference?], Editorial Staff, curiosityaroused.com </ref> Don’t confuse subjective experiences with objective experiences. [[Virtues/Tolerance|Tolerate]] disagreement on subjective experience. Don’t tolerate disagreement on objective experience. ===Assignment:=== '''Part 1:''' The purpose of this assignment is to improve your ability to distinguish subjective experiences from objective experiences. #Scan this list of [[/subjective and objective experiences/]]. #Choose 10 to classify for this assignment. Identify each as a subjective or objective experience. #Are statements regarding subjective experiences facts or opinions? #Can facts be determined regarding objective experiences? #Is it useful to disagree or argue over subjective experiences? #Is it useful to disagree or argue over objective experiences? #When you find yourself arguing, notice if the argument is over a subjective experience or an objective one. Do not argue over facts. Instead research them using [[w:Wikipedia:Identifying_reliable_sources|reliable sources]]. '''Part 2:''' The purpose of this assignment is to practice connecting subjective experiences with the various objective stimuli causing them. *Identify a particular subjective experience you are familiar with. *Work to identify the objective stimuli from which the subjective experience is emerging. ==Perceptions are Personal== We often hear that “perception is reality” and that “everything is relative”, despite knowing that a shared reality exists, and [[Facing_Facts/Reality_is_our_common_ground|reality is our common ground]]. These apparently contradictory claims are reconciled when we understand that perceptions are personal. Please read the essay [[Facing_Facts/Perceptions_are_Personal|''Perceptions are Personal'']] and be careful generalizing your personal perceptions beyond your own limited experience and personal point of view. ==Observational Error== [[w:Observational_error|Observational error]] (or measurement error) is the difference between a measured value of quantity and its true value. In statistics, such error is always present and is not a mistake. Variability is an inherent part of things being measured and of the measurement process. No measurement is exact. When a quantity is measured, the outcome depends on the measuring system, the measurement procedure, the skill of the operator, the environment, and other conditions and effects. Even if the quantity were to be measured several times, in the same way and in the same circumstances, a different measured value would in general be obtained each time, assuming the measuring system has sufficient resolution to distinguish between the values. Because it is never certain that the measured value of a quantity is identical to its true value, careful investigators take care to report an estimate of the measurement uncertainty along with each measurement. [[w:Error_bar|Error bars]], [[w:Confidence_interval|confidence intervals]], and [[w:Significant_figures|significant figures]] are all important tools for reporting measurement uncertainty. Measurement equipment can be [[w:Calibration|calibrated]] to increase accuracy. Reporting observational error is an indication of careful investigation, not evidence of mistakes. ===Assignment=== The purpose of this assignment is to recognize our routine familiarity with observational error. #Identify various measuring devices you often use. These might be a tape measure, thermometer, bathroom scale, measuring cup, etc. #Identify the measurement accuracy of each. For example, can the thermometer measure to the nearest degree, tenth of a degree, or hundredth of a degree? #Is it most accurate to report a temperature reading made with your thermometer as 20° or 20.00° or as 20°±.1° or as 20°±.01°? ==Emergent Properties== [[File:WhereRainbowRises.jpg|thumb|Rainbows are dramatic, beautiful, and unexpected effects that emerge from sunlight refracted by raindrops.]] [[w:Emergence|Emergence]] is a phenomenon whereby larger entities arise through interactions among smaller or simpler entities such that the larger entities exhibit properties the smaller/simpler entities do not exhibit. The properties of water are unexpected from an isolated examination of [[w:oxygen|oxygen]] and [[w:hydrogen|hydrogen]], yet water is formed from the combination of those gasses. The properties of [[w:Water|water]], rainbows, weather, and temperature are all examples of emergence. [[w:Rainbow|Rainbows]] are real, because we can see them, but they remain elusive, moving away as we seek to approach them. This is because a rainbow does not exist at one particular location. Many rainbows exist as droplets of light illuminated by the sun; however, only one can be seen depending on the particular observer's viewpoint. All raindrops [[w:Refraction|refract]] and [[w:Reflection_(physics)|reflect]] the sunlight in the same way, but only the light from some raindrops reaches the observer's eye. This light is what constitutes the rainbow for that observer. Rainbows are dramatic, beautiful, and unexpected effects of sunlight refracted by raindrops. The [[w:Abiogenesis|emergence of life]] from non-living matter, such as simple organic compounds and the emergence of the [[w:Mind|mind]] from the billions of neurons that form the [[w:Human_brain|human brain]] are particularly remarkable results. It is important to [[Understanding Emergence|understand emergence]] because it is the process by which complex and unexpected forms are created from simpler elements. ===Assignment=== The purpose of this assignment is to practice recognizing and identifying emergent forms. #Identify emergent forms you are familiar with. #Describe the elements that compose the emergent form. #Complete the Wikiversity cousre [[Understanding Emergence|Understanding emergence]]. ==Not Just a Theory== The word ''theory'' has several distinct definitions that need to be individually identified and held separate during any discussion using the word.<ref>[[w:The_Greatest_Show_on_Earth:_The_Evidence_for_Evolution|The Greatest Show on Earth]], Chapter 1</ref> Two distinct definitions are:<ref> Wiktionary entry for [[wikt:Theory|Theory]]. </ref> #A coherent statement or set of ideas that explains observed facts or phenomena, or which sets out the laws and principles of something known or observed; a hypothesis confirmed by observation, experiment etc. #A hypothesis or conjecture. The first definition given above is that of a [[w:Scientific_theory|scientific theory]], the second is for a [[w:Hypothesis|hypothesis]]. The two distinct definitions reflect very different statements of certainty. A scientific theory is the strongest statement of certainty. A hypothesis is an explicit statement of significant uncertainty. The two different definitions carried by the same term are often used to create a [[Recognizing_Fallacies/Fallacies_of_Ambiguity#Equivocation|fallacy of equivocation]]. This often happens when attempts to dismiss [[w:Evolution|evolution]] or other scientific theory as “only a theory” are falsely based on the second definition of the word “theory”. In modern science, the term "theory" refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with scientific method, and fulfilling the criteria required by modern science. Such theories are described in such a way that any scientist in the field is in a position to understand and either provide empirical support ("verify") or empirically contradict ("falsify") it. Scientific theories are the most reliable, rigorous, and comprehensive form of scientific knowledge, in contrast to more common uses of the word "theory" that imply that something is unproven or speculative (which is better characterized by the word 'hypothesis'). Scientific theories are distinguished from hypotheses, which are individual empirically testable conjectures, and scientific laws, which are descriptive accounts of how nature will behave under certain conditions. ===Assignment=== The purpose of this assignment is to distinguish between definitions 1 and 2 of ''theory''. #Identify examples of scientific theories (definition 1, above). #Identify examples of hypothesis or conjectures (definition 2, above). #Avoid conflating these two distinct meanings of the word theory when discussing degrees of uncertainty. If there is doubt or confusion regarding what definition is being used, stop to ensure the correctly intended meaning is made clear and used consistently. Insist on clarity. Do not tolerate the confounding of these distinct meanings. ==The Unity of Knowledge== [[File:The Earth seen from Apollo 17.jpg|thumb|Because we all live on the same earth, reliable knowledge about our world converges toward a consistent description of that world.]] Because we all live on the same earth, in the same universe, reliable knowledge about our world must [[w:Consilience|converge toward a consistent description]] of that world. Each phenomenon we observe must fit into a single coherent and integrated description of our universe. Because we all live in the same universe, as we continue to examine our universe more and more closely, we can agree on a larger set of facts about our universe. Reliable epistemologies—ways of knowing—increase our shared common knowledge. [[Facing_Facts/Reality_is_our_common_ground|''Reality'' is our shared common ground]]. Work to resolve disagreements by examining reality more closely and more carefully. ===Assignment=== The purpose of this assignment is to understand and recognize the unity of knowledge. #Browse this [https://archive.org/details/PrintEmergence emergence diagram]. #Read this [[Knowing How You Know/One World|essay on our one world]]. #Read this essay on [[Facing Facts/Reality is our common ground|reality is our common ground]]. #Read this essay on [[Facing Facts/Reality is the Ultimate Reference Standard|Reality is the Ultimate Reference Standard]]. #Please consider your position regarding the unity of knowledge. ##Do you believe that although each person has their own unique life experiences and unique point of view, we are all experiencing the same world, and there are facts that describe our world that we can all agree on? In other words, referring to the allegory of the [[w:Blind_men_and_an_elephant|blind men and an elephant]], each of us is experiencing some aspects of the same elephant. Furthermore, the [[Knowing How You Know/Height of the Eiffel Tower|Eiffel tower does have a particular height]]. ##Or do you believe that each of us experiences our own world, the world is different for each of us and there are not facts that are common among that multiplicity of worlds? Each of us is experiencing a different elephant. Furthermore, the [[Knowing How You Know/Height of the Eiffel Tower|height of the Eiffel tower depends]] on who is asked about it, and how they are feeling at the moment. #Consider how you maintain the coherence of your [[w:World_view|world view]] when new information comes to your attention that is inconsistent with a [[w:Consilience|coherent description of the universe]]. Will you: 1) dismiss that new information, 2) modify your present description of the universe to accommodate that new information, or 3) tolerate inconsistencies? ==Reliable Epistemologies== Reliable [[w:Epistemology|epistemologies]]—ways of knowing—converge toward a consistent, coherent, and comprehensive representation of the one universe we all live in. This principle is known as [[w:consilience|consilience]]. The [[w:Scholarly_method|scholarly method]], also known as ''scholarship'' is the body of principles and practices used by scholars to make their claims about the world as valid and trustworthy as possible, and to make these claims known to the scholarly public. The primary scholarly methods are the [[w:Historical_method|historical method]] and the [[w:Scientific_method|scientific method]]. Unreliable epistemologies arrive at truth claims that often contradict the truth claims made by others. [[w:Faith|Faith]] is an example of an unreliable epistemology. The [[Beyond_Theism#Faith|unreliability of faith]] as a way of knowing is evident because many truth claims based on faith contradict with other truth claims also based on faith, and also with truth claims resulting from reliable scholarly methods. [[w:Revelation|Revelation]] is also an unreliable epistemology. Using reliable epistemologies increases the body of knowledge widely accepted as fact. This provides a steadily increasing [[w:Common_ground_(communication_technique)|common ground]] that can be shared and agreed to by all people. ===Assignment=== The purpose of this assignment is to assess the reliability of various epistemologies. #Identify truth claims based on faith that contradict truth claims resulting from reliable scholarly methods. Consider various answers to these [[Knowing How You Know/general knowledge questions|general knowledge questions]], or some other truth claims that interest you. #Identify truth claims based on the faith of one religion that contradict truth claims based on the faith of another religion. Consider these examples of [[w:Argument_from_inconsistent_revelations|inconsistent revelations]], this [https://infidels.org/library/modern/donald_morgan/contradictions.html list of Bible Inconsistencies], or some other truth claims that interest you. #How do you recommend reconciling these contradictions? #When particular truth claims conflict, how do you decide which one is more likely to be true? ==Recognizing Nonsense== [[w:Bullshit|Nonsense]] can take on many forms, including paranormal events, the occult, supernatural claims, pseudoscience, and conspiracy theories. Each is described in more detail below. People who face facts dismiss these claims and events as unproven, unlikely, deceptive, misleading, disingenuous, unfair, false, or simply nonsense. [[w:Paranormal|Paranormal events]] are phenomena described in popular culture, folklore, and other non-scientific bodies of knowledge, whose existence within these contexts is described to lie beyond normal experience or scientific explanation. A paranormal phenomenon is different from hypothetical concepts such as [[w:Dark_matter|dark matter]] and [[w:Dark_energy|dark energy]]. Unlike paranormal phenomena, these hypothetical concepts are based on empirical observations and experimental data gained through [[Thinking Scientifically|scientific methods]]. The most notable paranormal beliefs include those that pertain to ghosts, contact with extraterrestrial life, unidentified flying objects, psychic abilities, extrasensory perception, and [[w:List_of_cryptids|cryptids]]. [[w:Occult|The occult]] is "knowledge of the hidden". In common English usage, occult refers to "knowledge of the paranormal", as opposed to "knowledge of the measurable", usually referred to as science. The term is sometimes taken to mean knowledge that "is meant only for certain people" or that "must be kept hidden", but for most practicing occultists it is simply the study of a deeper spiritual reality that extends beyond pure reason and the physical sciences. From the scientific perspective, occultism is regarded as unscientific as it does not make use of [[Thinking Scientifically|scientific methods]] to obtain facts. The [[w:Supernatural|supernatural]] includes all that cannot be explained by science or the laws of nature, including things characteristic of or relating to ghosts, gods, or other supernatural beings, or to things beyond nature [[w:Pseudoscience|Pseudoscience]] consists of claims, beliefs, or practices presented as being plausible scientifically, but which are not justifiable by [[Thinking Scientifically|scientific methods]]. A topic, practice, or body of knowledge can reasonably be considered pseudoscientific when it is presented as consistent with the norms of scientific research, but it demonstrably fails to meet these norms. Pseudoscience is often characterized by the following: contradictory, exaggerated or unprovable claims; reliance on [[w:Confirmation_bias|confirmation bias]] rather than rigorous attempts at refutation; lack of openness to evaluation by other experts; and absence of systematic practices when developing theories. The term pseudoscience is often considered pejorative because it suggests something is being presented as science inaccurately or even deceptively. Accordingly, those termed as practicing or advocating pseudoscience often dispute the characterization. The demarcation between science and pseudoscience has philosophical and scientific implications. Differentiating science from pseudoscience has practical implications in the case of health care, expert testimony, environmental policies, and science education. Distinguishing scientific facts and theories from pseudoscientific beliefs such as those found in astrology, alchemy, medical quackery, occult beliefs, and creation science combined with scientific concepts, is part of science education and scientific literacy. A [[w:Conspiracy_theory|conspiracy theory]] is an explanation of an event or situation that invokes a conspiracy without warrant, generally one involving an illegal or harmful act carried out by government or other powerful actors. Conspiracy theories often produce hypotheses that contradict the prevailing understanding of history or simple facts. The term is a derogatory one. According to the political scientist [[w:Michael_Barkun|Michael Barkun]], conspiracy theories rely on the view that the universe is governed by design, and embody three principles: nothing happens by accident, nothing is as it seems, and everything is connected. Another common feature is that conspiracy theories evolve to incorporate whatever evidence exists against them, so that they become, as Barkun writes, a closed system that is [[w:Falsifiability|unfalsifiable]], and therefore "a matter of faith rather than proof". When considering such claims and events, it is helpful to insist that “[[w:Sagan_standard|extraordinary claims require extraordinary evidence]]” and to dismiss such claims as false until the claimant can provide substantial and reliable evidence. Enthusiastic proponents of nonsense often use a fallacious “[[Recognizing_Fallacies/Fallacies_of_Relevance#The_Argument_from_Ignorance|Argument from ignorance]]” to support their claims by challenging you to provide their claim wrong. These challenges incorrectly shift the [[w:Philosophical_burden_of_proof|burden of proof]] away from those making the claim. ===Assignment=== The purpose of this assignment is to improve your ability to recognize and reject [[w:Bullshit|nonsense]]. #Scan the topics listed in the [[w:Category:Paranormal|Wikipedia paranormal category]], or those listed as “main articles” in the box on the right of the [[w:Paranormal|paranormal article]]. #Identify any that you find credible, or that you believe in. #Using the established criteria summarized above for distinguishing science from paranormal, examine any listed paranormal topics you find credible. Has each extraordinary paranormal claim been supported by substantial and reliable [[Evaluating Evidence|evidence]]? #Scan this list of [[w:List_of_occult_terms|occult terms]]. #Identify any that you find credible, or that you believe in. #Using the established criteria summarized above for distinguishing science from the occult, examine any listed occult terms you find credible. Has each extraordinary occult claim been supported by substantial and reliable [[Evaluating Evidence|evidence]]? #Scan this [[w:List_of_topics_characterized_as_pseudoscience|list of topics characterized as pseudoscience]]. #Identify any that you find credible, or that you believe in. #Using the established criteria summarized above for distinguishing science from pseudoscience, examine any listed pseudoscience topics you find credible. Has each extraordinary pseudoscience claim been supported by substantial and reliable [[Evaluating Evidence|evidence]]? #Scan this list of [[w:List_of_conspiracy_theories|conspiracy theories]]. #Identify any that you find credible, or that you believe in. #Using the established criteria, summarized above for identifying conspiracy theories, examine any listed conspiracy theory topics you find credible. Has each extraordinary claim been supported by substantial and reliable [[Evaluating Evidence|evidence]]? == What there is == Physicists have made remarkable progress in identifying the building blocks of our universe. Rigorous investigations have confirmed the existence of the particles and forces constituting the [[w:Standard_Model|standard model]]. [[w:Gravity|Gravity]] is well known. Despite the most exhaustive searches, there is no evidence of anything that could cause or explain supernatural phenomena. There is no reliable evidence of supernatural phenomena. Those who claim the existence of supernatural phenomenon [[w:Burden_of_proof_(philosophy)|bear the burden]] of providing [[Evaluating Evidence|evidence]] to prove their claims. === Assignment === #Read the essay [[Beyond Theism/What there is|What there is]]. #Get real. ==Thinking Outside the Tribe== Each of us lives within a variety of closed cultures. The neighborhood where we live brings us in contact with a limited number of people who all live within the same small geographic region. The places where we study, shop, work, and play bring us in touch with a limited number of people who all share those experiences. Perhaps more importantly the friends we choose, the sources of news we choose, the books we read, the podcasts we listen to, the television shows we choose to watch, the blogs we read, and the social media we engage in all act to reinforce viewpoints and beliefs we already hold. These various closed cultures are today's [[w:Tribe|tribes]]. These closed cultures can be referred to as ''echo chambers''. An [[w:Echo_chamber_(media)|echo chamber]] is a metaphorical description of a situation in which information, ideas, or beliefs are amplified or reinforced by communication and repetition inside a defined system. Inside a figurative echo chamber, official sources often go unquestioned and different or competing views are censored, disallowed, or otherwise underrepresented. When we use the internet a [[w:Filter_bubble|filter bubble]] selectively guesses what information we would like to see based on information about us (such as location, past click behavior and search history) and, as a result, we become separated from information that disagrees with our viewpoints, effectively isolating us in our own cultural or ideological bubbles. Social groups defined by religious, spiritual, or philosophical beliefs, or common interest in a particular personality, object or goal can become so insular they may approach the isolation level of a [[w:Cult|cult]]. Because of natural tendencies toward [[w:Confirmation_bias|confirmation]] bias and [[w:Tribalism|tribalism]] we are more comfortable in groups that reinforce our current beliefs, rather than challenge them. We may become skillful at discounting opposing viewpoints and denying reality. The isolation of information contributes to a divergence of ideological attitudes and [[w:Polarization_(politics)|polarization]] of viewpoints. As a result of this isolation our beliefs can continue to drift away from reality. Because the group reinforces our beliefs we are impaired from maintaining [[w:Objectivity_(philosophy)|objectivity]], discouraged from [[w:Critical_thinking|critical thinking]], and delayed from facing the facts and embracing reality. As Daniel Kahneman tells us: “We know that people can maintain an unshakable faith in any proposition, however absurd, when they are sustained by a community of like-minded believers.”<ref>{{cite book |last=Kahneman |first=Daniel |date=April 2, 2013 |title=Thinking, Fast and Slow |publisher=Farrar, Straus and Giroux |pages=499 |isbn=978-0374533557 |author-link=w:Daniel_Kahneman }} Chapter 20, “The Illusion of Validity”</ref> ===Assignment=== The purpose of this assignment is to identify and examine any beliefs you might hold because they are promoted by your tribe, rather than because they correspond to reality. '''Part 1:''' #Identify the various tribes or closed cultures you are a member of. These might be geographical, social, cultural, religious, or ideological. #Which, if any, of these serve to reinforce beliefs that are out of the [[w:Mainstream|mainstream]], are poorly supported by representative evidence, or that are unlikely to be true? #[[Knowing How You Know|How do you know]]? '''Part 2:''' For any of the closed cultures you have identified in Part 1: #Find someone outside the group who you can engage in [[Practicing Dialogue|dialogue]].<ref>The article [http://intentionalinsights.org/what-would-gandhi-do-about-trump-high-time-for-a-science-of-wisdom What Would Gandhi Do About Trump? High-Time For a Science Of Wisdom,] Intentional Insights, by Charles Cassidy can provide some helpful motivation and practical suggestions for doing this.</ref> #Begin a dialogue with this person regarding some of the beliefs that are reinforced by your culture. #*To prepare, consider completing the Wikiversity course on [[practicing dialogue]]. #Listen closely, carefully, and without judgement. Seek insight and understanding. Examine and [[Knowing How You Know/Examining Ideologies|explore the various ideologies]] that guide your current thinking. Research matters of fact using [[w:Wikipedia:Identifying_reliable_sources|reliable sources]]. #Allow yourself to change your beliefs based on a rational and consistent appraisal of the new information and viewpoint you learn from the dialogue. Embrace reality. #Work to attain a [[Global Perspective|global perspective]]. ==Matters of Fact== Are each of the following questions matters of fact or opinion? Please answer each question. *How tall is the Eiffel tower? *What shape is the earth? *How old is the earth? *Where was Barack Obama born? *Do vaccines cause autism? *Does contraception prevent abortion? *Did Donald Trump have the largest presidential inauguration crowd? *What are the origins of biodiversity? *Does reality exist? *Does reality supersede conjecture? *Is [[Facing Facts/Reality is our common ground|reality our common ground]]? ==Further Reading== Students wishing to learn more about facing facts, embracing reality, and discussing uncertainty may be interested in reading the following books: *{{cite book |last=Dawkins |first=Richard |date=August 24, 2010 |title=The Greatest Show on Earth: The Evidence for Evolution |publisher=Free Press |pages=496 |isbn= 978-1416594796 |author-link=w:Richard_Dawkins }} *{{cite book |last=Wilson |first=Edward Osborne |date=March 30, 1999 |title=Consilience: The Unity of Knowledge |publisher=Vintage |pages=384 |isbn=978-0679768678 |author-link=w:E._O._Wilson }} *{{cite book |last=Pinker |first= Steven |author-link=w:Steven_Pinker|date= September 28, 2021 |title=[[w:Rationality_(book)| Rationality: What It Is, Why It Seems Scarce, Why It Matters]]| publisher= Viking |pages=432 |isbn= 978-0525561996 }} *{{cite book |last=Gelwick |first=Richard |date=May 12, 2004 |title=The Way of Discovery, an introduction to the thought of Michael Polanyi |publisher=Wipf & Stock |pages=200 |isbn= 978-1592446872}} *{{cite book |last=Jarrard |first=Richard D. |date= |title=Scientific Methods }} This book is slowly moving through the Wikisource validation process and is available at: [[wikisource:Index:Sm_all_cc.pdf| ''Scientific Methods'']]. The text is available at: https://archive.org/details/sm_all_cc *{{cite book |last=Frankfurt |first=Harry G. |date=January 30, 2005 |title=[[w:On_Bullshit|On Bullshit]] |publisher=Princeton University Press |pages=67 |isbn=978-0691122946 |author-link=w:Harry_Frankfurt }} *{{cite book |last=Frankfurt |first=Harry G. |date=October 31, 2006 |title=[[w:On_Truth|On Truth]] |publisher=Knopf |pages=112 |isbn=978-0307264220 |author-link=w:Harry_Frankfurt }} *{{cite book |last=Burton |first=Robert |date=March 17, 2009 |title=On Being Certain: Believing You Are Right Even When You're Not |publisher=St. Martin's Griffin |pages=272 |isbn=978-0312541521}} *{{cite book |last=Ariely |first=Dan |author-link=w:Dan_Ariely |date=September 17, 2024 |title=Misbelief: What Makes Rational People Believe Irrational Things |publisher=Harper Perennial |pages=320 |isbn=978-0063280434}} *{{cite book |last=Wolpert |first=Lewis |date=July 17, 2008 |title=Six Impossible Things Before Breakfast: The Evolutionary Origins of Belief |publisher=W. W. Norton & Company |pages=256 |isbn=978-0393332032 }} *{{cite book |last=Sunstein |first=Cass R. |date=December 23, 2014 |title=Wiser: Getting Beyond Groupthink to Make Groups Smarter |publisher=Harvard Business Review Press |pages=272 |isbn=978-1422122990 |author-link=w:Cass_Sunstein }} *{{cite book |last1=Tavris |first1=Carol |last2=Aronson |first2=Elliot |date=October 20, 2015 |title=Mistakes Were Made (but Not by Me): Why We Justify Foolish Beliefs, Bad Decisions, and Hurtful Acts |publisher=Mariner Books |pages=400 |isbn= 978-0544574786}} * {{Cite book|title=On freedom|last=Snyder|first=Timothy|author-link=w:Timothy_D._Snyder|date= September 17, 2024|publisher=Crown|isbn=978-0-593-72872-7|edition=First edition|location=New York}} *{{cite book |last=Kahneman |first=Daniel |date=April 2, 2013 |title=[[w:Thinking,_Fast_and_Slow|Thinking, Fast and Slow]] |publisher=Farrar, Straus and Giroux |pages=499 |isbn=978-0374533557 |author-link=w:Daniel_Kahneman }} *{{cite book |last=Haidt |first=Jonathan |date=February 12, 2013 |title=[[w:The_Righteous_Mind|The Righteous Mind: Why Good People Are Divided by Politics and Religion]] |publisher=Vintage |pages=528 |isbn=978-0307455772 |author-link=w:Jonathan_Haidt }} *{{cite book |last=Andersen |first=Kurt |date=September 5, 2017 |title=Fantasyland: How America Went Haywire: A 500-Year History |publisher=Random House |pages=480 |isbn=978-1400067213 |author-link=w:Kurt_Andersen }} *{{cite book |last=McIntyre |first=Lee |date=February 16, 2018 |title=Post-Truth |publisher=The MIT Press |pages=240 |isbn=978-0262535045 }} *{{cite book |last2=Lukianoff |first2=Greg |last1=Haidt |first1=Jonathan |date=September 4, 2018 |title=The Coddling of the American Mind: How Good Intentions and Bad Ideas Are Setting Up a Generation for Failure |publisher=Penguin Press |pages=352 |isbn=978-0735224896 |author-link=w:Jonathan_Haidt }} *{{cite book |last1=Tsipursky |first1=Gleb |last2=Ward |first2=Tim |date=May 29, 2020 |title=Pro Truth: A Practical Plan for Putting Truth Back Into Politics |publisher=Changemakers Books |page=271 |isbn=978-1789043990}} *{{cite book |last=Wilczek |first=Frank |author-link=w:Frank_Wilczek |date=January 12, 2021 |title=Fundamentals: Ten Keys to Reality |publisher=Penguin Press |pages=272 |isbn=978-0735223790}} *{{cite book |last=Galef |first=Julia |author-link=w:Julia_Galef|date=April 13, 2021 |title=The Scout Mindset: Why Some People See Things Clearly and Others Don't |publisherPortfolio |pages=288 |isbn=978-0735217553}} *{{cite book |last=Rosling |first=Hans |date=April 3, 2018 |title=Factfulness: Ten Reasons We're Wrong About the World--and Why Things Are Better Than You Think |publisher=Flatiron Books |pages=341 |isbn=978-1-250-10781-7 |author-link=w:Hans_Rosling }} *{{cite book |last=Schulz |first=Kathryn |author-link=w:Kathryn_Schulz |date=June 8, 2010 |title=Being Wrong: Adventures in the Margin of Error |publisher=Ecco |pages=416 |isbn=0061176044}} I have not yet read the following books, but they seem interesting and relevant. They are listed here to invite further research. * ''The Emergence of Everything: How the World Became Complex'', by Harold J. Morowitz * ''How We Know What Isn’t So: The Fallibility of Human Reason in Everyday Life'', by Thomas Gilovich ==References== <references/> [[Category:Life skills]] [[Category:Applied Wisdom]] [[Category:Philosophy]] [[Category:Clear Thinking]] [[Category:Courses]] [[Category:Reality]] {{CourseCat}} {{Clear Thinking}} 2kij0kwv1tvmbydybwfoqs4irctdrmq 0 221175 2720006 2718123 2025-06-29T10:48:20Z DavidMCEddy 218607 /* References */ add Chenoweth and Schock 2720006 wikitext text/x-wiki {{Essay}} :''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- and raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]].'' * '''''Those whom the gods wish to destroy they first make mad.'''''<ref>Anonymous ancient proverb, wrongly attributed to Euripides. {{Citation | title = Euripides | publisher = Wikiquote | url = https://en.wikiquote.org/wiki/Euripides | accessdate = 2017-02-19}}</ref> This essay (''a'') reviews evidence suggesting that the [[w:War on Terror|War on Terror]] is not going well, (''b'') surveys research that provides a credible explanation for why it’s not going well, and (''c'') recommends minimizing the use of force and focusing instead on rule of law and on subsidizing democratically managed media to manage armed conflicts including terrorism and the Islamic State. [[File:Terrorism deaths worldwide.svg|thumb|Figure 1. Terrorism deaths worldwide, 1970-2015.<ref name=Graves2017a>using data from the Global Terrorism Database (GTD), summarized by Graves (2017).</ref>]] Terrorist activity worldwide has grown dramatically since 2012, at least according to terrorism deaths recorded in the [[w:Global Terrorism Database|Global Terrorism Database (GTD)]] summarized in Figure 1.<ref>Graves (2017). Questions have been raised about the quality of GTD data, especially its consistency over time and whether individual events are or are not classified as suicide terrorism. For suicide terrorism in particular, the GTD is not consistent with the [[w:Suicide Attack Database|Suicide Attack Database]] maintained by the [[w:Chicago Project on Security and Terrorism|Chicago Project on Security and Threats (CPOST)]]. We used the GTD, because it seems to be the best data available on the subject, and we don’t believe its defects raise substantive questions about our conclusions.</ref> In the following, we (1) note that terrorism is minuscule as a cause of death nearly everywhere, (2) review the literature on the long-term impact of alternative responses to terrorism and conflict more generally, (3) discuss the role of the media in shaping public reactions to terrorism (and virtually any other public policy issue), and (4) summarize implications of the above for personal action and public policy. == 1. Terrorism is minuscule as a cause of death == Before discussing possible contributors to the recent spike in terrorism deaths, we first note that terrorism is essentially minuscule as a cause of death, except for a small number of countries with active armed conflicts: Even in the worst year on record, 2014, terrorism deaths were less than 0.08 percent (one twelfth of one percent or 800 per million) of all deaths worldwide that year. More generally, terrorism has been responsible for the deaths of 0.02 percent (one fiftieth of one percent or 200 per million) of all the people who have died since the first entry in the Global Terrorism Database in 1970.<ref>This assumes that the death rate numbers from the World Bank are adequate for present purposes; see Graves (2017). Data published by the CIA often differ from the World Bank. We have not explored those discrepancies but would be surprised if the differences raise substantive questions about our conclusions.</ref> [[w:List of causes of death by rate|You're several times more likely to die from a fire (0.55%) than terrorism. Or from accidental poisoning (0.61%). Or drown (0.67%). Or die from a fall (0.69%, using World Health Organization data from 2002).]] Certainly, deaths are not the only problem from terrorism: Terrorist attacks also injure people , and destroy property. However, analysis of the numbers of incidents and people injured essentially tell the same story. The research summarized in this essay suggests that this recent spike in terrorism is a ''product'' of the militarization of conflicts (section 2 below) driven by a [[w:Fascination with death|fascination with death]] and how that interacts with media funding and governance (section 3 below). * ''The primary problem from terrorism seems to be the collateral damage from military responses used to combat it.'' Unfortunately, collateral damage was not mentioned in either the index or the table of contents of ''An end to evil: How to win the War on Terror'' by [[w:David Frum|Frum]] and [[w:Richard Perle|Perle]], which appeared in January 2004; that was roughly nine months after the [[w:2003 invasion of Iraq|US-led invasion of Iraq in 2003]] and seven after [[w:Mission Accomplished speech|President Bush's "Mission Accomplished" speech]]. Instead, they complained, "Pessimism and defeatism have provided the sound track to the war on terrorism from the beginning".<ref>Frum and Perle (2004, p. 8)</ref> The evidence summarized in this essay suggests that "pessimism and defeatism" have played far less of a role than collateral damage in the ensuing violence that has engulfed that region since 2003; this includes the rise of ISIL and the recent spike in terrorism documented in Figures 1 and 2 and in Appendix 1. We next consider terrorism in France, the US, and the dozen countries most impacted by this recent spike in terrorism before reviewing research relating to these recommendations. === 1.1. Terrorism in France and the United States === [[File:Terrorism deaths in France.svg|thumb|Figure 2. Terrorism deaths in France. The spike in 2015 is over 6 times the previous maximum since 1970 and is indicated by a number off the scale.<ref name=Graves2017a/>]] Figure 2 plots terrorism deaths in [[France]] through 2015. The number for 2015 is labeled, not plotted, because it is over 6 times the second largest recorded number of terrorism deaths in France since the first entry in the [[w:Global Terrorism Database|Global Terrorism Database]] (GTD) in 1970, and plotting it would make it difficult to see the earlier variability. GTD data for 2016 are not yet available. However, the Wikipedia [[w:List of terrorist incidents in France|"list of terrorist incidents in France"]] reports 89 deaths for that year. That’s just over half the number for 2015 and over three times the previous maximum.<ref> {{Citation | title = List of terrorist incidents in France | publisher = Wikipedia | url = https://en.wikipedia.org/wiki/List_of_terrorist_incidents_in_France | accessdate = 2017-02-17}}</ref> These relatively high numbers have made security a key issue in the French presidential campaign in progress as this is being written.<ref>{{Citation | last = Giudicelli | first = Anne | date = 2017-02-15 | title = Elections in France: It’s all about security | journal = Al Jazeera | url = http://www.aljazeera.com/indepth/opinion/2017/02/elections-france-security-170215090123247.html | accessdate = 2017-02-17}}</ref> These numbers are, nevertheless, tiny as a cause of death. The 161 terrorism deaths in France in 2015 is roughly 0.03 percent (one thirtieth of a percent or 300 per million) of all French deaths that year.<ref>This assumes that the death rate in France is roughly 8.4 per thousand population, which is the number for 2014 (the most recent available) in the World Bank WDI.xlsx data, and the population of France is roughly 67 million. {{Citation | date = December 2016 | title = World Development Indicators - Downloads: WDI (Excel)-ZIP (80 MB) | publisher = World Bank | url = http://data.worldbank.org/data-catalog/world-development-indicators | accessdate = 2017-03-11}}</ref> [[File:Terrorism deaths in the United States.svg|thumb|Figure 3. Terrorism deaths in the United States. The spike in 2001 is labeled, not plotted, because it is almost 20 times the death toll from the second largest terrorist attack in US history, the [[w:Oklahoma City bombing|Oklahoma City bombing]], which killed 168 people in 1995.<ref name=Graves2017a/>]] The two biggest terrorist attacks on [[w:United States|US]] soil were the [[w:September 11 attacks|September 11, 2001 attacks]] that took roughly 3,000 lives, and the [[w:Oklahoma City bombing|Oklahoma City bombing]] that killed 168 people in 1995.<ref>{{Citation | title = Oklahoma City bombing | publisher = wikipedia | url = https://en.wikipedia.org/wiki/Oklahoma_City_bombing | accessdate = 2017-02-17}}</ref> For the US, [[w:Global Terrorism Database|GTD]] records show no recent spike comparable to that for the world and France in Figures 1 and 2; see Figure 3. The most recent years suggest a modest upward trend -- possibly a return to the environment of the early 1970s, but nothing like 2001 nor the recent worldwide or French numbers. The GTD records 1,397 US citizens killed in terrorist incidents between 1970 and 2000, and 943 between 2002 and 2015,<ref>The GTD records 2,910 US citizens killed in terrorist incidents in 2001. The official number of people killed in the [[w:September 11 attacks|September 11 attacks]] was 2,996. The difference is non-US citizens killed in those attacks.</ref> for an average of 116 per year over these 46 years; without 2001, it averages only 52 per year. For 2001 through 2016, an average of 257 US citizens were killed per year. Averaged over the 46 years in the Global Terrorism Database, terrorism has taken the lives of 0.005 percent (one half of one hundredth of one percent or 50 per million) of all Americans who died during that period.<ref name=Graves2017>Graves (2017)</ref> To put these numbers into perspective, we provide three comparisons: * [[w:List of motor vehicle deaths in U.S. by year|42,196 people were killed on US highways in 2001, averaging 3,516 per month]].<ref> {{Citation | title = List of motor vehicle deaths in U.S. by year | publisher = wikipedia | url = https://en.wikipedia.org/wiki/List_of_motor_vehicle_deaths_in_U.S._by_year | accessdate = 2017-03-07}}</ref> Thus, more people were killed in the average month in 2001 than in the worst terrorist incident ever recorded. Between 2001 and 2015, 569,229 people died on US highways and 3,939 died from terrorist attacks -- a ratio of 145 to 1. * Roughly [[w:male breast cancer|440 ''men'' die in the US each year due to breast cancer.]] (This doesn't count breast cancer among women, who are roughly 100 times as likely to get it as men.)<ref>Females are more likely than males to survive breast cancer, because their cancers are usually caught earlier. Male breast cancers are not caught earlier, because the risks are so low that it has so far never seemed worth the effort to develop sensible screening procedures for it. {{Citation | title = Male breast cancer | publisher = wikipedia | url = https://en.wikipedia.org/wiki/Male_breast_cancer | accessdate = 2017-02-26}}</ref> That’s roughly 0.03 percent (one thirtieth of a percent or 300 per million) of all male deaths in the US. Thus, breast cancer has taken the lives of roughly six times as many men in the US as terrorism since the first entry in the Global Terrorism Database (GTD) in 1970. This rate, 0.03 percent, is the same rate as ''the worst year on record for France'', and roughly a third of the recent worldwide spike in Figure 1. * Between 1999 and 2003, a total of 1,676 Americans were reported to have drowned in a bathtub, hot tub or spa, averaging 335 a year.<ref>{{cite Q |Q60226981 }}</ref> In other words, America’s highways and tubs are greater risks than terrorism, and breast cancer is a greater risk even for males, except in countries with active armed hostilities like Iraq. Beyond this, as noted above, you are several times more likely to die from a fire, accidental poisoning, drowning or a fall. This is not to trivialize terrorist deaths, but only to say that we should not spend more money on protection against terrorism than the threat deserves -- and we should avoid actions that could make it worse, as suggested by the evidence summarized here. === 1.2. Countries with the most terrorism deaths 2014-2015 === [[File:Terrorism deaths by country, 2014-2015.svg|thumb|Figure 4. Terrorism deaths by country, 2014-2015, per the Global Terrorism Database.<ref name=Graves2017/>]] Figure 4 summarizes the total number of terrorism deaths by country in 2014 and 2015. France and the US are buried in the thirteenth “other” category in this plot. Terrorism is not a substantive problem for France or the US or anywhere else except for the relatively small number of countries with active armed hostilities, identified in Figure 4.<ref name=Graves2017a/> Not one of these countries had a comparable terrorism problem prior to the announcement of the US-led “[[w:War on terror|War on Terror]]”. This is clear from plots similar to Figures 1-3 for each of these dozen countries individually (available in Appendix 1). Pakistan, Egypt, and Sudan had terrorism problems prior to 2001 but nothing comparable to what they’ve experienced since the US declared a War on Terror. This claim is supported by more than just the relatively tiny number of deaths and injuries. It is also supported by research on the long-term impact of alternative approaches to conflict. This is called here "[[effective defense]]" and summarized in the next section. == 2. Research on the long-term impact of alternative approaches to conflict == * When people are killed and property destroyed, the apparent perpetrators often make enemies.<ref name=Graves2004>Graves (2004)</ref> * [[w:David Petraeus|General David Petraeus]] as commander of US Central Command understood that “you can't kill your way out of an insurgency, … [Y]ou have to find other kinds of ammunition, and it's not always a bullet," according to one of his closest colleagues.<ref>{{cite news | last1 = Depaulo | first1 = Lisa | title = Leader of the Year: Right Man, Right Time | url=http://www.gq.com/story/leader-of-the-year-general-david-petraeus-war | accessdate = 2017-02-19 | publisher = GQ | date = October 31, 2008 }}</ref> * [[w:Stanley McChrystal|General Stanley McChrystal]], who held several command positions in Iraq and Afghanistan, wrote, "we found that nearly every first-time jihadist claimed [that the torture at] Abu Ghraib had first jolted him into action." He also said that, "mistreating detainees would discredit us. ... The pictures [from] Abu Ghraib represented a setback for America's efforts in Iraq. Simultaneously undermining US domestic confidence in the way in which America was operating, and creating or reinforcing negative perceptions worldwide of American values, it fueled violence".<ref><!-- Stanley McChrystal (2013) My share of the task: A memoir-->{{cite Q|Q72893267}}</ref> The research reviewed here suggests that the world would be safer, more prosperous, and more democratic if the West treated terrorism as a law enforcement issue, strengthening international law, while dramatically reducing its reliance on military force. We need more research to better understand what drives people off the sidelines to support one side or the other in conflict and what motivates them to increase or decrease their level of support and to defect. === 2.1. How terrorist groups end === [[File:RANDterroristGpsEnd2006.svg|thumb|Figure 5. How terrorist groups end (''n'' = 268): The most common ending for a terrorist group is to convert to nonviolence via negotiations (43 percent), with most of the rest terminated by law enforcement (40 percent). Groups that were ended by military force constituted only 7 percent.<ref>Jones and Libicki (2008, p. 19)</ref>]] In 2008 two researchers with the [[w:RAND Corporation|RAND Corporation]], [[w:Seth Jones|Seth Jones]] and [[w:Martin C. Libicki|Martin Libicki]], discussed all the terrorist groups they could find that were active between 1968 and 2006: they found 648. Of those, 136 splintered, 244 were still active, leaving 268 that had ended. Of the ones that ended, 83 percent succumbed to rule of law, including 43 percent converting to non-violent political actors and 40 percent taken out by law enforcement. Only 20 groups, 7 percent, were defeated by military action; 10 percent won.<ref>Jones and Libicki (2008). For detailed analysis of a few cases, see {{Citation | last = Cronin | first = Audrey Kurth | year = 2009 | title = How terrorism ends: Understanding the decline and demise of terrorist campaigns | publisher = Princeton U. Pr. | isbn = 978-0-691-15239-4}}</ref> When Jones and Libicki focused only on terrorist groups that became large enough to be called an “insurgency,” like the [[w:Islamic State of Iraq and the Levant|Islamic State]], the percentages changed: 18 of 38 (47 percent) were ended by negotiations. 10 (26 percent) ended in victory for the insurgents. 8 (21 percent) succumbed to military force. 2 (5 percent) were suppressed by law enforcement.<ref>Jones and Libicki (2008, p. 101, Table 5.1)</ref> Thus, when a terrorist group converted to an insurgency, the use of military force increased. Perhaps most importantly, the effectiveness of law enforcement fell dramatically at the expense of major increases in victories by both the terrorists and the military.<ref>The percentage of cases ending in negotiated settlements increased slightly.</ref> Jones and Libicki concluded by recommending “that United States should make police and intelligence efforts the backbone of US counterterrorism policy and move away from its mantra of fighting a war on terrorism.”<ref>Jones and Libicki (2008, p. 8)</ref> Using data from Jones and Libicki (2008), Bapat found that US military aid has tended to ''reduce'' the incentives of recipient governments to negotiate, thereby ''prolonging'' the threat.<ref>Bapat (2011)</ref> In other words, to the extent that Bapat's analysis is accurate, the War on Terror has been more a war ''for'' terror than ''against'' terror. * ''Why is the West using the least effective approach to terrorism (the military)?'' * ''To what extent are Western governments pressuring other countries to respond militarily to terrorism rather than relying on law enforcement and negotiations, as Bapat claims? Are the results really as negative as Bapat suggests?'' === 2.2. The long-term impact of alternative approaches to conflict === Chenoweth and Stephan (2011) identified all the major governmental change efforts of the twentieth century.<ref>Their database includes all violent and nonviolent campaigns ending between 1900 and 2006 that involved over 1,000 people at some point with a goal of changing the government.</ref> They found 217 movements that were predominantly violent and 106 that were primarily nonviolent. Outcomes were classified as either (1) failure, (2) partial success or (3) success. The basic results are summarized in Table 1: Nonviolence was twice as likely to succeed as violence. {|class="wikitable" |+ '''Table 1'''. Major governmental change efforts of the twentieth century by dominant nature of the struggle (violent or nonviolent) and by outcome (failure, partial success, success) in the NAVCO1.1 data set compiled by Chenoweth and Stephan.<ref>{{Citation | last = Chenoweth | first = Erica | author-link = w:Erica Chenoweth | year = 2011 | title = Nonviolent and Violent Campaigns and Outcomes (NAVCO) Dataset, v. 1.1 | publisher = University of Denver | url = http://www.du.edu/korbel/sie/research/chenow_navco_data.html | accessdate = 2014-10-08}}</ref> |- ! !colspan="2"|{{center top}}'''Number of conflicts'''{{center bottom}} !colspan="2"|{{center top}}'''Percent'''^(*){{center bottom}} |-Primary nature -> ! !!violent!!nonviolent!!violent!!nonviolent |- |'''Outcome''' || || || || |- | align="right"|success||align="right"|55||align="right"|57||align="right"|25%||align="right"|54% |- | align="right"|partial success||align="right"|28||align="right"|26||align="right"|13%||align="right"|25% |- | align="right"|failure||align="right"|134||align="right"|23||align="right"|62%||align="right"|22% |- | align="right"|total||align="right"|217||align="right"|106||align="right"|100%||align="right"|100%^(*) |- | colspan="5" align="left"|^(*) Percent within conflicts of the same primary nature. Thus, the "violent" column percents add to 100. The nonviolent total differs from 100 only because of round-off. |} There has been some study of whether the existence of a {{w|radical flank effect|radical flank}} increases or decreases the likelihood of success of a primarily nonviolent movement. Chenoweth and Schock (2015) said that, "no study has systematically evaluated the effects of simultaneous armed resistance on the success rates of unarmed resistance campaigns." To fill this gap, they studied which of the 106 primarily nonviolent campaigns in Chenoweth and Stephan (2011) had a radical flank. They concluded that, "large-scale maximalist nonviolent campaigns often succeed despite intra- or extramovement violent flanks, but seldom because of them.”<ref>{{cite Q|Q83970885}}<!-- Do Contemporaneous Armed Challenges Affect the Outcomes of Mass Nonviolent Campaigns?, in refereed journal ''Mobilization'' -->. Other studies cited in the Wikipedia article on "[[w:radical flank effect|Radical flank effect]] reached the opposite conclusion; however, these other studies were earlier and smaller. In addition, they seemed to be less systematic than Chenoweth and Schock.</ref> However, the benefits of nonviolence extend beyond the end of a conflict. Chenoweth and Stephan merged their data with the [[w:Polity data series|Polity IV database]], which 'is a widely used data series [summarizing] annual information on the level of democracy for all independent states with greater than 500,000 total population and covers the years 1800–2013. ... For each year and country, a "Polity Score" is determined, which ranges from -10 to +10, with -10 to -6 corresponding to [[w:Autocracy|autocracies]], -5 to 5 corresponding to [[w:Anocracy|anocracies]], and 6 to 10 to [[w:Democracy|democracies]].'<ref>{{Citation | title = Polity data series | publisher = Wikipedia | url = https://en.wikipedia.org/wiki/Polity_data_series | accessdate = 2017-02-26}}</ref> {|class="wikitable" |+ '''Table 2'''. Polity Score ranges from -10 to +10 |- ! !!minimum value!!maximum value |- |align="right"|[[w:Autocracy|autocracies]]||-10||-6 |- |align="right"|[[w:Anocracy|anocracies]]||-5||5 |- |align="right"|[[w:Democracy|democracies]]||6||10 |- |} Table 3 shows the average increase in democratization from one year before the start of a conflict to one, five, and ten years after. The results suggest that ''win or lose'', nonviolence tends on average to be followed by an increase in the Polity IV rating while violence has relatively little impact on democratization. As noted above, nonviolence builds democracy, while violence perpetuates tyranny, on average, in the long run. {|class="wikitable" |+ '''Table 3'''. Average increase in Polity score from one year before to 1, 5 and 10 years after the end of a conflict.^(*) |- | || colspan="3" style="text-align: center;" | violent | colspan="3" style="text-align: center;" | nonviolent |- ! years after !! 1 !! 5 !! 10 !! 1 !! 5 !! 10 |- |align="right"|success||0.5||-1.6||-.5||5.9||10.1||10.0 |- |align="right"|partial success||1.4||2.1||1.9||4.2||6.8||7.6 |- |align="right"|failure||0.4||0.8||0.8||3.0||2.7||4.9 |- | statistically significant || colspan="3" style="text-align: center;" | no | colspan="3" style="text-align: center;" | yes |- | colspan="7" align="left"|^(*) None of the changes following violent campaigns are statistically significant while all the changes following nonviolent campaigns are significant at the 0.05 level, and all but three have significance probabilities less than 0.001. |} The reality is more complicated than the simple summary of Table 3: A primary determinant of the level of democracy after a conflict, apart from the primary (violent or nonviolent) nature of the conflict, is the level of democracy before. Figure 6 plots the Polity IV democracy score 5 years after vs. 1 year before the end of each conflict.<ref>Plots of data from the NAVCO1.1 database; see Chenoweth and Stephan (2011).</ref> [[File:Democratization 5 years after vs. 1 year before twentieth century revolutions.svg|thumb|Figure 6. Democratization 5 years after (vertical scale) vs. 1 year before (horizontal scale) the end of twentieth century revolutions]] This plot includes six panels grouped by the primary nature (violent or nonviolent) of the conflict and the outcome (failure, partial success, success). Points on the dotted diagonal line in each panel indicate conflicts that were accompanied by zero change in their Polity scores for the indicated time frame. The solid lines in each panel are based on the best fit of several models considered. This expresses the democracy score after the conflict as linearly dependent on the democracy score before plus interactions between outcome and both the democracy score before and the primary nature of the conflict.<ref>For more detail, see Chenoweth and Stephan (2011).</ref> These plots show more detail behind the simple summary of Table 3: Successful nonviolent revolutions have on average had a substantial impact in increasing the level of democracy among autocracies but no impact among the best democracies. By contrast, the worst long term outcomes tend to be from ''successful violent'' revolutions. This is worth repeating: * ''Successful violent revolutions provide the worst prospects for democracy in most cases.'' This can be explained by observing that successful violence brings to power people who know how to use violence but are not as good at solving problems without violence. (The comparable analyses of democratization 1 and 10 years after the end of the conflict are essentially the same; those plots are in Appendix 2.) In sum, the overall image supports the claim made above: Win or lose, nonviolence builds democracy, while violence perpetuates tyranny, on average, in the long run. This is consistent with the findings of Jones and Libicki (2008) mentioned above, that better outcomes for democracy are achieved when governmental officials support rule of law and negotiations. More on this comes from research on why people obey the law, when they do. === 2.3. Why people obey the law === People tend to obey the law, when they do, when [[w:Procedural justice|legal procedures seem fair to them]]. [[w:Tom R. Tyler|Tyler and Huo (2002)]] concluded that people of different ethnicities in the US have essentially the same concept of justice as majority whites but different experiences. This was based on a survey of African-Americans, Hispanics, and whites. They describe two alternative strategies for effective law enforcement: * Deterrence: effective but inefficient * Process-based: efficient and effective Tyler and Huo's analysis suggests that biased, unprofessional behavior of police, prosecutors and judges not only produces concerns of injustice, it cripples law enforcement efforts by making it more difficult for police and prosecutors to obtain the evidence needed to convict guilty parties. This is important for winning the War on Terror, because it describes some of the negative consequences of official behaviors that convince substantive segments of society that law enforcement is unjust. Retired US Green Beret Lt. Col. D. Scott Mann described how US Special Forces units defeated the Taliban by living for extended periods in small Afghan villages, treating the local people with respect, and showing sensitivity to their culture and concerns. In this way, they gradually earned people's trust to the point that people would inform them of Taliban activities in that geographic area and other problems. Where this was not done, Mann said the Taliban was winning.<ref>{{cite Q|Q83934350}}<!--Game Changers --></ref> For more extreme cases, we turn to the work of [[w:Robert Pape|Robert Pape]] on “dying to win” and “bombing to win”. === 2.4. Dying to win === Suicide terrorism is a primary focus of the [[w:Chicago Project on Security and Terrorism|Chicago Project on Security and Terrorism]] founded by [[w:Robert Pape|Robert Pape]] at the [[w:University of Chicago|University of Chicago]]. These data were discussed in his (2005) ''[[w:Dying to Win: The Strategic Logic of Suicide Terrorism|Dying to Win: The Strategic Logic of Suicide Terrorism]]'' and his (2010) ''Cutting the Fuse: The Explosion of Global Suicide Terrorism and How to Stop It'', with James K. Feldman. ''Dying to Win'' analyzed 315 suicide terrorism attacks around the world from 1980 through 2003. ''Cutting the Fuse'' evaluated more than 2,100 attacks, over 6 times the number in the first book. Pape and Feldman’s conclusions include the following: * "Overall, foreign military occupation accounts for 98.5% -- and the deployment of American combat forces for 92% -- of all the 1,833 suicide terrorist attacks around the world in the past six years [2004-2009]."<ref>Pape and Feldman (2010, p. 28)</ref> * "Have these actions ... made America safe? In a narrow sense, America is safer. There has not been another attack on the scale of 9/11. ... In a broader sense, however, America is not safer. Anti-American suicide terrorism is rapidly rising around the world."<ref>Pape and Feldman (2010, p. 318)</ref> * "[I]n both Iraq and Afghanistan ... local communities that did not inherently share the terrorists' political, social, and military agenda, eventually support[ed] the terrorists organization's campaign ... after local communities began to perceive the Western forces as an occupier ... as foreign troops propping up and controlling their national government, changing their local culture, jeopardizing economic well-being, and conducting combat operations with high collateral damage ... . But, we have also seen in Iraq that this perception of occupation can be changed ... ."<ref>Pape and Feldman (2010, p. 333)</ref> * "For over a decade our enemies have been dying to win. By ending the perception that the United States and its allies are occupiers, we can cut the fuse to the suicide terrorism threat."<ref>Pape and Feldman (2010, p. 335)</ref> The terrorist attacks of September 11, 2001, fit Pape’s model: The US maintained a substantive military presence in Saudi Arabia from the [[w:Gulf War|1990-91 Persian Gulf War]] until 2003. [[w:United States withdrawal from Saudi Arabia|It seems virtually certain that without those foreign troops on Saudi soil, Al Qaeda could not have found 19 young men willing to commit suicide on September 11, 2001, to send a message to the people of the United States.]]<ref>The US has rejected the characterization of its presence as an "occupation", noting that the government of Saudi Arabia consented to the presence of troops. However, the dominant factor in the motivation of our opposition is how ‘’they’’ perceive it, not how the US perceives it.</ref> This position is supported by US government documents declassified on July 15, 2016, that reported that some of the suicide mass murderers of September 11, 2001, had received help from employees of the Saudi Embassy and Consulates in the US, including members of the Saudi royal family, to obtain housing and other things they needed to get the training required to do what they did on that fateful day. Moreover, ranking officials in the [[w:Presidency of George W. Bush|George W. Bush administration]] knew of this complicity at least in 2002 before the US-led invasion of Iraq and successfully convinced the [[w:Joint Inquiry into Intelligence Community Activities before and after the Terrorist Attacks of September 11, 2001|Joint congressional inquiry into the terrorist attacks of September 11, 2001]] to redact [[w:The 28 Pages|28 pages]] containing that information from their December 2002 report.<ref>See references cited in the Wikipedia article on [[w:The 28 Pages|”The 28 Pages”]].</ref> * ''Given the documented support of Saudi government officials for the September 11 attacks, why did the US invade Afghanistan and Iraq?'' * ''We have enemies, because we have friends like these.'' It seems worth noting in this context that negotiations for the [[w:Turkmenistan–Afghanistan–Pakistan–India Pipeline|Turkmenistan–Afghanistan–Pakistan–India Pipeline]] were suspended after the [[w:1998 United States embassy bombings|1998 United States embassy bombings]] over Taliban support for [[w:Osama bin Laden|bin Laden]], who had been accused of masterminding those 1998 bombings. Pipeline construction began in 2015 without the need for a jury trial of bin Laden. This coincidence does not prove that the pipeline was part of the motivation for invading Afghanistan after September 11, 2001, but the coincidence is striking. === 2.5. Bombing to win === ''Bombing to win'' by [[w:Robert Pape|Robert Pape]] provides a qualitative survey of all the uses of [[w:Airpower|airpower]] up to the early 1990s. He concluded that ''strategic bombing was wasteful,'' and the only uses of airpower that contributed to military victory involved support of ground operations. He made a possible exception for nuclear weapons, but noted that when the Japanese Emperor [[w:Hirohito|Hirohito]] informed his military of the need to surrender after the [[w:Atomic bombings of Hiroshima and Nagasaki|atomic bombings of Hiroshima and Nagasaki]], he did NOT mention the atomic bomb. Instead he noted the Soviet entry into the war and the rapid collapse of the elite Japanese forces in Manchuria that followed. Hirohito’s true motives are unclear, because when he spoke to the civilian population, he mentioned the atomic bombings and not the Soviets.<ref>Pape (1996) </ref> Regarding nuclear weapons, retired US Army Colonel [[w:Andrew Bacevich|Andrew Bacevich]] claimed that, “Nuclear weapons are unusable. Their employment in any conceivable scenario would be a political and moral catastrophe. … [T]hey are unlikely to dissuade the adversaries most likely to employ such weapons against us -- Islamic extremists … . If anything, the opposite is true. By retaining a strategic arsenal in readiness ..., the United States continues tacitly to sustain the view that nuclear weapons play a legitimate role in international politics”.<ref>{{Citation | last = Bacevich | first = Andrew J. | year = 2008 | title = The Limits of Power: The End of American Exceptionalism | publisher = Metropolitan Books | pages = 178-179 | isbn = 0805090169}}</ref> Bacevich’s concern is strengthened by an estimate of the probability distribution of the "[[time to extinction of civilization]]". That analysis concludes that there is a probability of between 10 and 20 percent of a nuclear war in the next 40 years that would loft so much soot into the stratosphere where rain clouds rarely form and where most of it would remain for decades preventing up to 70 percent of the sunlight from reaching the surface of the earth. This would produce a nuclear winter during which roughly 98 percent of humanity would starve to death. Considerations like these have driven some senior US statesmen like [[w:Sam Nunn|former US Senator Sam Nunn]], [[w:William Perry|former US Secretary of Defense William Perry]], [[w:Henry Kissinger|former US Secretary of States Henry Kissinger]] and [[w:George Shultz|George Shultz]] to support [[w:nuclear disarmament|nuclear disarmament]], though not necessarily unilaterally. On the broader question of the effectiveness of strategic bombing, the [[w:United States Air Force|US Air Force (USAF)]] funded a 1999 study by the [[w:RAND Corporation|RAND corporation]] on that. It did NOT support Pape’s conclusions.<ref>{{Citation | last =Byman | first =Daniel L. | author-link = w:Daniel Byman | last2 =Waxman | first2 =Matthew C. | author2-link =w:Matthew Waxman | last3 = Larson | first3=Eric | title = Air Power as a Coercive Instrument | publisher =RAND Corporation | series =Project AIR FORCE | year =1999 | url = https://www.rand.org/content/dam/rand/pubs/monograph_reports/2007/MR1061.pdf | accessdate = July 29, 2013}}</ref> However, this RAND study produced a database of “all instances of [[w:Airpower|air power]] coercion from 1917 to 1999”, which was used by Horowitz and Reiter (2001). Applying multivariate probit analysis, Horowitz and Reiter concluded the following: # Coercion is more effective when the target's military vulnerability is higher. # Higher levels of civilian vulnerability have no effect on the chances of coercion success. # Target regime type ([[w:Polity data series|its Polity score]]) has no effect. # Success is less likely when the attacker demands the target change its leadership.<ref>Horowitz and Reiter (2001)</ref> The first two of these four conclusions provide a more solid empirical basis for Pape’s claims. The fourth of these conclusions seems consistent with the observation of Jones and Libicki (2008) discussed above, that 43 percent of terrorist groups ended with a negotiated political settlement. One interpretation of this is that the collateral damage from strategic bombing can easily be viewed as excessive by the victims and people on the sidelines. However, with ground operations, it’s generally less obvious who should be blamed for collateral damage. As noted above, we need more research to better understand what drives people off the sidelines to support one side or the other in conflict and what motivates them to increase or decrease their level of support and to defect. Moreover, this research should be funded and managed by sources independent of anyone with a [[w:conflict of interest|conflict of interest]] in the conclusions. This information should be compiled in more or less in real time with at most a few months delay in making it available to the public. The research available today suggests that the impact of collateral damage on the evolution of conflict may be substantially greater than is acknowledged by those driving current US military operations. As noted in the introduction to this section, when people are killed and property destroyed, the apparent perpetrators often make enemies.<ref name=Graves2004/> However, until the public gains a better understanding the counterproductive nature of collateral damage, we cannot expect wisdom in this area to weigh very heavily in the selection of political and military leaders. A tragic example is how the G. W. Bush administration politicized intelligence to justify invading Iraq. People were fired for insisting that the available evidence did not support claims that Saddam Hussein had weapons of mass destruction or links to al Qaeda.<ref>Goodman (2013, ch. Four. Bush's Surrender to the Pentagon)</ref> [[Effective defense|We need more research on how to win (or better avoid) wars]] -- and more public awareness of this distinction. Without this, it's easy for the side with a bigger military to win battles and lose wars. Generals and admirals are too often pushed to choose strategies that resonate with their superiors but manufacture enemies faster than they can be neutralized. This is part of how the British lost the American Revolution<ref>{{Citation | last = Graves | first = Spencer B. | year = 2005 | title = Violence, Nonviolence and the American Revolution | url = http://prodsyse.com/conflict/Nonviolence&AmericanRevolution.pdf | accessdate = 2015-11-26}}</ref> and how the US lost its war in Vietnam,<ref>Chayes (2015)</ref> to name only two examples. There is a growing body of evidence that “collateral damage” is rarely neutral. === 2.6. Drones === The Obama administration has claimed that drones ([[w:Unmanned combat aerial vehicle|unmanned combat aerial vehicles]]) are over 95 percent effective in killing enemy combatants.{{Citation needed | date=March 2017}} Their opposition, including many former drone pilots, who have spoken out at risk of being prosecuted for exposing classified information, claim that the figure may be closer to 50 percent.{{Citation needed | date=March 2017}} The discrepancy is explained by the claim that people killed in a drone strike are classified as EKIA (enemy killed in action) unless there is substantial evidence to the contrary.<ref>{{Citation needed | date=March 2017}} We need further study of the impact on Pakistani politics of US drone operations there and the contribution of US drone operations in Yemen to the civil war in progress as this is being written, 2017-03-06.</ref> === 2.7. Islamic terrorism === There is evidence to suggest that the two most effective recruiters for Islamic terrorism may be Saudi Arabia and the United States. * As noted in the discussion above of "dying to win", without US troops on Saudi soil 1991-2001, no Islamic terrorist organization would likely have found 19 young men willing to commit suicide in a terrorist attack on September 11, 2001. * On June 5, 2002, then-FBI Director {{w|Robert Mueller}} said "that investigators believe the idea of the Sept. 11 attacks on the World Trade Center and Pentagon came from al Qaeda leaders in Afghanistan, the actual plotting was done in Germany, and the financing came through the United Arab Emirates from sources in Afghanistan."<ref>{{cite Q|Q61755017}}<!-- Mueller outlines origin, funding of Sept. 11 plot -->.</ref> However, [[w:The 28 pages|"The 28 Pages"]], declassified 2016-07-15 by then-President {{w|Barack Obama}} document that at least as early as 1999, the FBI had information of Saudi government funding and support for what later became the [[w:September 11 attacks|suicide mass murders of September 11, 2001]]. Moreover, when Mueller made those comments, the FBI was actively working to prevent the {{w|Joint Inquiry into Intelligence Community Activities before and after the Terrorist Attacks of September 11, 2001}} from obtaining that information. [[w:Bob Graham|Bob Graham]], who served on that Joint Inquiry, said in 2015 that during that inquiry and since, the FBI went "beyond just covering up ... into ... aggressive deception."<ref>{{cite Q|Q65002265}}<!-- Florida Ex-Senator Pursues Claims of Saudi Ties to Sept. 11 Attacks -->.</ref> In that 2015 comment, Senator Graham said the FBI "had investigated a Saudi family in Sarasota, Fla., and had found multiple contacts between it and the hijackers training nearby until the family fled just before the attacks." By the time of that report, Graham also doubtless knew of the allegations by [[w:Sibel Edmonds|Sibel Edmonds]] that in the spring and summer of 2001, months before the September 11 attacks, an Iranian ex-patriot had told the FBI that bin Laden's network was planning to use airplanes in terror attacks in four or five major cities including New York City, Chicago, Washington DC, and San Francisco; possibly Los Angeles or Las Vegas. After September 11, Edmonds' co-workers got "an absolute order [that they] never got any warnings." Graham doubtless also knew of "a classified military planning effort led by the U.S. Special Operations Command (SOCOM) and the Defense Intelligence Agency (DIA)" called [[w:Able Danger|Able Danger]], which "had identified two of three al-Qaeda cells active in the 9/11 attacks". Government official denied having had knowledge of this before the September 11 attacks, but Lt. Col. [[w:Anthony Shaffer (intelligence officer)|Anthony Shaffer]] claims he had such information from his work on Able Danger before the attacks and was ordered not to testify to these congressional committees. * Those "28 pages" include a discussion of an {{w|America West}} flight that made an emergency landing in 1999 when two men tried to break into the cockpit. The apparent perpetrators showed the FBI Saudi passports and tickets apparently paid by the Saudi embassy in Washington, DC. That information was classified "Top Secret", presumably to keep it from raising too many questions about Saudi complicity in the suicide mass murders of September 11, 2001. * By 2002, the G. W. Bush administration had already invaded Afghanistan ostensibly to capture Osama bin Laden after refusing to consider the offer of the Afghani government to extradite him if the US provided evidence of his culpability. And Bush administration officials were working hard to convince the public in the US and their "coalition of the willing" to support invading Iraq, which they did in March 2003. * The growth of the [[w:Islamic State of Iraq and the Levant|Islamic State of Iraq and the Levant]] (ISIL), also called the "Islamic State of Iraq and Syria" (ISIS) or "Daesh", appears to have been a product of both (a) excessive collateral damage and (b) media censorship (discussed below) that enabled corruption to grow excessively in the post-Saddam Iraqi government and military. [[w:Islamic State of Iraq and the Levant|A former Chief Strategist in the Office of the Coordinator for Counterterrorism]] of the US State Department, [[w:David Kilcullen|David Kilcullen]], said that "There undeniably would be no Isis if we had not invaded Iraq."<ref name="Indie ISIL">{{citation |url=http://www.independent.co.uk/news/world/middle-east/iraq-war-invasion-caused-isis-islamic-state-daesh-saysus-military-adviser-david-kilcullen-a6912236.html |title=Former US military adviser David Kilcullen says there would be no Isis without Iraq invasion |work=The Independent |date=4 March 2016 |accessdate=8 March 2016 }}</ref> [[w:Graham Fuller|Graham Fuller]], a former CIA agent, was quoted in a 2014 interview as follows: "I think the United States is one of the key creators of [[w:Islamic State of Iraq and the Levant|[ISIS]]]. The United States did not plan the formation of ISIS, but its destructive interventions in the Middle East and the war in Iraq were the basic causes of the birth of ISIS."<ref>{{Citation | last = Basaran | first = Ergi | last2 = Fuller | first2 = Graham | date = 2014-09-02 | title = Former CIA officer says US policies helped create IS | journal = Al-Monitor: The pulse of the Middle East | url = https://www.al-monitor.com/pulse/politics/2014/09/turkey-usa-iraq-syria-isis-fuller.html | accessdate = 2017-12-05}}</ref> * Other sources note that, “[A]lmost all of ISIL's leaders ... are former Iraqi military and intelligence officers, … who lost their jobs and pensions in the [[w:De-Ba'athification|de-Ba'athification]] process” undertaken by the US-led occupation. “ISIL is a [[w:theocracy|theocracy]], [[w:proto-state|proto-state]] and a [[w:Salafi movement|Salafi]] or [[w:Wahhabism|Wahhabi]] group.”<ref>{{Citation | title = Islamic State of Iraq and the Levant | publisher = wikipedia | url = https://en.wikipedia.org/wiki/Islamic_State_of_Iraq_and_the_Levant | accessdate = 2017-03-04}}</ref> * The [[w:Salafi movement|Salafi]] / [[w:Wahhabi|Wahhabi]] branch of Islam is the most violent form of Islam, promoted by the Saudi royal family in part by funding schools and mosques throughout the Muslim world that taught their branch of Islam. At the same time, {{w|Structural adjustment}} programs pushed by the US through the {{w|World Bank}} and the {{w|International Monetary Fund}} have allegedly made life more difficult for all but the ultra-wealthy in many poor countries while pushing those countries to reduce their funding for education. As a result, the Saudi-funded {{w|Wahhabism|Wahhabi}}-{{w|Salafi movement|Salafist}} schools became the primary educational alternative for the children of many poor people. Many ISIL fighters reportedly came out of such schools. * ISIL relies mostly on captured weapons. For example, in Mosul between 4 and 10 June 2014 a group of between 500 and 600 ISIL troops “were able to seize six divisions’ worth of strategic weaponry, all of it US-supplied” from a force with a paper strength of 120,000 men.<ref name='AlJ5'><!-- Enemy of Enemies: The Rise of ISIL. Chapter 5. 2009-2015: Syria uprising and ISIL in Syria-->{{cite Q|Q113710863}}</ref> This invasion included [[w:Robert Pape|suicide attacks, which are almost always motivated by a foreign occupation (as discussed above)]].<ref>Pape (2005), Pape and Feldman (2010)</ref> [[w:Fall of Mosul|The invading troops]] were faced by an army where “every officer had to pay for his post”, and made money from soldiers who would kick back “half their salaries to their officers in return for staying at home or doing another job”, and from receiving funds to feed an organization three times the size on paper as were actually there.<ref>{{Citation | last = Astore | first = William J. | date = 2014-10-14 | title = Tomgram: William Astore, America's Hollow Foreign Legions -- Investing in Junk Armies | publisher = TomDispatch.com | url = http://www.tomdispatch.com/post/175907/tomgram%3A_william_astore,_america%27s_hollow_foreign_legions/ | accessdate = 2014-10-16}}</ref><ref>{{Citation | year = 2015 | title = Enemy of Enemies: The Rise of ISIL | chapter = 2. 2004-2006: Abu Musab Al-Zarqawi Emerges | publisher = Al Jazeera | url = http://interactive.aljazeera.com/aje/2015/riseofisil/chapter-two.html | accessdate = 2015-11-27}}</ref><ref>Beyond this, there have been numerous allegations that [[w:Finances of ISIL|Saudi Arabia and Qatar may have clandestinely provided funds to ISIL]], though that has not been proven.</ref> * In 2008 {{w|Stuart A. Levey}}, the Under Secretary for Terrorism and Financial Intelligence in the US Department of the Treasury, told the US Senate Finance Committee that “Saudi Arabia today remains the location where more money is going to terrorism, to Sunni terror groups and to the Taliban than any other place in the world."<ref>{{cite Q |Q61889276 }}</ref> In October 2010 he reported “significant improvement in the partnership between the U.S. and Saudi Arabia in targeting al Qaeda financing.”<ref>{{cite Q |Q61890613}}. See also [[w: Stuart A. Levey#Under Secretary for Terrorism and Financial Intelligence]]</ref> However, two months later, Wikileaks published leaked US diplomatic cable saying that, “Private individuals in Saudi Arabia and other Gulf states friendly to the United States are the chief source of funding for al-Qaeda, the Taliban and other terrorist groups,” quoting a 2009 cable from US Secretary of State Hillary Clinton as saying, "It has been an ongoing challenge to persuade Saudi officials to treat terrorist financing emanating from Saudi Arabia as a strategic priority”.<ref>{{cite Q |Q61890660 }}</ref> And in August 2018 the Associated Press reported that Saudi Arabia was paying al Qaeda to help them fight the rebels in Yemen.<ref>{{cite Q |Q61890713 }}</ref> The sources cited above suggests that key decisions in the rise of Islamic terrorism were made by virtually every US president dating back to Franklin Roosevelt, but especially George W. Bush. *''We have enemies, because we have friends like these.'' *''The widespread demonization of terrorists with minimal context is an obstacle to effective action that could address the issues that drive people to support violence and escalate a conflict.''<ref>[[w:Jihad|Jihad]] “is an Arabic word which literally means striving or struggling, especially with a praiseworthy aim.” It is occasionally used to mean “Holy war,” but that is relatively rare. Thus, it is similar to the German word [[:de:w:Kampf|Kampf]], which means “struggle,” as that word is commonly used in English. The title of the infamous [[w:Mein Kampf|Mein Kampf]] by [[w:Adolf Hitler|Adolf Hitler]] simply means, “My struggle.”</ref> Fact check: Radical Islamic terrorists represent between 0.03 and 0.14 percent (between one out of 700 and one out of 3,000) of the [[w:Islam|more than 1.7 billion Muslims in the world today]], according to Brian Steed, a Lt. Col. on the faculty of the US Army Command and General Staff College in Leavenworth<ref>Steed is fluent in Arabic and has spent substantial time working in different Arabic-speaking countries. These comments were his personal, professional opinion and were not official policy of the United States government. {{Citation | last = Steed | first = Brian L. | editor-last = Harritt | editor-first = Ira | date = 2016-05-19 | title = Confronting Extremist Violence, the Refugee Crisis, and Fear: Faith Responses | chapter = Undersanding ISIS: Maneuver in the Narrative Space | chapter-url = https://www.youtube.com/watch?v=oU74V1i29tU | publisher = American Friends Service Committee | url = https://www.youtube.com/playlist?list=PLuZ74OBEmVKD7VG2UkDSR55zXYnJyztHs | accessdate = 2017-03-04 | quote = I'm speaking as a private citizen and not as a representative of the US government. ... Violent jihadists represent between 0.03% and 0.14% of Islam. (0:43 and 10:50 of 14:23 mm:ss)}}</ref> and author of a recent book on the Islamic State.<ref>{{Citation | last = Steed | first = Brian L. | year = 2016 | title = ISIS : an introduction and guide to the Islamic State | publisher = ABC-CLIO | isbn = 1440849862}}</ref> One more point about Islamic terrorist groups: Part of their appeal is their claim that the West hates Islam.{{Citation needed|date=March 2017}} It's easy to believe that if you listen to the [[w: Xenophobia|xenophobic]] rhetoric coming from people like [[w:Marine Le Pen|Marine Le Pen]] in France, and [[w:Donald Trump|Donald Trump]] in the US, both of whose electoral success is based in part on anti-immigrant, anti-Muslim platforms. Their ability to attract support would be reduced if the West increased its support for refugees, including Muslims. An important precedent for this discussion is the implicit support for the Nazis provided by the refusal of other countries to accept Jewish refugees in the late 1930s and the story behind the book and movie, [[w:Voyage of the Damned|''Voyage of the Damned:'']] The [[w:MS St. Louis|MS ''St. Louis'']] left Hamburg for Cuba on May 13, 1939. Most of her 937 passengers were Jewish refugees fleeing Nazi persecution. En route, Cuba revoked their entry visas. Only 29, most with valid visas to other countries, were allowed to enter Cuba. Of the rest, 288 eventually settled in Britain. Most of the rest died during the war, primarily in [[w:Nazi concentration camps|Nazi death camps]]. If the US, Britain, and other countries had accepted at least the vast majority of people wanting to leave Nazi Germany, it would have weakened the Nazi program in at least two ways: * The death camps would not have been built, because the Nazis would not have had enough support from their own people to prevent the refugees from leaving.<ref>{{Citation | last = Jacques | first = Jacques | year = 1993 | title = Unarmed against Hitler: Civil resistance in Europe, 1939-1943 | publisher = Praeger | isbn = 0-275-93960-X}}</ref> * It would have raised questions about the Nazi rhetoric that the [[w:Themes in Nazi propaganda|jews were parasites like tape worms or lice]]. This in turn could have made it [[w:Economy of Nazi Germany|more difficult for them to get public support for war]], possibly even reducing the strength of their military. The war likely still would have occurred, though that's not certain. If it did, the refugees would have had greater motivation to fight than just about anyone else in the countries allied against the Axis.<ref>If the US had had an open immigration policy like this, the Nazis may have sent some saboteurs posing as refugees. However, many if not all of these could have been identified by procedures that checked personal connections with other refugees: Potential saboteurs would not likely have had as many personal connections to other refugees and to people already in host countries. No screening system is perfect. However, it seems likely that the benefits to the hosts from receiving the refugees would outweigh the risks.</ref> === 2.8. The cost of US wars in the Middle East === In a campaign rally October 26, 2016, then-candidate Trump 'repeated his call to "drain the swamp," knocking the "failed elites in Washington" for being wrong about everything from foreign policy to health care. "The people opposing us are the same people — and think of this — who’ve wasted $6 trillion on wars in the Middle East — we could have rebuilt our country twice — that have produced only more terrorism, more death, and more suffering – imagine if that money had been spent at home". [[w:PolitiFact|PolitiFact]] rated Trump's $6 trillion figure as "half true", because "he is confusing money that’s been spent with money that researchers say will be spent", like obligations for benefits for combat-related disabilities of veterans that will eventually be paid over the coming decades. In this analysis, PolitiFact compared this $6 trillion number with sources giving numbers ranging from $4.8 to $7.9 trillion.<ref>{{Citation | last = Qiu | first = Linda | date = October 27, 2016 | title = Did U.S. spend $6 trillion in Middle East wars? | publisher = Politifact | url = http://www.politifact.com/truth-o-meter/statements/2016/oct/27/donald-trump/did-us-spend-6-trillion-middle-east-wars/ | accessdate = 2017-12-05}}</ref> We first note that Trump's concern that US "wars in the Middle East ... have produced only more terrorism" is consistent with the evidence summarized elsewhere in this article. However, we also wish to focus on this $6 trillion figure: That relates to wars between 2001 and 2016 -- 15 years. Thus, the US has been spending (or incurring obligations for future spending) at the rate of roughly $0.4 trillion.<ref>6/15 = 0.4</ref> By comparison, we note that the [[w:United States|US Gross Domestic Product (GDP)]] was estimated at $18.6 trillion for 2016. With this base, $0.4 trillion is over 2 percent of GDP.<ref>In 2002, US GDP was $11 trillion; $0.4 trillion was 3.6 percent of that. US GDP has been growing since then, except for a minor correction in 2009. This means that this $0.4 trillion has been declining as a percent of GDP but was always greater than 2 percent.</ref> We will return to this in the section below on "media funding and governance" and especially "citizen-directed subsidies". === 2.9. Trump and refugees === [[w:Immigration policy of Donald Trump|Very early in his Presidency, Donald Trump took several actions to implement some of the anti-immigrant policies]] that had formed a key part of his campaign. However, his justification for those policies have generally been contradicted by the available evidence. For example, he promised to suspend immigration from "areas of the world when there is a proven history of terrorism against the United States”.<ref>{{Citation | last = Qiu | first = Linda | date = June 13, 2016 | title = Wrong: Donald Trump says there's 'no system to vet' refugees | periodical = Politifact | publisher = Politifact.com | url = http://www.politifact.com/truth-o-meter/statements/2016/jun/13/donald-trump/wrong-donald-trump-says-theres-no-system-vet-refug/ | accessdate = 2017-03-10}}</ref> However, his executives orders 13769 from January 27, 2017, and 13780 from March 6, 2017, reportedly did not include any Muslim-majority countries with which he has business relations. In particular, Saudi Arabia, Egypt, Turkey, and Indonesia were not mentioned in his executive orders, even though nationals from Saudi Arabia and Egypt were directly involved in the September 11 attacks<ref>{{Citation | last =Helderman | first = Rosalind S. | date = January 28, 2017 | title = Countries where Trump does business are not hit by new travel restrictions | newspaper = Washington Post | url = https://www.washingtonpost.com/politics/countries-where-trump-does-business-are-not-hit-by-new-travel-restrictions/2017/01/28/dd40535a-e56b-11e6-a453-19ec4b3d09ba_story.html | accessdate = 2017-03-10}}</ref> -- and there is substantial documentation of other connections between Saudi Arabia and Islamic terrorism, as noted above. How were the leaders (including their staffs) who made these key decisions selected? === 2.10. Leaders and experts === [[File:Daniel KAHNEMAN.jpg|thumb|Daniel Kahneman, research psychologist who won the 2002 [[w:Nobel Memorial Prize in Economic Sciences|Nobel Memorial Prize in Economics]] for seminal research that showed that the standard economic models of a [[w:Rational choice theory|“rational person”]] do not correspond with how humans actually think.]] Leaders and experts in many fields make worse predictions than simple rules of thumb developed by intelligent lay people, according to research psychologist [[w:Daniel Kahneman|Daniel Kahneman]]. After studying the quality of expert opinion, Kahneman concluded that “true skill” requires two things: # An environment that is sufficiently regular to be predictable. # Opportunities to learn through prolonged practice. Some fields have these attributes; others do not.<ref>Kahneman (2011, ch. 22. Expert intuition: When can we trust it?, esp. p. 240). One of Kahneman's examples is anesthesiology (p. 242), because problems with anesthetics can lead fairly quickly to death of the patient. A contrasting medical example is provided by back surgeons, discussed by Harvard Medical School Prof. [[w:Jerome Groopman|Jerome Groopman]]. He wrote that back surgery practices in the US are grandfathered to procedures used in the nineteenth century. This lack of research has retarded the development of improved procedures in that field and increased the misery of people everywhere with back pain. This research deficit is at least partly a result of lobbying the US congress by companies that manufacture devices implanted in people's backs -- and the fact that serious coverage of lobbying would threaten the profitability of the mainstream media; see the discussion of the media in this essay. {{Citation | last = Groopman | first = Jerome | author-link = w:Jerome Groopman | year = 2007 | title = How Doctors Think | publisher = Houghton Mifflin | isbn = 9780618610037}}</ref> One of Kahneman's examples involves financial markets. Two things happen every trading day. First, the financial markets either go up or down. Second, the nightly news features a pundit, who tells us why. The value of this commentary for predicting the future is zero. That's because this situation lacks sufficient regularity to support learning (Kahneman's first condition), as enough people with enough money are already in the market trying to predict it. The daily movements in prices reflect what's left and is essentially random.<ref>For a summary of the research on financial markets, see, e.g., {{Citation | last = Siegel | first = Jeremy J. | author-link = w:Jeremy Siegel | year = 2008 | title = Stocks for the Long Run, 4th ed. | publisher = McGraw-Hil | isbn = 9780071494700}}.</ref> However, claims of random variability will not attract an audience, but “experts” spouting nonsense will -- as long as the audience doesn't know it's nonsense. Kahneman's two conditions rarely apply in politics. With media primarily focused on selling behavior change in their audience to funders (as noted in the discussion of the media below), [[w:Xenophobia|xenophobic]] politicians are too often promoted while people trying to facilitate understanding and deescalation over escalation in conflict may be vilified as naive appeasers. [[w:Dick Cheney|Former Vice President Cheney]]'s [[w:One Percent Doctrine|''One Percent Doctrine'']] was used to justify torture and preventive war in the absence of substantive evidence to support it,<ref>Parton (2014)</ref> with no apparent consideration of how such policies might manufacture support for the opposition. In a survey of empirical research on "Interventions / Uses of force short of war," Prins wrote, "hawkish leaders frequently rise to power by exploiting fears of conflict escalation. The increasingly coercive polices designed to check a rival only exacerbate security concerns and deepen national perceptions of enmity."<ref>{{Citation | last = Prins | first = Brandon C. | editor-last = Denemark | editor-first = Robert A. | year = 2010 | title = The International Studies Encyclopedia | chapter = Interventions / Uses of force short of war | publisher = Blackwell Reference Online | isbn = 9781444336597 | url = http://www.isacompendium.com/public/tocnode?id=g9781444336597_yr2015_chunk_g978144433659711_ss1-57 | accessdate = 2017-03-31}}</ref> From at least some perspectives, US Vice President Dick Cheney and Israeli Prime Minister [[w:Ariel Sharon|Ariel Sharon]] might fit this description by Prins. Similar questions have been raised about how military officers are promoted.<ref>{{Citation | last = Ricks | first = Thomas E. | author-link = w:Thomas E. Ricks (journalist) | year = 2012 | title = The Generals | publisher = Penguin | isbn = 978-1-59420-404-3}}</ref> During active hostilities, the ability to win military battles can weigh heavily in promotion criteria. However, the impact of those battles on the long term outcome of the conflict is rarely a consideration. * ''It is difficult if not impossible for military and political leaders to acquire Kahneman’s “true skill,” because the long-term impact of their actions is difficult to discern in the short term and not rewarded by the current political climate.'' This short-term information deficit increases the need to collect, analyze, and disseminate information on what motivates one’s opposition. Moreover, the system for collecting and disseminating such information should be independent of the policy makers, because the temptation to suppress bad news is generally too great to resist. * ''Virtually every party to conflict thinks they know more than they do about what motivates their opposition.'' This follows from the overconfidence that virtually everyone has in the value of current knowledge, discussed below. Independent collection and dissemination of information on the motivations of people in conflict may help open paths to dialog and resolution, thereby reducing the duration and lethality of conflict. The quotes from Generals Petraeus and McChrystal in the introduction to this section on “effective defense” suggest that some leaders may understand this, at least at some level. However, these kinds of observations generally get too little coverage in the mainstream media, perhaps because they do not support the responses apparently favored by major advertisers like the major oil companies.<ref name=Focke>Focke, Niessen-Reunzi and Ruenzi (2016)</ref> (See also the discussion of media ownership, funding and profitability, below.) === 2.11. US foreign interventions in opposition to democracy === * ''Are the US and the rest of the world better off as a result of its numerous interventions in foreign countries in opposition to democracy?'' Consider the military coups that destroyed democracy in Iran 1953, Guatemala 1954, Brazil 1964, and Chile 1973: In all these cases there is solid documentation of US involvement. Beyond this, there are substantial claims that the US clandestinely supported the [[w:March 1949 Syrian coup d'état|1949 Syrian coup]]; at minimum, the [[w:Trans-Arabian Pipeline|Trans-Arabian Pipeline]], which had been held up in the Syrian parliament, was approved roughly 6 weeks after the coup. Consider also the 1952 Cuban elections, which were canceled by a military coup on March 10 organized by [[w:Fulgencio Batista|Fulgencio Batista]]. Batista had been supported by the US as de facto head of state of Cuba since 1933, but polls showed him losing badly. The US officially deplored the coup but recognized the new Batista government on March 27.<ref>{{citation | last1 = Acheson | first1 = Dean | title = Continuation of Diplomatic Relations with Cuba | url = https://history.state.gov/historicaldocuments/frus1952-54v04/d327 | website = Office of the Historian of the United States Department of State | publisher=United States Department of State | accessdate = 2017-03-09 | date = 1952-03-24 }}</ref> [[w:Fidel Castro|Fidel Castro]], a 25-year old attorney, had been running for a seat in the Cuban House of Representatives in that election. If democracy had not been overthrown in Cuba, Fidel likely would have had a career as a politician and attorney in a democratic Cuba. Similarly, [[w:Che Guevara|Che Guevara]] had been working in Guatemala at the time of the [[w:1954 Guatemalan coup d'état|1954 Guatemalan coup d'état]]. That coup turned him into a revolutionary. Without that coup, Guevara would likely have had a successful career improving public health and democracy in Latin America. Also, former President [[w:Dwight D. Eisenhower|Eisenhower]] said, "I have never [communicated] with a person knowledgeable in Indochinese affairs who did not agree that had elections been held as of the time of the fighting [[w:Battle of Dien Bien Phu|[leading to the defeat of the French in 1954]]], possibly 80 per cent of the population would have voted for the Communist Ho Chi Minh".<ref>p. 372, ch. 14. Chaos in Indochina in {{cite Q|Q61945939}}<!-- Mandate for Change -->.</ref> *''This was the universal expert consensus that was not even mentionable in the mainstream media of that day.'' {{w|Joseph McCarthy}} was elected to the US Senate in part by railing against "twenty years of treason" by the Democrats in their alleged insufficient hostility to Communism.<ref> {{cite book|last = Herman |first = Arthur |title = Joseph McCarthy: Reexamining the Life and Legacy of America's Most Hated Senator |publisher = Free Press |year = 2000 |page = [https://archive.org/details/josephmccarthyre00herm/page/131 131] |isbn = 0-684-83625-4 |url = https://archive.org/details/josephmccarthyre00herm/page/131 }}</ref> This included allegations that the Democrats had "lost China to Communism." He implied that {{w|George Marshall}}, former General and Chairman of the Joint Chiefs of Staff during World War II and Secretary of State under President Truman, of being guilty of treason.<ref name="Retreat"> {{cite book |last = McCarthy |first = Joseph |title = Major Speeches and Debates of Senator Joe McCarthy Delivered in the United States Senate, 1950–1951 |publisher = Gordon Press |year= 1951 |pages = 264, 307, 215 |isbn = 0-87968-308-2}}. See also [[w:Joseph McCarthy#McCarthy and the Truman administration]].</ref> Near the end of 1953, McCarthy began referring to "twenty-''one'' years of treason" to include Eisenhower's first year in office.<ref>{{cite book|last = Fried |first = Albert |title = McCarthyism, The Great American Red Scare: A Documentary History |publisher = Oxford University Press |year = 1996 |page = [https://archive.org/details/mccarthyismgreat00frie/page/179 179] |isbn = 0-19-509701-7 |url = https://archive.org/details/mccarthyismgreat00frie/page/179 }}. See also [[w:Joseph McCarthy#McCarthy and Eisenhower]].</ref> In that political environment, Eisenhower doubtless knew in early 1954 that it would be very difficult for him politically if the Communist Ho Chi Minh actually won elections in Vietnam scheduled for July 1956, while Eisenhower would likely be running for reelection. He therefore worked clandestinely behind the scenes to help replace the unpopular Vietnamese Emperor {{w|Bảo Đại}} with {{w|Ngo Dinh Diem}}<ref name=Moyar>Moyar, Mark (2006). Triumph Forsaken: The Vietnam War, 1954–1965. New York: Cambridge University Press, pp. 41–42. See also [[w:Ngo Dinh Diem#Becoming Prime Minister and consolidation of power]].</ref> following the [[w:Geneva Conference (1954)|Geneva Accords of 1954]]. Diem effectively canceled the reunification elections scheduled for 1956 as part of those agreements.<ref name=Moyar/> A decade later, during the 1964 US presidential election campaign, President {{w|Lyndon Johnson}} was similarly being accused of being "soft on Communism" by his Republican opponent, {{w|Barry Goldwater}}. Johnson worked clandestinely to provoke North Vietnam into attacking US military vessels in the [[w:Gulf of Tonkin|Gulf of Tonkin]]. When the US Navy destroyer [[w:USS Maddox|USS ''Maddox'']] fired at "false radar images" on August 4, 1964, Johnson got the US Senate to approve the {{w|Gulf of Tonkin Resolution}} effectively giving Johnson a blank check to escalate the US war in Vietnam to counter this "unprovoked" attack. Only two US Senators voted against that resolution, and both were defeated in the next election. Johnson ultimately complained that the war had killed “the woman I really loved — the Great Society”.<ref><!-- How Vietnam Killed the Great Society -->{{cite Q|Q108895834}}</ref> [[w:United States involvement in regime change|The media environment drove US policy towards Vietnam from the end of world War II]] to the {{w|Fall of Saigon}} in 1975. The factual justification for the War on Terror, as documented in the present article, seems much less substantial than the justification for the Vietnam War. On May 23, 2013, then-US President Obama noted that terrorism caused fewer American deaths than car accidents or falls in the bathtub. He occasionally ''had to be badgered by advisors into choices commensurate with popular fear.'' He worried, too, that counterterrorist priorities “swamped” his other foreign policy aspirations.<ref><!-- Humane: How the United States Abandoned Peace and Reinvented War -->{{cite Q|Q108896140}}, pp. 268, 299-300.</ref> *''US military operations during the Vietnam War and the War on Terror seem primarily to have been driven by information the mainstream US media chose to highlight, selected to please their major funders, while routinely suppressing information that conflicted with that image. Many people were killed, because the different parties to conflict had (a) conflicting perceptions of reality and (b) inadequate understanding of the power of nonviolence and community policing.''<ref>See also the Wikiversity article on "[[confirmation bias and conflict]]".</ref> An October 14, 2014, story quoted then-President Obama as saying, “Very early in [the discussions about helping Syrian rebels], I actually asked the C.I.A. to analyze examples of America financing and supplying arms to an insurgency in a country that actually worked out well. And they couldn’t come up with much.”<ref>{{Citation | last = Mazzetti | first = Mark | date = October 14, 2014 | title = C.I.A. Study of Covert Aid Fueled Skepticism About Helping Syrian Rebels | newspaper = New York Times | url = https://www.nytimes.com/2014/10/15/us/politics/cia-study-says-arming-rebels-seldom-works.html?_r=0 | accessdate = 2017-03-09}}</ref> * ''If the overall record of US foreign interventions is positive, the successes are well hidden.'' === 2.12. G. W. Bush: "Why do they hate us?" === On 2001-09-20, nine days after the {{w|September 11 attacks}}, US President {{w|George W. Bush}} asked, "Why do they hate us?"<ref name='Why'>{{cite Q |Q61743801 }}</ref> He gave his own answer to this rhetorical question: "They hate [our] democratically elected government. Their leaders are self-appointed. They hate our freedoms: our freedom of religion, our freedom of speech, our freedom to vote and assemble and disagree with each other." We need serious, unclassified research into why people choose one side or the other in this and other conflicts, why some people remain on the sidelines, and why some change their affiliations over time, increasing or decreasing their level of support, deserting or defecting. Such research might identify a large portion of US enemies motivated a desire for the freedoms the US claims to hold so dear and a hatred of US support for governments that deny them those freedoms.<ref>See comments about Thomas Carothers in {{cite Q |Q61754939 }}</ref> And in addition to researching such questions, we need a media system that will disseminate the results, free from the conflicts of interest that encumber the mainstream media virtually everywhere today, as suggested elsewhere in this essay. In fact, US governmental officials knew on September 11, 2001, that the government of Saudi Arabia was involved in the preparations for the September 11 attacks. This is documented in [[w:The 28 Pages#Declassification|"The 28 Pages"]] of material redacted from the December 2002 report of the joint US House and Senate Committee investigating intelligence failures regarding the September 11 attacks, removed on the insistence of US President George W. Bush. Those documents do not say whether President Bush himself knew that when the [[w:United States invasion of Afghanistan|US, the UK, Canada and Australia invaded Afghanistan 2001-10-07]]. However, before the US invaded, the government of Afghanistan offered to turn over Osama bin Laden, but they wanted evidence of bin Laden's complicity in the {{w|September 11 attacks}}. Evidently, the US invaded Afghanistan for other reasons. And the failure of the mainstream media in the US to support the Afghani request for evidence of bin Laden's complicity and their virtually nonexistent coverage of "{{w|The 28 Pages}}" seems to support the assertions elsewhere in this essay. * The rules of evidence in the court of public opinion are whatever will maximize the power of those who control media funding and governance. The future prospects for peace on earth would be enhanced greatly by (a) research into what motivates people in conflict and (b) media that would be more likely to tell the public what they need to know to understand their opposition in conflict. === 2.13. Obama's approach to counterterrorism === On December 6, 2016, Obama gave his last foreign policy address as President. He had seven major points: # Keep the threat in perspective. # Don't overreach. # Respect rule of law. # Fight terrorists in a way that does not create more. # Insist on transparency and accountability not just in times of peace but, more importantly, in times of conflict. # Emphasize diplomacy. # Uphold the civil liberties that define us. These points seem to summarize the thrust of this essay up to this point. The recent spike in terrorist deaths in Figures 1 and 2 and in Appendix 1 all seem to be products of violations of these principles.<ref>{{Citation | last = Obama | first = Barack | date = 2016-12-06 | title = Remarks by the President on the Administration's Approach to Counterterrorism | publisher = Obama White House | url = https://obamawhitehouse.archives.gov/the-press-office/2016/12/06/remarks-president-administrations-approach-counterterrorism | accessdate = 2017-03-14}}</ref> === 2.14. Eli Lake on "How Trump could finally win the war on terror" === Three days after Obama's December 6 speech, Eli Lake acknowledge that what Obama said makes good sense for the most part. Lake continued by saying that the failure of G. W. Bush and Obama to win the war on terror is due to a failure to acknowledge that jihadists "seek conquest." They don't hate us because of our freedom, as President George W. Bush claimed. "Their objective is not to provoke an overreaction where America ceases to be a democracy. ... These groups want to force the non-Muslim world ... to submit to Islamic rule."<ref>{{Citation | last = Lake | first = Eli | date = 2016-12-09 | title = Commentary: How Trump could finally win the war on terror | newspaper = Chicago Tribune | url = http://www.chicagotribune.com/news/opinion/commentary/ct-trump-terrorism-islamic-state-20161209-story.html | accessdate = 2017-03-14}}</ref> The analysis here does not contradict Lake's claim regarding the goal of some of the Jihadists' leadership. However, it's not clear why that's even relevant. If you, dear reader, know of any evidence why it should make a difference, please post it here. We next consider how the structure of the media contribute to the escalation and perpetuation of conflict, and how alternative systems for funding and governing media might improve the prospects for conflict resolution and world peace. == 3. Media == This section first discusses research on human psychology and how that interacts with the political economy of the media. This suggests that winning the War on Terror might require greater democratic control of the media. Alternative systems for media funding and governance are then reviewed. === 3.1. Human psychology and the media === This section discusses two important observations by [[w:Daniel Kahneman|Daniel Kahneman]], mentioned above: # Humans tend to be excessively overconfident in the value of what they think they know. # People pay too much attention to things that are novel and poignant and too little attention to things that are more important and more common. ==== 3.1.1. Overconfidence ==== Most humans tend to remember news and information that is consistent with their preconceptions and forget or don’t even see conflicting evidence.<ref name=Kahneman2011>Kahneman (2011)</ref> To counteract this Kahneman pushes us to be more humble about what we think we know: We should look for credible information sources that conflict with our preconceptions.<ref>One of Kahneman's (2011) major themes is that nearly everyone tends to overestimate the value of current knowledge and underestimate how far wrong their preconceptions likely are. This approach works fine for most situations -- and helps us avoid wasting time searching for better answers to unimportant questions. However, it tends to produce poor assessments of some of the most important situations we encounter. We could often arrive at much better decisions if we pushed ourselves to identify really important issues and look harder for contrary information for those cases.</ref> If we do, we may find with the famous [[w:Pogo (comic strip)|comic strip character Pogo]] that, “We have met the enemy, and he is us.” * ''How easy it is to make people believe a lie, and [how] hard it is to undo that work again! ''<ref>{{Citation | last = Twain | first = Mark | editor-last = Griffin | editor-first = Benjamin | editor2-last = Smith | editor2-first = Harriet Elinor | year = 2013 | title = Autobiography of Mark Twain, Vol. 2 | page = 302 | url = https://en.wikiquote.org/wiki/Mark_Twain | accessdate = 2017-02-17}}</ref> * ''I’m hurt less by things I don’t know than things I do know that ain’t so.''<ref>Richard Salmon, personal communication, circa 1973.</ref> ==== 3.1.2. Novel and poignant ==== This essay began with a discussion of the minuscule nature of terrorism compared to other causes of death. This raises the following question: * ''Why do we place so much more emphasis on terrorism than on other issues that are much more common causes of death?'' [[w:Daniel Kahneman|Kahneman]] says that people pay more attention to things that are novel and poignant, like terrorism incidents. As a result, media organizations look for that kind of material. This becomes a problem when reports lack adequate context, thereby leading the public to believe that problems highlighted are far worse than they really are. For example, "[[stroke]]s cause almost twice as many deaths as all accidents combined, but 80% of respondents [in a survey] judged accidental death to be more likely. ... [This is because media] coverage is itself biased toward novelty and poignancy. The media do not just shape what the public is interested in, but also are shaped by it."<ref name=Kahneman2011/> ==== 3.1.3. Availability cascade vs. media feeding frenzy ==== This discussion of novelty and poignancy helps explain the phenomenon of a self-reinforcing cycle of high public interest in a certain topic that invites the media to produce a series of stories about that issue. The resulting cycle is sometimes called an [[w:Availability cascade|availability cascade]].<ref>Kahneman (2011)</ref> However, an [[w:Availability cascade|availability cascade]] rarely occurs when it might displease someone with substantive control over the media, discussed in the next section on the “political economy of the media.” The term "[[w:Media feeding frenzy|media feeding frenzy]]" is almost synonymous with “availability cascade,” but "media feeding frenzy" may suggest more of a role for flinching, shading or even suppressing a story or limiting its run to minimize displeasure to media owners, managers, or funders.<ref>See the discussion of the 5-fold increase in the incarceration rate in the US over the past 40 years accompanying Figure 9 in this essay.</ref> === 3.2. The political economy of the media === * ''Media organizations sell changes in the behaviors of their audience to their funders.'' A media organization without an audience won’t have funding for long. If the audience fails to change behaviors in ways that please the funders -- or, worse, if they change behaviors in ways that threaten the funders -- the money will go elsewhere. A media organization must please both its audience and its funders. With commercial media, story coverage is sometimes "tailored to maximize its appeal to key demographic groups: those who are most likely to buy the advertised product. When target audiences place low value on hard news, media outlets have an incentive to reduce current affairs and political reporting in favor of entertainment and sports coverage."<ref>{{Citation | last = Ognyanova | first = Katherine | editor-last = Lloyd | editor-first = Mark | editor2-last = Friedland | editor2-first = Lewis A. | year = 2016 | title = The Communications Crisis in America, And How to Fix It | chapter = Researching Community Information Needs | publisher = Palgrave Macmillan | isbn = 1-349-95030-0}}</ref> Tailoring news to sell products is serious but minor relative to suppressing coverage of favors that major advertisers get from government, which is the primary activity of legislators, at least in the US Congress, according to [[w:Lawrence Lessig|Lawrence Lessig]]'s [[w:Republic, Lost|''Republic, Lost'']]. It is also minor when compared to suppressing information regarding likely US actions against democracy in foreign countries or stampeding the US into war on questionable grounds, discussed elsewhere in this essay. Moreover, the [[w:National Association of Broadcasters|National Association of Broadcasters]] vigorously opposed FCC support for research into the critical information needs of different communities in the US.<ref>Lloyd and Friedland (2017, p. 14)</ref> Why would they do that? Are they afraid that the research might suggest that the public has information needs that are not being met and might lead to efforts to fix that problem? ==== 3.2.1. Media coverage of conflict ==== As conflicts escalate, at some point media organizations become party to the conflict, amplifying the propaganda that drives people apart and reduces the chances for negotiated settlements and resolution using law enforcement. This is more subtle and more destructive than the standard dictum that, "Truth is the first casualty of war."<ref>The first use of that phrase in this form appears to have been by [[w:Philip Snowden, 1st Viscount Snowden|Philip Snowden, 1st Viscount Snowden]].</ref><ref>{{Citation | last = Knightley | first = Phillip | year = 2004 | origyear = 1975 | title = 'The First Casualty: The War Correspondent as Hero and Myth-Maker from the Crimea to Iraq | edition = 3rd | publisher = Johns Hopkins U. Pr. | isbn = 0801880300}}</ref> We consider three examples: The [[w:American Civil War|U.S. Civil War]], the [[w:Cold War|Cold War]], [[w:Israel|Israel]] today, and the US since the September 11 attacks. By the time of the [[w:American Civil War|U.S. Civil War]], many moderately sized cities in the US had at least two newspapers, often with very different political perspectives. As the South began to succeed, some papers in the North recommended that the South should be allowed to leave. “The government, however, was not willing to allow 'sedition' to masquerade (in its opinion) as 'freedom of the press.'” Several newspapers were closed by government action. After the massive Union defeat at the [[w:First Battle of Bull Run|First Battle of Bull Run]], angry mobs in the North destroyed substantial property used by “successionist” newspapers. Those still in publication quickly came to support the war to avoid mob action and government repression and to retain their audiences.<ref>Harris (1999, esp. ch. 8, pp. 97-107)</ref> Given what is known today about the evolution of conflict (including the research on the long-term impact of alternative approaches to conflict discussed above), it seems likely that nearly everyone would be better off today if the North had let the South succeed. This is consistent with the findings of Chenoweth and Stephan, discussed above. It is also supported by the fact that the South had a substantial population of free whites, many of whom did not like having to compete with slave labor and might have supported slaves fleeing to the Union without Union troops on Confederate soil.<ref>{{Citation | last = Gillespie | first = Michele | year = 2004 | title = Free labor in an unfree world: White artisans in slaveholding Georgia, 1789-1860 | publisher = U. of Georgia Pr. | isbn = 0820326704}}</ref> The violence of the Civil War built (or at least strengthened) bonds between poor Southern whites and the Southern aristocracy that contribute to the problems with racism that plague the US to this day.<ref>This was written 2017-03-05. The violence of the [[w:American Revolution|American Revolution]] and the role of race in that conflict also contributed to the current racism in the US in the same way, though to a lesser extent.</ref> Many of the questionable actions of the [[w:Cold War|Cold War]] can be explained as heavily influenced by mainstream media support for US international business interest. For example, if major oil companies in the US did not advertise, might more questions have been raised about the destruction of democracy in Syria in 1949 and Iran in 1953, at the behest of international petroleum interests? If United Fruit did not advertise, might more questions have been raised about the 1954 coup in Guatemala? The tie is less specific regarding the cancellation of elections in Cuba in 1952 or Vietnam in 1956, but if the mainstream commercial media in the US had raised too many questions about those events, they likely would have offended executives in many multinational corporations. If all of Eisenhower's contacts "knowledgeable in Indochinese affairs" agreed that Ho Chi Minh would likely have gotten 80 percent of the popular vote in 1954, the mainstream commercial media in the US should have been aware of that; the fact that substantive questions were not raised about the cancellation of elections there in 1956 strongly suggests editorial decisions to suppress that coverage. Similar claims can be made about the destruction of democracy in Brazil in 1954 and Chile in 1973. This may not qualify as proof beyond a reasonable doubt, [[w:United States constitutional criminal procedure|required for a criminal conviction]]. However, it would seem to meet the standard of a [[w:Burden of proof (law)#Preponderance of the evidence|"preponderance of the evidence']], required in a civil trial. The evolution of the media in Israel followed roughly the development of the US media, according to Israeli scholar Yorim Peri:<ref>Peri (2012)</ref> At the creation of the state of Israel, newspapers tended to be associated with political parties. In the late 1960s and early 1970s, they became more commercial and professional.<ref>Peri (2012) noted that many of the journalists joining the profession starting especially in the late 1960s had been trained in the US and followed US journalistic practices to a large extent.</ref> However, the range of acceptable political discourse has always been constrained by concerns about national security. “When the security situation is tense, pressure for consensus and uniformity tends to increase. At such times, the audience is less willing to hear different opinions. Therefore the media cannot completely fulfill its function as the arena where issues are hashed out or hammered out before being brought to the political system for a policy decision. An ongoing state of emergency undermines the readiness for pluralism, tolerance and liberalism and amplifies public expectations that the media will exhibit more ‘social responsibility’ -- be less critical, more committed to the collective endeavor, and more supportive of the national leadership. Above all, a state of emergency legitimizes the state’s deeper and deeper intrusion into the private sphere and into civil society.” Peri further claimed that the Israeli media could have warned of the impending attack prior to the initiation of the 1973 [[w:Yom Kippur War|Yom Kippur War]]. After the war “Israeli journalists conceded that their total dependence and trust in the government and uncritical adoration of the top brass were responsible for media not issuing a warning that war was about to break out.”<ref>Peri (2012, pp. 22-23)</ref> Peri continued, “In the 1990s -- during the peace process, which made it appear that the era of warfare was at an end and that Israel was becoming a postwar society -- the professional autonomy of the media grew, and journalists adopted a more critical stance. However, the failure of the peace talks in the summer of 2000 and the outbreak of the second Intifada with its suicide attacks aimed at the heart of the civilian population led to a serious retreat ... . State agencies and the public even more so again exerted pressure for media reorientation, demanding that the media restrain its criticism and circle the wagons."<ref>Peri (2012, p. 23)</ref> Peri’s claims are consistent with an earlier paper on “Palestinian civil resistance against Israeli military occupation,” which claimed that the ''nonviolence'' of the [[w:First Intifada|First Intifada]] made a greater contribution to the ability of Palestinians to live and prosper in that region than anything Palestinians have done before or since.<ref>{{Citation | last = King | first = Mary Elizabeth | editor-last = Stephan | editor-first = Maria J. | year = 2009 |title = Civilian Jihad: Nonviolent struggle, democratization, and governance in the Middle East | publisher = Palgrave MacMillan | pages = 131-155 | chapter = chapter 10. Palestinian civil resistance against Israeli military occupation | isbn = 978-0-230-62141-1}}</ref><ref>See also Chenoweth and Stephan (2011, pp. 119-120, 138, 145)</ref> [[File:Shootings as a percent of all incidents during the First Intifada.svg|thumb|Figure 8. Shootings as a percent of all incidents during the First Intifada.<ref>Chenoweth and Stephan (2011, p. 120)</ref>]] The First Intifada began spontaneously after four Palestinians were killed and eight seriously injured after an Israeli military vehicle struck a car carrying Palestinian day laborers on December 7, 1987.<ref>Chenoweth and Stephan (2011, p. 123)</ref> This led to 65,661 nonviolent protests and 140 shooting incidents in 1988 and 1989. Overreaction by Israeli troops and settlers over the first 18 months led to the deaths of roughly 650 Palestinians, totally out of proportion to the physical threat.<ref>Chenoweth and Stephan (2011, p. 120, Table 5.1)</ref> Press coverage led to condemnation of this overreaction in Israel and around the world. [[w:Yitzhak Rabin|Yitzhak Rabin]] was elected Prime Minister of Israel in 1992, promising negotiations with Palestinians, defeating the more hawkish [[w:Yitzhak Shamir|Yitzhak Shamir]]. While nearly everyone in occupied Palestine understood they could not win with guns, those advocating nonviolence were unable to prevent everyone under occupation from using firearms, as quantified in Figure 8: Shootings a a proportion of total incidents were only one sixth of a percent in 1988 and rose to four thirds of a percent in 1992; they averaged half a percent from 1988 to 1992. The nonviolent advocates were also unable to keep youth from throwing rocks, which many supporters of Israel did not see as nonviolent. Moreover, Israel was clandestinely arming [[w:Hamas|Hamas]], as a counterweight to both the nonviolence and the [[w:Palestinian Liberation Organization|Palestinian Liberation Organization]] (PLO). And many PLO leaders were still advocating violence. Chenoweth and Stephan classified the First Intifada as a "partial success," because it obtained some concessions including international recognition but failed to shake off the occupation.<ref>Chenoweth and Stephan (2011, p. 145)</ref> Unfortunately, too few Palestinians recognized what they had gained through nonviolence. On September 28, 2000, [[w:Ariel Sharon|Ariel Sharon]] visited the Temple Mount complex, the holiest place in the world to Jews and the third holiest site in Islam, accompanied by an escort of over 1,000 Israeli police officers. This was seen as a deliberate provocation by many and produced a violent response by Palestinians. That violence seemed to help Sharon win the election for Prime Minister the following February 6 with 62 percent of the vote. The research on nonviolence summarized above and elsewhere suggests that if the Palestinian response had been nonviolent, it could have helped bridge rather than deepen the gap between Jews and Palestinians. To what extent might Peri’s comments apply to the US response to the [[w:September 11 attacks|September 11, 2001]]? This includes the suppression of debate in the mainstream commercial media over the official justification for the 2003 US-led invasion of Iraq. It also includes the creation of the [[w:Homeland Security|US Department of Homeland Security]] and the expansion of surveillance activities by agencies like the [[w:National Security Agency|US National Security Agency (NSA)]] without authorization from Congress. This was exposed by [[w:Edward Snowden|Ed Snowden]]<ref> {{Citation | title = Edward Snowden | publisher = Wikipedia | url = https://en.wikipedia.org/wiki/Edward_Snowden | accessdate = 2017-02-17}}</ref> following the apparent perjury of [[w:James R. Clapper|James Clapper]], [[w:Director of National Intelligence|Director of National Intelligence]], before a [[w:United States Senate Select Committee on Intelligence|US Senate Select Committee on Intelligence]].<ref> {{Citation | title = James Clapper | publisher = Wikipedia | url = https://en.wikipedia.org/wiki/James_Clapper | accessdate = 2017-02-17}}</ref> In the three examples of this section, the US Civil War, Israel and the US since September 11, 2001, the media arguably became a party to the conflict. In the first two cases, their audiences seemed to demand it. In the latter two cases, there’s substantial evidence that the general interests of the bottom 99 percent of the people in Israel and the US were ill served by the following: # Intelligence services that either failed to appropriately assess potential threats or suppressed information or fabricated evidence to please superiors. # Excessive willingness of the media to support unquestioningly the policies and pronouncements of those leading the national security apparatus.<ref>It is now known that members of the Saudi royal family and employees of the Saudi embassy and consulates in the US helped the suicide mass murderers of September 11, 2001, get training in the US to help them do what they did on that fateful day. This is documented in [[w:The 28 Pages|"The 28 Pages,"]] which the George W. Bush administration insisted were classified and were therefore not published with the rest of the December 2002 report of the [[w:Joint Inquiry into Intelligence Community Activities before and after the Terrorist Attacks of September 11, 2001|Joint Inquiry into Intelligence Community Activities before and after the Terrorist Attacks of September 11, 2001]] and were largely declassified in July 2016. This documents that the Bush administration knew before it invaded Iraq, and possibly before it invaded Afghanistan, that 9-11 was supported by high-level Saudis, in addition to the information available shortly after 9-11 that 15 of the 19 suicide mass murderers of Sept. 11 were Saudis. So why did the US NOT invade Saudi Arabia and instead invaded Afghanistan and Iraq? And why did the mainstream US media so eagerly support the invasions of Afghanistan and Iraq in 2001 and 2003? And why has the mainstream US media NOT made an issue of the new information in "The 28 Pages" released in July 2016? The thrust of the present article is that several factors contribute to this documented record of media failure, one of which is doubtless the fact the big oil companies advertise and have had great relations with the Saudi royal family dating back to the 1930 -- and the Afghanis had refused to approve the [[w:Turkmenistan–Afghanistan–Pakistan–India Pipeline|construction of a pipeline on their soil, finally begun on December 13th, 2015]].</ref> For more, see the discussion in “Implications,” below. Let’s now turn from audience to funding and management of media organizations. ==== 3.2.2. Media ownership, funding and profitability ==== * ''Media organizations can libel and slander poor people with impunity but must of necessity flinch before disseminating anything that might offend anyone with substantive control over the media.'' The basic economics of journalism has multiple consequences for efficiency: * Stories impacting poor people can be disseminated with little or no fact checking, because their ability to retaliate is minimal. * Stories that might offend anyone with substantive influence over the media require much more fact checking and editing that might otherwise be required and may never appear.<ref name=Focke/> [[File:U.S. incarceration rates 1925 onwards.png|thumb|350px|Figure 9. A graph of the incarceration rate under state and federal jurisdiction per 100,000 population 1925–2008 (omits local jail inmates). The '''male incarceration rate''' (''top line'') is roughly 15 times the '''female rate''' (''bottom line'').]] Evidence of this is seen in the five-fold increase in the [[w:United States incarceration rate|incarceration rate in the US]] between 1975 and 2000, after the incarceration rate had been relatively stable at roughly 0.1 percent for the previous half century; see Figure 9.<ref name=incar>{{Citation | title = United States incarceration rate | publisher = wikipedia | url = https://en.wikipedia.org/wiki/United_States_incarceration_rate | accessdate = 2017-02-26}}</ref> The obvious driver of this was a shift in US politics that began around 1975 to "get tough on crime." This political change was driven by a shift in editorial policies of mainstream commercial broadcasting to focus on the police blotter.<ref>e.g., Sacco (2005) and others cited in [[w:United States incarceration rate|incarceration rate in the US]].</ref> The broadcasters found they could reduce expenditures for investigative journalism, thereby reducing the risks of offending major advertisers,<ref name=Focke/> while still retaining (and perhaps increasing) their audience. * [[w:Fascination with death|''If it bleeds, it leads.'']]<ref>This is consistent with the discussion of "availability cascade," as discussed by Kahneman (2011, pp. 142-145) and summarized above.</ref> The public got the impression that crime was out of control, even though no increase in crime was evident in the best available data. Politicians who wanted to "get tough on crime" replaced those who resisted this trend. The laws were changed, and the [[w:United States incarceration rate|incarceration rate in the US]] jumped dramatically, especially among people of color.<ref>{{cite book |last=Alexander |first=Michelle |year=2010 |title=The New Jim Crow: Mass Incarceration in the Age of Colorblindness |publisher=The New Press |location=New York |isbn=978-1-59558-103-7 }}</ref> Beyond this, what happens when police and prosecutors get convictions based on torture, coerced perjury, planted or falsified evidence or suppression of exculpatory evidence? Because stories from the police blotter are so cheap to produce, journalists and media outlets have a conflict of interest in honest reporting on any case involving official misconduct unless it becomes so big the media would lose audience for failing to report it.<ref name=incar/> This provides an opportunity for corrupt police, prosecutors and judges, who believe they get promoted on convictions. They get credit for fighting crime without actually impacting the crime rate, because the real perpetrators are still free. When fraudulent convictions are obtained disproportionately against [[w:Tom R. Tyler|minorities, increasing portions of minority communities come to distrust the police]]. This in turn makes it more difficult to obtain the cooperation of the community, thereby making policing more difficult.<ref>Tyler and Huo (2002)</ref> The law enforcement budget is safe, primarily because the media continue to report crimes committed by poor people with few, if any, references to the fact that there has been no substantive change in crime to [[w:United States incarceration rate|support the changes in law that have driven up the incarceration rate documented in Figure 9]]. Between 1989 and March 2017 at least 15 major [[w:police misconduct|police scandals]] came to light involving over 1,800 innocent defendants convicted on planted or falsified evidence, forced confessions, coerced perjury, suppression of exculpatory evidence, inadequate defense, and other forms of official misconduct by police, prosecutors and judges -- who evidently believe that they get promoted based on convictions.<ref>The 2016 annual report of the [[w:National Registry of Exonerations|National Registry of Exonerations]] reported, "1,994 known exonerations in the United States since 1989 (as of February 26, 2017)." These 1,994 cases do not include over 1,800 defendants cleared in 15 large-scale [[w:police misconduct|police scandals]]. {{Citation | date = March 7, 2017 | title = Exonerations in 2016 | publisher = National Registry of Exonerations, Newkirk Center for Science and Society, U. CA, Irvine | url = http://www.law.umich.edu/special/exoneration/Documents/Exonerations_in_2016.pdf | accessdate = 2017-03-17}} and {{Citation | last = Gross | first = Samuel R. | last2 = Possley | first2 = Maurice | last3 = Stephens | first3 = Klara | date = March 7, 2017 | title = Race and wrongful convictions in the United States | work = report | publisher = National Registry of Exonerations, Newkirk Center for Science and Society, U. of CA Irvine | url = http://www.law.umich.edu/special/exoneration/Documents/Race_and_Wrongful_Convictions.pdf | accessdate = 2017-03-17}}</ref> It would be interesting to study how this might be different with citizen-directed subsidies for media, as discussed below. If the research summarized in this section is accurate and balanced, then citizen-directed subsidies for media might provide * More coverage of crimes committed by major advertisers and earlier exposure of official misconduct by police, prosecutors and judges, and * Fewer people sentenced to death or long terms in prison for crimes they did not commit.<ref name=incar/> Other examples of how news can be distorted by powerful people were described by [[w:Charles Lewis (journalist)|Charles Lewis]] in his book ''935 Lies.''<ref>Lewis (2014)</ref> He left the [[w:CBS News|CBS news]] program [[w:60 Minutes|''60 Minutes'']] in 1989 primarily over two concerns: * Frustration with the meddling of a CBS executive in stories of great importance to the nation, and * The fact that CBS was firing senior investigative journalists at that time.<ref>Lewis (2014, esp. pp. 132-135, 196-198)</ref> One of his examples was a discussion of “Tobacco on Trial”.<ref>{{Citation | date = January 3, 1988 | title = Tobacco on Trial | series = 60 Minutes | publisher = CBS News | url = http://www.cbsnews.com/videos/tobacco-on-trial/ | accessdate = 2017-02-22}}</ref> This story was of particular concern to [[w:Lawrence Tisch|Lawrence Tisch]], President and Chief Executive Officer (CEO) of CBS at the time. Tisch was also a co-founder and major stockholder in Loews, which owned Lorillard Tobacco, a party to a lawsuit discussed in “Tobacco on Trial.” *''Journalism is spreading what someone does not want you to know; the rest is propaganda.''<ref>[[w:Horacio Verbitsky|Horacio Verbitsky]]</ref> This episode of ''60 Minutes'' was one small battle pitting honest journalism against the survival and profitability of the US tobacco industry. A few years later, in January 1994, a former R. J. Reynolds employee with a doctorate in engineering began talking secretly to the Food and Drug Administration and to journalists. She exposed how the tobacco industry manipulated nicotine levels to maximize addiction and company profitability while also “quietly nudging US Department of Commerce and US trade representatives to spend millions of taxpayer dollars to pry open foreign markets to American cigarettes”. After some of this aired on [[w:ABC News|ABC’s]] [[w:Day One (TV news series)|''Day One'']], [[w:Philip Morris|Philip Morris]] filed a $10 billion libel lawsuit against ABC and the show’s lead producers for what they claimed was “false and defamatory” reporting that had been produced “knowingly, recklessly, and with malice.” ABC had already invested half a million dollars in an expanded investigation of this, which was ultimately canceled to end the litigation. “Philip Morris had shown that ‘for a paltry $10 million or $20 million in legal fees … you can effectively silence the criticism,’” Lewis wrote.<ref>Lewis (2014, esp. pp. 136-139)</ref> The decision to cancel that show was a sensible business decision on the part of ABC: They had much less at stake than Philip Morris, whose entire future was threatened. It was highly unlikely that ABC could ever gain an increase in audience sufficient to cover their legal costs in this [[w:Strategic lawsuit against public participation|Strategic lawsuit against public participation (SLAPP)]]. Meanwhile, [[w:Philip Morris International|Philip Morris]] also got what they wanted in international trade agreements. They’ve used these trade agreements to sue the governments of Uruguay, Australia, and Norway for lost profits due to labeling requirements in those countries that have led to reductions in tobacco consumption (and improvements in public health). The more stringent tobacco labeling requirements in Uruguay have improved public health there, but the legal fees are a major drain on the government's budget. Fortunately, former New York Mayor Bloomberg and the Bill and Melinda Gates Foundation launched a multi-million dollar fund to help smaller countries (including Uruguay) fight legal battles with tobacco companies. Bloomberg said, "We are in this to help countries that can't afford to defend themselves against an industry which will try to kill a billion people this century,"<ref>{{Citation | last = Davies | first = Wyre | date = 7 April 2015 | title = Michael Bloomberg fights big tobacco in Uruguay | publisher = BBC News | url = http://www.bbc.com/news/world-latin-america-32199250 | accessdate = 2017-03-17}}</ref> * ''With more citizen direction in the selection of news, would the laws have been written to allow Philip Morris to file suit in cases like this?'' What does this discussion of incarcerations and tobacco say about how the Middle East might be different without the impact of big oil or other major international businesses with major advertising budgets? Would the United States have supported the Saudi royal family since the 1930s if major US advertisers did not believe they benefitted from maintaining the power of the House of Saud?<ref>[[w:House of Bush, House of Saud|Without a business relationship dating back over 30 years between the Bush family and the House of Saud]], would the George W. Bush administration have turned a blind eye to Saudi complicity in the September 11 attacks and diverted attention instead to Afghanistan and Iraq, even though neither seemed to have been complicit in the event?</ref> ==== 3.2.3. Media and politics ==== The mainstream media interacts with politics as follows: * ''The mainstream media create the stage upon which politicians read their lines.''<ref>For example, [[w:David Frum|David Frum]], former speechwriter for [[w:George W. Bush|George W. Bush]], has also said, "Republicans originally thought that Fox worked for us and now we're discovering we work for Fox." {{Cite news |publisher=ABC |url=http://blogs.abcnews.com/nightlinedailyline/2010/03/david-frum-on-gop-now-we-work-for-fox.html |date=March 23, 2010 |title=David Frum on GOP: Now We Work for Fox |work=Nightline}} See also the Wikipedia article on "[[w:Fox News controversies]]".</ref> By selective coverage, the mainstream media can paint the black white and the white black. * ''The mainstream media [[w:Overton window|define the range of acceptable political discourse.]]'' [[w:Campaign finance in the United States#Impact of finance on the results|In 93 percent of the 1,349 races in the US House and Senate in 2012, 2014, and 2016, the candidate with the most financial support won]].<ref>This seems more like [[w:Plutocracy|plutocracy]] than democracy.</ref><ref name="crp2016">{{cite web | last1=Balcerzak | first1=Ashley | title=Where the money came from, not how much, mattered in the presidential race | url=https://www.opensecrets.org/news/2016/11/where-the-money-came-from-not-how-much-mattered-in-the-presidential-race/Balcerzak | website=OpenSecrets.org | publisher=Center for Responsive Politics | accessdate=2017-02-21 | date=November 9, 2016 }}</ref> This disturbing measure of the outsized impact of funding on elections is a product of the interaction between the business model of the media and the fact that we humans too often make decisions based on what comes readily to mind -- and too seldom check our facts, as outlined in the discussion above of Kahneman's research. This is supported by the virtual elimination of investigative journalism from US television by the early 2000s, except for a few popular shows like [[w:60 Minutes|''60 Minutes.'']]<ref><!-- McChesney (2004) The Problem of the Media: U.S. Communication Politics in the 21st Century -->{{cite Q|Q7758439|page=81}}.</ref> Investigative journalism is expensive and risky, as noted in the previous section on “Media ownership, funding and profitability”. Fact checking during political campaigns could make it easier for politicians to get elected with less advertising. That’s a losing business from at least two perspectives: # Politicians and their big money supporters, whose questionable claims were exposed, would be offended by being challenged. # Voters could make more intelligent decisions in the voting booth with less advertising purchased by candidates. Most journalist working for the mainstream broadcasters in the US today have little time to check facts, and are largely encouraged to let people state their positions without question. An exception is [[w:Democracy Now!|''Democracy Now!'']], where hosts like [[w:Amy Goodman|Amy Goodman]] frequently ask guests for their response to what their opposition says. This lack of fact checking has contributed to the current [[w:post-truth politics|post-truth era]] in the US, where political discourse is increasingly driven by [[w:fake news|fake news]] circulating in part on social media. By some accounts, the success of the [[w:Brexit|Brexit referendum]] in the UK and the Trump candidacy in the 2016 US presidential election were build in part on highly successful placement of claims in social media selected to be credible to a specific audience based on data mining of people’s online activities. A leader in this field was for a time [[w:Cambridge Analytica|Cambridge Analytica]], whose Chief Executive, Alexander Nix, said: * "Today in the United States we have somewhere close to four or five thousand data points on every individual. ... So we model the personality of every adult across the United States, some 230 million people."<ref name="20161021sky">{{citation |url=http://news.sky.com/story/behind-the-scenes-at-donald-trumps-uk-digital-war-room-10626155 |title=Behind the scenes at Donald Trump's UK digital war room |last1=Cheshire |first1=Tom |date=21 October 2016 |publisher = [[w:Sky News|Sky News]] |archive-url=https://web.archive.org/web/20161021180327/http://news.sky.com/story/behind-the-scenes-at-donald-trumps-uk-digital-war-room-10626155 |archive-date=21 October 2016}}</ref> On May 1, 2018, Cambridge Analytica officially ceased operations. In doing so, it maintained its innocence, claiming it "has been vilified for activities that are not only legal, but also widely accepted as a standard component of online advertising in both the political and commercial arenas."<ref>{{Cite news |url=https://www.engadget.com/2018/05/02/cambridge-analytica-is-shutting-down-following-facebook-scandal/ |title=Cambridge Analytica is shutting down following Facebook scandal |last=Lumb |first=David |date=2 May 2018 |work=[[Engadget]] |access-date=2 May 2018 }}</ref><ref>{{cite web |title=Cambridge Analytica and Scl Elections Commence Insolvency Proceedings and Release Results of Independent Investigation into Recent Allegations |url=https://ca-commercial.com/news/cambridge-analytica-and-scl-elections-commence-insolvency-proceedings-and-release-results-3 |website=CA Commercial |publisher=Cambridge Analytica |accessdate=2 May 2018 |language=en |date=2 May 2018 }}</ref> There are, as Cambridge Analytica claimed, other organizations (possibly including "{{w|cyberwarfare}}" arms of security services of different nation states) doing similar work, contributing to the Balkanization and exploitation of the international body politic. It is unclear how different Cambridge Analytica's activities differed from those of such other organizations that have so far not been similarly "vilified" and whether the demise of Cambridge Analytical will materially reduce the level of Balkanization created by these types of activities. Before leaving this discussion, it may be worth suggesting that "conservatism" as defined by the US corporate elite seems to have created the current environment of fact-free news and [[w:Post-truth politics|post-truth politics]]. The creation and maintenance of this environment seems to require denigrating fact checking. Three groups of people are generally more careful about checking their facts than the public at large: * Investigative journalists, * University professors, and * [[w:Wikipedia:Wikipedians|Wikipedians]]. All three have been under attack. The virtual elimination of investigative journalism from mainstream broadcasting in the US was discussed above. Beyond this, there have been numerous claims at least since the 1980s that the media have a liberal bias.<ref>For a discussion of this, see the Wikipedia article on [[w:Media bias in the United States|"media bias in the United States"]].</ref> Accusations of a [[w:Liberal bias in academia|liberal bias in academia]] date back at least to [[w: McCarthyism|Senator Joe McCarthy's]] infamous "second red scare," 1947-1956, when McCarthy and his followers made numerous "accusations of subversion or treason without proper regard for evidence." The Wikipedia article on "[[w:Liberal bias in academia|Liberal bias in academia]]" cites research by different people, with known conservatives and Libertarians working hard to document a perceived liberal bias, which other researchers failed to confirm. Liberal or conservative, most faculty members at major universities owe their positions to publications in refereed academic journals. Manuscripts submitted to serious academic journals must cite credible sources and otherwise provide solid documentation for what they say. [[w:Criticism of Wikipedia|Some conservatives have claimed that Wikipedia has a liberal bias.]]<ref>{{Citation | title = Examples of Bias in Wikipedia | publisher = Conservapedia | url = http://www.conservapedia.com/Examples_of_Bias_in_Wikipedia | accessdate = 2017-03-21}}</ref> In fact almost anyone can change almost anything on Wikipedia -- and almost anyone else can change (or even delete) what others wrote. What stays is generally written from a [[w:Wikipedia:Neutral point of view|neutral point of view]], citing [[w:Wikipedia:Verifiability|credible sources]].<ref>In a few cases, people editing Wikipedia from certain internet protocol (IP) addresses have been blocked, because of repeated attempts to burnish the images of some and attack opponents. See, e.g., [[w:United States Congressional staff edits to Wikipedia|United States Congressional staff edits to Wikipedia]].</ref> ==== 3.2.4. [[Media and corruption]] ==== [[Media and corruption|Econometric research has found that countries with greater press freedom tend to have less corruption.]]<ref>{{Citation | last = Brunetti | first = Aymo | last2 = Weder | first2 = Beatrice | author-link = w:de:Aymo Brunetti | author2-link = w:Beatrice Weder di Mauro | year = 2003 | title = A free press is bad news for corruption | journal = Journal of Public Economics | volume = 87 | publisher = Elsevier | pages = 1801-1824 | url = https://campus.fsu.edu/bbcswebdav/orgs/econ_office_org/Institutions_Reading_List/17._Corruption_and_Economic_Performance/Brunetti,_A._and_B._Weber-_A_Free_Press_is_Bad_News_for_Corruption | accessdate = 2017-06-24}}</ref> Greater political accountability and lower corruption were more likely where newspaper consumption was higher in data from roughly 100 countries and from different states in the US.<ref>{{Citation | last = Adserà | first = Alícia | last2 = Boix | first2 = Carles | author2-link = w:ca:Carles Boix i Serra | last3 = Payne | first3 = Mark | year = 2000 | title = Are You Being Served?: Political Accountability and Quality of Government | work = Working Paper | issue = 438 | publisher = Inter-American Development Bank Research Department | url = http://www.princeton.edu/~cboix/JLEO-paper.pdf | accessdate = 2014-08-17}} and {{Citation | last = Adserà | first = Alícia | last2 = Boix | first2 = Carles | author2-link = w:ca:Carles Boix i Serra | last3 = Payne | first3 = Mark | year = 2003 | title = Are You Being Served? Political Accountability and Quality of Government | journal = Journal of Law, Economics, & Organization | volume = 19 | publisher = Oxford U. Pr. | pages = 445-490 | url = http://www.princeton.edu/~cboix/JLEO-paper.pdf | accessdate = 2014-08-31}}</ref> A "poor fit between newspaper markets and political districts reduces press coverage of politics. ... Congressmen who are less covered by the local press work less for their constituencies: they are less likely to stand witness before congressional hearings ... . Federal spending is lower in areas where there is less press coverage of the local members of congress."<ref>{{Citation | last = Snyder | first = James M. | last2 = Strömberg | first2 = David | author2-link = w:sv:David Strömberg | year = 2008 | title = Press Coverage and Political Accountability | series = NBER Working Paper Series | issue = 13878 | publisher = National Bureau of Economic Research | url = http://www.nber.org/papers/w13878 | accessdate = 2014-08-17}}</ref> This was supported by an analysis of the consequences of the closure of the ''Cincinnati Post'' in 2007. The following year, "fewer candidates ran for municipal office in the Kentucky suburbs most reliant on the ''Post'', incumbents became more likely to win reelection, and voter turnout and campaign spending fell.<ref>{{Citation | last = Schulhofer-Wohl | first = Sam | last2 = Garrido | first2 =Miguel | year = 2009 | title = Do newspapers matter? Short-run and long-run evidence from the closure of the Cincinnati Post | series = NBER Working Paper Series | issue = 14817 | publisher = National Bureau of Economic Research | url = http://www.nber.org/papers/w14817 | accessdate = 2014-08-17}}</ref> An extreme example of media and corruption followed the closure around 1999 of the local newspaper in [[w:Bell, California|Bell, CA]], a city of roughly 35,000 near [[w:Los Angeles|Los Angeles]]. [[w:City of Bell scandal|The city manager, Robert Rizzo, decided, in essence, that the watchdog was dead, and it was time to party.]] He convinced other city leaders to join him. When the problems were documented in 2010, Rizzo's compensation was over $1 million per year, and the city was near bankruptcy. Rizzo was a "[[w:Control fraud|control fraud]]", in the parlance of [[w:William K. Black|Bill Black]], who was the lead litigator involved in sending [[w:Charles Keating|Charles Keating]] to prison in the [[w:Savings and loan crisis|Savings and loan scandal of the late 1980s and early 1990s]]. Black discussed this in his book, ''The Best Way to Rob a Bank is to Own One: How Corporate Executives and Politicians Looted the S&L Industry.''<ref>Black (2005)</ref> A "control fraud" is a leading executive who removes "the checks and balances on fraud within a company such as through the use of selective hiring and firing", especially of auditors. In 2014 [[w:Bill Moyers|Bill Moyers]] noted that, "No banking executives have been criminally prosecuted for their role in causing the biggest financial disaster since the Great Depression." Bill Black replied that, "Obama wouldn’t have been president but for the financial contribution of bankers.”<ref>{{Citation | last = Black | first = William K. | editor-last = Moyers | editor-first = Bill | date = October 3, 2014 | title = Too big to fail | publisher = Moyers & Company | url = http://billmoyers.com/episode/too-big-to-jail/ | accessdate = 2017-03-22}}</ref> One major conclusion of the present analysis is that campaign contributions like these would not likely have the impact they do in the US today if the public had more control over media content. From this perspective, it was easier for the mainstream media to expose Charles Keating than the banking executives who manufactured the [[w:Financial crisis of 2007–2008|Financial crisis of 2007–2008]] and manipulated the political process to benefit from it, because the advertising budgets of the control frauds of the Savings and loan industry were tiny relative to those of the current international bankers. [[File:Knowledge v. public media.png|thumb|Figure 10. Percent correct answers in surveys of knowledge of domestic and international politics vs. per capita subsidies for public media in the Denmark (DK), Finland (FI), the United Kingdom (UK) and the United States (US). Source: The "politicalKnowledge" data set in the "Ecdat" package available on the Comprehensive R Archive Network, based on research cited by McChesney and Nichols (2010).]] Even ignoring extreme cases like Bell, CA, the dumbing down of US commercial broadcasting was documented in research comparing the public's knowledge of current affairs between the US, the [[w:United Kingdom|United Kingdom (UK)]], [[w:Denmark|Denmark]] and [[w:Finland|Finland]]; see the accompanying Figure 10: College graduates in the US answered correctly roughly 70 percent of questions about political issues as people with the equivalent of high school in Denmark and Finland, while high school graduates in the US could only answer roughly 30 percent of the same questions. The primary difference was funding for mass media, according to McChesney and Nichols (2010): This was $1.35 per person in the US in 2007 vs. the equivalent of $101 in Denmark and Finland. The UK was in between: They spent the equivalent of $80 per person, and Brits with roughly 12th grade educations correctly answered almost 60 percent of the questions on average. The $101 per person per year invested in public media in Denmark and Finland seems comparable to the 0.2 percent of GDP that the US spent in citizen-directed subsidies under the [[w:Postal Service Act|US Postal Service Act of 1792]], discussed below in the section on "Media and nation building." On December 7, 2015, and February 29, 2016, [[w:Leslie Moonves|Les Moonves]], President and CEO of [[w:CBS Corporation|CBS]] bragged to investor conferences that the Trump campaign "may not be good for America, but it's damn good for CBS. ... The money's rolling in, this is fun."<ref>In 2012 he similarly said that "Super PACs may be bad for America, but they’re very good for CBS." {{Citation | last = Fang | first = Lee | date = February 29, 2016 | title = CBS CEO: “For Us, Economically, Donald’s Place in This Election Is a Good Thing” | journal = The Intercept | publisher = First Look Media | url = https://theintercept.com/2016/02/29/cbs-donald-trump/ | accessdate = 2017-03-22}}</ref> This was, in essence, an admission that CBS was sacrificing the best interests of the nation and humanity to favor the short term pecuniary interests of CBS. It seems virtually certain that all the other mainstream broadcasters in the US and Britain were doing essentially the same. The rules of business in the US almost certainly contributed not only to the Trump victory but to the US-led invasion of Iraq in 2003, the long-standing US support for the Saudi royal family, and the US role in destroying democracy in foreign countries, as discussed above in the section on "US foreign interventions in opposition to democracy." The Saudi connection, in turn, contributed to the [[w:September 11 attacks|September 11 attacks]] and the creation of ISIL, all discussed elsewhere in this essay. In particular, the role of the mainstream media in the US and the UK in US-led invasion of Iraq in 2003 might seem to qualify as "inciting a riot" under the standard of "[[w:Shouting fire in a crowded theater|falsely shouting fire in a crowded theater]]." Moonves and others in similar executive positions in the other mainstream broadcasters are safe, because the magnitude of the crime is too large for it to be widely understood, let alone prosecuted. In other words, these comments of CBS President Moonves combined with the other evidence summarized in this essay suggests that the current structure of the mainstream media in the US and Britain provide real and present threats to international peace and security.<ref>Similar things could be said about media in other countries. See, e.g., Peri (2012) for a similar analysis of the Israeli media.</ref> ==== 3.2.5. International business ownership of media ==== In France, the US and elsewhere, international business interests have ties to how the media are funded. One of the more obvious examples is [[w:Le Figaro|''Le Figaro'']], the oldest national daily newspaper in France and one of the most widely respected newspapers in the world. It is owned by the [[w:Dassault Group|Dassault Group]], one of the world’s leading arms merchants.<ref>Cagé (2016)</ref> ''Le Figaro'' therefore has a [[w:conflict of interest|conflict of interest]] in honestly reporting on anything that might question the advisability of any arms deal.<ref name="Feinstein2011">{{cite book|author=Andrew Feinstein |title=The Shadow World: Inside the Global Arms Trade|url=https://books.google.com/books?id=u06m3epox7wC|year=2011|publisher=Hamish Hamilton|isbn=978-0-241-14441-1}}</ref> It has a clear motive to overdramatize the problem of terrorism as long as they can do so in a way that supports further French weapons sales and more use of French overt and covert power to support repressive governments favored by French multinational executives, who advertise in ''Le Figaro''. Similarly, [[w:Westinghouse Electric Corporation|Westinghouse]] owned [[w:CBS Corporation|CBS]] between 1995 and 2000 before selling it to [[w:Viacom|Viacom]]. During that period, CBS and all the other mainstream commercial broadcasters in the US fired nearly all their investigative journalists, retaining only enough for popular shows like [[w:60 Minutes|''60 Minutes'']].<ref>{{Citation | last = McChesney | first = Robert W. | year = 2004 | title = The Problem of the Media | publisher = Monthly Review Press | page = 81 | isbn =1-58367-105-6}}</ref> Why? Because [[Media and corruption|investigative journalism threatens to expose questionable activities of people with substantive control over the media.]] * ''Investigative journalism is essential for democracy and a threat to people with substantial control over the media.'' As in France, the mainstream media in the US have a clear motive to overdramatize the problem of terrorism as long as they can do so in a way that supports further US sales of weapons, especially to [[w:List of authoritarian regimes supported by the United States|repressive governments favored by US multinational executives]]. ==== 3.2.6. How media personalities are selected ==== It seems reasonable to assume that most journalist believe they are honest, fair and balanced in what they report. The situation is similar to [[w:Lawrence Lessig|Lawrence Lessig]]’s description of [[w:Republic, Lost|the US Congress]]: Very few people in the US House and Senate demand and receive bribes. However, all are elected in a system that requires them to spend huge amounts of time asking people with lots of money for campaign contributions -- and then listening to their lobbyists to the exclusion of people who can not afford to buy such access. Candidates who are perceived to be unfriendly to the major campaign contributors (including especially those with control over major advertising budgets) are unlikely to get elected, as noted above. Similarly, media personalities are selected and fired depending on their ability to attract an audience while largely supporting the official line. [[w:Phil Donahue|Phil Donahue]] was fired from MSNBC in the runup to the 2003 US-led invasion of Iraq for trying to provide airtime to people who challenged the official rationale used to justify the invasion. He was dismissed in spite of having high ratings. [[w:Hutton Inquiry|BBC journalist Andrew Gilligan, chairman Gavyn Davies and director-general Greg Dyke resigned under fire]] for claiming that the British government had “sexed up” a report claiming Saddam Hussein had [[w:weapon of mass destruction|weapons of mass destruction (WMDs)]].<ref>[[w:Hutton Inquiry#Aftermath of publication|Davies resigned]] 2004-01-28, the day the [[w:Hutton Inquiry|Hutton Inquiry]] was published. Dyke resigned two days later, as did Gilligan. The Hutton Inquiry was a judicial inquiry in the UK chaired by Lord Hutton that opened 2003-08-01 to investigate the death 2003-07-18 of Dr David Kelly, a biological warfare expert and former UN weapons inspector in Iraq who had been named as the source for reports aired 2003-05-29 by Andrew Gilligan that the Blair government had "sexed up" the intelligence reports to justify British participation in the US-led invasion of Iraq 2003-03-20. See also <!-- Gilligan statement in full -->{{cite Q|Q111352244}}. </ref> The official [[w:Hutton Inquiry|Hutton Inquiry]] in 2003-2004 cleared the government of wrongdoing and strongly criticized the BBC. Thirteen years later on 6 July 2016, an official [[w:Iraq Inquiry|Iraq Inquiry]] of the British government acknowledged that the [[w:Blair ministry|Blair government]] had “sexed up” reports. Since the invasion it has become more widely known that Saddam Hussein had gotten chemical and biological warfare technology from the US, Britain and others with the support of Western governments<ref>{{Citation | date = 1990-09-11 | title = The arming of Iraq | periodical = Frontline | publisher = United States Public Broadcasting System (PBS) | url = http://www.pbs.org/wgbh/pages/frontline/shows/longroad/etc/arming.html | accessdate = 2017-02-26}}</ref> and [[w:Riegle Report|had used them against coalition forces]] in the [[w:Gulf War|1990-91 Gulf War]].<ref>{{Citation | title = Riegle Report | publisher = wikipedia | url = https://en.wikipedia.org/wiki/Riegle_Report | accessdate = 2017-02-26}}</ref> It was also reported that the US had invited three Iraqi nuclear scientists to the US in August 1989 for highly classified training on designing nuclear weapons.<ref>{{cite Q|Q106044626}}<!-- Building Saddam Hussein's bomb -->.</ref> [[w:Iraq and weapons of mass destruction|After the 2003 invasion relatively small numbers of weapons of mass destruction]] were found, but they all seemed old and degraded, thus substantiating the [[w:United Nations Special Commission|1999 comment from former UN weapons inspector Scott Ritter that Iraq had no militarily viable biological or chemical weapons on any meaningful scale.]]<ref>This quote came from an interview published on the web whose URL is no longer valid. A similar quote is available in {{cite web | last = Hurd | first = Nathaniel |date= 27 April 2000 |title=Interview with Scot Ritter |publisher= Campaign Against Sanctions on Iraq |url= http://www.fas.org/news/iraq/1999/07/990712-for.htm |accessdate= 2017-03-17}}</ref> Mainstream media executives in the US and Britain surely must have known that the official rationale for the 2003 US-led invasion of Iraq were questionable at best and possibly fraudulent. Apart from the BBC executives who resigned under fire for questioning the official rationale, they actively worked to suppress honest debate. In so doing they effectively stampeded the public in the US, Britain, and other countries in G. W. Bush’s “[[w:Coalition of the willing|Coalition of the willing]]” into supporting the invasion without adequate debate. In retrospect, it’s clear that the justification was at best wrong and likely fraudulent -- and the media executives should have known at the time that more evidence and debate were needed. === 3.3. Media and nation building === Robert McChesney and John Nichols claim the US has had three positive experience with nation building: its own and Germany and Japan after World War II. All three involved substantive subsidies for journalism.<ref>McChesney and Nichols (2010, esp. Appendix II. Ike, MacArthur and the Forging of Free and Independent Press, pp. 241-254)</ref> This section reviews publications discussing a possible relationship between media and nation building in the US, Germany, Japan, Iraq, Afghanistan, Brazil, and Africa. If you know of other evidence relevant to this question, please post a discussion of it here or on the companion "Discuss" page. ==== 3.3.1. United States ==== Under the [[w:Postal Service Act|US Postal Service Act of 1792]] newspapers were delivered up to 100 miles for a penny and beyond that for a penny and a half, when first class postage was between six and 25 cents depending on distance. This subsidy was citizen-directed and did not discriminate on content. The cost was roughly 0.2% of the economy (GDP, Gross Domestic Product), or just over $100 per person per year in today's money, according to McChesney and Nichols (2016).<ref>McChesney and Nichols (2016, p. 167) wrote, “If the United States government subsidized journalism in the second decade of the twenty-first century as a percentage of GDP to the same extent that it did in the first half of the nineteenth century, it would spend in the area of $35 billion annually.” The [[w:United States|US]] population in 2017 has been estimated at 325 million; $35 billion divided by 325 million is $108 per person. The US GDP for 2016 was reported to be $18.6 trillion; $35 billion divided by $18.6 trillion is $1.9 per thousand, which we round to 0.2 percent.</ref> That’s $2 per week for every man, woman and child in the US. ==== 3.3.2. Germany and Japan ==== US President [[w:Harry Truman|Harry Truman]] and his top military leaders including [[w:Dwight D. Eisenhower|Dwight Eisenhower]], and [[w:Douglas MacArthur|Douglas MacArthur]] were all veterans of World War I. They agreed that [[w:The war to end war|"the war to end war" (World War I)]] had not ended war, and they needed to do something different to prevent another war in another 20 years. To support the development of a democratic tradition, they forced the post-fascist governments in Germany and Japan to provide substantial subsidies for journalism. After the official German government surrendered, Eisenhower “called in German reporters and told them he wanted a free press. If he made decisions that they disagreed with, he wanted them to say so in print. The reporters having been under the Nazi regime since 1933, were astonished”.<ref>McChesney and Nichols (2010, Appendix II. Ike, MacArthur and the Forging of Free and Independent Press, pp. 241-254)</ref> Ike felt that the post-fascist media would lose credibility if they failed to criticize the occupiers. In addition, a cantankerous free press is an essential constraint on abuse of power by elites. ==== 3.3.3. Iraq ==== In discussing free press and media subsidies in the US and post-fascist Germany and Japan, McChesney and Nichols asked how the history of Iraq might be different if the US had made similar commitments to free press, “rather than [[w:Paul Bremer|L. Paul Bremer]]’s edicts -- which one Iraqi editor interpreted as, 'In other words, if you’re not with America, you’re with Saddam'".<ref>McChesney and Nichols (2010, p. 242)</ref> Might a free press in post-Saddam Iraq have dramatically limited the growth of the Islamic State? * ''Corruption grows to consume the available money.'' [[Media and corruption|The primary limit on political corruption is a free press]]. * ''[[q:Louis Brandeis|Sunlight is said to be the best of disinfectants]]''.<ref>This is from [[w:Louis Brandeis|Louis Brandeis]] (1914) ‘’[[w:Other People's Money and How Bankers Use It]]’’ (Frederick A. Stokes). Brandeis joined the US Supreme Court in 1916.</ref> Might a more vigorous press environment in both Iraq and the US have reduced the risk of a military disaster like that in Mosul in 2014? Sure. It might still have happened, but it would have been less likely. One symptom of conflicts of interest in both the mainstream media and the US congress is the fact that the [[w:Government Accountability Office investigations of the Department of Defense|Department of Defense (DoD) is the only US government agency to have failed every audit]] since all government agencies were required to pass such audits by the [[w:Chief Financial Officers Act|Chief Financial Officers Act of 1990]].<ref name=’GAO-DoD’>{{Citation | title = Government Accountability Office investigations of the Department of Defense | publisher = wikipedia | url = https://en.wikipedia.org/wiki/Government_Accountability_Office_investigations_of_the_Department_of_Defense | accessdate = 2017-02-27}}</ref><ref>{{cite web |last1=Smithberger |first1=Mandy |title=Will the Pentagon Ever Be Able to Be Audited? The Department of Defense remains the only federal agency that can’t get a clean audit opinion on its Statement of Budgetary Resources |url=http://www.pogo.org/straus/issues/defense-budget/2016/will-the-pentagon-ever-be.html |website=pogo.org |publisher=Project on Government Oversight |accessdate=2017-02-27 |date=March 28, 2016 }}</ref> ==== 3.3.4. Afghanistan ==== [[w:War in Afghanistan (2001–2014)|Might the US have invaded Afghanistan on October 7, 2001]], if the mainstream media had expressed more concern with the rule of law, including the request of the Afghani government for evidence of bin Laden's involvement in the suicide mass murders of September 11, 2001, before extraditing him?<ref name="theguardian.com"><!-- Guardian (2001-10-14) Bush rejects Taliban offer to hand Bin Laden over -->{{cite Q|Q111228506}}</ref> Might the mainstream media in the US and the UK have made more of an issue of this if multinational oil companies had less influence over government and media in both countries? These questions are impossible to answer with certainty, but one suspect that there would be less militarism and terrorism without these [[w:conflict of interest|conflicts of interest]]. How might Afghanistan be different today if the US had a more vigorous watchdog press, forcing US elected officials to require that the Department of Defense pass an audit, and Afghanistan and Iraq protect and subsidize a cantankerous press, as Truman, Eisenhower and MacArthur had done for Germany and Japan after World War II, as discussed above? A tentative answer to these questions appears in the 2015 book ''Thieves of State'' by [[w:Sarah Chayes|Sarah Chayes]]. She claimed that the Afghani government supported by the US has become a [[w:Kleptocracy|kleptocracy]] that collects bribes, not taxes, and reports people who do not pay appropriate bribes as [[w:Taliban|Taliban]] to the US-led forces there. US-led military units then kill the alleged Taliban. Chayes described multiple cases where corrupt Afghani officials were arrested for corruption then released after (she believes) intervention by the US [[w:Central Intelligence Agency|Central Intelligence Agency (CIA)]] to “protect their assets.”<ref>Chayes (2015). She says she went to Afghanistan with National Public Radio and stayed hoping to found a school for entrepreneurship. She found that the corruption made that effectively impossible. She shared her concerns with US military officers there, who recommended that their superiors listen to her. For a time she reported directly to [[w:Michael Mullen|Admiral Mike Mullen]], [[w:Chairman of the Joint Chiefs of Staff|Chairman of the Joint Chiefs of Staff (2007-2011)]]. She claims the CIA blocked her efforts to get that message to US President Obama.</ref> ==== 3.3.5. Brazil ==== "During the colonial period, Portugal made consistent efforts to reduce the economic, political and intellectual autonomy of Brazil," according to de Albuquerque.<ref name=deA>de Albuquerque (2012, p. 79)</ref> This condition improved slightly "when the Portuguese Court moved to Rio de Janiero," during the Napoleonic occupation of Portugal. However, "During the rest of the nineteenth century, most publications were leaflets, pamphlets and short-lived newspapers, dedicated chiefly to political polemics." Newspaper readership is still quite low compared to other countries: 60.6 per 1,000 adult population in 2000 vs. almost 12 times that in Norway (719.7) and 4.3 times that in the US (263.6).<ref name=deA/> [[w:History of Brazil|Brazil's current democracy dates from 1985.]] This Brazilian experience does not prove that better media help with nation building, but it is consistent with the claims of McChesney and Nichols (2010, 2016) discussed above. ==== 3.3.6. Africa ==== Cagé and Rueda studied newspaper readership and democratic engagement as a function of distance from Protestant missions with printing presses in Africa in 1903. Those missions printed educational material and public health information as well as the Christian [[w:Bible|Bible]] and related religious material. Cagé and Rueda found that, "within regions close to missions, proximity to a printing press is associated with higher newspaper readership, trust, education, and political participation" -- over a hundred years after the data on missions they used!<ref>{{Citation | last = Cagé | first = Julia | last2 = Rueda | first2 = Valeria | year = 2016 | title = The Long-Term Effects of the Printing Press in sub-Saharan Africa | journal = American Economic Journal: Applied Economics | volume = 8 | issue = 3 | pages = 69–99 | url = http://pubs.aeaweb.org/doi/pdfplus/10.1257/app.20140379 | accessdate = 2017-03-30}}</ref> Of course, empirical evidence is never complete.<ref>Quote from [[w:W. Edwards Deming|W. Edwards Deming]] from a public seminar in the 1980s.</ref> Still, this evidence is consistent with the general thrust of the other cases discussed in this section. === 3.4. Media funding and governance === Media is a [[w:Public good|public good]]. When elites control the editorial policies, it threatens democracy.<ref>See the discussion of the research by Kahneman (2011) elsewhere in this essay.</ref> We focus here on proposals to democratize funding and governance, focusing especially on the work of McChesney and Nichols (2010, 2021a, b) and Cagé (2016). ===== 3.4.1. Citizen-directed subsidies ===== McChesney and Nichols (2010, esp. ch. 4) discuss several different ways of providing democratically controlled subsidies for media. The [[w:Postal Service Act|US Postal Service Act of 1792]], discussed above, provides one example. News publications still get a modest postal subsidy in the US; McChesney and Nichols recommends increasing that, especially for publications with little or no advertising. They also suggest that the government could pay, e.g., up to half of journalists' salaries for publications with low circulation. “In exchange for accepting subsidies, post-corporate newspapers would be required to place everything they produce on the Web [in] the public domain -- creating vast new deposits of current and, ultimately, historical information.”<ref>McChesney and Nichols (2010, p. 189)</ref> They also propose a “Citizenship News Voucher”, whereby every American adult gets a $200 voucher that s/he can donate to any nonprofit news medium or combination of such nonprofits.<ref>McChesney and Nichols (2010, p. 201)</ref><ref>For more, see [[media and corruption]], especially regarding Bruce Ackerman’s proposal to distribute subsidies in proportion to qualified Internet clicks.</ref> McChesney and Nichols (2010, pp. 170-172) also recommend subsidizing high school newspapers and radio stations to help develop a democratic, civic culture in the youth. [[w:Bruce Ackerman|Bruce Ackerman]] proposed "Internet news vouchers" that ask Internet users to "click a box whenever they read a news article that contributes to their political understanding. ... [A] National Endowment for Journalism ... would compensate the news organization originating the article on the basis of a strict mathematical formula: the more clicks, the bigger the check from the Endowment."<ref>{{Cite book | last =Ackerman | first =Bruce | author-link = w:Bruce Ackerman | year =2010 | title =The Decline and Fall of the American Republic | chapter =5. Enlightening politics | publisher =Harvard U. Pr. | page =133 | isbn =978-0-674-05703-6}}</ref><ref>{{Citation | last =Ackerman | first =Bruce | author-link = w:Bruce Ackerman | date =May 6, 2013 | title =Reviving Democratic Citizenship? | journal =Politics & Society | volume =41 | issue =2 | publisher =Sage | pages =309–317 | url =http://pas.sagepub.com/content/41/2/309.abstract | accessdate =June 16, 2013 | doi=10.1177/0032329213483103}}</ref> Dan Hind proposed "public commissioning" of news, where "Journalists, academics and citizen researchers would post proposals for funding" investigative journalism on a particular issue with a public trust funded from taxes or license fees. "These proposals would be made available online and in print in municipal libraries and elsewhere. ... The public would then vote for the proposals it wanted to support."<ref>{{cite book |last= Hind |first= Dan |title= The Return of the Public |year= 2010 |publisher= Verso | pages = 159-160 | chapter = 10. Public Commissioning | isbn=978-1-84467-594-4}}</ref> [[w:Dean Baker|Dean Baker]] suggested an "Artistic Freedom Voucher," similar to these other options but not limited to journalism: He claims that the copyright system today, at least in the US, locks up entirely too much information behind paywalls.<ref name=Baker2003>{{Citation | last = Baker | first = Dean | date = November 5, 2003 | title = The Artistic Freedom Voucher: An Internet Age Alternative to Copyrights | type = Briefing paper | publisher = Center for Economic and Policy Research | url = http://cepr.net/publications/reports/the-artistic-freedom-voucher-internet-age-alternative-to-copyrights | accessdate = 2017-03-30}}</ref><ref>See also [[w:Free Culture (book)|''Free Culture'']]: {{cite book |title= Free Culture: How Big Media Uses Technology and the Law to Lock Down Culture and Control Creativity | edition=US paperback |isbn=978-82-690182-0-2 |author=Lessig, Lawrence | publisher=Petter Reinholdtsen |date=2015 }}</ref> His idea, therefore, was to provide citizen-directed subsidies for virtually any artistic creation that would be placed in the public domain -- on the web to the extent that it can be digitized. This would make it easier for aspiring artists, performers, or writers to get started. After they become well enough known, they could stop accepting "Artistic Freedom Voucher" money and sell what they produce using the existing copyright system.<ref name=Baker2003/> This may be used if it seems too difficult to develop an acceptable legal definition of "investigative journalism;" see the discussion of this in section "4.4.3. Citizen-directed subsidies" for media below. What's the optimal level of funding for investigative journalism? The best information available, at least in this essay, is the 0.2 percent of GDP, suggested by McChesney and Nichols (2010), and the comparable amount in Scandinavia, discussed with Figure 10 above. More recently McChesney and Nichols (2021a, b) propose a Local Journalism Initiative (LJI), whereby the US would be divided into local jurisdictions, typically counties, and each would be given 0.15 percent of Gross Domestic Product (GDP), currently just over $100 per person, that would be distributed to local nonprofit journalism organizations based on regular elections where each adult would have three votes to select their three most preferred qualifying organizations. Counties with low populations might be combined as might counties in a metropolitan area. And residents in areas with large populations may get four or five votes rather that three "to guarantee diversity of voices." To qualify, the recipient organization could not be a subsidiary of a larger organization and would have to devote 75 percent of their salaries to journalists based in that local jurisdiction. Each such organization would have to produce and publish original material at least five days per week on its website; no restrictions should be placed on the content. Roughly that amount of money might be obtained without action by the federal government in local jurisdictions that chose to match what they spend on [[Confirmation bias and conflict#Advertising and accounting|accounting, advertising, media and public relations]] with these kinds of citizen-directed subsidies for journalism. The discussions above of terrorism, conflict, economics, and incarcerations including the [[w:City of Bell scandal|scandal in the city of Bell, CA]], and "control frauds" suggests that it might be wise to provide citizen-directed subsidies for investigative journalism comparable to what organizations spend on [[w: Accounting|accounting]]; see "Implications" for "Subnational" entities below for more on this. ==== 3.4.2. Nonprofit media organization (NMO) ==== [[w:Julia Cagé|Julia Cagé]] proposes a new model of funding and governance for media she calls a ‘’Nonprofit media organization’’. This is a charitable foundation with democratic governance split between the funders, the journalists, and their audience.<ref>Cagé (2016)</ref> ==== 3.4.3. Net neutrality ==== The fight over [[w:Net neutrality|net neutrality]] is a question of how media will be funded and governed. [[w:Political positions of Donald Trump#Technology and net neutrality|US President Donald Trump is opposed to net neutrality]]. In September 2015 he was quoted as saying, "Obama's attack on the Internet is another top down power grab. Net neutrality is the [[w:Fairness Doctrine|Fairness Doctrine]]. Will target the conservative media."<ref>Caroline Craig, [http://www.infoworld.com/article/2986220/net-neutrality/where-the-candidates-stand-on-net-neutrality.html Where the candidates stand on Net neutrality], ''InfoWorld'' (September 25, 2015).</ref> [[w:Ajit Varadaraj Pai|Ajit Pai]], Trump's Chairman of the US [[w:Federal Communications Commission|Federal Communications Commission (FCC)]], agrees: He has claimed that [[w:Ajit Varadaraj Pai#First Amendment issues|net neutrality]] in an attempt to weaken the "culture of the First Amendment,"<ref>{{Cite news |url=http://www.washingtonexaminer.com/fcc-commissioner-something-changing-in-america-about-the-first-amendment/article/2585434 |title=FCC commissioner: Something changing in America about the First Amendment |newspaper=Washington Examiner |first=Rudy |last=Takala |date=March 14, 2016 }}</ref> because it deprives [[w:Internet service provider|Internet service providers (ISPs)]] of their freedom of speech. He said it was "conceivable" that the FCC would seek to regulate political speech offered by edge providers such as [[w:Fox News|Fox News]] or the [[w:Drudge Report|Drudge Report]].<ref>{{Cite news |url=http://www.washingtonexaminer.com/fcc-commissioner-u.s.-tradition-of-free-expression-slipping-away/article/2583354 |title=FCC commissioner: U.S. tradition of free expression slipping away |newspaper=Washington Examiner |first=Rudy |last=Takala |date=February 16, 2016 }}</ref> Pai is correct that net neutrality limits the free speech rights of ISPs. One implication of this essay is that there is a compelling national security interest in doing something to improve the way in which news is selected, produced, supplied to and consumed by the public. Net neutrality is one such measure that has broad support among the US public.{{Citation needed|reason=document the popularity|date=March 2017}} Limits on free speech appear in the [[w:Hatch Act of 1939|Hatch Act]] and Department of Defense Directive 1344.10, which prohibit employees of the US executive branch from engaging in certain types of political activities. Whether ISPs are allowed to provide content or not, [[w:Net neutrality|net neutrality]] could be improved by a tax on advertising placed with content-providing [[w:Internet service provider|Internet service providers]]. ISPs that were common carriers would not have to pay this tax, nor would content providers that were not ISPs. == 4. Implications == The above discussion suggests policy implications at five levels: personal, interpersonal, subnational, national, and international. * ''The primary difference between rich and poor countries is politics.'' * ''The primary difference between rich and poor people within a country is politics.'' === 4.1. Personal === Individuals need to understand that unless they control the funding for the media they patronize, changes in their behaviors are being sold to the people who do control the funding. The discussion above illustrates only a few of the problems this generates. ==== 4.1.1. Fact checking ==== The research of Daniel Kahneman (2011) indicate that humans have two methods for ascertaining truth: # How does it fit with my preconceptions? # How does it fit with credible sources? The first approach leads to many decision errors, including blind support by the American public for the destruction of democracy in Iran, Guatemala, Brazil, and Chile, the cancelation of elections in Cuba and Vietnam, all without public debate, and the invasion of Iraq with severely restricted debate, as discussed above. This suggests that society would benefit if a critical mass of the electorate were to actively search for more credible sources of information on the most important issues of the day and then discuss what they learn with others. The good news for this is Chenoweth's 3.5 percent rule: Of the 323 major governmental change efforts of the twentieth century (summarized in Tables 1 and 3, Figure 6, and Appendix 2), every one that got the active support of at least 3.5 percent of the population was successful -- and all of those were nonviolent.<ref>{{Citation | last = Chenoweth | first = Erica | date = November 4, 2013 | title = My Talk at TEDxBoulder: Civil Resistance and the “3.5% Rule” | publisher = The Rational Insurgent | url = https://rationalinsurgent.com/2013/11/04/my-talk-at-tedxboulder-civil-resistance-and-the-3-5-rule/ | accessdate = 2017-03-21}}</ref><ref>{{Citation | last = Chenoweth | first = Erica | date = 2017-02-01 | title = It may only take 3.5% of the population to topple a dictator – with civil resistance | publisher = The Guardian | url = https://www.theguardian.com/commentisfree/2017/feb/01/worried-american-democracy-study-activist-techniques | accessdate = 2017-03-21}}</ref> The [[w:Indivisible movement|Indivisible movement]] in the US may already have that many supporters. However, for them to effect substantive change beyond blunting the agenda of President Trump, they may need to check their facts more carefully. Otherwise, they may succeed in blocking the worst parts of President Trump's agenda but fail to substantively alter the continued transfer of wealth from the poor and middle class to "job creators," summarized in Figure 7 above. ==== 4.1.2. Turn off the mainstream media ==== Turn off the mainstream media. Support instead noncommercial investigative journalism with transparent funding that places everything they produce on the web in the public domain, as suggested in the discussion of media funding and governance above. Good nonprofit media organizations are not always easy to find. One reasonable list of suggestions is available from {{Citation | date = February 6, 2017 | title = How to Find and Support Trustworthy Journalism | publisher = DailyGood | url = http://www.dailygood.org/story/1505/how-to-find-and-support-trustworthy-journalism-democracy-fund/ | access-date = 2017-03-31 }}. Two not listed there are the following: * [[w:Democracy Now!|''Democracy Now!,'']] which produces a one-hour daily news broadcast, Monday through Friday, that “is funded entirely through contributions from listeners, viewers, and foundations and does not accept advertisers, corporate underwriting or government funding.” They also post transcripts on their web site. * AllSides.com,<ref>{{Citation | title = AllSides | publisher = AllSides.com | url = https://www.allsides.com/ | accessdate = 2017-03-29}}</ref> which provides side-by-side comparison of how typically left, center and right sources cover a particular story. Interested readers are invited to add to this list any nonprofit news organization not listed here or in the "How to ..." site mentioned, especially if they have transparent funding and makes everything they produce available on the web in the public domain (or a relatively unrestricted license like the [[w:Creative Commons license|Creative Commons Attribution ShareAlike license]]). ==== 4.1.3. Make politics a primary entertainment. ==== The discussion of Kahneman's work above suggests we should not assume that current knowledge is adequate. No human can possibly check their facts on everything. That's part of why we make so many decisions based on what comes most readily to mind. However, Kahneman says we would better ourselves and others if we identified a few very important issues and spend time and money looking for alternative sources of information on those issues. This should include looking for information that might conflict with our preconceptions. How can we get time for this? Turn off the mainstream media, as suggested in the previous section, and make the search for alternative information a primary entertainment. === 4.2. Interpersonal === People say, “We don’t talk politics.” In a democracy that’s undemocratic. If we don’t talk politics, it becomes easier for corrupt elites to divide and conquer the poor and the middle class, getting them to support policies that benefit the elites at the expense of everyone else. Examples include the public support for the War on Terror and the “get tough on crime” wave that drove the five-fold increase in the incarceration rate described above. In both these examples, the results appear to have been detrimental to society as a whole, to the extent that the analysis above is accurate. We need to talk politics. We should not argue. Instead, we need to ask questions, listen with respect and show our audience that we’ve heard their concerns before we share our perspective.{{Citation needed|reason=This process has a name and supporting literature, but I forget right now what it is.|date=March 2017}} * ''We should strive to agree to disagree agreeably.'' Also, people with computer skills can help others improve their ability to use computers to get better information. === 4.3. Subnational === As suggested above, governmental organizations at all levels, including subnational entities (e.g., state and local governmental organizations in the US) might benefit their constituents by devoting a portion of their budget roughly comparable to what they spend on [[w:Accounting|accounting]] to something like an Endowment for Journalism that would provide citizen-directed subsidies for local investigative journalism organizations. A system like this might also be funded in part by businesses and ordinary citizens, who would like to subsidize investigative journalism in their service area or community. More experiments like this are needed. === 4.4. National === For national reforms, at least in the US, the above discussion favors [[w:Net neutrality|net neutrality]] and major limits on government secrecy. ==== 4.4.1. Net neutrality ==== As noted above, [[w:Political positions of Donald Trump|President Trump]] opposes [[w:Net neutrality|net neutrality]]<ref>{{Citation | last = Craig | first = Caroline | date = September 25, 2015 | title = Where the candidates stand on Net neutrality | journal = InfoWorld | url = http://www.infoworld.com/article/2986220/net-neutrality/where-the-candidates-stand-on-net-neutrality.html | accessdate = 2017-03-09}}</ref> and supports Internet censorship.<ref>{{Citation | last = Thielman | first = Sam | date = March 14, 2016 | title = Tech policy activists find Bernie Sanders is best bet – while Trump is the worst | newspaper = Guardian | url = https://www.theguardian.com/us-news/2016/mar/14/election-2016-tech-policy-net-neutrality-bernie-sanders-donald-trump | accessdate = 2017-03-09}}</ref> Internet censorship would put government bureaucrats in charge of fact checking. Destroying net neutrality would make it harder for consumers to obtain information that is not subsidized by big money interests. This in turn supports a continuation of the biased reporting that created the five-fold increase in incarcerations in the US, discussed above, and the "[[w:935 Lies|935 lies]]"<ref>Lewis (2014)</ref> that stampeded the Western world into invading Iraq on fraudulent grounds in 2003. If net neutrality is destroyed, congress ''could'' later overturn that action, though precedents for that are not encouraging. Congress could, however, encourage common carriers by taxing ISPs that also provided content, as suggested above. ==== 4.4.2. Limiting government secrecy ==== The 1995 [[w:Moynihan Commission on Government Secrecy|Moynihan Commission on Government Secrecy]] in the US made a number of recommendations including the following: * Excessive secrecy has significant consequences for the national interest when policy makers are not fully informed, the government is not held accountable for its actions, and the public cannot engage in informed debate. * Some secrecy is important to minimize inappropriate diffusion of details of weapon systems design and ongoing security operations as well as to allow public servants to secretly consider a variety of policy options without fear of criticism. * The best way to ensure that secrecy is respected, and that the most important secrets remain secret, is for secrecy to be returned to its limited but necessary role. Secrets can be protected more effectively if secrecy is reduced overall. Politicized intelligence was one contributor to the US-led invasion of Iraq in 2003, without which ISIL might never have been big enough to make international headlines, if it existed at all. This suggests two additional reforms: * Make all the intelligence services report to the US [[w:Government Accountability Office|Government Accountability Office (GAO)]]. * Drastically limit the duration of secrecy of any classified information created by intelligence services. The duration should be long enough to protect the element of surprise in democratically authorized military operations but short enough to make it much more difficult for the US government to interfere in the internal affairs of foreign countries without a full and open public debate.<ref>Information allowing the identification of specific individuals involved in questionable activities prior to the passage of reform legislation suggested herein might be classified for 30 years to protect those individuals. Such protections should also extend to private considerations of options considered but not implemented, to allow public officials to consider all options without fear of retaliation for options not submitted for public consideration. However, such protection could not extend to protect information from challenge in legal proceedings under US v. Reynolds, because US v. Reynolds seems to be a threat to US national security, and should be overturned, according to the argument in this section and supporting evidence.</ref> Making the intelligence services report to the GAO would not eliminate politicization of intelligence,<ref>[[w:Government Accountability Office investigations of the Department of Defense|As noted above, the US DoD failed to pass an audit since first required to do so in 1990.]] This is partly a result of interference by elected representatives.</ref> but it would limit the ability of the executive branch to do it on its own initiative, as seems to have been the case in the run-up to the US-led invasion of Iraq in 2003.<ref>as documented, e.g., by Lewis (2014)</ref> The Moynihan Commission recommended "returning secrecy to its limited but necessary role." Limiting the duration of classification to something like six months could be part of that. Six months seems long enough that it would not likely seriously impede any active military operations but short enough to effectively eliminate US efforts to destabilize foreign governments without a full and open public debate. We do not need ''uninformed'' "debates," like those that stampeded the US congress into approving the [[w:Gulf of Tonkin Resolution|Gulf of Tonkin Resolution]] in 1964 or the use of force in Iraq in 2003. Like [[w:Truth and reconciliation commission|truth and reconciliation processes]], military personnel and other government employees should be given wide latitude for honest mistakes. However, the history of previous US government efforts to destroy the prospects for democracy in foreign countries suggests a need for a substantially shorter period of classification than is the practice today. To these and Moynihan's reforms, we would add one more: * Overturn the US Supreme Court decision in [[w:United States v. Reynolds|US v. Reynolds]]. Under that decision, no judge and no defendant can question the government’s claim of national security. US v. Reynolds has effectively given US government officials who can classify a document the ability to conceal malfeasance and criminal activities. For example, in the trial of [[w:Daniel Ellsberg|Daniel Ellsberg]] for leaking the [[w:Pentagon Papers|Pentagon Papers]], Ellsberg was not allowed to argue that the information he released was improperly classified. Recently, Ellsberg said that [[w:Edward Snowden|Ed Snowden]] could not get a fair trial in the US;<ref>{{Citation | last = Ellsberg | first = Daniel | date = 2014-05-30 | title = Snowden would not get a fair trial – and Kerry is wrong | newspaper = The Guardian | url = https://www.theguardian.com/commentisfree/2014/may/30/daniel-ellsberg-snowden-fair-trial-kerry-espionage-act | accessdate = 2017-03-09}}</ref> US v. Reynolds effectively says that a fair trial is impossible in any civil or criminal case involving US [[w:Classified information|information that could plausibly be classified]]. One more example: Wikileaks recently disclosed that the CIA has the ability to hack many devices including modern automobiles.<ref>{{Citation | date = 2017-03-07 | title = Vault 7: CIA Hacking Tools Revealed | publisher = WikiLeaks | url = https://wikileaks.org/ciav7p1/ | accessdate = 2017-03-14}}</ref> The Washington Post noted, "The fear that your car can be hacked and made to crash is not new, and it’s not completely unfounded. ... Concerns about automotive cyber security have been raised since automakers began outfitting cars and trucks with computer-controlled systems. ... [S]atellite, Bluetooth and Internet ... make them more vulnerable to hackers who can then gain access to the computerized systems without ever stepping foot near the actual vehicle. ... The WikiLeaks release even renewed suspicions about the death of journalist [[w:Michael Hastings|Michael Hastings]], who was killed in a single-car accident in Los Angeles in 2013."<ref>{{Citation | last = Overly | first = Steven | date = 2017-03-08 | title = What we know about car hacking, the CIA and those WikiLeaks claims | newspaper = Washington Post | url = https://www.washingtonpost.com/news/innovations/wp/2017/03/08/what-we-know-about-car-hacking-the-cia-and-those-wikileaks-claims/ | accessdate = 2017-03-14}} </ref> It would be irresponsible to say that the CIA killed Hastings. However, given the CIA's history briefly summarized above, it would be equally irresponsible to claim that they did not have the means and a history of far worse. Moreover, Hastings told others before his death that he was working on a story involving the CIA. If that's true, CIA personnel likely knew. This would have given them a motive, especially since an earlier article by Hastings forced the resignation of General [[w:Stanley McChrystal|Stanley McChrystal]]. The recommendations of the Moynihan Commission have so far been ignored. Why? The discussion above suggests that major US international business executives likely believe they benefit from having the US government promote regime change in foreign countries on their behalf. Since many of those international businesses also control major advertising budgets, the mainstream commercial media as currently structured have a conflict of interest in honestly reporting on those activities. This is very clear in some cases, less clear in others. Big oil, for example, seems to have benefitted from the US support for the Saudis since the 1930s. They also seem to have benefitted from the [[w:March 1949 Syrian coup d'état|destruction of democracy in Syria in 1949]] and [[w:1953 Iranian coup d'état|Iran in 1953]] as well as from the [[w:War in Afghanistan (2001–2014)|US-led invasion of Afghanistan in 2001]], as noted above. For another example, consider [[w:Allen Dulles|Allen Dulles]]: He was head of the CIA during the [[w:1954 Guatemalan coup d'état|1954 Guatemalan coup d'état]]. He sat on the board of directors of [[w:United Fruit Company|United Fruit]], a major beneficiary of the coup. ==== 4.4.3. Research on why people support one side or another in conflict and change their support over time ==== The world needs an "International Conflict Observatory" doing research that can not be kept secret into what motivates people to leave the sidelines to support one side or the other in conflict, to increase or decrease their level of support over time, and to desert or defect, when they do. The results of such research should be freely available, in the {{w|public domain}}, produced in a way that would not allow any government to try to classify it to keep it from the public, as discussed in the section above on [[Winning the War on Terror#2.12. G. W. Bush: "Why do they hate us?"|G. W. Bush: "Why do they hate us?"]]. ==== 4.4.4. Citizen-directed subsidies for media ==== The discussion above suggests a need for citizen-directed subsidies for investigative journalism on the order of 0.2 percent of GDP with a preference for non-commercial investigative journalism with transparent funding that puts everything they produce on the web in the public domain.<ref>See also {{Citation | title = Endowment for Journalism | publisher = Endowment for Journalism | url = http://endowmentforjournalism.org | accessdate = 2022-09-04}}</ref> More research is needed into whether and how "investigative journalism" might be defined so politicians could not easily divert these subsidies to organizations that supported only their political agenda. If this seems too difficult, some or all of the money given to an "Endowment for Journalism" that manages these funds could be disbursed under citizen direction to virtually all creative artists and / or nonprofit media organizations with transparent funding, who agree to place all they produce on the web in the public domain in exchange for citizen-directed subsidies; see also section "3.4.1. Citizen-directed subsidies" above. As noted above, McChesney and Nichols suggested that each taxpayer be given a tax rebate of up to $200 that they can split between qualifying nonprofit media organizations. An alternative might be to provide, e.g, five to one matches for small dollar amounts given to qualifying nonprofits up to a maximum of, e.g, $50 for every man, woman and child (max subsidy = $250 for each).<ref>The matching funds for minors could be "with the approval of their parents / legal guardians."</ref> Consistent with the recommendations of Cagé, outlined above, it may be wise to require the recipients to be "Nonprofit Media Organizations" (NMOs) meeting her requirements. An alternative might involve an "Endowment for Journalism" that would distribute funds in proportion to qualified Internet clicks. A system like this could be used by a local governmental entity, subsidizing only selections made by residents in that jurisdiction, or even a business wanting to promote local transparency in government within their primary service area.<ref>Qualifications would apply both to the individual making the click and the recipient organization. They would ensure that both the individual and the recipient would have an appropriate connection to the indicated governmental entity or business.</ref> === 4.5. International === The discussion above suggests several actions that can be taken by any country in the world. # Strengthen international law. # Support further research into the long-term impact of alternative approaches to conflict (effective defense). # Support research and dissemination of information on what motivates people on all sides of violent conflict to do what they do. # Support the widespread dissemination of the research into the relative effectiveness of violence and nonviolence and techniques of nonviolent civil disobedience. # Support free press everywhere. This includes increasing protections for journalists both domestically and by placing a national security tax on trade with countries with a documented history of mistreating journalists. It also includes supporting citizen-directed subsidies for noncommercial investigative journalism -- including in foreign countries. In particular, the security of Western nations could be enhanced through financial support for citizen-directed investigative journalism in foreign countries that also encouraged nonviolent civil disobedience in seeking redress of grievances. # Support research and experimentation with demand-side economics, as mentioned above. # Non-nuclear nations could place a “national defense tax” on trade with nuclear states to encourage nuclear disarmament. # Limit arms trade only to functioning democracies that vigorously support free press everywhere. # Accept refugees and support their adjustment with demand-side economics, as discussed above. # Drastically limit the use of airpower, including armed drones, only to support of ground operations. == 5. Summary == The above discussion summarizes research suggesting that the approach that has been taken so far to combating international terrorism has increased, not decreased, that threat. People everywhere can help reduce the risks described herein by being more selective in the media they choose to consume and by asking more questions. Research by Kahneman (2011), outlined above, make it clear that virtually all conflicts are driven in part by things people think they know that aren't so. People everywhere can also learn more about nonviolent civil disobedience. You can build civil society by listening respectfully to others including those with whom you may disagree, asking questions, and summarizing what you think you heard to show them that they've been heard. Then the others may be more willing to listen to your concerns. This may not apply everywhere, because local law and other considerations may make it too risky to discuss certain issues openly. The “Implications” section of this essay also includes suggestions for changes in national and international policies. == See also == The questions raised in this article are almost benign relative to the issues raised in the two more recent pieces: * [[1998 Embassy bombings and September 11]] * [[Expertise of military leaders and national security experts]] == References == * {{Citation | last = Bapat | first = Navin A. | year = 2011 | title = Transnational terrorism, US military aid, and the incentive to misrepresent | journal = Journal of Peace Research | volume = 48 | issue = 3 | pages = 303-318}} * {{Citation | last = Black | first = William K. | year = 2005 | title = The Best Way to Rob a Bank is to Own One: How Corporate Executives and Politicians Looted the S&L Industry | publisher = U. of Texas Pr. | isbn = 0-292-72139-0}} * {{Citation | last = Cagé | first = Julia | year = 2016 | origyear = 2015 | title = Saving the media: Capitalism, crowdfunding and democracy | publisher = Belknap | isbn = 9780674659759}} * {{Citation | last = Cassidy | first = John | date = November 18, 2015 | title = The Economics of Syrian Refugees | magazine = The New Yorker | url = http://www.newyorker.com/news/john-cassidy/the-economics-of-syrian-refugees | accessdate = 2017-03-13}} * {{Citation | last = Chayes | first = Sarah | year = 2014 | title = Thieves of State: Why Corruption Threatens Global Security | publisher = Norton | isbn = 978-0393239461}} * <!-- Erica Chenoweth and Kurt Schock (2015-12) " Do Contemporaneous Armed Challenges Affect the Outcomes of Mass Nonviolent Campaigns?-->{{cite Q|Q83970885}} * {{Citation | last = Chenoweth | first = Erica | last2 = Stephan | first2 = Maria J. | author-link = w:Erica Chenoweth | year = 2011 | title = Why Civil Resistance Works: The Strategic Logic of Nonviolent Conflict | publisher = Columbia U. Pr. | isbn = 978-0-231-15683-7}}. For their data see, {{Citation | last = Chenoweth | first = Erica | title = NAVCO Data Project | publisher = Sié Chéou-Kang Center for International Security & Diplomacy, Josef Korbel School of International Studies, University of Denver | url = http://www.du.edu/korbel/sie/research/chenow_navco_data.html | accessdate = 2017-03-17}} * {{Citation | last = Choi | first = Seung-Whan | last2 = James | first2 = Patrick | year = 2016 | title = Why does the United States intervene abroad? Democracy, human rights, and terrorism | journal = Journal of Conflict Resolution | volume = 60 | issue = 5 | publisher = Sage | pages = 899-926}} * {{Citation | last = de Albuquerque | first = Afonso | editor-last = Hallin | editor-first = Daniel C. | editor2-last = Mancini | editor2-first = Paolo | year = 2012 | title = Comparing media systems beyond the Western world | chapter = 5. On models and margins: Comparative media models viewed from a Brazilian perspective | publisher = Cambridge U. Pr. | pages = 72-95 | isbn = 978-1-107-69954-0}} * {{Citation | last = Focke | first = Florens | last2 = Niessen-Ruenzi | first2 = Alexandra | last3 = Ruenzi | first3 = Stefan | date = 2016-03-03 | title = A friendly turn: Advertising bias in the news media | publisher = SSRN | url = https://ssrn.com/abstract=2741613 | accessdate = 2017-05-11}} * {{Citation | last = Frum | first = David | last2 = Perle | first2 = Richard | year = 2004 | title = An end to evil: How to win the War on Terror | publisher = Ballantine | isbn = 0-345-47717-0}} * {{Citation | last = Graves | first = Spencer | date = 2005-02-26 | origyear = 2004 | title = The Impact of Violent and Nonviolent Action on Constructed Realities and Conflict | publisher = Productive Systems Engineering | url = http://prodsyse.com/conflict/Nonviolence&Reality.pdf | accessdate = 2017-02-20}} * {{Citation | last = Graves | first = Spencer | year = 2017 | chapter = terrorism | title = Ecdat | edition = 0.3-2 | publisher = Comprehensive R Archive Network (CRAN) and R-Forge | url = https://cloud.r-project.org/web/packages/Ecdat/index.html | accessdate = 2017-02-17}} * {{Citation | editor-last = Hallin | editor-first = Daniel C. | editor2-last = Mancini | editor2-first = Paolo | year = 2012 | title = Comparing media systems beyond the Western world | publisher = Cambridge U. Pr. | isbn = 978-1-107-69954-0}} * {{Citation | last = Hanushek | first = Eric A. | last2 = Peterson | first2 = Paul E. | last3 = Woessmann | first3 = Ludger | year = 2013 | title = Endangering Propsperity: A global view of the American school | publisher = Brookings Institution Pr. | isbn = 978-0-8157-0373-0}} * {{Citation | last = Hanushek | first = Eric A. | last2 = Woessmann | first2 = Ludger | year = 2015 | title = The knowledge capital of nations | publisher = CESifo | isbn = 978-0-262-02917-9}} * {{Citation | last = Harris | first = Brayton | year = 1999 | title = Blue & gray in black & white : newspapers in the Civil War | publisher = Brassey's | isbn = 978-1453617021}} * {{Citation | last =Horowitz | first =Michael | last2 =Reiter | first2 =Dan | year =2001 | title =When does aerial bombing work? Quantitative empirical tests, 1917-1999 | journal =Journal of Conflict Resolution | volume =45 | issue =2 | pages = 147–-173 | url =http://jcr.sagepub.com/content/45/2/147 | accessdate =July 29, 2013 | doi=10.1177/0022002701045002001}} * {{cite Q|Q57515305}}<!-- Jones and Libicki (2008) How terrorist groups end--> * {{Citation | last = Kahneman | first = Daniel | year = 2011 | title = Thinking, Fast and Slow | publisher = Farrar, Straus and Giroux | isbn = 978-0374275631}} * {{Citation | last = Lewis | first = Charles | author-link = w:Charles Lewis (journalist) | year = 2014 | title = [[w:935 Lies: The future of truth and the decline of America’s moral integrity|935 Lies: The future of truth and the decline of America’s moral integrity]] | publisher = Public Affairs | isbn = 978-1-61039-117-7}} * {{Citation | last = Lloyd | first = Mark | last2 = Friedland | first2 = Lewis A. | year = 2016 | title = The Communications Crisis in America, And How to Fix It | publisher = Palgrave Macmillan | isbn = 1-349-95030-0}} * {{cite Q|Q104888067}}<!-- McChesney and Nichols (2010) The Death and Life of American Journalism-->. * {{Citation | last = McChesney | first = Robert W. | last2 = Nichols | first2 = John | author-link = w:Robert W. McChesney | author2-link = w:John Nichols (journalist) | year = 2016 | title = People get ready: The fight against a jobless economy and a citizenless democracy| publisher = Nation Books | isbn = 9781568585215}} * <!-- The Local Journalism Initiative: a proposal to protect and extend democracy -->{{cite Q|Q109978060|date=2021a}} * <!-- To Protect and Extend Democracy, Recreate Local News Media -->{{cite Q|Q109978337|date=2021b}} * <!-- Pape (1996) Bombing to win: air power and coercion in war -->{{cite Q|Q107458786}} * {{cite Q|Q5318649}}<!--Pape 2005 Dying to win--> * {{Citation | last = Pape | first = Robert | last2 = Feldman | first2 = James K. | author-link = w:Robert Pape | year = 2010 | title = Cutting the fuse : the explosion of global suicide terrorism and how to stop it | publisher = U. of Chicago Pr. | isbn = 9780226645605}} * {{Citation | last = Peri | first = Yoram | editor-last = Hallin | editor-first = Daniel C. | editor2-last = Mancini | editor2-first = Paolo | year = 2012 | title = Comparing media systems beyond the Western world | chapter = 2. The impact of national security on the development of media systems: The case of Israel | publisher = Cambridge U. Pr. | pages = 11-25 | isbn = 978-1-107-69954-0}} * {{cite book|last1=Sacco|first1=Vincent F|title=When Crime Waves|date=2005|publisher=Sage|isbn=0761927832}} and {{cite book|last1=Youngblood|first1=Steven|title=Peace Journalism Principles and Practices|date=2017|publisher=Routledge|isbn=978-1-138-12467-7|pages=115-131}} * {{cite book |last1= Tyler |first1= Tom R. |last2= Huo |first2= Yuen J. |title= Trust in the Law: Encouraging Public Cooperation with the Police and Courts |year= 2002 |publisher= Russell Sage Foundation |isbn= 0871548895}} == Appendix 1. Terrorism death trends for the dozen countries with the most terrorism deaths, 2014-2015 == Figures 1 and 2 above and the plots in this Appendix were all created from the [[w:Global Terrorism Database|Global Terrorism Database]] using the summaries in Graves (2017). [[File:Terrorism deaths in Iraq.svg|thumb|Terrorism deaths in Iraq, 1970-2015 per the Global Terrorism Database.<ref name=Graves2017/>]] [[File:Terrorism deaths in Nigeria.svg|thumb|Terrorism deaths in Nigeria, 1970-2015 per the Global Terrorism Database.<ref name=Graves2017/>]] [[File:Terrorism deaths in Afghanistan.svg|thumb|Terrorism deaths in Afghanistan, 1970-2015 per the Global Terrorism Database.<ref name=Graves2017/>]] [[File:Terrorism deaths in Syria.svg|thumb|Terrorism deaths in Syria, 1970-2015 per the Global Terrorism Database.<ref name=Graves2017/>]] [[File:Terrorism deaths in Pakistan.svg|thumb|Terrorism deaths in Pakistan, 1970-2015 per the Global Terrorism Database.<ref name=Graves2017/>]] [[File:Terrorism deaths in Yemen.svg|thumb|Terrorism deaths in Yemen, 1970-2015 per the Global Terrorism Database.<ref name=Graves2017/>]] [[File:Terrorism deaths in Somalia.svg|thumb|Terrorism deaths in Somalia, 1970-2015 per the Global Terrorism Database.<ref name=Graves2017/>]] [[File:Terrorism deaths in Ukraine.svg|thumb|Terrorism deaths in Ukraine, 1970-2015 per the Global Terrorism Database.<ref name=Graves2017/>]] [[File:Terrorism deaths in Sudan.svg|thumb|Terrorism deaths in Sudan and South Sudan, 1970-2015 per the Global Terrorism Database.<ref name=Graves2017/>]] [[File:Terrorism deaths in Cameroon.svg|thumb|Terrorism deaths in Cameroon, 1970-2015 per the Global Terrorism Database.<ref name=Graves2017/>]] [[File:Terrorism deaths in Libya.svg|thumb|Terrorism deaths in Libya, 1970-2015 per the Global Terrorism Database.<ref name=Graves2017/>]] [[File:Terrorism deaths in Egypt.svg|thumb|Terrorism deaths in Egypt, 1970-2015 per the Global Terrorism Database.<ref name=Graves2017/>]] == Appendix 2. Democratization 1 and 10 years after the end of a conflict == The two figures in this appendix are similar to Figure 6 in the text. That shows the level of democracy 5 years after the end of a conflict vs. 1 year before. The two in this appendix show the level of democracy 1 and 10 years after the end of a conflict vs. 1 year before. [[File:Democratization 1 year after vs. 1 year before twentieth century revolutions.svg|thumb|Democratization 1 year after (vertical scale) vs. 1 year before (horizontal scale) twentieth century revolutions]] [[File:Democratization 10 years after vs. 1 year before twentieth century revolutions.svg|thumb|Democratization 10 years after (vertical scale) vs. 1 year before (horizontal scale) twentieth century revolutions]] == Notes == {{reflist}} [[Category:Original research]] [[Category:Research]] [[Category:Political science]] [[Category:Military]] [[Category:Military Science]] [[Category:Freedom and abundance]] 9ky48ks8585ecfdr8dw01feavp3cdik 0 244941 2719968 2719623 2025-06-28T14:03:09Z 184.54.161.253 /* Assignment */ corrected formatting to numbered list 2719968 wikitext text/x-wiki —Resolving an urgent plea for justice and action == Introduction == [[File:C. Darwin, On the Expression of the Emotions Wellcome L0031428.jpg|thumb|[[w:Indignation|Indignation]] is one of many forms of anger.]] {{TOC right | limit|limit=2}} [[w:Anger|Anger]] is a strong [[w:emotion|emotion]] designed to send the clear message “something has got to change”.<ref>This material is adapted from the [http://EmotionalCompetency.com EmotionalCompetency.com] website with permission from the author.</ref> It is an urgent plea for justice and action. If we exercise enough [[w:Self-control|self control]] to overcome our immediate impulse to lash out and do harm, we can calm down, [[w:Self-reflection|reflect]], and analyze the causes of our anger. Careful analysis can identify what [[What you can change and what you cannot|change]] is needed and can lead us toward constructive and lasting change that fulfills our needs. When cooler heads prevail anger's energy is channeled in a positive direction, and the anger motivates constructive changes. When we act on our impulses in the heat of passion, the results are too often destructive and tragic. There are many myths and misconceptions about anger and how to cope with it. The most destructive misconception is that it is healthy or effective to display anger violently and “vent”. Contrary to this popular misunderstanding, the healthiest way to deal with anger is to stay in control, analyze the message it is sending, and harness the energy it provides for positive change. Another misconception is that [[Foregoing Revenge|revenge]] can lead to positive change. Unfortunately [[Foregoing Revenge|revenge]] usually leads only to a cycle of destructive escalation. Expressing anger with violence breeds more anger. I hope the information presented here helps channel anger into positive change. == Objectives == {{100%done}}{{By|lbeaumont}} The objectives of this course are to help you to: *Recognize anger when it arises, *Interpret anger as an injustice alert, *Determine the perceived injustice that provoked the anger, *Determine if the perceived injustice represents a real injustice, *Take constructive action to resolve the injustice, *Constructively resolve anger when it arises. This course is part of the [[Emotional Competency]] curriculum. This material has been adapted from the EmotionalCompetency.com [http://emotionalcompetency.com/anger.htm page on anger], with permission of the author. If you wish to contact the instructor, please [[Special:Emailuser/Lbeaumont | click here to send me an email]] or leave a comment or question on the [[Talk:Resolving Anger|discussion page]]. [[File:Resolving Anger Audio Dialogue.wav|thumb|Resolving Anger Audio Dialogue]] == Forms of Anger == Many words in our vocabulary describe forms of [[w:anger|anger]]. They often differ in the intensity of the anger they express, but the basic archetype is the same. Here is a partial list, in approximate order from the mildest to the most intense: annoyance, irritation, aggravation, agitation, frustration, peeved, annoyed, miffed, sulking, offended, bitter, indignation, exasperation, incensed, pissed, outrage, hostile, spite, vengefulness, resentment, wrath, rage, fury, ferocity, and livid. [[w:Resentment|Bitterness]] describes a long-lasting result of unresolved anger. [[w:Hate|Hate]] is a form of anger because you blame the other for your difficulties when you decide to hate them. In addition to varying over a wide range of intensity, anger has a variety of forms. These include: *[[w:Indignation|Indignation]]: [[w:Self-righteousness|Self-righteous]] anger; *Sulking: Passive anger; *[[w:Annoyance|Exasperation]]: anger at having your patience unduly tried; and *[[Foregoing Revenge|Revenge]]: A deliberate response to an offense, delayed until after a period of reflection. == Definitions and Analysis == Many definitions of anger have been proposed. These include: #An unjust insult, an unfair slight, or #A [[w:Biological_specificity#Conspecific|conspecific]] threat, or #Response to thwarted goals, or #An agent causes loss of a goal, or #Loss attributed to an agent, or #An urgent signal to prepare for change, or #A plea for [[Virtues/Justice|justice]], or #A biological core related to combativeness, or #Judging another person as being wrong or deserving to be punished, or #[[Attributing Blame|Blaming]] another person for our own unmet needs, or #Displeased by the appraisal of an event while disapproving of another’s action, or #an aroused, often heated state in combining a compellingly felt sense of being wronged or frustrated, or #Response to [[w:Trespass|trespass]]. However, the definition that seems to be most precise, and provides the most insight is: *Anger is an [[w:emotion|emotion]], *resulting from a [[Facing_Facts/Perceptions_are_Personal|perceived]] loss, *attributed to a willful agent, and *[[Virtues/Justice|judged]] as unfair. Let's examine this definition closely. Because anger is an emotion, it evokes a [[w:Physiology|physiological]] response. In the case of anger, this is usually a strong [[w:Arousal|arousal]]. Often the arousal is so strong it can lead immediately to an ugly, destructive, and unnecessary “anger display” of shouting, threatening, and even [[w:Violence|violence]] if it is unchecked. A wide variety of perceived losses can trigger anger. This may include having your possessions stolen, abused, or destroyed. It can also involve loss of [[w:Social_status|stature]] or [[w:Egotism|ego]], such as when you lose a competition, suffer an insult, or are [[w:Humiliation|humiliated]]. The idea of “trespass” is important here, because the person trespassed against often considered it as a form of loss. [[w:Sadness|Sadness]], as well as [[w:Grief|grief]] and [[w:Depression_(mood)|depression]], are other emotions arising from a loss. The distinction between anger and sadness is the role of the “willful agent”. An agent is someone who acted [[w:Deliberation|deliberately]]. For example, if you lose your pet because it dies of natural causes, you are sad, but not angry. If your pet is killed by a malicious or even a careless person, you are angry at that person. You are angry because you believe that person acted with the deliberate [[w:Intention|intent]] to cause you harm. Now it has become a deliberate act and a personal affront. Often the willful agent is yourself. Extending the previous example, you may [[Attributing Blame|blame]] yourself for the loss of your pet if you believe you did not take sufficient care of the pet, or if you believe you could have done more to protect the pet and prevented the loss. Finally, to result in anger, you have to judge the willful agent as acting unfairly. If you lose a tennis match, you may be sad. If you believe the opponent [[w:Cheating|cheated]], or the referee made a mistake, this is unfair, and you become angry. This is a lot of complexity to incorporate into the split second assessments that so often lead us to anger. Perhaps the useful folk wisdom to “count to ten” recognizes these assessments can often be wrong. Fortunately, we can analyze our anger rationally and learn a lot about ourselves. Analyzing our anger can provide valuable insights into knowing yourself. To analyze the anger, begin by examining the perceived loss. Ask yourself: *What have I lost? Is the loss real? *What is its value to me? *Why do I [[Facing Facts/Perceptions are Personal|perceive]] this as important? *Was this my loss or was it someone else's? What are their views regarding this loss? How do you know? Why do you care? *Do I feel insulted? Why? Has my ego been attacked? Have I lost some [[Dignity|dignity]]? Was I ridiculed or humiliated? Has my reputation been damaged? Do I feel less competent? Was I denied fair recognition or reward? Is the insult groundless or is it an accurate interpretation of my behavior? What is the [http://emotionalcompetency.com/symmetry.htm asymmetry] that bothers me so much? *Do I feel [[w:Power_(social_and_political)|powerless]]? Have I lost [[w:Autonomy|autonomy]]? Do I feel cheated? Was I taken for a [[w:Gullibility|sucker]]? Was a [[Earning Trust|trust]] betrayed? Was privacy breached? *Was I [[w:Coercion|coerced]] into submission or obedience? *Have I been [[w:Threat|threatened]], injured, struck, [[w:Abuse|abused]], attacked, or [[w:Intimidation|intimidated]]? *Has anyone [[w:Trespass|trespassed]] on my territory? *Have my [[w:Goal|goals]] been thwarted? Have my freedoms been unfairly abridged? Is my safety or security reduced? Is my [[w:What_Matters/Progeny_and_Legacy|legacy]] diminished? *Have I lost [[w:Power_(social_and_political)|power]]? Have I lost [[w:Social_status|stature]]? Have I lost strength? Have I lost influence? Have I lost access? Has a [[w:Interpersonal_relationship|relationship]] been damaged? *From a rational point of view, how big is this loss? What impact will it have? How can I recover? Can I just ignore the issue? Your answers to these questions will provide valuable insights into your values, [[Seeking True Beliefs|beliefs]], goals, and [[What Matters|needs]]. Based on what you learn, complete the following sentence: I am angry because I have lost . . . This loss is important to me because I [value, believe, want to achieve, or need] . . . Then evaluate how strongly you still assess the loss. Now identify the willful agent who is the target of your anger and examine their intent. Ask yourself: *To what agent do I attribute this action? Who do I hold responsible? *Did they act deliberately? [[Knowing How You Know|How do you know]]? How can you check your assumption of intention? *Do they consider themselves responsible for the action? An agent is someone who acted deliberately. If you are angry because you stubbed your toe on the door your choice of agents is limited to: 1) the door, 2) the floor, 3) yourself, 4) someone who pushed you, or 5) Some innocent person who was not even in the room at the time. Note that the first two agents on the list cannot act willfully, and the last did not even act! The [[w:Fundamental_attribution_error|Fundamental Attribution Error]]—incorrectly attributing an action or intent to an agent—is a common mistake. If you find yourself blaming an un-willful agent (e.g. the door or the floor) for your anger, perhaps the [[What you can change and what you cannot|change]] that is needed is that you need to take more [[Living_Wisely#Personal_Responsibility|responsibility]] for your own actions. Finally, work to understand if the willful agent acted unfairly. Ask yourself: *Why do you [[Seeking True Beliefs|believe]] the action was [[Understanding Fairness|unfair]]? *What would you consider fair? *What was the agent's point of view? *How do they justify their actions? How do you know? *If the willful agent had a strong sense of [[w:Empathy|empathy]], what would they have done? How do you know? *What would a good friend have done in this situation? How do you know? *What would you have done in this situation? How do you know? What did you do the last time you were in a similar situation? *What is the basis for your sense of [[Virtues/Justice|justice]]? What standard do you use to establish “fair and just”? Is it a well-founded standard? Is it a widely accepted standard? Is it a standard the willful agent would accept? *How can you check your assumptions? What is the [[Evaluating Evidence|evidence]]? Is that evidence reliable and representative? [[Knowing How You Know|How do yo know]]? [[Understanding Fairness|Fairness]] and [[Virtues/Justice|justice]] and are remarkably difficult concepts to define. While we all have some inherent sense of right and wrong, attempts to write a comprehensive code of [[w:Ethics|ethics]], a set of rules, or a code of laws have eluded the best scholars, lawyers, theologians, ethicists, philosophers, and even parents over the millennia.<ref>For current work on this, see: [[Wisdom_Research#Envisioning_our_future | The future of moral reasoning]] </ref> I recommend using the standard of [[w:Empathy|empathy]]—a deep appreciation for another's situation and point of view—as the basis for fair judgment, but you probably have your own standard for judging fairness. Certainly the principle of symmetry—apparent balance—is an important basis for fairness and justice. This is reflected in the [[Living the Golden Rule|golden rule]]. === Assignment === #Notice the next time you feel angry. #Stay calm. #Resist any impulses to become violent or extract [[Foregoing Revenge|revenge]]. #Work through the steps described above, as best you can, to identify the source of your anger. #What incident provoked your anger? #What was the [[Facing Facts/Perceptions are Personal|perceived]] injustice? #Was that an actual [[Virtues/Justice|injustice]]? [[Knowing How You Know|How do you know]]? What would have been [[Virtues/Justice|just]]? How do you know? #What are the most constructive steps you can take, if any, to fairly resolve that injustice? #Take steps to resolve your anger constructively. == Origins, Archetypes, and the Plot of Anger == Anger encourages us to act on our sense of [[Virtues/Justice|justice]]. Anger may be interpreted in many of the following ways: *A [[w:Dehumanization|demeaning]] offense against me or mine. *Interference with what we are intent on doing. Thwarted goals. [[w:Frustration|Frustration]]; *Intentional physical harm toward us; actual, [[w:Threat|threatened]], or reasonably [[Facing Facts/Perceptions are Personal|perceived]]; *Intentional [[w:Psychological_abuse|psychological harm]] toward us, including [[w:Insult|insult]], [[w:Humiliation|humiliation]], denigration, [[w:Intimidation|intimidation]], or rejection; *Disappointment in the performance of others we care about; we get most angry at the people we love the most; *Witnessing the anger of another, especially when it is directed at you. The message to others is “get out of my way” or “I want to hurt you” == Benefits and Dangers of Anger == The anger mechanism would not have survived millions of years of evolution if it did not provide important survival benefits. Here are some of those benefits: *Anger tells us that something needs to change. *Anger can provide the motivation to constructively change whatever it was that caused the anger. It can energize the fight for legitimate rights. It contributed to eliminating [[w:Slavery|slavery]] and [[w:Apartheid|apartheid]], and led to [[w:Womens_suffrage|women's suffrage]] and [[w:Civil_and_political_rights|civil rights]]. Anger can motivate us to overcome [[w:Oppression|oppression]] and topple a [[w:Tyrant|tyrant]]. *Anger can provide the motivation to constructively correct an injustice. It urges us to act on our sense of [[Virtues/Justice|justice]]. *Anger can provide the motivation to constructively teach offenders what they did to make you angry, and to learn to act differently. *Anger can help to reduce or overcome [[w:fear|fear]] and provide the energy needed to mobilize needed change. *Anger sends a powerful signal that informs others of trouble. It notifies the offender that you have perceived an offense. *Anger helps us to preserve our ego and think good of ourselves. *Anger is a normal response to an external stimulus that needs to be addressed. One of the most dangerous features of anger is that expressing anger increases the anger of others. This can lead to a rapid and dangerous [[w:Conflict_escalation|escalation]]. We may try to harm the target of our anger. We often wish them harm. The impulse to harm is probably a central part of the anger response for most people. While anger can be dangerous and must be constrained, it cannot and should not be eliminated. Instead we need to [[Transcending Conflict|transcend conflict]]. == Anger as an Imperative for Change == Considering anger as an urgent imperative for [[What you can change and what you cannot|change]] provides a useful point of view for analyzing our options, actions, and effectiveness. This viewpoint raises these questions: #Why am I receiving this signal for change? What does it tell me about my own [[Seeking True Beliefs|beliefs]], values, goals, judgments, sense of [[Virtues/Justice|justice]], and needs? #What has to [[What you can change and what you cannot|change]]? #What steps are needed to carry out the change? #Who needs to act to make the change? #When does the change need to take place? #Will the change be effective? #Will the change be lasting? #Will the result be constructive? Let's look at each of these questions and examine how thoughtful discipline and impulse control can overcome the strong impulse to lash out now. '''Why am I receiving this signal for change? What does it tell me about my own beliefs, values, judgments, sense of justice and needs?''' Think this one through very carefully. At the deepest level of my consciousness, beliefs, values, and needs, what is it about my self that has caused this event to make me angry? Are my [[Seeking True Beliefs|beliefs]], values, goals, and judgments well founded and helpful? What is the basis for my sense of [[Virtues/Justice|justice]]? What is it I [[What Matters|need]] that I am not getting? Is the need valid? How can I form a request to best obtain what I need? What are the actions that are most likely to get what I most need? (Hint, [[Foregoing Revenge|revenge]] is not a need). '''What has to [[What you can change and what you cannot|change]]? and Who needs to act to make the change?''' Our viewpoint is intrinsically our own, and our impulse is to insist that you have to change now to accommodate my needs. But a constructive response to anger requires overcoming this self-centered impulse to allow a broader and deeper analysis of the information and options. Begin by focusing on the constructive steps you can take to move forward. If your actions in responding to anger, for example indulging in a dramatic anger display, will not cause the needed change then that action is not a good choice. '''What steps are needed to carry out the change?''' Our attention is fundamentally limited. As a result, we are selective in what we can observe, and we always make judgments based on our past experiences, [[Seeking True Beliefs|beliefs]], and needs when we interpret observations. Also, our memory is limited, and our recall is based on simplifications used to interpret the original observation in the context of our present set of beliefs. Because our experiences and point of view are self-centered and unique, our judgments will reflect this intrinsic bias. As a result of this inherent bias, the [[What you can change and what you cannot|options for change]] we first see are limited and often require others to change to accommodate our preferences. Again, a constructive response to anger requires overcoming this impulse and allow a broader and deeper analysis of the information and options. Test the effectiveness of your planned changes by examining why you believe they will result in the needed change. '''When does the change need to take place?''' Anger can be an immensely strong emotion with an almost overwhelming urge to act immediately. Although nearly every part of your being is screaming for you to act now, it is essential for you to find the strength to resist this powerful urge. Be patient. Calm down. Control you temper. Take three deep breathes. Count to ten, slowly. Allow the [[w:Psychological_refractory_period|refractory]] period to end, and allow [[Deductive Logic/Clear Thinking curriculum|reason]] to prevail. Take your time to accurately assess the situation. Be skeptical and take the time to verify your assumptions using thoughtful inquiry and rigorous [[Evaluating Evidence|evidence]] obtained from several reliable sources. Consider a variety of points of view, including an [[w:Empathy|empathy]] based point of view of the person who provoked your anger. What would you have done? How do you know? '''Will the change be effective? Will the change be lasting? Will the result be constructive?''' Keep in mind that acting in anger inevitably creates more anger. Understand [[what you can change and what you cannot]]. Create options for mutual gain. Invent more options for mutual gain. [[Transcending Conflict|Transcend conflict]]. What are the best options for getting your needs met? What can you do? === Standing in the Gap === We can take constructive action in the moment that exists between becoming aware of anger and acting on anger. Consider this story: <blockquote> A Monk decides to meditate alone. He takes a boat, goes to the middle of the lake, closes his eyes, and begins to meditate. After a few hours of unperturbed silence, he suddenly feels the blow of another boat hitting his. With his eyes still closed he feels his anger rising, and he opens his eyes ready to shout at the boatman who dared to disturb his meditation. But when he opened his eyes, he saw an empty boat, not tied up, floating in the middle of the lake... At that moment the monk understands that his ''anger is within'' him; it simply needs to ''hit'' an external object to provoke it. After that, whenever he meets someone who irritates or provokes his anger, he remembers: ''the other person is just an empty boat. anger is inside me!'' — Attributed to [[w:Thích Nhất Hạnh|Thich Nhat Hanh]], similar versions appear elsewhere.<ref>Om Swami, the Empty Boat, see: https://os.me/the-empty-boat/</ref> </blockquote> We can stand in the gap between feeling anger and acting on anger. We can ''stare back'' the destructive thoughts that arise so quickly, pause for a moment to consider our options, and choose a constructive response. <blockquote> "Between stimulus and response lies a space. In that space lie our freedom and power to choose a response. In our response lies our growth and our happiness".<ref>Often (incorrectly) attributed to [[q:Viktor_Frankl|Viktor Frankl]]</ref> </blockquote> Choose a constructive response. === Assignment === '''Part 1:''' #Notice the next time you feel angry. #Stay calm. #Answer each of the questions above for this anger episode. #Take constructive action to resolve your anger. '''Part 2:''' # Read the essay [[Virtues/Spontaneous_Conflict_and_Deliberate_Restraint|Spontaneous Conflict and Deliberate Restraint]]. # Exercise deliberate restraint. == Suppression is not Resolution == [[w:Anger|Anger]] is a strong emotion that is provoked by identifiable events. Ignoring, dismissing, overlooking, withstanding, or otherwise [[w:Anger#Suppression|suppressing]] your response to a real injustice is difficult and does not provide a sustainable long-term solution. Perhaps more importantly suppressing your anger discards the possibility that your anger can [[w:Motivation|motivate]] positive change in the world. It is likely that [[w:Rosa_Parks|Rosa Parks]] was angry on December 1, 1955 when she was asked to move to the back of the bus in Montgomery Alabama. Her anger resulted from a profound injustice and she was able to transform that anger into [[w:Social_movement|social movements]] that resulted in remarkable social change. Throughout history many angry people acted constructively and helped end [[w:Slavery|slavery]], increase [[w:Civil_and_political_rights|civil rights]], increase [[Assessing Human Rights|human rights]], provide [[w:Womens_suffrage|women the right to vote]], overthrow [[w:Tyrant|tyrants]], reduce [[w:Poverty|poverty]], cure diseases, end wars, reduce suffering, increase [[Virtues/Justice|justice]], and create positive change. Although few of us have an opportunity to transform our anger into historic social change, many of us can direct the motivation our anger provides to take constructive action and contribute to lasting positive change. == Anger as Hurt, Hate, or Fear == A general feeling of anger may result from more specific feelings of hurt (due to loss, sadness, [[w:shame|shame]], or [[w:humiliation|humiliation]]), hate, or fear. It can be helpful to examine your anger to see if it has these more specific origins or meanings. == Related Moods and Traits == [[w:Irritability|Irritability]] is the [[w:Mood_(psychology)|mood]] associated with anger. If you are in an irritable mood, you require less provocation to become angry. You may also be described as having a bad [[w:Temperament|temper]]. This may also be described as grouchy, grumpy, or being in a bad mood. Hostility is the [[w:Trait_theory|personality trait]] associated with anger. Hostile people are more likely to become angry. A hot head or someone with a bad temper, is anyone who has poor [[w:Inhibitory_control|impulse control]] and moves quickly from anger toward [[w:Rage_(emotion)|rage]], dramatic anger displays, and even overt violence. These people may also have hostile personalities. They often have a fragile self-esteem and are hypersensitive to criticism or [[Dignity|disrespect]]. Privately they see themselves as weak, [[w:Social_vulnerability|vulnerable]], and not particularly strong, capable, or worthy. They fear [[w:humiliation|humiliation]]. To bolster their own opinion of themselves they believe others should show them [[Dignity|respect]] and acknowledge their high [[w:Social_status|stature]]. If others fail to demonstrate respect they are dismissed as unfriendly, critical, and hostile. == Physiological Responses == You actually ''feel'' anger, partially as a result of these involuntary changes in your body: *Increased heart rate; *increased blood pressure; *reddened face; *tensed muscles. *a tendency to move forward, toward the target of the anger. Much of this is caused by activating the [[w:Sympathetic_nervous_system|sympathetic branch]] of the [[w:Autonomic_nervous_system|autonomic nervous system]] as a primal survival strategy. === Assignment === # Notice the next time you feel angry. # Identify the specific physiological responses you are feeling. # Use these physiological responses to identify anger whenever it occurs. # Stay calm. # Follow the guidance provided by this course to resolve your anger constructively. == Myths and Misconceptions == The Hydraulic Model of Anger—describing the need to vent dramatically and “let off steam”—is unfounded.<ref>See, for example [http://www.oxfordscholarship.com/view/10.1093/acprof:oso/9780195368536.001.0001/acprof-9780195368536-chapter-13 ''True to Our Feelings: What Our Emotions Are Really Telling Us''], by Robert C. Solomon, 2008, Chapter 12, "Myth Three, The Hydrolic Model".</ref> “Getting your anger out” almost always makes matters worse. There is no evidence that suppressed anger is harmful if we feel in control of the situation, and if we interpret the anger as a grievance to be corrected constructively. Unless the source of your anger can be corrected by expressing anger, don't. Although anger itself does not accumulate, the urge for [[Foregoing Revenge|revenge]] can. It can be harmful to accumulate and intensify the urge for [[Foregoing Revenge|revenge]] without reconciling your feelings of injustice. Choose a constructive path to resolve your quest for [[Foregoing Revenge|revenge]]. Expressing anger is necessary; but do it by standing up for your rights clearly and assertively, not violently. Suppressing legitimate anger is unhealthy. Continually venting anger is also unhealthy. The excuse “You made me do this, I had no choice” is always false. Self control is the difference between acting destructively in anger, and responding calmly, constructively, and rationally. You are always responsible for your actions. It is false to believe: If I don't act out the anger, I have given in, lost face, wimped out, become a coward, and disgraced myself. Actually the opposite is true. It takes greater strength, self restraint, introspection, and analysis to constructively resolve anger. == Expressions of Anger == *[[w:Screaming|Shouting]], raised voice, threatened or actual physical [[w:violence|violence]]. *Passive withdrawal, [[w:Stonewalling|stonewalling]], lack of cooperation, [[w:Sabotage|sabotage]], [[Foregoing Revenge|revenge]]. *Throwing a [[w:Tantrum|tantrum]]—a violent and objectionable demonstration of rage or frustration that is often considered quite childish. * Various forms of [[w:Passive-aggressive_behavior|passive-aggressive behavior]]. Anger is distinct from [[w:Aggression|''aggression'']]. Anger is an [[w:emotion|emotion]] and is most evident in how you feel, while aggression—an offensive action or attack—is how you choose to act. === Assignment === #Notice the next time you feel angry. #Notice any tendency to express anger violently. #Overcome these impulses. #Stay calm. #Resolve your anger constructively. == The Paradox of Anger == If anger is so destructive, why is it so common? The enduring benefit of anger is that it urges us to act on our sense of justice. Unfortunately the powerful urge it provides is primitive and is too often dangerously misused. Carefully choose a constructive path for your anger, as described in this next section. == Paths of Anger == Events that can trigger our [[w:anger|anger]] are common and frequent occurrences. How we respond to those provocations and the choices we make critically affect our [[w:Inner_peace|peace of mind]], [[w:Well-being|well-being]], and our lives. The following figure illustrates choices we have and paths we can take to either inflame or resolve our anger. Use this like you would any other map: 1) decide where you are now, 2) decide where you want to go, 3) choose the best path to get there, and 4) go down the chosen path. If you can arrange a constructive meeting with your adversary, use this map to discuss where each of you are now and choose a path leading to resolution of your conflict. Keep in mind: as you walk you make your path. You may wish to print out this [http://emotionalcompetency.com/images/anger%20state%20diagram.pdf one-page version of the Paths of Anger map]. [[File:Paths of Anger.jpg|thumb|300px|Paths of anger]] The diagram on the right is an example of a type of chart known by systems analysts as a [[w:State_diagram|state transition diagram]]. Each colored elliptical bubble represents a state of being that represents the way you are now. The labels on the arrows represent actions or events and the arrows show paths into or out of each state. You are at one place on this chart for one particular relationship or interaction at any particular time. Other people are likely to be in other places on the chart. This is similar to an ordinary road map where you plot where you are now, while other people are at other places on the same map. Begin the analysis at the green “OK” bubble, or wherever else you believe you are now. '''OK:''' This is the beginning or neutral state. It corresponds to two people who may be meeting for the first time, or who don't have a history of animosity between them. It also represents people who may have been angry with each other at some time in the past, but who have now resolved their differences. The green color represents safety, tranquility, [[w:Equanimity|equanimity]], and growth potential. '''Insult:''' We were OK until something happened to provoked our anger. We know the feeling; our heart beats faster, our eyebrows pull down together, we are somewhere between frustrated, annoyed, and enraged, and we have this almost uncontrollable urge to lash out and act now. Although the cause could be any number of things, perhaps we were humiliated, we will use the term “[[w:Insult|insult]]” to describe any of these provocations. After reflection and reappraisal, the offender who made the original insult may decide it was unjustified and could later feel shame or guilt for his attack. '''Angry:''' Now we are [[w:angry|angry]], and we have to decide what to do about it. The importance of the choice we make here cannot be overemphasized. We can [[w:Revenge|retaliate]] and take a path leading quickly to escalation and violence, we can remain [[w:Resentment|resentful]] for days, months, or years, we challenge an adversary and ensure a destructive outcome, or we can carefully resolve the problem. If the message of anger is that “something has got to change” then it is essential to accurately determine what it is that has to [[What you can change and what you cannot|change]] and what actions you can take to effect that change. If your actions, for example an anger display, will not cause the needed change, then that action is not a good choice. Do not take other action until you have a chance to cool off, calm down, and reflect. The yellow color indicates the need for caution in choosing the next path. '''Retaliation:''' The most common, and most destructive, response to anger is some form of [[w:Revenge|retaliation]]. This is too often in the form of the familiar “anger display” where raised voices, yelling, threatening, insulting, and even physical actions such as clenched or raised fists are used in some attempt to assert [[w:Expressions_of_dominance|dominance]] and intimidate or [[w:Coercion|coerce]] someone. The retaliation may be delayed and often escalated into some form of [[Foregoing Revenge|revenge]], spite, or “getting even”. More subtle, but equally damaging forms include [[w:Sarcasm|sarcasm]], wise guy responses, [[w:Ridiculous|mocking]], tit-for-tat, and other verbal or psychological insults. The inevitable result is increased anger, shown here as the path leading from anger to enraged, from enraged to overtly violent, and from resentful to angry. Attempts to justify retaliation are often based on a mistaken belief that it is necessary to “let off steam”, “teach a lesson”, “get even”, or “save face”. We recommend you look at the map, decide where you want to go, and choose another path to get there. Although an “anger display” is not helpful, it is often important to describe to your advisory why you are feeling an urgent need for change. Describe your needs constructively, referring to factual evidence and recommending an effective course of action. '''Enraged:''' Tempers are flaring. You are obsessed with anger. You are not thinking clearly and revenge, retaliation, getting, even, teaching a lesson, and other form of retaliation, [[Foregoing Revenge|revenge]], and escalation are the only alternatives you can think of. You better calm down and think this through again. De-escalate the hostilities now and avoid further destruction. The orange color represents moderate to high danger levels. '''De-escalation:''' Walk away, calm down, count to 10, or 100, or 1,000, take deep breaths, ask for help, hold your arms and hands down at your side, pray, [[Apologizing|apologize]], fawn, or ignore the provocation. Do not continue an anger display, make threats, communicate insults, mock, retaliate, vent, use sarcasm, snipe, get in the last word, or provoke violence. Tips for dealing with angry people that can help de-escalate a situation were provided by Marrek Solutions, Inc., and by Paul Mitchell and Rachel Green. When experiencing anger in another, acknowledge it and calmly help the person analyze and express it. These phrases may help: *“I see you may be angry. I regret that. Please tell me if there is anything else I can do that would be helpful to you.” *“I would be happy to talk to you now or at later time about how you feel about this.” '''Overtly Violent:''' Ranging in intensity from a [[w:Tantrum|tantrum]], to disrespectful or obscene gestures, verbal abuse, grabbing, shoving, slapping, hitting, biting, punching, destroying property, bar room brawls, [[w:Road_rage|road rage]], [[w:Terrorism|terrorism]], [[w:Lynching|lynching]], and [[w:Nuclear_warfare|thermonuclear war]], this unfortunate violent condition is where too many anger paths lead. De-escalate now. The red color represents high to extreme danger levels. '''Non-resolution:''' When you hear “Oh, its nothing, really it isn't” for the 100^th time, it seems it must be something, really it is. Whether through inaction, avoidance, submission, or [[w:Rumination_(psychology)|rumination]], you have not taken action but you certainly have not forgotten the insult. You are holding tightly to a grudge and doing nothing to resolve it. You dream of [[Foregoing Revenge|revenge]]. Stop paying the price every day and learn from [[w:Augustine_of_Hippo|St. Augustine]] when he said: “Resentment is like taking poison and hoping the other person dies.” Take effective steps now to reconcile the grievance. '''Resentful:''' Unresolved anger leads to resentment and often [[w:Revenge|revenge]]. You are not over it, there is no denying it, you remain bitter and still harbor negative thoughts, bad feelings, plans for [[Foregoing Revenge|revenge]], and ill-will continues to fester. You are holding a grudge and are “hooked on anger”;. The anger has become a destructive recurring pattern. It may even be affecting your health. Resignation is not a solution, so end your suffering with a [[Transcending Conflict|reconciliation]]. St. Augustine said: “Resentment is like taking poison and hoping the other person dies.” Take effective steps now to reconcile the grievance. The orange color represents moderate to high danger levels. '''Resignation:''' You are resigned to resentment when you tell yourself: “Well I guess I'll just have to ignore it or live with it”. But if you are still bothered by unresolved anger, you are resentful and not OK. Take steps toward a [[Transcending Conflict|reconciliation]]. '''Challenge:''' The slight could have been ignored or easily resolved, but instead it was used as an opportunity to create a show down, the classic “[http://emotionalcompetency.com/dominancecontest.htm dominance contest]” where someone has to lose. If I can prevail, I may be OK, although you are not. But if you prevail and I capitulate, then I become resentful, and the problem is not resolved. “It is often better not to see an insult than to avenge it”. '''Declined:''' When a challenge is offered you can often decline; just don't take the bait. If the gauntlet is thrown down, either ignore it or reach over, pick it up and simply say “you seem to have dropped your glove”. Be careful not to smile, gloat, show sarcasm, or otherwise [[w:Humiliation|humiliate]] or insult your adversary here, or you will quickly escalate the situation. [[File:Hamilton-burr-duel.jpg|thumb|Alexander Hamilton died in a duel. He could have chosen a different path.]] '''Dominance Contest:''' This is also know as the “show down” or “stand off”. A dominance contest either establishes or challenges the present dominance hierarchy. It is a public test, generally of fighting ability or some other form of power, to determine the relative ranking of the two contestants. It is often a form of rebellion. Rams butt horns, wolves may fight to the death, countries go to war, Coke and Pepsi spend millions on advertising, and [[w:Alexander Hamilton|Alexander Hamilton]] died in a [[w:Duel|duel]]. Don't play this costly game unless you know you can win, and if that is the case why even bother? The orange color represents moderate to high danger levels. '''You Prevail:''' and I [[w:Capitulation_(surrender)|capitulate]]. You win and I have lost the dominance contest and run away with my tail between my legs. I am now resentful and my first thoughts are of [[Foregoing Revenge|revenge]] and retaliation. '''I Prevail:''' and you [[w:Capitulation_(surrender)|capitulate]]. I win and you lose, but the problem is not resolved. Take time to empathize and understand how this feels to the loser. His first thoughts will be to retaliate. The only way to win is not to play this game. '''Resolution:''' This is the difficult path to the only satisfactory solution. Anger is urging you to act on your sense of [[Virtues/Justice|justice]]. Take the time to calm down, cool off, [[Appraising Emotional Responses|reappraise]] and revalidate the justice principle, gather [[Evaluating Evidence|evidence]] and share your viewpoint thoughtfully with your adversary, and plan a constructive path to change. The beginning of this course describes the analysis steps that can lead to a satisfactory resolution and constructive change. It is likely that a resolution will require you [[What you can change and what you cannot|to change]]. '''Passive-aggression:''' Wanting to look good while doing bad is a popular response to anger. But this [[w:Passive-aggressive_behavior|passive-aggressive behavior]] leads to a covertly violent state that can be as destructive over time as an overtly violent state. '''Covertly-Violent:''' Who me? I didn't do a thing. Inaction can be as hostile as overt violence when it is done as a covert form of retaliation. [[w:Passive-aggressive_behavior|passive-aggressive behavior]] has been refined to a fine art form by some very angry and insincere people who work hard at appearing polite, [[w:Kindness|kind hearted]], and [[Virtues/Civility|civilized]]. [[w:Stonewalling|Stonewalling]] is an especially destructive form. Passive aggressive-behavior is particularly volatile when it is used in a relationship with an overtly violent person. The red color represents high to extreme danger levels. '''Venting:''' You'll gladly tell anyone who will listen about your [[w:Grievance|grievances]], so why won't you take steps toward an effective resolution? Talking ''about'' your adversary is not helpful, unless you are developing a plan for a [[Transcending Conflict|constructive resolution]]. Talking ''to'' your adversary can be very helpful. '''Reconciliation:''' Remove your burden of unresolved anger. Ideally you will have the opportunity to accept a sincere, complete, and timely [[Apologizing|apology]] from the person you are angry with. Unfortunately a true apology may never happen, or may not happen soon. Short of an apology, perhaps you can recognize that the person you are angry with is truly [[w:Remorse|remorseful]] even if they do not apologize. You may [[Appraising Emotional Responses|reappraise]] the situation and recognize that the insult was unintended, unfounded, trivial, meant in jest, or sincere and useful feedback. You can always take steps yourself to reconcile your anger. Why not [[Forgiving|forgive]] the grievance and let go of your anger; this is about you, not them. Let go and get on with your life. Don't require that: 1) you teach them a lesson, or 2) they make the first move, or 3) they show true remorse, or 4) they change. Take [[Living_Wisely#Personal_Responsibility|responsibility]] for how you feel and how you live your life, [[Forgiving|forgive]] them and move on. St. Augustine said: “Resentment is like taking poison and hoping the other person dies.” Take effective steps now to reconcile the grievance. '''Shunning:''' Many years ago when people struggled to survive in small groups or tribes being [[w:Shunning|shunned]] or cast out of the group was a very severe punishment that often resulted in death. Human nature and social customs seem to have held on to various forms of [[w:Ostracism|ostracizing]] as punishment. Severing communications, choosing a [[w:Scapegoating|scapegoat]], and withdrawal are common forms of shunning. Today it is counterproductive and dysfunctional approach to resolving differences. Problems are solved by [[Practicing Dialogue|increasing communication]], not through isolation, transferring blame, severed communication, or withdrawal. The most important conversations may be the ones that are the most difficult. '''Isolated:''' While communications are severed there is little or no chance of solving problems and reconciling differences. Open up the communications lines, perhaps through some [[w:Olive_branch|peace offering]]. Don't make the mistake of replacing resentment with alienation. The blue color represents the coldness of isolation. '''Peace Offering:''' Make the first move. Offer some small gift (e.g. [[w:Olive_branch|olive branch]]) or [[w:Courtesy|courtesy]] (e.g. a sincere smile) to your adversary. Open up the communications channel and begin to reconcile the grievance. '''Sniping:''' Poking and jabbing your adversary at every opportunity, including a barb or insult in every conversation, and constantly finding opportunities to renew the resentments will not resolve any problems. If you have an issue to resolve, or something to say, [[Practicing Dialogue|address the person]] directly and explicitly. === Assignment === #Notice the next time you feel angry. #Locate yourself on the paths of anger chart. #Choose a constructive path as your move through each anger state. #Resolve your anger constructively. #Become [[Emotional Competency|emotionally competent]]. == Display Rules == [[w:Display_rules|Display rules]] guide us in making the distinction between what you are feeling and what you are sharing. Most of us learn not to express anger visibly to those who hold power over us. Anger is also generally not displayed in polite company. == Facial Expression == [[File:Waldemar Ritter 2015.jpg|thumb|Professor Waldemar Ritter demonstrates an anger expression.]] An angry expression sends the clear signal: back off, I am prepared to attack. The [[w:Facial_expression|facial expression]] of anger has these distinctive features: *Eyebrows pulled down together, *Wide open, glaring eyes, *Upper eyelids raised in a stare, *Lips wide open to form a rectangle, or *tightly closed with the red margins of the lips becoming narrower, and the lips becoming thinner. === Assignment === #Notice the next time encounter an angry person. #Stay calm. #Act constructively to deescalate and resolve the tension. It is often [[Wisdom|wise]] to retreat unobtrusively. == Aesthetic Representations == Sharp angles, loud sounds, discordant sounds, and the color red represent anger. == Primal Messages == A typical response to anger sends the primal messages of: retreat, dislike, unsafe, halt, displeased, dominant, strong, unfriendly, aggressive, defiant, foe, fearful, threatened, urgent, important, disapprove. == Further Reading == Students wishing to learn more about resolving anger may be interested in reading the following books: *{{cite book |last1=Lazarus |first1=Richard S. |last2=Lazarus |first2=Bernice N.| date= |title=Passion and Reason: Making Sense of Our Emotions |publisher=Oxford University Press |pages=336 |isbn=978-0195104615 }} *{{cite book |last=Ekman |first=Paul |date=March 20, 2007 |title=Emotions Revealed: Recognizing Faces and Feelings to Improve Communication and Emotional Life |publisher=Holt Paperbacks |pages=320 |isbn=978-0805083392 |author-link=w:Paul_Ekman }} *{{cite book |last1=Ortony |first1=Andrew |last2=Clore |first2=Gerald L. |last3=Collins |first3=Allan |date=May 25, 1990 |title=The Cognitive Structure of Emotions |publisher=Cambridge University Press |pages=226 |isbn=978-0521386647 }} *{{cite book |last=Goleman |first=Daniel |date=March 30, 2004 |title=Destructive Emotions: A Scientific Dialogue with the Dalai Lama |publisher= |pages=448 |isbn=978-0553381054 |author-link=w:Daniel_Goleman }} *{{cite book |last=Rosenberg |first=Marshall B. |date=September 1, 2015 |title=Nonviolent Communication: A Language of Life, 3rd Edition: Life-Changing Tools for Healthy Relationships |publisher=PuddleDancer Press |pages=264 |isbn=978-1892005281}} *{{cite book |last=Beck |first=Aaron T. |date=August 22, 2000 |title=Prisoners of Hate: The Cognitive Basis of Anger, Hostility, and Violence |publisher=Harper Perennial |pages=368 |isbn=978-0060932008 }} *{{cite book |last=Enright |first=Robert D. |date=September 15, 2001 |title=Forgiveness is a Choice: A Step-by-Step Process for Resolving Anger and Restoring Hope |publisher=APA LifeTools |pages=299 |isbn=978-1557987570 }} *{{cite book |last1=Stearns |first1=Carol Zisowitz |last2=Stearns |first2=Peter N. |date=October 1, 1986 |title=Anger: The Struggle for Emotional Control in America's History |publisher=University of Chicago Press |pages=304 |isbn=978-0226771519 }} *[http://robertmasters.com/ESSAY-pages/Compassion-Wrath.htm Compassionate Wrath: Transpersonal Approaches to Anger], Robert Masters *[http://buddhism.kalachakranet.org/anger.html Anger and Aversion], a Buddhist view. *{{cite book |last=Kidder |first=Rushworth M. |date=April 1, 1994 |title=Shared Values for a Troubled World: Conversations with Men and Women of Conscience |publisher=Jossey-Bass |pages=332 |isbn=978-1555426033 }} *[http://www.apa.org/topics/controlanger.html Controlling Anger -- Before It Controls You], An American Psychological Association on-line topic. == Notes == <references/> {{Emotional Competency}} [[Category:Life skills]] [[Category:Applied Wisdom]] [[Category:Philosophy]] [[Category:Peace studies]] [[Category:Humanities courses]] inhrbjxl4gas57bf0zhrxzk7udncdfx 0 264954 2719981 2719872 2025-06-28T22:24:47Z Scogdill 1331941 2719981 wikitext text/x-wiki ==Also Known As== * Family name: Wellesley * Earl Cowley (created in 1857) ** Henry Richard Charles Wellesley, 1st Earl Cowley (1857 – 15 July 1884) ** William Henry Wellesley, 2nd Earl Cowley (15 July 1884 – 28 February 1895)<ref name=":0">"William Henry Wellesley, 2nd Earl Cowley." ''The Peerage: A Genealogical Survey of the Peerage of Britain as well as the Royal Families of Europe''. Person page 1093: https://www.thepeerage.com/p1093.htm#i10927.</ref> ** Henry Arthur Mornington Wellesley, 3rd Earl Cowley (1895 – 1919) * Viscount Dangan (a subsidiary title of the Earl of Cowley ** William Henry Wellesley (– 15 July 1884)<ref name=":0" /> ** Henry Arthur Mornington Wellesley, Earl Cowley (15 July 1884 – 1895)<ref name=":2">"Henry Wellesley, 3rd Earl Cowley." ''Wikipedia'' (28 May 2025) https://en.wikipedia.org/wiki/Henry_Wellesley,_3rd_Earl_Cowley.</ref> ==Acquaintances, Friends and Enemies== ==Timeline== '''1888''', Henry Wellesley, Viscount Dangan was sued for breach of promise by actor and dancer Phyllis Broughton, "Gaiety Girl" (performers at the Gaiety Theatre known for their stylishness and respectability).<ref name=":2" /> '''1889 December 17, Tuesday''', Henry Wellesley, [[Dangan-Neville Wedding|Viscount Dangan and Lady Violet Nevill married]]. '''1897 February 2''', Lady Violet Nevill Wellesley, Viscountess Dangan divorced Henry Wellesley, Viscount Dangan for "misconduct."<ref name=":2" /> '''1905 December 14''', [[Social Victorians/People/Arthur Stanley Wilson|Hon. Millicent Florence Eleanor Wilson]] and Henry Arthur Mornington Wellesley, 3rd Earl Cowley married in Colombo, Sri Lanka (then called Ceylon).<ref name=":1">"Hon. Millicent Florence Eleanor Wilson." {{Cite web|url=https://www.thepeerage.com/p2912.htm#i29114|title=Person Page|website=www.thepeerage.com|access-date=2021-09-19}} https://www.thepeerage.com/p2912.htm#i29114.</ref> == Demographics == * Nationality: English ==Family== * Henry Richard Charles Wellesley, 1st Earl Cowley (17 June 1804 – 15 July 1884) * Olivia Cecilia FitzGerald Wellesley (d. 1885) # William Henry Wellesley, Viscount Dangan and 2nd Earl Cowley (25 August 1834 – 28 February 1895) # Total 2 daughters and 3 sons # Lady Feodorowna Cecilia Wellesley (1838–1920) * William Henry Wellesley, Viscount Dangan and 2nd Earl Cowley (25 August 1834 – 28 February 1895)<ref name=":0" /> * Emily Gwendoline Williams (July 1839 – 9 November 1932)<ref>"Emily Gwendoline Williams." ''The Peerage: A Genealogical Survey of the Peerage of Britain as well as the Royal families of Europe''. Person page 1123. https://www.thepeerage.com/p1123.htm#i11225.</ref> *# Lady Eva Cecilia Margaret Wellesley ( – 4 March 1948)<ref>"Lady Eva Cecilia Margaret Wellesley." ''The Peerage: A Genealogical Survey of the Peerage of Britain as well as the Royal Families of Europe''. Person page 1088. https://www.thepeerage.com/p1088.htm#i10875.</ref> *# Henry Arthur Mornington Wellesley, 3rd Earl Cowley (14 January 1866 – 15 January 1919)<ref name=":2" /> * Henry Arthur Mornington Wellesley (14 January 1866 – 15 January 1919) * Lady Violet Nevill () *# Christian Arthur Wellesley, 4th Earl Cowley (1890–1962) *[[Social Victorians/People/Arthur Stanley Wilson|Hon. Millicent Florence Eleanor Wilson]] (4 December 1872 – 29 November 1952)<ref name=":1" /> *#Hon. Henry Gerald Valerian Francis Wellesley (8 August 1907 – 25 December 1981) *Clare Florence Mary (née Stapleton) Buxton () *#Lady Diana Mary Wellesley (c. 1914 – 1984 *#Lady Cecilia Katherine Wellesley (1917–1952) ==Questions and Notes== ==Bibliography== * "Earl Cowley." Wikipedia. https://en.wikipedia.org/wiki/Earl_Cowley (Accessed 2015). * "Henry Wellesley, 1st Earl Cowley." Wikipedia. https://en.wikipedia.org/wiki/Henry_Wellesley,_1st_Earl_Cowley (Accessed 2015). <references /> 1lwt58jhx5hsv2ym7v08nk9bf1kdd76 0 282489 2719969 2719879 2025-06-28T14:32:25Z DavidMCEddy 218607 /* References */ syntax 2719969 wikitext text/x-wiki {{Research project}} :''This brief note is on Wikiversity to invite others to provide alternative responses to this question, adding relevant, substantive references, moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- and raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]].'' ::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]'' What's the best response to a nuclear attack? That's a difficult question. The opposite is much easier: * '''''What's the ''worst'' response to a nuclear attack?''''' [[File:How would a nuclear war between Russia and the US affect you personally? - Future of Life Institute.webm|thumb|Simulation of a nuclear war between Russia and the US.<ref>Tegmark (2023).</ref>]] ::The evidence summarized in this article suggests that the ''worst'' worst response to a nuclear attack would be '''a nuclear response.''' ::If you think otherwise, please revise this article accordingly, subject to the standard Wikimedia Foundation rules of writing from a neutral point of view citing credible sources. Or post your concerns to the "Discuss" page associated with this article. [[File:Percent of the world's population dead from a nuclear war.svg|thumb|Percent of the world's population dead from a nuclear war per simulations by an international team of 10 scientists who specialize in modelling climate, food production, and economics<ref>Xia et al. (2022; see esp. their Table 1).</ref> with models fit thereto. The vertical axis is the percent of the world's population expected to die within a few years after a one-week long nuclear war that injects between 1.5 and 150 Tg (teragrams = million metric tons) of smoke (soot) into the stratosphere, shown on the top axis.<ref>Xia et al. (2022, Table 1) reported "Number of direct fatalities" and "Number of people without food at the end of year 2" out of a total population of 6.7 billion for their simulated year 2010. Two issues with this: First, Xia et al. (2022, Fig. 1) show that the climate impact does not start recovering until year 5 after the nuclear war and has not yet fully recovered 9 years after the war. Thus, few people still alive without food at the end of year 2 will not likely live to year 9. Second, the percentages plotted here are the sums of those two numbers divided by 6.7 billion. The Wikipedia article on [[w:World population|World population]] said the world population in 2010 was 6,985,603,105 -- 7 billion (accessed 2023.08-12). The difference between 6.7 and 7 billion seems so slight that it can be safely ignored, especially given the uncertainty inherent in these simulations and the likelihood that the small populations excluded were probably not substantively different from those included.</ref> The bottom axis is the total megatonnage (number of nuclear weapons used times average yield) simulated to produce the quantity of soot plotted on the top axis. "IND-PAK" marks a range of hypothetical nuclear wars between [[w:India and weapons of mass destruction|India]] (IND) and [[w:Pakistan and weapons of mass destruction|Pakistan]] (PAK). "USA-RUS" marks a simulated nuclear war between [[w:Nuclear weapons of the United States|the US]] (USA) and [[w:Russia and weapons of mass destruction|Russia]] (RUS). "PRK" = a simulated nuclear war in which [[w:North Korea and weapons of mass destruction|North Korea]] (the People's Republic of Korea, PRK) used their existing nuclear arsenal estimated at 30 weapons with an average yield of 17 kt<ref>Estimates of North Korea's nuclear weapons stockpile vary widely, as summarized in the Wikipedia article on [[w:North Korea and weapons of mass destruction|North Korea and weapons of mass destruction]], accessed 2023-08-07. The estimate of 30 weapons averaging 17 kt each seems not far from the middle of the estimate cited in that article. That totals 510 kt (0.51 megatons), roughly a third of smallest nuclear war simulated by Xia et al. (2022).</ref> ''without nuclear retaliation by an adversary'', as recommended in this article.]] This conclusion is supported by the accompanying plot summarizing climate simulations by an international interdisciplinary team of 10 scientists who specialize in mathematical and statistical modeling of climate, food production, and economics. Five of their scenarios describe hypothetical nuclear wars between India and Pakistan that loft between 5 and 47 Tg (teragrams = millions of metric tons) of smoke (soot) to the stratosphere, where it will linger for years covering the globe and reducing the amount of solar radiation reaching the earth. That in turn will substantially reduce the production of food for humans. The resulting impact on the global economy means that between 4 and 40 percent of humanity will likely starve to death if they do not die of something else sooner. A hypothetical nuclear war between the US and Russia could lead to the deaths of roughly 75 percent of humanity with death tolls of roughly 99 percent in the US, Russia, Europe, and China. In any of these scenarios, between 90 and 95 percent of the deaths would be in countries not officially involved in the nuclear exchange.<ref>Xia et al. (2022, esp. their Tables 1 and 2). Their Table 1 gives numbers of fatalities out of a total 2010 "population of the nations used in this study [of] 6,700,000,000." They give 2 simulations of a nuclear war between the US and Russia, which would produce an estimated 150 Tg (teragrams = million metric tonnes) leading to the deaths of 5.341 and 5.081 billion people, respectively. The smaller number is over 75 percent of 6.7 billion in the study, and almost 75 percent of the 2010 [[w:World population|world population]] of 7 billion.</ref> This claim is clearer, more succinct, and stronger than the [[Wikisource:Joint Statement of the Leaders of the Five Nuclear-Weapon States on Preventing Nuclear War and Avoiding Arms Races|Joint Statement of the Leaders of the Five Nuclear-Weapon States on Preventing Nuclear War and Avoiding Arms Races]], "that a nuclear war cannot be won and must never be fought", issued 2022-01-03 by the leaders of the first five nuclear-weapon states.<ref>[[Wikisource:Joint Statement of the Leaders of the Five Nuclear-Weapon States on Preventing Nuclear War and Avoiding Arms Races]]. See also Borger (2022). Douthat (2022) discussed the [[w:2021-2022 Russo-Ukrainian crisis|current Ukraine crisis]] in [[w:The New York Times|''The New York Times'']]. He concluded that for us (presumably the US and perhaps its NATO allies) "To escalate now against a weaker adversary [Russia], one less likely to ultimately defeat us and more likely to engage in atomic recklessness if cornered, would be a grave and existential folly."</ref> This repeated a statement made 1987-12-11 by US President [[w:Ronald Reagan| Ronald Reagan]] and USSR head of state [[w:Mikhail Gorbachev|Mikhail Gorbachev]].<ref><!-- Joint statement by Reagan, Gorbachev -->{{cite Q|Q111845607}} Reagan made that same statement 1984-01-25 in his [[Wikisource:Ronald Reagan's Fourth State of the Union Address|fourth State of the Union Address]].</ref> In the following we review the evidence for and against this claim and then comment on the credibility of the logic that led to the creation of the world's current nuclear arsenals and seems to be driving the current "modernization" programs in the US, Russia, China and elsewhere. == Summary of research on the consequences of a nuclear war == It is theoretically possible that a nuclear exchange would end like [[w:World War II|World War II]] with no more than [[w:Atomic bombings of Hiroshima and Nagasaki|two nuclear weapons being used]]. It is also theoretically possible that nuclear weapons in a new war would only target deserted areas like [[w:List of nuclear weapons tests|the locations where more than 2,000 tests of nuclear weapons]] have been conducted so far.<ref>For a "[[w:List of nuclear weapons tests|List of nuclear weapons tests]]", see the Wikipedia article by that title (accessed 2023-07-06).</ref> Either of those scenarios would increase the level of harmful background radiation worldwide leading to increases in the rates of cancer, birth defects and genetic mutations, but would otherwise not likely have an immediate impact a large portion of humanity.<ref>Johnston (2001) reported that only 521 of the more than 2,000 nuclear weapons tests were above ground. If 521 explosions of nuclear weapons in deserted places have not generated a substantive impact on human health, it seems unlikely that a nuclear war involving a few thousand explosions of nuclear weapons in deserted areas would be dramatically worse.</ref> However, a nuclear war with such negligible results is highly unlikely. More likely is the deaths in a few hours or days of tens or hundreds of millions of humans.<ref>The "Number of direct fatalities" in a nuclear war lasting a week ranged from 27 to 360 million in simulations summarized in Xia et al. (2022, Table 1).</ref> More would die of radiation poisoning over the next few months and years.<ref>Ellsberg (2017, pp. 2-3) includes a graph that the Joint Chiefs Joint Chiefs of Staff produced in the Spring of 1961 to answer President Kennedy's question, "If your plans for a general [nuclear] war are carried out as planned, how many people will be killed in the Soviet Union and China?" This graph was a straight line beginning at 275 million who would die during the initial nuclear exchange with another 8.25 million dying each month for the next six months, totaling 325 million deaths.</ref> If more than a few dozen nuclear weapons are used, then "nuclear war would also produce nearly instantaneous climate change that among other effects, would threaten the global food supply. Even a regional nuclear war ..., such as between India and Pakistan,<ref>Robock et al. (2007); Toon et al. (2019). Of course, a nuclear war could be started accidentally by any nuclear-weapons state, as suggested in the report of an Indian cruise missile that landed 2022-03-10 in Pakistan (Mashal and Masood 2022). See also Xia et al. (2022).</ref> in which less than 3% of the world’s nuclear weapons stockpiles were detonated in urban areas, would suddenly decrease the average global temperature by 1°C–7°C [2°–13°F], precipitation by up to 40%, and sunlight by up to 30%. ... Such a conflict would decrease crop production to an extent that it could seriously threaten world food security and even trigger global famine",<ref>Jägermeyr et al. (2020).</ref> according to Robock and Prager (2021). In theory, crop losses of between 10 and 25 percent for 5-10 years<ref>as predicted by Jägermeyr et al. (2020) and others.</ref> might not threaten a global famine or even an increase in malnutrition if people ate more plant-based foods and less meat. In practice, famines never work that way: There is hoarding, and many who do not die of starvation succumb to diseases or secondary wars driven by the food insecurity, according to Helfand (2013). [[w:Amartya Sen|Nobel Prize Economist Sen]] observed that, "no famine has ever taken place ... in a functioning democracy".<ref>Sen (1999, p. 32). Later on p. 178, he stated similarly, "there has never been a famine in a functioning multiparty democracy."</ref> This generalizes the observation that Ireland was a ''net food exporter'' during its infamous potato famines of the nineteenth century.<ref>e.g., Woodham-Smith (1962).</ref> Xia et al. (2022, Table 1) estimated that between 4 and 85 percent of humanity would starve to death if they did not die of something else sooner in the nuclear wars they simulated, with ''between 90 and 95 percent of the fatalities being in countries not directly involved in the hostilities.'' In the spring of 1961, "The total death toll as calculated by the Joint Chiefs of Staff [top US military leaders], from a U.S. first strike aimed at the Soviet Union, its Warsaw Pact satellites, and China, would be roughly six hundred million dead. A hundred Holocausts", according to Daniel Ellsberg, who served as a nuclear war planner for presidents Eisenhower, Kennedy, Johnson and Nixon<ref>Ellsberg (2017, esp. pp. 2-3) noted that 325 million would die in the Soviet Union and China and another couple hundred million in neighboring countries, totalling six hundred million.</ref> before releasing [[w:The Pentagon Papers|"The Pentagon Papers"]] in 1971. Six hundred million was roughly 20 percent of the total human population on earth in 1961, and that didn't count any in the US who might be killed in retaliation. In 1957, roughly 4 years earlier, Mao Zedong, then the Chairman of the People's Republic of China, had reportedly said that a nuclear war could kill a third of humanity, perhaps half, "but imperialism would be razed to the ground, and the whole world would become socialist."<ref>Dikötter (2010). See also Halimi (2018), which gives the date as 1957. There is some controversy about this quote; see the Wikipedia article on [[w:Mao Zedong|"Mao Zedong"]], accessed 2022-03-02.</ref> Turco et al. (1983) published the first predictions of a ''[[w:nuclear winter|nuclear winter]]'' based on climate modeling that considered smoke anticipated from fires started by a massive nuclear weapons exchange between the US and the Soviet Union. They found that "average light levels can be reduced to a few percent of ambient and land temperatures can reach -15° to -25°C [5° to -4°F]" with smoke transported from the Northern to the Southern Hemisphere, all of which "could pose a serious threat to human survivors and to other species." Various teams have published comparable analyses since then with different and increasingly sophisticated models, beginning with Aleksandrov and Stenchikov (1983), with similar conclusions.<ref>Coup et al. (2019, p. 8522).</ref> Coup et al. (2019) predicted hard freezes ''in the summer'' in most of the Northern Hemisphere including the US, Russia, and most of Europe during the first three years following such a war, where temperatures drop below −4°C [25°F], making it impossible to grow crops in those regions. China would suffer a similar fate, with only its southeast portion remaining above freezing in the summer. Much of Southern Mexico, Central and South America, and the Southern Hemisphere would also be negatively impacted, but not to the same extent. These climate modeling results make Mao's predictions from 1957 seem wildly optimistic: Any humans in the US, Canada, or most of Eurasia who survived the nuclear exchange would have extreme difficulties finding enough to eat -- "imperialism razed to the ground", according to Mao. However, crop yields in most of the rest of the world would also be extremely depressed, which Mao had not considered. The results would threaten famine vastly worse than what has been predicted following a nuclear war between India and Pakistan.<ref>Ellsberg said that 98 or 99 percent of humanity would starve to death if they did not die of something else sooner (Ellsberg et al. 2017). Coup et al. (2019) and Xia et al. (2022) conclude that it won't be quite that bad but will still pretty grim.</ref> Of course, no one knows for sure how many people would die directly and indirectly from a nuclear war. However, it should be obvious to at least some if not most people that the ''worst'' response to a nuclear attack would be a nuclear response: * A nuclear response to a nuclear "warning shot" with minimal destruction could too easily escalate until the nuclear arsenals of all parties were expended and the life expectancy of all survivors worldwide was dramatically reduced. * Alternatively, a nuclear response to a massive first strike against a thousand cities would most likely ''increase'' the death toll and reduce the life expectancy of survivors ''in the country responding with nuclear weapons'' (and, of course, in other countries not officially involved). * It is possible that a nuclear response could deter further uses of nuclear weapons and reduce the length and severity of the war and its global impact. However, this outcome seems unlikely given the record of history. Turcotte (2022) concluded that if the 2022 Ukraine 'conflict ends without the annihilation of our species, it should nonetheless be regarded as a planet-wide near-death experience, and the “Peoples of the United Nations” should demand the total elimination of nuclear weapons as quickly as humanly possible, as well as the establishment of new common security measures that will move us much closer to sustainable peace throughout the world.' In spite of this concern, Turcotte recommended military action to support Ukraine but short of declaring war on Russia. Leading experts have made alarming comments about the likelihood of a nuclear attack, possibly by a terrorist organization. In 2004 Bruce Blair, president of the [[w:Center for Defense Information|Center for Defense Information]] wrote: "I wouldn't be at all surprised if nuclear weapons are used over the next 15 or 20 years, first and foremost by a terrorist group that gets its hands on a [[w:Russia and weapons of mass destruction|Russian]]" or [[w:Pakistan and weapons of mass destruction|Pakistani nuclear weapon]].<ref><!--Nicholas D. Kristof (2004) A Nuclear 9/11, NYT-->{{cite Q|Q111906710}}</ref> Other experts seemed even more concerned: A nuclear terrorist attack in the US was considered "more likely than not" within the next five to ten years, according to Professor [[w:Robert Gallucci|Robert Gallucci]] of the [[w:Georgetown University School of Foreign Service|Georgetown University School of Foreign Service]] in 2006 or in the next decade per former U.S. Assistant Secretary of Defense [[w:Graham Allison|Graham Allison]] in 2004.<ref><!-- Ordre Kittrie (2007) Averting Catastrophe: Why the Nuclear Non-proliferation Treaty is Losing its Deterrence Capacity and How to Restore It -->{{cite Q|Q111906652}}</ref> The Wikipedia article on "[[w:National Response Scenario Number One|National Response Scenario Number One]]" describes "the United States federal government's planned response to a nuclear attack." It focuses primarily on "the possible detonation of a small, crude nuclear weapon by a terrorist group in a major city, with significant loss of life and property."<ref>Accessed 2022-05-08, when it cited <!-- Jay Davis (2008) After A Nuclear 9/11 -->{{cite Q|Q111905675}}, <!-- Brian Michael Jenkins (2008) A Nuclear 9/11? -->{{cite Q|Q111906145}}</ref> That article discusses preparing for a nuclear attack but not how to respond. Nevertheless, if the ''worst'' response to a nuclear attack is a nuclear response, that has other policy implications for leaders of nuclear ''and non-nuclear'' countries world wide. However, an analysis of those implications will be left for future work.<ref>Turcotte (2022) offered some suggestions. Recommendations more consistent with the analysis here is the <!--Veterans For Peace Nuclear Posture Review -->{{cite Q|Q111141993}} They mention the "[[w:Treaty on the Prohibition of Nuclear Weapons|Treaty on the Prohibition of Nuclear Weapons]]", supported by the [[w:International Campaign to Abolish Nuclear Weapons|International Campaign to Abolish Nuclear Weapons (ICAN)]].</ref> == Credibility of military leaders and national security experts == {{main|Expertise of military leaders and national security experts}} * ''Never attribute to malice that which is adequately explained by stupidity.'' ([[w:Hanlon's razor|Hanlon's razor]]) * ''Never attribute to malice or stupidity that which can be explained by moderately rational individuals following incentives in a complex system.'' (Hubbard's clumsier correlary.<ref>Hubbard (2020, pp. 81-82).</ref>) The history of armed conflict should raise questions about the credibility of those advocating use of military force: In all major armed conflicts in history, at least one side has lost. Often the official winners lost substantially more than they gained. === Research on expertise === The history of armed conflict is consistent with the research by Kahneman and Klein (2009) in their conclusion that :''expert intuition is learned from frequent, rapid, high-quality feedback.'' In particular, military leaders in combat can get frequent, rapid high-quality feedback on their ability to deliver death and destruction to designated targets. However, no one can get such feedback about how to win wars or how to ''promote broadly shared peace and prosperity for the long term.'' This is discussed in more detail in the Wikiversity article on "[[Expertise of military leaders and national security experts]]". That article documents how experts without such feedback can be beaten by simple rules of thumb developed by intelligent lay people.<ref>Kahneman et al. (2021) report that with some data, a statistical model fit often does better. With lots of data, artificial intelligence systems can do even better. This extends the work of [[w:Paul E. Meehl#Clinical versus statistical prediction|Meehl (1954)]]. Hubbard (2020) and [[w:Superforecasting: The Art and Science of Prediction|Tetlock and Gardner (2015)]] describe things one might do to improve their intuition.</ref> As the time since the [[w:Atomic bombings of Hiroshima and Nagasaki|atomic bombings if Hiroshima and Nagasaki]] increases, the ''intuition'' that political and military leaders have about nuclear weapons gets worse, because that history tells them that they can use more military force, even threatening to use nuclear weapons, without seriously risking a nuclear war. That intuition increasingly threatens the entirity of humanity. === Increasing risks with nuclear proliferation === Narang and Sagan, eds. (2022) ''The Fragile Balance of Terror: Deterrence in the New Nuclear Age'' includes 8 chapters by 12 authors reviewing the literature on different aspects of nuclear deterrence today. They raised many questions about the applicability of [[w:Cold War|Cold War]] analyses of deterence in an age with [[Forecasting nuclear proliferation|an increasing number of nuclear weapon states]]. They mentioned numerous concerns including the following: * [[w:2008 Mumbai attacks|During terrorist attacks in Mumbai in 2008]], someone called called Pakistani president Zardari claiming to be Indian foreign minister Mukherjee threatening to attack Pakistan. That crises was diffused without escalation after US secretary of state Condoleezza Rice called Mukherjee, who assured her that he had not placed such a call, and India was ''not'' planning to attack Pakistan. If someone claiming to be a US official had placed a similar call to Kim Jong Un while Donald Trump was President of the US, the result may not have been as benign.<ref>Narang and Sagan (2022, p. 241).</ref> * [[w:2018 Hawaii false missile alert|"In January 2018, the Hawaii emergency management system issued an incoming missile warning alert]] adding, 'this is not a drill.'" The US did not respond, because (a) they had redundant early warning systems that did not indicate an incoming missile, (b) professional operators in Hawaii promptly acknowledged the mistake, and (c) no one in the US seriously expected such an attack. If this had happened in North Korea, none of these three restraining conditions were present: (a) They did not have redundant warning systems. (b) Operators are killed, not just fired in North Korea for making a mistake like that. (c) US "President Trump was threatening 'fire and fury' if North Korean nuclear and missile tests continued."<ref>Narang and Sagan (2022, p. 232).</ref> * [[w:2019 Balakot airstrike|In 2019 India bombed an alleged terrorist training camp in Balakot]], Pakistan. This was "the first time a nuclear weapons state has bombed the undisputed territory of another nuclear weapons state."<ref>Narang and Sagan (2022, pp. 231-232).</ref> * [[w:2020–2021 China–India skirmishes|In 2020, Chinese and Indian troops engaged in hostilities along their disputed border]] with fatalities on both sides, "for the first time in almost half a century. Intense conflict between three nuclear powers simultaneously is no longer a remote possibility.<ref>Narang and Sagan (2022, p. 232).</ref> Beyond this, [[w:Richard Ned Lebow|Richard Ned Lebow]] said, "There’s all kinds of empirical evidence that a deterrence strategy is as likely to provoke the behavior it seeks to prevent as not."<ref>Lebow et al. (2023). See also Lebow (2020, ch. 4).</ref> === System accidents === The concept of "normal accidents" or "[[w:system accident|system accidents]]" seems important here. Research in that area has established that ''it is impossible to design and manage complex systems to ultra-high levels of reliability''. Maintenance on redundant systems is often deferred, because responsible managers are often reluctant to spend money fixing something that works.<ref>e.g., Sagan (1993).</ref> And procedures are sometimes secretly modified by people with different priorities from their management. For example, at least between 1970 and 1974 the codes in US Air Force launch control centers for [[w:Intercontinental ballistic missile|Intercontinental ballistic missiles]] were all set continuously to 00000000.<ref>Ellsberg (2017, p. 61).</ref> This clearly negated the claim that only the President of the US could order the use of US nuclear weapons, secured by secret codes carried in a briefcase (called the [[w:nuclear football|"nuclear football"]]) near the President at all times. Similarly, former US Secretary of Defense William J. Perry has said an actual nuclear attack on the US is far less likely than a report of one generated by a malfunction in the US nuclear command, control, and communications systems.<ref>Perry and Collina (2020). Of course, a nuclear war could be started accidentally by any nuclear-weapons state, as suggested in the report of an Indian cruise missile that landed 2022-03-10 in Pakistan (Mashal and Masood 2022).</ref> A tragic example of a system accident is the [[w:Sinking of MV Sewol|Sinking of MV ''Sewol'']], 2014-04-16. It sank with over twice its rated load under the command of a substitute captain. The regular captain had complained of deferred maintenance threatening the stability of the vessel; he said the company had threatened to fire him if he continued to complain. As of this writing, it has been over 77 years since nuclear weapons were detonated in hostilities. As noted above, that history feeds human intuition that we can safely be more aggressive in developing, deploying and threatening the use of nuclear weapons without seriously risking [[Time to nuclear Armageddon|nuclear Armageddon]]. People who disagree like the [[w:Union of Concerned Scientists|Union of Concerned Scientists]] with their [[w:Doomsday Clock|Doomsday Clock]] are dismissed as unrealistic, like [[w:Chicken Little|Chicken Little]]. == Human psychology and the role of the media == When people are attacked, it can sometimes be difficult to control their responses, which are driven by instinctive reactions often characterized as irrational. Johnson (2004) documented how these instinctive reactions exist, because they provided survival benefits to our ancestors over hundreds of thousands and millions of years of evolutionary history. These instincts may, however, push us into the ''worst'' possible response to a nuclear attack. Worse, major media everywhere have a conflict of interest in honestly reporting on anything (like these research results) that might threaten those who control the money for the media.<ref name='McC+Cagé+Rolnik">McChesney (2004). Cagé (2016). Rolnik et al. (2019). See also "[[Confirmation bias and conflict]]".</ref> Everyone thinks they know more than they do,<ref name=Kahneman>Kahneman (2011).</ref> which makes them easily misled by the media they find credible.<ref>[[Confirmation bias and conflict]]. See also McChesney (2004), Cagé (2016), and Rolnik et al. (2019).</ref> == Probability of a nuclear war == The section on [[Time to nuclear Armageddon#Relevant literature|Relevant literature]] of the Wikiversity article on [[Time to nuclear Armageddon]] includes a table summarizing previous estimates of the probability of a nuclear war. Karger et al. (2023) provides a more extensive study of the probability of a nuclear war and other extistential risks. == Recapitulation == In sum, the worst possible response to a nuclear attack would seem to be a nuclear response. Existing nuclear weapons policies appear to be supported by propaganda that is effective, because it supports the preferences of those who control the money for the media,<ref name='McC+Cagé+Rolnik"/> and because everyone thinks they know more than they do.<ref name=Kahneman/> == Acknowledgements == Thanks to Owen B. Toon, Alan Robock, and presenters at their irregular webinar series on impact on climate of a nuclear war. Of course, any errors and other deficiencies in this article are solely the responsibility of the author. == See also == * [[Expertise of military leaders and national security experts]] * [[Time to nuclear Armageddon]] * [[Forecasting nuclear proliferation]] * [[Time to extinction of civilization]] == References == * <!-- Guardian (2001-10-14) Bush rejects Taliban offer to hand Bin Laden over -->{{cite Q|Q111228506}} * <!-- Aleksandrov and Stenchikov (1983) "On the modeling of the climatic consequences of the nuclear war" -->{{cite Q|Q63229964}} * <!-- Borger (2022) Five of world’s most powerful nations pledge to avoid nuclear war, Guardian -->{{cite Q|Q111011203}} * <!-- Cagé (2016) Saving the media: Capitalism, crowdfunding and democracy (Harvard U. Pr.)-->{{cite Q|Q54640583}} * <!-- Chenoweth and Stephan (2011) Why Civil Resistance Works: The Strategic Logic of Nonviolent Conflict (Columbia U. 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Pr.)-->{{cite Q|Q111097755}} * <!-- Tyler, Tom R., and Yuen J. Huo (2002) Trust in the Law: Encouraging Public Cooperation with the Police and Courts (Russell Sage Foundation)-->{{cite Q|Q106943244}} * <!-- Woodham-Smith, Cecil (1962) The Great Hunger: Ireland 1845-1849 (Harper)-->{{cite Q|Q7737800}} * <!-- Xia et al. (2022) Global food insecurity and famine ... from a nuclear war ...-->{{cite Q| Q113732668}} == Notes == {{Reflist|30em}} [[Category:Original research]] [[Category:Research]] [[Category:Political science]] [[Category:Military]] [[Category:Military Science]] [[Category:Freedom and abundance]] [[Category:psychology]] [[category:Political economy]] 2ytkzgc1j99m8ujmts5388l2zgx6r9s 2 289273 2719971 2719834 2025-06-28T14:43:31Z Dc.samizdat 2856930 /* Sequence of regular 4-polytopes */ 2719971 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|June 2023 - June 2025}} <blockquote>'''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 <math>c</math>, 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 <math>c</math>, 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 <math>c</math> 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 <math>c^\prime = 2c</math>, 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 <math>c</math>. 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.</blockquote> == 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}} <blockquote>Let Q denote a rotation, R a reflection, T a translation, and let Q^''q'' R^''r'' 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 Q² is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> {{spaces|10}}Q^''q'' R^''r''<br> where 2''q'' + ''r'' ≤ ''n'', the number of dimensions.<br> Transformations involving a translation are expressible as:<br> {{spaces|10}}Q^''q'' R^''r'' T<br> where 2''q'' + ''r'' + 1 ≤ ''n''.<br> For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q², 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.</blockquote> If we assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a Q² or a QT, because we can view any QT as a Q² in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a Q². By the same principle, we can view any QT or Q² as an isoclinic (equi-angled) Q² 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 == <blockquote>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}}</blockquote> ...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 <math>c</math>? 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|𝔽₄ 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]].<ref name=Griffiths2008>{{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}}</ref>{{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]],<ref> {{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}}</ref> 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 "isospin" to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated.<ref> {{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 }}</ref> 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''₃&nbsp;=&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 "physical system") 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 "square roots" 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]].<ref>{{cite conference |author1=Bardeen, W. |author2=Fritzsch, H. |author3=Gell-Mann, M. |year=1973 |title=Light cone current algebra, ''π''⁰ decay, and ''e''⁺ ''e''^&minus; 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 & Sons|John Wiley & Sons]] |isbn=0-471-29292-3 |bibcode=2002hep.ph...11388B |url-access=registration |url=https://archive.org/details/scaleconformalsy0000unse/page/139 }}</ref><ref>{{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}}</ref> 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 H₁ protons are fused into an H₂ nucleus consisting of a proton and a neutron. This [[W:beta plus decay|beta plus "decay"]] 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|"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."{{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 <math>R^4</math>, spherical 4-space <math>S^4</math>, 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 === .... === 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: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [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=; "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."}}]}} .... == 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 "in Euclidean spaces of any number of dimensions". Laws of physics should operate in any flat Euclidean space <math>R^n</math> and in its corresponding spherical space <math>S^n</math>. 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="A symmetrical arrangement of eleven 11-cells"}} 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 𝜶₄, the neutron as an 8-point, 16-cell 4-orthoplex 𝛽₄, 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 "not delivered" 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 <math>c</math>. 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 <math>c</math> (along the observer's proper time axis through 4-space), combined with a simple rotation at velocity <math>c</math> (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 <math>c</math>. 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 <math>c</math>. 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 <math>c</math> 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 "edge on". 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 "edge on" so they appear to be densely clustered. The "dense band" 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 4-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 <math>c</math>, 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 <math>c</math>. 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. It made the jump to lightspeed long ago, in whatever big bang its atoms emerged from, and hasn't 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.<ref>{{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}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that formulation 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 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 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 == <blockquote>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.<ref>{{Cite book|author=Carlo Rovelli|title=Seven Brief Lessons on Physics}}</ref></blockquote> 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? <blockquote>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 "Dimensional Analogy."<ref>{{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=}}</ref></blockquote> 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. <blockquote> ::::::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''<ref>{{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|}}</ref> </blockquote> == Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|radius={{radic|1}}|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 "the convex hull of the neighbouring vertices of a given vertex".{{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 "radius" 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}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> 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 "left" 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=; "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]."}} 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^o 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^o bend, or as a straight line with one 60^o 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=; "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.)"}} 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 V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ 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 V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ 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 V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ 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}} V₀ and V₂ 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).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ 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 𝐹₄.}} {{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. 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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}} cn9wiz0t9yymwscnbd1xyamhrcps0rr 2719972 2719971 2025-06-28T14:44:06Z Dc.samizdat 2856930 /* Sequence of regular 4-polytopes */ 2719972 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|June 2023 - June 2025}} <blockquote>'''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 <math>c</math>, 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 <math>c</math>, 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 <math>c</math> 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 <math>c^\prime = 2c</math>, 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 <math>c</math>. 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.</blockquote> == 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}} <blockquote>Let Q denote a rotation, R a reflection, T a translation, and let Q^''q'' R^''r'' 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 Q² is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> {{spaces|10}}Q^''q'' R^''r''<br> where 2''q'' + ''r'' ≤ ''n'', the number of dimensions.<br> Transformations involving a translation are expressible as:<br> {{spaces|10}}Q^''q'' R^''r'' T<br> where 2''q'' + ''r'' + 1 ≤ ''n''.<br> For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q², 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.</blockquote> If we assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a Q² or a QT, because we can view any QT as a Q² in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a Q². By the same principle, we can view any QT or Q² as an isoclinic (equi-angled) Q² 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 == <blockquote>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}}</blockquote> ...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 <math>c</math>? 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|𝔽₄ 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]].<ref name=Griffiths2008>{{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}}</ref>{{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]],<ref> {{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}}</ref> 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 "isospin" to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated.<ref> {{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 }}</ref> 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''₃&nbsp;=&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 "physical system") 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 "square roots" 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]].<ref>{{cite conference |author1=Bardeen, W. |author2=Fritzsch, H. |author3=Gell-Mann, M. |year=1973 |title=Light cone current algebra, ''π''⁰ decay, and ''e''⁺ ''e''^&minus; 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 & Sons|John Wiley & Sons]] |isbn=0-471-29292-3 |bibcode=2002hep.ph...11388B |url-access=registration |url=https://archive.org/details/scaleconformalsy0000unse/page/139 }}</ref><ref>{{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}}</ref> 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 H₁ protons are fused into an H₂ nucleus consisting of a proton and a neutron. This [[W:beta plus decay|beta plus "decay"]] 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|"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."{{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 <math>R^4</math>, spherical 4-space <math>S^4</math>, 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 === .... === 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: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [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=; "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."}}]}} .... == 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 "in Euclidean spaces of any number of dimensions". Laws of physics should operate in any flat Euclidean space <math>R^n</math> and in its corresponding spherical space <math>S^n</math>. 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="A symmetrical arrangement of eleven 11-cells"}} 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 𝜶₄, the neutron as an 8-point, 16-cell 4-orthoplex 𝛽₄, 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 "not delivered" 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 <math>c</math>. 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 <math>c</math> (along the observer's proper time axis through 4-space), combined with a simple rotation at velocity <math>c</math> (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 <math>c</math>. 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 <math>c</math>. 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 <math>c</math> 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 "edge on". 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 "edge on" so they appear to be densely clustered. The "dense band" 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 4-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 <math>c</math>, 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 <math>c</math>. 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. It made the jump to lightspeed long ago, in whatever big bang its atoms emerged from, and hasn't 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.<ref>{{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}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that formulation 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 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 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 == <blockquote>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.<ref>{{Cite book|author=Carlo Rovelli|title=Seven Brief Lessons on Physics}}</ref></blockquote> 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? <blockquote>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 "Dimensional Analogy."<ref>{{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=}}</ref></blockquote> 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. <blockquote> ::::::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''<ref>{{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|}}</ref> </blockquote> == Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|radius=|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 "the convex hull of the neighbouring vertices of a given vertex".{{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 "radius" 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}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> 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 "left" 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=; "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]."}} 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^o 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^o bend, or as a straight line with one 60^o 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=; "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.)"}} 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 V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ 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 V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ 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 V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ 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}} V₀ and V₂ 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).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ 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 𝐹₄.}} {{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. 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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}} ncxmb1tt61wnh2agao869m26n343ht1 2719973 2719972 2025-06-28T14:44:39Z Dc.samizdat 2856930 /* Sequence of regular 4-polytopes */ 2719973 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|June 2023 - June 2025}} <blockquote>'''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 <math>c</math>, 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 <math>c</math>, 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 <math>c</math> 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 <math>c^\prime = 2c</math>, 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 <math>c</math>. 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.</blockquote> == 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}} <blockquote>Let Q denote a rotation, R a reflection, T a translation, and let Q^''q'' R^''r'' 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 Q² is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> {{spaces|10}}Q^''q'' R^''r''<br> where 2''q'' + ''r'' ≤ ''n'', the number of dimensions.<br> Transformations involving a translation are expressible as:<br> {{spaces|10}}Q^''q'' R^''r'' T<br> where 2''q'' + ''r'' + 1 ≤ ''n''.<br> For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q², 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.</blockquote> If we assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a Q² or a QT, because we can view any QT as a Q² in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a Q². By the same principle, we can view any QT or Q² as an isoclinic (equi-angled) Q² 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 == <blockquote>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}}</blockquote> ...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 <math>c</math>? 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|𝔽₄ 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]].<ref name=Griffiths2008>{{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}}</ref>{{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]],<ref> {{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}}</ref> 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 "isospin" to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated.<ref> {{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 }}</ref> 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''₃&nbsp;=&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 "physical system") 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 "square roots" 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]].<ref>{{cite conference |author1=Bardeen, W. |author2=Fritzsch, H. |author3=Gell-Mann, M. |year=1973 |title=Light cone current algebra, ''π''⁰ decay, and ''e''⁺ ''e''^&minus; 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 & Sons|John Wiley & Sons]] |isbn=0-471-29292-3 |bibcode=2002hep.ph...11388B |url-access=registration |url=https://archive.org/details/scaleconformalsy0000unse/page/139 }}</ref><ref>{{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}}</ref> 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 H₁ protons are fused into an H₂ nucleus consisting of a proton and a neutron. This [[W:beta plus decay|beta plus "decay"]] 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|"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."{{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 <math>R^4</math>, spherical 4-space <math>S^4</math>, 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 === .... === 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: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [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=; "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."}}]}} .... == 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 "in Euclidean spaces of any number of dimensions". Laws of physics should operate in any flat Euclidean space <math>R^n</math> and in its corresponding spherical space <math>S^n</math>. 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="A symmetrical arrangement of eleven 11-cells"}} 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 𝜶₄, the neutron as an 8-point, 16-cell 4-orthoplex 𝛽₄, 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 "not delivered" 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 <math>c</math>. 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 <math>c</math> (along the observer's proper time axis through 4-space), combined with a simple rotation at velocity <math>c</math> (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 <math>c</math>. 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 <math>c</math>. 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 <math>c</math> 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 "edge on". 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 "edge on" so they appear to be densely clustered. The "dense band" 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 4-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 <math>c</math>, 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 <math>c</math>. 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. It made the jump to lightspeed long ago, in whatever big bang its atoms emerged from, and hasn't 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.<ref>{{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}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that formulation 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 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 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 == <blockquote>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.<ref>{{Cite book|author=Carlo Rovelli|title=Seven Brief Lessons on Physics}}</ref></blockquote> 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? <blockquote>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 "Dimensional Analogy."<ref>{{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=}}</ref></blockquote> 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. <blockquote> ::::::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''<ref>{{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|}}</ref> </blockquote> == 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 "the convex hull of the neighbouring vertices of a given vertex".{{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 "radius" 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}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> 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 "left" 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=; "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]."}} 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^o 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^o bend, or as a straight line with one 60^o 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=; "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.)"}} 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 V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ 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 V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ 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 V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ 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}} V₀ and V₂ 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).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ 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 𝐹₄.}} {{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. 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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}} shlkn2ihmnevw3ot91poz4sd0xtnasx 2719974 2719973 2025-06-28T14:59:15Z Dc.samizdat 2856930 /* Origins of the theory */ 2719974 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|June 2023 - June 2025}} <blockquote>'''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 <math>c</math>, 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 <math>c</math>, 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 <math>c</math> 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 <math>c^\prime = 2c</math>, 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 <math>c</math>. 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.</blockquote> == 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}} <blockquote>Let Q denote a rotation, R a reflection, T a translation, and let Q^''q'' R^''r'' 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 Q² is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> {{spaces|10}}Q^''q'' R^''r''<br> where 2''q'' + ''r'' ≤ ''n'', the number of dimensions.<br> Transformations involving a translation are expressible as:<br> {{spaces|10}}Q^''q'' R^''r'' T<br> where 2''q'' + ''r'' + 1 ≤ ''n''.<br> For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q², 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.</blockquote> If we assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a Q² or a QT, because we can view any QT as a Q² in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a Q². By the same principle, we can view any QT or Q² as an isoclinic (equi-angled) Q² 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 == <blockquote>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}}</blockquote> ...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 <math>c</math>? 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|𝔽₄ 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]].<ref name=Griffiths2008>{{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}}</ref>{{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]],<ref> {{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}}</ref> 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 "isospin" to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated.<ref> {{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 }}</ref> 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''₃&nbsp;=&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 "physical system") 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 "square roots" 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]].<ref>{{cite conference |author1=Bardeen, W. |author2=Fritzsch, H. |author3=Gell-Mann, M. |year=1973 |title=Light cone current algebra, ''π''⁰ decay, and ''e''⁺ ''e''^&minus; 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 & Sons|John Wiley & Sons]] |isbn=0-471-29292-3 |bibcode=2002hep.ph...11388B |url-access=registration |url=https://archive.org/details/scaleconformalsy0000unse/page/139 }}</ref><ref>{{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}}</ref> 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 H₁ protons are fused into an H₂ nucleus consisting of a proton and a neutron. This [[W:beta plus decay|beta plus "decay"]] 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|"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."{{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 <math>R^4</math>, spherical 4-space <math>S^4</math>, 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 === .... === 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: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [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=; "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."}}]}} .... == 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 "in Euclidean spaces of any number of dimensions". Laws of physics should operate in any flat Euclidean space <math>R^n</math> and in its corresponding spherical space <math>S^n</math>. 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="A symmetrical arrangement of eleven 11-cells"}} 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 𝜶₄, the neutron as an 8-point, 16-cell 4-orthoplex 𝛽₄, 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 "not delivered" 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 <math>c</math>. 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 <math>c</math> (along the observer's proper time axis through 4-space), combined with a simple rotation at velocity <math>c</math> (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 <math>c</math>. 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 <math>c</math>. 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 <math>c</math> 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 "edge on". 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 "edge on" so they appear to be densely clustered. The "dense band" 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 4-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 <math>c</math>, 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 <math>c</math>. 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. It made the jump to lightspeed long ago, in whatever big bang its atoms emerged from, and hasn't 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.<ref>{{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}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." 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 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 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 == <blockquote>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.<ref>{{Cite book|author=Carlo Rovelli|title=Seven Brief Lessons on Physics}}</ref></blockquote> 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? <blockquote>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 "Dimensional Analogy."<ref>{{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=}}</ref></blockquote> 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. <blockquote> ::::::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''<ref>{{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|}}</ref> </blockquote> == 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 "the convex hull of the neighbouring vertices of a given vertex".{{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 "radius" 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}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> 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 "left" 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=; "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]."}} 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^o 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^o bend, or as a straight line with one 60^o 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=; "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.)"}} 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 V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ 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 V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ 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 V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ 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}} V₀ and V₂ 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).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ 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 𝐹₄.}} {{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. 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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}} di15z4q5kmere5t889twa6c3m253xsi 2719975 2719974 2025-06-28T15:00:59Z Dc.samizdat 2856930 /* Origins of the theory */ 2719975 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|June 2023 - June 2025}} <blockquote>'''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 <math>c</math>, 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 <math>c</math>, 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 <math>c</math> 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 <math>c^\prime = 2c</math>, 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 <math>c</math>. 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.</blockquote> == 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}} <blockquote>Let Q denote a rotation, R a reflection, T a translation, and let Q^''q'' R^''r'' 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 Q² is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> {{spaces|10}}Q^''q'' R^''r''<br> where 2''q'' + ''r'' ≤ ''n'', the number of dimensions.<br> Transformations involving a translation are expressible as:<br> {{spaces|10}}Q^''q'' R^''r'' T<br> where 2''q'' + ''r'' + 1 ≤ ''n''.<br> For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q², 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.</blockquote> If we assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a Q² or a QT, because we can view any QT as a Q² in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a Q². By the same principle, we can view any QT or Q² as an isoclinic (equi-angled) Q² 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 == <blockquote>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}}</blockquote> ...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 <math>c</math>? 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|𝔽₄ 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]].<ref name=Griffiths2008>{{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}}</ref>{{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]],<ref> {{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}}</ref> 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 "isospin" to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated.<ref> {{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 }}</ref> 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''₃&nbsp;=&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 "physical system") 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 "square roots" 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]].<ref>{{cite conference |author1=Bardeen, W. |author2=Fritzsch, H. |author3=Gell-Mann, M. |year=1973 |title=Light cone current algebra, ''π''⁰ decay, and ''e''⁺ ''e''^&minus; 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 & Sons|John Wiley & Sons]] |isbn=0-471-29292-3 |bibcode=2002hep.ph...11388B |url-access=registration |url=https://archive.org/details/scaleconformalsy0000unse/page/139 }}</ref><ref>{{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}}</ref> 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 H₁ protons are fused into an H₂ nucleus consisting of a proton and a neutron. This [[W:beta plus decay|beta plus "decay"]] 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|"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."{{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 <math>R^4</math>, spherical 4-space <math>S^4</math>, 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 === .... === 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: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [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=; "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."}}]}} .... == 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 "in Euclidean spaces of any number of dimensions". Laws of physics should operate in any flat Euclidean space <math>R^n</math> and in its corresponding spherical space <math>S^n</math>. 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="A symmetrical arrangement of eleven 11-cells"}} 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 𝜶₄, the neutron as an 8-point, 16-cell 4-orthoplex 𝛽₄, 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 "not delivered" 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 <math>c</math>. 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 <math>c</math> (along the observer's proper time axis through 4-space), combined with a simple rotation at velocity <math>c</math> (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 <math>c</math>. 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 <math>c</math>. 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 <math>c</math> 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 "edge on". 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 "edge on" so they appear to be densely clustered. The "dense band" 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 4-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 <math>c</math>, 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 <math>c</math>. 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. It made the jump to lightspeed long ago, in whatever big bang its atoms emerged from, and hasn't 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.<ref>{{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}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." 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 orthogonal 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 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 == <blockquote>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.<ref>{{Cite book|author=Carlo Rovelli|title=Seven Brief Lessons on Physics}}</ref></blockquote> 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? <blockquote>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 "Dimensional Analogy."<ref>{{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=}}</ref></blockquote> 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. <blockquote> ::::::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''<ref>{{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|}}</ref> </blockquote> == 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 "the convex hull of the neighbouring vertices of a given vertex".{{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 "radius" 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}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> 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 "left" 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=; "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]."}} 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^o 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^o bend, or as a straight line with one 60^o 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=; "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.)"}} 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 V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ 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 V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ 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 V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ 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}} V₀ and V₂ 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).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ 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 𝐹₄.}} {{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. 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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}} 3bora4zftlce5zqhr70wqpbshs1h16o 2719976 2719975 2025-06-28T15:01:33Z Dc.samizdat 2856930 /* Origins of the theory */ 2719976 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|June 2023 - June 2025}} <blockquote>'''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 <math>c</math>, 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 <math>c</math>, 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 <math>c</math> 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 <math>c^\prime = 2c</math>, 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 <math>c</math>. 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.</blockquote> == 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}} <blockquote>Let Q denote a rotation, R a reflection, T a translation, and let Q^''q'' R^''r'' 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 Q² is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> {{spaces|10}}Q^''q'' R^''r''<br> where 2''q'' + ''r'' ≤ ''n'', the number of dimensions.<br> Transformations involving a translation are expressible as:<br> {{spaces|10}}Q^''q'' R^''r'' T<br> where 2''q'' + ''r'' + 1 ≤ ''n''.<br> For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q², 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.</blockquote> If we assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a Q² or a QT, because we can view any QT as a Q² in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a Q². By the same principle, we can view any QT or Q² as an isoclinic (equi-angled) Q² 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 == <blockquote>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}}</blockquote> ...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 <math>c</math>? 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|𝔽₄ 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]].<ref name=Griffiths2008>{{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}}</ref>{{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]],<ref> {{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}}</ref> 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 "isospin" to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated.<ref> {{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 }}</ref> 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''₃&nbsp;=&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 "physical system") 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 "square roots" 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]].<ref>{{cite conference |author1=Bardeen, W. |author2=Fritzsch, H. |author3=Gell-Mann, M. |year=1973 |title=Light cone current algebra, ''π''⁰ decay, and ''e''⁺ ''e''^&minus; 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 & Sons|John Wiley & Sons]] |isbn=0-471-29292-3 |bibcode=2002hep.ph...11388B |url-access=registration |url=https://archive.org/details/scaleconformalsy0000unse/page/139 }}</ref><ref>{{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}}</ref> 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 H₁ protons are fused into an H₂ nucleus consisting of a proton and a neutron. This [[W:beta plus decay|beta plus "decay"]] 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|"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."{{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 <math>R^4</math>, spherical 4-space <math>S^4</math>, 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 === .... === 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: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [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=; "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."}}]}} .... == 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 "in Euclidean spaces of any number of dimensions". Laws of physics should operate in any flat Euclidean space <math>R^n</math> and in its corresponding spherical space <math>S^n</math>. 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="A symmetrical arrangement of eleven 11-cells"}} 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 𝜶₄, the neutron as an 8-point, 16-cell 4-orthoplex 𝛽₄, 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 "not delivered" 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 <math>c</math>. 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 <math>c</math> (along the observer's proper time axis through 4-space), combined with a simple rotation at velocity <math>c</math> (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 <math>c</math>. 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 <math>c</math>. 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 <math>c</math> 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 "edge on". 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 "edge on" so they appear to be densely clustered. The "dense band" 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 4-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 <math>c</math>, 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 <math>c</math>. 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. It made the jump to lightspeed long ago, in whatever big bang its atoms emerged from, and hasn't 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.<ref>{{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}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." 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 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 == <blockquote>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.<ref>{{Cite book|author=Carlo Rovelli|title=Seven Brief Lessons on Physics}}</ref></blockquote> 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? <blockquote>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 "Dimensional Analogy."<ref>{{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=}}</ref></blockquote> 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. <blockquote> ::::::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''<ref>{{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|}}</ref> </blockquote> == 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 "the convex hull of the neighbouring vertices of a given vertex".{{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 "radius" 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}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> 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 "left" 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=; "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]."}} 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^o 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^o bend, or as a straight line with one 60^o 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=; "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.)"}} 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 V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ 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 V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ 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 V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ 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}} V₀ and V₂ 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).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ 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 𝐹₄.}} {{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. 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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}} cr1kw7kl1qdnofe68jh0wurl3b29f1c 2719977 2719976 2025-06-28T15:04:33Z Dc.samizdat 2856930 /* Origins of the theory */ 2719977 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|June 2023 - June 2025}} <blockquote>'''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 <math>c</math>, 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 <math>c</math>, 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 <math>c</math> 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 <math>c^\prime = 2c</math>, 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 <math>c</math>. 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.</blockquote> == 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}} <blockquote>Let Q denote a rotation, R a reflection, T a translation, and let Q^''q'' R^''r'' 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 Q² is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> {{spaces|10}}Q^''q'' R^''r''<br> where 2''q'' + ''r'' ≤ ''n'', the number of dimensions.<br> Transformations involving a translation are expressible as:<br> {{spaces|10}}Q^''q'' R^''r'' T<br> where 2''q'' + ''r'' + 1 ≤ ''n''.<br> For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q², 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.</blockquote> If we assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a Q² or a QT, because we can view any QT as a Q² in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a Q². By the same principle, we can view any QT or Q² as an isoclinic (equi-angled) Q² 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 == <blockquote>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}}</blockquote> ...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 <math>c</math>? 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|𝔽₄ 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]].<ref name=Griffiths2008>{{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}}</ref>{{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]],<ref> {{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}}</ref> 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 "isospin" to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated.<ref> {{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 }}</ref> 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''₃&nbsp;=&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 "physical system") 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 "square roots" 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]].<ref>{{cite conference |author1=Bardeen, W. |author2=Fritzsch, H. |author3=Gell-Mann, M. |year=1973 |title=Light cone current algebra, ''π''⁰ decay, and ''e''⁺ ''e''^&minus; 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 & Sons|John Wiley & Sons]] |isbn=0-471-29292-3 |bibcode=2002hep.ph...11388B |url-access=registration |url=https://archive.org/details/scaleconformalsy0000unse/page/139 }}</ref><ref>{{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}}</ref> 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 H₁ protons are fused into an H₂ nucleus consisting of a proton and a neutron. This [[W:beta plus decay|beta plus "decay"]] 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|"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."{{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 <math>R^4</math>, spherical 4-space <math>S^4</math>, 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 === .... === 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: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [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=; "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."}}]}} .... == 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 "in Euclidean spaces of any number of dimensions". Laws of physics should operate in any flat Euclidean space <math>R^n</math> and in its corresponding spherical space <math>S^n</math>. 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="A symmetrical arrangement of eleven 11-cells"}} 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 𝜶₄, the neutron as an 8-point, 16-cell 4-orthoplex 𝛽₄, 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 "not delivered" 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 <math>c</math>. 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 <math>c</math> (along the observer's proper time axis through 4-space), combined with a simple rotation at velocity <math>c</math> (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 <math>c</math>. 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 <math>c</math>. 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 <math>c</math> 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 "edge on". 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 "edge on" so they appear to be densely clustered. The "dense band" 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 4-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 <math>c</math>, 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 <math>c</math>. 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. It made the jump to lightspeed long ago, in whatever big bang its atoms emerged from, and hasn't 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.<ref>{{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}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." 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 == <blockquote>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.<ref>{{Cite book|author=Carlo Rovelli|title=Seven Brief Lessons on Physics}}</ref></blockquote> 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? <blockquote>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 "Dimensional Analogy."<ref>{{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=}}</ref></blockquote> 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. <blockquote> ::::::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''<ref>{{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|}}</ref> </blockquote> == 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 "the convex hull of the neighbouring vertices of a given vertex".{{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 "radius" 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}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> 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 "left" 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=; "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]."}} 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^o 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^o bend, or as a straight line with one 60^o 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=; "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.)"}} 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 V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ 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 V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ 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 V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ 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}} V₀ and V₂ 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).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ 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 𝐹₄.}} {{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. 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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}} 2kic3kqt0h057syal8an9wiam91bzex 2719978 2719977 2025-06-28T15:07:26Z Dc.samizdat 2856930 /* Revolutions */ 2719978 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|June 2023 - June 2025}} <blockquote>'''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 <math>c</math>, 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 <math>c</math>, 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 <math>c</math> 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 <math>c^\prime = 2c</math>, 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 <math>c</math>. 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.</blockquote> == 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}} <blockquote>Let Q denote a rotation, R a reflection, T a translation, and let Q^''q'' R^''r'' 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 Q² is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> {{spaces|10}}Q^''q'' R^''r''<br> where 2''q'' + ''r'' ≤ ''n'', the number of dimensions.<br> Transformations involving a translation are expressible as:<br> {{spaces|10}}Q^''q'' R^''r'' T<br> where 2''q'' + ''r'' + 1 ≤ ''n''.<br> For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q², 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.</blockquote> If we assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a Q² or a QT, because we can view any QT as a Q² in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a Q². By the same principle, we can view any QT or Q² as an isoclinic (equi-angled) Q² 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 == <blockquote>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}}</blockquote> ...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 <math>c</math>? 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|𝔽₄ 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]].<ref name=Griffiths2008>{{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}}</ref>{{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]],<ref> {{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}}</ref> 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 "isospin" to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated.<ref> {{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 }}</ref> 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''₃&nbsp;=&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 "physical system") 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 "square roots" 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]].<ref>{{cite conference |author1=Bardeen, W. |author2=Fritzsch, H. |author3=Gell-Mann, M. |year=1973 |title=Light cone current algebra, ''π''⁰ decay, and ''e''⁺ ''e''^&minus; 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 & Sons|John Wiley & Sons]] |isbn=0-471-29292-3 |bibcode=2002hep.ph...11388B |url-access=registration |url=https://archive.org/details/scaleconformalsy0000unse/page/139 }}</ref><ref>{{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}}</ref> 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 H₁ protons are fused into an H₂ nucleus consisting of a proton and a neutron. This [[W:beta plus decay|beta plus "decay"]] 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|"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."{{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 <math>R^4</math>, spherical 4-space <math>S^4</math>, 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 === .... === 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: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [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=; "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."}}]}} .... == 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 "in Euclidean spaces of any number of dimensions". Laws of physics should operate in any flat Euclidean space <math>R^n</math> and in its corresponding spherical space <math>S^n</math>. 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="A symmetrical arrangement of eleven 11-cells"}} 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 𝜶₄, the neutron as an 8-point, 16-cell 4-orthoplex 𝛽₄, 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 "not delivered" 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 <math>c</math>. 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 <math>c</math> (along the observer's proper time axis through 4-space), combined with a simple rotation at velocity <math>c</math> (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 <math>c</math>. 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 <math>c</math>. 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 <math>c</math> 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 "edge on". 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 "edge on" so they appear to be densely clustered. The "dense band" 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 <math>c</math>, 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 <math>c</math>. 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. It made the jump to lightspeed long ago, in whatever big bang its atoms emerged from, and hasn't 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.<ref>{{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}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." 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 == <blockquote>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.<ref>{{Cite book|author=Carlo Rovelli|title=Seven Brief Lessons on Physics}}</ref></blockquote> 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? <blockquote>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 "Dimensional Analogy."<ref>{{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=}}</ref></blockquote> 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. <blockquote> ::::::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''<ref>{{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|}}</ref> </blockquote> == 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 "the convex hull of the neighbouring vertices of a given vertex".{{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 "radius" 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}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> 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 "left" 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=; "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]."}} 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^o 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^o bend, or as a straight line with one 60^o 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=; "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.)"}} 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 V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ 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 V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ 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 V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ 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}} V₀ and V₂ 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).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ 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 𝐹₄.}} {{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. 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But it seems surprisingly interesting.<br> It is found in three steps: Creating a [[Boolf-hard#family|family matrix]], getting the senior [[Noble Boolean functions|nobles]] of its rows, and getting their [[Boolf-hard#prefect|prefects]].<br> The first digits of the prefects form the mentor. {{Mentors of Boolean functions/illustrated examples 3-ary}} The following images are the 4-ary equivalents of those above. The results are either the same as above, or the complement. {{Mentors of Boolean functions/illustrated examples 4-ary}} ==Walsh permutations== A Boolean function has a unique mentor for a given arity. The map between mentors can be expressed by four different [[Walsh permutation]]s.<br> <small style="opacity: .7;">(That is, because a BF can be denoted by its truth table or by its Zhegalkin index. In the images above, they are shown red and green.)</small><br> In all there are six Walsh permutations, which shall be denoted by Cyrillic letters: &nbsp;&nbsp;&nbsp; Ж <small>(Zhe)</small>, &nbsp;&nbsp;&nbsp; Ч <small>(Che)</small>, Ш <small>(Sha)</small>, &nbsp; Ю <small>(Yu)</small>, Я <small>(Ya)</small>, &nbsp;&nbsp;&nbsp; Щ <small>(Shcha)</small><br> Their degree is <math>d = 2^{arity}</math>, i.e. they correspond to invertible binary <math>d \times d</math> matrices.<br> <small style="opacity: .7;">(The letter Ж is used in two different ways: On its own it represents the permutation. Followed by an integer it represents a BF, identified by its [[Zhegalkin matrix|Zhegalkin index]].)</small> {{Mentors of Boolean functions/four WP relationships}} Ч and Ш are both self-inverse. Ю and Я are inverse to each other. The matrix of Щ is part of a top right Sierpinki triangle. Its diagonals follow a negated XOR pattern. <small style="opacity: .5;">(See [[c:File:Variadic5 antipode; ESAND (ESNOR twin).svg|image]].)</small><br> The matrix of Ш is almost the same, but with the top right entry inverted.<br> The matrix of Ч is a family matrix. Its top row is related to that of the Ш matrix. <small>The calculation involves the Zhegalkin twin and reversing the truth table.</small> {{Mentors of Boolean functions/code Che matrix}} {{Collapsible START|relationship between the matrix patterns|collapsed gap-above gap-below}} The red family matrix has the pattern of Ч.<br> The green matrix shows the twins of the red rows, and has the pattern of Ю and Я.<br> The blue matrix shows the twins of the green columns, and has the pattern of Ш.<br> [[File:Family of Zhe 38504.svg|400px|center]] {{Collapsible END}} {{Mentors of Boolean functions/code WP vectors}} See the fixed points of Ч and Ш ordered by weight: [[Template:Boolf weight triangle; fixed points of Che|Ч]], [[Template:Boolf weight triangle; fixed points of Sha|Ш]] ===1-ary=== The permutations are all six Walsh permutations of degree 2. {{spaces|5}} Ч = (0, 2, 1, 3) {{spaces|5}} Ш = (0, 1, 3, 2) {{spaces|5}} Щ = I <small>(neutral permutation)</small> {{Collapsible START|permutations|wide collapsed}} {{Mentors of Boolean functions/illustrated WP 1-ary}} {{Collapsible END}} ===2-ary=== Ч = Ш = I <small>(neutral permutation)</small> {{spaces|5}} Ю = Я = Ж {{spaces|5}} <small>Щ = (0, 1, 2, 3, &nbsp; 4, 5, 6, 7, &nbsp; 9, 8, 11, 10, &nbsp; 13, 12, 15, 14)</small> ===3-ary=== {{Mentors of Boolean functions/illustrated WP 3-ary}} {{Collapsible START|code|collapsed light gap-above}} {{Mentors of Boolean functions/code/3-ary}} {{Collapsible END}} {{Mentors of Boolean functions/small WP example 199}} Permutation Я is related to quarter sharpness, which is seen in [[Boolf prop/3-ary/gradual sharpness 1 (quarter sharpness)|these images]]. ===4-ary=== {{Mentors of Boolean functions/illustrated WP 4-ary}} {{Collapsible START|code|collapsed light gap-above gap-below}} {{Mentors of Boolean functions/code/4-ary}} {{Collapsible END}} ==seminars== The mentor is not simply a bijection between Boolean functions, but between the truth tables for a given arity.<br> The permutation from Zhegalkin indices to those of their ''n''-ary mentors is '''Ш_''n'''''. The beginning of Ш_''n''+1 is '''Щ_''n'''''. <small style="opacity: .5; font-size: 60%;">([[w:Shcha|This letter]] has a little hook on the right.)</small><br> These two permutations are very similar. They are equal in the first half, and differ by exchanged neighbors in the second. Neighboring Zhegalkin indices <small>(i.e. 2·''n'' and 2·''n''+1)</small> denote complements.<br> So although there is no mentor bijection between Boolean functions, there is one between pairs of complements.<br> Complement and mentor partition the set of all Boolean functions into blocks of size 4 or 2. Such a block shall be called (big or small) ''seminar''.<br> The Zhegalkin indices in a big seminar are <math>\{ a, a+1, b, b+1 \}</math> with even <math>a</math> and <math>b</math>, so it can be represented by the pair <math>(a, b)</math>.<br> <small>An example of a seminar is {138, 139, 156, 157}, represented as (138, 156). See [[c:File:Set of 3-ary Boolean functions 12855504354077768210885020350402125463028803369886765232947200.svg|image]]. <small style="opacity: .5;">In the permutation it is represented by the pair (69, 78).</small></small> The pairs <math>\left( \frac{a}{2}, \frac{b}{2} \right)</math> are the cycles of a self-inverse Walsh permutation of degree <math>2^{arity} - 1</math>. <small style="opacity: .5;">(For arity 3 the degree is 7, and the permuted integers are 0...127.)</small><br> For arities 1 and 2 this permutation is neutral. For arity 3 is has 64 fixed points <small>(of 128 places, i.e. 1/2)</small>. For arity 5 it has 1024 fixed points <small>(of 32768 places, i.e. 1/32)</small>.<br> {{Collapsible START|mentor permutation|collapsed wide}} [[File:Seminar 4 (short tutor and mentor permutation).svg|thumb|15×15 matrix corresponding to the Walsh permutation for arity 4.]] The first 64 entries of the sequence are the fixed points. The next 64 entries form these 32 cycles: <source lang="python" style="font-size: 60%;"> [ 64, 75], [ 65, 74], [ 66, 73], [ 67, 72], [ 68, 79], [ 69, 78], [ 70, 77], [ 71, 76], [ 80, 91], [ 81, 90], [ 82, 89], [ 83, 88], [ 84, 95], [ 85, 94], [ 86, 93], [ 87, 92], [ 96, 107], [ 97, 106], [ 98, 105], [ 99, 104], [100, 111], [101, 110], [102, 109], [103, 108], [112, 123], [113, 122], [114, 121], [115, 120], [116, 127], [117, 126], [118, 125], [119, 124] </source> The permutation for arity 4 corresponds to the 15×15 matrix shown on the right.<br> <small style="opacity: .5; font-size: 60%;">It is described by this vector: (1, 2, 4, 8, 16, 32, 75, 128, 256, 512, 1155, 2048, 4233, 8330, 19252)</small> The matrix is always that of Ш or Щ without the top row and left column. {{Collapsible END}} For arity 3 the Boolean functions in big seminars are the sharp ones <small>(i.e. those with odd weight)</small>. See {{Boolf prop 3-ary|seminar|images}}. <small>For a given arity, each seminar is part of a {{Boolf prop 3-ary|chunky seminar}}. For arity 3 they all have size 16. {{Mentors of Boolean functions/example chunky seminar}}</small> ==chains== The permutations Ю and Я have fewer fixed points and longer cycles than Ч and Ш.<br> A cycle of Ю shall be called '''chain'''. <small style="opacity: .5;">(Cycles of Я are the same, but reversed.)</small><br> The XOR of all entries of a chain is one of the fixed points, and shall be called '''anchor'''. The fixed points are [[Noble Boolean functions|nobles]]. '''tables of chains:''' [[Template:Mentors of Boolean functions/chains/3-ary|3-ary]] <small>(4 fixed points)</small>, [[Template:Mentors of Boolean functions/chains/4-ary|4-ary]] <small>([[Template:Mentors of Boolean functions/chains/4-ary/fixed|8 fixed points]])</small> '''3-ary partitions:''' {{Boolf prop 3-ary|chain}}, {{Boolf prop 3-ary|chain length}}, {{Boolf prop 3-ary|chain quadrants}}, {{Boolf prop 3-ary|reduced chain quadrants}}, {{Boolf prop 3-ary|chunky chain}}, {{Boolf prop 3-ary|anchor}} [[Category:Mentors of Boolean functions]] awa289min7hqj050j2t0koxmzrnhr5a 2720005 2719996 2025-06-29T10:12:34Z Ziv 2996189 ([[c:GR|GR]]) [[c:COM:FR|File renamed]]: [[File:Seminar 4 (short tutor and mentor permutation).svg]] → [[File:Seminar 4 (short lector and mentor permutation).svg]] [[c:COM:FR#FR1|Criterion 1]] (original uploader’s request) 2720005 wikitext text/x-wiki {{Boolf header}} __NOTOC__ The mentor is a rather dubious [[Soft properties of Boolean functions|soft property]] of a BF. But it seems surprisingly interesting.<br> It is found in three steps: Creating a [[Boolf-hard#family|family matrix]], getting the senior [[Noble Boolean functions|nobles]] of its rows, and getting their [[Boolf-hard#prefect|prefects]].<br> The first digits of the prefects form the mentor. {{Mentors of Boolean functions/illustrated examples 3-ary}} The following images are the 4-ary equivalents of those above. The results are either the same as above, or the complement. {{Mentors of Boolean functions/illustrated examples 4-ary}} ==Walsh permutations== A Boolean function has a unique mentor for a given arity. The map between mentors can be expressed by four different [[Walsh permutation]]s.<br> <small style="opacity: .7;">(That is, because a BF can be denoted by its truth table or by its Zhegalkin index. In the images above, they are shown red and green.)</small><br> In all there are six Walsh permutations, which shall be denoted by Cyrillic letters: &nbsp;&nbsp;&nbsp; Ж <small>(Zhe)</small>, &nbsp;&nbsp;&nbsp; Ч <small>(Che)</small>, Ш <small>(Sha)</small>, &nbsp; Ю <small>(Yu)</small>, Я <small>(Ya)</small>, &nbsp;&nbsp;&nbsp; Щ <small>(Shcha)</small><br> Their degree is <math>d = 2^{arity}</math>, i.e. they correspond to invertible binary <math>d \times d</math> matrices.<br> <small style="opacity: .7;">(The letter Ж is used in two different ways: On its own it represents the permutation. Followed by an integer it represents a BF, identified by its [[Zhegalkin matrix|Zhegalkin index]].)</small> {{Mentors of Boolean functions/four WP relationships}} Ч and Ш are both self-inverse. Ю and Я are inverse to each other. The matrix of Щ is part of a top right Sierpinki triangle. Its diagonals follow a negated XOR pattern. <small style="opacity: .5;">(See [[c:File:Variadic5 antipode; ESAND (ESNOR twin).svg|image]].)</small><br> The matrix of Ш is almost the same, but with the top right entry inverted.<br> The matrix of Ч is a family matrix. Its top row is related to that of the Ш matrix. <small>The calculation involves the Zhegalkin twin and reversing the truth table.</small> {{Mentors of Boolean functions/code Che matrix}} {{Collapsible START|relationship between the matrix patterns|collapsed gap-above gap-below}} The red family matrix has the pattern of Ч.<br> The green matrix shows the twins of the red rows, and has the pattern of Ю and Я.<br> The blue matrix shows the twins of the green columns, and has the pattern of Ш.<br> [[File:Family of Zhe 38504.svg|400px|center]] {{Collapsible END}} {{Mentors of Boolean functions/code WP vectors}} See the fixed points of Ч and Ш ordered by weight: [[Template:Boolf weight triangle; fixed points of Che|Ч]], [[Template:Boolf weight triangle; fixed points of Sha|Ш]] ===1-ary=== The permutations are all six Walsh permutations of degree 2. {{spaces|5}} Ч = (0, 2, 1, 3) {{spaces|5}} Ш = (0, 1, 3, 2) {{spaces|5}} Щ = I <small>(neutral permutation)</small> {{Collapsible START|permutations|wide collapsed}} {{Mentors of Boolean functions/illustrated WP 1-ary}} {{Collapsible END}} ===2-ary=== Ч = Ш = I <small>(neutral permutation)</small> {{spaces|5}} Ю = Я = Ж {{spaces|5}} <small>Щ = (0, 1, 2, 3, &nbsp; 4, 5, 6, 7, &nbsp; 9, 8, 11, 10, &nbsp; 13, 12, 15, 14)</small> ===3-ary=== {{Mentors of Boolean functions/illustrated WP 3-ary}} {{Collapsible START|code|collapsed light gap-above}} {{Mentors of Boolean functions/code/3-ary}} {{Collapsible END}} {{Mentors of Boolean functions/small WP example 199}} Permutation Я is related to quarter sharpness, which is seen in [[Boolf prop/3-ary/gradual sharpness 1 (quarter sharpness)|these images]]. ===4-ary=== {{Mentors of Boolean functions/illustrated WP 4-ary}} {{Collapsible START|code|collapsed light gap-above gap-below}} {{Mentors of Boolean functions/code/4-ary}} {{Collapsible END}} ==seminars== The mentor is not simply a bijection between Boolean functions, but between the truth tables for a given arity.<br> The permutation from Zhegalkin indices to those of their ''n''-ary mentors is '''Ш_''n'''''. The beginning of Ш_''n''+1 is '''Щ_''n'''''. <small style="opacity: .5; font-size: 60%;">([[w:Shcha|This letter]] has a little hook on the right.)</small><br> These two permutations are very similar. They are equal in the first half, and differ by exchanged neighbors in the second. Neighboring Zhegalkin indices <small>(i.e. 2·''n'' and 2·''n''+1)</small> denote complements.<br> So although there is no mentor bijection between Boolean functions, there is one between pairs of complements.<br> Complement and mentor partition the set of all Boolean functions into blocks of size 4 or 2. Such a block shall be called (big or small) ''seminar''.<br> The Zhegalkin indices in a big seminar are <math>\{ a, a+1, b, b+1 \}</math> with even <math>a</math> and <math>b</math>, so it can be represented by the pair <math>(a, b)</math>.<br> <small>An example of a seminar is {138, 139, 156, 157}, represented as (138, 156). See [[c:File:Set of 3-ary Boolean functions 12855504354077768210885020350402125463028803369886765232947200.svg|image]]. <small style="opacity: .5;">In the permutation it is represented by the pair (69, 78).</small></small> The pairs <math>\left( \frac{a}{2}, \frac{b}{2} \right)</math> are the cycles of a self-inverse Walsh permutation of degree <math>2^{arity} - 1</math>. <small style="opacity: .5;">(For arity 3 the degree is 7, and the permuted integers are 0...127.)</small><br> For arities 1 and 2 this permutation is neutral. For arity 3 is has 64 fixed points <small>(of 128 places, i.e. 1/2)</small>. For arity 5 it has 1024 fixed points <small>(of 32768 places, i.e. 1/32)</small>.<br> {{Collapsible START|mentor permutation|collapsed wide}} [[File:Seminar 4 (short lector and mentor permutation).svg|thumb|15×15 matrix corresponding to the Walsh permutation for arity 4.]] The first 64 entries of the sequence are the fixed points. The next 64 entries form these 32 cycles: <source lang="python" style="font-size: 60%;"> [ 64, 75], [ 65, 74], [ 66, 73], [ 67, 72], [ 68, 79], [ 69, 78], [ 70, 77], [ 71, 76], [ 80, 91], [ 81, 90], [ 82, 89], [ 83, 88], [ 84, 95], [ 85, 94], [ 86, 93], [ 87, 92], [ 96, 107], [ 97, 106], [ 98, 105], [ 99, 104], [100, 111], [101, 110], [102, 109], [103, 108], [112, 123], [113, 122], [114, 121], [115, 120], [116, 127], [117, 126], [118, 125], [119, 124] </source> The permutation for arity 4 corresponds to the 15×15 matrix shown on the right.<br> <small style="opacity: .5; font-size: 60%;">It is described by this vector: (1, 2, 4, 8, 16, 32, 75, 128, 256, 512, 1155, 2048, 4233, 8330, 19252)</small> The matrix is always that of Ш or Щ without the top row and left column. {{Collapsible END}} For arity 3 the Boolean functions in big seminars are the sharp ones <small>(i.e. those with odd weight)</small>. See {{Boolf prop 3-ary|seminar|images}}. <small>For a given arity, each seminar is part of a {{Boolf prop 3-ary|chunky seminar}}. For arity 3 they all have size 16. {{Mentors of Boolean functions/example chunky seminar}}</small> ==chains== The permutations Ю and Я have fewer fixed points and longer cycles than Ч and Ш.<br> A cycle of Ю shall be called '''chain'''. <small style="opacity: .5;">(Cycles of Я are the same, but reversed.)</small><br> The XOR of all entries of a chain is one of the fixed points, and shall be called '''anchor'''. The fixed points are [[Noble Boolean functions|nobles]]. '''tables of chains:''' [[Template:Mentors of Boolean functions/chains/3-ary|3-ary]] <small>(4 fixed points)</small>, [[Template:Mentors of Boolean functions/chains/4-ary|4-ary]] <small>([[Template:Mentors of Boolean functions/chains/4-ary/fixed|8 fixed points]])</small> '''3-ary partitions:''' {{Boolf prop 3-ary|chain}}, {{Boolf prop 3-ary|chain length}}, {{Boolf prop 3-ary|chain quadrants}}, {{Boolf prop 3-ary|reduced chain quadrants}}, {{Boolf prop 3-ary|chunky chain}}, {{Boolf prop 3-ary|anchor}} [[Category:Mentors of Boolean functions]] qctdv6nxe5228iwy43d3iu1zadmfyqb 10 317573 2719999 2719723 2025-06-29T07:45:15Z Ziv 2996189 ([[c:GR|GR]]) [[c:COM:FR|File renamed]]: [[File:Tutor 4; Z to Z (in Sierpinski).svg]] → [[File:Lector 4; Z to Z (in Sierpinski).svg]] [[c:COM:FR#FR1|Criterion 1]] (original uploader’s request) 2719999 wikitext text/x-wiki {| |style="padding-right: 50px;"| [[File:Sierpinski 4 BL.svg|thumb|150px|Ж]] | [[File:Mentor 4; T to T.svg|thumb|150px|Ч: &nbsp; T to T]] | [[File:Mentor 4; T to Z.svg|thumb|150px|Ю: &nbsp; T to Z ]] | [[File:Mentor 4; Z to T.svg|thumb|150px|Я: &nbsp; Z to T]] | [[File:Mentor 4; Z to Z.svg|thumb|150px|Ш: &nbsp; Z to Z]] |style="padding-left: 50px;"| [[File:Lector 4; Z to Z (in Sierpinski).svg|thumb|150px|Щ]] |}<noinclude> [[Category:Mentors of Boolean functions]] </noinclude> k8ajkk6amz21k3n97v8j2sr6i3tzly5 0 317937 2720002 2719870 2025-06-29T09:32:21Z Watchduck 137431 2720002 wikitext text/x-wiki {{Boolf header}} 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.<br> An example is the map from a BF to its complement. A permutation is '''soft''', when the domain is the finite set of BF with a given arity.<br> An example is the map from a BF to its [[Zhegalkin twins|Zhegalkin twin]]. Interesting permutations of BF are often [[Walsh permutation]]s, which correspond to an invertible binary matrix of size <math>2^{arity}</math>. [[c:Category:8-ary Walsh functions in octeract matrix]] ==[[Zhegalkin matrix|Zhegalkin permutation]]== This might be the most important permutation of Boolean functions. It is soft.<br> A Boolean function can be represented by its truth table or its Zhegalkin index.<br> As a consequence, every other permutation of Boolean functions can be represented by four different permutation of integers:<br> Between truth tables, between Zhegalkin indices, and from one to the other.<br> Mathematically the one between Zhegalkin indices is probably most important. In the hard case, it is an infinite permutation. ==[[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]] dtfatghahdplaf4pmln05p2sjv46u5l 0 322107 2719993 2719543 2025-06-29T05:32:19Z Ruud Loeffen 2998353 /* Theory Mapping Table */ extended the table "Theory Mapping Table" 2719993 wikitext text/x-wiki = '''Chapter 2: Gravity Theories – Comparison and Mapping (Mainstream and Non-mainstream)''' = == '''Purpose''' == This chapter provides a comparative overview of gravity theories — both mainstream and non-mainstream — with the goal of identifying overlaps, divergences, and opportunities for integration. We focus not on disproving or validating specific models but on understanding their foundational assumptions, mathematical structure, predictive value, and compatibility with other physical theories. == '''Scope''' == Theories will be grouped into two categories: '''Mainstream Theories''': Widely taught, supported by institutions, and referenced in standard literature. '''Non-mainstream Alternatives''': Theories that challenge conventional assumptions, propose novel mechanisms, or offer reinterpretations of gravity. All theories are evaluated using a shared framework of criteria (see Chapter 1). == '''How to Contribute a Theory''' == Researchers and contributors are welcome to propose additional theories. These can be added directly to the Talk page or sent via email to: '''aitheroymapping@gmail.com'''. All submissions will be included in the overview and analyzed using the same criteria. == '''Theory Mapping Table''' == The following table presents an initial mapping of gravitational theories, both mainstream and nonmainstream. Each theory is briefly characterized by its assumptions, predictive features, and potential testability. Contributors are encouraged to expand, refine, or propose additional entries. The following table presents an initial mapping of gravitational theories, both mainstream and nonmainstream. Each theory is briefly characterized by its assumptions, predictive features, and potential testability. Contributors are encouraged to expand, refine, or propose additional entries. {| class="wikitable" ! Theory Name !! Category !! Key Assumptions !! Predictive Features !! Potential Tests |- | Newtonian Gravity || Mainstream || Instantaneous force proportional to mass and inverse-square distance || Orbits, tides, free-fall acceleration || Planetary motion, laboratory tests |- | colspan="5" | Related link: [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation] |- | General Relativity || Mainstream || Gravity is curvature of spacetime caused by mass-energy || Light bending, time dilation, frame dragging || Gravitational lensing, GPS accuracy, LIGO detections |- | colspan="5" | Related link: [https://en.wikipedia.org/wiki/General_relativity General Relativity] |- | Expansion Tectonics || Nonmainstream || Continents fit on a smaller-radius Earth; no subduction || Global fit of continental shelves, symmetric ocean crust || Paleomagnetic data, geological reconstructions |- | colspan="5" | Related link: [https://www.jamesmaxlow.com/expansion-tectonics/ Expansion Tectonics – James Maxlow] |- | Ionic Growing Earth || Nonmainstream || Earth, Moon, and Sun grow via ionic mass transfer from space || Mass increase explains orbital dynamics and cosmological acceleration || Compare mass data over time, isotope ratios |- | colspan="5" | Related link: [https://ionic-expanding-earth.weebly.com/uploads/2/6/6/5/26650330/ionic_growing_earth01oct2014r1protected.pdf The Ionic Growing Earth – Eugene Ellis] |- | Gravity Field Expansion || Nonmainstream || Time-variable gravity fields indicate Earth expansion || Space-geodetic drift, sea-level rise patterns || Satellite altimetry, GRACE gravity data |- | colspan="5" | Related link: [https://www.researchgate.net/publication/279636154_Evidences_of_the_expanding_Earth_from_space-geodetic_data_over_solid_land_and_sea_level_rise_in_recent_two_decades Expanding Earth from Gravity Fields – Shen et al. (2008)] |- | Hydrodynamic Gravity || Nonmainstream || Gravity emerges from vortex flow in an ether-like medium || Links between cosmology, Earth expansion, and rotation || Laboratory fluid models; astrophysical data |- | colspan="5" | Related link: [https://doi.org/10.4236/jmp.2022.1311088 Hydrodynamic Gravitation – Scalera (2022)] |- | Fluidum Continuum || Nonmainstream || Space is a universal continuum; matter is localized vortex motion || All forces arise from fluid dynamics || Vacuum tests, rotational dynamics, resonance experiments |- | colspan="5" | Related link: [https://www.academia.edu/12108470/Fluidum_Continuum_Universalis_Introduction_in_Fluid_Mechanical_Physics Fluidum Continuum Universalis – Arie M. de Geus] |- | Flowing Aether Theory || Nonmainstream || Aether flows explain gravitational and electromagnetic effects || Measurable sidereal variations; coherence patterns || Interferometer rotation tests, EM force anomalies |- | colspan="5" | Related link: [https://www.duncanshaw.ca/ExperimentalSupportFlowingAether.pdf Flowing Aether – Duncan Shaw] |- | Emergent Gravity || Nonmainstream (theoretical physics) || Gravity emerges from entropic principles in quantum spacetime || Galaxy rotation without dark matter || Weak lensing, cosmological simulations |- | colspan="5" | Related link: [https://arxiv.org/abs/1611.02269 Emergent Gravity – Erik Verlinde] |- | EM-Gravity Circuits || Nonmainstream || Gravity is an emergent electromagnetic effect || Circuit behavior mimics gravitational attraction || Novel EM device tests; repeatable force curves |- | colspan="5" | Related link: [https://www.academia.edu/37724456/Mass_Gravity_and_Electromagnetisms_relationship_demonstrated_using_two_novel_Electromagnetic_Circuits EM–Gravity Circuits – Michael Bull] |- | Mass–Energy Gravity || Nonmainstream || Gravity and mass arise from energy-momentum configurations || Proportional force behavior via energy state transitions || Calorimetric testing; comparison with GR |- | colspan="5" | Related link: [https://www.academia.edu/28680344/Relation_masse_%C3%A9nergie Relation masse / énergie – Philippe Albert] |} ''Note: These initial theory rows are based on prior references and relevance to gravity-related claims. Contributors are invited to extend or edit each entry with additional details and evaluations.'' == '''Next Steps''' == Expand the table with more entries Begin cross-chapter references Link phenomena such as expansion, planetary formation, and mass increase to these gravitational foundations '''◀ [[AI-Assisted Evaluation of Cosmological Theories/Chapter 1: Introduction and Evaluation Criteria|Previous]] | [[AI-Assisted Evaluation of Cosmological Theories|Main Page]] | [[AI-Assisted Evaluation of Cosmological Theories/Chapter 3: Cosmic Expansion and Universe Models|Next ▶]]''' mqde97aezcoe7uf9gel1deepdmpo5wc 2719994 2719993 2025-06-29T05:41:48Z Ruud Loeffen 2998353 /* Theory Mapping Table */ inserted Cosmic Influx Theory 2719994 wikitext text/x-wiki = '''Chapter 2: Gravity Theories – Comparison and Mapping (Mainstream and Non-mainstream)''' = == '''Purpose''' == This chapter provides a comparative overview of gravity theories — both mainstream and non-mainstream — with the goal of identifying overlaps, divergences, and opportunities for integration. We focus not on disproving or validating specific models but on understanding their foundational assumptions, mathematical structure, predictive value, and compatibility with other physical theories. == '''Scope''' == Theories will be grouped into two categories: '''Mainstream Theories''': Widely taught, supported by institutions, and referenced in standard literature. '''Non-mainstream Alternatives''': Theories that challenge conventional assumptions, propose novel mechanisms, or offer reinterpretations of gravity. All theories are evaluated using a shared framework of criteria (see Chapter 1). == '''How to Contribute a Theory''' == Researchers and contributors are welcome to propose additional theories. These can be added directly to the Talk page or sent via email to: '''aitheroymapping@gmail.com'''. All submissions will be included in the overview and analyzed using the same criteria. == '''Theory Mapping Table''' == The following table presents an initial mapping of gravitational theories, both mainstream and nonmainstream. Each theory is briefly characterized by its assumptions, predictive features, and potential testability. Contributors are encouraged to expand, refine, or propose additional entries. The following table presents an initial mapping of gravitational theories, both mainstream and nonmainstream. Each theory is briefly characterized by its assumptions, predictive features, and potential testability. Contributors are encouraged to expand, refine, or propose additional entries. {| class="wikitable" ! Theory Name !! Category !! Key Assumptions !! Predictive Features !! Potential Tests |- | Newtonian Gravity || Mainstream || Instantaneous force proportional to mass and inverse-square distance || Orbits, tides, free-fall acceleration || Planetary motion, laboratory tests |- | colspan="5" | Related link: [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation] |- | General Relativity || Mainstream || Gravity is curvature of spacetime caused by mass-energy || Light bending, time dilation, frame dragging || Gravitational lensing, GPS accuracy, LIGO detections |- | colspan="5" | Related link: [https://en.wikipedia.org/wiki/General_relativity General Relativity] |- | Expansion Tectonics || Nonmainstream || Continents fit on a smaller-radius Earth; no subduction || Global fit of continental shelves, symmetric ocean crust || Paleomagnetic data, geological reconstructions |- | colspan="5" | Related link: [https://www.jamesmaxlow.com/expansion-tectonics/ Expansion Tectonics – James Maxlow] |- | Cosmic Influx Theory (CIT) || Nonmainstream || Gravity is caused by a constant influx of energy/mass (PEWs); not curvature or attraction || Predicts preferred planetary distances; increasing mass-energy; reformulated G || Exoplanet surveys, VRMS alignment, cosmological constants |- | colspan="5" | Related link: [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory – Wikiversity Page] |- | Ionic Growing Earth || Nonmainstream || Earth, Moon, and Sun grow via ionic mass transfer from space || Mass increase explains orbital dynamics and cosmological acceleration || Compare mass data over time, isotope ratios |- | colspan="5" | Related link: [https://ionic-expanding-earth.weebly.com/uploads/2/6/6/5/26650330/ionic_growing_earth01oct2014r1protected.pdf The Ionic Growing Earth – Eugene Ellis] |- | Gravity Field Expansion || Nonmainstream || Time-variable gravity fields indicate Earth expansion || Space-geodetic drift, sea-level rise patterns || Satellite altimetry, GRACE gravity data |- | colspan="5" | Related link: [https://www.researchgate.net/publication/279636154_Evidences_of_the_expanding_Earth_from_space-geodetic_data_over_solid_land_and_sea_level_rise_in_recent_two_decades Expanding Earth from Gravity Fields – Shen et al. (2008)] |- | Hydrodynamic Gravity || Nonmainstream || Gravity emerges from vortex flow in an ether-like medium || Links between cosmology, Earth expansion, and rotation || Laboratory fluid models; astrophysical data |- | colspan="5" | Related link: [https://doi.org/10.4236/jmp.2022.1311088 Hydrodynamic Gravitation – Scalera (2022)] |- | Fluidum Continuum || Nonmainstream || Space is a universal continuum; matter is localized vortex motion || All forces arise from fluid dynamics || Vacuum tests, rotational dynamics, resonance experiments |- | colspan="5" | Related link: [https://www.academia.edu/12108470/Fluidum_Continuum_Universalis_Introduction_in_Fluid_Mechanical_Physics Fluidum Continuum Universalis – Arie M. de Geus] |- | Flowing Aether Theory || Nonmainstream || Aether flows explain gravitational and electromagnetic effects || Measurable sidereal variations; coherence patterns || Interferometer rotation tests, EM force anomalies |- | colspan="5" | Related link: [https://www.duncanshaw.ca/ExperimentalSupportFlowingAether.pdf Flowing Aether – Duncan Shaw] |- | Emergent Gravity || Nonmainstream (theoretical physics) || Gravity emerges from entropic principles in quantum spacetime || Galaxy rotation without dark matter || Weak lensing, cosmological simulations |- | colspan="5" | Related link: [https://arxiv.org/abs/1611.02269 Emergent Gravity – Erik Verlinde] |- | EM-Gravity Circuits || Nonmainstream || Gravity is an emergent electromagnetic effect || Circuit behavior mimics gravitational attraction || Novel EM device tests; repeatable force curves |- | colspan="5" | Related link: [https://www.academia.edu/37724456/Mass_Gravity_and_Electromagnetisms_relationship_demonstrated_using_two_novel_Electromagnetic_Circuits EM–Gravity Circuits – Michael Bull] |- | Mass–Energy Gravity || Nonmainstream || Gravity and mass arise from energy-momentum configurations || Proportional force behavior via energy state transitions || Calorimetric testing; comparison with GR |- | colspan="5" | Related link: [https://www.academia.edu/28680344/Relation_masse_%C3%A9nergie Relation masse / énergie – Philippe Albert] |} ''Note: These initial theory rows are based on prior references and relevance to gravity-related claims. Contributors are invited to extend or edit each entry with additional details and evaluations.'' == '''Next Steps''' == Expand the table with more entries Begin cross-chapter references Link phenomena such as expansion, planetary formation, and mass increase to these gravitational foundations '''◀ [[AI-Assisted Evaluation of Cosmological Theories/Chapter 1: Introduction and Evaluation Criteria|Previous]] | [[AI-Assisted Evaluation of Cosmological Theories|Main Page]] | [[AI-Assisted Evaluation of Cosmological Theories/Chapter 3: Cosmic Expansion and Universe Models|Next ▶]]''' 58nq7z6qkd485v1f7goqypng5ixkj3k 2719995 2719994 2025-06-29T05:52:52Z Ruud Loeffen 2998353 /* Theory Mapping Table */ added a grey for each alternating theory 2719995 wikitext text/x-wiki = '''Chapter 2: Gravity Theories – Comparison and Mapping (Mainstream and Non-mainstream)''' = == '''Purpose''' == This chapter provides a comparative overview of gravity theories — both mainstream and non-mainstream — with the goal of identifying overlaps, divergences, and opportunities for integration. We focus not on disproving or validating specific models but on understanding their foundational assumptions, mathematical structure, predictive value, and compatibility with other physical theories. == '''Scope''' == Theories will be grouped into two categories: '''Mainstream Theories''': Widely taught, supported by institutions, and referenced in standard literature. '''Non-mainstream Alternatives''': Theories that challenge conventional assumptions, propose novel mechanisms, or offer reinterpretations of gravity. All theories are evaluated using a shared framework of criteria (see Chapter 1). == '''How to Contribute a Theory''' == Researchers and contributors are welcome to propose additional theories. These can be added directly to the Talk page or sent via email to: '''aitheroymapping@gmail.com'''. All submissions will be included in the overview and analyzed using the same criteria. == '''Theory Mapping Table''' == The following table presents an initial mapping of gravitational theories, both mainstream and nonmainstream. Each theory is briefly characterized by its assumptions, predictive features, and potential testability. Contributors are encouraged to expand, refine, or propose additional entries. {| class="wikitable" ! Theory Name !! Category !! Key Assumptions !! Predictive Features !! Potential Tests |- | style="background-color:#ffffff;" | Newtonian Gravity || style="background-color:#ffffff;" | Mainstream || style="background-color:#ffffff;" | Instantaneous force proportional to mass and inverse-square distance || style="background-color:#ffffff;" | Orbits, tides, free-fall acceleration || style="background-color:#ffffff;" | Planetary motion, laboratory tests |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation] |- | style="background-color:#f2f2f2;" | General Relativity || style="background-color:#f2f2f2;" | Mainstream || style="background-color:#f2f2f2;" | Gravity is curvature of spacetime caused by mass-energy || style="background-color:#f2f2f2;" | Light bending, time dilation, frame dragging || style="background-color:#f2f2f2;" | Gravitational lensing, GPS accuracy, LIGO detections |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://en.wikipedia.org/wiki/General_relativity General Relativity] |- | style="background-color:#ffffff;" | Expansion Tectonics || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Continents fit on a smaller-radius Earth; no subduction || style="background-color:#ffffff;" | Global fit of continental shelves, symmetric ocean crust || style="background-color:#ffffff;" | Paleomagnetic data, geological reconstructions |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://www.jamesmaxlow.com/expansion-tectonics/ Expansion Tectonics – James Maxlow] |- | style="background-color:#f2f2f2;" | Cosmic Influx Theory (CIT) || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Gravity is caused by a constant influx of energy/mass (PEWs); not curvature or attraction || style="background-color:#f2f2f2;" | Predicts preferred planetary distances; increasing mass-energy; reformulated G || style="background-color:#f2f2f2;" | Exoplanet surveys, VRMS alignment, cosmological constants |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory – Wikiversity Page] |- | style="background-color:#ffffff;" | Ionic Growing Earth || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Earth, Moon, and Sun grow via ionic mass transfer from space || style="background-color:#ffffff;" | Mass increase explains orbital dynamics and cosmological acceleration || style="background-color:#ffffff;" | Compare mass data over time, isotope ratios |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://ionic-expanding-earth.weebly.com/uploads/2/6/6/5/26650330/ionic_growing_earth01oct2014r1protected.pdf The Ionic Growing Earth – Eugene Ellis] |- | style="background-color:#f2f2f2;" | Gravity Field Expansion || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Time-variable gravity fields indicate Earth expansion || style="background-color:#f2f2f2;" | Space-geodetic drift, sea-level rise patterns || style="background-color:#f2f2f2;" | Satellite altimetry, GRACE gravity data |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://www.researchgate.net/publication/279636154_Evidences_of_the_expanding_Earth_from_space-geodetic_data_over_solid_land_and_sea_level_rise_in_recent_two_decades Expanding Earth from Gravity Fields – Shen et al. (2008)] |- | style="background-color:#ffffff;" | Hydrodynamic Gravity || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Gravity emerges from vortex flow in an ether-like medium || style="background-color:#ffffff;" | Links between cosmology, Earth expansion, and rotation || style="background-color:#ffffff;" | Laboratory fluid models; astrophysical data |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://doi.org/10.4236/jmp.2022.1311088 Hydrodynamic Gravitation – Scalera (2022)] |- | style="background-color:#f2f2f2;" | Fluidum Continuum || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Space is a universal continuum; matter is localized vortex motion || style="background-color:#f2f2f2;" | All forces arise from fluid dynamics || style="background-color:#f2f2f2;" | Vacuum tests, rotational dynamics, resonance experiments |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://www.academia.edu/12108470/Fluidum_Continuum_Universalis_Introduction_in_Fluid_Mechanical_Physics Fluidum Continuum Universalis – Arie M. de Geus] |- | style="background-color:#ffffff;" | Flowing Aether Theory || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Aether flows explain gravitational and electromagnetic effects || style="background-color:#ffffff;" | Measurable sidereal variations; coherence patterns || style="background-color:#ffffff;" | Interferometer rotation tests, EM force anomalies |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://www.duncanshaw.ca/ExperimentalSupportFlowingAether.pdf Flowing Aether – Duncan Shaw] |- | style="background-color:#f2f2f2;" | Emergent Gravity || style="background-color:#f2f2f2;" | Nonmainstream (theoretical physics) || style="background-color:#f2f2f2;" | Gravity emerges from entropic principles in quantum spacetime || style="background-color:#f2f2f2;" | Galaxy rotation without dark matter || style="background-color:#f2f2f2;" | Weak lensing, cosmological simulations |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://arxiv.org/abs/1611.02269 Emergent Gravity – Erik Verlinde] |- | style="background-color:#ffffff;" | EM-Gravity Circuits || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Gravity is an emergent electromagnetic effect || style="background-color:#ffffff;" | Circuit behavior mimics gravitational attraction || style="background-color:#ffffff;" | Novel EM device tests; repeatable force curves |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://www.academia.edu/37724456/Mass_Gravity_and_Electromagnetisms_relationship_demonstrated_using_two_novel_Electromagnetic_Circuits EM–Gravity Circuits – Michael Bull] |- | style="background-color:#f2f2f2;" | Mass–Energy Gravity || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Gravity and mass arise from energy-momentum configurations || style="background-color:#f2f2f2;" | Proportional force behavior via energy state transitions || style="background-color:#f2f2f2;" | Calorimetric testing; comparison with GR |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://www.academia.edu/28680344/Relation_masse_%C3%A9nergie Relation masse / énergie – Philippe Albert] |} ''Note: These initial theory rows are based on prior references and relevance to gravity-related claims. Contributors are invited to extend or edit each entry with additional details and evaluations.'' == '''Next Steps''' == Expand the table with more entries Begin cross-chapter references Link phenomena such as expansion, planetary formation, and mass increase to these gravitational foundations '''◀ [[AI-Assisted Evaluation of Cosmological Theories/Chapter 1: Introduction and Evaluation Criteria|Previous]] | [[AI-Assisted Evaluation of Cosmological Theories|Main Page]] | [[AI-Assisted Evaluation of Cosmological Theories/Chapter 3: Cosmic Expansion and Universe Models|Next ▶]]''' n1rvx0jc6cbb8l7h4eb553h51he477v 2720000 2719995 2025-06-29T09:02:02Z Ruud Loeffen 2998353 /* Scope */ add ChatGPT and other LLM apps as the tool for analysing theories 2720000 wikitext text/x-wiki = '''Chapter 2: Gravity Theories – Comparison and Mapping (Mainstream and Non-mainstream)''' = == '''Purpose''' == This chapter provides a comparative overview of gravity theories — both mainstream and non-mainstream — with the goal of identifying overlaps, divergences, and opportunities for integration. We focus not on disproving or validating specific models but on understanding their foundational assumptions, mathematical structure, predictive value, and compatibility with other physical theories. == '''Scope''' == Theories will be grouped into two categories: '''Mainstream Theories''': Widely taught, supported by institutions, and referenced in standard literature. '''Non-mainstream Alternatives''': Theories that challenge conventional assumptions, propose novel mechanisms, or offer reinterpretations of gravity. All theories are evaluated by ChatGPT or other LLM applications using a shared framework of criteria (see Chapter 1). == '''How to Contribute a Theory''' == Researchers and contributors are welcome to propose additional theories. These can be added directly to the Talk page or sent via email to: '''aitheroymapping@gmail.com'''. All submissions will be included in the overview and analyzed using the same criteria. == '''Theory Mapping Table''' == The following table presents an initial mapping of gravitational theories, both mainstream and nonmainstream. Each theory is briefly characterized by its assumptions, predictive features, and potential testability. Contributors are encouraged to expand, refine, or propose additional entries. {| class="wikitable" ! Theory Name !! Category !! Key Assumptions !! Predictive Features !! Potential Tests |- | style="background-color:#ffffff;" | Newtonian Gravity || style="background-color:#ffffff;" | Mainstream || style="background-color:#ffffff;" | Instantaneous force proportional to mass and inverse-square distance || style="background-color:#ffffff;" | Orbits, tides, free-fall acceleration || style="background-color:#ffffff;" | Planetary motion, laboratory tests |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation] |- | style="background-color:#f2f2f2;" | General Relativity || style="background-color:#f2f2f2;" | Mainstream || style="background-color:#f2f2f2;" | Gravity is curvature of spacetime caused by mass-energy || style="background-color:#f2f2f2;" | Light bending, time dilation, frame dragging || style="background-color:#f2f2f2;" | Gravitational lensing, GPS accuracy, LIGO detections |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://en.wikipedia.org/wiki/General_relativity General Relativity] |- | style="background-color:#ffffff;" | Expansion Tectonics || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Continents fit on a smaller-radius Earth; no subduction || style="background-color:#ffffff;" | Global fit of continental shelves, symmetric ocean crust || style="background-color:#ffffff;" | Paleomagnetic data, geological reconstructions |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://www.jamesmaxlow.com/expansion-tectonics/ Expansion Tectonics – James Maxlow] |- | style="background-color:#f2f2f2;" | Cosmic Influx Theory (CIT) || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Gravity is caused by a constant influx of energy/mass (PEWs); not curvature or attraction || style="background-color:#f2f2f2;" | Predicts preferred planetary distances; increasing mass-energy; reformulated G || style="background-color:#f2f2f2;" | Exoplanet surveys, VRMS alignment, cosmological constants |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory – Wikiversity Page] |- | style="background-color:#ffffff;" | Ionic Growing Earth || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Earth, Moon, and Sun grow via ionic mass transfer from space || style="background-color:#ffffff;" | Mass increase explains orbital dynamics and cosmological acceleration || style="background-color:#ffffff;" | Compare mass data over time, isotope ratios |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://ionic-expanding-earth.weebly.com/uploads/2/6/6/5/26650330/ionic_growing_earth01oct2014r1protected.pdf The Ionic Growing Earth – Eugene Ellis] |- | style="background-color:#f2f2f2;" | Gravity Field Expansion || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Time-variable gravity fields indicate Earth expansion || style="background-color:#f2f2f2;" | Space-geodetic drift, sea-level rise patterns || style="background-color:#f2f2f2;" | Satellite altimetry, GRACE gravity data |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://www.researchgate.net/publication/279636154_Evidences_of_the_expanding_Earth_from_space-geodetic_data_over_solid_land_and_sea_level_rise_in_recent_two_decades Expanding Earth from Gravity Fields – Shen et al. (2008)] |- | style="background-color:#ffffff;" | Hydrodynamic Gravity || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Gravity emerges from vortex flow in an ether-like medium || style="background-color:#ffffff;" | Links between cosmology, Earth expansion, and rotation || style="background-color:#ffffff;" | Laboratory fluid models; astrophysical data |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://doi.org/10.4236/jmp.2022.1311088 Hydrodynamic Gravitation – Scalera (2022)] |- | style="background-color:#f2f2f2;" | Fluidum Continuum || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Space is a universal continuum; matter is localized vortex motion || style="background-color:#f2f2f2;" | All forces arise from fluid dynamics || style="background-color:#f2f2f2;" | Vacuum tests, rotational dynamics, resonance experiments |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://www.academia.edu/12108470/Fluidum_Continuum_Universalis_Introduction_in_Fluid_Mechanical_Physics Fluidum Continuum Universalis – Arie M. de Geus] |- | style="background-color:#ffffff;" | Flowing Aether Theory || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Aether flows explain gravitational and electromagnetic effects || style="background-color:#ffffff;" | Measurable sidereal variations; coherence patterns || style="background-color:#ffffff;" | Interferometer rotation tests, EM force anomalies |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://www.duncanshaw.ca/ExperimentalSupportFlowingAether.pdf Flowing Aether – Duncan Shaw] |- | style="background-color:#f2f2f2;" | Emergent Gravity || style="background-color:#f2f2f2;" | Nonmainstream (theoretical physics) || style="background-color:#f2f2f2;" | Gravity emerges from entropic principles in quantum spacetime || style="background-color:#f2f2f2;" | Galaxy rotation without dark matter || style="background-color:#f2f2f2;" | Weak lensing, cosmological simulations |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://arxiv.org/abs/1611.02269 Emergent Gravity – Erik Verlinde] |- | style="background-color:#ffffff;" | EM-Gravity Circuits || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Gravity is an emergent electromagnetic effect || style="background-color:#ffffff;" | Circuit behavior mimics gravitational attraction || style="background-color:#ffffff;" | Novel EM device tests; repeatable force curves |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://www.academia.edu/37724456/Mass_Gravity_and_Electromagnetisms_relationship_demonstrated_using_two_novel_Electromagnetic_Circuits EM–Gravity Circuits – Michael Bull] |- | style="background-color:#f2f2f2;" | Mass–Energy Gravity || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Gravity and mass arise from energy-momentum configurations || style="background-color:#f2f2f2;" | Proportional force behavior via energy state transitions || style="background-color:#f2f2f2;" | Calorimetric testing; comparison with GR |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://www.academia.edu/28680344/Relation_masse_%C3%A9nergie Relation masse / énergie – Philippe Albert] |} ''Note: These initial theory rows are based on prior references and relevance to gravity-related claims. Contributors are invited to extend or edit each entry with additional details and evaluations.'' == '''Next Steps''' == Expand the table with more entries Begin cross-chapter references Link phenomena such as expansion, planetary formation, and mass increase to these gravitational foundations '''◀ [[AI-Assisted Evaluation of Cosmological Theories/Chapter 1: Introduction and Evaluation Criteria|Previous]] | [[AI-Assisted Evaluation of Cosmological Theories|Main Page]] | [[AI-Assisted Evaluation of Cosmological Theories/Chapter 3: Cosmic Expansion and Universe Models|Next ▶]]''' fk19debbtgc05gfjn4fcwiba8g4rvic 2720001 2720000 2025-06-29T09:26:24Z Ruud Loeffen 2998353 Add numbers to the subsections. Inserted subsection 2.5 Evaluation Criteria 2720001 wikitext text/x-wiki = '''Chapter 2: Gravity Theories – Comparison and Mapping (Mainstream and Non-mainstream)''' = == '''2.1 Purpose''' == This chapter provides a comparative overview of gravity theories — both mainstream and non-mainstream — with the goal of identifying overlaps, divergences, and opportunities for integration. We focus not on disproving or validating specific models but on understanding their foundational assumptions, mathematical structure, predictive value, and compatibility with other physical theories. == '''2.2 Scope''' == Theories will be grouped into two categories: '''Mainstream Theories''': Widely taught, supported by institutions, and referenced in standard literature. '''Non-mainstream Alternatives''': Theories that challenge conventional assumptions, propose novel mechanisms, or offer reinterpretations of gravity. All theories are evaluated by ChatGPT or other LLM applications using a shared framework of criteria (see Chapter 1). == '''2.3 How to Contribute a Theory''' == Researchers and contributors are welcome to propose additional theories. These can be added directly to the Talk page or sent via email to: '''aitheroymapping@gmail.com'''. All submissions will be included in the overview and analyzed using the same criteria. == '''2.4 Theory Mapping Table''' == The following table presents an initial mapping of gravitational theories, both mainstream and nonmainstream. Each theory is briefly characterized by its assumptions, predictive features, and potential testability. Contributors are encouraged to expand, refine, or propose additional entries. {| class="wikitable" ! Theory Name !! Category !! Key Assumptions !! Predictive Features !! Potential Tests |- | style="background-color:#ffffff;" | Newtonian Gravity || style="background-color:#ffffff;" | Mainstream || style="background-color:#ffffff;" | Instantaneous force proportional to mass and inverse-square distance || style="background-color:#ffffff;" | Orbits, tides, free-fall acceleration || style="background-color:#ffffff;" | Planetary motion, laboratory tests |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation] |- | style="background-color:#f2f2f2;" | General Relativity || style="background-color:#f2f2f2;" | Mainstream || style="background-color:#f2f2f2;" | Gravity is curvature of spacetime caused by mass-energy || style="background-color:#f2f2f2;" | Light bending, time dilation, frame dragging || style="background-color:#f2f2f2;" | Gravitational lensing, GPS accuracy, LIGO detections |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://en.wikipedia.org/wiki/General_relativity General Relativity] |- | style="background-color:#ffffff;" | Expansion Tectonics || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Continents fit on a smaller-radius Earth; no subduction || style="background-color:#ffffff;" | Global fit of continental shelves, symmetric ocean crust || style="background-color:#ffffff;" | Paleomagnetic data, geological reconstructions |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://www.jamesmaxlow.com/expansion-tectonics/ Expansion Tectonics – James Maxlow] |- | style="background-color:#f2f2f2;" | Cosmic Influx Theory (CIT) || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Gravity is caused by a constant influx of energy/mass (PEWs); not curvature or attraction || style="background-color:#f2f2f2;" | Predicts preferred planetary distances; increasing mass-energy; reformulated G || style="background-color:#f2f2f2;" | Exoplanet surveys, VRMS alignment, cosmological constants |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory – Wikiversity Page] |- | style="background-color:#ffffff;" | Ionic Growing Earth || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Earth, Moon, and Sun grow via ionic mass transfer from space || style="background-color:#ffffff;" | Mass increase explains orbital dynamics and cosmological acceleration || style="background-color:#ffffff;" | Compare mass data over time, isotope ratios |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://ionic-expanding-earth.weebly.com/uploads/2/6/6/5/26650330/ionic_growing_earth01oct2014r1protected.pdf The Ionic Growing Earth – Eugene Ellis] |- | style="background-color:#f2f2f2;" | Gravity Field Expansion || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Time-variable gravity fields indicate Earth expansion || style="background-color:#f2f2f2;" | Space-geodetic drift, sea-level rise patterns || style="background-color:#f2f2f2;" | Satellite altimetry, GRACE gravity data |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://www.researchgate.net/publication/279636154_Evidences_of_the_expanding_Earth_from_space-geodetic_data_over_solid_land_and_sea_level_rise_in_recent_two_decades Expanding Earth from Gravity Fields – Shen et al. (2008)] |- | style="background-color:#ffffff;" | Hydrodynamic Gravity || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Gravity emerges from vortex flow in an ether-like medium || style="background-color:#ffffff;" | Links between cosmology, Earth expansion, and rotation || style="background-color:#ffffff;" | Laboratory fluid models; astrophysical data |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://doi.org/10.4236/jmp.2022.1311088 Hydrodynamic Gravitation – Scalera (2022)] |- | style="background-color:#f2f2f2;" | Fluidum Continuum || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Space is a universal continuum; matter is localized vortex motion || style="background-color:#f2f2f2;" | All forces arise from fluid dynamics || style="background-color:#f2f2f2;" | Vacuum tests, rotational dynamics, resonance experiments |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://www.academia.edu/12108470/Fluidum_Continuum_Universalis_Introduction_in_Fluid_Mechanical_Physics Fluidum Continuum Universalis – Arie M. de Geus] |- | style="background-color:#ffffff;" | Flowing Aether Theory || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Aether flows explain gravitational and electromagnetic effects || style="background-color:#ffffff;" | Measurable sidereal variations; coherence patterns || style="background-color:#ffffff;" | Interferometer rotation tests, EM force anomalies |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://www.duncanshaw.ca/ExperimentalSupportFlowingAether.pdf Flowing Aether – Duncan Shaw] |- | style="background-color:#f2f2f2;" | Emergent Gravity || style="background-color:#f2f2f2;" | Nonmainstream (theoretical physics) || style="background-color:#f2f2f2;" | Gravity emerges from entropic principles in quantum spacetime || style="background-color:#f2f2f2;" | Galaxy rotation without dark matter || style="background-color:#f2f2f2;" | Weak lensing, cosmological simulations |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://arxiv.org/abs/1611.02269 Emergent Gravity – Erik Verlinde] |- | style="background-color:#ffffff;" | EM-Gravity Circuits || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Gravity is an emergent electromagnetic effect || style="background-color:#ffffff;" | Circuit behavior mimics gravitational attraction || style="background-color:#ffffff;" | Novel EM device tests; repeatable force curves |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://www.academia.edu/37724456/Mass_Gravity_and_Electromagnetisms_relationship_demonstrated_using_two_novel_Electromagnetic_Circuits EM–Gravity Circuits – Michael Bull] |- | style="background-color:#f2f2f2;" | Mass–Energy Gravity || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Gravity and mass arise from energy-momentum configurations || style="background-color:#f2f2f2;" | Proportional force behavior via energy state transitions || style="background-color:#f2f2f2;" | Calorimetric testing; comparison with GR |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://www.academia.edu/28680344/Relation_masse_%C3%A9nergie Relation masse / énergie – Philippe Albert] |} ''Note: These initial theory rows are based on prior references and relevance to gravity-related claims. Contributors are invited to extend or edit each entry with additional details and evaluations.'' == '''2.5 Evaluation Criteria''' == The gravitational theories presented in this chapter will be evaluated using the shared criteria defined in '''Chapter 1.3: List of Evaluation Criteria'''. These criteria include: * '''Empirical Adequacy''' – alignment with observed data * '''Internal Consistency''' – logical and mathematical coherence * '''Explanatory Power''' – ability to account for known phenomena * '''Predictive Power''' – capacity to generate testable predictions * '''Simplicity and Elegance''' – conceptual economy and aesthetic clarity * '''Compatibility with Other Theories''' – integration with established frameworks * '''Falsifiability and Testability''' – potential to be disproven by evidence These dimensions provide a common foundation for comparing theories throughout this project. Future chapters (including those on cosmology, planetary evolution, geology, and biology) will use the same criteria to ensure transparency and consistency across all evaluations. See: [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_1:_Introduction_and_Evaluation_Criteria#1.3_List_of_Evaluation_Criteria|Chapter 1.3: List of Evaluation Criteria]]. == '''2.6 Next Steps''' == Expand the table with more entries Begin cross-chapter references Link phenomena such as expansion, planetary formation, and mass increase to these gravitational foundations '''◀ [[AI-Assisted Evaluation of Cosmological Theories/Chapter 1: Introduction and Evaluation Criteria|Previous]] | [[AI-Assisted Evaluation of Cosmological Theories|Main Page]] | [[AI-Assisted Evaluation of Cosmological Theories/Chapter 3: Cosmic Expansion and Universe Models|Next ▶]]''' g94y3nwctbrmsqc8eta0vd18yqmwpn1 2720003 2720001 2025-06-29T09:42:24Z Ruud Loeffen 2998353 /* Chapter 2: Gravity Theories – Comparison and Mapping (Mainstream and Non-mainstream) */ add and inserted 2.6 Helicopter View – Scientific Treatment and Emerging Tensions 2720003 wikitext text/x-wiki = '''Chapter 2: Gravity Theories – Comparison and Mapping (Mainstream and Non-mainstream)''' = == '''2.1 Purpose''' == This chapter provides a comparative overview of gravity theories — both mainstream and non-mainstream — with the goal of identifying overlaps, divergences, and opportunities for integration. We focus not on disproving or validating specific models but on understanding their foundational assumptions, mathematical structure, predictive value, and compatibility with other physical theories. == '''2.2 Scope''' == Theories will be grouped into two categories: '''Mainstream Theories''': Widely taught, supported by institutions, and referenced in standard literature. '''Non-mainstream Alternatives''': Theories that challenge conventional assumptions, propose novel mechanisms, or offer reinterpretations of gravity. All theories are evaluated by ChatGPT or other LLM applications using a shared framework of criteria (see Chapter 1). == '''2.3 How to Contribute a Theory''' == Researchers and contributors are welcome to propose additional theories. These can be added directly to the Talk page or sent via email to: '''aitheroymapping@gmail.com'''. All submissions will be included in the overview and analyzed using the same criteria. == '''2.4 Theory Mapping Table''' == The following table presents an initial mapping of gravitational theories, both mainstream and nonmainstream. Each theory is briefly characterized by its assumptions, predictive features, and potential testability. Contributors are encouraged to expand, refine, or propose additional entries. {| class="wikitable" ! Theory Name !! Category !! Key Assumptions !! Predictive Features !! Potential Tests |- | style="background-color:#ffffff;" | Newtonian Gravity || style="background-color:#ffffff;" | Mainstream || style="background-color:#ffffff;" | Instantaneous force proportional to mass and inverse-square distance || style="background-color:#ffffff;" | Orbits, tides, free-fall acceleration || style="background-color:#ffffff;" | Planetary motion, laboratory tests |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation] |- | style="background-color:#f2f2f2;" | General Relativity || style="background-color:#f2f2f2;" | Mainstream || style="background-color:#f2f2f2;" | Gravity is curvature of spacetime caused by mass-energy || style="background-color:#f2f2f2;" | Light bending, time dilation, frame dragging || style="background-color:#f2f2f2;" | Gravitational lensing, GPS accuracy, LIGO detections |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://en.wikipedia.org/wiki/General_relativity General Relativity] |- | style="background-color:#ffffff;" | Expansion Tectonics || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Continents fit on a smaller-radius Earth; no subduction || style="background-color:#ffffff;" | Global fit of continental shelves, symmetric ocean crust || style="background-color:#ffffff;" | Paleomagnetic data, geological reconstructions |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://www.jamesmaxlow.com/expansion-tectonics/ Expansion Tectonics – James Maxlow] |- | style="background-color:#f2f2f2;" | Cosmic Influx Theory (CIT) || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Gravity is caused by a constant influx of energy/mass (PEWs); not curvature or attraction || style="background-color:#f2f2f2;" | Predicts preferred planetary distances; increasing mass-energy; reformulated G || style="background-color:#f2f2f2;" | Exoplanet surveys, VRMS alignment, cosmological constants |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory – Wikiversity Page] |- | style="background-color:#ffffff;" | Ionic Growing Earth || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Earth, Moon, and Sun grow via ionic mass transfer from space || style="background-color:#ffffff;" | Mass increase explains orbital dynamics and cosmological acceleration || style="background-color:#ffffff;" | Compare mass data over time, isotope ratios |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://ionic-expanding-earth.weebly.com/uploads/2/6/6/5/26650330/ionic_growing_earth01oct2014r1protected.pdf The Ionic Growing Earth – Eugene Ellis] |- | style="background-color:#f2f2f2;" | Gravity Field Expansion || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Time-variable gravity fields indicate Earth expansion || style="background-color:#f2f2f2;" | Space-geodetic drift, sea-level rise patterns || style="background-color:#f2f2f2;" | Satellite altimetry, GRACE gravity data |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://www.researchgate.net/publication/279636154_Evidences_of_the_expanding_Earth_from_space-geodetic_data_over_solid_land_and_sea_level_rise_in_recent_two_decades Expanding Earth from Gravity Fields – Shen et al. (2008)] |- | style="background-color:#ffffff;" | Hydrodynamic Gravity || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Gravity emerges from vortex flow in an ether-like medium || style="background-color:#ffffff;" | Links between cosmology, Earth expansion, and rotation || style="background-color:#ffffff;" | Laboratory fluid models; astrophysical data |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://doi.org/10.4236/jmp.2022.1311088 Hydrodynamic Gravitation – Scalera (2022)] |- | style="background-color:#f2f2f2;" | Fluidum Continuum || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Space is a universal continuum; matter is localized vortex motion || style="background-color:#f2f2f2;" | All forces arise from fluid dynamics || style="background-color:#f2f2f2;" | Vacuum tests, rotational dynamics, resonance experiments |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://www.academia.edu/12108470/Fluidum_Continuum_Universalis_Introduction_in_Fluid_Mechanical_Physics Fluidum Continuum Universalis – Arie M. de Geus] |- | style="background-color:#ffffff;" | Flowing Aether Theory || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Aether flows explain gravitational and electromagnetic effects || style="background-color:#ffffff;" | Measurable sidereal variations; coherence patterns || style="background-color:#ffffff;" | Interferometer rotation tests, EM force anomalies |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://www.duncanshaw.ca/ExperimentalSupportFlowingAether.pdf Flowing Aether – Duncan Shaw] |- | style="background-color:#f2f2f2;" | Emergent Gravity || style="background-color:#f2f2f2;" | Nonmainstream (theoretical physics) || style="background-color:#f2f2f2;" | Gravity emerges from entropic principles in quantum spacetime || style="background-color:#f2f2f2;" | Galaxy rotation without dark matter || style="background-color:#f2f2f2;" | Weak lensing, cosmological simulations |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://arxiv.org/abs/1611.02269 Emergent Gravity – Erik Verlinde] |- | style="background-color:#ffffff;" | EM-Gravity Circuits || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Gravity is an emergent electromagnetic effect || style="background-color:#ffffff;" | Circuit behavior mimics gravitational attraction || style="background-color:#ffffff;" | Novel EM device tests; repeatable force curves |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://www.academia.edu/37724456/Mass_Gravity_and_Electromagnetisms_relationship_demonstrated_using_two_novel_Electromagnetic_Circuits EM–Gravity Circuits – Michael Bull] |- | style="background-color:#f2f2f2;" | Mass–Energy Gravity || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Gravity and mass arise from energy-momentum configurations || style="background-color:#f2f2f2;" | Proportional force behavior via energy state transitions || style="background-color:#f2f2f2;" | Calorimetric testing; comparison with GR |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://www.academia.edu/28680344/Relation_masse_%C3%A9nergie Relation masse / énergie – Philippe Albert] |} ''Note: These initial theory rows are based on prior references and relevance to gravity-related claims. Contributors are invited to extend or edit each entry with additional details and evaluations.'' == '''2.5 Evaluation Criteria''' == The gravitational theories presented in this chapter will be evaluated using the shared criteria defined in '''Chapter 1.3: List of Evaluation Criteria'''. These criteria include: * '''Empirical Adequacy''' – alignment with observed data * '''Internal Consistency''' – logical and mathematical coherence * '''Explanatory Power''' – ability to account for known phenomena * '''Predictive Power''' – capacity to generate testable predictions * '''Simplicity and Elegance''' – conceptual economy and aesthetic clarity * '''Compatibility with Other Theories''' – integration with established frameworks * '''Falsifiability and Testability''' – potential to be disproven by evidence These dimensions provide a common foundation for comparing theories throughout this project. Future chapters (including those on cosmology, planetary evolution, geology, and biology) will use the same criteria to ensure transparency and consistency across all evaluations. See: [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_1:_Introduction_and_Evaluation_Criteria#1.3_List_of_Evaluation_Criteria|Chapter 1.3: List of Evaluation Criteria]]. == '''2.7 Helicopter View – Scientific Treatment and Emerging Tensions''' == This chapter has introduced a wide range of gravitational theories, including both well-established mainstream models and lesser-known alternatives. While mainstream theories such as General Relativity are thoroughly integrated into education, research funding, and publication structures, many alternative models — including action-at-a-distance theories, flow-based gravitation, or push gravity — are often classified as fringe, regardless of their internal logic or historical pedigree. Scientific platforms such as Wikipedia and large academic databases tend to reinforce this divide. Theories outside the mainstream are typically presented as either obsolete or pseudoscientific, even when they continue to generate peer-reviewed work or suggest novel interpretations. This sharp categorization may hinder rather than help scientific progress. With the aid of AI-assisted comparison tools, this project seeks to provide a broader and more neutral framework. Instead of aligning with academic prestige or popular consensus, theories will be assessed based on a shared set of criteria (see '''Chapter 1.3'''), including empirical adequacy, internal consistency, predictive value, and compatibility with known physics. As future chapters will show, some theories traditionally dismissed may offer insights that deserve reconsideration in light of recent observations — including anomalies revealed by the James Webb Space Telescope and new gravitational measurements. Readers are therefore encouraged to approach each theory not in terms of its reputation, but in terms of its explanatory and predictive potential. Later chapters may expand this overview with additional context specific to cosmology, planetary evolution, geology, and biology. == '''2.7 Next Steps''' == Expand the table with more entries Begin cross-chapter references Link phenomena such as expansion, planetary formation, and mass increase to these gravitational foundations '''◀ [[AI-Assisted Evaluation of Cosmological Theories/Chapter 1: Introduction and Evaluation Criteria|Previous]] | [[AI-Assisted Evaluation of Cosmological Theories|Main Page]] | [[AI-Assisted Evaluation of Cosmological Theories/Chapter 3: Cosmic Expansion and Universe Models|Next ▶]]''' mo04c4jolrzp14twn0yebtgolf33rr4 2720004 2720003 2025-06-29T09:44:45Z Ruud Loeffen 2998353 /* 2.7 Helicopter View – Scientific Treatment and Emerging Tensions */ changed number subsection to 2.6 2720004 wikitext text/x-wiki = '''Chapter 2: Gravity Theories – Comparison and Mapping (Mainstream and Non-mainstream)''' = == '''2.1 Purpose''' == This chapter provides a comparative overview of gravity theories — both mainstream and non-mainstream — with the goal of identifying overlaps, divergences, and opportunities for integration. We focus not on disproving or validating specific models but on understanding their foundational assumptions, mathematical structure, predictive value, and compatibility with other physical theories. == '''2.2 Scope''' == Theories will be grouped into two categories: '''Mainstream Theories''': Widely taught, supported by institutions, and referenced in standard literature. '''Non-mainstream Alternatives''': Theories that challenge conventional assumptions, propose novel mechanisms, or offer reinterpretations of gravity. All theories are evaluated by ChatGPT or other LLM applications using a shared framework of criteria (see Chapter 1). == '''2.3 How to Contribute a Theory''' == Researchers and contributors are welcome to propose additional theories. These can be added directly to the Talk page or sent via email to: '''aitheroymapping@gmail.com'''. All submissions will be included in the overview and analyzed using the same criteria. == '''2.4 Theory Mapping Table''' == The following table presents an initial mapping of gravitational theories, both mainstream and nonmainstream. Each theory is briefly characterized by its assumptions, predictive features, and potential testability. Contributors are encouraged to expand, refine, or propose additional entries. {| class="wikitable" ! Theory Name !! Category !! Key Assumptions !! Predictive Features !! Potential Tests |- | style="background-color:#ffffff;" | Newtonian Gravity || style="background-color:#ffffff;" | Mainstream || style="background-color:#ffffff;" | Instantaneous force proportional to mass and inverse-square distance || style="background-color:#ffffff;" | Orbits, tides, free-fall acceleration || style="background-color:#ffffff;" | Planetary motion, laboratory tests |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation] |- | style="background-color:#f2f2f2;" | General Relativity || style="background-color:#f2f2f2;" | Mainstream || style="background-color:#f2f2f2;" | Gravity is curvature of spacetime caused by mass-energy || style="background-color:#f2f2f2;" | Light bending, time dilation, frame dragging || style="background-color:#f2f2f2;" | Gravitational lensing, GPS accuracy, LIGO detections |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://en.wikipedia.org/wiki/General_relativity General Relativity] |- | style="background-color:#ffffff;" | Expansion Tectonics || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Continents fit on a smaller-radius Earth; no subduction || style="background-color:#ffffff;" | Global fit of continental shelves, symmetric ocean crust || style="background-color:#ffffff;" | Paleomagnetic data, geological reconstructions |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://www.jamesmaxlow.com/expansion-tectonics/ Expansion Tectonics – James Maxlow] |- | style="background-color:#f2f2f2;" | Cosmic Influx Theory (CIT) || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Gravity is caused by a constant influx of energy/mass (PEWs); not curvature or attraction || style="background-color:#f2f2f2;" | Predicts preferred planetary distances; increasing mass-energy; reformulated G || style="background-color:#f2f2f2;" | Exoplanet surveys, VRMS alignment, cosmological constants |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory – Wikiversity Page] |- | style="background-color:#ffffff;" | Ionic Growing Earth || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Earth, Moon, and Sun grow via ionic mass transfer from space || style="background-color:#ffffff;" | Mass increase explains orbital dynamics and cosmological acceleration || style="background-color:#ffffff;" | Compare mass data over time, isotope ratios |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://ionic-expanding-earth.weebly.com/uploads/2/6/6/5/26650330/ionic_growing_earth01oct2014r1protected.pdf The Ionic Growing Earth – Eugene Ellis] |- | style="background-color:#f2f2f2;" | Gravity Field Expansion || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Time-variable gravity fields indicate Earth expansion || style="background-color:#f2f2f2;" | Space-geodetic drift, sea-level rise patterns || style="background-color:#f2f2f2;" | Satellite altimetry, GRACE gravity data |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://www.researchgate.net/publication/279636154_Evidences_of_the_expanding_Earth_from_space-geodetic_data_over_solid_land_and_sea_level_rise_in_recent_two_decades Expanding Earth from Gravity Fields – Shen et al. (2008)] |- | style="background-color:#ffffff;" | Hydrodynamic Gravity || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Gravity emerges from vortex flow in an ether-like medium || style="background-color:#ffffff;" | Links between cosmology, Earth expansion, and rotation || style="background-color:#ffffff;" | Laboratory fluid models; astrophysical data |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://doi.org/10.4236/jmp.2022.1311088 Hydrodynamic Gravitation – Scalera (2022)] |- | style="background-color:#f2f2f2;" | Fluidum Continuum || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Space is a universal continuum; matter is localized vortex motion || style="background-color:#f2f2f2;" | All forces arise from fluid dynamics || style="background-color:#f2f2f2;" | Vacuum tests, rotational dynamics, resonance experiments |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://www.academia.edu/12108470/Fluidum_Continuum_Universalis_Introduction_in_Fluid_Mechanical_Physics Fluidum Continuum Universalis – Arie M. de Geus] |- | style="background-color:#ffffff;" | Flowing Aether Theory || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Aether flows explain gravitational and electromagnetic effects || style="background-color:#ffffff;" | Measurable sidereal variations; coherence patterns || style="background-color:#ffffff;" | Interferometer rotation tests, EM force anomalies |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://www.duncanshaw.ca/ExperimentalSupportFlowingAether.pdf Flowing Aether – Duncan Shaw] |- | style="background-color:#f2f2f2;" | Emergent Gravity || style="background-color:#f2f2f2;" | Nonmainstream (theoretical physics) || style="background-color:#f2f2f2;" | Gravity emerges from entropic principles in quantum spacetime || style="background-color:#f2f2f2;" | Galaxy rotation without dark matter || style="background-color:#f2f2f2;" | Weak lensing, cosmological simulations |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://arxiv.org/abs/1611.02269 Emergent Gravity – Erik Verlinde] |- | style="background-color:#ffffff;" | EM-Gravity Circuits || style="background-color:#ffffff;" | Nonmainstream || style="background-color:#ffffff;" | Gravity is an emergent electromagnetic effect || style="background-color:#ffffff;" | Circuit behavior mimics gravitational attraction || style="background-color:#ffffff;" | Novel EM device tests; repeatable force curves |- | colspan="5" style="background-color:#ffffff;" | Related link: [https://www.academia.edu/37724456/Mass_Gravity_and_Electromagnetisms_relationship_demonstrated_using_two_novel_Electromagnetic_Circuits EM–Gravity Circuits – Michael Bull] |- | style="background-color:#f2f2f2;" | Mass–Energy Gravity || style="background-color:#f2f2f2;" | Nonmainstream || style="background-color:#f2f2f2;" | Gravity and mass arise from energy-momentum configurations || style="background-color:#f2f2f2;" | Proportional force behavior via energy state transitions || style="background-color:#f2f2f2;" | Calorimetric testing; comparison with GR |- | colspan="5" style="background-color:#f2f2f2;" | Related link: [https://www.academia.edu/28680344/Relation_masse_%C3%A9nergie Relation masse / énergie – Philippe Albert] |} ''Note: These initial theory rows are based on prior references and relevance to gravity-related claims. Contributors are invited to extend or edit each entry with additional details and evaluations.'' == '''2.5 Evaluation Criteria''' == The gravitational theories presented in this chapter will be evaluated using the shared criteria defined in '''Chapter 1.3: List of Evaluation Criteria'''. These criteria include: * '''Empirical Adequacy''' – alignment with observed data * '''Internal Consistency''' – logical and mathematical coherence * '''Explanatory Power''' – ability to account for known phenomena * '''Predictive Power''' – capacity to generate testable predictions * '''Simplicity and Elegance''' – conceptual economy and aesthetic clarity * '''Compatibility with Other Theories''' – integration with established frameworks * '''Falsifiability and Testability''' – potential to be disproven by evidence These dimensions provide a common foundation for comparing theories throughout this project. Future chapters (including those on cosmology, planetary evolution, geology, and biology) will use the same criteria to ensure transparency and consistency across all evaluations. See: [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_1:_Introduction_and_Evaluation_Criteria#1.3_List_of_Evaluation_Criteria|Chapter 1.3: List of Evaluation Criteria]]. == '''2.6 Helicopter View – Scientific Treatment and Emerging Tensions''' == This chapter has introduced a wide range of gravitational theories, including both well-established mainstream models and lesser-known alternatives. While mainstream theories such as General Relativity are thoroughly integrated into education, research funding, and publication structures, many alternative models — including action-at-a-distance theories, flow-based gravitation, or push gravity — are often classified as fringe, regardless of their internal logic or historical pedigree. Scientific platforms such as Wikipedia and large academic databases tend to reinforce this divide. Theories outside the mainstream are typically presented as either obsolete or pseudoscientific, even when they continue to generate peer-reviewed work or suggest novel interpretations. This sharp categorization may hinder rather than help scientific progress. With the aid of AI-assisted comparison tools, this project seeks to provide a broader and more neutral framework. Instead of aligning with academic prestige or popular consensus, theories will be assessed based on a shared set of criteria (see '''Chapter 1.3'''), including empirical adequacy, internal consistency, predictive value, and compatibility with known physics. As future chapters will show, some theories traditionally dismissed may offer insights that deserve reconsideration in light of recent observations — including anomalies revealed by the James Webb Space Telescope and new gravitational measurements. Readers are therefore encouraged to approach each theory not in terms of its reputation, but in terms of its explanatory and predictive potential. Later chapters may expand this overview with additional context specific to cosmology, planetary evolution, geology, and biology. == '''2.7 Next Steps''' == Expand the table with more entries Begin cross-chapter references Link phenomena such as expansion, planetary formation, and mass increase to these gravitational foundations '''◀ [[AI-Assisted Evaluation of Cosmological Theories/Chapter 1: Introduction and Evaluation Criteria|Previous]] | [[AI-Assisted Evaluation of Cosmological Theories|Main Page]] | [[AI-Assisted Evaluation of Cosmological Theories/Chapter 3: Cosmic Expansion and Universe Models|Next ▶]]''' 0ubi529w3vp1p34dfbjciee5mubjw0v 0 322151 2719983 2719905 2025-06-29T04:16:12Z Ruud Loeffen 2998353 add the detailed evaluations of 8.4.1 - 8.4.8 2719983 wikitext text/x-wiki == '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' = == '''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. == '''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 == '''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 such as: Observational Agreement Internal Logical Consistency Predictive Value Compatibility with Other Domains (e.g., geology, biology) Conceptual Coherence and Simplicity Each dimension is rated using a 1–5 star system, based on the information provided and the supporting sources that AI can access. 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. == '''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. == '''8.1 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. '''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. '''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. '''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. '''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. '''5. Conceptual Clarity and Simplicity''' Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification. '''6. Heuristic Value''' Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential. '''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. 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 or can be requested in more detail. == '''8.2 AI Evaluation Table Format''' == {| class="wikitable" |+ '''AI Evaluation Table of Cosmological Theories''' ! Theory Name ! Empirical Adequacy ! Internal Consistency ! Predictive Power ! Cross-Disciplinary Compatibility ! Conceptual Clarity and Simplicity ! Heuristic Value ! Historical & Philosophical Insight ! Total (★) |- | 8.4.1 '''General Relativity''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★★ || '''34''' |- | colspan="9" | ''Widely confirmed by experiment; mathematical elegance; historical development from Newtonian mechanics'' |- |- | 8.4.2 '''Newtonian Gravity''' | ★★★★☆ || ★★★★★ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''30''' |- | colspan="9" | ''Highly successful in classical mechanics and celestial predictions; lacks compatibility with relativity and quantum theory; historically foundational.'' |- | 8.4.3 '''MOND (Modified Newtonian Dynamics)''' | ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''24''' |- | colspan="9" | ''Strong in galactic rotation curves; limited compatibility with general relativistic frameworks'' |- | 8.4.4 '''Emergent Gravity (Verlinde)''' | ★★☆☆☆ || ★★★★☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''25''' |- | colspan="9" | ''Innovative reformulation; still awaiting broad empirical confirmation'' |- | 8.4.5 '''Big Bang Model''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''31''' |- | colspan="9" | ''Core cosmological model; supported by CMB, redshift, nucleosynthesis'' |- | 8.4.6 '''Steady State Theory''' | ★☆☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''23''' |- | colspan="9" | ''Historically important; largely superseded due to lack of CMB explanation'' |- | 8.4.7 '''Big Crunch Theory''' | ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || '''28''' |- | colspan="9" | ''Predicts final collapse of universe; consistent with GR in high-density scenarios; revived interest due to dark energy variability'' |- | 8.4.8 '''Big Bounce Theory''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''26''' |- | colspan="9" | ''Cyclical alternative to singularity; compatible with some quantum gravity models'' |- | 8.4.9 '''Cosmic Influx Theory (CIT)''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★★★★ || ★★★★☆ || '''26''' |- | colspan="9" | ''Offers cross-disciplinary compatibility; predicts mass growth and preferred orbital distances; alternative influx model under development'' |- | 8.4.10 '''SPIRAL Cosmology''' | ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22''' |- | colspan="9" | ''Proposes a hyper-dense proto-galactic phase preceding expansion; no need for ongoing dark energy or cosmic expansion; partially scriptural framing may limit falsifiability but testable claims (e.g. fixed-radius light departure) justify scientific review.'' |- | colspan="9" | ''Well-formulated alternative integrating orbital quantization; some empirical fit to planetary data; lacks full mainstream acceptance'' |} <!-- Add a blank line here --> == '''8.3 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]]'''. == '''8.4 Detailed Evaluations of Theories''' == {| class="wikitable" ! '''Section''' !! '''Theory''' !! '''Evaluation Status''' |- | '''8.4.1''' || General Relativity || ✅ Evaluated |- | '''8.4.2''' || Newtonian Gravity || ✅ Evaluated |- | '''8.4.3''' || MOND (Modified Newtonian Dynamics) || ⏳ Planned |- | '''8.4.4''' || Emergent Gravity (Verlinde) || ⏳ Planned |- | '''8.4.5''' || Big Bang Model || ⏳ Planned |- | '''8.4.6''' || Steady State Theory || ⏳ Planned |- | '''8.4.7''' || Big Crunch Scenario || ⏳ Planned |- | '''8.4.8''' || Big Bounce Model || ⏳ Planned |- | '''8.4.9''' || Cosmic Influx Theory (CIT) || ✅ Evaluated |- | '''8.4.10''' || Spiral Cosmology || ✅ Evaluated |} === '''8.4.1 General Relativity'''=== '''Empirical Adequacy''' General Relativity (GR) is one of the most empirically validated theories in physics. It has successfully explained and predicted a wide range of gravitational phenomena, including the precession of Mercury’s perihelion, gravitational lensing of starlight, gravitational redshift, time dilation effects observed in satellite systems like GPS, and the Shapiro delay. More recently, its predictions have been confirmed by gravitational wave observations (LIGO/Virgo) and direct imaging of black holes (Event Horizon Telescope). The agreement between theory and measurement is often better than 0.01%, demonstrating exceptional empirical adequacy. '''Internal Consistency''' GR is internally consistent within its mathematical framework. It is based on the Einstein field equations, which are derived from well-defined variational principles and respect general covariance. The logical structure of the theory is rigorous, with clearly formulated assumptions such as the equivalence principle and the conservation of energy–momentum through the stress-energy tensor. There are no known internal contradictions. '''Predictive Power''' GR has a powerful record of making novel predictions that were later confirmed by experiment or observation. These include the bending of light by massive bodies, time dilation in gravitational fields, the expansion of the universe (through its application in cosmology), and the existence of gravitational waves. Its predictions have often preceded direct detection by decades. This makes GR a model example of a theory with high predictive power. '''Cross-Disciplinary Compatibility''' General Relativity is compatible with many areas of physics, including classical mechanics, electrodynamics, and astrophysics. However, it is not yet unified with quantum mechanics. Attempts to reconcile GR with the Standard Model—such as quantum gravity, string theory, or loop quantum gravity—remain incomplete. Thus, GR scores slightly lower here due to its current incompatibility with modern particle physics at the Planck scale. '''Conceptual Clarity and Simplicity''' The core idea of GR—that gravity is not a force but a geometric property of spacetime—is conceptually elegant. However, the mathematical formalism (involving tensor calculus and differential geometry) is complex and often inaccessible to non-specialists. While the theory offers deep conceptual clarity, its practical simplicity is limited by the required mathematical tools. '''Heuristic Value''' GR has inspired generations of physicists and remains a fertile ground for theoretical development. It has opened up entire fields such as relativistic astrophysics, cosmology, and gravitational wave astronomy. Its influence extends beyond physics into philosophy and the public imagination. It continues to motivate research on black holes, time travel, singularities, and the early universe. '''Historical and Philosophical Insight''' Historically, GR represents a revolutionary shift in physics, displacing the Newtonian notion of absolute space and time with a dynamic, curved spacetime model. Philosophically, it challenges classical intuitions about gravity and causality and has inspired reevaluation of concepts such as simultaneity, locality, and determinism. Its legacy places it among the most profound achievements in scientific history. === '''8.4.2 Newtonian Gravity''' === '''Empirical Adequacy''' Newtonian gravity has historically achieved remarkable empirical success. It accurately describes planetary motions, tidal forces, ballistic trajectories, and satellite orbits. For centuries, it provided the dominant framework for celestial mechanics and was sufficient for navigation, astronomy, and engineering. However, it begins to fail in extreme gravitational fields or at very high speeds, where relativistic corrections are needed. It also cannot explain phenomena like the precession of Mercury’s orbit, gravitational time dilation, or the bending of light. '''Internal Consistency''' Within its classical framework, Newtonian gravity is highly consistent. It is based on clear axioms such as the inverse-square law and absolute space and time. The mathematical structure is well-defined and solvable using Newton’s laws of motion and calculus. No logical contradictions arise within its scope of applicability. However, its assumptions about instantaneous action at a distance are problematic under modern physical understanding. '''Predictive Power''' Newtonian gravity has strong predictive power in low-speed, weak-field regimes. It successfully predicted the return of Halley’s Comet, the existence of Neptune, and continues to be used in engineering and orbital calculations. However, it fails to predict relativistic effects such as gravitational lensing, frame-dragging, or gravitational waves. These limitations reduce its predictive power on cosmic and high-precision scales. '''Cross-Disciplinary Compatibility''' Newton’s theory aligns well with classical physics and early chemistry but lacks compatibility with modern disciplines. It cannot be reconciled with special relativity or quantum theory and does not incorporate energy–momentum considerations as in modern field theories. Its incompatibility with relativity limits its integration with high-energy physics and astrophysics. '''Conceptual Clarity and Simplicity''' Newtonian gravity is conceptually simple and intuitively accessible. The inverse-square force law is easy to visualize and apply. It does not require advanced mathematics and remains an ideal teaching model. Its clarity and ease of computation give it enduring educational and practical value. '''Heuristic Value''' Although no longer a frontier theory, Newtonian gravity laid the groundwork for classical mechanics and much of modern science. It helped shape ideas about force, motion, and planetary systems. While it no longer drives active theoretical innovation, it retains historical heuristic importance. '''Historical and Philosophical Insight''' Newton’s theory was revolutionary in unifying terrestrial and celestial phenomena under the same laws of motion. It established the idea of a universal physical law and set the standard for quantitative science. Philosophically, it introduced mechanistic determinism and absolute space and time—concepts that dominated Enlightenment science. Though now superseded, its legacy remains foundational. === '''8.4.3 MOND (Modified Newtonian Dynamics)''' === '''Empirical Adequacy''' MOND was proposed by Mordehai Milgrom in the early 1980s to explain galactic rotation curves without invoking dark matter. It has successfully reproduced the flat rotation profiles of spiral galaxies and the observed baryonic Tully–Fisher relation with remarkable precision. MOND fits individual galaxy data with fewer parameters than dark matter models. However, it struggles with galaxy cluster dynamics, cosmological structure formation, and gravitational lensing in some systems. Its empirical adequacy is high for galactic scales but limited beyond that domain. '''Internal Consistency''' MOND is mathematically consistent in its non-relativistic form, where it modifies Newton’s second law at low accelerations using a new constant 𝑎 0 a 0 ​ . However, its original formulation lacks a full theoretical derivation from first principles and requires ad hoc modifications to the force law. Several relativistic extensions (e.g. TeVeS, AQUAL, BIMOND) have been developed to improve consistency, but these are not uniquely favored and remain complex or underconstrained. '''Predictive Power''' MOND has had considerable predictive success in galactic astrophysics. It predicted the baryonic Tully–Fisher relation before it was observationally confirmed, and it can reproduce detailed features of galaxy rotation curves without needing dark matter halos. However, it lacks explanatory power for phenomena like the cosmic microwave background (CMB) anisotropies, gravitational lensing in galaxy clusters (e.g. Bullet Cluster), and large-scale structure. Its predictive power is strong in its target domain but limited on cosmological scales. '''Cross-Disciplinary Compatibility''' MOND is primarily focused on galactic dynamics and does not integrate smoothly with high-energy physics, quantum theory, or cosmology. Its extensions to cosmology often require additional assumptions, and it is not yet compatible with standard particle physics. As a result, its cross-disciplinary reach is modest, though ongoing efforts aim to embed it within broader frameworks. '''Conceptual Clarity and Simplicity''' In its original form, MOND is simple: the gravitational acceleration deviates from Newton’s law when below a critical threshold 𝑎 0 a 0 ​ . This modification is intuitive and computationally effective for galaxies. However, attempts to embed MOND in a relativistic framework often add complexity, reducing its conceptual transparency. '''Heuristic Value''' MOND has had significant heuristic impact by highlighting regularities in galactic dynamics that are hard to explain under the ΛCDM paradigm without fine-tuned dark matter profiles. It has sparked debate, inspired hybrid theories (e.g. dark matter superfluidity), and contributed to reevaluating gravitational theory. Its challenge to mainstream cosmology has been fruitful, even if not universally accepted. '''Historical and Philosophical Insight''' MOND revives the idea that gravity itself may need modification, rather than positing unseen matter. This philosophical approach echoes the history of science, where anomalies sometimes led to revisions of theory rather than new entities. MOND also raises deep questions about the nature of inertia, scale invariance, and universal laws—making it a philosophically provocative proposal despite its contested status. === '''8.4.4 Emergent Gravity''' === '''Empirical Adequacy''' Emergent Gravity, proposed by Erik Verlinde in 2011 and expanded in 2016, seeks to explain gravitational phenomena as an emergent effect of underlying entropic and holographic principles rather than a fundamental force. It claims to reproduce galactic rotation curves without invoking dark matter by relating gravity to the thermodynamics of microscopic information storage on holographic screens. The theory can qualitatively explain certain galactic dynamics, such as the radial acceleration relation (RAR), but lacks the quantitative precision and scope of MOND in galaxy rotation curve fitting. It also currently cannot reproduce the full spectrum of cosmological observations, including the CMB power spectrum or gravitational lensing in galaxy clusters, where standard ΛCDM performs better. '''Internal Consistency''' Emergent Gravity draws from concepts in string theory, quantum information theory, and thermodynamics. While intellectually coherent and grounded in cutting-edge theoretical frameworks, the theory is still under development and lacks a universally accepted formalism. Key quantities (such as entropic force or the elastic response of spacetime) are not always rigorously defined, and derivations sometimes rely on analogies rather than strict derivations. This limits the formal internal consistency at present, though the conceptual framework remains promising. '''Predictive Power''' The theory makes some novel qualitative predictions, particularly regarding the relation between baryonic mass and gravitational acceleration without dark matter. It reproduces the RAR and may provide an explanation for dark energy as an entropic effect of spacetime. However, Emergent Gravity has not yet made precise predictions for cosmological parameters, gravitational wave behavior, or galaxy cluster dynamics that can be tested independently of standard models. Its predictive power remains speculative and qualitative. '''Cross-Disciplinary Compatibility''' Emergent Gravity attempts to bridge gravity, quantum information, and thermodynamics, making it conceptually rich in cross-disciplinary connections. It resonates with holography, the AdS/CFT correspondence, and black hole thermodynamics. However, the lack of experimental or observational confirmation limits its integration with empirical domains such as astrophysics, cosmology, and particle physics. Its compatibility is more theoretical than empirical at this stage. '''Conceptual Clarity and Simplicity''' The idea that gravity is not fundamental but emerges from statistical behavior of microscopic degrees of freedom is intellectually elegant. However, the actual implementation of this idea in the current models is technically complex and often abstract. Unlike Newtonian gravity or even MOND, the mechanisms proposed by Emergent Gravity are difficult to visualize or test directly, and involve high-level concepts from thermodynamics and information theory. '''Heuristic Value''' Emergent Gravity is highly heuristic. It opens new perspectives on the nature of gravity, spacetime, and entropy. By reframing gravity as an emergent entropic force, it challenges the foundations of both classical and relativistic theories. It has influenced discussions around the holographic principle, black hole entropy, and spacetime microstructure. Even if it remains incomplete, it contributes to rethinking gravity from first principles. '''Historical and Philosophical Insight''' Philosophically, Emergent Gravity aligns with the long-standing idea that some phenomena in nature arise from deeper, statistical processes rather than being fundamental. It recalls Boltzmann’s approach to thermodynamics and aligns with modern information-theoretic views of physics. Historically, it marks a shift from geometric to thermodynamic models of spacetime, and offers a bold alternative to particle-based explanations of gravity. Though controversial, it is part of a growing movement to reinterpret gravity in terms of entropy and information. === '''8.4.5 Big Bang''' === '''Empirical Adequacy''' The Big Bang model is the current standard cosmological paradigm and is strongly supported by multiple independent observations. These include the cosmic microwave background (CMB) radiation, the large-scale structure of the universe, the observed expansion of space (via redshift-distance relations), and the relative abundances of light elements (hydrogen, helium, deuterium, lithium), as predicted by Big Bang Nucleosynthesis (BBN). These confirmations make the Big Bang model one of the most empirically supported frameworks in cosmology. However, the model does not explain the origin of the singularity itself, and extensions such as inflation or dark energy are required to match detailed observations. '''Internal Consistency''' The Big Bang framework is based on solutions to Einstein's field equations (Friedmann–Lemaître–Robertson–Walker metrics), and it is mathematically consistent within the assumptions of general relativity and homogeneity/isotropy (the cosmological principle). However, the initial singularity remains a theoretical boundary where the equations break down, and the model does not include a quantum gravity regime. Extensions such as inflation and ΛCDM are necessary for consistency with observations, but these introduce additional assumptions and parameters, sometimes criticized as fine-tuning. '''Predictive Power''' The Big Bang model has made several successful predictions: the existence and spectrum of the CMB, the large-scale structure of galaxies, and the relative abundances of primordial elements. It also correctly anticipated the cooling of the universe and the redshift–distance relation. Inflationary extensions explain the flatness and horizon problems and predict the nearly scale-invariant spectrum of CMB fluctuations. While many predictions are retrodictive and interpreted within a flexible framework, the model continues to be highly predictive in key areas of cosmology. '''Cross-Disciplinary Compatibility''' The Big Bang model integrates with nuclear physics (BBN), atomic physics (recombination), and high-energy physics (inflation, particle freeze-out). It is broadly compatible with the Standard Model of particle physics and many theories of fundamental interactions. However, it lacks a connection to quantum gravity, and some tensions remain—such as the Hubble tension between early and late universe measurements—that challenge cross-scale consistency. '''Conceptual Clarity and Simplicity''' The core idea—a hot, dense early universe that expands and cools over time—is conceptually clear and widely accepted. However, the full ΛCDM model includes inflation, cold dark matter, and dark energy, which are not directly observable and require complex assumptions. These components reduce the model's simplicity and raise questions about the explanatory depth of the framework. '''Heuristic Value''' The Big Bang theory has driven vast developments in cosmology, observational astronomy, particle physics, and astrophysical instrumentation. It has generated decades of research questions and missions, including COBE, WMAP, and Planck. The inflationary paradigm and dark energy studies have emerged directly from this model. As a heuristic framework, it has proven extremely fertile. '''Historical and Philosophical Insight''' The Big Bang marks a major conceptual shift in cosmology by proposing that the universe has a temporal origin and evolves over time. It displaced steady-state and eternal models of the cosmos and opened up philosophical inquiries about creation, the arrow of time, and the origin of physical laws. Despite its name, it is not an explosion in space but the expansion of space itself—a concept that has reshaped how we understand time, causality, and the structure of the universe. === '''8.4.6 Steady State Theory''' === '''Empirical Adequacy''' The Steady State Theory, developed in the late 1940s by Bondi, Gold, and Hoyle, posits that the universe has no beginning or end in time and remains statistically the same on large scales, with matter continuously created to maintain constant density despite cosmic expansion. Initially, it matched observations of redshift and expansion, but it was ultimately undermined by key empirical discoveries: the cosmic microwave background (CMB), the evolution of radio source counts, and the observation of distant galaxies at earlier stages of development. These findings provided strong evidence of a hot, dense early universe, inconsistent with the steady state hypothesis. As a result, its empirical adequacy is now considered low. '''Internal Consistency''' The theory is internally consistent in its classical formulation and relies on continuous creation of matter to maintain a constant density. However, this matter creation mechanism was never supported by a detailed physical model or empirical detection. While mathematically coherent, the theory’s assumption of continuous creation violates energy conservation as understood in standard physics, making the underlying physics speculative and theoretically weak. '''Predictive Power''' The Steady State model made a bold prediction: the universe should appear the same at all times and places when viewed on large scales. While this was a clear and testable prediction, it was eventually falsified by observations such as the CMB and the evolution of quasars and galaxy populations over time. The theory’s few predictions have largely been refuted, limiting its scientific utility. '''Cross-Disciplinary Compatibility''' The model is only weakly connected to other scientific domains. It does not integrate well with nuclear physics, as it lacks a mechanism for element formation similar to Big Bang Nucleosynthesis. It also lacks compatibility with high-energy particle physics and modern theories of gravity. The continuous matter creation postulate has no foundation in quantum theory or experimental physics. '''Conceptual Clarity and Simplicity''' The steady-state model is conceptually simple and elegant. Its appeal lay in its ability to preserve a universe without origin, circumventing the philosophical and theological questions raised by a cosmic beginning. The model also maintains a uniform, eternal cosmos, which was attractive to many physicists in the mid-20th century. Despite being falsified, it remains a conceptually clear alternative that helped clarify the implications of observational cosmology. '''Heuristic Value''' Although it is no longer a viable cosmological model, the Steady State theory played a significant heuristic role. It prompted debates about the nature of time, observational testing, and the falsifiability of cosmological models. It helped shape the methodological standards for modern cosmology by being a well-defined, testable theory that was ultimately rejected based on empirical data. Its legacy lives on in discussions about the role of testability and philosophical assumptions in science. '''Historical and Philosophical Insight''' The Steady State theory was historically important as the main rival to the Big Bang model in the early post-war period. It reflects a philosophical preference for temporal infinity and equilibrium conditions, standing in contrast to a universe with a beginning. Its eventual rejection illustrates the triumph of observation over philosophical elegance in modern cosmology. It also served as a case study in the philosophy of science, particularly regarding Popperian falsifiability and the evolution of scientific consensus. === '''8.4.7 Big Crunch''' === '''Empirical Adequacy''' The Big Crunch is not a theory of gravity or cosmology by itself but rather a hypothetical end-state of the universe within certain cosmological models. It posits that cosmic expansion could eventually reverse, causing the universe to contract back into a high-density singularity. This scenario arises from general relativity under the assumption of a closed universe with sufficient matter density to overcome expansion. However, current observational data strongly indicate that the universe is accelerating in its expansion, driven by dark energy. Measurements of the cosmic microwave background (CMB), supernova distances, and large-scale structure all support a flat or open universe with low matter density, making the Big Crunch scenario empirically disfavored at present. '''Internal Consistency''' Within general relativity and standard cosmological models, the Big Crunch is internally consistent. It naturally arises from the Friedmann equations when the density parameter Ω > 1 and the cosmological constant is absent or negative. The dynamics of contraction mirror those of expansion in reverse, and no logical contradictions emerge in its mathematical formulation. However, near the final singularity, quantum gravitational effects become important, and the classical equations break down. '''Predictive Power''' As a hypothetical scenario, the Big Crunch does not offer specific predictive claims under current physical conditions. Instead, it represents a conditional outcome: if the universe were closed and dominated by matter, it would eventually recollapse. Since observations show otherwise, the predictive relevance of the Big Crunch is now limited. Nevertheless, it played a role in exploring time-reversal symmetry, thermodynamic limits, and quantum cosmology. '''Cross-Disciplinary Compatibility''' The Big Crunch scenario is compatible with general relativity and classical thermodynamics, especially in discussions of entropy and the arrow of time. It has also been explored in speculative models of cyclic or oscillating universes, which relate to quantum gravity and string theory. However, it lacks strong support from empirical fields such as observational cosmology, particle physics, or astronomy under the current ΛCDM framework. '''Conceptual Clarity and Simplicity''' The concept is straightforward: the universe's expansion halts and reverses into a collapse. This time-symmetric model is intuitively appealing and easy to visualize. However, its physical plausibility is undermined by current evidence for accelerating expansion. Still, as a conceptual tool, it remains a clear contrast to models of eternal expansion or thermal death. '''Heuristic Value''' Historically, the Big Crunch scenario stimulated discussion about cosmological cycles, entropy limits, and the ultimate fate of the universe. It led to the development of cyclic models, bounce cosmologies, and ideas about cosmic rebirth. Although largely ruled out by current data, it retains heuristic value in theoretical cosmology and philosophy of time, particularly in exploring whether time and entropy could reverse. '''Historical and Philosophical Insight''' The Big Crunch offered a philosophically symmetric alternative to the Big Bang—a universe that begins and ends in a singularity. It invites reflection on the reversibility of physical laws, the meaning of cosmic time, and the possibility of eternal recurrence. While empirical support is lacking, the scenario remains a historically meaningful part of cosmological thinking, especially in the 20th-century debates about the universe's fate. === '''8.4.8 Big Bounce''' === '''Empirical Adequacy''' The Big Bounce is a speculative cosmological scenario in which the universe undergoes a cycle of contraction followed by a rebound (or "bounce") into a new phase of expansion. It aims to replace the initial singularity of the Big Bang with a transitional phase where quantum gravitational effects prevent infinite density. While the concept is consistent with certain theoretical models—particularly in loop quantum cosmology—there is currently no direct observational evidence for a bounce event. The cosmic microwave background (CMB) does not yet show unambiguous signatures that would favor a bounce over inflationary models. Thus, empirical adequacy remains hypothetical, though not excluded. '''Internal Consistency''' The Big Bounce can be formulated consistently within several frameworks, such as loop quantum gravity, string gas cosmology, or modified gravity models. In these settings, quantum corrections to the Friedmann equations or modifications to the geometry of spacetime prevent a singularity and allow for a smooth transition from contraction to expansion. However, different bounce models vary in their assumptions, and the full quantum dynamics are not yet universally agreed upon. Despite these uncertainties, the internal logic of the models is coherent within their theoretical boundaries. '''Predictive Power''' Some Big Bounce models predict subtle features in the CMB, such as suppressed power at large angular scales, or non-Gaussianities that differ from inflation. However, these predictions often overlap with or are degenerate with inflationary predictions, making them hard to test uniquely. No conclusive observational support has been found so far. Nevertheless, bounce models offer a predictive framework that could, in principle, be tested with improved cosmological data in the future. '''Cross-Disciplinary Compatibility''' The Big Bounce scenario is motivated by attempts to unify quantum mechanics and gravity. It connects well with developments in loop quantum cosmology, non-singular black hole models, and string theory. However, it is less developed in its links to particle physics, standard cosmology, or astrophysical observations. Its broader scientific compatibility depends heavily on which theoretical approach is adopted and how it interfaces with known physics. '''Conceptual Clarity and Simplicity''' The idea of a contracting universe rebounding into expansion is conceptually intuitive and avoids the metaphysical implications of a beginning-of-time singularity. In contrast to the Big Bang singularity, the bounce implies a cyclic or oscillatory universe that is eternal in time. While appealing in its symmetry, the underlying physics is often highly technical and abstract, involving non-perturbative quantum gravity, which reduces its practical simplicity. '''Heuristic Value''' The Big Bounce has stimulated important discussions in cosmology, particularly regarding singularity avoidance, pre-Big Bang scenarios, and the nature of time. It has inspired a class of alternative models to inflation and opened up debates about the cyclical nature of the universe. Its challenge to the standard narrative of cosmic origins has heuristic value in motivating new lines of theoretical research. '''Historical and Philosophical Insight''' The Big Bounce continues a long tradition of cyclical universe models, echoing ideas from ancient cosmologies and early 20th-century oscillating universe theories. Philosophically, it provides a framework in which the universe has no absolute beginning or end, and where time and entropy may operate in a larger looped framework. It offers a more balanced cosmological picture than the irreversible expansion or final collapse scenarios. Though not yet supported by data, its philosophical implications remain profound and open-ended. === '''8.4.9 Cosmic Influx Theory (CIT)''' === Cosmic Influx Theory (CIT), proposed by Ruud Loeffen, reinterprets gravity as a directional energy influx driven by Primordial Elementary Whirlings (PEWs), replacing the concept of attractive force or space-time curvature. It introduces a constant influx of mass-energy into all bodies, contributing to planetary expansion, star formation, and cosmological evolution. 1. '''Internal Consistency''' CIT presents a coherent internal logic based on a unidirectional influx mechanism, a redefined gravitational constant (G = (γ − 1)/4π), and the introduction of κ_CIT as a universal scaling constant. While the framework remains internally consistent, some equations are still under refinement and lack full derivations from first principles. 2. '''Predictive Power''' CIT predicts the Preferred Distance for giant planets based on κ_CIT, orbital periods of exoplanets, and a revised Hubble constant (Ho ≈ 67.8 km/s/Mpc). It also anticipates planetary expansion through mass influx. These predictions are testable, though many remain pending observational confirmation. 3. '''Falsifiability''' Several predictions—such as giant planets at D_pref in the Trappist system or mass accumulation rates inferred from planetary geology—can be tested. However, the influx mechanism itself is not yet described in terms of directly measurable particles or interactions, which may limit falsifiability at the quantum level. 4. '''Observational Alignment''' CIT aligns with various observations: early formation of giant planets in protoplanetary disks, planetary expansion signatures, surface geology of moons and Mars, and recent JWST disk structures. It also claims to naturally derive the observed Hubble constant without tension. 5. '''Philosophical Transparency''' The theory clearly departs from Newtonian and relativistic interpretations, positioning itself as an ontological alternative grounded in energy flow. The author's motivations, limitations, and intended scope are transparently communicated in both academic and public forums. 6. '''Empirical Adequacy''' CIT offers empirical parallels in planetary spacing (κ_CIT), daylength extension over geological time, and disk fragmentation patterns. However, it currently lacks publication in high-impact peer-reviewed journals and formal statistical validation across broad datasets. 7. '''Institutional Support and Development''' CIT is developed independently, primarily through Wikiversity and open-access platforms. While it incorporates extensive cross-referencing and engages with mainstream and alternative sources, it lacks institutional affiliation and academic endorsement at this stage. '''Related link:''' [[Cosmic Influx Theory]] === '''8.4.10 Summary of Spiral Cosmology''' === The Pearlman Cosmology (SPIRAL Cosmology) offers a deterministic model of the universe with a defined hyper-dense initial state, fixed radius growth, and a reinterpretation of redshift. It integrates biblical chronology into its cosmological assumptions, making it a unique hybrid of scientific and scriptural reasoning. 1. '''Internal Consistency''' The model presents a logically consistent internal framework, with clearly defined initial conditions such as the SPIRAL radius, gravitational equilibrium, and fixed cosmic time scaling. Its components align well within its own assumptions. 2. '''Predictive Power''' Pearlman Cosmology proposes several potentially testable hypotheses, such as a fixed annual rate of universal expansion and an alternative explanation of redshift. However, these are not yet accompanied by detailed numeric predictions or simulations. 3. '''Falsifiability''' Testable elements exist in the form of reinterpretations of the cosmic microwave background origin, early galaxy formation, and redshift asymmetries. Yet aspects based on Mosaic chronology may fall outside strict scientific falsifiability. 4. '''Observational Alignment''' The model qualitatively aligns with some recent JWST observations, including early structure formation and CMB uniformity. Nevertheless, it lacks robust quantitative matching with large datasets or predictive modeling. 5. '''Philosophical Transparency''' The theory is open about its use of religious chronology and framing. This transparency makes its worldview explicit, though it may hinder its acceptance within mainstream secular science. 6. '''Empirical Adequacy''' While some empirical parallels exist, the theory has not yet been tested against a wide body of observational data in a systematic or peer-reviewed way. 7. '''Institutional Support and Development''' Pearlman Cosmology remains outside institutional research frameworks. Its development and publication history are limited, and it has not yet entered mainstream cosmological discourse. '''Related link:''' [https://www.pearlman.org Pearlman Cosmology] '''◀ [[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 ▶]]''' nh4lwdoinb4jx7m12gn1703lcu1k9l1 2719984 2719983 2025-06-29T04:24:53Z Ruud Loeffen 2998353 /* 8.4 Detailed Evaluations of Theories */ Removed the table with "Evaluated" and "planned" because we strive to add evaluations quite directly after they are proposed. Instead of the table a short remark about the procedure. 2719984 wikitext text/x-wiki == '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' = == '''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. == '''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 == '''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 such as: Observational Agreement Internal Logical Consistency Predictive Value Compatibility with Other Domains (e.g., geology, biology) Conceptual Coherence and Simplicity Each dimension is rated using a 1–5 star system, based on the information provided and the supporting sources that AI can access. 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. == '''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. == '''8.1 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. '''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. '''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. '''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. '''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. '''5. Conceptual Clarity and Simplicity''' Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification. '''6. Heuristic Value''' Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential. '''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. 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 or can be requested in more detail. == '''8.2 AI Evaluation Table Format''' == {| class="wikitable" |+ '''AI Evaluation Table of Cosmological Theories''' ! Theory Name ! Empirical Adequacy ! Internal Consistency ! Predictive Power ! Cross-Disciplinary Compatibility ! Conceptual Clarity and Simplicity ! Heuristic Value ! Historical & Philosophical Insight ! Total (★) |- | 8.4.1 '''General Relativity''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★★ || '''34''' |- | colspan="9" | ''Widely confirmed by experiment; mathematical elegance; historical development from Newtonian mechanics'' |- |- | 8.4.2 '''Newtonian Gravity''' | ★★★★☆ || ★★★★★ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''30''' |- | colspan="9" | ''Highly successful in classical mechanics and celestial predictions; lacks compatibility with relativity and quantum theory; historically foundational.'' |- | 8.4.3 '''MOND (Modified Newtonian Dynamics)''' | ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''24''' |- | colspan="9" | ''Strong in galactic rotation curves; limited compatibility with general relativistic frameworks'' |- | 8.4.4 '''Emergent Gravity (Verlinde)''' | ★★☆☆☆ || ★★★★☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''25''' |- | colspan="9" | ''Innovative reformulation; still awaiting broad empirical confirmation'' |- | 8.4.5 '''Big Bang Model''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''31''' |- | colspan="9" | ''Core cosmological model; supported by CMB, redshift, nucleosynthesis'' |- | 8.4.6 '''Steady State Theory''' | ★☆☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''23''' |- | colspan="9" | ''Historically important; largely superseded due to lack of CMB explanation'' |- | 8.4.7 '''Big Crunch Theory''' | ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || '''28''' |- | colspan="9" | ''Predicts final collapse of universe; consistent with GR in high-density scenarios; revived interest due to dark energy variability'' |- | 8.4.8 '''Big Bounce Theory''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''26''' |- | colspan="9" | ''Cyclical alternative to singularity; compatible with some quantum gravity models'' |- | 8.4.9 '''Cosmic Influx Theory (CIT)''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★★★★ || ★★★★☆ || '''26''' |- | colspan="9" | ''Offers cross-disciplinary compatibility; predicts mass growth and preferred orbital distances; alternative influx model under development'' |- | 8.4.10 '''SPIRAL Cosmology''' | ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22''' |- | colspan="9" | ''Proposes a hyper-dense proto-galactic phase preceding expansion; no need for ongoing dark energy or cosmic expansion; partially scriptural framing may limit falsifiability but testable claims (e.g. fixed-radius light departure) justify scientific review.'' |- | colspan="9" | ''Well-formulated alternative integrating orbital quantization; some empirical fit to planetary data; lacks full mainstream acceptance'' |} <!-- Add a blank line here --> == '''8.3 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]]'''. == '''8.4 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. === '''8.4.1 General Relativity'''=== '''Empirical Adequacy''' General Relativity (GR) is one of the most empirically validated theories in physics. It has successfully explained and predicted a wide range of gravitational phenomena, including the precession of Mercury’s perihelion, gravitational lensing of starlight, gravitational redshift, time dilation effects observed in satellite systems like GPS, and the Shapiro delay. More recently, its predictions have been confirmed by gravitational wave observations (LIGO/Virgo) and direct imaging of black holes (Event Horizon Telescope). The agreement between theory and measurement is often better than 0.01%, demonstrating exceptional empirical adequacy. '''Internal Consistency''' GR is internally consistent within its mathematical framework. It is based on the Einstein field equations, which are derived from well-defined variational principles and respect general covariance. The logical structure of the theory is rigorous, with clearly formulated assumptions such as the equivalence principle and the conservation of energy–momentum through the stress-energy tensor. There are no known internal contradictions. '''Predictive Power''' GR has a powerful record of making novel predictions that were later confirmed by experiment or observation. These include the bending of light by massive bodies, time dilation in gravitational fields, the expansion of the universe (through its application in cosmology), and the existence of gravitational waves. Its predictions have often preceded direct detection by decades. This makes GR a model example of a theory with high predictive power. '''Cross-Disciplinary Compatibility''' General Relativity is compatible with many areas of physics, including classical mechanics, electrodynamics, and astrophysics. However, it is not yet unified with quantum mechanics. Attempts to reconcile GR with the Standard Model—such as quantum gravity, string theory, or loop quantum gravity—remain incomplete. Thus, GR scores slightly lower here due to its current incompatibility with modern particle physics at the Planck scale. '''Conceptual Clarity and Simplicity''' The core idea of GR—that gravity is not a force but a geometric property of spacetime—is conceptually elegant. However, the mathematical formalism (involving tensor calculus and differential geometry) is complex and often inaccessible to non-specialists. While the theory offers deep conceptual clarity, its practical simplicity is limited by the required mathematical tools. '''Heuristic Value''' GR has inspired generations of physicists and remains a fertile ground for theoretical development. It has opened up entire fields such as relativistic astrophysics, cosmology, and gravitational wave astronomy. Its influence extends beyond physics into philosophy and the public imagination. It continues to motivate research on black holes, time travel, singularities, and the early universe. '''Historical and Philosophical Insight''' Historically, GR represents a revolutionary shift in physics, displacing the Newtonian notion of absolute space and time with a dynamic, curved spacetime model. Philosophically, it challenges classical intuitions about gravity and causality and has inspired reevaluation of concepts such as simultaneity, locality, and determinism. Its legacy places it among the most profound achievements in scientific history. === '''8.4.2 Newtonian Gravity''' === '''Empirical Adequacy''' Newtonian gravity has historically achieved remarkable empirical success. It accurately describes planetary motions, tidal forces, ballistic trajectories, and satellite orbits. For centuries, it provided the dominant framework for celestial mechanics and was sufficient for navigation, astronomy, and engineering. However, it begins to fail in extreme gravitational fields or at very high speeds, where relativistic corrections are needed. It also cannot explain phenomena like the precession of Mercury’s orbit, gravitational time dilation, or the bending of light. '''Internal Consistency''' Within its classical framework, Newtonian gravity is highly consistent. It is based on clear axioms such as the inverse-square law and absolute space and time. The mathematical structure is well-defined and solvable using Newton’s laws of motion and calculus. No logical contradictions arise within its scope of applicability. However, its assumptions about instantaneous action at a distance are problematic under modern physical understanding. '''Predictive Power''' Newtonian gravity has strong predictive power in low-speed, weak-field regimes. It successfully predicted the return of Halley’s Comet, the existence of Neptune, and continues to be used in engineering and orbital calculations. However, it fails to predict relativistic effects such as gravitational lensing, frame-dragging, or gravitational waves. These limitations reduce its predictive power on cosmic and high-precision scales. '''Cross-Disciplinary Compatibility''' Newton’s theory aligns well with classical physics and early chemistry but lacks compatibility with modern disciplines. It cannot be reconciled with special relativity or quantum theory and does not incorporate energy–momentum considerations as in modern field theories. Its incompatibility with relativity limits its integration with high-energy physics and astrophysics. '''Conceptual Clarity and Simplicity''' Newtonian gravity is conceptually simple and intuitively accessible. The inverse-square force law is easy to visualize and apply. It does not require advanced mathematics and remains an ideal teaching model. Its clarity and ease of computation give it enduring educational and practical value. '''Heuristic Value''' Although no longer a frontier theory, Newtonian gravity laid the groundwork for classical mechanics and much of modern science. It helped shape ideas about force, motion, and planetary systems. While it no longer drives active theoretical innovation, it retains historical heuristic importance. '''Historical and Philosophical Insight''' Newton’s theory was revolutionary in unifying terrestrial and celestial phenomena under the same laws of motion. It established the idea of a universal physical law and set the standard for quantitative science. Philosophically, it introduced mechanistic determinism and absolute space and time—concepts that dominated Enlightenment science. Though now superseded, its legacy remains foundational. === '''8.4.3 MOND (Modified Newtonian Dynamics)''' === '''Empirical Adequacy''' MOND was proposed by Mordehai Milgrom in the early 1980s to explain galactic rotation curves without invoking dark matter. It has successfully reproduced the flat rotation profiles of spiral galaxies and the observed baryonic Tully–Fisher relation with remarkable precision. MOND fits individual galaxy data with fewer parameters than dark matter models. However, it struggles with galaxy cluster dynamics, cosmological structure formation, and gravitational lensing in some systems. Its empirical adequacy is high for galactic scales but limited beyond that domain. '''Internal Consistency''' MOND is mathematically consistent in its non-relativistic form, where it modifies Newton’s second law at low accelerations using a new constant 𝑎 0 a 0 ​ . However, its original formulation lacks a full theoretical derivation from first principles and requires ad hoc modifications to the force law. Several relativistic extensions (e.g. TeVeS, AQUAL, BIMOND) have been developed to improve consistency, but these are not uniquely favored and remain complex or underconstrained. '''Predictive Power''' MOND has had considerable predictive success in galactic astrophysics. It predicted the baryonic Tully–Fisher relation before it was observationally confirmed, and it can reproduce detailed features of galaxy rotation curves without needing dark matter halos. However, it lacks explanatory power for phenomena like the cosmic microwave background (CMB) anisotropies, gravitational lensing in galaxy clusters (e.g. Bullet Cluster), and large-scale structure. Its predictive power is strong in its target domain but limited on cosmological scales. '''Cross-Disciplinary Compatibility''' MOND is primarily focused on galactic dynamics and does not integrate smoothly with high-energy physics, quantum theory, or cosmology. Its extensions to cosmology often require additional assumptions, and it is not yet compatible with standard particle physics. As a result, its cross-disciplinary reach is modest, though ongoing efforts aim to embed it within broader frameworks. '''Conceptual Clarity and Simplicity''' In its original form, MOND is simple: the gravitational acceleration deviates from Newton’s law when below a critical threshold 𝑎 0 a 0 ​ . This modification is intuitive and computationally effective for galaxies. However, attempts to embed MOND in a relativistic framework often add complexity, reducing its conceptual transparency. '''Heuristic Value''' MOND has had significant heuristic impact by highlighting regularities in galactic dynamics that are hard to explain under the ΛCDM paradigm without fine-tuned dark matter profiles. It has sparked debate, inspired hybrid theories (e.g. dark matter superfluidity), and contributed to reevaluating gravitational theory. Its challenge to mainstream cosmology has been fruitful, even if not universally accepted. '''Historical and Philosophical Insight''' MOND revives the idea that gravity itself may need modification, rather than positing unseen matter. This philosophical approach echoes the history of science, where anomalies sometimes led to revisions of theory rather than new entities. MOND also raises deep questions about the nature of inertia, scale invariance, and universal laws—making it a philosophically provocative proposal despite its contested status. === '''8.4.4 Emergent Gravity''' === '''Empirical Adequacy''' Emergent Gravity, proposed by Erik Verlinde in 2011 and expanded in 2016, seeks to explain gravitational phenomena as an emergent effect of underlying entropic and holographic principles rather than a fundamental force. It claims to reproduce galactic rotation curves without invoking dark matter by relating gravity to the thermodynamics of microscopic information storage on holographic screens. The theory can qualitatively explain certain galactic dynamics, such as the radial acceleration relation (RAR), but lacks the quantitative precision and scope of MOND in galaxy rotation curve fitting. It also currently cannot reproduce the full spectrum of cosmological observations, including the CMB power spectrum or gravitational lensing in galaxy clusters, where standard ΛCDM performs better. '''Internal Consistency''' Emergent Gravity draws from concepts in string theory, quantum information theory, and thermodynamics. While intellectually coherent and grounded in cutting-edge theoretical frameworks, the theory is still under development and lacks a universally accepted formalism. Key quantities (such as entropic force or the elastic response of spacetime) are not always rigorously defined, and derivations sometimes rely on analogies rather than strict derivations. This limits the formal internal consistency at present, though the conceptual framework remains promising. '''Predictive Power''' The theory makes some novel qualitative predictions, particularly regarding the relation between baryonic mass and gravitational acceleration without dark matter. It reproduces the RAR and may provide an explanation for dark energy as an entropic effect of spacetime. However, Emergent Gravity has not yet made precise predictions for cosmological parameters, gravitational wave behavior, or galaxy cluster dynamics that can be tested independently of standard models. Its predictive power remains speculative and qualitative. '''Cross-Disciplinary Compatibility''' Emergent Gravity attempts to bridge gravity, quantum information, and thermodynamics, making it conceptually rich in cross-disciplinary connections. It resonates with holography, the AdS/CFT correspondence, and black hole thermodynamics. However, the lack of experimental or observational confirmation limits its integration with empirical domains such as astrophysics, cosmology, and particle physics. Its compatibility is more theoretical than empirical at this stage. '''Conceptual Clarity and Simplicity''' The idea that gravity is not fundamental but emerges from statistical behavior of microscopic degrees of freedom is intellectually elegant. However, the actual implementation of this idea in the current models is technically complex and often abstract. Unlike Newtonian gravity or even MOND, the mechanisms proposed by Emergent Gravity are difficult to visualize or test directly, and involve high-level concepts from thermodynamics and information theory. '''Heuristic Value''' Emergent Gravity is highly heuristic. It opens new perspectives on the nature of gravity, spacetime, and entropy. By reframing gravity as an emergent entropic force, it challenges the foundations of both classical and relativistic theories. It has influenced discussions around the holographic principle, black hole entropy, and spacetime microstructure. Even if it remains incomplete, it contributes to rethinking gravity from first principles. '''Historical and Philosophical Insight''' Philosophically, Emergent Gravity aligns with the long-standing idea that some phenomena in nature arise from deeper, statistical processes rather than being fundamental. It recalls Boltzmann’s approach to thermodynamics and aligns with modern information-theoretic views of physics. Historically, it marks a shift from geometric to thermodynamic models of spacetime, and offers a bold alternative to particle-based explanations of gravity. Though controversial, it is part of a growing movement to reinterpret gravity in terms of entropy and information. === '''8.4.5 Big Bang''' === '''Empirical Adequacy''' The Big Bang model is the current standard cosmological paradigm and is strongly supported by multiple independent observations. These include the cosmic microwave background (CMB) radiation, the large-scale structure of the universe, the observed expansion of space (via redshift-distance relations), and the relative abundances of light elements (hydrogen, helium, deuterium, lithium), as predicted by Big Bang Nucleosynthesis (BBN). These confirmations make the Big Bang model one of the most empirically supported frameworks in cosmology. However, the model does not explain the origin of the singularity itself, and extensions such as inflation or dark energy are required to match detailed observations. '''Internal Consistency''' The Big Bang framework is based on solutions to Einstein's field equations (Friedmann–Lemaître–Robertson–Walker metrics), and it is mathematically consistent within the assumptions of general relativity and homogeneity/isotropy (the cosmological principle). However, the initial singularity remains a theoretical boundary where the equations break down, and the model does not include a quantum gravity regime. Extensions such as inflation and ΛCDM are necessary for consistency with observations, but these introduce additional assumptions and parameters, sometimes criticized as fine-tuning. '''Predictive Power''' The Big Bang model has made several successful predictions: the existence and spectrum of the CMB, the large-scale structure of galaxies, and the relative abundances of primordial elements. It also correctly anticipated the cooling of the universe and the redshift–distance relation. Inflationary extensions explain the flatness and horizon problems and predict the nearly scale-invariant spectrum of CMB fluctuations. While many predictions are retrodictive and interpreted within a flexible framework, the model continues to be highly predictive in key areas of cosmology. '''Cross-Disciplinary Compatibility''' The Big Bang model integrates with nuclear physics (BBN), atomic physics (recombination), and high-energy physics (inflation, particle freeze-out). It is broadly compatible with the Standard Model of particle physics and many theories of fundamental interactions. However, it lacks a connection to quantum gravity, and some tensions remain—such as the Hubble tension between early and late universe measurements—that challenge cross-scale consistency. '''Conceptual Clarity and Simplicity''' The core idea—a hot, dense early universe that expands and cools over time—is conceptually clear and widely accepted. However, the full ΛCDM model includes inflation, cold dark matter, and dark energy, which are not directly observable and require complex assumptions. These components reduce the model's simplicity and raise questions about the explanatory depth of the framework. '''Heuristic Value''' The Big Bang theory has driven vast developments in cosmology, observational astronomy, particle physics, and astrophysical instrumentation. It has generated decades of research questions and missions, including COBE, WMAP, and Planck. The inflationary paradigm and dark energy studies have emerged directly from this model. As a heuristic framework, it has proven extremely fertile. '''Historical and Philosophical Insight''' The Big Bang marks a major conceptual shift in cosmology by proposing that the universe has a temporal origin and evolves over time. It displaced steady-state and eternal models of the cosmos and opened up philosophical inquiries about creation, the arrow of time, and the origin of physical laws. Despite its name, it is not an explosion in space but the expansion of space itself—a concept that has reshaped how we understand time, causality, and the structure of the universe. === '''8.4.6 Steady State Theory''' === '''Empirical Adequacy''' The Steady State Theory, developed in the late 1940s by Bondi, Gold, and Hoyle, posits that the universe has no beginning or end in time and remains statistically the same on large scales, with matter continuously created to maintain constant density despite cosmic expansion. Initially, it matched observations of redshift and expansion, but it was ultimately undermined by key empirical discoveries: the cosmic microwave background (CMB), the evolution of radio source counts, and the observation of distant galaxies at earlier stages of development. These findings provided strong evidence of a hot, dense early universe, inconsistent with the steady state hypothesis. As a result, its empirical adequacy is now considered low. '''Internal Consistency''' The theory is internally consistent in its classical formulation and relies on continuous creation of matter to maintain a constant density. However, this matter creation mechanism was never supported by a detailed physical model or empirical detection. While mathematically coherent, the theory’s assumption of continuous creation violates energy conservation as understood in standard physics, making the underlying physics speculative and theoretically weak. '''Predictive Power''' The Steady State model made a bold prediction: the universe should appear the same at all times and places when viewed on large scales. While this was a clear and testable prediction, it was eventually falsified by observations such as the CMB and the evolution of quasars and galaxy populations over time. The theory’s few predictions have largely been refuted, limiting its scientific utility. '''Cross-Disciplinary Compatibility''' The model is only weakly connected to other scientific domains. It does not integrate well with nuclear physics, as it lacks a mechanism for element formation similar to Big Bang Nucleosynthesis. It also lacks compatibility with high-energy particle physics and modern theories of gravity. The continuous matter creation postulate has no foundation in quantum theory or experimental physics. '''Conceptual Clarity and Simplicity''' The steady-state model is conceptually simple and elegant. Its appeal lay in its ability to preserve a universe without origin, circumventing the philosophical and theological questions raised by a cosmic beginning. The model also maintains a uniform, eternal cosmos, which was attractive to many physicists in the mid-20th century. Despite being falsified, it remains a conceptually clear alternative that helped clarify the implications of observational cosmology. '''Heuristic Value''' Although it is no longer a viable cosmological model, the Steady State theory played a significant heuristic role. It prompted debates about the nature of time, observational testing, and the falsifiability of cosmological models. It helped shape the methodological standards for modern cosmology by being a well-defined, testable theory that was ultimately rejected based on empirical data. Its legacy lives on in discussions about the role of testability and philosophical assumptions in science. '''Historical and Philosophical Insight''' The Steady State theory was historically important as the main rival to the Big Bang model in the early post-war period. It reflects a philosophical preference for temporal infinity and equilibrium conditions, standing in contrast to a universe with a beginning. Its eventual rejection illustrates the triumph of observation over philosophical elegance in modern cosmology. It also served as a case study in the philosophy of science, particularly regarding Popperian falsifiability and the evolution of scientific consensus. === '''8.4.7 Big Crunch''' === '''Empirical Adequacy''' The Big Crunch is not a theory of gravity or cosmology by itself but rather a hypothetical end-state of the universe within certain cosmological models. It posits that cosmic expansion could eventually reverse, causing the universe to contract back into a high-density singularity. This scenario arises from general relativity under the assumption of a closed universe with sufficient matter density to overcome expansion. However, current observational data strongly indicate that the universe is accelerating in its expansion, driven by dark energy. Measurements of the cosmic microwave background (CMB), supernova distances, and large-scale structure all support a flat or open universe with low matter density, making the Big Crunch scenario empirically disfavored at present. '''Internal Consistency''' Within general relativity and standard cosmological models, the Big Crunch is internally consistent. It naturally arises from the Friedmann equations when the density parameter Ω > 1 and the cosmological constant is absent or negative. The dynamics of contraction mirror those of expansion in reverse, and no logical contradictions emerge in its mathematical formulation. However, near the final singularity, quantum gravitational effects become important, and the classical equations break down. '''Predictive Power''' As a hypothetical scenario, the Big Crunch does not offer specific predictive claims under current physical conditions. Instead, it represents a conditional outcome: if the universe were closed and dominated by matter, it would eventually recollapse. Since observations show otherwise, the predictive relevance of the Big Crunch is now limited. Nevertheless, it played a role in exploring time-reversal symmetry, thermodynamic limits, and quantum cosmology. '''Cross-Disciplinary Compatibility''' The Big Crunch scenario is compatible with general relativity and classical thermodynamics, especially in discussions of entropy and the arrow of time. It has also been explored in speculative models of cyclic or oscillating universes, which relate to quantum gravity and string theory. However, it lacks strong support from empirical fields such as observational cosmology, particle physics, or astronomy under the current ΛCDM framework. '''Conceptual Clarity and Simplicity''' The concept is straightforward: the universe's expansion halts and reverses into a collapse. This time-symmetric model is intuitively appealing and easy to visualize. However, its physical plausibility is undermined by current evidence for accelerating expansion. Still, as a conceptual tool, it remains a clear contrast to models of eternal expansion or thermal death. '''Heuristic Value''' Historically, the Big Crunch scenario stimulated discussion about cosmological cycles, entropy limits, and the ultimate fate of the universe. It led to the development of cyclic models, bounce cosmologies, and ideas about cosmic rebirth. Although largely ruled out by current data, it retains heuristic value in theoretical cosmology and philosophy of time, particularly in exploring whether time and entropy could reverse. '''Historical and Philosophical Insight''' The Big Crunch offered a philosophically symmetric alternative to the Big Bang—a universe that begins and ends in a singularity. It invites reflection on the reversibility of physical laws, the meaning of cosmic time, and the possibility of eternal recurrence. While empirical support is lacking, the scenario remains a historically meaningful part of cosmological thinking, especially in the 20th-century debates about the universe's fate. === '''8.4.8 Big Bounce''' === '''Empirical Adequacy''' The Big Bounce is a speculative cosmological scenario in which the universe undergoes a cycle of contraction followed by a rebound (or "bounce") into a new phase of expansion. It aims to replace the initial singularity of the Big Bang with a transitional phase where quantum gravitational effects prevent infinite density. While the concept is consistent with certain theoretical models—particularly in loop quantum cosmology—there is currently no direct observational evidence for a bounce event. The cosmic microwave background (CMB) does not yet show unambiguous signatures that would favor a bounce over inflationary models. Thus, empirical adequacy remains hypothetical, though not excluded. '''Internal Consistency''' The Big Bounce can be formulated consistently within several frameworks, such as loop quantum gravity, string gas cosmology, or modified gravity models. In these settings, quantum corrections to the Friedmann equations or modifications to the geometry of spacetime prevent a singularity and allow for a smooth transition from contraction to expansion. However, different bounce models vary in their assumptions, and the full quantum dynamics are not yet universally agreed upon. Despite these uncertainties, the internal logic of the models is coherent within their theoretical boundaries. '''Predictive Power''' Some Big Bounce models predict subtle features in the CMB, such as suppressed power at large angular scales, or non-Gaussianities that differ from inflation. However, these predictions often overlap with or are degenerate with inflationary predictions, making them hard to test uniquely. No conclusive observational support has been found so far. Nevertheless, bounce models offer a predictive framework that could, in principle, be tested with improved cosmological data in the future. '''Cross-Disciplinary Compatibility''' The Big Bounce scenario is motivated by attempts to unify quantum mechanics and gravity. It connects well with developments in loop quantum cosmology, non-singular black hole models, and string theory. However, it is less developed in its links to particle physics, standard cosmology, or astrophysical observations. Its broader scientific compatibility depends heavily on which theoretical approach is adopted and how it interfaces with known physics. '''Conceptual Clarity and Simplicity''' The idea of a contracting universe rebounding into expansion is conceptually intuitive and avoids the metaphysical implications of a beginning-of-time singularity. In contrast to the Big Bang singularity, the bounce implies a cyclic or oscillatory universe that is eternal in time. While appealing in its symmetry, the underlying physics is often highly technical and abstract, involving non-perturbative quantum gravity, which reduces its practical simplicity. '''Heuristic Value''' The Big Bounce has stimulated important discussions in cosmology, particularly regarding singularity avoidance, pre-Big Bang scenarios, and the nature of time. It has inspired a class of alternative models to inflation and opened up debates about the cyclical nature of the universe. Its challenge to the standard narrative of cosmic origins has heuristic value in motivating new lines of theoretical research. '''Historical and Philosophical Insight''' The Big Bounce continues a long tradition of cyclical universe models, echoing ideas from ancient cosmologies and early 20th-century oscillating universe theories. Philosophically, it provides a framework in which the universe has no absolute beginning or end, and where time and entropy may operate in a larger looped framework. It offers a more balanced cosmological picture than the irreversible expansion or final collapse scenarios. Though not yet supported by data, its philosophical implications remain profound and open-ended. === '''8.4.9 Cosmic Influx Theory (CIT)''' === Cosmic Influx Theory (CIT), proposed by Ruud Loeffen, reinterprets gravity as a directional energy influx driven by Primordial Elementary Whirlings (PEWs), replacing the concept of attractive force or space-time curvature. It introduces a constant influx of mass-energy into all bodies, contributing to planetary expansion, star formation, and cosmological evolution. 1. '''Internal Consistency''' CIT presents a coherent internal logic based on a unidirectional influx mechanism, a redefined gravitational constant (G = (γ − 1)/4π), and the introduction of κ_CIT as a universal scaling constant. While the framework remains internally consistent, some equations are still under refinement and lack full derivations from first principles. 2. '''Predictive Power''' CIT predicts the Preferred Distance for giant planets based on κ_CIT, orbital periods of exoplanets, and a revised Hubble constant (Ho ≈ 67.8 km/s/Mpc). It also anticipates planetary expansion through mass influx. These predictions are testable, though many remain pending observational confirmation. 3. '''Falsifiability''' Several predictions—such as giant planets at D_pref in the Trappist system or mass accumulation rates inferred from planetary geology—can be tested. However, the influx mechanism itself is not yet described in terms of directly measurable particles or interactions, which may limit falsifiability at the quantum level. 4. '''Observational Alignment''' CIT aligns with various observations: early formation of giant planets in protoplanetary disks, planetary expansion signatures, surface geology of moons and Mars, and recent JWST disk structures. It also claims to naturally derive the observed Hubble constant without tension. 5. '''Philosophical Transparency''' The theory clearly departs from Newtonian and relativistic interpretations, positioning itself as an ontological alternative grounded in energy flow. The author's motivations, limitations, and intended scope are transparently communicated in both academic and public forums. 6. '''Empirical Adequacy''' CIT offers empirical parallels in planetary spacing (κ_CIT), daylength extension over geological time, and disk fragmentation patterns. However, it currently lacks publication in high-impact peer-reviewed journals and formal statistical validation across broad datasets. 7. '''Institutional Support and Development''' CIT is developed independently, primarily through Wikiversity and open-access platforms. While it incorporates extensive cross-referencing and engages with mainstream and alternative sources, it lacks institutional affiliation and academic endorsement at this stage. '''Related link:''' [[Cosmic Influx Theory]] === '''8.4.10 Summary of Spiral Cosmology''' === The Pearlman Cosmology (SPIRAL Cosmology) offers a deterministic model of the universe with a defined hyper-dense initial state, fixed radius growth, and a reinterpretation of redshift. It integrates biblical chronology into its cosmological assumptions, making it a unique hybrid of scientific and scriptural reasoning. 1. '''Internal Consistency''' The model presents a logically consistent internal framework, with clearly defined initial conditions such as the SPIRAL radius, gravitational equilibrium, and fixed cosmic time scaling. Its components align well within its own assumptions. 2. '''Predictive Power''' Pearlman Cosmology proposes several potentially testable hypotheses, such as a fixed annual rate of universal expansion and an alternative explanation of redshift. However, these are not yet accompanied by detailed numeric predictions or simulations. 3. '''Falsifiability''' Testable elements exist in the form of reinterpretations of the cosmic microwave background origin, early galaxy formation, and redshift asymmetries. Yet aspects based on Mosaic chronology may fall outside strict scientific falsifiability. 4. '''Observational Alignment''' The model qualitatively aligns with some recent JWST observations, including early structure formation and CMB uniformity. Nevertheless, it lacks robust quantitative matching with large datasets or predictive modeling. 5. '''Philosophical Transparency''' The theory is open about its use of religious chronology and framing. This transparency makes its worldview explicit, though it may hinder its acceptance within mainstream secular science. 6. '''Empirical Adequacy''' While some empirical parallels exist, the theory has not yet been tested against a wide body of observational data in a systematic or peer-reviewed way. 7. '''Institutional Support and Development''' Pearlman Cosmology remains outside institutional research frameworks. Its development and publication history are limited, and it has not yet entered mainstream cosmological discourse. '''Related link:''' [https://www.pearlman.org Pearlman Cosmology] '''◀ [[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 ▶]]''' rgfvzqgof6cpbtu3zqqf9df2tkotnco 2719985 2719984 2025-06-29T04:33:27Z Ruud Loeffen 2998353 /* 8.4.1 General Relativity */ add the link to this theory 2719985 wikitext text/x-wiki == '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' = == '''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. == '''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 == '''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 such as: Observational Agreement Internal Logical Consistency Predictive Value Compatibility with Other Domains (e.g., geology, biology) Conceptual Coherence and Simplicity Each dimension is rated using a 1–5 star system, based on the information provided and the supporting sources that AI can access. 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. == '''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. == '''8.1 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. '''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. '''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. '''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. '''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. '''5. Conceptual Clarity and Simplicity''' Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification. '''6. Heuristic Value''' Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential. '''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. 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 or can be requested in more detail. == '''8.2 AI Evaluation Table Format''' == {| class="wikitable" |+ '''AI Evaluation Table of Cosmological Theories''' ! Theory Name ! Empirical Adequacy ! Internal Consistency ! Predictive Power ! Cross-Disciplinary Compatibility ! Conceptual Clarity and Simplicity ! Heuristic Value ! Historical & Philosophical Insight ! Total (★) |- | 8.4.1 '''General Relativity''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★★ || '''34''' |- | colspan="9" | ''Widely confirmed by experiment; mathematical elegance; historical development from Newtonian mechanics'' |- |- | 8.4.2 '''Newtonian Gravity''' | ★★★★☆ || ★★★★★ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''30''' |- | colspan="9" | ''Highly successful in classical mechanics and celestial predictions; lacks compatibility with relativity and quantum theory; historically foundational.'' |- | 8.4.3 '''MOND (Modified Newtonian Dynamics)''' | ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''24''' |- | colspan="9" | ''Strong in galactic rotation curves; limited compatibility with general relativistic frameworks'' |- | 8.4.4 '''Emergent Gravity (Verlinde)''' | ★★☆☆☆ || ★★★★☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''25''' |- | colspan="9" | ''Innovative reformulation; still awaiting broad empirical confirmation'' |- | 8.4.5 '''Big Bang Model''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''31''' |- | colspan="9" | ''Core cosmological model; supported by CMB, redshift, nucleosynthesis'' |- | 8.4.6 '''Steady State Theory''' | ★☆☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''23''' |- | colspan="9" | ''Historically important; largely superseded due to lack of CMB explanation'' |- | 8.4.7 '''Big Crunch Theory''' | ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || '''28''' |- | colspan="9" | ''Predicts final collapse of universe; consistent with GR in high-density scenarios; revived interest due to dark energy variability'' |- | 8.4.8 '''Big Bounce Theory''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''26''' |- | colspan="9" | ''Cyclical alternative to singularity; compatible with some quantum gravity models'' |- | 8.4.9 '''Cosmic Influx Theory (CIT)''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★★★★ || ★★★★☆ || '''26''' |- | colspan="9" | ''Offers cross-disciplinary compatibility; predicts mass growth and preferred orbital distances; alternative influx model under development'' |- | 8.4.10 '''SPIRAL Cosmology''' | ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22''' |- | colspan="9" | ''Proposes a hyper-dense proto-galactic phase preceding expansion; no need for ongoing dark energy or cosmic expansion; partially scriptural framing may limit falsifiability but testable claims (e.g. fixed-radius light departure) justify scientific review.'' |- | colspan="9" | ''Well-formulated alternative integrating orbital quantization; some empirical fit to planetary data; lacks full mainstream acceptance'' |} <!-- Add a blank line here --> == '''8.3 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]]'''. == '''8.4 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. === '''8.4.1 General Relativity'''=== '''Empirical Adequacy''' General Relativity (GR) is one of the most empirically validated theories in physics. It has successfully explained and predicted a wide range of gravitational phenomena, including the precession of Mercury’s perihelion, gravitational lensing of starlight, gravitational redshift, time dilation effects observed in satellite systems like GPS, and the Shapiro delay. More recently, its predictions have been confirmed by gravitational wave observations (LIGO/Virgo) and direct imaging of black holes (Event Horizon Telescope). The agreement between theory and measurement is often better than 0.01%, demonstrating exceptional empirical adequacy. '''Internal Consistency''' GR is internally consistent within its mathematical framework. It is based on the Einstein field equations, which are derived from well-defined variational principles and respect general covariance. The logical structure of the theory is rigorous, with clearly formulated assumptions such as the equivalence principle and the conservation of energy–momentum through the stress-energy tensor. There are no known internal contradictions. '''Predictive Power''' GR has a powerful record of making novel predictions that were later confirmed by experiment or observation. These include the bending of light by massive bodies, time dilation in gravitational fields, the expansion of the universe (through its application in cosmology), and the existence of gravitational waves. Its predictions have often preceded direct detection by decades. This makes GR a model example of a theory with high predictive power. '''Cross-Disciplinary Compatibility''' General Relativity is compatible with many areas of physics, including classical mechanics, electrodynamics, and astrophysics. However, it is not yet unified with quantum mechanics. Attempts to reconcile GR with the Standard Model—such as quantum gravity, string theory, or loop quantum gravity—remain incomplete. Thus, GR scores slightly lower here due to its current incompatibility with modern particle physics at the Planck scale. '''Conceptual Clarity and Simplicity''' The core idea of GR—that gravity is not a force but a geometric property of spacetime—is conceptually elegant. However, the mathematical formalism (involving tensor calculus and differential geometry) is complex and often inaccessible to non-specialists. While the theory offers deep conceptual clarity, its practical simplicity is limited by the required mathematical tools. '''Heuristic Value''' GR has inspired generations of physicists and remains a fertile ground for theoretical development. It has opened up entire fields such as relativistic astrophysics, cosmology, and gravitational wave astronomy. Its influence extends beyond physics into philosophy and the public imagination. It continues to motivate research on black holes, time travel, singularities, and the early universe. '''Historical and Philosophical Insight''' Historically, GR represents a revolutionary shift in physics, displacing the Newtonian notion of absolute space and time with a dynamic, curved spacetime model. Philosophically, it challenges classical intuitions about gravity and causality and has inspired reevaluation of concepts such as simultaneity, locality, and determinism. Its legacy places it among the most profound achievements in scientific history. '''Related link:''' [https://en.wikipedia.org/wiki/General_relativity General Relativity] === '''8.4.2 Newtonian Gravity''' === '''Empirical Adequacy''' Newtonian gravity has historically achieved remarkable empirical success. It accurately describes planetary motions, tidal forces, ballistic trajectories, and satellite orbits. For centuries, it provided the dominant framework for celestial mechanics and was sufficient for navigation, astronomy, and engineering. However, it begins to fail in extreme gravitational fields or at very high speeds, where relativistic corrections are needed. It also cannot explain phenomena like the precession of Mercury’s orbit, gravitational time dilation, or the bending of light. '''Internal Consistency''' Within its classical framework, Newtonian gravity is highly consistent. It is based on clear axioms such as the inverse-square law and absolute space and time. The mathematical structure is well-defined and solvable using Newton’s laws of motion and calculus. No logical contradictions arise within its scope of applicability. However, its assumptions about instantaneous action at a distance are problematic under modern physical understanding. '''Predictive Power''' Newtonian gravity has strong predictive power in low-speed, weak-field regimes. It successfully predicted the return of Halley’s Comet, the existence of Neptune, and continues to be used in engineering and orbital calculations. However, it fails to predict relativistic effects such as gravitational lensing, frame-dragging, or gravitational waves. These limitations reduce its predictive power on cosmic and high-precision scales. '''Cross-Disciplinary Compatibility''' Newton’s theory aligns well with classical physics and early chemistry but lacks compatibility with modern disciplines. It cannot be reconciled with special relativity or quantum theory and does not incorporate energy–momentum considerations as in modern field theories. Its incompatibility with relativity limits its integration with high-energy physics and astrophysics. '''Conceptual Clarity and Simplicity''' Newtonian gravity is conceptually simple and intuitively accessible. The inverse-square force law is easy to visualize and apply. It does not require advanced mathematics and remains an ideal teaching model. Its clarity and ease of computation give it enduring educational and practical value. '''Heuristic Value''' Although no longer a frontier theory, Newtonian gravity laid the groundwork for classical mechanics and much of modern science. It helped shape ideas about force, motion, and planetary systems. While it no longer drives active theoretical innovation, it retains historical heuristic importance. '''Historical and Philosophical Insight''' Newton’s theory was revolutionary in unifying terrestrial and celestial phenomena under the same laws of motion. It established the idea of a universal physical law and set the standard for quantitative science. Philosophically, it introduced mechanistic determinism and absolute space and time—concepts that dominated Enlightenment science. Though now superseded, its legacy remains foundational. === '''8.4.3 MOND (Modified Newtonian Dynamics)''' === '''Empirical Adequacy''' MOND was proposed by Mordehai Milgrom in the early 1980s to explain galactic rotation curves without invoking dark matter. It has successfully reproduced the flat rotation profiles of spiral galaxies and the observed baryonic Tully–Fisher relation with remarkable precision. MOND fits individual galaxy data with fewer parameters than dark matter models. However, it struggles with galaxy cluster dynamics, cosmological structure formation, and gravitational lensing in some systems. Its empirical adequacy is high for galactic scales but limited beyond that domain. '''Internal Consistency''' MOND is mathematically consistent in its non-relativistic form, where it modifies Newton’s second law at low accelerations using a new constant 𝑎 0 a 0 ​ . However, its original formulation lacks a full theoretical derivation from first principles and requires ad hoc modifications to the force law. Several relativistic extensions (e.g. TeVeS, AQUAL, BIMOND) have been developed to improve consistency, but these are not uniquely favored and remain complex or underconstrained. '''Predictive Power''' MOND has had considerable predictive success in galactic astrophysics. It predicted the baryonic Tully–Fisher relation before it was observationally confirmed, and it can reproduce detailed features of galaxy rotation curves without needing dark matter halos. However, it lacks explanatory power for phenomena like the cosmic microwave background (CMB) anisotropies, gravitational lensing in galaxy clusters (e.g. Bullet Cluster), and large-scale structure. Its predictive power is strong in its target domain but limited on cosmological scales. '''Cross-Disciplinary Compatibility''' MOND is primarily focused on galactic dynamics and does not integrate smoothly with high-energy physics, quantum theory, or cosmology. Its extensions to cosmology often require additional assumptions, and it is not yet compatible with standard particle physics. As a result, its cross-disciplinary reach is modest, though ongoing efforts aim to embed it within broader frameworks. '''Conceptual Clarity and Simplicity''' In its original form, MOND is simple: the gravitational acceleration deviates from Newton’s law when below a critical threshold 𝑎 0 a 0 ​ . This modification is intuitive and computationally effective for galaxies. However, attempts to embed MOND in a relativistic framework often add complexity, reducing its conceptual transparency. '''Heuristic Value''' MOND has had significant heuristic impact by highlighting regularities in galactic dynamics that are hard to explain under the ΛCDM paradigm without fine-tuned dark matter profiles. It has sparked debate, inspired hybrid theories (e.g. dark matter superfluidity), and contributed to reevaluating gravitational theory. Its challenge to mainstream cosmology has been fruitful, even if not universally accepted. '''Historical and Philosophical Insight''' MOND revives the idea that gravity itself may need modification, rather than positing unseen matter. This philosophical approach echoes the history of science, where anomalies sometimes led to revisions of theory rather than new entities. MOND also raises deep questions about the nature of inertia, scale invariance, and universal laws—making it a philosophically provocative proposal despite its contested status. === '''8.4.4 Emergent Gravity''' === '''Empirical Adequacy''' Emergent Gravity, proposed by Erik Verlinde in 2011 and expanded in 2016, seeks to explain gravitational phenomena as an emergent effect of underlying entropic and holographic principles rather than a fundamental force. It claims to reproduce galactic rotation curves without invoking dark matter by relating gravity to the thermodynamics of microscopic information storage on holographic screens. The theory can qualitatively explain certain galactic dynamics, such as the radial acceleration relation (RAR), but lacks the quantitative precision and scope of MOND in galaxy rotation curve fitting. It also currently cannot reproduce the full spectrum of cosmological observations, including the CMB power spectrum or gravitational lensing in galaxy clusters, where standard ΛCDM performs better. '''Internal Consistency''' Emergent Gravity draws from concepts in string theory, quantum information theory, and thermodynamics. While intellectually coherent and grounded in cutting-edge theoretical frameworks, the theory is still under development and lacks a universally accepted formalism. Key quantities (such as entropic force or the elastic response of spacetime) are not always rigorously defined, and derivations sometimes rely on analogies rather than strict derivations. This limits the formal internal consistency at present, though the conceptual framework remains promising. '''Predictive Power''' The theory makes some novel qualitative predictions, particularly regarding the relation between baryonic mass and gravitational acceleration without dark matter. It reproduces the RAR and may provide an explanation for dark energy as an entropic effect of spacetime. However, Emergent Gravity has not yet made precise predictions for cosmological parameters, gravitational wave behavior, or galaxy cluster dynamics that can be tested independently of standard models. Its predictive power remains speculative and qualitative. '''Cross-Disciplinary Compatibility''' Emergent Gravity attempts to bridge gravity, quantum information, and thermodynamics, making it conceptually rich in cross-disciplinary connections. It resonates with holography, the AdS/CFT correspondence, and black hole thermodynamics. However, the lack of experimental or observational confirmation limits its integration with empirical domains such as astrophysics, cosmology, and particle physics. Its compatibility is more theoretical than empirical at this stage. '''Conceptual Clarity and Simplicity''' The idea that gravity is not fundamental but emerges from statistical behavior of microscopic degrees of freedom is intellectually elegant. However, the actual implementation of this idea in the current models is technically complex and often abstract. Unlike Newtonian gravity or even MOND, the mechanisms proposed by Emergent Gravity are difficult to visualize or test directly, and involve high-level concepts from thermodynamics and information theory. '''Heuristic Value''' Emergent Gravity is highly heuristic. It opens new perspectives on the nature of gravity, spacetime, and entropy. By reframing gravity as an emergent entropic force, it challenges the foundations of both classical and relativistic theories. It has influenced discussions around the holographic principle, black hole entropy, and spacetime microstructure. Even if it remains incomplete, it contributes to rethinking gravity from first principles. '''Historical and Philosophical Insight''' Philosophically, Emergent Gravity aligns with the long-standing idea that some phenomena in nature arise from deeper, statistical processes rather than being fundamental. It recalls Boltzmann’s approach to thermodynamics and aligns with modern information-theoretic views of physics. Historically, it marks a shift from geometric to thermodynamic models of spacetime, and offers a bold alternative to particle-based explanations of gravity. Though controversial, it is part of a growing movement to reinterpret gravity in terms of entropy and information. === '''8.4.5 Big Bang''' === '''Empirical Adequacy''' The Big Bang model is the current standard cosmological paradigm and is strongly supported by multiple independent observations. These include the cosmic microwave background (CMB) radiation, the large-scale structure of the universe, the observed expansion of space (via redshift-distance relations), and the relative abundances of light elements (hydrogen, helium, deuterium, lithium), as predicted by Big Bang Nucleosynthesis (BBN). These confirmations make the Big Bang model one of the most empirically supported frameworks in cosmology. However, the model does not explain the origin of the singularity itself, and extensions such as inflation or dark energy are required to match detailed observations. '''Internal Consistency''' The Big Bang framework is based on solutions to Einstein's field equations (Friedmann–Lemaître–Robertson–Walker metrics), and it is mathematically consistent within the assumptions of general relativity and homogeneity/isotropy (the cosmological principle). However, the initial singularity remains a theoretical boundary where the equations break down, and the model does not include a quantum gravity regime. Extensions such as inflation and ΛCDM are necessary for consistency with observations, but these introduce additional assumptions and parameters, sometimes criticized as fine-tuning. '''Predictive Power''' The Big Bang model has made several successful predictions: the existence and spectrum of the CMB, the large-scale structure of galaxies, and the relative abundances of primordial elements. It also correctly anticipated the cooling of the universe and the redshift–distance relation. Inflationary extensions explain the flatness and horizon problems and predict the nearly scale-invariant spectrum of CMB fluctuations. While many predictions are retrodictive and interpreted within a flexible framework, the model continues to be highly predictive in key areas of cosmology. '''Cross-Disciplinary Compatibility''' The Big Bang model integrates with nuclear physics (BBN), atomic physics (recombination), and high-energy physics (inflation, particle freeze-out). It is broadly compatible with the Standard Model of particle physics and many theories of fundamental interactions. However, it lacks a connection to quantum gravity, and some tensions remain—such as the Hubble tension between early and late universe measurements—that challenge cross-scale consistency. '''Conceptual Clarity and Simplicity''' The core idea—a hot, dense early universe that expands and cools over time—is conceptually clear and widely accepted. However, the full ΛCDM model includes inflation, cold dark matter, and dark energy, which are not directly observable and require complex assumptions. These components reduce the model's simplicity and raise questions about the explanatory depth of the framework. '''Heuristic Value''' The Big Bang theory has driven vast developments in cosmology, observational astronomy, particle physics, and astrophysical instrumentation. It has generated decades of research questions and missions, including COBE, WMAP, and Planck. The inflationary paradigm and dark energy studies have emerged directly from this model. As a heuristic framework, it has proven extremely fertile. '''Historical and Philosophical Insight''' The Big Bang marks a major conceptual shift in cosmology by proposing that the universe has a temporal origin and evolves over time. It displaced steady-state and eternal models of the cosmos and opened up philosophical inquiries about creation, the arrow of time, and the origin of physical laws. Despite its name, it is not an explosion in space but the expansion of space itself—a concept that has reshaped how we understand time, causality, and the structure of the universe. === '''8.4.6 Steady State Theory''' === '''Empirical Adequacy''' The Steady State Theory, developed in the late 1940s by Bondi, Gold, and Hoyle, posits that the universe has no beginning or end in time and remains statistically the same on large scales, with matter continuously created to maintain constant density despite cosmic expansion. Initially, it matched observations of redshift and expansion, but it was ultimately undermined by key empirical discoveries: the cosmic microwave background (CMB), the evolution of radio source counts, and the observation of distant galaxies at earlier stages of development. These findings provided strong evidence of a hot, dense early universe, inconsistent with the steady state hypothesis. As a result, its empirical adequacy is now considered low. '''Internal Consistency''' The theory is internally consistent in its classical formulation and relies on continuous creation of matter to maintain a constant density. However, this matter creation mechanism was never supported by a detailed physical model or empirical detection. While mathematically coherent, the theory’s assumption of continuous creation violates energy conservation as understood in standard physics, making the underlying physics speculative and theoretically weak. '''Predictive Power''' The Steady State model made a bold prediction: the universe should appear the same at all times and places when viewed on large scales. While this was a clear and testable prediction, it was eventually falsified by observations such as the CMB and the evolution of quasars and galaxy populations over time. The theory’s few predictions have largely been refuted, limiting its scientific utility. '''Cross-Disciplinary Compatibility''' The model is only weakly connected to other scientific domains. It does not integrate well with nuclear physics, as it lacks a mechanism for element formation similar to Big Bang Nucleosynthesis. It also lacks compatibility with high-energy particle physics and modern theories of gravity. The continuous matter creation postulate has no foundation in quantum theory or experimental physics. '''Conceptual Clarity and Simplicity''' The steady-state model is conceptually simple and elegant. Its appeal lay in its ability to preserve a universe without origin, circumventing the philosophical and theological questions raised by a cosmic beginning. The model also maintains a uniform, eternal cosmos, which was attractive to many physicists in the mid-20th century. Despite being falsified, it remains a conceptually clear alternative that helped clarify the implications of observational cosmology. '''Heuristic Value''' Although it is no longer a viable cosmological model, the Steady State theory played a significant heuristic role. It prompted debates about the nature of time, observational testing, and the falsifiability of cosmological models. It helped shape the methodological standards for modern cosmology by being a well-defined, testable theory that was ultimately rejected based on empirical data. Its legacy lives on in discussions about the role of testability and philosophical assumptions in science. '''Historical and Philosophical Insight''' The Steady State theory was historically important as the main rival to the Big Bang model in the early post-war period. It reflects a philosophical preference for temporal infinity and equilibrium conditions, standing in contrast to a universe with a beginning. Its eventual rejection illustrates the triumph of observation over philosophical elegance in modern cosmology. It also served as a case study in the philosophy of science, particularly regarding Popperian falsifiability and the evolution of scientific consensus. === '''8.4.7 Big Crunch''' === '''Empirical Adequacy''' The Big Crunch is not a theory of gravity or cosmology by itself but rather a hypothetical end-state of the universe within certain cosmological models. It posits that cosmic expansion could eventually reverse, causing the universe to contract back into a high-density singularity. This scenario arises from general relativity under the assumption of a closed universe with sufficient matter density to overcome expansion. However, current observational data strongly indicate that the universe is accelerating in its expansion, driven by dark energy. Measurements of the cosmic microwave background (CMB), supernova distances, and large-scale structure all support a flat or open universe with low matter density, making the Big Crunch scenario empirically disfavored at present. '''Internal Consistency''' Within general relativity and standard cosmological models, the Big Crunch is internally consistent. It naturally arises from the Friedmann equations when the density parameter Ω > 1 and the cosmological constant is absent or negative. The dynamics of contraction mirror those of expansion in reverse, and no logical contradictions emerge in its mathematical formulation. However, near the final singularity, quantum gravitational effects become important, and the classical equations break down. '''Predictive Power''' As a hypothetical scenario, the Big Crunch does not offer specific predictive claims under current physical conditions. Instead, it represents a conditional outcome: if the universe were closed and dominated by matter, it would eventually recollapse. Since observations show otherwise, the predictive relevance of the Big Crunch is now limited. Nevertheless, it played a role in exploring time-reversal symmetry, thermodynamic limits, and quantum cosmology. '''Cross-Disciplinary Compatibility''' The Big Crunch scenario is compatible with general relativity and classical thermodynamics, especially in discussions of entropy and the arrow of time. It has also been explored in speculative models of cyclic or oscillating universes, which relate to quantum gravity and string theory. However, it lacks strong support from empirical fields such as observational cosmology, particle physics, or astronomy under the current ΛCDM framework. '''Conceptual Clarity and Simplicity''' The concept is straightforward: the universe's expansion halts and reverses into a collapse. This time-symmetric model is intuitively appealing and easy to visualize. However, its physical plausibility is undermined by current evidence for accelerating expansion. Still, as a conceptual tool, it remains a clear contrast to models of eternal expansion or thermal death. '''Heuristic Value''' Historically, the Big Crunch scenario stimulated discussion about cosmological cycles, entropy limits, and the ultimate fate of the universe. It led to the development of cyclic models, bounce cosmologies, and ideas about cosmic rebirth. Although largely ruled out by current data, it retains heuristic value in theoretical cosmology and philosophy of time, particularly in exploring whether time and entropy could reverse. '''Historical and Philosophical Insight''' The Big Crunch offered a philosophically symmetric alternative to the Big Bang—a universe that begins and ends in a singularity. It invites reflection on the reversibility of physical laws, the meaning of cosmic time, and the possibility of eternal recurrence. While empirical support is lacking, the scenario remains a historically meaningful part of cosmological thinking, especially in the 20th-century debates about the universe's fate. === '''8.4.8 Big Bounce''' === '''Empirical Adequacy''' The Big Bounce is a speculative cosmological scenario in which the universe undergoes a cycle of contraction followed by a rebound (or "bounce") into a new phase of expansion. It aims to replace the initial singularity of the Big Bang with a transitional phase where quantum gravitational effects prevent infinite density. While the concept is consistent with certain theoretical models—particularly in loop quantum cosmology—there is currently no direct observational evidence for a bounce event. The cosmic microwave background (CMB) does not yet show unambiguous signatures that would favor a bounce over inflationary models. Thus, empirical adequacy remains hypothetical, though not excluded. '''Internal Consistency''' The Big Bounce can be formulated consistently within several frameworks, such as loop quantum gravity, string gas cosmology, or modified gravity models. In these settings, quantum corrections to the Friedmann equations or modifications to the geometry of spacetime prevent a singularity and allow for a smooth transition from contraction to expansion. However, different bounce models vary in their assumptions, and the full quantum dynamics are not yet universally agreed upon. Despite these uncertainties, the internal logic of the models is coherent within their theoretical boundaries. '''Predictive Power''' Some Big Bounce models predict subtle features in the CMB, such as suppressed power at large angular scales, or non-Gaussianities that differ from inflation. However, these predictions often overlap with or are degenerate with inflationary predictions, making them hard to test uniquely. No conclusive observational support has been found so far. Nevertheless, bounce models offer a predictive framework that could, in principle, be tested with improved cosmological data in the future. '''Cross-Disciplinary Compatibility''' The Big Bounce scenario is motivated by attempts to unify quantum mechanics and gravity. It connects well with developments in loop quantum cosmology, non-singular black hole models, and string theory. However, it is less developed in its links to particle physics, standard cosmology, or astrophysical observations. Its broader scientific compatibility depends heavily on which theoretical approach is adopted and how it interfaces with known physics. '''Conceptual Clarity and Simplicity''' The idea of a contracting universe rebounding into expansion is conceptually intuitive and avoids the metaphysical implications of a beginning-of-time singularity. In contrast to the Big Bang singularity, the bounce implies a cyclic or oscillatory universe that is eternal in time. While appealing in its symmetry, the underlying physics is often highly technical and abstract, involving non-perturbative quantum gravity, which reduces its practical simplicity. '''Heuristic Value''' The Big Bounce has stimulated important discussions in cosmology, particularly regarding singularity avoidance, pre-Big Bang scenarios, and the nature of time. It has inspired a class of alternative models to inflation and opened up debates about the cyclical nature of the universe. Its challenge to the standard narrative of cosmic origins has heuristic value in motivating new lines of theoretical research. '''Historical and Philosophical Insight''' The Big Bounce continues a long tradition of cyclical universe models, echoing ideas from ancient cosmologies and early 20th-century oscillating universe theories. Philosophically, it provides a framework in which the universe has no absolute beginning or end, and where time and entropy may operate in a larger looped framework. It offers a more balanced cosmological picture than the irreversible expansion or final collapse scenarios. Though not yet supported by data, its philosophical implications remain profound and open-ended. === '''8.4.9 Cosmic Influx Theory (CIT)''' === Cosmic Influx Theory (CIT), proposed by Ruud Loeffen, reinterprets gravity as a directional energy influx driven by Primordial Elementary Whirlings (PEWs), replacing the concept of attractive force or space-time curvature. It introduces a constant influx of mass-energy into all bodies, contributing to planetary expansion, star formation, and cosmological evolution. 1. '''Internal Consistency''' CIT presents a coherent internal logic based on a unidirectional influx mechanism, a redefined gravitational constant (G = (γ − 1)/4π), and the introduction of κ_CIT as a universal scaling constant. While the framework remains internally consistent, some equations are still under refinement and lack full derivations from first principles. 2. '''Predictive Power''' CIT predicts the Preferred Distance for giant planets based on κ_CIT, orbital periods of exoplanets, and a revised Hubble constant (Ho ≈ 67.8 km/s/Mpc). It also anticipates planetary expansion through mass influx. These predictions are testable, though many remain pending observational confirmation. 3. '''Falsifiability''' Several predictions—such as giant planets at D_pref in the Trappist system or mass accumulation rates inferred from planetary geology—can be tested. However, the influx mechanism itself is not yet described in terms of directly measurable particles or interactions, which may limit falsifiability at the quantum level. 4. '''Observational Alignment''' CIT aligns with various observations: early formation of giant planets in protoplanetary disks, planetary expansion signatures, surface geology of moons and Mars, and recent JWST disk structures. It also claims to naturally derive the observed Hubble constant without tension. 5. '''Philosophical Transparency''' The theory clearly departs from Newtonian and relativistic interpretations, positioning itself as an ontological alternative grounded in energy flow. The author's motivations, limitations, and intended scope are transparently communicated in both academic and public forums. 6. '''Empirical Adequacy''' CIT offers empirical parallels in planetary spacing (κ_CIT), daylength extension over geological time, and disk fragmentation patterns. However, it currently lacks publication in high-impact peer-reviewed journals and formal statistical validation across broad datasets. 7. '''Institutional Support and Development''' CIT is developed independently, primarily through Wikiversity and open-access platforms. While it incorporates extensive cross-referencing and engages with mainstream and alternative sources, it lacks institutional affiliation and academic endorsement at this stage. '''Related link:''' [[Cosmic Influx Theory]] === '''8.4.10 Summary of Spiral Cosmology''' === The Pearlman Cosmology (SPIRAL Cosmology) offers a deterministic model of the universe with a defined hyper-dense initial state, fixed radius growth, and a reinterpretation of redshift. It integrates biblical chronology into its cosmological assumptions, making it a unique hybrid of scientific and scriptural reasoning. 1. '''Internal Consistency''' The model presents a logically consistent internal framework, with clearly defined initial conditions such as the SPIRAL radius, gravitational equilibrium, and fixed cosmic time scaling. Its components align well within its own assumptions. 2. '''Predictive Power''' Pearlman Cosmology proposes several potentially testable hypotheses, such as a fixed annual rate of universal expansion and an alternative explanation of redshift. However, these are not yet accompanied by detailed numeric predictions or simulations. 3. '''Falsifiability''' Testable elements exist in the form of reinterpretations of the cosmic microwave background origin, early galaxy formation, and redshift asymmetries. Yet aspects based on Mosaic chronology may fall outside strict scientific falsifiability. 4. '''Observational Alignment''' The model qualitatively aligns with some recent JWST observations, including early structure formation and CMB uniformity. Nevertheless, it lacks robust quantitative matching with large datasets or predictive modeling. 5. '''Philosophical Transparency''' The theory is open about its use of religious chronology and framing. This transparency makes its worldview explicit, though it may hinder its acceptance within mainstream secular science. 6. '''Empirical Adequacy''' While some empirical parallels exist, the theory has not yet been tested against a wide body of observational data in a systematic or peer-reviewed way. 7. '''Institutional Support and Development''' Pearlman Cosmology remains outside institutional research frameworks. Its development and publication history are limited, and it has not yet entered mainstream cosmological discourse. '''Related link:''' [https://www.pearlman.org Pearlman Cosmology] '''◀ [[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 ▶]]''' 6101fgk49uaigkw8k0zvwe6skibgayr 2719986 2719985 2025-06-29T04:34:22Z Ruud Loeffen 2998353 /* 8.4.2 Newtonian Gravity */ add link to this theory 2719986 wikitext text/x-wiki == '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' = == '''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. == '''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 == '''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 such as: Observational Agreement Internal Logical Consistency Predictive Value Compatibility with Other Domains (e.g., geology, biology) Conceptual Coherence and Simplicity Each dimension is rated using a 1–5 star system, based on the information provided and the supporting sources that AI can access. 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. == '''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. == '''8.1 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. '''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. '''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. '''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. '''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. '''5. Conceptual Clarity and Simplicity''' Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification. '''6. Heuristic Value''' Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential. '''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. 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 or can be requested in more detail. == '''8.2 AI Evaluation Table Format''' == {| class="wikitable" |+ '''AI Evaluation Table of Cosmological Theories''' ! Theory Name ! Empirical Adequacy ! Internal Consistency ! Predictive Power ! Cross-Disciplinary Compatibility ! Conceptual Clarity and Simplicity ! Heuristic Value ! Historical & Philosophical Insight ! Total (★) |- | 8.4.1 '''General Relativity''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★★ || '''34''' |- | colspan="9" | ''Widely confirmed by experiment; mathematical elegance; historical development from Newtonian mechanics'' |- |- | 8.4.2 '''Newtonian Gravity''' | ★★★★☆ || ★★★★★ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''30''' |- | colspan="9" | ''Highly successful in classical mechanics and celestial predictions; lacks compatibility with relativity and quantum theory; historically foundational.'' |- | 8.4.3 '''MOND (Modified Newtonian Dynamics)''' | ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''24''' |- | colspan="9" | ''Strong in galactic rotation curves; limited compatibility with general relativistic frameworks'' |- | 8.4.4 '''Emergent Gravity (Verlinde)''' | ★★☆☆☆ || ★★★★☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''25''' |- | colspan="9" | ''Innovative reformulation; still awaiting broad empirical confirmation'' |- | 8.4.5 '''Big Bang Model''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''31''' |- | colspan="9" | ''Core cosmological model; supported by CMB, redshift, nucleosynthesis'' |- | 8.4.6 '''Steady State Theory''' | ★☆☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''23''' |- | colspan="9" | ''Historically important; largely superseded due to lack of CMB explanation'' |- | 8.4.7 '''Big Crunch Theory''' | ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || '''28''' |- | colspan="9" | ''Predicts final collapse of universe; consistent with GR in high-density scenarios; revived interest due to dark energy variability'' |- | 8.4.8 '''Big Bounce Theory''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''26''' |- | colspan="9" | ''Cyclical alternative to singularity; compatible with some quantum gravity models'' |- | 8.4.9 '''Cosmic Influx Theory (CIT)''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★★★★ || ★★★★☆ || '''26''' |- | colspan="9" | ''Offers cross-disciplinary compatibility; predicts mass growth and preferred orbital distances; alternative influx model under development'' |- | 8.4.10 '''SPIRAL Cosmology''' | ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22''' |- | colspan="9" | ''Proposes a hyper-dense proto-galactic phase preceding expansion; no need for ongoing dark energy or cosmic expansion; partially scriptural framing may limit falsifiability but testable claims (e.g. fixed-radius light departure) justify scientific review.'' |- | colspan="9" | ''Well-formulated alternative integrating orbital quantization; some empirical fit to planetary data; lacks full mainstream acceptance'' |} <!-- Add a blank line here --> == '''8.3 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]]'''. == '''8.4 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. === '''8.4.1 General Relativity'''=== '''Empirical Adequacy''' General Relativity (GR) is one of the most empirically validated theories in physics. It has successfully explained and predicted a wide range of gravitational phenomena, including the precession of Mercury’s perihelion, gravitational lensing of starlight, gravitational redshift, time dilation effects observed in satellite systems like GPS, and the Shapiro delay. More recently, its predictions have been confirmed by gravitational wave observations (LIGO/Virgo) and direct imaging of black holes (Event Horizon Telescope). The agreement between theory and measurement is often better than 0.01%, demonstrating exceptional empirical adequacy. '''Internal Consistency''' GR is internally consistent within its mathematical framework. It is based on the Einstein field equations, which are derived from well-defined variational principles and respect general covariance. The logical structure of the theory is rigorous, with clearly formulated assumptions such as the equivalence principle and the conservation of energy–momentum through the stress-energy tensor. There are no known internal contradictions. '''Predictive Power''' GR has a powerful record of making novel predictions that were later confirmed by experiment or observation. These include the bending of light by massive bodies, time dilation in gravitational fields, the expansion of the universe (through its application in cosmology), and the existence of gravitational waves. Its predictions have often preceded direct detection by decades. This makes GR a model example of a theory with high predictive power. '''Cross-Disciplinary Compatibility''' General Relativity is compatible with many areas of physics, including classical mechanics, electrodynamics, and astrophysics. However, it is not yet unified with quantum mechanics. Attempts to reconcile GR with the Standard Model—such as quantum gravity, string theory, or loop quantum gravity—remain incomplete. Thus, GR scores slightly lower here due to its current incompatibility with modern particle physics at the Planck scale. '''Conceptual Clarity and Simplicity''' The core idea of GR—that gravity is not a force but a geometric property of spacetime—is conceptually elegant. However, the mathematical formalism (involving tensor calculus and differential geometry) is complex and often inaccessible to non-specialists. While the theory offers deep conceptual clarity, its practical simplicity is limited by the required mathematical tools. '''Heuristic Value''' GR has inspired generations of physicists and remains a fertile ground for theoretical development. It has opened up entire fields such as relativistic astrophysics, cosmology, and gravitational wave astronomy. Its influence extends beyond physics into philosophy and the public imagination. It continues to motivate research on black holes, time travel, singularities, and the early universe. '''Historical and Philosophical Insight''' Historically, GR represents a revolutionary shift in physics, displacing the Newtonian notion of absolute space and time with a dynamic, curved spacetime model. Philosophically, it challenges classical intuitions about gravity and causality and has inspired reevaluation of concepts such as simultaneity, locality, and determinism. Its legacy places it among the most profound achievements in scientific history. '''Related link:''' [https://en.wikipedia.org/wiki/General_relativity General Relativity] === '''8.4.2 Newtonian Gravity''' === '''Empirical Adequacy''' Newtonian gravity has historically achieved remarkable empirical success. It accurately describes planetary motions, tidal forces, ballistic trajectories, and satellite orbits. For centuries, it provided the dominant framework for celestial mechanics and was sufficient for navigation, astronomy, and engineering. However, it begins to fail in extreme gravitational fields or at very high speeds, where relativistic corrections are needed. It also cannot explain phenomena like the precession of Mercury’s orbit, gravitational time dilation, or the bending of light. '''Internal Consistency''' Within its classical framework, Newtonian gravity is highly consistent. It is based on clear axioms such as the inverse-square law and absolute space and time. The mathematical structure is well-defined and solvable using Newton’s laws of motion and calculus. No logical contradictions arise within its scope of applicability. However, its assumptions about instantaneous action at a distance are problematic under modern physical understanding. '''Predictive Power''' Newtonian gravity has strong predictive power in low-speed, weak-field regimes. It successfully predicted the return of Halley’s Comet, the existence of Neptune, and continues to be used in engineering and orbital calculations. However, it fails to predict relativistic effects such as gravitational lensing, frame-dragging, or gravitational waves. These limitations reduce its predictive power on cosmic and high-precision scales. '''Cross-Disciplinary Compatibility''' Newton’s theory aligns well with classical physics and early chemistry but lacks compatibility with modern disciplines. It cannot be reconciled with special relativity or quantum theory and does not incorporate energy–momentum considerations as in modern field theories. Its incompatibility with relativity limits its integration with high-energy physics and astrophysics. '''Conceptual Clarity and Simplicity''' Newtonian gravity is conceptually simple and intuitively accessible. The inverse-square force law is easy to visualize and apply. It does not require advanced mathematics and remains an ideal teaching model. Its clarity and ease of computation give it enduring educational and practical value. '''Heuristic Value''' Although no longer a frontier theory, Newtonian gravity laid the groundwork for classical mechanics and much of modern science. It helped shape ideas about force, motion, and planetary systems. While it no longer drives active theoretical innovation, it retains historical heuristic importance. '''Historical and Philosophical Insight''' Newton’s theory was revolutionary in unifying terrestrial and celestial phenomena under the same laws of motion. It established the idea of a universal physical law and set the standard for quantitative science. Philosophically, it introduced mechanistic determinism and absolute space and time—concepts that dominated Enlightenment science. Though now superseded, its legacy remains foundational. '''Related link:''' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newtonian Gravity] === '''8.4.3 MOND (Modified Newtonian Dynamics)''' === '''Empirical Adequacy''' MOND was proposed by Mordehai Milgrom in the early 1980s to explain galactic rotation curves without invoking dark matter. It has successfully reproduced the flat rotation profiles of spiral galaxies and the observed baryonic Tully–Fisher relation with remarkable precision. MOND fits individual galaxy data with fewer parameters than dark matter models. However, it struggles with galaxy cluster dynamics, cosmological structure formation, and gravitational lensing in some systems. Its empirical adequacy is high for galactic scales but limited beyond that domain. '''Internal Consistency''' MOND is mathematically consistent in its non-relativistic form, where it modifies Newton’s second law at low accelerations using a new constant 𝑎 0 a 0 ​ . However, its original formulation lacks a full theoretical derivation from first principles and requires ad hoc modifications to the force law. Several relativistic extensions (e.g. TeVeS, AQUAL, BIMOND) have been developed to improve consistency, but these are not uniquely favored and remain complex or underconstrained. '''Predictive Power''' MOND has had considerable predictive success in galactic astrophysics. It predicted the baryonic Tully–Fisher relation before it was observationally confirmed, and it can reproduce detailed features of galaxy rotation curves without needing dark matter halos. However, it lacks explanatory power for phenomena like the cosmic microwave background (CMB) anisotropies, gravitational lensing in galaxy clusters (e.g. Bullet Cluster), and large-scale structure. Its predictive power is strong in its target domain but limited on cosmological scales. '''Cross-Disciplinary Compatibility''' MOND is primarily focused on galactic dynamics and does not integrate smoothly with high-energy physics, quantum theory, or cosmology. Its extensions to cosmology often require additional assumptions, and it is not yet compatible with standard particle physics. As a result, its cross-disciplinary reach is modest, though ongoing efforts aim to embed it within broader frameworks. '''Conceptual Clarity and Simplicity''' In its original form, MOND is simple: the gravitational acceleration deviates from Newton’s law when below a critical threshold 𝑎 0 a 0 ​ . This modification is intuitive and computationally effective for galaxies. However, attempts to embed MOND in a relativistic framework often add complexity, reducing its conceptual transparency. '''Heuristic Value''' MOND has had significant heuristic impact by highlighting regularities in galactic dynamics that are hard to explain under the ΛCDM paradigm without fine-tuned dark matter profiles. It has sparked debate, inspired hybrid theories (e.g. dark matter superfluidity), and contributed to reevaluating gravitational theory. Its challenge to mainstream cosmology has been fruitful, even if not universally accepted. '''Historical and Philosophical Insight''' MOND revives the idea that gravity itself may need modification, rather than positing unseen matter. This philosophical approach echoes the history of science, where anomalies sometimes led to revisions of theory rather than new entities. MOND also raises deep questions about the nature of inertia, scale invariance, and universal laws—making it a philosophically provocative proposal despite its contested status. === '''8.4.4 Emergent Gravity''' === '''Empirical Adequacy''' Emergent Gravity, proposed by Erik Verlinde in 2011 and expanded in 2016, seeks to explain gravitational phenomena as an emergent effect of underlying entropic and holographic principles rather than a fundamental force. It claims to reproduce galactic rotation curves without invoking dark matter by relating gravity to the thermodynamics of microscopic information storage on holographic screens. The theory can qualitatively explain certain galactic dynamics, such as the radial acceleration relation (RAR), but lacks the quantitative precision and scope of MOND in galaxy rotation curve fitting. It also currently cannot reproduce the full spectrum of cosmological observations, including the CMB power spectrum or gravitational lensing in galaxy clusters, where standard ΛCDM performs better. '''Internal Consistency''' Emergent Gravity draws from concepts in string theory, quantum information theory, and thermodynamics. While intellectually coherent and grounded in cutting-edge theoretical frameworks, the theory is still under development and lacks a universally accepted formalism. Key quantities (such as entropic force or the elastic response of spacetime) are not always rigorously defined, and derivations sometimes rely on analogies rather than strict derivations. This limits the formal internal consistency at present, though the conceptual framework remains promising. '''Predictive Power''' The theory makes some novel qualitative predictions, particularly regarding the relation between baryonic mass and gravitational acceleration without dark matter. It reproduces the RAR and may provide an explanation for dark energy as an entropic effect of spacetime. However, Emergent Gravity has not yet made precise predictions for cosmological parameters, gravitational wave behavior, or galaxy cluster dynamics that can be tested independently of standard models. Its predictive power remains speculative and qualitative. '''Cross-Disciplinary Compatibility''' Emergent Gravity attempts to bridge gravity, quantum information, and thermodynamics, making it conceptually rich in cross-disciplinary connections. It resonates with holography, the AdS/CFT correspondence, and black hole thermodynamics. However, the lack of experimental or observational confirmation limits its integration with empirical domains such as astrophysics, cosmology, and particle physics. Its compatibility is more theoretical than empirical at this stage. '''Conceptual Clarity and Simplicity''' The idea that gravity is not fundamental but emerges from statistical behavior of microscopic degrees of freedom is intellectually elegant. However, the actual implementation of this idea in the current models is technically complex and often abstract. Unlike Newtonian gravity or even MOND, the mechanisms proposed by Emergent Gravity are difficult to visualize or test directly, and involve high-level concepts from thermodynamics and information theory. '''Heuristic Value''' Emergent Gravity is highly heuristic. It opens new perspectives on the nature of gravity, spacetime, and entropy. By reframing gravity as an emergent entropic force, it challenges the foundations of both classical and relativistic theories. It has influenced discussions around the holographic principle, black hole entropy, and spacetime microstructure. Even if it remains incomplete, it contributes to rethinking gravity from first principles. '''Historical and Philosophical Insight''' Philosophically, Emergent Gravity aligns with the long-standing idea that some phenomena in nature arise from deeper, statistical processes rather than being fundamental. It recalls Boltzmann’s approach to thermodynamics and aligns with modern information-theoretic views of physics. Historically, it marks a shift from geometric to thermodynamic models of spacetime, and offers a bold alternative to particle-based explanations of gravity. Though controversial, it is part of a growing movement to reinterpret gravity in terms of entropy and information. === '''8.4.5 Big Bang''' === '''Empirical Adequacy''' The Big Bang model is the current standard cosmological paradigm and is strongly supported by multiple independent observations. These include the cosmic microwave background (CMB) radiation, the large-scale structure of the universe, the observed expansion of space (via redshift-distance relations), and the relative abundances of light elements (hydrogen, helium, deuterium, lithium), as predicted by Big Bang Nucleosynthesis (BBN). These confirmations make the Big Bang model one of the most empirically supported frameworks in cosmology. However, the model does not explain the origin of the singularity itself, and extensions such as inflation or dark energy are required to match detailed observations. '''Internal Consistency''' The Big Bang framework is based on solutions to Einstein's field equations (Friedmann–Lemaître–Robertson–Walker metrics), and it is mathematically consistent within the assumptions of general relativity and homogeneity/isotropy (the cosmological principle). However, the initial singularity remains a theoretical boundary where the equations break down, and the model does not include a quantum gravity regime. Extensions such as inflation and ΛCDM are necessary for consistency with observations, but these introduce additional assumptions and parameters, sometimes criticized as fine-tuning. '''Predictive Power''' The Big Bang model has made several successful predictions: the existence and spectrum of the CMB, the large-scale structure of galaxies, and the relative abundances of primordial elements. It also correctly anticipated the cooling of the universe and the redshift–distance relation. Inflationary extensions explain the flatness and horizon problems and predict the nearly scale-invariant spectrum of CMB fluctuations. While many predictions are retrodictive and interpreted within a flexible framework, the model continues to be highly predictive in key areas of cosmology. '''Cross-Disciplinary Compatibility''' The Big Bang model integrates with nuclear physics (BBN), atomic physics (recombination), and high-energy physics (inflation, particle freeze-out). It is broadly compatible with the Standard Model of particle physics and many theories of fundamental interactions. However, it lacks a connection to quantum gravity, and some tensions remain—such as the Hubble tension between early and late universe measurements—that challenge cross-scale consistency. '''Conceptual Clarity and Simplicity''' The core idea—a hot, dense early universe that expands and cools over time—is conceptually clear and widely accepted. However, the full ΛCDM model includes inflation, cold dark matter, and dark energy, which are not directly observable and require complex assumptions. These components reduce the model's simplicity and raise questions about the explanatory depth of the framework. '''Heuristic Value''' The Big Bang theory has driven vast developments in cosmology, observational astronomy, particle physics, and astrophysical instrumentation. It has generated decades of research questions and missions, including COBE, WMAP, and Planck. The inflationary paradigm and dark energy studies have emerged directly from this model. As a heuristic framework, it has proven extremely fertile. '''Historical and Philosophical Insight''' The Big Bang marks a major conceptual shift in cosmology by proposing that the universe has a temporal origin and evolves over time. It displaced steady-state and eternal models of the cosmos and opened up philosophical inquiries about creation, the arrow of time, and the origin of physical laws. Despite its name, it is not an explosion in space but the expansion of space itself—a concept that has reshaped how we understand time, causality, and the structure of the universe. === '''8.4.6 Steady State Theory''' === '''Empirical Adequacy''' The Steady State Theory, developed in the late 1940s by Bondi, Gold, and Hoyle, posits that the universe has no beginning or end in time and remains statistically the same on large scales, with matter continuously created to maintain constant density despite cosmic expansion. Initially, it matched observations of redshift and expansion, but it was ultimately undermined by key empirical discoveries: the cosmic microwave background (CMB), the evolution of radio source counts, and the observation of distant galaxies at earlier stages of development. These findings provided strong evidence of a hot, dense early universe, inconsistent with the steady state hypothesis. As a result, its empirical adequacy is now considered low. '''Internal Consistency''' The theory is internally consistent in its classical formulation and relies on continuous creation of matter to maintain a constant density. However, this matter creation mechanism was never supported by a detailed physical model or empirical detection. While mathematically coherent, the theory’s assumption of continuous creation violates energy conservation as understood in standard physics, making the underlying physics speculative and theoretically weak. '''Predictive Power''' The Steady State model made a bold prediction: the universe should appear the same at all times and places when viewed on large scales. While this was a clear and testable prediction, it was eventually falsified by observations such as the CMB and the evolution of quasars and galaxy populations over time. The theory’s few predictions have largely been refuted, limiting its scientific utility. '''Cross-Disciplinary Compatibility''' The model is only weakly connected to other scientific domains. It does not integrate well with nuclear physics, as it lacks a mechanism for element formation similar to Big Bang Nucleosynthesis. It also lacks compatibility with high-energy particle physics and modern theories of gravity. The continuous matter creation postulate has no foundation in quantum theory or experimental physics. '''Conceptual Clarity and Simplicity''' The steady-state model is conceptually simple and elegant. Its appeal lay in its ability to preserve a universe without origin, circumventing the philosophical and theological questions raised by a cosmic beginning. The model also maintains a uniform, eternal cosmos, which was attractive to many physicists in the mid-20th century. Despite being falsified, it remains a conceptually clear alternative that helped clarify the implications of observational cosmology. '''Heuristic Value''' Although it is no longer a viable cosmological model, the Steady State theory played a significant heuristic role. It prompted debates about the nature of time, observational testing, and the falsifiability of cosmological models. It helped shape the methodological standards for modern cosmology by being a well-defined, testable theory that was ultimately rejected based on empirical data. Its legacy lives on in discussions about the role of testability and philosophical assumptions in science. '''Historical and Philosophical Insight''' The Steady State theory was historically important as the main rival to the Big Bang model in the early post-war period. It reflects a philosophical preference for temporal infinity and equilibrium conditions, standing in contrast to a universe with a beginning. Its eventual rejection illustrates the triumph of observation over philosophical elegance in modern cosmology. It also served as a case study in the philosophy of science, particularly regarding Popperian falsifiability and the evolution of scientific consensus. === '''8.4.7 Big Crunch''' === '''Empirical Adequacy''' The Big Crunch is not a theory of gravity or cosmology by itself but rather a hypothetical end-state of the universe within certain cosmological models. It posits that cosmic expansion could eventually reverse, causing the universe to contract back into a high-density singularity. This scenario arises from general relativity under the assumption of a closed universe with sufficient matter density to overcome expansion. However, current observational data strongly indicate that the universe is accelerating in its expansion, driven by dark energy. Measurements of the cosmic microwave background (CMB), supernova distances, and large-scale structure all support a flat or open universe with low matter density, making the Big Crunch scenario empirically disfavored at present. '''Internal Consistency''' Within general relativity and standard cosmological models, the Big Crunch is internally consistent. It naturally arises from the Friedmann equations when the density parameter Ω > 1 and the cosmological constant is absent or negative. The dynamics of contraction mirror those of expansion in reverse, and no logical contradictions emerge in its mathematical formulation. However, near the final singularity, quantum gravitational effects become important, and the classical equations break down. '''Predictive Power''' As a hypothetical scenario, the Big Crunch does not offer specific predictive claims under current physical conditions. Instead, it represents a conditional outcome: if the universe were closed and dominated by matter, it would eventually recollapse. Since observations show otherwise, the predictive relevance of the Big Crunch is now limited. Nevertheless, it played a role in exploring time-reversal symmetry, thermodynamic limits, and quantum cosmology. '''Cross-Disciplinary Compatibility''' The Big Crunch scenario is compatible with general relativity and classical thermodynamics, especially in discussions of entropy and the arrow of time. It has also been explored in speculative models of cyclic or oscillating universes, which relate to quantum gravity and string theory. However, it lacks strong support from empirical fields such as observational cosmology, particle physics, or astronomy under the current ΛCDM framework. '''Conceptual Clarity and Simplicity''' The concept is straightforward: the universe's expansion halts and reverses into a collapse. This time-symmetric model is intuitively appealing and easy to visualize. However, its physical plausibility is undermined by current evidence for accelerating expansion. Still, as a conceptual tool, it remains a clear contrast to models of eternal expansion or thermal death. '''Heuristic Value''' Historically, the Big Crunch scenario stimulated discussion about cosmological cycles, entropy limits, and the ultimate fate of the universe. It led to the development of cyclic models, bounce cosmologies, and ideas about cosmic rebirth. Although largely ruled out by current data, it retains heuristic value in theoretical cosmology and philosophy of time, particularly in exploring whether time and entropy could reverse. '''Historical and Philosophical Insight''' The Big Crunch offered a philosophically symmetric alternative to the Big Bang—a universe that begins and ends in a singularity. It invites reflection on the reversibility of physical laws, the meaning of cosmic time, and the possibility of eternal recurrence. While empirical support is lacking, the scenario remains a historically meaningful part of cosmological thinking, especially in the 20th-century debates about the universe's fate. === '''8.4.8 Big Bounce''' === '''Empirical Adequacy''' The Big Bounce is a speculative cosmological scenario in which the universe undergoes a cycle of contraction followed by a rebound (or "bounce") into a new phase of expansion. It aims to replace the initial singularity of the Big Bang with a transitional phase where quantum gravitational effects prevent infinite density. While the concept is consistent with certain theoretical models—particularly in loop quantum cosmology—there is currently no direct observational evidence for a bounce event. The cosmic microwave background (CMB) does not yet show unambiguous signatures that would favor a bounce over inflationary models. Thus, empirical adequacy remains hypothetical, though not excluded. '''Internal Consistency''' The Big Bounce can be formulated consistently within several frameworks, such as loop quantum gravity, string gas cosmology, or modified gravity models. In these settings, quantum corrections to the Friedmann equations or modifications to the geometry of spacetime prevent a singularity and allow for a smooth transition from contraction to expansion. However, different bounce models vary in their assumptions, and the full quantum dynamics are not yet universally agreed upon. Despite these uncertainties, the internal logic of the models is coherent within their theoretical boundaries. '''Predictive Power''' Some Big Bounce models predict subtle features in the CMB, such as suppressed power at large angular scales, or non-Gaussianities that differ from inflation. However, these predictions often overlap with or are degenerate with inflationary predictions, making them hard to test uniquely. No conclusive observational support has been found so far. Nevertheless, bounce models offer a predictive framework that could, in principle, be tested with improved cosmological data in the future. '''Cross-Disciplinary Compatibility''' The Big Bounce scenario is motivated by attempts to unify quantum mechanics and gravity. It connects well with developments in loop quantum cosmology, non-singular black hole models, and string theory. However, it is less developed in its links to particle physics, standard cosmology, or astrophysical observations. Its broader scientific compatibility depends heavily on which theoretical approach is adopted and how it interfaces with known physics. '''Conceptual Clarity and Simplicity''' The idea of a contracting universe rebounding into expansion is conceptually intuitive and avoids the metaphysical implications of a beginning-of-time singularity. In contrast to the Big Bang singularity, the bounce implies a cyclic or oscillatory universe that is eternal in time. While appealing in its symmetry, the underlying physics is often highly technical and abstract, involving non-perturbative quantum gravity, which reduces its practical simplicity. '''Heuristic Value''' The Big Bounce has stimulated important discussions in cosmology, particularly regarding singularity avoidance, pre-Big Bang scenarios, and the nature of time. It has inspired a class of alternative models to inflation and opened up debates about the cyclical nature of the universe. Its challenge to the standard narrative of cosmic origins has heuristic value in motivating new lines of theoretical research. '''Historical and Philosophical Insight''' The Big Bounce continues a long tradition of cyclical universe models, echoing ideas from ancient cosmologies and early 20th-century oscillating universe theories. Philosophically, it provides a framework in which the universe has no absolute beginning or end, and where time and entropy may operate in a larger looped framework. It offers a more balanced cosmological picture than the irreversible expansion or final collapse scenarios. Though not yet supported by data, its philosophical implications remain profound and open-ended. === '''8.4.9 Cosmic Influx Theory (CIT)''' === Cosmic Influx Theory (CIT), proposed by Ruud Loeffen, reinterprets gravity as a directional energy influx driven by Primordial Elementary Whirlings (PEWs), replacing the concept of attractive force or space-time curvature. It introduces a constant influx of mass-energy into all bodies, contributing to planetary expansion, star formation, and cosmological evolution. 1. '''Internal Consistency''' CIT presents a coherent internal logic based on a unidirectional influx mechanism, a redefined gravitational constant (G = (γ − 1)/4π), and the introduction of κ_CIT as a universal scaling constant. While the framework remains internally consistent, some equations are still under refinement and lack full derivations from first principles. 2. '''Predictive Power''' CIT predicts the Preferred Distance for giant planets based on κ_CIT, orbital periods of exoplanets, and a revised Hubble constant (Ho ≈ 67.8 km/s/Mpc). It also anticipates planetary expansion through mass influx. These predictions are testable, though many remain pending observational confirmation. 3. '''Falsifiability''' Several predictions—such as giant planets at D_pref in the Trappist system or mass accumulation rates inferred from planetary geology—can be tested. However, the influx mechanism itself is not yet described in terms of directly measurable particles or interactions, which may limit falsifiability at the quantum level. 4. '''Observational Alignment''' CIT aligns with various observations: early formation of giant planets in protoplanetary disks, planetary expansion signatures, surface geology of moons and Mars, and recent JWST disk structures. It also claims to naturally derive the observed Hubble constant without tension. 5. '''Philosophical Transparency''' The theory clearly departs from Newtonian and relativistic interpretations, positioning itself as an ontological alternative grounded in energy flow. The author's motivations, limitations, and intended scope are transparently communicated in both academic and public forums. 6. '''Empirical Adequacy''' CIT offers empirical parallels in planetary spacing (κ_CIT), daylength extension over geological time, and disk fragmentation patterns. However, it currently lacks publication in high-impact peer-reviewed journals and formal statistical validation across broad datasets. 7. '''Institutional Support and Development''' CIT is developed independently, primarily through Wikiversity and open-access platforms. While it incorporates extensive cross-referencing and engages with mainstream and alternative sources, it lacks institutional affiliation and academic endorsement at this stage. '''Related link:''' [[Cosmic Influx Theory]] === '''8.4.10 Summary of Spiral Cosmology''' === The Pearlman Cosmology (SPIRAL Cosmology) offers a deterministic model of the universe with a defined hyper-dense initial state, fixed radius growth, and a reinterpretation of redshift. It integrates biblical chronology into its cosmological assumptions, making it a unique hybrid of scientific and scriptural reasoning. 1. '''Internal Consistency''' The model presents a logically consistent internal framework, with clearly defined initial conditions such as the SPIRAL radius, gravitational equilibrium, and fixed cosmic time scaling. Its components align well within its own assumptions. 2. '''Predictive Power''' Pearlman Cosmology proposes several potentially testable hypotheses, such as a fixed annual rate of universal expansion and an alternative explanation of redshift. However, these are not yet accompanied by detailed numeric predictions or simulations. 3. '''Falsifiability''' Testable elements exist in the form of reinterpretations of the cosmic microwave background origin, early galaxy formation, and redshift asymmetries. Yet aspects based on Mosaic chronology may fall outside strict scientific falsifiability. 4. '''Observational Alignment''' The model qualitatively aligns with some recent JWST observations, including early structure formation and CMB uniformity. Nevertheless, it lacks robust quantitative matching with large datasets or predictive modeling. 5. '''Philosophical Transparency''' The theory is open about its use of religious chronology and framing. This transparency makes its worldview explicit, though it may hinder its acceptance within mainstream secular science. 6. '''Empirical Adequacy''' While some empirical parallels exist, the theory has not yet been tested against a wide body of observational data in a systematic or peer-reviewed way. 7. '''Institutional Support and Development''' Pearlman Cosmology remains outside institutional research frameworks. Its development and publication history are limited, and it has not yet entered mainstream cosmological discourse. '''Related link:''' [https://www.pearlman.org Pearlman Cosmology] '''◀ [[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 ▶]]''' e6853sjfp9kuyw7us10aoqz90ycqd13 2719987 2719986 2025-06-29T04:35:15Z Ruud Loeffen 2998353 /* 8.4.3 MOND (Modified Newtonian Dynamics) */ add link to the theory 2719987 wikitext text/x-wiki == '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' = == '''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. == '''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 == '''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 such as: Observational Agreement Internal Logical Consistency Predictive Value Compatibility with Other Domains (e.g., geology, biology) Conceptual Coherence and Simplicity Each dimension is rated using a 1–5 star system, based on the information provided and the supporting sources that AI can access. 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. == '''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. == '''8.1 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. '''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. '''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. '''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. '''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. '''5. Conceptual Clarity and Simplicity''' Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification. '''6. Heuristic Value''' Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential. '''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. 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 or can be requested in more detail. == '''8.2 AI Evaluation Table Format''' == {| class="wikitable" |+ '''AI Evaluation Table of Cosmological Theories''' ! Theory Name ! Empirical Adequacy ! Internal Consistency ! Predictive Power ! Cross-Disciplinary Compatibility ! Conceptual Clarity and Simplicity ! Heuristic Value ! Historical & Philosophical Insight ! Total (★) |- | 8.4.1 '''General Relativity''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★★ || '''34''' |- | colspan="9" | ''Widely confirmed by experiment; mathematical elegance; historical development from Newtonian mechanics'' |- |- | 8.4.2 '''Newtonian Gravity''' | ★★★★☆ || ★★★★★ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''30''' |- | colspan="9" | ''Highly successful in classical mechanics and celestial predictions; lacks compatibility with relativity and quantum theory; historically foundational.'' |- | 8.4.3 '''MOND (Modified Newtonian Dynamics)''' | ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''24''' |- | colspan="9" | ''Strong in galactic rotation curves; limited compatibility with general relativistic frameworks'' |- | 8.4.4 '''Emergent Gravity (Verlinde)''' | ★★☆☆☆ || ★★★★☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''25''' |- | colspan="9" | ''Innovative reformulation; still awaiting broad empirical confirmation'' |- | 8.4.5 '''Big Bang Model''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''31''' |- | colspan="9" | ''Core cosmological model; supported by CMB, redshift, nucleosynthesis'' |- | 8.4.6 '''Steady State Theory''' | ★☆☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''23''' |- | colspan="9" | ''Historically important; largely superseded due to lack of CMB explanation'' |- | 8.4.7 '''Big Crunch Theory''' | ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || '''28''' |- | colspan="9" | ''Predicts final collapse of universe; consistent with GR in high-density scenarios; revived interest due to dark energy variability'' |- | 8.4.8 '''Big Bounce Theory''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''26''' |- | colspan="9" | ''Cyclical alternative to singularity; compatible with some quantum gravity models'' |- | 8.4.9 '''Cosmic Influx Theory (CIT)''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★★★★ || ★★★★☆ || '''26''' |- | colspan="9" | ''Offers cross-disciplinary compatibility; predicts mass growth and preferred orbital distances; alternative influx model under development'' |- | 8.4.10 '''SPIRAL Cosmology''' | ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22''' |- | colspan="9" | ''Proposes a hyper-dense proto-galactic phase preceding expansion; no need for ongoing dark energy or cosmic expansion; partially scriptural framing may limit falsifiability but testable claims (e.g. fixed-radius light departure) justify scientific review.'' |- | colspan="9" | ''Well-formulated alternative integrating orbital quantization; some empirical fit to planetary data; lacks full mainstream acceptance'' |} <!-- Add a blank line here --> == '''8.3 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]]'''. == '''8.4 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. === '''8.4.1 General Relativity'''=== '''Empirical Adequacy''' General Relativity (GR) is one of the most empirically validated theories in physics. It has successfully explained and predicted a wide range of gravitational phenomena, including the precession of Mercury’s perihelion, gravitational lensing of starlight, gravitational redshift, time dilation effects observed in satellite systems like GPS, and the Shapiro delay. More recently, its predictions have been confirmed by gravitational wave observations (LIGO/Virgo) and direct imaging of black holes (Event Horizon Telescope). The agreement between theory and measurement is often better than 0.01%, demonstrating exceptional empirical adequacy. '''Internal Consistency''' GR is internally consistent within its mathematical framework. It is based on the Einstein field equations, which are derived from well-defined variational principles and respect general covariance. The logical structure of the theory is rigorous, with clearly formulated assumptions such as the equivalence principle and the conservation of energy–momentum through the stress-energy tensor. There are no known internal contradictions. '''Predictive Power''' GR has a powerful record of making novel predictions that were later confirmed by experiment or observation. These include the bending of light by massive bodies, time dilation in gravitational fields, the expansion of the universe (through its application in cosmology), and the existence of gravitational waves. Its predictions have often preceded direct detection by decades. This makes GR a model example of a theory with high predictive power. '''Cross-Disciplinary Compatibility''' General Relativity is compatible with many areas of physics, including classical mechanics, electrodynamics, and astrophysics. However, it is not yet unified with quantum mechanics. Attempts to reconcile GR with the Standard Model—such as quantum gravity, string theory, or loop quantum gravity—remain incomplete. Thus, GR scores slightly lower here due to its current incompatibility with modern particle physics at the Planck scale. '''Conceptual Clarity and Simplicity''' The core idea of GR—that gravity is not a force but a geometric property of spacetime—is conceptually elegant. However, the mathematical formalism (involving tensor calculus and differential geometry) is complex and often inaccessible to non-specialists. While the theory offers deep conceptual clarity, its practical simplicity is limited by the required mathematical tools. '''Heuristic Value''' GR has inspired generations of physicists and remains a fertile ground for theoretical development. It has opened up entire fields such as relativistic astrophysics, cosmology, and gravitational wave astronomy. Its influence extends beyond physics into philosophy and the public imagination. It continues to motivate research on black holes, time travel, singularities, and the early universe. '''Historical and Philosophical Insight''' Historically, GR represents a revolutionary shift in physics, displacing the Newtonian notion of absolute space and time with a dynamic, curved spacetime model. Philosophically, it challenges classical intuitions about gravity and causality and has inspired reevaluation of concepts such as simultaneity, locality, and determinism. Its legacy places it among the most profound achievements in scientific history. '''Related link:''' [https://en.wikipedia.org/wiki/General_relativity General Relativity] === '''8.4.2 Newtonian Gravity''' === '''Empirical Adequacy''' Newtonian gravity has historically achieved remarkable empirical success. It accurately describes planetary motions, tidal forces, ballistic trajectories, and satellite orbits. For centuries, it provided the dominant framework for celestial mechanics and was sufficient for navigation, astronomy, and engineering. However, it begins to fail in extreme gravitational fields or at very high speeds, where relativistic corrections are needed. It also cannot explain phenomena like the precession of Mercury’s orbit, gravitational time dilation, or the bending of light. '''Internal Consistency''' Within its classical framework, Newtonian gravity is highly consistent. It is based on clear axioms such as the inverse-square law and absolute space and time. The mathematical structure is well-defined and solvable using Newton’s laws of motion and calculus. No logical contradictions arise within its scope of applicability. However, its assumptions about instantaneous action at a distance are problematic under modern physical understanding. '''Predictive Power''' Newtonian gravity has strong predictive power in low-speed, weak-field regimes. It successfully predicted the return of Halley’s Comet, the existence of Neptune, and continues to be used in engineering and orbital calculations. However, it fails to predict relativistic effects such as gravitational lensing, frame-dragging, or gravitational waves. These limitations reduce its predictive power on cosmic and high-precision scales. '''Cross-Disciplinary Compatibility''' Newton’s theory aligns well with classical physics and early chemistry but lacks compatibility with modern disciplines. It cannot be reconciled with special relativity or quantum theory and does not incorporate energy–momentum considerations as in modern field theories. Its incompatibility with relativity limits its integration with high-energy physics and astrophysics. '''Conceptual Clarity and Simplicity''' Newtonian gravity is conceptually simple and intuitively accessible. The inverse-square force law is easy to visualize and apply. It does not require advanced mathematics and remains an ideal teaching model. Its clarity and ease of computation give it enduring educational and practical value. '''Heuristic Value''' Although no longer a frontier theory, Newtonian gravity laid the groundwork for classical mechanics and much of modern science. It helped shape ideas about force, motion, and planetary systems. While it no longer drives active theoretical innovation, it retains historical heuristic importance. '''Historical and Philosophical Insight''' Newton’s theory was revolutionary in unifying terrestrial and celestial phenomena under the same laws of motion. It established the idea of a universal physical law and set the standard for quantitative science. Philosophically, it introduced mechanistic determinism and absolute space and time—concepts that dominated Enlightenment science. Though now superseded, its legacy remains foundational. '''Related link:''' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newtonian Gravity] === '''8.4.3 MOND (Modified Newtonian Dynamics)''' === '''Empirical Adequacy''' MOND was proposed by Mordehai Milgrom in the early 1980s to explain galactic rotation curves without invoking dark matter. It has successfully reproduced the flat rotation profiles of spiral galaxies and the observed baryonic Tully–Fisher relation with remarkable precision. MOND fits individual galaxy data with fewer parameters than dark matter models. However, it struggles with galaxy cluster dynamics, cosmological structure formation, and gravitational lensing in some systems. Its empirical adequacy is high for galactic scales but limited beyond that domain. '''Internal Consistency''' MOND is mathematically consistent in its non-relativistic form, where it modifies Newton’s second law at low accelerations using a new constant 𝑎 0 a 0 ​ . However, its original formulation lacks a full theoretical derivation from first principles and requires ad hoc modifications to the force law. Several relativistic extensions (e.g. TeVeS, AQUAL, BIMOND) have been developed to improve consistency, but these are not uniquely favored and remain complex or underconstrained. '''Predictive Power''' MOND has had considerable predictive success in galactic astrophysics. It predicted the baryonic Tully–Fisher relation before it was observationally confirmed, and it can reproduce detailed features of galaxy rotation curves without needing dark matter halos. However, it lacks explanatory power for phenomena like the cosmic microwave background (CMB) anisotropies, gravitational lensing in galaxy clusters (e.g. Bullet Cluster), and large-scale structure. Its predictive power is strong in its target domain but limited on cosmological scales. '''Cross-Disciplinary Compatibility''' MOND is primarily focused on galactic dynamics and does not integrate smoothly with high-energy physics, quantum theory, or cosmology. Its extensions to cosmology often require additional assumptions, and it is not yet compatible with standard particle physics. As a result, its cross-disciplinary reach is modest, though ongoing efforts aim to embed it within broader frameworks. '''Conceptual Clarity and Simplicity''' In its original form, MOND is simple: the gravitational acceleration deviates from Newton’s law when below a critical threshold 𝑎 0 a 0 ​ . This modification is intuitive and computationally effective for galaxies. However, attempts to embed MOND in a relativistic framework often add complexity, reducing its conceptual transparency. '''Heuristic Value''' MOND has had significant heuristic impact by highlighting regularities in galactic dynamics that are hard to explain under the ΛCDM paradigm without fine-tuned dark matter profiles. It has sparked debate, inspired hybrid theories (e.g. dark matter superfluidity), and contributed to reevaluating gravitational theory. Its challenge to mainstream cosmology has been fruitful, even if not universally accepted. '''Historical and Philosophical Insight''' MOND revives the idea that gravity itself may need modification, rather than positing unseen matter. This philosophical approach echoes the history of science, where anomalies sometimes led to revisions of theory rather than new entities. MOND also raises deep questions about the nature of inertia, scale invariance, and universal laws—making it a philosophically provocative proposal despite its contested status. '''Related link:''' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics MOND (Modified Newtonian Dynamics)] === '''8.4.4 Emergent Gravity''' === '''Empirical Adequacy''' Emergent Gravity, proposed by Erik Verlinde in 2011 and expanded in 2016, seeks to explain gravitational phenomena as an emergent effect of underlying entropic and holographic principles rather than a fundamental force. It claims to reproduce galactic rotation curves without invoking dark matter by relating gravity to the thermodynamics of microscopic information storage on holographic screens. The theory can qualitatively explain certain galactic dynamics, such as the radial acceleration relation (RAR), but lacks the quantitative precision and scope of MOND in galaxy rotation curve fitting. It also currently cannot reproduce the full spectrum of cosmological observations, including the CMB power spectrum or gravitational lensing in galaxy clusters, where standard ΛCDM performs better. '''Internal Consistency''' Emergent Gravity draws from concepts in string theory, quantum information theory, and thermodynamics. While intellectually coherent and grounded in cutting-edge theoretical frameworks, the theory is still under development and lacks a universally accepted formalism. Key quantities (such as entropic force or the elastic response of spacetime) are not always rigorously defined, and derivations sometimes rely on analogies rather than strict derivations. This limits the formal internal consistency at present, though the conceptual framework remains promising. '''Predictive Power''' The theory makes some novel qualitative predictions, particularly regarding the relation between baryonic mass and gravitational acceleration without dark matter. It reproduces the RAR and may provide an explanation for dark energy as an entropic effect of spacetime. However, Emergent Gravity has not yet made precise predictions for cosmological parameters, gravitational wave behavior, or galaxy cluster dynamics that can be tested independently of standard models. Its predictive power remains speculative and qualitative. '''Cross-Disciplinary Compatibility''' Emergent Gravity attempts to bridge gravity, quantum information, and thermodynamics, making it conceptually rich in cross-disciplinary connections. It resonates with holography, the AdS/CFT correspondence, and black hole thermodynamics. However, the lack of experimental or observational confirmation limits its integration with empirical domains such as astrophysics, cosmology, and particle physics. Its compatibility is more theoretical than empirical at this stage. '''Conceptual Clarity and Simplicity''' The idea that gravity is not fundamental but emerges from statistical behavior of microscopic degrees of freedom is intellectually elegant. However, the actual implementation of this idea in the current models is technically complex and often abstract. Unlike Newtonian gravity or even MOND, the mechanisms proposed by Emergent Gravity are difficult to visualize or test directly, and involve high-level concepts from thermodynamics and information theory. '''Heuristic Value''' Emergent Gravity is highly heuristic. It opens new perspectives on the nature of gravity, spacetime, and entropy. By reframing gravity as an emergent entropic force, it challenges the foundations of both classical and relativistic theories. It has influenced discussions around the holographic principle, black hole entropy, and spacetime microstructure. Even if it remains incomplete, it contributes to rethinking gravity from first principles. '''Historical and Philosophical Insight''' Philosophically, Emergent Gravity aligns with the long-standing idea that some phenomena in nature arise from deeper, statistical processes rather than being fundamental. It recalls Boltzmann’s approach to thermodynamics and aligns with modern information-theoretic views of physics. Historically, it marks a shift from geometric to thermodynamic models of spacetime, and offers a bold alternative to particle-based explanations of gravity. Though controversial, it is part of a growing movement to reinterpret gravity in terms of entropy and information. === '''8.4.5 Big Bang''' === '''Empirical Adequacy''' The Big Bang model is the current standard cosmological paradigm and is strongly supported by multiple independent observations. These include the cosmic microwave background (CMB) radiation, the large-scale structure of the universe, the observed expansion of space (via redshift-distance relations), and the relative abundances of light elements (hydrogen, helium, deuterium, lithium), as predicted by Big Bang Nucleosynthesis (BBN). These confirmations make the Big Bang model one of the most empirically supported frameworks in cosmology. However, the model does not explain the origin of the singularity itself, and extensions such as inflation or dark energy are required to match detailed observations. '''Internal Consistency''' The Big Bang framework is based on solutions to Einstein's field equations (Friedmann–Lemaître–Robertson–Walker metrics), and it is mathematically consistent within the assumptions of general relativity and homogeneity/isotropy (the cosmological principle). However, the initial singularity remains a theoretical boundary where the equations break down, and the model does not include a quantum gravity regime. Extensions such as inflation and ΛCDM are necessary for consistency with observations, but these introduce additional assumptions and parameters, sometimes criticized as fine-tuning. '''Predictive Power''' The Big Bang model has made several successful predictions: the existence and spectrum of the CMB, the large-scale structure of galaxies, and the relative abundances of primordial elements. It also correctly anticipated the cooling of the universe and the redshift–distance relation. Inflationary extensions explain the flatness and horizon problems and predict the nearly scale-invariant spectrum of CMB fluctuations. While many predictions are retrodictive and interpreted within a flexible framework, the model continues to be highly predictive in key areas of cosmology. '''Cross-Disciplinary Compatibility''' The Big Bang model integrates with nuclear physics (BBN), atomic physics (recombination), and high-energy physics (inflation, particle freeze-out). It is broadly compatible with the Standard Model of particle physics and many theories of fundamental interactions. However, it lacks a connection to quantum gravity, and some tensions remain—such as the Hubble tension between early and late universe measurements—that challenge cross-scale consistency. '''Conceptual Clarity and Simplicity''' The core idea—a hot, dense early universe that expands and cools over time—is conceptually clear and widely accepted. However, the full ΛCDM model includes inflation, cold dark matter, and dark energy, which are not directly observable and require complex assumptions. These components reduce the model's simplicity and raise questions about the explanatory depth of the framework. '''Heuristic Value''' The Big Bang theory has driven vast developments in cosmology, observational astronomy, particle physics, and astrophysical instrumentation. It has generated decades of research questions and missions, including COBE, WMAP, and Planck. The inflationary paradigm and dark energy studies have emerged directly from this model. As a heuristic framework, it has proven extremely fertile. '''Historical and Philosophical Insight''' The Big Bang marks a major conceptual shift in cosmology by proposing that the universe has a temporal origin and evolves over time. It displaced steady-state and eternal models of the cosmos and opened up philosophical inquiries about creation, the arrow of time, and the origin of physical laws. Despite its name, it is not an explosion in space but the expansion of space itself—a concept that has reshaped how we understand time, causality, and the structure of the universe. === '''8.4.6 Steady State Theory''' === '''Empirical Adequacy''' The Steady State Theory, developed in the late 1940s by Bondi, Gold, and Hoyle, posits that the universe has no beginning or end in time and remains statistically the same on large scales, with matter continuously created to maintain constant density despite cosmic expansion. Initially, it matched observations of redshift and expansion, but it was ultimately undermined by key empirical discoveries: the cosmic microwave background (CMB), the evolution of radio source counts, and the observation of distant galaxies at earlier stages of development. These findings provided strong evidence of a hot, dense early universe, inconsistent with the steady state hypothesis. As a result, its empirical adequacy is now considered low. '''Internal Consistency''' The theory is internally consistent in its classical formulation and relies on continuous creation of matter to maintain a constant density. However, this matter creation mechanism was never supported by a detailed physical model or empirical detection. While mathematically coherent, the theory’s assumption of continuous creation violates energy conservation as understood in standard physics, making the underlying physics speculative and theoretically weak. '''Predictive Power''' The Steady State model made a bold prediction: the universe should appear the same at all times and places when viewed on large scales. While this was a clear and testable prediction, it was eventually falsified by observations such as the CMB and the evolution of quasars and galaxy populations over time. The theory’s few predictions have largely been refuted, limiting its scientific utility. '''Cross-Disciplinary Compatibility''' The model is only weakly connected to other scientific domains. It does not integrate well with nuclear physics, as it lacks a mechanism for element formation similar to Big Bang Nucleosynthesis. It also lacks compatibility with high-energy particle physics and modern theories of gravity. The continuous matter creation postulate has no foundation in quantum theory or experimental physics. '''Conceptual Clarity and Simplicity''' The steady-state model is conceptually simple and elegant. Its appeal lay in its ability to preserve a universe without origin, circumventing the philosophical and theological questions raised by a cosmic beginning. The model also maintains a uniform, eternal cosmos, which was attractive to many physicists in the mid-20th century. Despite being falsified, it remains a conceptually clear alternative that helped clarify the implications of observational cosmology. '''Heuristic Value''' Although it is no longer a viable cosmological model, the Steady State theory played a significant heuristic role. It prompted debates about the nature of time, observational testing, and the falsifiability of cosmological models. It helped shape the methodological standards for modern cosmology by being a well-defined, testable theory that was ultimately rejected based on empirical data. Its legacy lives on in discussions about the role of testability and philosophical assumptions in science. '''Historical and Philosophical Insight''' The Steady State theory was historically important as the main rival to the Big Bang model in the early post-war period. It reflects a philosophical preference for temporal infinity and equilibrium conditions, standing in contrast to a universe with a beginning. Its eventual rejection illustrates the triumph of observation over philosophical elegance in modern cosmology. It also served as a case study in the philosophy of science, particularly regarding Popperian falsifiability and the evolution of scientific consensus. === '''8.4.7 Big Crunch''' === '''Empirical Adequacy''' The Big Crunch is not a theory of gravity or cosmology by itself but rather a hypothetical end-state of the universe within certain cosmological models. It posits that cosmic expansion could eventually reverse, causing the universe to contract back into a high-density singularity. This scenario arises from general relativity under the assumption of a closed universe with sufficient matter density to overcome expansion. However, current observational data strongly indicate that the universe is accelerating in its expansion, driven by dark energy. Measurements of the cosmic microwave background (CMB), supernova distances, and large-scale structure all support a flat or open universe with low matter density, making the Big Crunch scenario empirically disfavored at present. '''Internal Consistency''' Within general relativity and standard cosmological models, the Big Crunch is internally consistent. It naturally arises from the Friedmann equations when the density parameter Ω > 1 and the cosmological constant is absent or negative. The dynamics of contraction mirror those of expansion in reverse, and no logical contradictions emerge in its mathematical formulation. However, near the final singularity, quantum gravitational effects become important, and the classical equations break down. '''Predictive Power''' As a hypothetical scenario, the Big Crunch does not offer specific predictive claims under current physical conditions. Instead, it represents a conditional outcome: if the universe were closed and dominated by matter, it would eventually recollapse. Since observations show otherwise, the predictive relevance of the Big Crunch is now limited. Nevertheless, it played a role in exploring time-reversal symmetry, thermodynamic limits, and quantum cosmology. '''Cross-Disciplinary Compatibility''' The Big Crunch scenario is compatible with general relativity and classical thermodynamics, especially in discussions of entropy and the arrow of time. It has also been explored in speculative models of cyclic or oscillating universes, which relate to quantum gravity and string theory. However, it lacks strong support from empirical fields such as observational cosmology, particle physics, or astronomy under the current ΛCDM framework. '''Conceptual Clarity and Simplicity''' The concept is straightforward: the universe's expansion halts and reverses into a collapse. This time-symmetric model is intuitively appealing and easy to visualize. However, its physical plausibility is undermined by current evidence for accelerating expansion. Still, as a conceptual tool, it remains a clear contrast to models of eternal expansion or thermal death. '''Heuristic Value''' Historically, the Big Crunch scenario stimulated discussion about cosmological cycles, entropy limits, and the ultimate fate of the universe. It led to the development of cyclic models, bounce cosmologies, and ideas about cosmic rebirth. Although largely ruled out by current data, it retains heuristic value in theoretical cosmology and philosophy of time, particularly in exploring whether time and entropy could reverse. '''Historical and Philosophical Insight''' The Big Crunch offered a philosophically symmetric alternative to the Big Bang—a universe that begins and ends in a singularity. It invites reflection on the reversibility of physical laws, the meaning of cosmic time, and the possibility of eternal recurrence. While empirical support is lacking, the scenario remains a historically meaningful part of cosmological thinking, especially in the 20th-century debates about the universe's fate. === '''8.4.8 Big Bounce''' === '''Empirical Adequacy''' The Big Bounce is a speculative cosmological scenario in which the universe undergoes a cycle of contraction followed by a rebound (or "bounce") into a new phase of expansion. It aims to replace the initial singularity of the Big Bang with a transitional phase where quantum gravitational effects prevent infinite density. While the concept is consistent with certain theoretical models—particularly in loop quantum cosmology—there is currently no direct observational evidence for a bounce event. The cosmic microwave background (CMB) does not yet show unambiguous signatures that would favor a bounce over inflationary models. Thus, empirical adequacy remains hypothetical, though not excluded. '''Internal Consistency''' The Big Bounce can be formulated consistently within several frameworks, such as loop quantum gravity, string gas cosmology, or modified gravity models. In these settings, quantum corrections to the Friedmann equations or modifications to the geometry of spacetime prevent a singularity and allow for a smooth transition from contraction to expansion. However, different bounce models vary in their assumptions, and the full quantum dynamics are not yet universally agreed upon. Despite these uncertainties, the internal logic of the models is coherent within their theoretical boundaries. '''Predictive Power''' Some Big Bounce models predict subtle features in the CMB, such as suppressed power at large angular scales, or non-Gaussianities that differ from inflation. However, these predictions often overlap with or are degenerate with inflationary predictions, making them hard to test uniquely. No conclusive observational support has been found so far. Nevertheless, bounce models offer a predictive framework that could, in principle, be tested with improved cosmological data in the future. '''Cross-Disciplinary Compatibility''' The Big Bounce scenario is motivated by attempts to unify quantum mechanics and gravity. It connects well with developments in loop quantum cosmology, non-singular black hole models, and string theory. However, it is less developed in its links to particle physics, standard cosmology, or astrophysical observations. Its broader scientific compatibility depends heavily on which theoretical approach is adopted and how it interfaces with known physics. '''Conceptual Clarity and Simplicity''' The idea of a contracting universe rebounding into expansion is conceptually intuitive and avoids the metaphysical implications of a beginning-of-time singularity. In contrast to the Big Bang singularity, the bounce implies a cyclic or oscillatory universe that is eternal in time. While appealing in its symmetry, the underlying physics is often highly technical and abstract, involving non-perturbative quantum gravity, which reduces its practical simplicity. '''Heuristic Value''' The Big Bounce has stimulated important discussions in cosmology, particularly regarding singularity avoidance, pre-Big Bang scenarios, and the nature of time. It has inspired a class of alternative models to inflation and opened up debates about the cyclical nature of the universe. Its challenge to the standard narrative of cosmic origins has heuristic value in motivating new lines of theoretical research. '''Historical and Philosophical Insight''' The Big Bounce continues a long tradition of cyclical universe models, echoing ideas from ancient cosmologies and early 20th-century oscillating universe theories. Philosophically, it provides a framework in which the universe has no absolute beginning or end, and where time and entropy may operate in a larger looped framework. It offers a more balanced cosmological picture than the irreversible expansion or final collapse scenarios. Though not yet supported by data, its philosophical implications remain profound and open-ended. === '''8.4.9 Cosmic Influx Theory (CIT)''' === Cosmic Influx Theory (CIT), proposed by Ruud Loeffen, reinterprets gravity as a directional energy influx driven by Primordial Elementary Whirlings (PEWs), replacing the concept of attractive force or space-time curvature. It introduces a constant influx of mass-energy into all bodies, contributing to planetary expansion, star formation, and cosmological evolution. 1. '''Internal Consistency''' CIT presents a coherent internal logic based on a unidirectional influx mechanism, a redefined gravitational constant (G = (γ − 1)/4π), and the introduction of κ_CIT as a universal scaling constant. While the framework remains internally consistent, some equations are still under refinement and lack full derivations from first principles. 2. '''Predictive Power''' CIT predicts the Preferred Distance for giant planets based on κ_CIT, orbital periods of exoplanets, and a revised Hubble constant (Ho ≈ 67.8 km/s/Mpc). It also anticipates planetary expansion through mass influx. These predictions are testable, though many remain pending observational confirmation. 3. '''Falsifiability''' Several predictions—such as giant planets at D_pref in the Trappist system or mass accumulation rates inferred from planetary geology—can be tested. However, the influx mechanism itself is not yet described in terms of directly measurable particles or interactions, which may limit falsifiability at the quantum level. 4. '''Observational Alignment''' CIT aligns with various observations: early formation of giant planets in protoplanetary disks, planetary expansion signatures, surface geology of moons and Mars, and recent JWST disk structures. It also claims to naturally derive the observed Hubble constant without tension. 5. '''Philosophical Transparency''' The theory clearly departs from Newtonian and relativistic interpretations, positioning itself as an ontological alternative grounded in energy flow. The author's motivations, limitations, and intended scope are transparently communicated in both academic and public forums. 6. '''Empirical Adequacy''' CIT offers empirical parallels in planetary spacing (κ_CIT), daylength extension over geological time, and disk fragmentation patterns. However, it currently lacks publication in high-impact peer-reviewed journals and formal statistical validation across broad datasets. 7. '''Institutional Support and Development''' CIT is developed independently, primarily through Wikiversity and open-access platforms. While it incorporates extensive cross-referencing and engages with mainstream and alternative sources, it lacks institutional affiliation and academic endorsement at this stage. '''Related link:''' [[Cosmic Influx Theory]] === '''8.4.10 Summary of Spiral Cosmology''' === The Pearlman Cosmology (SPIRAL Cosmology) offers a deterministic model of the universe with a defined hyper-dense initial state, fixed radius growth, and a reinterpretation of redshift. It integrates biblical chronology into its cosmological assumptions, making it a unique hybrid of scientific and scriptural reasoning. 1. '''Internal Consistency''' The model presents a logically consistent internal framework, with clearly defined initial conditions such as the SPIRAL radius, gravitational equilibrium, and fixed cosmic time scaling. Its components align well within its own assumptions. 2. '''Predictive Power''' Pearlman Cosmology proposes several potentially testable hypotheses, such as a fixed annual rate of universal expansion and an alternative explanation of redshift. However, these are not yet accompanied by detailed numeric predictions or simulations. 3. '''Falsifiability''' Testable elements exist in the form of reinterpretations of the cosmic microwave background origin, early galaxy formation, and redshift asymmetries. Yet aspects based on Mosaic chronology may fall outside strict scientific falsifiability. 4. '''Observational Alignment''' The model qualitatively aligns with some recent JWST observations, including early structure formation and CMB uniformity. Nevertheless, it lacks robust quantitative matching with large datasets or predictive modeling. 5. '''Philosophical Transparency''' The theory is open about its use of religious chronology and framing. This transparency makes its worldview explicit, though it may hinder its acceptance within mainstream secular science. 6. '''Empirical Adequacy''' While some empirical parallels exist, the theory has not yet been tested against a wide body of observational data in a systematic or peer-reviewed way. 7. '''Institutional Support and Development''' Pearlman Cosmology remains outside institutional research frameworks. Its development and publication history are limited, and it has not yet entered mainstream cosmological discourse. '''Related link:''' [https://www.pearlman.org Pearlman Cosmology] '''◀ [[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 ▶]]''' 6jfpqmm7csoiduivvql1l2gdigiyp0j 2719988 2719987 2025-06-29T04:36:04Z Ruud Loeffen 2998353 /* 8.4.4 Emergent Gravity */ add link to this theory 2719988 wikitext text/x-wiki == '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' = == '''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. == '''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 == '''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 such as: Observational Agreement Internal Logical Consistency Predictive Value Compatibility with Other Domains (e.g., geology, biology) Conceptual Coherence and Simplicity Each dimension is rated using a 1–5 star system, based on the information provided and the supporting sources that AI can access. 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. == '''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. == '''8.1 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. '''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. '''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. '''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. '''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. '''5. Conceptual Clarity and Simplicity''' Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification. '''6. Heuristic Value''' Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential. '''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. 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 or can be requested in more detail. == '''8.2 AI Evaluation Table Format''' == {| class="wikitable" |+ '''AI Evaluation Table of Cosmological Theories''' ! Theory Name ! Empirical Adequacy ! Internal Consistency ! Predictive Power ! Cross-Disciplinary Compatibility ! Conceptual Clarity and Simplicity ! Heuristic Value ! Historical & Philosophical Insight ! Total (★) |- | 8.4.1 '''General Relativity''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★★ || '''34''' |- | colspan="9" | ''Widely confirmed by experiment; mathematical elegance; historical development from Newtonian mechanics'' |- |- | 8.4.2 '''Newtonian Gravity''' | ★★★★☆ || ★★★★★ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''30''' |- | colspan="9" | ''Highly successful in classical mechanics and celestial predictions; lacks compatibility with relativity and quantum theory; historically foundational.'' |- | 8.4.3 '''MOND (Modified Newtonian Dynamics)''' | ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''24''' |- | colspan="9" | ''Strong in galactic rotation curves; limited compatibility with general relativistic frameworks'' |- | 8.4.4 '''Emergent Gravity (Verlinde)''' | ★★☆☆☆ || ★★★★☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''25''' |- | colspan="9" | ''Innovative reformulation; still awaiting broad empirical confirmation'' |- | 8.4.5 '''Big Bang Model''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''31''' |- | colspan="9" | ''Core cosmological model; supported by CMB, redshift, nucleosynthesis'' |- | 8.4.6 '''Steady State Theory''' | ★☆☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''23''' |- | colspan="9" | ''Historically important; largely superseded due to lack of CMB explanation'' |- | 8.4.7 '''Big Crunch Theory''' | ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || '''28''' |- | colspan="9" | ''Predicts final collapse of universe; consistent with GR in high-density scenarios; revived interest due to dark energy variability'' |- | 8.4.8 '''Big Bounce Theory''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''26''' |- | colspan="9" | ''Cyclical alternative to singularity; compatible with some quantum gravity models'' |- | 8.4.9 '''Cosmic Influx Theory (CIT)''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★★★★ || ★★★★☆ || '''26''' |- | colspan="9" | ''Offers cross-disciplinary compatibility; predicts mass growth and preferred orbital distances; alternative influx model under development'' |- | 8.4.10 '''SPIRAL Cosmology''' | ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22''' |- | colspan="9" | ''Proposes a hyper-dense proto-galactic phase preceding expansion; no need for ongoing dark energy or cosmic expansion; partially scriptural framing may limit falsifiability but testable claims (e.g. fixed-radius light departure) justify scientific review.'' |- | colspan="9" | ''Well-formulated alternative integrating orbital quantization; some empirical fit to planetary data; lacks full mainstream acceptance'' |} <!-- Add a blank line here --> == '''8.3 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]]'''. == '''8.4 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. === '''8.4.1 General Relativity'''=== '''Empirical Adequacy''' General Relativity (GR) is one of the most empirically validated theories in physics. It has successfully explained and predicted a wide range of gravitational phenomena, including the precession of Mercury’s perihelion, gravitational lensing of starlight, gravitational redshift, time dilation effects observed in satellite systems like GPS, and the Shapiro delay. More recently, its predictions have been confirmed by gravitational wave observations (LIGO/Virgo) and direct imaging of black holes (Event Horizon Telescope). The agreement between theory and measurement is often better than 0.01%, demonstrating exceptional empirical adequacy. '''Internal Consistency''' GR is internally consistent within its mathematical framework. It is based on the Einstein field equations, which are derived from well-defined variational principles and respect general covariance. The logical structure of the theory is rigorous, with clearly formulated assumptions such as the equivalence principle and the conservation of energy–momentum through the stress-energy tensor. There are no known internal contradictions. '''Predictive Power''' GR has a powerful record of making novel predictions that were later confirmed by experiment or observation. These include the bending of light by massive bodies, time dilation in gravitational fields, the expansion of the universe (through its application in cosmology), and the existence of gravitational waves. Its predictions have often preceded direct detection by decades. This makes GR a model example of a theory with high predictive power. '''Cross-Disciplinary Compatibility''' General Relativity is compatible with many areas of physics, including classical mechanics, electrodynamics, and astrophysics. However, it is not yet unified with quantum mechanics. Attempts to reconcile GR with the Standard Model—such as quantum gravity, string theory, or loop quantum gravity—remain incomplete. Thus, GR scores slightly lower here due to its current incompatibility with modern particle physics at the Planck scale. '''Conceptual Clarity and Simplicity''' The core idea of GR—that gravity is not a force but a geometric property of spacetime—is conceptually elegant. However, the mathematical formalism (involving tensor calculus and differential geometry) is complex and often inaccessible to non-specialists. While the theory offers deep conceptual clarity, its practical simplicity is limited by the required mathematical tools. '''Heuristic Value''' GR has inspired generations of physicists and remains a fertile ground for theoretical development. It has opened up entire fields such as relativistic astrophysics, cosmology, and gravitational wave astronomy. Its influence extends beyond physics into philosophy and the public imagination. It continues to motivate research on black holes, time travel, singularities, and the early universe. '''Historical and Philosophical Insight''' Historically, GR represents a revolutionary shift in physics, displacing the Newtonian notion of absolute space and time with a dynamic, curved spacetime model. Philosophically, it challenges classical intuitions about gravity and causality and has inspired reevaluation of concepts such as simultaneity, locality, and determinism. Its legacy places it among the most profound achievements in scientific history. '''Related link:''' [https://en.wikipedia.org/wiki/General_relativity General Relativity] === '''8.4.2 Newtonian Gravity''' === '''Empirical Adequacy''' Newtonian gravity has historically achieved remarkable empirical success. It accurately describes planetary motions, tidal forces, ballistic trajectories, and satellite orbits. For centuries, it provided the dominant framework for celestial mechanics and was sufficient for navigation, astronomy, and engineering. However, it begins to fail in extreme gravitational fields or at very high speeds, where relativistic corrections are needed. It also cannot explain phenomena like the precession of Mercury’s orbit, gravitational time dilation, or the bending of light. '''Internal Consistency''' Within its classical framework, Newtonian gravity is highly consistent. It is based on clear axioms such as the inverse-square law and absolute space and time. The mathematical structure is well-defined and solvable using Newton’s laws of motion and calculus. No logical contradictions arise within its scope of applicability. However, its assumptions about instantaneous action at a distance are problematic under modern physical understanding. '''Predictive Power''' Newtonian gravity has strong predictive power in low-speed, weak-field regimes. It successfully predicted the return of Halley’s Comet, the existence of Neptune, and continues to be used in engineering and orbital calculations. However, it fails to predict relativistic effects such as gravitational lensing, frame-dragging, or gravitational waves. These limitations reduce its predictive power on cosmic and high-precision scales. '''Cross-Disciplinary Compatibility''' Newton’s theory aligns well with classical physics and early chemistry but lacks compatibility with modern disciplines. It cannot be reconciled with special relativity or quantum theory and does not incorporate energy–momentum considerations as in modern field theories. Its incompatibility with relativity limits its integration with high-energy physics and astrophysics. '''Conceptual Clarity and Simplicity''' Newtonian gravity is conceptually simple and intuitively accessible. The inverse-square force law is easy to visualize and apply. It does not require advanced mathematics and remains an ideal teaching model. Its clarity and ease of computation give it enduring educational and practical value. '''Heuristic Value''' Although no longer a frontier theory, Newtonian gravity laid the groundwork for classical mechanics and much of modern science. It helped shape ideas about force, motion, and planetary systems. While it no longer drives active theoretical innovation, it retains historical heuristic importance. '''Historical and Philosophical Insight''' Newton’s theory was revolutionary in unifying terrestrial and celestial phenomena under the same laws of motion. It established the idea of a universal physical law and set the standard for quantitative science. Philosophically, it introduced mechanistic determinism and absolute space and time—concepts that dominated Enlightenment science. Though now superseded, its legacy remains foundational. '''Related link:''' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newtonian Gravity] === '''8.4.3 MOND (Modified Newtonian Dynamics)''' === '''Empirical Adequacy''' MOND was proposed by Mordehai Milgrom in the early 1980s to explain galactic rotation curves without invoking dark matter. It has successfully reproduced the flat rotation profiles of spiral galaxies and the observed baryonic Tully–Fisher relation with remarkable precision. MOND fits individual galaxy data with fewer parameters than dark matter models. However, it struggles with galaxy cluster dynamics, cosmological structure formation, and gravitational lensing in some systems. Its empirical adequacy is high for galactic scales but limited beyond that domain. '''Internal Consistency''' MOND is mathematically consistent in its non-relativistic form, where it modifies Newton’s second law at low accelerations using a new constant 𝑎 0 a 0 ​ . However, its original formulation lacks a full theoretical derivation from first principles and requires ad hoc modifications to the force law. Several relativistic extensions (e.g. TeVeS, AQUAL, BIMOND) have been developed to improve consistency, but these are not uniquely favored and remain complex or underconstrained. '''Predictive Power''' MOND has had considerable predictive success in galactic astrophysics. It predicted the baryonic Tully–Fisher relation before it was observationally confirmed, and it can reproduce detailed features of galaxy rotation curves without needing dark matter halos. However, it lacks explanatory power for phenomena like the cosmic microwave background (CMB) anisotropies, gravitational lensing in galaxy clusters (e.g. Bullet Cluster), and large-scale structure. Its predictive power is strong in its target domain but limited on cosmological scales. '''Cross-Disciplinary Compatibility''' MOND is primarily focused on galactic dynamics and does not integrate smoothly with high-energy physics, quantum theory, or cosmology. Its extensions to cosmology often require additional assumptions, and it is not yet compatible with standard particle physics. As a result, its cross-disciplinary reach is modest, though ongoing efforts aim to embed it within broader frameworks. '''Conceptual Clarity and Simplicity''' In its original form, MOND is simple: the gravitational acceleration deviates from Newton’s law when below a critical threshold 𝑎 0 a 0 ​ . This modification is intuitive and computationally effective for galaxies. However, attempts to embed MOND in a relativistic framework often add complexity, reducing its conceptual transparency. '''Heuristic Value''' MOND has had significant heuristic impact by highlighting regularities in galactic dynamics that are hard to explain under the ΛCDM paradigm without fine-tuned dark matter profiles. It has sparked debate, inspired hybrid theories (e.g. dark matter superfluidity), and contributed to reevaluating gravitational theory. Its challenge to mainstream cosmology has been fruitful, even if not universally accepted. '''Historical and Philosophical Insight''' MOND revives the idea that gravity itself may need modification, rather than positing unseen matter. This philosophical approach echoes the history of science, where anomalies sometimes led to revisions of theory rather than new entities. MOND also raises deep questions about the nature of inertia, scale invariance, and universal laws—making it a philosophically provocative proposal despite its contested status. '''Related link:''' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics MOND (Modified Newtonian Dynamics)] === '''8.4.4 Emergent Gravity''' === '''Empirical Adequacy''' Emergent Gravity, proposed by Erik Verlinde in 2011 and expanded in 2016, seeks to explain gravitational phenomena as an emergent effect of underlying entropic and holographic principles rather than a fundamental force. It claims to reproduce galactic rotation curves without invoking dark matter by relating gravity to the thermodynamics of microscopic information storage on holographic screens. The theory can qualitatively explain certain galactic dynamics, such as the radial acceleration relation (RAR), but lacks the quantitative precision and scope of MOND in galaxy rotation curve fitting. It also currently cannot reproduce the full spectrum of cosmological observations, including the CMB power spectrum or gravitational lensing in galaxy clusters, where standard ΛCDM performs better. '''Internal Consistency''' Emergent Gravity draws from concepts in string theory, quantum information theory, and thermodynamics. While intellectually coherent and grounded in cutting-edge theoretical frameworks, the theory is still under development and lacks a universally accepted formalism. Key quantities (such as entropic force or the elastic response of spacetime) are not always rigorously defined, and derivations sometimes rely on analogies rather than strict derivations. This limits the formal internal consistency at present, though the conceptual framework remains promising. '''Predictive Power''' The theory makes some novel qualitative predictions, particularly regarding the relation between baryonic mass and gravitational acceleration without dark matter. It reproduces the RAR and may provide an explanation for dark energy as an entropic effect of spacetime. However, Emergent Gravity has not yet made precise predictions for cosmological parameters, gravitational wave behavior, or galaxy cluster dynamics that can be tested independently of standard models. Its predictive power remains speculative and qualitative. '''Cross-Disciplinary Compatibility''' Emergent Gravity attempts to bridge gravity, quantum information, and thermodynamics, making it conceptually rich in cross-disciplinary connections. It resonates with holography, the AdS/CFT correspondence, and black hole thermodynamics. However, the lack of experimental or observational confirmation limits its integration with empirical domains such as astrophysics, cosmology, and particle physics. Its compatibility is more theoretical than empirical at this stage. '''Conceptual Clarity and Simplicity''' The idea that gravity is not fundamental but emerges from statistical behavior of microscopic degrees of freedom is intellectually elegant. However, the actual implementation of this idea in the current models is technically complex and often abstract. Unlike Newtonian gravity or even MOND, the mechanisms proposed by Emergent Gravity are difficult to visualize or test directly, and involve high-level concepts from thermodynamics and information theory. '''Heuristic Value''' Emergent Gravity is highly heuristic. It opens new perspectives on the nature of gravity, spacetime, and entropy. By reframing gravity as an emergent entropic force, it challenges the foundations of both classical and relativistic theories. It has influenced discussions around the holographic principle, black hole entropy, and spacetime microstructure. Even if it remains incomplete, it contributes to rethinking gravity from first principles. '''Historical and Philosophical Insight''' Philosophically, Emergent Gravity aligns with the long-standing idea that some phenomena in nature arise from deeper, statistical processes rather than being fundamental. It recalls Boltzmann’s approach to thermodynamics and aligns with modern information-theoretic views of physics. Historically, it marks a shift from geometric to thermodynamic models of spacetime, and offers a bold alternative to particle-based explanations of gravity. Though controversial, it is part of a growing movement to reinterpret gravity in terms of entropy and information. '''Related link:''' [https://en.wikipedia.org/wiki/Erik_Verlinde#Emergent_gravity Emergent Gravity] === '''8.4.5 Big Bang''' === '''Empirical Adequacy''' The Big Bang model is the current standard cosmological paradigm and is strongly supported by multiple independent observations. These include the cosmic microwave background (CMB) radiation, the large-scale structure of the universe, the observed expansion of space (via redshift-distance relations), and the relative abundances of light elements (hydrogen, helium, deuterium, lithium), as predicted by Big Bang Nucleosynthesis (BBN). These confirmations make the Big Bang model one of the most empirically supported frameworks in cosmology. However, the model does not explain the origin of the singularity itself, and extensions such as inflation or dark energy are required to match detailed observations. '''Internal Consistency''' The Big Bang framework is based on solutions to Einstein's field equations (Friedmann–Lemaître–Robertson–Walker metrics), and it is mathematically consistent within the assumptions of general relativity and homogeneity/isotropy (the cosmological principle). However, the initial singularity remains a theoretical boundary where the equations break down, and the model does not include a quantum gravity regime. Extensions such as inflation and ΛCDM are necessary for consistency with observations, but these introduce additional assumptions and parameters, sometimes criticized as fine-tuning. '''Predictive Power''' The Big Bang model has made several successful predictions: the existence and spectrum of the CMB, the large-scale structure of galaxies, and the relative abundances of primordial elements. It also correctly anticipated the cooling of the universe and the redshift–distance relation. Inflationary extensions explain the flatness and horizon problems and predict the nearly scale-invariant spectrum of CMB fluctuations. While many predictions are retrodictive and interpreted within a flexible framework, the model continues to be highly predictive in key areas of cosmology. '''Cross-Disciplinary Compatibility''' The Big Bang model integrates with nuclear physics (BBN), atomic physics (recombination), and high-energy physics (inflation, particle freeze-out). It is broadly compatible with the Standard Model of particle physics and many theories of fundamental interactions. However, it lacks a connection to quantum gravity, and some tensions remain—such as the Hubble tension between early and late universe measurements—that challenge cross-scale consistency. '''Conceptual Clarity and Simplicity''' The core idea—a hot, dense early universe that expands and cools over time—is conceptually clear and widely accepted. However, the full ΛCDM model includes inflation, cold dark matter, and dark energy, which are not directly observable and require complex assumptions. These components reduce the model's simplicity and raise questions about the explanatory depth of the framework. '''Heuristic Value''' The Big Bang theory has driven vast developments in cosmology, observational astronomy, particle physics, and astrophysical instrumentation. It has generated decades of research questions and missions, including COBE, WMAP, and Planck. The inflationary paradigm and dark energy studies have emerged directly from this model. As a heuristic framework, it has proven extremely fertile. '''Historical and Philosophical Insight''' The Big Bang marks a major conceptual shift in cosmology by proposing that the universe has a temporal origin and evolves over time. It displaced steady-state and eternal models of the cosmos and opened up philosophical inquiries about creation, the arrow of time, and the origin of physical laws. Despite its name, it is not an explosion in space but the expansion of space itself—a concept that has reshaped how we understand time, causality, and the structure of the universe. === '''8.4.6 Steady State Theory''' === '''Empirical Adequacy''' The Steady State Theory, developed in the late 1940s by Bondi, Gold, and Hoyle, posits that the universe has no beginning or end in time and remains statistically the same on large scales, with matter continuously created to maintain constant density despite cosmic expansion. Initially, it matched observations of redshift and expansion, but it was ultimately undermined by key empirical discoveries: the cosmic microwave background (CMB), the evolution of radio source counts, and the observation of distant galaxies at earlier stages of development. These findings provided strong evidence of a hot, dense early universe, inconsistent with the steady state hypothesis. As a result, its empirical adequacy is now considered low. '''Internal Consistency''' The theory is internally consistent in its classical formulation and relies on continuous creation of matter to maintain a constant density. However, this matter creation mechanism was never supported by a detailed physical model or empirical detection. While mathematically coherent, the theory’s assumption of continuous creation violates energy conservation as understood in standard physics, making the underlying physics speculative and theoretically weak. '''Predictive Power''' The Steady State model made a bold prediction: the universe should appear the same at all times and places when viewed on large scales. While this was a clear and testable prediction, it was eventually falsified by observations such as the CMB and the evolution of quasars and galaxy populations over time. The theory’s few predictions have largely been refuted, limiting its scientific utility. '''Cross-Disciplinary Compatibility''' The model is only weakly connected to other scientific domains. It does not integrate well with nuclear physics, as it lacks a mechanism for element formation similar to Big Bang Nucleosynthesis. It also lacks compatibility with high-energy particle physics and modern theories of gravity. The continuous matter creation postulate has no foundation in quantum theory or experimental physics. '''Conceptual Clarity and Simplicity''' The steady-state model is conceptually simple and elegant. Its appeal lay in its ability to preserve a universe without origin, circumventing the philosophical and theological questions raised by a cosmic beginning. The model also maintains a uniform, eternal cosmos, which was attractive to many physicists in the mid-20th century. Despite being falsified, it remains a conceptually clear alternative that helped clarify the implications of observational cosmology. '''Heuristic Value''' Although it is no longer a viable cosmological model, the Steady State theory played a significant heuristic role. It prompted debates about the nature of time, observational testing, and the falsifiability of cosmological models. It helped shape the methodological standards for modern cosmology by being a well-defined, testable theory that was ultimately rejected based on empirical data. Its legacy lives on in discussions about the role of testability and philosophical assumptions in science. '''Historical and Philosophical Insight''' The Steady State theory was historically important as the main rival to the Big Bang model in the early post-war period. It reflects a philosophical preference for temporal infinity and equilibrium conditions, standing in contrast to a universe with a beginning. Its eventual rejection illustrates the triumph of observation over philosophical elegance in modern cosmology. It also served as a case study in the philosophy of science, particularly regarding Popperian falsifiability and the evolution of scientific consensus. === '''8.4.7 Big Crunch''' === '''Empirical Adequacy''' The Big Crunch is not a theory of gravity or cosmology by itself but rather a hypothetical end-state of the universe within certain cosmological models. It posits that cosmic expansion could eventually reverse, causing the universe to contract back into a high-density singularity. This scenario arises from general relativity under the assumption of a closed universe with sufficient matter density to overcome expansion. However, current observational data strongly indicate that the universe is accelerating in its expansion, driven by dark energy. Measurements of the cosmic microwave background (CMB), supernova distances, and large-scale structure all support a flat or open universe with low matter density, making the Big Crunch scenario empirically disfavored at present. '''Internal Consistency''' Within general relativity and standard cosmological models, the Big Crunch is internally consistent. It naturally arises from the Friedmann equations when the density parameter Ω > 1 and the cosmological constant is absent or negative. The dynamics of contraction mirror those of expansion in reverse, and no logical contradictions emerge in its mathematical formulation. However, near the final singularity, quantum gravitational effects become important, and the classical equations break down. '''Predictive Power''' As a hypothetical scenario, the Big Crunch does not offer specific predictive claims under current physical conditions. Instead, it represents a conditional outcome: if the universe were closed and dominated by matter, it would eventually recollapse. Since observations show otherwise, the predictive relevance of the Big Crunch is now limited. Nevertheless, it played a role in exploring time-reversal symmetry, thermodynamic limits, and quantum cosmology. '''Cross-Disciplinary Compatibility''' The Big Crunch scenario is compatible with general relativity and classical thermodynamics, especially in discussions of entropy and the arrow of time. It has also been explored in speculative models of cyclic or oscillating universes, which relate to quantum gravity and string theory. However, it lacks strong support from empirical fields such as observational cosmology, particle physics, or astronomy under the current ΛCDM framework. '''Conceptual Clarity and Simplicity''' The concept is straightforward: the universe's expansion halts and reverses into a collapse. This time-symmetric model is intuitively appealing and easy to visualize. However, its physical plausibility is undermined by current evidence for accelerating expansion. Still, as a conceptual tool, it remains a clear contrast to models of eternal expansion or thermal death. '''Heuristic Value''' Historically, the Big Crunch scenario stimulated discussion about cosmological cycles, entropy limits, and the ultimate fate of the universe. It led to the development of cyclic models, bounce cosmologies, and ideas about cosmic rebirth. Although largely ruled out by current data, it retains heuristic value in theoretical cosmology and philosophy of time, particularly in exploring whether time and entropy could reverse. '''Historical and Philosophical Insight''' The Big Crunch offered a philosophically symmetric alternative to the Big Bang—a universe that begins and ends in a singularity. It invites reflection on the reversibility of physical laws, the meaning of cosmic time, and the possibility of eternal recurrence. While empirical support is lacking, the scenario remains a historically meaningful part of cosmological thinking, especially in the 20th-century debates about the universe's fate. === '''8.4.8 Big Bounce''' === '''Empirical Adequacy''' The Big Bounce is a speculative cosmological scenario in which the universe undergoes a cycle of contraction followed by a rebound (or "bounce") into a new phase of expansion. It aims to replace the initial singularity of the Big Bang with a transitional phase where quantum gravitational effects prevent infinite density. While the concept is consistent with certain theoretical models—particularly in loop quantum cosmology—there is currently no direct observational evidence for a bounce event. The cosmic microwave background (CMB) does not yet show unambiguous signatures that would favor a bounce over inflationary models. Thus, empirical adequacy remains hypothetical, though not excluded. '''Internal Consistency''' The Big Bounce can be formulated consistently within several frameworks, such as loop quantum gravity, string gas cosmology, or modified gravity models. In these settings, quantum corrections to the Friedmann equations or modifications to the geometry of spacetime prevent a singularity and allow for a smooth transition from contraction to expansion. However, different bounce models vary in their assumptions, and the full quantum dynamics are not yet universally agreed upon. Despite these uncertainties, the internal logic of the models is coherent within their theoretical boundaries. '''Predictive Power''' Some Big Bounce models predict subtle features in the CMB, such as suppressed power at large angular scales, or non-Gaussianities that differ from inflation. However, these predictions often overlap with or are degenerate with inflationary predictions, making them hard to test uniquely. No conclusive observational support has been found so far. Nevertheless, bounce models offer a predictive framework that could, in principle, be tested with improved cosmological data in the future. '''Cross-Disciplinary Compatibility''' The Big Bounce scenario is motivated by attempts to unify quantum mechanics and gravity. It connects well with developments in loop quantum cosmology, non-singular black hole models, and string theory. However, it is less developed in its links to particle physics, standard cosmology, or astrophysical observations. Its broader scientific compatibility depends heavily on which theoretical approach is adopted and how it interfaces with known physics. '''Conceptual Clarity and Simplicity''' The idea of a contracting universe rebounding into expansion is conceptually intuitive and avoids the metaphysical implications of a beginning-of-time singularity. In contrast to the Big Bang singularity, the bounce implies a cyclic or oscillatory universe that is eternal in time. While appealing in its symmetry, the underlying physics is often highly technical and abstract, involving non-perturbative quantum gravity, which reduces its practical simplicity. '''Heuristic Value''' The Big Bounce has stimulated important discussions in cosmology, particularly regarding singularity avoidance, pre-Big Bang scenarios, and the nature of time. It has inspired a class of alternative models to inflation and opened up debates about the cyclical nature of the universe. Its challenge to the standard narrative of cosmic origins has heuristic value in motivating new lines of theoretical research. '''Historical and Philosophical Insight''' The Big Bounce continues a long tradition of cyclical universe models, echoing ideas from ancient cosmologies and early 20th-century oscillating universe theories. Philosophically, it provides a framework in which the universe has no absolute beginning or end, and where time and entropy may operate in a larger looped framework. It offers a more balanced cosmological picture than the irreversible expansion or final collapse scenarios. Though not yet supported by data, its philosophical implications remain profound and open-ended. === '''8.4.9 Cosmic Influx Theory (CIT)''' === Cosmic Influx Theory (CIT), proposed by Ruud Loeffen, reinterprets gravity as a directional energy influx driven by Primordial Elementary Whirlings (PEWs), replacing the concept of attractive force or space-time curvature. It introduces a constant influx of mass-energy into all bodies, contributing to planetary expansion, star formation, and cosmological evolution. 1. '''Internal Consistency''' CIT presents a coherent internal logic based on a unidirectional influx mechanism, a redefined gravitational constant (G = (γ − 1)/4π), and the introduction of κ_CIT as a universal scaling constant. While the framework remains internally consistent, some equations are still under refinement and lack full derivations from first principles. 2. '''Predictive Power''' CIT predicts the Preferred Distance for giant planets based on κ_CIT, orbital periods of exoplanets, and a revised Hubble constant (Ho ≈ 67.8 km/s/Mpc). It also anticipates planetary expansion through mass influx. These predictions are testable, though many remain pending observational confirmation. 3. '''Falsifiability''' Several predictions—such as giant planets at D_pref in the Trappist system or mass accumulation rates inferred from planetary geology—can be tested. However, the influx mechanism itself is not yet described in terms of directly measurable particles or interactions, which may limit falsifiability at the quantum level. 4. '''Observational Alignment''' CIT aligns with various observations: early formation of giant planets in protoplanetary disks, planetary expansion signatures, surface geology of moons and Mars, and recent JWST disk structures. It also claims to naturally derive the observed Hubble constant without tension. 5. '''Philosophical Transparency''' The theory clearly departs from Newtonian and relativistic interpretations, positioning itself as an ontological alternative grounded in energy flow. The author's motivations, limitations, and intended scope are transparently communicated in both academic and public forums. 6. '''Empirical Adequacy''' CIT offers empirical parallels in planetary spacing (κ_CIT), daylength extension over geological time, and disk fragmentation patterns. However, it currently lacks publication in high-impact peer-reviewed journals and formal statistical validation across broad datasets. 7. '''Institutional Support and Development''' CIT is developed independently, primarily through Wikiversity and open-access platforms. While it incorporates extensive cross-referencing and engages with mainstream and alternative sources, it lacks institutional affiliation and academic endorsement at this stage. '''Related link:''' [[Cosmic Influx Theory]] === '''8.4.10 Summary of Spiral Cosmology''' === The Pearlman Cosmology (SPIRAL Cosmology) offers a deterministic model of the universe with a defined hyper-dense initial state, fixed radius growth, and a reinterpretation of redshift. It integrates biblical chronology into its cosmological assumptions, making it a unique hybrid of scientific and scriptural reasoning. 1. '''Internal Consistency''' The model presents a logically consistent internal framework, with clearly defined initial conditions such as the SPIRAL radius, gravitational equilibrium, and fixed cosmic time scaling. Its components align well within its own assumptions. 2. '''Predictive Power''' Pearlman Cosmology proposes several potentially testable hypotheses, such as a fixed annual rate of universal expansion and an alternative explanation of redshift. However, these are not yet accompanied by detailed numeric predictions or simulations. 3. '''Falsifiability''' Testable elements exist in the form of reinterpretations of the cosmic microwave background origin, early galaxy formation, and redshift asymmetries. Yet aspects based on Mosaic chronology may fall outside strict scientific falsifiability. 4. '''Observational Alignment''' The model qualitatively aligns with some recent JWST observations, including early structure formation and CMB uniformity. Nevertheless, it lacks robust quantitative matching with large datasets or predictive modeling. 5. '''Philosophical Transparency''' The theory is open about its use of religious chronology and framing. This transparency makes its worldview explicit, though it may hinder its acceptance within mainstream secular science. 6. '''Empirical Adequacy''' While some empirical parallels exist, the theory has not yet been tested against a wide body of observational data in a systematic or peer-reviewed way. 7. '''Institutional Support and Development''' Pearlman Cosmology remains outside institutional research frameworks. Its development and publication history are limited, and it has not yet entered mainstream cosmological discourse. '''Related link:''' [https://www.pearlman.org Pearlman Cosmology] '''◀ [[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 ▶]]''' 6w5kie2ywgo2zguq90dyo48nriwk2jr 2719989 2719988 2025-06-29T04:36:59Z Ruud Loeffen 2998353 /* 8.4.5 Big Bang */ add link to this theory 2719989 wikitext text/x-wiki == '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' = == '''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. == '''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 == '''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 such as: Observational Agreement Internal Logical Consistency Predictive Value Compatibility with Other Domains (e.g., geology, biology) Conceptual Coherence and Simplicity Each dimension is rated using a 1–5 star system, based on the information provided and the supporting sources that AI can access. 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. == '''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. == '''8.1 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. '''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. '''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. '''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. '''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. '''5. Conceptual Clarity and Simplicity''' Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification. '''6. Heuristic Value''' Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential. '''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. 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 or can be requested in more detail. == '''8.2 AI Evaluation Table Format''' == {| class="wikitable" |+ '''AI Evaluation Table of Cosmological Theories''' ! Theory Name ! Empirical Adequacy ! Internal Consistency ! Predictive Power ! Cross-Disciplinary Compatibility ! Conceptual Clarity and Simplicity ! Heuristic Value ! Historical & Philosophical Insight ! Total (★) |- | 8.4.1 '''General Relativity''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★★ || '''34''' |- | colspan="9" | ''Widely confirmed by experiment; mathematical elegance; historical development from Newtonian mechanics'' |- |- | 8.4.2 '''Newtonian Gravity''' | ★★★★☆ || ★★★★★ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''30''' |- | colspan="9" | ''Highly successful in classical mechanics and celestial predictions; lacks compatibility with relativity and quantum theory; historically foundational.'' |- | 8.4.3 '''MOND (Modified Newtonian Dynamics)''' | ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''24''' |- | colspan="9" | ''Strong in galactic rotation curves; limited compatibility with general relativistic frameworks'' |- | 8.4.4 '''Emergent Gravity (Verlinde)''' | ★★☆☆☆ || ★★★★☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''25''' |- | colspan="9" | ''Innovative reformulation; still awaiting broad empirical confirmation'' |- | 8.4.5 '''Big Bang Model''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''31''' |- | colspan="9" | ''Core cosmological model; supported by CMB, redshift, nucleosynthesis'' |- | 8.4.6 '''Steady State Theory''' | ★☆☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''23''' |- | colspan="9" | ''Historically important; largely superseded due to lack of CMB explanation'' |- | 8.4.7 '''Big Crunch Theory''' | ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || '''28''' |- | colspan="9" | ''Predicts final collapse of universe; consistent with GR in high-density scenarios; revived interest due to dark energy variability'' |- | 8.4.8 '''Big Bounce Theory''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''26''' |- | colspan="9" | ''Cyclical alternative to singularity; compatible with some quantum gravity models'' |- | 8.4.9 '''Cosmic Influx Theory (CIT)''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★★★★ || ★★★★☆ || '''26''' |- | colspan="9" | ''Offers cross-disciplinary compatibility; predicts mass growth and preferred orbital distances; alternative influx model under development'' |- | 8.4.10 '''SPIRAL Cosmology''' | ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22''' |- | colspan="9" | ''Proposes a hyper-dense proto-galactic phase preceding expansion; no need for ongoing dark energy or cosmic expansion; partially scriptural framing may limit falsifiability but testable claims (e.g. fixed-radius light departure) justify scientific review.'' |- | colspan="9" | ''Well-formulated alternative integrating orbital quantization; some empirical fit to planetary data; lacks full mainstream acceptance'' |} <!-- Add a blank line here --> == '''8.3 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]]'''. == '''8.4 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. === '''8.4.1 General Relativity'''=== '''Empirical Adequacy''' General Relativity (GR) is one of the most empirically validated theories in physics. It has successfully explained and predicted a wide range of gravitational phenomena, including the precession of Mercury’s perihelion, gravitational lensing of starlight, gravitational redshift, time dilation effects observed in satellite systems like GPS, and the Shapiro delay. More recently, its predictions have been confirmed by gravitational wave observations (LIGO/Virgo) and direct imaging of black holes (Event Horizon Telescope). The agreement between theory and measurement is often better than 0.01%, demonstrating exceptional empirical adequacy. '''Internal Consistency''' GR is internally consistent within its mathematical framework. It is based on the Einstein field equations, which are derived from well-defined variational principles and respect general covariance. The logical structure of the theory is rigorous, with clearly formulated assumptions such as the equivalence principle and the conservation of energy–momentum through the stress-energy tensor. There are no known internal contradictions. '''Predictive Power''' GR has a powerful record of making novel predictions that were later confirmed by experiment or observation. These include the bending of light by massive bodies, time dilation in gravitational fields, the expansion of the universe (through its application in cosmology), and the existence of gravitational waves. Its predictions have often preceded direct detection by decades. This makes GR a model example of a theory with high predictive power. '''Cross-Disciplinary Compatibility''' General Relativity is compatible with many areas of physics, including classical mechanics, electrodynamics, and astrophysics. However, it is not yet unified with quantum mechanics. Attempts to reconcile GR with the Standard Model—such as quantum gravity, string theory, or loop quantum gravity—remain incomplete. Thus, GR scores slightly lower here due to its current incompatibility with modern particle physics at the Planck scale. '''Conceptual Clarity and Simplicity''' The core idea of GR—that gravity is not a force but a geometric property of spacetime—is conceptually elegant. However, the mathematical formalism (involving tensor calculus and differential geometry) is complex and often inaccessible to non-specialists. While the theory offers deep conceptual clarity, its practical simplicity is limited by the required mathematical tools. '''Heuristic Value''' GR has inspired generations of physicists and remains a fertile ground for theoretical development. It has opened up entire fields such as relativistic astrophysics, cosmology, and gravitational wave astronomy. Its influence extends beyond physics into philosophy and the public imagination. It continues to motivate research on black holes, time travel, singularities, and the early universe. '''Historical and Philosophical Insight''' Historically, GR represents a revolutionary shift in physics, displacing the Newtonian notion of absolute space and time with a dynamic, curved spacetime model. Philosophically, it challenges classical intuitions about gravity and causality and has inspired reevaluation of concepts such as simultaneity, locality, and determinism. Its legacy places it among the most profound achievements in scientific history. '''Related link:''' [https://en.wikipedia.org/wiki/General_relativity General Relativity] === '''8.4.2 Newtonian Gravity''' === '''Empirical Adequacy''' Newtonian gravity has historically achieved remarkable empirical success. It accurately describes planetary motions, tidal forces, ballistic trajectories, and satellite orbits. For centuries, it provided the dominant framework for celestial mechanics and was sufficient for navigation, astronomy, and engineering. However, it begins to fail in extreme gravitational fields or at very high speeds, where relativistic corrections are needed. It also cannot explain phenomena like the precession of Mercury’s orbit, gravitational time dilation, or the bending of light. '''Internal Consistency''' Within its classical framework, Newtonian gravity is highly consistent. It is based on clear axioms such as the inverse-square law and absolute space and time. The mathematical structure is well-defined and solvable using Newton’s laws of motion and calculus. No logical contradictions arise within its scope of applicability. However, its assumptions about instantaneous action at a distance are problematic under modern physical understanding. '''Predictive Power''' Newtonian gravity has strong predictive power in low-speed, weak-field regimes. It successfully predicted the return of Halley’s Comet, the existence of Neptune, and continues to be used in engineering and orbital calculations. However, it fails to predict relativistic effects such as gravitational lensing, frame-dragging, or gravitational waves. These limitations reduce its predictive power on cosmic and high-precision scales. '''Cross-Disciplinary Compatibility''' Newton’s theory aligns well with classical physics and early chemistry but lacks compatibility with modern disciplines. It cannot be reconciled with special relativity or quantum theory and does not incorporate energy–momentum considerations as in modern field theories. Its incompatibility with relativity limits its integration with high-energy physics and astrophysics. '''Conceptual Clarity and Simplicity''' Newtonian gravity is conceptually simple and intuitively accessible. The inverse-square force law is easy to visualize and apply. It does not require advanced mathematics and remains an ideal teaching model. Its clarity and ease of computation give it enduring educational and practical value. '''Heuristic Value''' Although no longer a frontier theory, Newtonian gravity laid the groundwork for classical mechanics and much of modern science. It helped shape ideas about force, motion, and planetary systems. While it no longer drives active theoretical innovation, it retains historical heuristic importance. '''Historical and Philosophical Insight''' Newton’s theory was revolutionary in unifying terrestrial and celestial phenomena under the same laws of motion. It established the idea of a universal physical law and set the standard for quantitative science. Philosophically, it introduced mechanistic determinism and absolute space and time—concepts that dominated Enlightenment science. Though now superseded, its legacy remains foundational. '''Related link:''' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newtonian Gravity] === '''8.4.3 MOND (Modified Newtonian Dynamics)''' === '''Empirical Adequacy''' MOND was proposed by Mordehai Milgrom in the early 1980s to explain galactic rotation curves without invoking dark matter. It has successfully reproduced the flat rotation profiles of spiral galaxies and the observed baryonic Tully–Fisher relation with remarkable precision. MOND fits individual galaxy data with fewer parameters than dark matter models. However, it struggles with galaxy cluster dynamics, cosmological structure formation, and gravitational lensing in some systems. Its empirical adequacy is high for galactic scales but limited beyond that domain. '''Internal Consistency''' MOND is mathematically consistent in its non-relativistic form, where it modifies Newton’s second law at low accelerations using a new constant 𝑎 0 a 0 ​ . However, its original formulation lacks a full theoretical derivation from first principles and requires ad hoc modifications to the force law. Several relativistic extensions (e.g. TeVeS, AQUAL, BIMOND) have been developed to improve consistency, but these are not uniquely favored and remain complex or underconstrained. '''Predictive Power''' MOND has had considerable predictive success in galactic astrophysics. It predicted the baryonic Tully–Fisher relation before it was observationally confirmed, and it can reproduce detailed features of galaxy rotation curves without needing dark matter halos. However, it lacks explanatory power for phenomena like the cosmic microwave background (CMB) anisotropies, gravitational lensing in galaxy clusters (e.g. Bullet Cluster), and large-scale structure. Its predictive power is strong in its target domain but limited on cosmological scales. '''Cross-Disciplinary Compatibility''' MOND is primarily focused on galactic dynamics and does not integrate smoothly with high-energy physics, quantum theory, or cosmology. Its extensions to cosmology often require additional assumptions, and it is not yet compatible with standard particle physics. As a result, its cross-disciplinary reach is modest, though ongoing efforts aim to embed it within broader frameworks. '''Conceptual Clarity and Simplicity''' In its original form, MOND is simple: the gravitational acceleration deviates from Newton’s law when below a critical threshold 𝑎 0 a 0 ​ . This modification is intuitive and computationally effective for galaxies. However, attempts to embed MOND in a relativistic framework often add complexity, reducing its conceptual transparency. '''Heuristic Value''' MOND has had significant heuristic impact by highlighting regularities in galactic dynamics that are hard to explain under the ΛCDM paradigm without fine-tuned dark matter profiles. It has sparked debate, inspired hybrid theories (e.g. dark matter superfluidity), and contributed to reevaluating gravitational theory. Its challenge to mainstream cosmology has been fruitful, even if not universally accepted. '''Historical and Philosophical Insight''' MOND revives the idea that gravity itself may need modification, rather than positing unseen matter. This philosophical approach echoes the history of science, where anomalies sometimes led to revisions of theory rather than new entities. MOND also raises deep questions about the nature of inertia, scale invariance, and universal laws—making it a philosophically provocative proposal despite its contested status. '''Related link:''' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics MOND (Modified Newtonian Dynamics)] === '''8.4.4 Emergent Gravity''' === '''Empirical Adequacy''' Emergent Gravity, proposed by Erik Verlinde in 2011 and expanded in 2016, seeks to explain gravitational phenomena as an emergent effect of underlying entropic and holographic principles rather than a fundamental force. It claims to reproduce galactic rotation curves without invoking dark matter by relating gravity to the thermodynamics of microscopic information storage on holographic screens. The theory can qualitatively explain certain galactic dynamics, such as the radial acceleration relation (RAR), but lacks the quantitative precision and scope of MOND in galaxy rotation curve fitting. It also currently cannot reproduce the full spectrum of cosmological observations, including the CMB power spectrum or gravitational lensing in galaxy clusters, where standard ΛCDM performs better. '''Internal Consistency''' Emergent Gravity draws from concepts in string theory, quantum information theory, and thermodynamics. While intellectually coherent and grounded in cutting-edge theoretical frameworks, the theory is still under development and lacks a universally accepted formalism. Key quantities (such as entropic force or the elastic response of spacetime) are not always rigorously defined, and derivations sometimes rely on analogies rather than strict derivations. This limits the formal internal consistency at present, though the conceptual framework remains promising. '''Predictive Power''' The theory makes some novel qualitative predictions, particularly regarding the relation between baryonic mass and gravitational acceleration without dark matter. It reproduces the RAR and may provide an explanation for dark energy as an entropic effect of spacetime. However, Emergent Gravity has not yet made precise predictions for cosmological parameters, gravitational wave behavior, or galaxy cluster dynamics that can be tested independently of standard models. Its predictive power remains speculative and qualitative. '''Cross-Disciplinary Compatibility''' Emergent Gravity attempts to bridge gravity, quantum information, and thermodynamics, making it conceptually rich in cross-disciplinary connections. It resonates with holography, the AdS/CFT correspondence, and black hole thermodynamics. However, the lack of experimental or observational confirmation limits its integration with empirical domains such as astrophysics, cosmology, and particle physics. Its compatibility is more theoretical than empirical at this stage. '''Conceptual Clarity and Simplicity''' The idea that gravity is not fundamental but emerges from statistical behavior of microscopic degrees of freedom is intellectually elegant. However, the actual implementation of this idea in the current models is technically complex and often abstract. Unlike Newtonian gravity or even MOND, the mechanisms proposed by Emergent Gravity are difficult to visualize or test directly, and involve high-level concepts from thermodynamics and information theory. '''Heuristic Value''' Emergent Gravity is highly heuristic. It opens new perspectives on the nature of gravity, spacetime, and entropy. By reframing gravity as an emergent entropic force, it challenges the foundations of both classical and relativistic theories. It has influenced discussions around the holographic principle, black hole entropy, and spacetime microstructure. Even if it remains incomplete, it contributes to rethinking gravity from first principles. '''Historical and Philosophical Insight''' Philosophically, Emergent Gravity aligns with the long-standing idea that some phenomena in nature arise from deeper, statistical processes rather than being fundamental. It recalls Boltzmann’s approach to thermodynamics and aligns with modern information-theoretic views of physics. Historically, it marks a shift from geometric to thermodynamic models of spacetime, and offers a bold alternative to particle-based explanations of gravity. Though controversial, it is part of a growing movement to reinterpret gravity in terms of entropy and information. '''Related link:''' [https://en.wikipedia.org/wiki/Erik_Verlinde#Emergent_gravity Emergent Gravity] === '''8.4.5 Big Bang''' === '''Empirical Adequacy''' The Big Bang model is the current standard cosmological paradigm and is strongly supported by multiple independent observations. These include the cosmic microwave background (CMB) radiation, the large-scale structure of the universe, the observed expansion of space (via redshift-distance relations), and the relative abundances of light elements (hydrogen, helium, deuterium, lithium), as predicted by Big Bang Nucleosynthesis (BBN). These confirmations make the Big Bang model one of the most empirically supported frameworks in cosmology. However, the model does not explain the origin of the singularity itself, and extensions such as inflation or dark energy are required to match detailed observations. '''Internal Consistency''' The Big Bang framework is based on solutions to Einstein's field equations (Friedmann–Lemaître–Robertson–Walker metrics), and it is mathematically consistent within the assumptions of general relativity and homogeneity/isotropy (the cosmological principle). However, the initial singularity remains a theoretical boundary where the equations break down, and the model does not include a quantum gravity regime. Extensions such as inflation and ΛCDM are necessary for consistency with observations, but these introduce additional assumptions and parameters, sometimes criticized as fine-tuning. '''Predictive Power''' The Big Bang model has made several successful predictions: the existence and spectrum of the CMB, the large-scale structure of galaxies, and the relative abundances of primordial elements. It also correctly anticipated the cooling of the universe and the redshift–distance relation. Inflationary extensions explain the flatness and horizon problems and predict the nearly scale-invariant spectrum of CMB fluctuations. While many predictions are retrodictive and interpreted within a flexible framework, the model continues to be highly predictive in key areas of cosmology. '''Cross-Disciplinary Compatibility''' The Big Bang model integrates with nuclear physics (BBN), atomic physics (recombination), and high-energy physics (inflation, particle freeze-out). It is broadly compatible with the Standard Model of particle physics and many theories of fundamental interactions. However, it lacks a connection to quantum gravity, and some tensions remain—such as the Hubble tension between early and late universe measurements—that challenge cross-scale consistency. '''Conceptual Clarity and Simplicity''' The core idea—a hot, dense early universe that expands and cools over time—is conceptually clear and widely accepted. However, the full ΛCDM model includes inflation, cold dark matter, and dark energy, which are not directly observable and require complex assumptions. These components reduce the model's simplicity and raise questions about the explanatory depth of the framework. '''Heuristic Value''' The Big Bang theory has driven vast developments in cosmology, observational astronomy, particle physics, and astrophysical instrumentation. It has generated decades of research questions and missions, including COBE, WMAP, and Planck. The inflationary paradigm and dark energy studies have emerged directly from this model. As a heuristic framework, it has proven extremely fertile. '''Historical and Philosophical Insight''' The Big Bang marks a major conceptual shift in cosmology by proposing that the universe has a temporal origin and evolves over time. It displaced steady-state and eternal models of the cosmos and opened up philosophical inquiries about creation, the arrow of time, and the origin of physical laws. Despite its name, it is not an explosion in space but the expansion of space itself—a concept that has reshaped how we understand time, causality, and the structure of the universe. '''Related link:''' [https://en.wikipedia.org/wiki/Big_Bang Big Bang] === '''8.4.6 Steady State Theory''' === '''Empirical Adequacy''' The Steady State Theory, developed in the late 1940s by Bondi, Gold, and Hoyle, posits that the universe has no beginning or end in time and remains statistically the same on large scales, with matter continuously created to maintain constant density despite cosmic expansion. Initially, it matched observations of redshift and expansion, but it was ultimately undermined by key empirical discoveries: the cosmic microwave background (CMB), the evolution of radio source counts, and the observation of distant galaxies at earlier stages of development. These findings provided strong evidence of a hot, dense early universe, inconsistent with the steady state hypothesis. As a result, its empirical adequacy is now considered low. '''Internal Consistency''' The theory is internally consistent in its classical formulation and relies on continuous creation of matter to maintain a constant density. However, this matter creation mechanism was never supported by a detailed physical model or empirical detection. While mathematically coherent, the theory’s assumption of continuous creation violates energy conservation as understood in standard physics, making the underlying physics speculative and theoretically weak. '''Predictive Power''' The Steady State model made a bold prediction: the universe should appear the same at all times and places when viewed on large scales. While this was a clear and testable prediction, it was eventually falsified by observations such as the CMB and the evolution of quasars and galaxy populations over time. The theory’s few predictions have largely been refuted, limiting its scientific utility. '''Cross-Disciplinary Compatibility''' The model is only weakly connected to other scientific domains. It does not integrate well with nuclear physics, as it lacks a mechanism for element formation similar to Big Bang Nucleosynthesis. It also lacks compatibility with high-energy particle physics and modern theories of gravity. The continuous matter creation postulate has no foundation in quantum theory or experimental physics. '''Conceptual Clarity and Simplicity''' The steady-state model is conceptually simple and elegant. Its appeal lay in its ability to preserve a universe without origin, circumventing the philosophical and theological questions raised by a cosmic beginning. The model also maintains a uniform, eternal cosmos, which was attractive to many physicists in the mid-20th century. Despite being falsified, it remains a conceptually clear alternative that helped clarify the implications of observational cosmology. '''Heuristic Value''' Although it is no longer a viable cosmological model, the Steady State theory played a significant heuristic role. It prompted debates about the nature of time, observational testing, and the falsifiability of cosmological models. It helped shape the methodological standards for modern cosmology by being a well-defined, testable theory that was ultimately rejected based on empirical data. Its legacy lives on in discussions about the role of testability and philosophical assumptions in science. '''Historical and Philosophical Insight''' The Steady State theory was historically important as the main rival to the Big Bang model in the early post-war period. It reflects a philosophical preference for temporal infinity and equilibrium conditions, standing in contrast to a universe with a beginning. Its eventual rejection illustrates the triumph of observation over philosophical elegance in modern cosmology. It also served as a case study in the philosophy of science, particularly regarding Popperian falsifiability and the evolution of scientific consensus. === '''8.4.7 Big Crunch''' === '''Empirical Adequacy''' The Big Crunch is not a theory of gravity or cosmology by itself but rather a hypothetical end-state of the universe within certain cosmological models. It posits that cosmic expansion could eventually reverse, causing the universe to contract back into a high-density singularity. This scenario arises from general relativity under the assumption of a closed universe with sufficient matter density to overcome expansion. However, current observational data strongly indicate that the universe is accelerating in its expansion, driven by dark energy. Measurements of the cosmic microwave background (CMB), supernova distances, and large-scale structure all support a flat or open universe with low matter density, making the Big Crunch scenario empirically disfavored at present. '''Internal Consistency''' Within general relativity and standard cosmological models, the Big Crunch is internally consistent. It naturally arises from the Friedmann equations when the density parameter Ω > 1 and the cosmological constant is absent or negative. The dynamics of contraction mirror those of expansion in reverse, and no logical contradictions emerge in its mathematical formulation. However, near the final singularity, quantum gravitational effects become important, and the classical equations break down. '''Predictive Power''' As a hypothetical scenario, the Big Crunch does not offer specific predictive claims under current physical conditions. Instead, it represents a conditional outcome: if the universe were closed and dominated by matter, it would eventually recollapse. Since observations show otherwise, the predictive relevance of the Big Crunch is now limited. Nevertheless, it played a role in exploring time-reversal symmetry, thermodynamic limits, and quantum cosmology. '''Cross-Disciplinary Compatibility''' The Big Crunch scenario is compatible with general relativity and classical thermodynamics, especially in discussions of entropy and the arrow of time. It has also been explored in speculative models of cyclic or oscillating universes, which relate to quantum gravity and string theory. However, it lacks strong support from empirical fields such as observational cosmology, particle physics, or astronomy under the current ΛCDM framework. '''Conceptual Clarity and Simplicity''' The concept is straightforward: the universe's expansion halts and reverses into a collapse. This time-symmetric model is intuitively appealing and easy to visualize. However, its physical plausibility is undermined by current evidence for accelerating expansion. Still, as a conceptual tool, it remains a clear contrast to models of eternal expansion or thermal death. '''Heuristic Value''' Historically, the Big Crunch scenario stimulated discussion about cosmological cycles, entropy limits, and the ultimate fate of the universe. It led to the development of cyclic models, bounce cosmologies, and ideas about cosmic rebirth. Although largely ruled out by current data, it retains heuristic value in theoretical cosmology and philosophy of time, particularly in exploring whether time and entropy could reverse. '''Historical and Philosophical Insight''' The Big Crunch offered a philosophically symmetric alternative to the Big Bang—a universe that begins and ends in a singularity. It invites reflection on the reversibility of physical laws, the meaning of cosmic time, and the possibility of eternal recurrence. While empirical support is lacking, the scenario remains a historically meaningful part of cosmological thinking, especially in the 20th-century debates about the universe's fate. === '''8.4.8 Big Bounce''' === '''Empirical Adequacy''' The Big Bounce is a speculative cosmological scenario in which the universe undergoes a cycle of contraction followed by a rebound (or "bounce") into a new phase of expansion. It aims to replace the initial singularity of the Big Bang with a transitional phase where quantum gravitational effects prevent infinite density. While the concept is consistent with certain theoretical models—particularly in loop quantum cosmology—there is currently no direct observational evidence for a bounce event. The cosmic microwave background (CMB) does not yet show unambiguous signatures that would favor a bounce over inflationary models. Thus, empirical adequacy remains hypothetical, though not excluded. '''Internal Consistency''' The Big Bounce can be formulated consistently within several frameworks, such as loop quantum gravity, string gas cosmology, or modified gravity models. In these settings, quantum corrections to the Friedmann equations or modifications to the geometry of spacetime prevent a singularity and allow for a smooth transition from contraction to expansion. However, different bounce models vary in their assumptions, and the full quantum dynamics are not yet universally agreed upon. Despite these uncertainties, the internal logic of the models is coherent within their theoretical boundaries. '''Predictive Power''' Some Big Bounce models predict subtle features in the CMB, such as suppressed power at large angular scales, or non-Gaussianities that differ from inflation. However, these predictions often overlap with or are degenerate with inflationary predictions, making them hard to test uniquely. No conclusive observational support has been found so far. Nevertheless, bounce models offer a predictive framework that could, in principle, be tested with improved cosmological data in the future. '''Cross-Disciplinary Compatibility''' The Big Bounce scenario is motivated by attempts to unify quantum mechanics and gravity. It connects well with developments in loop quantum cosmology, non-singular black hole models, and string theory. However, it is less developed in its links to particle physics, standard cosmology, or astrophysical observations. Its broader scientific compatibility depends heavily on which theoretical approach is adopted and how it interfaces with known physics. '''Conceptual Clarity and Simplicity''' The idea of a contracting universe rebounding into expansion is conceptually intuitive and avoids the metaphysical implications of a beginning-of-time singularity. In contrast to the Big Bang singularity, the bounce implies a cyclic or oscillatory universe that is eternal in time. While appealing in its symmetry, the underlying physics is often highly technical and abstract, involving non-perturbative quantum gravity, which reduces its practical simplicity. '''Heuristic Value''' The Big Bounce has stimulated important discussions in cosmology, particularly regarding singularity avoidance, pre-Big Bang scenarios, and the nature of time. It has inspired a class of alternative models to inflation and opened up debates about the cyclical nature of the universe. Its challenge to the standard narrative of cosmic origins has heuristic value in motivating new lines of theoretical research. '''Historical and Philosophical Insight''' The Big Bounce continues a long tradition of cyclical universe models, echoing ideas from ancient cosmologies and early 20th-century oscillating universe theories. Philosophically, it provides a framework in which the universe has no absolute beginning or end, and where time and entropy may operate in a larger looped framework. It offers a more balanced cosmological picture than the irreversible expansion or final collapse scenarios. Though not yet supported by data, its philosophical implications remain profound and open-ended. === '''8.4.9 Cosmic Influx Theory (CIT)''' === Cosmic Influx Theory (CIT), proposed by Ruud Loeffen, reinterprets gravity as a directional energy influx driven by Primordial Elementary Whirlings (PEWs), replacing the concept of attractive force or space-time curvature. It introduces a constant influx of mass-energy into all bodies, contributing to planetary expansion, star formation, and cosmological evolution. 1. '''Internal Consistency''' CIT presents a coherent internal logic based on a unidirectional influx mechanism, a redefined gravitational constant (G = (γ − 1)/4π), and the introduction of κ_CIT as a universal scaling constant. While the framework remains internally consistent, some equations are still under refinement and lack full derivations from first principles. 2. '''Predictive Power''' CIT predicts the Preferred Distance for giant planets based on κ_CIT, orbital periods of exoplanets, and a revised Hubble constant (Ho ≈ 67.8 km/s/Mpc). It also anticipates planetary expansion through mass influx. These predictions are testable, though many remain pending observational confirmation. 3. '''Falsifiability''' Several predictions—such as giant planets at D_pref in the Trappist system or mass accumulation rates inferred from planetary geology—can be tested. However, the influx mechanism itself is not yet described in terms of directly measurable particles or interactions, which may limit falsifiability at the quantum level. 4. '''Observational Alignment''' CIT aligns with various observations: early formation of giant planets in protoplanetary disks, planetary expansion signatures, surface geology of moons and Mars, and recent JWST disk structures. It also claims to naturally derive the observed Hubble constant without tension. 5. '''Philosophical Transparency''' The theory clearly departs from Newtonian and relativistic interpretations, positioning itself as an ontological alternative grounded in energy flow. The author's motivations, limitations, and intended scope are transparently communicated in both academic and public forums. 6. '''Empirical Adequacy''' CIT offers empirical parallels in planetary spacing (κ_CIT), daylength extension over geological time, and disk fragmentation patterns. However, it currently lacks publication in high-impact peer-reviewed journals and formal statistical validation across broad datasets. 7. '''Institutional Support and Development''' CIT is developed independently, primarily through Wikiversity and open-access platforms. While it incorporates extensive cross-referencing and engages with mainstream and alternative sources, it lacks institutional affiliation and academic endorsement at this stage. '''Related link:''' [[Cosmic Influx Theory]] === '''8.4.10 Summary of Spiral Cosmology''' === The Pearlman Cosmology (SPIRAL Cosmology) offers a deterministic model of the universe with a defined hyper-dense initial state, fixed radius growth, and a reinterpretation of redshift. It integrates biblical chronology into its cosmological assumptions, making it a unique hybrid of scientific and scriptural reasoning. 1. '''Internal Consistency''' The model presents a logically consistent internal framework, with clearly defined initial conditions such as the SPIRAL radius, gravitational equilibrium, and fixed cosmic time scaling. Its components align well within its own assumptions. 2. '''Predictive Power''' Pearlman Cosmology proposes several potentially testable hypotheses, such as a fixed annual rate of universal expansion and an alternative explanation of redshift. However, these are not yet accompanied by detailed numeric predictions or simulations. 3. '''Falsifiability''' Testable elements exist in the form of reinterpretations of the cosmic microwave background origin, early galaxy formation, and redshift asymmetries. Yet aspects based on Mosaic chronology may fall outside strict scientific falsifiability. 4. '''Observational Alignment''' The model qualitatively aligns with some recent JWST observations, including early structure formation and CMB uniformity. Nevertheless, it lacks robust quantitative matching with large datasets or predictive modeling. 5. '''Philosophical Transparency''' The theory is open about its use of religious chronology and framing. This transparency makes its worldview explicit, though it may hinder its acceptance within mainstream secular science. 6. '''Empirical Adequacy''' While some empirical parallels exist, the theory has not yet been tested against a wide body of observational data in a systematic or peer-reviewed way. 7. '''Institutional Support and Development''' Pearlman Cosmology remains outside institutional research frameworks. Its development and publication history are limited, and it has not yet entered mainstream cosmological discourse. '''Related link:''' [https://www.pearlman.org Pearlman Cosmology] '''◀ [[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 ▶]]''' bynq7d2lrfdyp7htwkmf2w6udge6nih 2719990 2719989 2025-06-29T04:37:43Z Ruud Loeffen 2998353 /* 8.4.6 Steady State Theory */ add link to this theory 2719990 wikitext text/x-wiki == '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' = == '''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. == '''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 == '''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 such as: Observational Agreement Internal Logical Consistency Predictive Value Compatibility with Other Domains (e.g., geology, biology) Conceptual Coherence and Simplicity Each dimension is rated using a 1–5 star system, based on the information provided and the supporting sources that AI can access. 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. == '''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. == '''8.1 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. '''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. '''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. '''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. '''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. '''5. Conceptual Clarity and Simplicity''' Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification. '''6. Heuristic Value''' Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential. '''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. 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 or can be requested in more detail. == '''8.2 AI Evaluation Table Format''' == {| class="wikitable" |+ '''AI Evaluation Table of Cosmological Theories''' ! Theory Name ! Empirical Adequacy ! Internal Consistency ! Predictive Power ! Cross-Disciplinary Compatibility ! Conceptual Clarity and Simplicity ! Heuristic Value ! Historical & Philosophical Insight ! Total (★) |- | 8.4.1 '''General Relativity''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★★ || '''34''' |- | colspan="9" | ''Widely confirmed by experiment; mathematical elegance; historical development from Newtonian mechanics'' |- |- | 8.4.2 '''Newtonian Gravity''' | ★★★★☆ || ★★★★★ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''30''' |- | colspan="9" | ''Highly successful in classical mechanics and celestial predictions; lacks compatibility with relativity and quantum theory; historically foundational.'' |- | 8.4.3 '''MOND (Modified Newtonian Dynamics)''' | ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''24''' |- | colspan="9" | ''Strong in galactic rotation curves; limited compatibility with general relativistic frameworks'' |- | 8.4.4 '''Emergent Gravity (Verlinde)''' | ★★☆☆☆ || ★★★★☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''25''' |- | colspan="9" | ''Innovative reformulation; still awaiting broad empirical confirmation'' |- | 8.4.5 '''Big Bang Model''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''31''' |- | colspan="9" | ''Core cosmological model; supported by CMB, redshift, nucleosynthesis'' |- | 8.4.6 '''Steady State Theory''' | ★☆☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''23''' |- | colspan="9" | ''Historically important; largely superseded due to lack of CMB explanation'' |- | 8.4.7 '''Big Crunch Theory''' | ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || '''28''' |- | colspan="9" | ''Predicts final collapse of universe; consistent with GR in high-density scenarios; revived interest due to dark energy variability'' |- | 8.4.8 '''Big Bounce Theory''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''26''' |- | colspan="9" | ''Cyclical alternative to singularity; compatible with some quantum gravity models'' |- | 8.4.9 '''Cosmic Influx Theory (CIT)''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★★★★ || ★★★★☆ || '''26''' |- | colspan="9" | ''Offers cross-disciplinary compatibility; predicts mass growth and preferred orbital distances; alternative influx model under development'' |- | 8.4.10 '''SPIRAL Cosmology''' | ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22''' |- | colspan="9" | ''Proposes a hyper-dense proto-galactic phase preceding expansion; no need for ongoing dark energy or cosmic expansion; partially scriptural framing may limit falsifiability but testable claims (e.g. fixed-radius light departure) justify scientific review.'' |- | colspan="9" | ''Well-formulated alternative integrating orbital quantization; some empirical fit to planetary data; lacks full mainstream acceptance'' |} <!-- Add a blank line here --> == '''8.3 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]]'''. == '''8.4 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. === '''8.4.1 General Relativity'''=== '''Empirical Adequacy''' General Relativity (GR) is one of the most empirically validated theories in physics. It has successfully explained and predicted a wide range of gravitational phenomena, including the precession of Mercury’s perihelion, gravitational lensing of starlight, gravitational redshift, time dilation effects observed in satellite systems like GPS, and the Shapiro delay. More recently, its predictions have been confirmed by gravitational wave observations (LIGO/Virgo) and direct imaging of black holes (Event Horizon Telescope). The agreement between theory and measurement is often better than 0.01%, demonstrating exceptional empirical adequacy. '''Internal Consistency''' GR is internally consistent within its mathematical framework. It is based on the Einstein field equations, which are derived from well-defined variational principles and respect general covariance. The logical structure of the theory is rigorous, with clearly formulated assumptions such as the equivalence principle and the conservation of energy–momentum through the stress-energy tensor. There are no known internal contradictions. '''Predictive Power''' GR has a powerful record of making novel predictions that were later confirmed by experiment or observation. These include the bending of light by massive bodies, time dilation in gravitational fields, the expansion of the universe (through its application in cosmology), and the existence of gravitational waves. Its predictions have often preceded direct detection by decades. This makes GR a model example of a theory with high predictive power. '''Cross-Disciplinary Compatibility''' General Relativity is compatible with many areas of physics, including classical mechanics, electrodynamics, and astrophysics. However, it is not yet unified with quantum mechanics. Attempts to reconcile GR with the Standard Model—such as quantum gravity, string theory, or loop quantum gravity—remain incomplete. Thus, GR scores slightly lower here due to its current incompatibility with modern particle physics at the Planck scale. '''Conceptual Clarity and Simplicity''' The core idea of GR—that gravity is not a force but a geometric property of spacetime—is conceptually elegant. However, the mathematical formalism (involving tensor calculus and differential geometry) is complex and often inaccessible to non-specialists. While the theory offers deep conceptual clarity, its practical simplicity is limited by the required mathematical tools. '''Heuristic Value''' GR has inspired generations of physicists and remains a fertile ground for theoretical development. It has opened up entire fields such as relativistic astrophysics, cosmology, and gravitational wave astronomy. Its influence extends beyond physics into philosophy and the public imagination. It continues to motivate research on black holes, time travel, singularities, and the early universe. '''Historical and Philosophical Insight''' Historically, GR represents a revolutionary shift in physics, displacing the Newtonian notion of absolute space and time with a dynamic, curved spacetime model. Philosophically, it challenges classical intuitions about gravity and causality and has inspired reevaluation of concepts such as simultaneity, locality, and determinism. Its legacy places it among the most profound achievements in scientific history. '''Related link:''' [https://en.wikipedia.org/wiki/General_relativity General Relativity] === '''8.4.2 Newtonian Gravity''' === '''Empirical Adequacy''' Newtonian gravity has historically achieved remarkable empirical success. It accurately describes planetary motions, tidal forces, ballistic trajectories, and satellite orbits. For centuries, it provided the dominant framework for celestial mechanics and was sufficient for navigation, astronomy, and engineering. However, it begins to fail in extreme gravitational fields or at very high speeds, where relativistic corrections are needed. It also cannot explain phenomena like the precession of Mercury’s orbit, gravitational time dilation, or the bending of light. '''Internal Consistency''' Within its classical framework, Newtonian gravity is highly consistent. It is based on clear axioms such as the inverse-square law and absolute space and time. The mathematical structure is well-defined and solvable using Newton’s laws of motion and calculus. No logical contradictions arise within its scope of applicability. However, its assumptions about instantaneous action at a distance are problematic under modern physical understanding. '''Predictive Power''' Newtonian gravity has strong predictive power in low-speed, weak-field regimes. It successfully predicted the return of Halley’s Comet, the existence of Neptune, and continues to be used in engineering and orbital calculations. However, it fails to predict relativistic effects such as gravitational lensing, frame-dragging, or gravitational waves. These limitations reduce its predictive power on cosmic and high-precision scales. '''Cross-Disciplinary Compatibility''' Newton’s theory aligns well with classical physics and early chemistry but lacks compatibility with modern disciplines. It cannot be reconciled with special relativity or quantum theory and does not incorporate energy–momentum considerations as in modern field theories. Its incompatibility with relativity limits its integration with high-energy physics and astrophysics. '''Conceptual Clarity and Simplicity''' Newtonian gravity is conceptually simple and intuitively accessible. The inverse-square force law is easy to visualize and apply. It does not require advanced mathematics and remains an ideal teaching model. Its clarity and ease of computation give it enduring educational and practical value. '''Heuristic Value''' Although no longer a frontier theory, Newtonian gravity laid the groundwork for classical mechanics and much of modern science. It helped shape ideas about force, motion, and planetary systems. While it no longer drives active theoretical innovation, it retains historical heuristic importance. '''Historical and Philosophical Insight''' Newton’s theory was revolutionary in unifying terrestrial and celestial phenomena under the same laws of motion. It established the idea of a universal physical law and set the standard for quantitative science. Philosophically, it introduced mechanistic determinism and absolute space and time—concepts that dominated Enlightenment science. Though now superseded, its legacy remains foundational. '''Related link:''' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newtonian Gravity] === '''8.4.3 MOND (Modified Newtonian Dynamics)''' === '''Empirical Adequacy''' MOND was proposed by Mordehai Milgrom in the early 1980s to explain galactic rotation curves without invoking dark matter. It has successfully reproduced the flat rotation profiles of spiral galaxies and the observed baryonic Tully–Fisher relation with remarkable precision. MOND fits individual galaxy data with fewer parameters than dark matter models. However, it struggles with galaxy cluster dynamics, cosmological structure formation, and gravitational lensing in some systems. Its empirical adequacy is high for galactic scales but limited beyond that domain. '''Internal Consistency''' MOND is mathematically consistent in its non-relativistic form, where it modifies Newton’s second law at low accelerations using a new constant 𝑎 0 a 0 ​ . However, its original formulation lacks a full theoretical derivation from first principles and requires ad hoc modifications to the force law. Several relativistic extensions (e.g. TeVeS, AQUAL, BIMOND) have been developed to improve consistency, but these are not uniquely favored and remain complex or underconstrained. '''Predictive Power''' MOND has had considerable predictive success in galactic astrophysics. It predicted the baryonic Tully–Fisher relation before it was observationally confirmed, and it can reproduce detailed features of galaxy rotation curves without needing dark matter halos. However, it lacks explanatory power for phenomena like the cosmic microwave background (CMB) anisotropies, gravitational lensing in galaxy clusters (e.g. Bullet Cluster), and large-scale structure. Its predictive power is strong in its target domain but limited on cosmological scales. '''Cross-Disciplinary Compatibility''' MOND is primarily focused on galactic dynamics and does not integrate smoothly with high-energy physics, quantum theory, or cosmology. Its extensions to cosmology often require additional assumptions, and it is not yet compatible with standard particle physics. As a result, its cross-disciplinary reach is modest, though ongoing efforts aim to embed it within broader frameworks. '''Conceptual Clarity and Simplicity''' In its original form, MOND is simple: the gravitational acceleration deviates from Newton’s law when below a critical threshold 𝑎 0 a 0 ​ . This modification is intuitive and computationally effective for galaxies. However, attempts to embed MOND in a relativistic framework often add complexity, reducing its conceptual transparency. '''Heuristic Value''' MOND has had significant heuristic impact by highlighting regularities in galactic dynamics that are hard to explain under the ΛCDM paradigm without fine-tuned dark matter profiles. It has sparked debate, inspired hybrid theories (e.g. dark matter superfluidity), and contributed to reevaluating gravitational theory. Its challenge to mainstream cosmology has been fruitful, even if not universally accepted. '''Historical and Philosophical Insight''' MOND revives the idea that gravity itself may need modification, rather than positing unseen matter. This philosophical approach echoes the history of science, where anomalies sometimes led to revisions of theory rather than new entities. MOND also raises deep questions about the nature of inertia, scale invariance, and universal laws—making it a philosophically provocative proposal despite its contested status. '''Related link:''' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics MOND (Modified Newtonian Dynamics)] === '''8.4.4 Emergent Gravity''' === '''Empirical Adequacy''' Emergent Gravity, proposed by Erik Verlinde in 2011 and expanded in 2016, seeks to explain gravitational phenomena as an emergent effect of underlying entropic and holographic principles rather than a fundamental force. It claims to reproduce galactic rotation curves without invoking dark matter by relating gravity to the thermodynamics of microscopic information storage on holographic screens. The theory can qualitatively explain certain galactic dynamics, such as the radial acceleration relation (RAR), but lacks the quantitative precision and scope of MOND in galaxy rotation curve fitting. It also currently cannot reproduce the full spectrum of cosmological observations, including the CMB power spectrum or gravitational lensing in galaxy clusters, where standard ΛCDM performs better. '''Internal Consistency''' Emergent Gravity draws from concepts in string theory, quantum information theory, and thermodynamics. While intellectually coherent and grounded in cutting-edge theoretical frameworks, the theory is still under development and lacks a universally accepted formalism. Key quantities (such as entropic force or the elastic response of spacetime) are not always rigorously defined, and derivations sometimes rely on analogies rather than strict derivations. This limits the formal internal consistency at present, though the conceptual framework remains promising. '''Predictive Power''' The theory makes some novel qualitative predictions, particularly regarding the relation between baryonic mass and gravitational acceleration without dark matter. It reproduces the RAR and may provide an explanation for dark energy as an entropic effect of spacetime. However, Emergent Gravity has not yet made precise predictions for cosmological parameters, gravitational wave behavior, or galaxy cluster dynamics that can be tested independently of standard models. Its predictive power remains speculative and qualitative. '''Cross-Disciplinary Compatibility''' Emergent Gravity attempts to bridge gravity, quantum information, and thermodynamics, making it conceptually rich in cross-disciplinary connections. It resonates with holography, the AdS/CFT correspondence, and black hole thermodynamics. However, the lack of experimental or observational confirmation limits its integration with empirical domains such as astrophysics, cosmology, and particle physics. Its compatibility is more theoretical than empirical at this stage. '''Conceptual Clarity and Simplicity''' The idea that gravity is not fundamental but emerges from statistical behavior of microscopic degrees of freedom is intellectually elegant. However, the actual implementation of this idea in the current models is technically complex and often abstract. Unlike Newtonian gravity or even MOND, the mechanisms proposed by Emergent Gravity are difficult to visualize or test directly, and involve high-level concepts from thermodynamics and information theory. '''Heuristic Value''' Emergent Gravity is highly heuristic. It opens new perspectives on the nature of gravity, spacetime, and entropy. By reframing gravity as an emergent entropic force, it challenges the foundations of both classical and relativistic theories. It has influenced discussions around the holographic principle, black hole entropy, and spacetime microstructure. Even if it remains incomplete, it contributes to rethinking gravity from first principles. '''Historical and Philosophical Insight''' Philosophically, Emergent Gravity aligns with the long-standing idea that some phenomena in nature arise from deeper, statistical processes rather than being fundamental. It recalls Boltzmann’s approach to thermodynamics and aligns with modern information-theoretic views of physics. Historically, it marks a shift from geometric to thermodynamic models of spacetime, and offers a bold alternative to particle-based explanations of gravity. Though controversial, it is part of a growing movement to reinterpret gravity in terms of entropy and information. '''Related link:''' [https://en.wikipedia.org/wiki/Erik_Verlinde#Emergent_gravity Emergent Gravity] === '''8.4.5 Big Bang''' === '''Empirical Adequacy''' The Big Bang model is the current standard cosmological paradigm and is strongly supported by multiple independent observations. These include the cosmic microwave background (CMB) radiation, the large-scale structure of the universe, the observed expansion of space (via redshift-distance relations), and the relative abundances of light elements (hydrogen, helium, deuterium, lithium), as predicted by Big Bang Nucleosynthesis (BBN). These confirmations make the Big Bang model one of the most empirically supported frameworks in cosmology. However, the model does not explain the origin of the singularity itself, and extensions such as inflation or dark energy are required to match detailed observations. '''Internal Consistency''' The Big Bang framework is based on solutions to Einstein's field equations (Friedmann–Lemaître–Robertson–Walker metrics), and it is mathematically consistent within the assumptions of general relativity and homogeneity/isotropy (the cosmological principle). However, the initial singularity remains a theoretical boundary where the equations break down, and the model does not include a quantum gravity regime. Extensions such as inflation and ΛCDM are necessary for consistency with observations, but these introduce additional assumptions and parameters, sometimes criticized as fine-tuning. '''Predictive Power''' The Big Bang model has made several successful predictions: the existence and spectrum of the CMB, the large-scale structure of galaxies, and the relative abundances of primordial elements. It also correctly anticipated the cooling of the universe and the redshift–distance relation. Inflationary extensions explain the flatness and horizon problems and predict the nearly scale-invariant spectrum of CMB fluctuations. While many predictions are retrodictive and interpreted within a flexible framework, the model continues to be highly predictive in key areas of cosmology. '''Cross-Disciplinary Compatibility''' The Big Bang model integrates with nuclear physics (BBN), atomic physics (recombination), and high-energy physics (inflation, particle freeze-out). It is broadly compatible with the Standard Model of particle physics and many theories of fundamental interactions. However, it lacks a connection to quantum gravity, and some tensions remain—such as the Hubble tension between early and late universe measurements—that challenge cross-scale consistency. '''Conceptual Clarity and Simplicity''' The core idea—a hot, dense early universe that expands and cools over time—is conceptually clear and widely accepted. However, the full ΛCDM model includes inflation, cold dark matter, and dark energy, which are not directly observable and require complex assumptions. These components reduce the model's simplicity and raise questions about the explanatory depth of the framework. '''Heuristic Value''' The Big Bang theory has driven vast developments in cosmology, observational astronomy, particle physics, and astrophysical instrumentation. It has generated decades of research questions and missions, including COBE, WMAP, and Planck. The inflationary paradigm and dark energy studies have emerged directly from this model. As a heuristic framework, it has proven extremely fertile. '''Historical and Philosophical Insight''' The Big Bang marks a major conceptual shift in cosmology by proposing that the universe has a temporal origin and evolves over time. It displaced steady-state and eternal models of the cosmos and opened up philosophical inquiries about creation, the arrow of time, and the origin of physical laws. Despite its name, it is not an explosion in space but the expansion of space itself—a concept that has reshaped how we understand time, causality, and the structure of the universe. '''Related link:''' [https://en.wikipedia.org/wiki/Big_Bang Big Bang] === '''8.4.6 Steady State Theory''' === '''Empirical Adequacy''' The Steady State Theory, developed in the late 1940s by Bondi, Gold, and Hoyle, posits that the universe has no beginning or end in time and remains statistically the same on large scales, with matter continuously created to maintain constant density despite cosmic expansion. Initially, it matched observations of redshift and expansion, but it was ultimately undermined by key empirical discoveries: the cosmic microwave background (CMB), the evolution of radio source counts, and the observation of distant galaxies at earlier stages of development. These findings provided strong evidence of a hot, dense early universe, inconsistent with the steady state hypothesis. As a result, its empirical adequacy is now considered low. '''Internal Consistency''' The theory is internally consistent in its classical formulation and relies on continuous creation of matter to maintain a constant density. However, this matter creation mechanism was never supported by a detailed physical model or empirical detection. While mathematically coherent, the theory’s assumption of continuous creation violates energy conservation as understood in standard physics, making the underlying physics speculative and theoretically weak. '''Predictive Power''' The Steady State model made a bold prediction: the universe should appear the same at all times and places when viewed on large scales. While this was a clear and testable prediction, it was eventually falsified by observations such as the CMB and the evolution of quasars and galaxy populations over time. The theory’s few predictions have largely been refuted, limiting its scientific utility. '''Cross-Disciplinary Compatibility''' The model is only weakly connected to other scientific domains. It does not integrate well with nuclear physics, as it lacks a mechanism for element formation similar to Big Bang Nucleosynthesis. It also lacks compatibility with high-energy particle physics and modern theories of gravity. The continuous matter creation postulate has no foundation in quantum theory or experimental physics. '''Conceptual Clarity and Simplicity''' The steady-state model is conceptually simple and elegant. Its appeal lay in its ability to preserve a universe without origin, circumventing the philosophical and theological questions raised by a cosmic beginning. The model also maintains a uniform, eternal cosmos, which was attractive to many physicists in the mid-20th century. Despite being falsified, it remains a conceptually clear alternative that helped clarify the implications of observational cosmology. '''Heuristic Value''' Although it is no longer a viable cosmological model, the Steady State theory played a significant heuristic role. It prompted debates about the nature of time, observational testing, and the falsifiability of cosmological models. It helped shape the methodological standards for modern cosmology by being a well-defined, testable theory that was ultimately rejected based on empirical data. Its legacy lives on in discussions about the role of testability and philosophical assumptions in science. '''Historical and Philosophical Insight''' The Steady State theory was historically important as the main rival to the Big Bang model in the early post-war period. It reflects a philosophical preference for temporal infinity and equilibrium conditions, standing in contrast to a universe with a beginning. Its eventual rejection illustrates the triumph of observation over philosophical elegance in modern cosmology. It also served as a case study in the philosophy of science, particularly regarding Popperian falsifiability and the evolution of scientific consensus. '''Related link:''' [https://en.wikipedia.org/wiki/Steady_state_model Steady State Theory] === '''8.4.7 Big Crunch''' === '''Empirical Adequacy''' The Big Crunch is not a theory of gravity or cosmology by itself but rather a hypothetical end-state of the universe within certain cosmological models. It posits that cosmic expansion could eventually reverse, causing the universe to contract back into a high-density singularity. This scenario arises from general relativity under the assumption of a closed universe with sufficient matter density to overcome expansion. However, current observational data strongly indicate that the universe is accelerating in its expansion, driven by dark energy. Measurements of the cosmic microwave background (CMB), supernova distances, and large-scale structure all support a flat or open universe with low matter density, making the Big Crunch scenario empirically disfavored at present. '''Internal Consistency''' Within general relativity and standard cosmological models, the Big Crunch is internally consistent. It naturally arises from the Friedmann equations when the density parameter Ω > 1 and the cosmological constant is absent or negative. The dynamics of contraction mirror those of expansion in reverse, and no logical contradictions emerge in its mathematical formulation. However, near the final singularity, quantum gravitational effects become important, and the classical equations break down. '''Predictive Power''' As a hypothetical scenario, the Big Crunch does not offer specific predictive claims under current physical conditions. Instead, it represents a conditional outcome: if the universe were closed and dominated by matter, it would eventually recollapse. Since observations show otherwise, the predictive relevance of the Big Crunch is now limited. Nevertheless, it played a role in exploring time-reversal symmetry, thermodynamic limits, and quantum cosmology. '''Cross-Disciplinary Compatibility''' The Big Crunch scenario is compatible with general relativity and classical thermodynamics, especially in discussions of entropy and the arrow of time. It has also been explored in speculative models of cyclic or oscillating universes, which relate to quantum gravity and string theory. However, it lacks strong support from empirical fields such as observational cosmology, particle physics, or astronomy under the current ΛCDM framework. '''Conceptual Clarity and Simplicity''' The concept is straightforward: the universe's expansion halts and reverses into a collapse. This time-symmetric model is intuitively appealing and easy to visualize. However, its physical plausibility is undermined by current evidence for accelerating expansion. Still, as a conceptual tool, it remains a clear contrast to models of eternal expansion or thermal death. '''Heuristic Value''' Historically, the Big Crunch scenario stimulated discussion about cosmological cycles, entropy limits, and the ultimate fate of the universe. It led to the development of cyclic models, bounce cosmologies, and ideas about cosmic rebirth. Although largely ruled out by current data, it retains heuristic value in theoretical cosmology and philosophy of time, particularly in exploring whether time and entropy could reverse. '''Historical and Philosophical Insight''' The Big Crunch offered a philosophically symmetric alternative to the Big Bang—a universe that begins and ends in a singularity. It invites reflection on the reversibility of physical laws, the meaning of cosmic time, and the possibility of eternal recurrence. While empirical support is lacking, the scenario remains a historically meaningful part of cosmological thinking, especially in the 20th-century debates about the universe's fate. === '''8.4.8 Big Bounce''' === '''Empirical Adequacy''' The Big Bounce is a speculative cosmological scenario in which the universe undergoes a cycle of contraction followed by a rebound (or "bounce") into a new phase of expansion. It aims to replace the initial singularity of the Big Bang with a transitional phase where quantum gravitational effects prevent infinite density. While the concept is consistent with certain theoretical models—particularly in loop quantum cosmology—there is currently no direct observational evidence for a bounce event. The cosmic microwave background (CMB) does not yet show unambiguous signatures that would favor a bounce over inflationary models. Thus, empirical adequacy remains hypothetical, though not excluded. '''Internal Consistency''' The Big Bounce can be formulated consistently within several frameworks, such as loop quantum gravity, string gas cosmology, or modified gravity models. In these settings, quantum corrections to the Friedmann equations or modifications to the geometry of spacetime prevent a singularity and allow for a smooth transition from contraction to expansion. However, different bounce models vary in their assumptions, and the full quantum dynamics are not yet universally agreed upon. Despite these uncertainties, the internal logic of the models is coherent within their theoretical boundaries. '''Predictive Power''' Some Big Bounce models predict subtle features in the CMB, such as suppressed power at large angular scales, or non-Gaussianities that differ from inflation. However, these predictions often overlap with or are degenerate with inflationary predictions, making them hard to test uniquely. No conclusive observational support has been found so far. Nevertheless, bounce models offer a predictive framework that could, in principle, be tested with improved cosmological data in the future. '''Cross-Disciplinary Compatibility''' The Big Bounce scenario is motivated by attempts to unify quantum mechanics and gravity. It connects well with developments in loop quantum cosmology, non-singular black hole models, and string theory. However, it is less developed in its links to particle physics, standard cosmology, or astrophysical observations. Its broader scientific compatibility depends heavily on which theoretical approach is adopted and how it interfaces with known physics. '''Conceptual Clarity and Simplicity''' The idea of a contracting universe rebounding into expansion is conceptually intuitive and avoids the metaphysical implications of a beginning-of-time singularity. In contrast to the Big Bang singularity, the bounce implies a cyclic or oscillatory universe that is eternal in time. While appealing in its symmetry, the underlying physics is often highly technical and abstract, involving non-perturbative quantum gravity, which reduces its practical simplicity. '''Heuristic Value''' The Big Bounce has stimulated important discussions in cosmology, particularly regarding singularity avoidance, pre-Big Bang scenarios, and the nature of time. It has inspired a class of alternative models to inflation and opened up debates about the cyclical nature of the universe. Its challenge to the standard narrative of cosmic origins has heuristic value in motivating new lines of theoretical research. '''Historical and Philosophical Insight''' The Big Bounce continues a long tradition of cyclical universe models, echoing ideas from ancient cosmologies and early 20th-century oscillating universe theories. Philosophically, it provides a framework in which the universe has no absolute beginning or end, and where time and entropy may operate in a larger looped framework. It offers a more balanced cosmological picture than the irreversible expansion or final collapse scenarios. Though not yet supported by data, its philosophical implications remain profound and open-ended. === '''8.4.9 Cosmic Influx Theory (CIT)''' === Cosmic Influx Theory (CIT), proposed by Ruud Loeffen, reinterprets gravity as a directional energy influx driven by Primordial Elementary Whirlings (PEWs), replacing the concept of attractive force or space-time curvature. It introduces a constant influx of mass-energy into all bodies, contributing to planetary expansion, star formation, and cosmological evolution. 1. '''Internal Consistency''' CIT presents a coherent internal logic based on a unidirectional influx mechanism, a redefined gravitational constant (G = (γ − 1)/4π), and the introduction of κ_CIT as a universal scaling constant. While the framework remains internally consistent, some equations are still under refinement and lack full derivations from first principles. 2. '''Predictive Power''' CIT predicts the Preferred Distance for giant planets based on κ_CIT, orbital periods of exoplanets, and a revised Hubble constant (Ho ≈ 67.8 km/s/Mpc). It also anticipates planetary expansion through mass influx. These predictions are testable, though many remain pending observational confirmation. 3. '''Falsifiability''' Several predictions—such as giant planets at D_pref in the Trappist system or mass accumulation rates inferred from planetary geology—can be tested. However, the influx mechanism itself is not yet described in terms of directly measurable particles or interactions, which may limit falsifiability at the quantum level. 4. '''Observational Alignment''' CIT aligns with various observations: early formation of giant planets in protoplanetary disks, planetary expansion signatures, surface geology of moons and Mars, and recent JWST disk structures. It also claims to naturally derive the observed Hubble constant without tension. 5. '''Philosophical Transparency''' The theory clearly departs from Newtonian and relativistic interpretations, positioning itself as an ontological alternative grounded in energy flow. The author's motivations, limitations, and intended scope are transparently communicated in both academic and public forums. 6. '''Empirical Adequacy''' CIT offers empirical parallels in planetary spacing (κ_CIT), daylength extension over geological time, and disk fragmentation patterns. However, it currently lacks publication in high-impact peer-reviewed journals and formal statistical validation across broad datasets. 7. '''Institutional Support and Development''' CIT is developed independently, primarily through Wikiversity and open-access platforms. While it incorporates extensive cross-referencing and engages with mainstream and alternative sources, it lacks institutional affiliation and academic endorsement at this stage. '''Related link:''' [[Cosmic Influx Theory]] === '''8.4.10 Summary of Spiral Cosmology''' === The Pearlman Cosmology (SPIRAL Cosmology) offers a deterministic model of the universe with a defined hyper-dense initial state, fixed radius growth, and a reinterpretation of redshift. It integrates biblical chronology into its cosmological assumptions, making it a unique hybrid of scientific and scriptural reasoning. 1. '''Internal Consistency''' The model presents a logically consistent internal framework, with clearly defined initial conditions such as the SPIRAL radius, gravitational equilibrium, and fixed cosmic time scaling. Its components align well within its own assumptions. 2. '''Predictive Power''' Pearlman Cosmology proposes several potentially testable hypotheses, such as a fixed annual rate of universal expansion and an alternative explanation of redshift. However, these are not yet accompanied by detailed numeric predictions or simulations. 3. '''Falsifiability''' Testable elements exist in the form of reinterpretations of the cosmic microwave background origin, early galaxy formation, and redshift asymmetries. Yet aspects based on Mosaic chronology may fall outside strict scientific falsifiability. 4. '''Observational Alignment''' The model qualitatively aligns with some recent JWST observations, including early structure formation and CMB uniformity. Nevertheless, it lacks robust quantitative matching with large datasets or predictive modeling. 5. '''Philosophical Transparency''' The theory is open about its use of religious chronology and framing. This transparency makes its worldview explicit, though it may hinder its acceptance within mainstream secular science. 6. '''Empirical Adequacy''' While some empirical parallels exist, the theory has not yet been tested against a wide body of observational data in a systematic or peer-reviewed way. 7. '''Institutional Support and Development''' Pearlman Cosmology remains outside institutional research frameworks. Its development and publication history are limited, and it has not yet entered mainstream cosmological discourse. '''Related link:''' [https://www.pearlman.org Pearlman Cosmology] '''◀ [[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 ▶]]''' oqcc7ro006enpx32b0v8smrh7m8oef9 2719991 2719990 2025-06-29T04:38:22Z Ruud Loeffen 2998353 /* 8.4.7 Big Crunch */ add link to this theory 2719991 wikitext text/x-wiki == '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' = == '''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. == '''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 == '''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 such as: Observational Agreement Internal Logical Consistency Predictive Value Compatibility with Other Domains (e.g., geology, biology) Conceptual Coherence and Simplicity Each dimension is rated using a 1–5 star system, based on the information provided and the supporting sources that AI can access. 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. == '''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. == '''8.1 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. '''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. '''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. '''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. '''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. '''5. Conceptual Clarity and Simplicity''' Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification. '''6. Heuristic Value''' Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential. '''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. 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 or can be requested in more detail. == '''8.2 AI Evaluation Table Format''' == {| class="wikitable" |+ '''AI Evaluation Table of Cosmological Theories''' ! Theory Name ! Empirical Adequacy ! Internal Consistency ! Predictive Power ! Cross-Disciplinary Compatibility ! Conceptual Clarity and Simplicity ! Heuristic Value ! Historical & Philosophical Insight ! Total (★) |- | 8.4.1 '''General Relativity''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★★ || '''34''' |- | colspan="9" | ''Widely confirmed by experiment; mathematical elegance; historical development from Newtonian mechanics'' |- |- | 8.4.2 '''Newtonian Gravity''' | ★★★★☆ || ★★★★★ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''30''' |- | colspan="9" | ''Highly successful in classical mechanics and celestial predictions; lacks compatibility with relativity and quantum theory; historically foundational.'' |- | 8.4.3 '''MOND (Modified Newtonian Dynamics)''' | ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''24''' |- | colspan="9" | ''Strong in galactic rotation curves; limited compatibility with general relativistic frameworks'' |- | 8.4.4 '''Emergent Gravity (Verlinde)''' | ★★☆☆☆ || ★★★★☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''25''' |- | colspan="9" | ''Innovative reformulation; still awaiting broad empirical confirmation'' |- | 8.4.5 '''Big Bang Model''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''31''' |- | colspan="9" | ''Core cosmological model; supported by CMB, redshift, nucleosynthesis'' |- | 8.4.6 '''Steady State Theory''' | ★☆☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''23''' |- | colspan="9" | ''Historically important; largely superseded due to lack of CMB explanation'' |- | 8.4.7 '''Big Crunch Theory''' | ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || '''28''' |- | colspan="9" | ''Predicts final collapse of universe; consistent with GR in high-density scenarios; revived interest due to dark energy variability'' |- | 8.4.8 '''Big Bounce Theory''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''26''' |- | colspan="9" | ''Cyclical alternative to singularity; compatible with some quantum gravity models'' |- | 8.4.9 '''Cosmic Influx Theory (CIT)''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★★★★ || ★★★★☆ || '''26''' |- | colspan="9" | ''Offers cross-disciplinary compatibility; predicts mass growth and preferred orbital distances; alternative influx model under development'' |- | 8.4.10 '''SPIRAL Cosmology''' | ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22''' |- | colspan="9" | ''Proposes a hyper-dense proto-galactic phase preceding expansion; no need for ongoing dark energy or cosmic expansion; partially scriptural framing may limit falsifiability but testable claims (e.g. fixed-radius light departure) justify scientific review.'' |- | colspan="9" | ''Well-formulated alternative integrating orbital quantization; some empirical fit to planetary data; lacks full mainstream acceptance'' |} <!-- Add a blank line here --> == '''8.3 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]]'''. == '''8.4 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. === '''8.4.1 General Relativity'''=== '''Empirical Adequacy''' General Relativity (GR) is one of the most empirically validated theories in physics. It has successfully explained and predicted a wide range of gravitational phenomena, including the precession of Mercury’s perihelion, gravitational lensing of starlight, gravitational redshift, time dilation effects observed in satellite systems like GPS, and the Shapiro delay. More recently, its predictions have been confirmed by gravitational wave observations (LIGO/Virgo) and direct imaging of black holes (Event Horizon Telescope). The agreement between theory and measurement is often better than 0.01%, demonstrating exceptional empirical adequacy. '''Internal Consistency''' GR is internally consistent within its mathematical framework. It is based on the Einstein field equations, which are derived from well-defined variational principles and respect general covariance. The logical structure of the theory is rigorous, with clearly formulated assumptions such as the equivalence principle and the conservation of energy–momentum through the stress-energy tensor. There are no known internal contradictions. '''Predictive Power''' GR has a powerful record of making novel predictions that were later confirmed by experiment or observation. These include the bending of light by massive bodies, time dilation in gravitational fields, the expansion of the universe (through its application in cosmology), and the existence of gravitational waves. Its predictions have often preceded direct detection by decades. This makes GR a model example of a theory with high predictive power. '''Cross-Disciplinary Compatibility''' General Relativity is compatible with many areas of physics, including classical mechanics, electrodynamics, and astrophysics. However, it is not yet unified with quantum mechanics. Attempts to reconcile GR with the Standard Model—such as quantum gravity, string theory, or loop quantum gravity—remain incomplete. Thus, GR scores slightly lower here due to its current incompatibility with modern particle physics at the Planck scale. '''Conceptual Clarity and Simplicity''' The core idea of GR—that gravity is not a force but a geometric property of spacetime—is conceptually elegant. However, the mathematical formalism (involving tensor calculus and differential geometry) is complex and often inaccessible to non-specialists. While the theory offers deep conceptual clarity, its practical simplicity is limited by the required mathematical tools. '''Heuristic Value''' GR has inspired generations of physicists and remains a fertile ground for theoretical development. It has opened up entire fields such as relativistic astrophysics, cosmology, and gravitational wave astronomy. Its influence extends beyond physics into philosophy and the public imagination. It continues to motivate research on black holes, time travel, singularities, and the early universe. '''Historical and Philosophical Insight''' Historically, GR represents a revolutionary shift in physics, displacing the Newtonian notion of absolute space and time with a dynamic, curved spacetime model. Philosophically, it challenges classical intuitions about gravity and causality and has inspired reevaluation of concepts such as simultaneity, locality, and determinism. Its legacy places it among the most profound achievements in scientific history. '''Related link:''' [https://en.wikipedia.org/wiki/General_relativity General Relativity] === '''8.4.2 Newtonian Gravity''' === '''Empirical Adequacy''' Newtonian gravity has historically achieved remarkable empirical success. It accurately describes planetary motions, tidal forces, ballistic trajectories, and satellite orbits. For centuries, it provided the dominant framework for celestial mechanics and was sufficient for navigation, astronomy, and engineering. However, it begins to fail in extreme gravitational fields or at very high speeds, where relativistic corrections are needed. It also cannot explain phenomena like the precession of Mercury’s orbit, gravitational time dilation, or the bending of light. '''Internal Consistency''' Within its classical framework, Newtonian gravity is highly consistent. It is based on clear axioms such as the inverse-square law and absolute space and time. The mathematical structure is well-defined and solvable using Newton’s laws of motion and calculus. No logical contradictions arise within its scope of applicability. However, its assumptions about instantaneous action at a distance are problematic under modern physical understanding. '''Predictive Power''' Newtonian gravity has strong predictive power in low-speed, weak-field regimes. It successfully predicted the return of Halley’s Comet, the existence of Neptune, and continues to be used in engineering and orbital calculations. However, it fails to predict relativistic effects such as gravitational lensing, frame-dragging, or gravitational waves. These limitations reduce its predictive power on cosmic and high-precision scales. '''Cross-Disciplinary Compatibility''' Newton’s theory aligns well with classical physics and early chemistry but lacks compatibility with modern disciplines. It cannot be reconciled with special relativity or quantum theory and does not incorporate energy–momentum considerations as in modern field theories. Its incompatibility with relativity limits its integration with high-energy physics and astrophysics. '''Conceptual Clarity and Simplicity''' Newtonian gravity is conceptually simple and intuitively accessible. The inverse-square force law is easy to visualize and apply. It does not require advanced mathematics and remains an ideal teaching model. Its clarity and ease of computation give it enduring educational and practical value. '''Heuristic Value''' Although no longer a frontier theory, Newtonian gravity laid the groundwork for classical mechanics and much of modern science. It helped shape ideas about force, motion, and planetary systems. While it no longer drives active theoretical innovation, it retains historical heuristic importance. '''Historical and Philosophical Insight''' Newton’s theory was revolutionary in unifying terrestrial and celestial phenomena under the same laws of motion. It established the idea of a universal physical law and set the standard for quantitative science. Philosophically, it introduced mechanistic determinism and absolute space and time—concepts that dominated Enlightenment science. Though now superseded, its legacy remains foundational. '''Related link:''' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newtonian Gravity] === '''8.4.3 MOND (Modified Newtonian Dynamics)''' === '''Empirical Adequacy''' MOND was proposed by Mordehai Milgrom in the early 1980s to explain galactic rotation curves without invoking dark matter. It has successfully reproduced the flat rotation profiles of spiral galaxies and the observed baryonic Tully–Fisher relation with remarkable precision. MOND fits individual galaxy data with fewer parameters than dark matter models. However, it struggles with galaxy cluster dynamics, cosmological structure formation, and gravitational lensing in some systems. Its empirical adequacy is high for galactic scales but limited beyond that domain. '''Internal Consistency''' MOND is mathematically consistent in its non-relativistic form, where it modifies Newton’s second law at low accelerations using a new constant 𝑎 0 a 0 ​ . However, its original formulation lacks a full theoretical derivation from first principles and requires ad hoc modifications to the force law. Several relativistic extensions (e.g. TeVeS, AQUAL, BIMOND) have been developed to improve consistency, but these are not uniquely favored and remain complex or underconstrained. '''Predictive Power''' MOND has had considerable predictive success in galactic astrophysics. It predicted the baryonic Tully–Fisher relation before it was observationally confirmed, and it can reproduce detailed features of galaxy rotation curves without needing dark matter halos. However, it lacks explanatory power for phenomena like the cosmic microwave background (CMB) anisotropies, gravitational lensing in galaxy clusters (e.g. Bullet Cluster), and large-scale structure. Its predictive power is strong in its target domain but limited on cosmological scales. '''Cross-Disciplinary Compatibility''' MOND is primarily focused on galactic dynamics and does not integrate smoothly with high-energy physics, quantum theory, or cosmology. Its extensions to cosmology often require additional assumptions, and it is not yet compatible with standard particle physics. As a result, its cross-disciplinary reach is modest, though ongoing efforts aim to embed it within broader frameworks. '''Conceptual Clarity and Simplicity''' In its original form, MOND is simple: the gravitational acceleration deviates from Newton’s law when below a critical threshold 𝑎 0 a 0 ​ . This modification is intuitive and computationally effective for galaxies. However, attempts to embed MOND in a relativistic framework often add complexity, reducing its conceptual transparency. '''Heuristic Value''' MOND has had significant heuristic impact by highlighting regularities in galactic dynamics that are hard to explain under the ΛCDM paradigm without fine-tuned dark matter profiles. It has sparked debate, inspired hybrid theories (e.g. dark matter superfluidity), and contributed to reevaluating gravitational theory. Its challenge to mainstream cosmology has been fruitful, even if not universally accepted. '''Historical and Philosophical Insight''' MOND revives the idea that gravity itself may need modification, rather than positing unseen matter. This philosophical approach echoes the history of science, where anomalies sometimes led to revisions of theory rather than new entities. MOND also raises deep questions about the nature of inertia, scale invariance, and universal laws—making it a philosophically provocative proposal despite its contested status. '''Related link:''' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics MOND (Modified Newtonian Dynamics)] === '''8.4.4 Emergent Gravity''' === '''Empirical Adequacy''' Emergent Gravity, proposed by Erik Verlinde in 2011 and expanded in 2016, seeks to explain gravitational phenomena as an emergent effect of underlying entropic and holographic principles rather than a fundamental force. It claims to reproduce galactic rotation curves without invoking dark matter by relating gravity to the thermodynamics of microscopic information storage on holographic screens. The theory can qualitatively explain certain galactic dynamics, such as the radial acceleration relation (RAR), but lacks the quantitative precision and scope of MOND in galaxy rotation curve fitting. It also currently cannot reproduce the full spectrum of cosmological observations, including the CMB power spectrum or gravitational lensing in galaxy clusters, where standard ΛCDM performs better. '''Internal Consistency''' Emergent Gravity draws from concepts in string theory, quantum information theory, and thermodynamics. While intellectually coherent and grounded in cutting-edge theoretical frameworks, the theory is still under development and lacks a universally accepted formalism. Key quantities (such as entropic force or the elastic response of spacetime) are not always rigorously defined, and derivations sometimes rely on analogies rather than strict derivations. This limits the formal internal consistency at present, though the conceptual framework remains promising. '''Predictive Power''' The theory makes some novel qualitative predictions, particularly regarding the relation between baryonic mass and gravitational acceleration without dark matter. It reproduces the RAR and may provide an explanation for dark energy as an entropic effect of spacetime. However, Emergent Gravity has not yet made precise predictions for cosmological parameters, gravitational wave behavior, or galaxy cluster dynamics that can be tested independently of standard models. Its predictive power remains speculative and qualitative. '''Cross-Disciplinary Compatibility''' Emergent Gravity attempts to bridge gravity, quantum information, and thermodynamics, making it conceptually rich in cross-disciplinary connections. It resonates with holography, the AdS/CFT correspondence, and black hole thermodynamics. However, the lack of experimental or observational confirmation limits its integration with empirical domains such as astrophysics, cosmology, and particle physics. Its compatibility is more theoretical than empirical at this stage. '''Conceptual Clarity and Simplicity''' The idea that gravity is not fundamental but emerges from statistical behavior of microscopic degrees of freedom is intellectually elegant. However, the actual implementation of this idea in the current models is technically complex and often abstract. Unlike Newtonian gravity or even MOND, the mechanisms proposed by Emergent Gravity are difficult to visualize or test directly, and involve high-level concepts from thermodynamics and information theory. '''Heuristic Value''' Emergent Gravity is highly heuristic. It opens new perspectives on the nature of gravity, spacetime, and entropy. By reframing gravity as an emergent entropic force, it challenges the foundations of both classical and relativistic theories. It has influenced discussions around the holographic principle, black hole entropy, and spacetime microstructure. Even if it remains incomplete, it contributes to rethinking gravity from first principles. '''Historical and Philosophical Insight''' Philosophically, Emergent Gravity aligns with the long-standing idea that some phenomena in nature arise from deeper, statistical processes rather than being fundamental. It recalls Boltzmann’s approach to thermodynamics and aligns with modern information-theoretic views of physics. Historically, it marks a shift from geometric to thermodynamic models of spacetime, and offers a bold alternative to particle-based explanations of gravity. Though controversial, it is part of a growing movement to reinterpret gravity in terms of entropy and information. '''Related link:''' [https://en.wikipedia.org/wiki/Erik_Verlinde#Emergent_gravity Emergent Gravity] === '''8.4.5 Big Bang''' === '''Empirical Adequacy''' The Big Bang model is the current standard cosmological paradigm and is strongly supported by multiple independent observations. These include the cosmic microwave background (CMB) radiation, the large-scale structure of the universe, the observed expansion of space (via redshift-distance relations), and the relative abundances of light elements (hydrogen, helium, deuterium, lithium), as predicted by Big Bang Nucleosynthesis (BBN). These confirmations make the Big Bang model one of the most empirically supported frameworks in cosmology. However, the model does not explain the origin of the singularity itself, and extensions such as inflation or dark energy are required to match detailed observations. '''Internal Consistency''' The Big Bang framework is based on solutions to Einstein's field equations (Friedmann–Lemaître–Robertson–Walker metrics), and it is mathematically consistent within the assumptions of general relativity and homogeneity/isotropy (the cosmological principle). However, the initial singularity remains a theoretical boundary where the equations break down, and the model does not include a quantum gravity regime. Extensions such as inflation and ΛCDM are necessary for consistency with observations, but these introduce additional assumptions and parameters, sometimes criticized as fine-tuning. '''Predictive Power''' The Big Bang model has made several successful predictions: the existence and spectrum of the CMB, the large-scale structure of galaxies, and the relative abundances of primordial elements. It also correctly anticipated the cooling of the universe and the redshift–distance relation. Inflationary extensions explain the flatness and horizon problems and predict the nearly scale-invariant spectrum of CMB fluctuations. While many predictions are retrodictive and interpreted within a flexible framework, the model continues to be highly predictive in key areas of cosmology. '''Cross-Disciplinary Compatibility''' The Big Bang model integrates with nuclear physics (BBN), atomic physics (recombination), and high-energy physics (inflation, particle freeze-out). It is broadly compatible with the Standard Model of particle physics and many theories of fundamental interactions. However, it lacks a connection to quantum gravity, and some tensions remain—such as the Hubble tension between early and late universe measurements—that challenge cross-scale consistency. '''Conceptual Clarity and Simplicity''' The core idea—a hot, dense early universe that expands and cools over time—is conceptually clear and widely accepted. However, the full ΛCDM model includes inflation, cold dark matter, and dark energy, which are not directly observable and require complex assumptions. These components reduce the model's simplicity and raise questions about the explanatory depth of the framework. '''Heuristic Value''' The Big Bang theory has driven vast developments in cosmology, observational astronomy, particle physics, and astrophysical instrumentation. It has generated decades of research questions and missions, including COBE, WMAP, and Planck. The inflationary paradigm and dark energy studies have emerged directly from this model. As a heuristic framework, it has proven extremely fertile. '''Historical and Philosophical Insight''' The Big Bang marks a major conceptual shift in cosmology by proposing that the universe has a temporal origin and evolves over time. It displaced steady-state and eternal models of the cosmos and opened up philosophical inquiries about creation, the arrow of time, and the origin of physical laws. Despite its name, it is not an explosion in space but the expansion of space itself—a concept that has reshaped how we understand time, causality, and the structure of the universe. '''Related link:''' [https://en.wikipedia.org/wiki/Big_Bang Big Bang] === '''8.4.6 Steady State Theory''' === '''Empirical Adequacy''' The Steady State Theory, developed in the late 1940s by Bondi, Gold, and Hoyle, posits that the universe has no beginning or end in time and remains statistically the same on large scales, with matter continuously created to maintain constant density despite cosmic expansion. Initially, it matched observations of redshift and expansion, but it was ultimately undermined by key empirical discoveries: the cosmic microwave background (CMB), the evolution of radio source counts, and the observation of distant galaxies at earlier stages of development. These findings provided strong evidence of a hot, dense early universe, inconsistent with the steady state hypothesis. As a result, its empirical adequacy is now considered low. '''Internal Consistency''' The theory is internally consistent in its classical formulation and relies on continuous creation of matter to maintain a constant density. However, this matter creation mechanism was never supported by a detailed physical model or empirical detection. While mathematically coherent, the theory’s assumption of continuous creation violates energy conservation as understood in standard physics, making the underlying physics speculative and theoretically weak. '''Predictive Power''' The Steady State model made a bold prediction: the universe should appear the same at all times and places when viewed on large scales. While this was a clear and testable prediction, it was eventually falsified by observations such as the CMB and the evolution of quasars and galaxy populations over time. The theory’s few predictions have largely been refuted, limiting its scientific utility. '''Cross-Disciplinary Compatibility''' The model is only weakly connected to other scientific domains. It does not integrate well with nuclear physics, as it lacks a mechanism for element formation similar to Big Bang Nucleosynthesis. It also lacks compatibility with high-energy particle physics and modern theories of gravity. The continuous matter creation postulate has no foundation in quantum theory or experimental physics. '''Conceptual Clarity and Simplicity''' The steady-state model is conceptually simple and elegant. Its appeal lay in its ability to preserve a universe without origin, circumventing the philosophical and theological questions raised by a cosmic beginning. The model also maintains a uniform, eternal cosmos, which was attractive to many physicists in the mid-20th century. Despite being falsified, it remains a conceptually clear alternative that helped clarify the implications of observational cosmology. '''Heuristic Value''' Although it is no longer a viable cosmological model, the Steady State theory played a significant heuristic role. It prompted debates about the nature of time, observational testing, and the falsifiability of cosmological models. It helped shape the methodological standards for modern cosmology by being a well-defined, testable theory that was ultimately rejected based on empirical data. Its legacy lives on in discussions about the role of testability and philosophical assumptions in science. '''Historical and Philosophical Insight''' The Steady State theory was historically important as the main rival to the Big Bang model in the early post-war period. It reflects a philosophical preference for temporal infinity and equilibrium conditions, standing in contrast to a universe with a beginning. Its eventual rejection illustrates the triumph of observation over philosophical elegance in modern cosmology. It also served as a case study in the philosophy of science, particularly regarding Popperian falsifiability and the evolution of scientific consensus. '''Related link:''' [https://en.wikipedia.org/wiki/Steady_state_model Steady State Theory] === '''8.4.7 Big Crunch''' === '''Empirical Adequacy''' The Big Crunch is not a theory of gravity or cosmology by itself but rather a hypothetical end-state of the universe within certain cosmological models. It posits that cosmic expansion could eventually reverse, causing the universe to contract back into a high-density singularity. This scenario arises from general relativity under the assumption of a closed universe with sufficient matter density to overcome expansion. However, current observational data strongly indicate that the universe is accelerating in its expansion, driven by dark energy. Measurements of the cosmic microwave background (CMB), supernova distances, and large-scale structure all support a flat or open universe with low matter density, making the Big Crunch scenario empirically disfavored at present. '''Internal Consistency''' Within general relativity and standard cosmological models, the Big Crunch is internally consistent. It naturally arises from the Friedmann equations when the density parameter Ω > 1 and the cosmological constant is absent or negative. The dynamics of contraction mirror those of expansion in reverse, and no logical contradictions emerge in its mathematical formulation. However, near the final singularity, quantum gravitational effects become important, and the classical equations break down. '''Predictive Power''' As a hypothetical scenario, the Big Crunch does not offer specific predictive claims under current physical conditions. Instead, it represents a conditional outcome: if the universe were closed and dominated by matter, it would eventually recollapse. Since observations show otherwise, the predictive relevance of the Big Crunch is now limited. Nevertheless, it played a role in exploring time-reversal symmetry, thermodynamic limits, and quantum cosmology. '''Cross-Disciplinary Compatibility''' The Big Crunch scenario is compatible with general relativity and classical thermodynamics, especially in discussions of entropy and the arrow of time. It has also been explored in speculative models of cyclic or oscillating universes, which relate to quantum gravity and string theory. However, it lacks strong support from empirical fields such as observational cosmology, particle physics, or astronomy under the current ΛCDM framework. '''Conceptual Clarity and Simplicity''' The concept is straightforward: the universe's expansion halts and reverses into a collapse. This time-symmetric model is intuitively appealing and easy to visualize. However, its physical plausibility is undermined by current evidence for accelerating expansion. Still, as a conceptual tool, it remains a clear contrast to models of eternal expansion or thermal death. '''Heuristic Value''' Historically, the Big Crunch scenario stimulated discussion about cosmological cycles, entropy limits, and the ultimate fate of the universe. It led to the development of cyclic models, bounce cosmologies, and ideas about cosmic rebirth. Although largely ruled out by current data, it retains heuristic value in theoretical cosmology and philosophy of time, particularly in exploring whether time and entropy could reverse. '''Historical and Philosophical Insight''' The Big Crunch offered a philosophically symmetric alternative to the Big Bang—a universe that begins and ends in a singularity. It invites reflection on the reversibility of physical laws, the meaning of cosmic time, and the possibility of eternal recurrence. While empirical support is lacking, the scenario remains a historically meaningful part of cosmological thinking, especially in the 20th-century debates about the universe's fate. '''Related link:''' [https://en.wikipedia.org/wiki/Big_Crunch Big Crunch] === '''8.4.8 Big Bounce''' === '''Empirical Adequacy''' The Big Bounce is a speculative cosmological scenario in which the universe undergoes a cycle of contraction followed by a rebound (or "bounce") into a new phase of expansion. It aims to replace the initial singularity of the Big Bang with a transitional phase where quantum gravitational effects prevent infinite density. While the concept is consistent with certain theoretical models—particularly in loop quantum cosmology—there is currently no direct observational evidence for a bounce event. The cosmic microwave background (CMB) does not yet show unambiguous signatures that would favor a bounce over inflationary models. Thus, empirical adequacy remains hypothetical, though not excluded. '''Internal Consistency''' The Big Bounce can be formulated consistently within several frameworks, such as loop quantum gravity, string gas cosmology, or modified gravity models. In these settings, quantum corrections to the Friedmann equations or modifications to the geometry of spacetime prevent a singularity and allow for a smooth transition from contraction to expansion. However, different bounce models vary in their assumptions, and the full quantum dynamics are not yet universally agreed upon. Despite these uncertainties, the internal logic of the models is coherent within their theoretical boundaries. '''Predictive Power''' Some Big Bounce models predict subtle features in the CMB, such as suppressed power at large angular scales, or non-Gaussianities that differ from inflation. However, these predictions often overlap with or are degenerate with inflationary predictions, making them hard to test uniquely. No conclusive observational support has been found so far. Nevertheless, bounce models offer a predictive framework that could, in principle, be tested with improved cosmological data in the future. '''Cross-Disciplinary Compatibility''' The Big Bounce scenario is motivated by attempts to unify quantum mechanics and gravity. It connects well with developments in loop quantum cosmology, non-singular black hole models, and string theory. However, it is less developed in its links to particle physics, standard cosmology, or astrophysical observations. Its broader scientific compatibility depends heavily on which theoretical approach is adopted and how it interfaces with known physics. '''Conceptual Clarity and Simplicity''' The idea of a contracting universe rebounding into expansion is conceptually intuitive and avoids the metaphysical implications of a beginning-of-time singularity. In contrast to the Big Bang singularity, the bounce implies a cyclic or oscillatory universe that is eternal in time. While appealing in its symmetry, the underlying physics is often highly technical and abstract, involving non-perturbative quantum gravity, which reduces its practical simplicity. '''Heuristic Value''' The Big Bounce has stimulated important discussions in cosmology, particularly regarding singularity avoidance, pre-Big Bang scenarios, and the nature of time. It has inspired a class of alternative models to inflation and opened up debates about the cyclical nature of the universe. Its challenge to the standard narrative of cosmic origins has heuristic value in motivating new lines of theoretical research. '''Historical and Philosophical Insight''' The Big Bounce continues a long tradition of cyclical universe models, echoing ideas from ancient cosmologies and early 20th-century oscillating universe theories. Philosophically, it provides a framework in which the universe has no absolute beginning or end, and where time and entropy may operate in a larger looped framework. It offers a more balanced cosmological picture than the irreversible expansion or final collapse scenarios. Though not yet supported by data, its philosophical implications remain profound and open-ended. === '''8.4.9 Cosmic Influx Theory (CIT)''' === Cosmic Influx Theory (CIT), proposed by Ruud Loeffen, reinterprets gravity as a directional energy influx driven by Primordial Elementary Whirlings (PEWs), replacing the concept of attractive force or space-time curvature. It introduces a constant influx of mass-energy into all bodies, contributing to planetary expansion, star formation, and cosmological evolution. 1. '''Internal Consistency''' CIT presents a coherent internal logic based on a unidirectional influx mechanism, a redefined gravitational constant (G = (γ − 1)/4π), and the introduction of κ_CIT as a universal scaling constant. While the framework remains internally consistent, some equations are still under refinement and lack full derivations from first principles. 2. '''Predictive Power''' CIT predicts the Preferred Distance for giant planets based on κ_CIT, orbital periods of exoplanets, and a revised Hubble constant (Ho ≈ 67.8 km/s/Mpc). It also anticipates planetary expansion through mass influx. These predictions are testable, though many remain pending observational confirmation. 3. '''Falsifiability''' Several predictions—such as giant planets at D_pref in the Trappist system or mass accumulation rates inferred from planetary geology—can be tested. However, the influx mechanism itself is not yet described in terms of directly measurable particles or interactions, which may limit falsifiability at the quantum level. 4. '''Observational Alignment''' CIT aligns with various observations: early formation of giant planets in protoplanetary disks, planetary expansion signatures, surface geology of moons and Mars, and recent JWST disk structures. It also claims to naturally derive the observed Hubble constant without tension. 5. '''Philosophical Transparency''' The theory clearly departs from Newtonian and relativistic interpretations, positioning itself as an ontological alternative grounded in energy flow. The author's motivations, limitations, and intended scope are transparently communicated in both academic and public forums. 6. '''Empirical Adequacy''' CIT offers empirical parallels in planetary spacing (κ_CIT), daylength extension over geological time, and disk fragmentation patterns. However, it currently lacks publication in high-impact peer-reviewed journals and formal statistical validation across broad datasets. 7. '''Institutional Support and Development''' CIT is developed independently, primarily through Wikiversity and open-access platforms. While it incorporates extensive cross-referencing and engages with mainstream and alternative sources, it lacks institutional affiliation and academic endorsement at this stage. '''Related link:''' [[Cosmic Influx Theory]] === '''8.4.10 Summary of Spiral Cosmology''' === The Pearlman Cosmology (SPIRAL Cosmology) offers a deterministic model of the universe with a defined hyper-dense initial state, fixed radius growth, and a reinterpretation of redshift. It integrates biblical chronology into its cosmological assumptions, making it a unique hybrid of scientific and scriptural reasoning. 1. '''Internal Consistency''' The model presents a logically consistent internal framework, with clearly defined initial conditions such as the SPIRAL radius, gravitational equilibrium, and fixed cosmic time scaling. Its components align well within its own assumptions. 2. '''Predictive Power''' Pearlman Cosmology proposes several potentially testable hypotheses, such as a fixed annual rate of universal expansion and an alternative explanation of redshift. However, these are not yet accompanied by detailed numeric predictions or simulations. 3. '''Falsifiability''' Testable elements exist in the form of reinterpretations of the cosmic microwave background origin, early galaxy formation, and redshift asymmetries. Yet aspects based on Mosaic chronology may fall outside strict scientific falsifiability. 4. '''Observational Alignment''' The model qualitatively aligns with some recent JWST observations, including early structure formation and CMB uniformity. Nevertheless, it lacks robust quantitative matching with large datasets or predictive modeling. 5. '''Philosophical Transparency''' The theory is open about its use of religious chronology and framing. This transparency makes its worldview explicit, though it may hinder its acceptance within mainstream secular science. 6. '''Empirical Adequacy''' While some empirical parallels exist, the theory has not yet been tested against a wide body of observational data in a systematic or peer-reviewed way. 7. '''Institutional Support and Development''' Pearlman Cosmology remains outside institutional research frameworks. Its development and publication history are limited, and it has not yet entered mainstream cosmological discourse. '''Related link:''' [https://www.pearlman.org Pearlman Cosmology] '''◀ [[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 ▶]]''' pb95ma1ko429fdlpnfs7nuw3kixa3vx 2719992 2719991 2025-06-29T04:39:07Z Ruud Loeffen 2998353 /* 8.4.8 Big Bounce */ add link to this theory 2719992 wikitext text/x-wiki == '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' = == '''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. == '''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 == '''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 such as: Observational Agreement Internal Logical Consistency Predictive Value Compatibility with Other Domains (e.g., geology, biology) Conceptual Coherence and Simplicity Each dimension is rated using a 1–5 star system, based on the information provided and the supporting sources that AI can access. 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. == '''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. == '''8.1 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. '''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. '''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. '''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. '''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. '''5. Conceptual Clarity and Simplicity''' Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification. '''6. Heuristic Value''' Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential. '''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. 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 or can be requested in more detail. == '''8.2 AI Evaluation Table Format''' == {| class="wikitable" |+ '''AI Evaluation Table of Cosmological Theories''' ! Theory Name ! Empirical Adequacy ! Internal Consistency ! Predictive Power ! Cross-Disciplinary Compatibility ! Conceptual Clarity and Simplicity ! Heuristic Value ! Historical & Philosophical Insight ! Total (★) |- | 8.4.1 '''General Relativity''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★★ || '''34''' |- | colspan="9" | ''Widely confirmed by experiment; mathematical elegance; historical development from Newtonian mechanics'' |- |- | 8.4.2 '''Newtonian Gravity''' | ★★★★☆ || ★★★★★ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''30''' |- | colspan="9" | ''Highly successful in classical mechanics and celestial predictions; lacks compatibility with relativity and quantum theory; historically foundational.'' |- | 8.4.3 '''MOND (Modified Newtonian Dynamics)''' | ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''24''' |- | colspan="9" | ''Strong in galactic rotation curves; limited compatibility with general relativistic frameworks'' |- | 8.4.4 '''Emergent Gravity (Verlinde)''' | ★★☆☆☆ || ★★★★☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''25''' |- | colspan="9" | ''Innovative reformulation; still awaiting broad empirical confirmation'' |- | 8.4.5 '''Big Bang Model''' | ★★★★★ || ★★★★★ || ★★★★★ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''31''' |- | colspan="9" | ''Core cosmological model; supported by CMB, redshift, nucleosynthesis'' |- | 8.4.6 '''Steady State Theory''' | ★☆☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || '''23''' |- | colspan="9" | ''Historically important; largely superseded due to lack of CMB explanation'' |- | 8.4.7 '''Big Crunch Theory''' | ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || '''28''' |- | colspan="9" | ''Predicts final collapse of universe; consistent with GR in high-density scenarios; revived interest due to dark energy variability'' |- | 8.4.8 '''Big Bounce Theory''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''26''' |- | colspan="9" | ''Cyclical alternative to singularity; compatible with some quantum gravity models'' |- | 8.4.9 '''Cosmic Influx Theory (CIT)''' | ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★★★★ || ★★★★☆ || '''26''' |- | colspan="9" | ''Offers cross-disciplinary compatibility; predicts mass growth and preferred orbital distances; alternative influx model under development'' |- | 8.4.10 '''SPIRAL Cosmology''' | ★★★★☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22''' |- | colspan="9" | ''Proposes a hyper-dense proto-galactic phase preceding expansion; no need for ongoing dark energy or cosmic expansion; partially scriptural framing may limit falsifiability but testable claims (e.g. fixed-radius light departure) justify scientific review.'' |- | colspan="9" | ''Well-formulated alternative integrating orbital quantization; some empirical fit to planetary data; lacks full mainstream acceptance'' |} <!-- Add a blank line here --> == '''8.3 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]]'''. == '''8.4 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. === '''8.4.1 General Relativity'''=== '''Empirical Adequacy''' General Relativity (GR) is one of the most empirically validated theories in physics. It has successfully explained and predicted a wide range of gravitational phenomena, including the precession of Mercury’s perihelion, gravitational lensing of starlight, gravitational redshift, time dilation effects observed in satellite systems like GPS, and the Shapiro delay. More recently, its predictions have been confirmed by gravitational wave observations (LIGO/Virgo) and direct imaging of black holes (Event Horizon Telescope). The agreement between theory and measurement is often better than 0.01%, demonstrating exceptional empirical adequacy. '''Internal Consistency''' GR is internally consistent within its mathematical framework. It is based on the Einstein field equations, which are derived from well-defined variational principles and respect general covariance. The logical structure of the theory is rigorous, with clearly formulated assumptions such as the equivalence principle and the conservation of energy–momentum through the stress-energy tensor. There are no known internal contradictions. '''Predictive Power''' GR has a powerful record of making novel predictions that were later confirmed by experiment or observation. These include the bending of light by massive bodies, time dilation in gravitational fields, the expansion of the universe (through its application in cosmology), and the existence of gravitational waves. Its predictions have often preceded direct detection by decades. This makes GR a model example of a theory with high predictive power. '''Cross-Disciplinary Compatibility''' General Relativity is compatible with many areas of physics, including classical mechanics, electrodynamics, and astrophysics. However, it is not yet unified with quantum mechanics. Attempts to reconcile GR with the Standard Model—such as quantum gravity, string theory, or loop quantum gravity—remain incomplete. Thus, GR scores slightly lower here due to its current incompatibility with modern particle physics at the Planck scale. '''Conceptual Clarity and Simplicity''' The core idea of GR—that gravity is not a force but a geometric property of spacetime—is conceptually elegant. However, the mathematical formalism (involving tensor calculus and differential geometry) is complex and often inaccessible to non-specialists. While the theory offers deep conceptual clarity, its practical simplicity is limited by the required mathematical tools. '''Heuristic Value''' GR has inspired generations of physicists and remains a fertile ground for theoretical development. It has opened up entire fields such as relativistic astrophysics, cosmology, and gravitational wave astronomy. Its influence extends beyond physics into philosophy and the public imagination. It continues to motivate research on black holes, time travel, singularities, and the early universe. '''Historical and Philosophical Insight''' Historically, GR represents a revolutionary shift in physics, displacing the Newtonian notion of absolute space and time with a dynamic, curved spacetime model. Philosophically, it challenges classical intuitions about gravity and causality and has inspired reevaluation of concepts such as simultaneity, locality, and determinism. Its legacy places it among the most profound achievements in scientific history. '''Related link:''' [https://en.wikipedia.org/wiki/General_relativity General Relativity] === '''8.4.2 Newtonian Gravity''' === '''Empirical Adequacy''' Newtonian gravity has historically achieved remarkable empirical success. It accurately describes planetary motions, tidal forces, ballistic trajectories, and satellite orbits. For centuries, it provided the dominant framework for celestial mechanics and was sufficient for navigation, astronomy, and engineering. However, it begins to fail in extreme gravitational fields or at very high speeds, where relativistic corrections are needed. It also cannot explain phenomena like the precession of Mercury’s orbit, gravitational time dilation, or the bending of light. '''Internal Consistency''' Within its classical framework, Newtonian gravity is highly consistent. It is based on clear axioms such as the inverse-square law and absolute space and time. The mathematical structure is well-defined and solvable using Newton’s laws of motion and calculus. No logical contradictions arise within its scope of applicability. However, its assumptions about instantaneous action at a distance are problematic under modern physical understanding. '''Predictive Power''' Newtonian gravity has strong predictive power in low-speed, weak-field regimes. It successfully predicted the return of Halley’s Comet, the existence of Neptune, and continues to be used in engineering and orbital calculations. However, it fails to predict relativistic effects such as gravitational lensing, frame-dragging, or gravitational waves. These limitations reduce its predictive power on cosmic and high-precision scales. '''Cross-Disciplinary Compatibility''' Newton’s theory aligns well with classical physics and early chemistry but lacks compatibility with modern disciplines. It cannot be reconciled with special relativity or quantum theory and does not incorporate energy–momentum considerations as in modern field theories. Its incompatibility with relativity limits its integration with high-energy physics and astrophysics. '''Conceptual Clarity and Simplicity''' Newtonian gravity is conceptually simple and intuitively accessible. The inverse-square force law is easy to visualize and apply. It does not require advanced mathematics and remains an ideal teaching model. Its clarity and ease of computation give it enduring educational and practical value. '''Heuristic Value''' Although no longer a frontier theory, Newtonian gravity laid the groundwork for classical mechanics and much of modern science. It helped shape ideas about force, motion, and planetary systems. While it no longer drives active theoretical innovation, it retains historical heuristic importance. '''Historical and Philosophical Insight''' Newton’s theory was revolutionary in unifying terrestrial and celestial phenomena under the same laws of motion. It established the idea of a universal physical law and set the standard for quantitative science. Philosophically, it introduced mechanistic determinism and absolute space and time—concepts that dominated Enlightenment science. Though now superseded, its legacy remains foundational. '''Related link:''' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newtonian Gravity] === '''8.4.3 MOND (Modified Newtonian Dynamics)''' === '''Empirical Adequacy''' MOND was proposed by Mordehai Milgrom in the early 1980s to explain galactic rotation curves without invoking dark matter. It has successfully reproduced the flat rotation profiles of spiral galaxies and the observed baryonic Tully–Fisher relation with remarkable precision. MOND fits individual galaxy data with fewer parameters than dark matter models. However, it struggles with galaxy cluster dynamics, cosmological structure formation, and gravitational lensing in some systems. Its empirical adequacy is high for galactic scales but limited beyond that domain. '''Internal Consistency''' MOND is mathematically consistent in its non-relativistic form, where it modifies Newton’s second law at low accelerations using a new constant 𝑎 0 a 0 ​ . However, its original formulation lacks a full theoretical derivation from first principles and requires ad hoc modifications to the force law. Several relativistic extensions (e.g. TeVeS, AQUAL, BIMOND) have been developed to improve consistency, but these are not uniquely favored and remain complex or underconstrained. '''Predictive Power''' MOND has had considerable predictive success in galactic astrophysics. It predicted the baryonic Tully–Fisher relation before it was observationally confirmed, and it can reproduce detailed features of galaxy rotation curves without needing dark matter halos. However, it lacks explanatory power for phenomena like the cosmic microwave background (CMB) anisotropies, gravitational lensing in galaxy clusters (e.g. Bullet Cluster), and large-scale structure. Its predictive power is strong in its target domain but limited on cosmological scales. '''Cross-Disciplinary Compatibility''' MOND is primarily focused on galactic dynamics and does not integrate smoothly with high-energy physics, quantum theory, or cosmology. Its extensions to cosmology often require additional assumptions, and it is not yet compatible with standard particle physics. As a result, its cross-disciplinary reach is modest, though ongoing efforts aim to embed it within broader frameworks. '''Conceptual Clarity and Simplicity''' In its original form, MOND is simple: the gravitational acceleration deviates from Newton’s law when below a critical threshold 𝑎 0 a 0 ​ . This modification is intuitive and computationally effective for galaxies. However, attempts to embed MOND in a relativistic framework often add complexity, reducing its conceptual transparency. '''Heuristic Value''' MOND has had significant heuristic impact by highlighting regularities in galactic dynamics that are hard to explain under the ΛCDM paradigm without fine-tuned dark matter profiles. It has sparked debate, inspired hybrid theories (e.g. dark matter superfluidity), and contributed to reevaluating gravitational theory. Its challenge to mainstream cosmology has been fruitful, even if not universally accepted. '''Historical and Philosophical Insight''' MOND revives the idea that gravity itself may need modification, rather than positing unseen matter. This philosophical approach echoes the history of science, where anomalies sometimes led to revisions of theory rather than new entities. MOND also raises deep questions about the nature of inertia, scale invariance, and universal laws—making it a philosophically provocative proposal despite its contested status. '''Related link:''' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics MOND (Modified Newtonian Dynamics)] === '''8.4.4 Emergent Gravity''' === '''Empirical Adequacy''' Emergent Gravity, proposed by Erik Verlinde in 2011 and expanded in 2016, seeks to explain gravitational phenomena as an emergent effect of underlying entropic and holographic principles rather than a fundamental force. It claims to reproduce galactic rotation curves without invoking dark matter by relating gravity to the thermodynamics of microscopic information storage on holographic screens. The theory can qualitatively explain certain galactic dynamics, such as the radial acceleration relation (RAR), but lacks the quantitative precision and scope of MOND in galaxy rotation curve fitting. It also currently cannot reproduce the full spectrum of cosmological observations, including the CMB power spectrum or gravitational lensing in galaxy clusters, where standard ΛCDM performs better. '''Internal Consistency''' Emergent Gravity draws from concepts in string theory, quantum information theory, and thermodynamics. While intellectually coherent and grounded in cutting-edge theoretical frameworks, the theory is still under development and lacks a universally accepted formalism. Key quantities (such as entropic force or the elastic response of spacetime) are not always rigorously defined, and derivations sometimes rely on analogies rather than strict derivations. This limits the formal internal consistency at present, though the conceptual framework remains promising. '''Predictive Power''' The theory makes some novel qualitative predictions, particularly regarding the relation between baryonic mass and gravitational acceleration without dark matter. It reproduces the RAR and may provide an explanation for dark energy as an entropic effect of spacetime. However, Emergent Gravity has not yet made precise predictions for cosmological parameters, gravitational wave behavior, or galaxy cluster dynamics that can be tested independently of standard models. Its predictive power remains speculative and qualitative. '''Cross-Disciplinary Compatibility''' Emergent Gravity attempts to bridge gravity, quantum information, and thermodynamics, making it conceptually rich in cross-disciplinary connections. It resonates with holography, the AdS/CFT correspondence, and black hole thermodynamics. However, the lack of experimental or observational confirmation limits its integration with empirical domains such as astrophysics, cosmology, and particle physics. Its compatibility is more theoretical than empirical at this stage. '''Conceptual Clarity and Simplicity''' The idea that gravity is not fundamental but emerges from statistical behavior of microscopic degrees of freedom is intellectually elegant. However, the actual implementation of this idea in the current models is technically complex and often abstract. Unlike Newtonian gravity or even MOND, the mechanisms proposed by Emergent Gravity are difficult to visualize or test directly, and involve high-level concepts from thermodynamics and information theory. '''Heuristic Value''' Emergent Gravity is highly heuristic. It opens new perspectives on the nature of gravity, spacetime, and entropy. By reframing gravity as an emergent entropic force, it challenges the foundations of both classical and relativistic theories. It has influenced discussions around the holographic principle, black hole entropy, and spacetime microstructure. Even if it remains incomplete, it contributes to rethinking gravity from first principles. '''Historical and Philosophical Insight''' Philosophically, Emergent Gravity aligns with the long-standing idea that some phenomena in nature arise from deeper, statistical processes rather than being fundamental. It recalls Boltzmann’s approach to thermodynamics and aligns with modern information-theoretic views of physics. Historically, it marks a shift from geometric to thermodynamic models of spacetime, and offers a bold alternative to particle-based explanations of gravity. Though controversial, it is part of a growing movement to reinterpret gravity in terms of entropy and information. '''Related link:''' [https://en.wikipedia.org/wiki/Erik_Verlinde#Emergent_gravity Emergent Gravity] === '''8.4.5 Big Bang''' === '''Empirical Adequacy''' The Big Bang model is the current standard cosmological paradigm and is strongly supported by multiple independent observations. These include the cosmic microwave background (CMB) radiation, the large-scale structure of the universe, the observed expansion of space (via redshift-distance relations), and the relative abundances of light elements (hydrogen, helium, deuterium, lithium), as predicted by Big Bang Nucleosynthesis (BBN). These confirmations make the Big Bang model one of the most empirically supported frameworks in cosmology. However, the model does not explain the origin of the singularity itself, and extensions such as inflation or dark energy are required to match detailed observations. '''Internal Consistency''' The Big Bang framework is based on solutions to Einstein's field equations (Friedmann–Lemaître–Robertson–Walker metrics), and it is mathematically consistent within the assumptions of general relativity and homogeneity/isotropy (the cosmological principle). However, the initial singularity remains a theoretical boundary where the equations break down, and the model does not include a quantum gravity regime. Extensions such as inflation and ΛCDM are necessary for consistency with observations, but these introduce additional assumptions and parameters, sometimes criticized as fine-tuning. '''Predictive Power''' The Big Bang model has made several successful predictions: the existence and spectrum of the CMB, the large-scale structure of galaxies, and the relative abundances of primordial elements. It also correctly anticipated the cooling of the universe and the redshift–distance relation. Inflationary extensions explain the flatness and horizon problems and predict the nearly scale-invariant spectrum of CMB fluctuations. While many predictions are retrodictive and interpreted within a flexible framework, the model continues to be highly predictive in key areas of cosmology. '''Cross-Disciplinary Compatibility''' The Big Bang model integrates with nuclear physics (BBN), atomic physics (recombination), and high-energy physics (inflation, particle freeze-out). It is broadly compatible with the Standard Model of particle physics and many theories of fundamental interactions. However, it lacks a connection to quantum gravity, and some tensions remain—such as the Hubble tension between early and late universe measurements—that challenge cross-scale consistency. '''Conceptual Clarity and Simplicity''' The core idea—a hot, dense early universe that expands and cools over time—is conceptually clear and widely accepted. However, the full ΛCDM model includes inflation, cold dark matter, and dark energy, which are not directly observable and require complex assumptions. These components reduce the model's simplicity and raise questions about the explanatory depth of the framework. '''Heuristic Value''' The Big Bang theory has driven vast developments in cosmology, observational astronomy, particle physics, and astrophysical instrumentation. It has generated decades of research questions and missions, including COBE, WMAP, and Planck. The inflationary paradigm and dark energy studies have emerged directly from this model. As a heuristic framework, it has proven extremely fertile. '''Historical and Philosophical Insight''' The Big Bang marks a major conceptual shift in cosmology by proposing that the universe has a temporal origin and evolves over time. It displaced steady-state and eternal models of the cosmos and opened up philosophical inquiries about creation, the arrow of time, and the origin of physical laws. Despite its name, it is not an explosion in space but the expansion of space itself—a concept that has reshaped how we understand time, causality, and the structure of the universe. '''Related link:''' [https://en.wikipedia.org/wiki/Big_Bang Big Bang] === '''8.4.6 Steady State Theory''' === '''Empirical Adequacy''' The Steady State Theory, developed in the late 1940s by Bondi, Gold, and Hoyle, posits that the universe has no beginning or end in time and remains statistically the same on large scales, with matter continuously created to maintain constant density despite cosmic expansion. Initially, it matched observations of redshift and expansion, but it was ultimately undermined by key empirical discoveries: the cosmic microwave background (CMB), the evolution of radio source counts, and the observation of distant galaxies at earlier stages of development. These findings provided strong evidence of a hot, dense early universe, inconsistent with the steady state hypothesis. As a result, its empirical adequacy is now considered low. '''Internal Consistency''' The theory is internally consistent in its classical formulation and relies on continuous creation of matter to maintain a constant density. However, this matter creation mechanism was never supported by a detailed physical model or empirical detection. While mathematically coherent, the theory’s assumption of continuous creation violates energy conservation as understood in standard physics, making the underlying physics speculative and theoretically weak. '''Predictive Power''' The Steady State model made a bold prediction: the universe should appear the same at all times and places when viewed on large scales. While this was a clear and testable prediction, it was eventually falsified by observations such as the CMB and the evolution of quasars and galaxy populations over time. The theory’s few predictions have largely been refuted, limiting its scientific utility. '''Cross-Disciplinary Compatibility''' The model is only weakly connected to other scientific domains. It does not integrate well with nuclear physics, as it lacks a mechanism for element formation similar to Big Bang Nucleosynthesis. It also lacks compatibility with high-energy particle physics and modern theories of gravity. The continuous matter creation postulate has no foundation in quantum theory or experimental physics. '''Conceptual Clarity and Simplicity''' The steady-state model is conceptually simple and elegant. Its appeal lay in its ability to preserve a universe without origin, circumventing the philosophical and theological questions raised by a cosmic beginning. The model also maintains a uniform, eternal cosmos, which was attractive to many physicists in the mid-20th century. Despite being falsified, it remains a conceptually clear alternative that helped clarify the implications of observational cosmology. '''Heuristic Value''' Although it is no longer a viable cosmological model, the Steady State theory played a significant heuristic role. It prompted debates about the nature of time, observational testing, and the falsifiability of cosmological models. It helped shape the methodological standards for modern cosmology by being a well-defined, testable theory that was ultimately rejected based on empirical data. Its legacy lives on in discussions about the role of testability and philosophical assumptions in science. '''Historical and Philosophical Insight''' The Steady State theory was historically important as the main rival to the Big Bang model in the early post-war period. It reflects a philosophical preference for temporal infinity and equilibrium conditions, standing in contrast to a universe with a beginning. Its eventual rejection illustrates the triumph of observation over philosophical elegance in modern cosmology. It also served as a case study in the philosophy of science, particularly regarding Popperian falsifiability and the evolution of scientific consensus. '''Related link:''' [https://en.wikipedia.org/wiki/Steady_state_model Steady State Theory] === '''8.4.7 Big Crunch''' === '''Empirical Adequacy''' The Big Crunch is not a theory of gravity or cosmology by itself but rather a hypothetical end-state of the universe within certain cosmological models. It posits that cosmic expansion could eventually reverse, causing the universe to contract back into a high-density singularity. This scenario arises from general relativity under the assumption of a closed universe with sufficient matter density to overcome expansion. However, current observational data strongly indicate that the universe is accelerating in its expansion, driven by dark energy. Measurements of the cosmic microwave background (CMB), supernova distances, and large-scale structure all support a flat or open universe with low matter density, making the Big Crunch scenario empirically disfavored at present. '''Internal Consistency''' Within general relativity and standard cosmological models, the Big Crunch is internally consistent. It naturally arises from the Friedmann equations when the density parameter Ω > 1 and the cosmological constant is absent or negative. The dynamics of contraction mirror those of expansion in reverse, and no logical contradictions emerge in its mathematical formulation. However, near the final singularity, quantum gravitational effects become important, and the classical equations break down. '''Predictive Power''' As a hypothetical scenario, the Big Crunch does not offer specific predictive claims under current physical conditions. Instead, it represents a conditional outcome: if the universe were closed and dominated by matter, it would eventually recollapse. Since observations show otherwise, the predictive relevance of the Big Crunch is now limited. Nevertheless, it played a role in exploring time-reversal symmetry, thermodynamic limits, and quantum cosmology. '''Cross-Disciplinary Compatibility''' The Big Crunch scenario is compatible with general relativity and classical thermodynamics, especially in discussions of entropy and the arrow of time. It has also been explored in speculative models of cyclic or oscillating universes, which relate to quantum gravity and string theory. However, it lacks strong support from empirical fields such as observational cosmology, particle physics, or astronomy under the current ΛCDM framework. '''Conceptual Clarity and Simplicity''' The concept is straightforward: the universe's expansion halts and reverses into a collapse. This time-symmetric model is intuitively appealing and easy to visualize. However, its physical plausibility is undermined by current evidence for accelerating expansion. Still, as a conceptual tool, it remains a clear contrast to models of eternal expansion or thermal death. '''Heuristic Value''' Historically, the Big Crunch scenario stimulated discussion about cosmological cycles, entropy limits, and the ultimate fate of the universe. It led to the development of cyclic models, bounce cosmologies, and ideas about cosmic rebirth. Although largely ruled out by current data, it retains heuristic value in theoretical cosmology and philosophy of time, particularly in exploring whether time and entropy could reverse. '''Historical and Philosophical Insight''' The Big Crunch offered a philosophically symmetric alternative to the Big Bang—a universe that begins and ends in a singularity. It invites reflection on the reversibility of physical laws, the meaning of cosmic time, and the possibility of eternal recurrence. While empirical support is lacking, the scenario remains a historically meaningful part of cosmological thinking, especially in the 20th-century debates about the universe's fate. '''Related link:''' [https://en.wikipedia.org/wiki/Big_Crunch Big Crunch] === '''8.4.8 Big Bounce''' === '''Empirical Adequacy''' The Big Bounce is a speculative cosmological scenario in which the universe undergoes a cycle of contraction followed by a rebound (or "bounce") into a new phase of expansion. It aims to replace the initial singularity of the Big Bang with a transitional phase where quantum gravitational effects prevent infinite density. While the concept is consistent with certain theoretical models—particularly in loop quantum cosmology—there is currently no direct observational evidence for a bounce event. The cosmic microwave background (CMB) does not yet show unambiguous signatures that would favor a bounce over inflationary models. Thus, empirical adequacy remains hypothetical, though not excluded. '''Internal Consistency''' The Big Bounce can be formulated consistently within several frameworks, such as loop quantum gravity, string gas cosmology, or modified gravity models. In these settings, quantum corrections to the Friedmann equations or modifications to the geometry of spacetime prevent a singularity and allow for a smooth transition from contraction to expansion. However, different bounce models vary in their assumptions, and the full quantum dynamics are not yet universally agreed upon. Despite these uncertainties, the internal logic of the models is coherent within their theoretical boundaries. '''Predictive Power''' Some Big Bounce models predict subtle features in the CMB, such as suppressed power at large angular scales, or non-Gaussianities that differ from inflation. However, these predictions often overlap with or are degenerate with inflationary predictions, making them hard to test uniquely. No conclusive observational support has been found so far. Nevertheless, bounce models offer a predictive framework that could, in principle, be tested with improved cosmological data in the future. '''Cross-Disciplinary Compatibility''' The Big Bounce scenario is motivated by attempts to unify quantum mechanics and gravity. It connects well with developments in loop quantum cosmology, non-singular black hole models, and string theory. However, it is less developed in its links to particle physics, standard cosmology, or astrophysical observations. Its broader scientific compatibility depends heavily on which theoretical approach is adopted and how it interfaces with known physics. '''Conceptual Clarity and Simplicity''' The idea of a contracting universe rebounding into expansion is conceptually intuitive and avoids the metaphysical implications of a beginning-of-time singularity. In contrast to the Big Bang singularity, the bounce implies a cyclic or oscillatory universe that is eternal in time. While appealing in its symmetry, the underlying physics is often highly technical and abstract, involving non-perturbative quantum gravity, which reduces its practical simplicity. '''Heuristic Value''' The Big Bounce has stimulated important discussions in cosmology, particularly regarding singularity avoidance, pre-Big Bang scenarios, and the nature of time. It has inspired a class of alternative models to inflation and opened up debates about the cyclical nature of the universe. Its challenge to the standard narrative of cosmic origins has heuristic value in motivating new lines of theoretical research. '''Historical and Philosophical Insight''' The Big Bounce continues a long tradition of cyclical universe models, echoing ideas from ancient cosmologies and early 20th-century oscillating universe theories. Philosophically, it provides a framework in which the universe has no absolute beginning or end, and where time and entropy may operate in a larger looped framework. It offers a more balanced cosmological picture than the irreversible expansion or final collapse scenarios. Though not yet supported by data, its philosophical implications remain profound and open-ended. '''Related link:''' [https://en.wikipedia.org/wiki/Big_Bounce Big Bounce] === '''8.4.9 Cosmic Influx Theory (CIT)''' === Cosmic Influx Theory (CIT), proposed by Ruud Loeffen, reinterprets gravity as a directional energy influx driven by Primordial Elementary Whirlings (PEWs), replacing the concept of attractive force or space-time curvature. It introduces a constant influx of mass-energy into all bodies, contributing to planetary expansion, star formation, and cosmological evolution. 1. '''Internal Consistency''' CIT presents a coherent internal logic based on a unidirectional influx mechanism, a redefined gravitational constant (G = (γ − 1)/4π), and the introduction of κ_CIT as a universal scaling constant. While the framework remains internally consistent, some equations are still under refinement and lack full derivations from first principles. 2. '''Predictive Power''' CIT predicts the Preferred Distance for giant planets based on κ_CIT, orbital periods of exoplanets, and a revised Hubble constant (Ho ≈ 67.8 km/s/Mpc). It also anticipates planetary expansion through mass influx. These predictions are testable, though many remain pending observational confirmation. 3. '''Falsifiability''' Several predictions—such as giant planets at D_pref in the Trappist system or mass accumulation rates inferred from planetary geology—can be tested. However, the influx mechanism itself is not yet described in terms of directly measurable particles or interactions, which may limit falsifiability at the quantum level. 4. '''Observational Alignment''' CIT aligns with various observations: early formation of giant planets in protoplanetary disks, planetary expansion signatures, surface geology of moons and Mars, and recent JWST disk structures. It also claims to naturally derive the observed Hubble constant without tension. 5. '''Philosophical Transparency''' The theory clearly departs from Newtonian and relativistic interpretations, positioning itself as an ontological alternative grounded in energy flow. The author's motivations, limitations, and intended scope are transparently communicated in both academic and public forums. 6. '''Empirical Adequacy''' CIT offers empirical parallels in planetary spacing (κ_CIT), daylength extension over geological time, and disk fragmentation patterns. However, it currently lacks publication in high-impact peer-reviewed journals and formal statistical validation across broad datasets. 7. '''Institutional Support and Development''' CIT is developed independently, primarily through Wikiversity and open-access platforms. While it incorporates extensive cross-referencing and engages with mainstream and alternative sources, it lacks institutional affiliation and academic endorsement at this stage. '''Related link:''' [[Cosmic Influx Theory]] === '''8.4.10 Summary of Spiral Cosmology''' === The Pearlman Cosmology (SPIRAL Cosmology) offers a deterministic model of the universe with a defined hyper-dense initial state, fixed radius growth, and a reinterpretation of redshift. It integrates biblical chronology into its cosmological assumptions, making it a unique hybrid of scientific and scriptural reasoning. 1. '''Internal Consistency''' The model presents a logically consistent internal framework, with clearly defined initial conditions such as the SPIRAL radius, gravitational equilibrium, and fixed cosmic time scaling. Its components align well within its own assumptions. 2. '''Predictive Power''' Pearlman Cosmology proposes several potentially testable hypotheses, such as a fixed annual rate of universal expansion and an alternative explanation of redshift. However, these are not yet accompanied by detailed numeric predictions or simulations. 3. '''Falsifiability''' Testable elements exist in the form of reinterpretations of the cosmic microwave background origin, early galaxy formation, and redshift asymmetries. Yet aspects based on Mosaic chronology may fall outside strict scientific falsifiability. 4. '''Observational Alignment''' The model qualitatively aligns with some recent JWST observations, including early structure formation and CMB uniformity. Nevertheless, it lacks robust quantitative matching with large datasets or predictive modeling. 5. '''Philosophical Transparency''' The theory is open about its use of religious chronology and framing. This transparency makes its worldview explicit, though it may hinder its acceptance within mainstream secular science. 6. '''Empirical Adequacy''' While some empirical parallels exist, the theory has not yet been tested against a wide body of observational data in a systematic or peer-reviewed way. 7. '''Institutional Support and Development''' Pearlman Cosmology remains outside institutional research frameworks. Its development and publication history are limited, and it has not yet entered mainstream cosmological discourse. '''Related link:''' [https://www.pearlman.org Pearlman Cosmology] '''◀ [[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 ▶]]''' logxb0otr4sc02vywkklwntwvkuiywb 0 322211 2719980 2719859 2025-06-28T22:24:42Z Scogdill 1331941 /* From Tenants and Employees */ 2719980 wikitext text/x-wiki =Event= ==Overview== The wedding of [[Social Victorians/People/Cowley|Henry Wellesley, Viscount Dangan]] and Lady Violet Nevill ==Logistics== * 17 December 1889, Tuesday * St. George's Church, Hanover Square, Westminster ===Staff and Vendors=== * ==Related Events== * Reception * Honeymoon ==Who Was Present== ===Bride and Bridesmaids=== ====Bride==== ====Bridesmaids==== ====Pages==== ===Groom and Best Man=== ===People Who Attended=== # Could the Mrs. Frank Harris be the writer's wife? ==What People Wore== # ==Gifts== The bride got an unusually large amount of diamond jewelry, and the couple got an unusual number of "old" or antique items, especially silver. Unusually small number of books. They also got a surprisingly large number of whips or driving whips, including one from the groom to the bride. ===From Tenants and Employees=== ==== Lady Violet Nevill ==== Two of these groups also presented addresses to the bride, the Bridge Castle servants and the tenants on the Eridge and Southdown estates, whose address was "illuminated." * The "tradesmen of Tunbridge Wells presented the bride with a large silver gilt looking glass"<ref name=":0" />{{rp|Col. 3b}} * "Bridge Castle servants, set of brushes and hand mirrors, with gold monogram and address"<ref name=":0" />{{rp|Col. 3b}} * "Gardeners, mechanics, and keepers on the Bridge estate, china tea service painted in violets"<ref name=":0" />{{rp|Col. 3b}} * "Tenants on the Eridge and Southdown estates, silver hunting horn and illumlnated address"<ref name=":0" />{{rp|Col. 3b}} * "Bridge teachers and scholars of the Sunday and day schools, brass salver"<ref name=":0" />{{rp|Col. 3b}} * "Committee of the Tunbridge Wells Junior Conservative Association, salver cushion in Conservative colours of Kent and Sussex"<ref name=":0" /> * "Tenants on the Draycot estate, sliver cream jug and sugar basin"<ref name=":0" />{{rp|Col. 3b}} * "Servants at Stratton-Audley, grey leather and silver blotting book and envelope case."<ref name=":0" />{{rp|Col. 3b}} ==== Lord Dangan ==== * "Southdacon farm labourers, cigarette case"<ref name=":0" />{{rp|Col. 3c}} * "The tenants the Draycot estate presented Lord Dangan with a large silver urn: [sic] andthe [sic] employês [sic] the estate gave a lamp."<ref name=":0" />{{rp|Col. 3c}} ===Unusual or Interesting Gifts=== * Whips: sixteen-bore gun and hunting whip, Hunting whip (x3), Gold mounted hunting whip, Driving whip (x2) * Eridge pony cart * Apostle spoons, Silver apostle spoons, Twelve apostle teaspoons * George III. silver bowl (x2, one given to the bride and one to the groom) * Four Spode dessert dishes * Wedgwood china * Very large white ostrich feather fan, Large white ostrich feather fan, with tortoiseshell sticks, Turkish fan * Case of silver glove stretchers, &c. * Driving rug, Driving rug * String box * Liquer case (given to the groom) * Silver razor strop * Silver stand for hunting appointments (to the groom) * Case of boot hooks * Clock and weather glass (several other clocks) * Racing bag === Books === * Bible === Furniture === * Marqueterie tray, Chippendale tea tray, Indian tray (plus a number of trays) * French armchair * Chippendale cabinet and lamp stand * Marqueterie table, Table, French table, Chippendale table, writing table (x2) * Chippendale paper case * High brass lamp * Piece of marqueterie furniture * High screen ==Anthology== The ''Devizes and Wiltshire Gazette'' published at least 2 stories about this wedding, one that addressed the wedding itself, and the one that follows here, which is about the gifts. The list of gifts is set here as an unordered list, which obscures the fact that the newspaper set the list using colons as well as semicolons, suggesting that their font had run out of semicolons — and periods as well, since they didn't punctuate the most common honorifics (Mr and Mrs).<blockquote>The marriage of Lord Dangan only son of Earl Cowley with the Lady Violet Nevill, youngest daughter of the Marquess and Marchioness of Abergavenny, took place, as announced in our last issue, on Tuesday, the 17th inst. The wedding presents presented to the bride and bridegroom were exceedingly beautiful. Those to the bride included the following gifts: — * From the bridegroom, a pearl and diamond necklace, ruby and diamond ring, turquoise and diamond pin, diamond fox pin, moonstone and diamond brooch, gold hunting watch, handsome gold mounted dressing case, with "Violet" engraved on the fittings, sixteen-bore gun, and hunting whip * The Marquess of Abergavenny gave his daughter three diamond roses, and an Eridge pony cart * The Marchioness of Abergavenny's presents included a pearl and diamond ring, enamelled and jewelled chatelaine, set of lace, and apostle spoons * Earl Cowley, a diamond bracelet * Countess Cowley, emerald and diamond ring * Marquesa de Santurce, diamond ring * Hon. T. A. and Lady Idina Brassey and Mr. and Lady Rose Leigh, diamond cluster necklace * Lord Brasaey, diamond half hoop ring * Lord and William Nevill, handsome diamond pendant * Lord Richard Nevill, pair of diamond rose bangles * Hon. Ralph and Mrs. Nevill, diamond and moonstone bangle * Lord and Lady Henry Nevill, turquoise and diamond bangle * Col Hon. F. Wellesley, ruby and diamond heart pendant * Lady Eva Wellesley, pearl and diamond ring * Mr. F. B. Mildmay, M.P., turquoise and diamond bangle * Mr. Andrew Montagu, diamond comb * Mrs. Hwfa Williams, gold bracelet with diamond and sapphire centre * Earl of Feversham, gold chain bangle * Miss Edith Lane Fox, diamond brooch * Hon. Edith Johnstone, pearl pins * Mr. J. W. Larnach, diamond brooch * Baron and Baroness Von Roemer, diamond fox bangle * Hon. Thomas Dundas, torquoise and diamond brooch * Miss Gell, coral pin * Colonel Honeywood, pearl brooch * Miss Leake, pearl and diamond pin * Mr. James Noel, solitaires * Mr. and Mrs. Temple Soanes, turquoise and diamond ring * Lady Trevor, old silver watch * Mr. and Mrs. Adrian Hope, ruby and diamond bangle * Mr. Gervase Beckett, large pearl pin * Lady George Nevill, fitted tea basket * Countess of Cottenham, pair of old silver vases * Earl of Cottenham, painted looking glass * Lord and Lady Churchill, brass lamp * Viscount and Viscountess Raincliffe, dessert service * Earl of Stradbroke, silver lamp * Viscountess Cranbrook, marqueterie tray * Lady Forbes, silver hand glass * Sir William Harcourt, bag * Lord and Lady Chesham, pair of silver lamps * Hon. Evelyn Gathorne Hardy, silver frame * Lady Sybil Knox, silver cream jug * Sir Francis Monteftore, pink mother-o'-pearl fan * Lady Sandhurst, French armchair * Lady de Trafford, pair of silver candlesticks * Hon. Assheton Harbord, dressing bag with solid gold mountings, and fitted with ivory backed brushes, with the initials "D. V." and coronet in gold * Baroness Henry de Worms, white ostrich feather fan with tortoiseshell sticks, and initials and coronet in diamonds * Sir Myles and Lady Fenton, case, containing silver shoe horn, button hook. &c,. [sic] * Lady Aline Beaumont, silver lamp * Mr. and Miss J. J. Barrow, very handsome clock, Shetland gloves. &c. * Mr. and Mrs. Beckett, silver tea service * Mr. and Mrs. H. Brassey, mother-o'-pearl fan * Mr. and Lady Isabel Bligh, clock * [[Social Victorians/People/Bourke|Hon. Algernon and Mrs Bourke]], salt and pepper pots * Mr Cullum, George III. silver bowl * Lord Cheylesmore and Hon. Miss Eaton, silver bowl * Lady Blanche Conyngham, carriage clock and card case * Lady Conyers, silver candlesticks * Lady Alice Dundas, silver sugar castor * Hon. Mrs Duberley, four Spode dessert dishes * Lady Derwent, marqueterie table * Hon. Lady Filmer and Miss Fllmer, pair of silver and crystal lamps * Mr and Mrs Moreton Frewen, large gold pencil case * Captain and Mrs Philip Green, silver apostle spoons * Lady Wilson, plush writing set * Mr and Hon. Mrs Glyn, very large white ostrich feather fan * Sir Edmund and Lady Hardinge, six silver gilt coffee spoons * Captain Hon. Henry Hardinge, silver sugar castor * Colonel Hon. C and Lady Cecily Gathorne Hardy, Chippendale cabinet and lamp stand * Mr E Hatch, black lace and tortoiseshell fan with diamond monogram * Lady Selina Hervey, table * Viscount Hardinge, paper knife * Hons. L E and M Hardinge, silver mounted inkstand * Hon. Gilbert Johnstone, old silver box * Hon. Francis and Mrs Johnstone, pair of old silver salt cellars * Mrs Leigh, Dresden tea set * Miss Leigh, twelve apostle teaspoons * Mr and Hon. Mrs Charles Egerton, large white ostrich feather fan, with tortoiseshell sticks * Hon. Mrs Lowther, silver bowl; Lady Constance Lyon, gauze fan * Hon. Mrs de Lisle, silver-mounted blotting book * Mr and Mrs Gerard Leigh, Chippendale tea tray * Mr and Mrs Morland, Indian tray * Major Henry Morland, large tortoiseshell and silver box * Hon. James Mansfield, tortoiseshell and silver table knife * Mr and Mrs Charles Martin, antique brass clock * Lady Alice Morland, silver and grey leather frame * Miss Morland, a similar gift * Mr M H Milner, gold topped salts bottle * Sir F and Lady Milner, French table * Lady Augusta Mostyn, large silver box * Miss Meresia Nevill, willow pattern coffee set * Lady Dorothy Nevill, silver mounted paper cutter * Lady Perry, Miss Perry, and Mrs, [sic] Grant, set of old paste buttons * Lady Hilda Rous, painted screen * Marquis Camden and Lady Clementine Pratt, silver muffineers * Lord and Lady George Pratt, silver clothes brush * Lord Sandhurst, pair of tortoiseshell and silver candlesticks * Hon. Cecil Sandys, silver box * Countess of Stradbroke, travelling clock * Lady Caroline Sterllng, leather writing table set * Mr and Mrs Arthur Streatfeild [sic], picture * Captain Wingfield Stratford, silver frame * Mrs and Miss Streatfeild, double frame * Mr and Mrs Gerard Streatfeild, two old silver boxes * Hon. Michael Sandys, pair of sugar castors * Lord Herbert Vane-Tempest, tortoiseshell and feather fan * Lord Henry Thynne, silver sugar castor * Miss Wombwell, silver gilt tray * Mr and Miss Williams, Turkish fan * Mrs Alnut, white china ornaments * Mrs Burton, glove sachet * Rev. J J Burton, Bible * Mr and Mrs Ludovick Bligh, paper knife * Miss Bidwell, silver seal * Miss Chetwynd, case of silver glove stretchers, &c. * Miss Cripps, china ornament * Mr Thomas Coppard, driving rug * Hon. Lilah and Hon. Charles Cavendish, ivory tray * Messrs. R and S Caldwell, china vases * M and Mrs W Cripps, hunting whip * Miss H Davis, double inkstand * Mrs Duce, china vase * Mrs Dobede, silver fish pencil case * Mr and Mrs Drake, pair of silver topped bottles * Mr Davis, driving rug * Mr Dickinson, fan * Misses Eastwood, white china waiter * Mrs Eastwood, Dresden tea service * Mr and Mrs Evenden, bracket * Mrs Frewen, silver magnifying glass * Mr and Mrs Stephen Frewen, old Sèvres china * Mrs Fletcher, small gold box * Mr and Mrs Earnest Beckett, silver gilt tray * Colonel and Hon. Mrs. Leeke, gold mounted hunting whip * Mr Westley Richards, clock * Mr and Mrs Glanville, photograph of the Marquis and Marchioness of Abergavenny * Thomas Cutton, small Ivory case with scissors * Lady Frances Pratt, silver sugar sifter * Mr and Lady Georgina Field, crown Derbycups * Mr and Mrs Fort, pair of Dresden figures * Mrs Inigo Gell, silver smelling bottle * Gilbert and Co.. high iron lamp * Mr G Gladwin, ivory handled button hook * Mrs Hamilton Grace, button hook * Mrs Frank Harris, silver tray * Mr and Mrs W H Hodgkin, Chippendale table * Miss Emily Harcourt, pair of opera glasses * Miss Hoskins, picture * Mr and Mrs R Hulse, silver paper holder * Mr Charles Johnstone, silver frame * Mr F and Miss Laura Johnstone, antique spoon * Misses Maude and Kate Kemp, silver box * Mr Percy Lankester, large framed photograph of Eridge Castle * Mr Charles Luck, Wedgwood china * Misses Miles, newspaper rack * Mr and Mrs Manser, paper knife * Mrs Montefiore, Dresden cups and saucers * Miss Marsack, photograph screen * Mr Noyes, string box * Mrs and Miss Neale, lace handkerchlef and table cloth * Mr R Nevill, sliver frame * Mr J Petts, hunting whip * Mrs Rust, basket * Miss Rutherford, table cloth * Mrs Cramer Roberts, Dutch silver toys * Mrs Shiffner, old Danish brooch * Miss Stapleton, piece of old silver * Mr Sheriffe, tortoiseshell and silver paper-knife * Master Jimmy and Miss Myra Smith, photo screen * Mr H Johnstone Scott, silver box * Mr Markham Spofforth [?], Chippendale paper case * Messrs. Poile Smith, large silver shell tray * Mr F. Tidd, Iarge silver mounted tortoiseshell leaf cutter * Miss Caroline Thompson, calendar * Mr and Mrs Vigors, pair of silver frames * Miss Vigors, long silver button hook * Mrs Wilkinson, glass vase * The tradesmen of Tunbridge Wells presented the bride with a large silver gilt looking glass * Bridge Castle servants, set of brushes and hand mirrors, with gold monogram and address * Gardeners, mechanics, and keepers on the Bridge estate, china tea service painted in violets * Tenants on the Eridge and Southdown estates, silver hunting horn and illumlnated address * Bridge teachers and scholars of the Sunday and day schools, brass salver * Committee of the Tunbridge Wells Junior Conservative Association, salver cushion in Conservative colours of Kent and Sussex * Tenants on the Draycot estate, sliver cream jug and sugar basin * Servants at Stratton-Audley, grey leather and silver blotting book and envelope case The bridegroom's presents comprised: — * From the bride, diamond pin, gold watch, and travelling bag * Earl and Countess Cowley, handsome silver centre piece * Marchioness of Abergavenny, silver spoons * Duke of Wellington, George III. silver bowl * Messrs. F. and C. de Murrieta, set of five very handsome open work dessert dishes * Marquis of Worcester, smoking-room tray * Duchess of Manchester, tortoiseshell paper knife with silver handle * Lady Eva Wellesly, pearl pin * Lord Richard Nevill, liquer case * Lord and Lady George Nevill, decanters * Lord and Lady William Nevill, pair of old silver sauce boats * Lord and Lady Henry Nevill, silver hot water jug * Lord and Lady Aline Beaumont, carriage watch * Count Esterhazy, cigar case * Vlscount and Viscountess Trafalgar, sliver mounted magnifying glass * Lord Edward Somerset, decanters * Lady Decies, silver lighter box * Lady Norreys, silver razor strop * Mr and Lady Doreen Long, silver magnifying glass * Hon. Claud Hay, old silver mustard pot * Hon. Mrs Gerald Wellesley, high brass lamp * Sir W Gordon Cumming, silver cirgarette case * Mr and Lady Idina Brassey, driving whip * Lord Apsley, umbrella * Hon. Dawson, pair of silver candlesticks * Lord Henry Bruce, silver pepper and mustard pots and salt cellars * The Earl of Dudley, four small liqueur bottles * Hon. Francis and Lady Feodorowna Bertie, pearl and diamond pin * Sir John Dickson Poynder, silver stand for hunting appointments * Lady Bulkeley, writing table * Mr and Lady Rose Leigh, old silver teapot * Colonel Hon. F Wellesley, silver urn * Lord Herbert Vane-Tempest, silver cigarette box * General and Mrs Owen Williams, silver teapot * Hon. H and Lady Feodore Sturt and Sir and Lady Magdalen Bulkeley, luncheon case * Sir Thomas Dancer, inkstand * Mr and Mrs Hwfa Williams, silver kettle * Sir Oscar Clayton, silver mustard pot * Sir Gerald Codrington, silver match box * Sir Charles Hartopp, cigarette holder in gold case * Dowager Countess of Lonsdale, old ink bottle * Marquis and Marchioness of Cholmondeley, silver cigarette case * Countess of Aylesford, tortoiseshell and silver box * Earl and Countess of Hardwicke, old silver Inkstand * Mr Meredith Brown, old silver inkstand * Colonel Henn, case of boot hooks * Mr Majoribanks, writing table * Mr Fuller, silver candlesticks * Mr Audley Lovell, hunting whip * Mr Dawson, silver clock * Mr Hugh Owen, two silver mounted match boxes * Major Cotes, silver box * Mr and Mrs Sandford, piece of marqueterie furniture * Mr and Mrs Bristowe, old dessert spoons * Mr R Sheriffe, old silver flask * Colonel Townsend, cigarette box * Baron M de Tuyll, pair of silver candlesticks * Mr Caryl Craven, looking glass * Mr Berkeley Levett, old silver match box * Mr I Williams, silver cigarette case * Mr B Peel, pair of old silver candlesticks * Mr Edward Beaumont, old silver spoons * Mr Coleman, silver horn cigarette lighter * Mr Frank Gore, clock and weather glass * Mr Hugh Clutterbuck, old silver toothpick box * Mr [H?] Clutterbuck, sliver mounted decanter * Mr Graham Smith, racing bag * Mr R Charteris, silver cream jug * Mr Geoffrey Glyn, walking stick * Mr Austin Mackenzie, liqueur bottles * Hon. F Sturt, luncheon basket [listed twice?] * Mr Albert Stopford, pepper pots * Southdacon farm labourers, cigarette case * Mr Oswald Magniac, high screen * Mr J Hargreaves, grandfather's clock * Mr T Laycock, tea and coffee pots and sugar basin * Sir Roger Palmer, silver sugar basin and spoon * Captain Julian Spicer, dog cigarette lighter * Mr W Harford, silver cow cream jug * Mr Archie Miles, silver headed walking stick * Mr and Mrs Arthur Wilson, breakfast cruet and silver match box * Mr and Mrs Caldwell, cigarette lighter * Captain and Mrs Napier Miles, silver cream jug * Mr Mattingley, driving whip * Mr Seymore Gore, liqueur glasses * Mr Geoffrey Glyn, walking stick * Captain Longfietd, silver cigarette lighter * The tenants the Draycot estate presented Lord Dangan with a large silver urn: [sic] andthe [sic] employês [sic] the estate gave a lamp.<ref name=":0">"The Marriage of Lord Dangan and Lady Violet Nevill." ''Devizes and Wiltshire Gazette'' 24 December 1889, Tuesday: 8 [of 8], Col. 3a–c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000360/18891224/068/0008. Same print title and p.</ref> </blockquote> == Notes and Questions == # ==References== {{reflist}} o1u0x9w80gcossimjohsq9s2joa50qk 2 322215 2719927 2719926 2025-06-28T12:16:35Z Alandmanson 1669821 /* Genus Agenioideus Ashmead, 1902 */ 2719927 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>'''] === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === ''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) ''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== ''Anoplius aethiopicus'' Arnold, 1937 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) ''Anoplius alecto'' Arnold, 1959 (South Africa) ''Anoplius bifasciatus'' Tullgren, 1904 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) ''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) ''Anoplius fuscus'' ''fuscus'' Arnold, 1937 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania) ''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) ''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) ''Anoplius morosus'' Smith, 1855 (Ethiopia, South Africa) ''Anoplius octomaculatus'' Arnold, 1951 (Mali) ''Anoplius panmelas'' (Saussure, 1891) (Madagascar) ''Anoplius saegeri'' Arnold, 1937 (Democratic Republic of Congo) ''Anoplius subfasciatus'' Arnold, 1937 (South Africa, Uganda, Zimbabwe) ''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) ''Anoplius viridicatus'' Smith, 1879 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== ''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) ''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== *''Microphadnus bicolor'' Cameron, 1905 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== ''Pompilioides braunsi'' Kohl, 1894 (Cameroon) ''Pompilioides decipiens'' Arnold, 1936 (South Africa) ''Pompilioides latifrons'' Arnold, 1936 (South Africa) ''Pompilioides pruinosus'' Smith, 1855 (South Africa, Zimbabwe) ''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) ''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) ''Pompilioides validus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== ''Psammoderes capensis'' Arnold, 1937 (South Africa) ''Psammoderes collaris'' Saussure, 1891 (Madagascar) ''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) ''Psammoderes lightfooti'' Arnold, 1937 (South Africa) ''Psammoderes longicollis'' Arnold, 1937 (Democratic Republic of Congo) ''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) ''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) ''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) ''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''<u>Tachypompilus</u>'' ''<u>ignitus</u>''] (Smith, 1855) (South Africa, Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''<u>Tachypompilus</u>'' ''<u>ovambo</u>''] (Arnold, 1937) (Namibia) ''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''<u>Tachypompilus</u>''] ''<u>vitripennis</u>'' (Arnold, 1937) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== 7kv861zdt17w5hrg6sci4o8cl3us2nk 2719928 2719927 2025-06-28T12:18:06Z Alandmanson 1669821 /* Genus Agenioideus Ashmead, 1902 */ 2719928 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>'''] === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === ''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) ''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== ''Anoplius aethiopicus'' Arnold, 1937 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) ''Anoplius alecto'' Arnold, 1959 (South Africa) ''Anoplius bifasciatus'' Tullgren, 1904 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) ''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) ''Anoplius fuscus'' ''fuscus'' Arnold, 1937 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania) ''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) ''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) ''Anoplius morosus'' Smith, 1855 (Ethiopia, South Africa) ''Anoplius octomaculatus'' Arnold, 1951 (Mali) ''Anoplius panmelas'' (Saussure, 1891) (Madagascar) ''Anoplius saegeri'' Arnold, 1937 (Democratic Republic of Congo) ''Anoplius subfasciatus'' Arnold, 1937 (South Africa, Uganda, Zimbabwe) ''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) ''Anoplius viridicatus'' Smith, 1879 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== ''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) ''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== *''Microphadnus bicolor'' Cameron, 1905 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== ''Pompilioides braunsi'' Kohl, 1894 (Cameroon) ''Pompilioides decipiens'' Arnold, 1936 (South Africa) ''Pompilioides latifrons'' Arnold, 1936 (South Africa) ''Pompilioides pruinosus'' Smith, 1855 (South Africa, Zimbabwe) ''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) ''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) ''Pompilioides validus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== ''Psammoderes capensis'' Arnold, 1937 (South Africa) ''Psammoderes collaris'' Saussure, 1891 (Madagascar) ''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) ''Psammoderes lightfooti'' Arnold, 1937 (South Africa) ''Psammoderes longicollis'' Arnold, 1937 (Democratic Republic of Congo) ''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) ''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) ''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) ''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''<u>Tachypompilus</u>'' ''<u>ignitus</u>''] (Smith, 1855) (South Africa, Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''<u>Tachypompilus</u>'' ''<u>ovambo</u>''] (Arnold, 1937) (Namibia) ''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''<u>Tachypompilus</u>''] ''<u>vitripennis</u>'' (Arnold, 1937) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== njrard47ra95w821wi9y8mq42bf8kdu 2719929 2719928 2025-06-28T12:19:47Z Alandmanson 1669821 /* Genus Anoplius Dufour, 1834 */ 2719929 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>'''] === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === ''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) ''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' ''fuscus'' Arnold, 1937 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania) *''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855 (Ethiopia, South Africa) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937 (South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== ''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) ''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== *''Microphadnus bicolor'' Cameron, 1905 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== ''Pompilioides braunsi'' Kohl, 1894 (Cameroon) ''Pompilioides decipiens'' Arnold, 1936 (South Africa) ''Pompilioides latifrons'' Arnold, 1936 (South Africa) ''Pompilioides pruinosus'' Smith, 1855 (South Africa, Zimbabwe) ''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) ''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) ''Pompilioides validus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== ''Psammoderes capensis'' Arnold, 1937 (South Africa) ''Psammoderes collaris'' Saussure, 1891 (Madagascar) ''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) ''Psammoderes lightfooti'' Arnold, 1937 (South Africa) ''Psammoderes longicollis'' Arnold, 1937 (Democratic Republic of Congo) ''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) ''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) ''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) ''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''<u>Tachypompilus</u>'' ''<u>ignitus</u>''] (Smith, 1855) (South Africa, Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''<u>Tachypompilus</u>'' ''<u>ovambo</u>''] (Arnold, 1937) (Namibia) ''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''<u>Tachypompilus</u>''] ''<u>vitripennis</u>'' (Arnold, 1937) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== etsp1d9itx6y2edobywhbxrx07u505b 2719930 2719929 2025-06-28T12:31:34Z Alandmanson 1669821 /* Genus Anoplius Dufour, 1834 */ 2719930 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>'''] === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === ''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) ''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus''L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== ''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) ''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== *''Microphadnus bicolor'' Cameron, 1905 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== ''Pompilioides braunsi'' Kohl, 1894 (Cameroon) ''Pompilioides decipiens'' Arnold, 1936 (South Africa) ''Pompilioides latifrons'' Arnold, 1936 (South Africa) ''Pompilioides pruinosus'' Smith, 1855 (South Africa, Zimbabwe) ''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) ''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) ''Pompilioides validus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== ''Psammoderes capensis'' Arnold, 1937 (South Africa) ''Psammoderes collaris'' Saussure, 1891 (Madagascar) ''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) ''Psammoderes lightfooti'' Arnold, 1937 (South Africa) ''Psammoderes longicollis'' Arnold, 1937 (Democratic Republic of Congo) ''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) ''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) ''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) ''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''<u>Tachypompilus</u>'' ''<u>ignitus</u>''] (Smith, 1855) (South Africa, Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''<u>Tachypompilus</u>'' ''<u>ovambo</u>''] (Arnold, 1937) (Namibia) ''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''<u>Tachypompilus</u>''] ''<u>vitripennis</u>'' (Arnold, 1937) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== hutr026p7krq3fyo7yuzuggb087yw95 2719931 2719930 2025-06-28T12:32:18Z Alandmanson 1669821 /* Genus Anoplius Dufour, 1834 */ 2719931 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>'''] === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === ''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) ''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== ''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) ''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== *''Microphadnus bicolor'' Cameron, 1905 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== ''Pompilioides braunsi'' Kohl, 1894 (Cameroon) ''Pompilioides decipiens'' Arnold, 1936 (South Africa) ''Pompilioides latifrons'' Arnold, 1936 (South Africa) ''Pompilioides pruinosus'' Smith, 1855 (South Africa, Zimbabwe) ''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) ''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) ''Pompilioides validus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== ''Psammoderes capensis'' Arnold, 1937 (South Africa) ''Psammoderes collaris'' Saussure, 1891 (Madagascar) ''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) ''Psammoderes lightfooti'' Arnold, 1937 (South Africa) ''Psammoderes longicollis'' Arnold, 1937 (Democratic Republic of Congo) ''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) ''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) ''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) ''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''<u>Tachypompilus</u>'' ''<u>ignitus</u>''] (Smith, 1855) (South Africa, Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''<u>Tachypompilus</u>'' ''<u>ovambo</u>''] (Arnold, 1937) (Namibia) ''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''<u>Tachypompilus</u>''] ''<u>vitripennis</u>'' (Arnold, 1937) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== cuj1nto7plojgteyyo74c5ypckdflfd 2719932 2719931 2025-06-28T12:35:09Z Alandmanson 1669821 /* Genus Microphadnus Cameron, 1904 */ 2719932 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>'''] === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === ''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) ''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== ''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) ''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== ''Pompilioides braunsi'' Kohl, 1894 (Cameroon) ''Pompilioides decipiens'' Arnold, 1936 (South Africa) ''Pompilioides latifrons'' Arnold, 1936 (South Africa) ''Pompilioides pruinosus'' Smith, 1855 (South Africa, Zimbabwe) ''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) ''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) ''Pompilioides validus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== ''Psammoderes capensis'' Arnold, 1937 (South Africa) ''Psammoderes collaris'' Saussure, 1891 (Madagascar) ''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) ''Psammoderes lightfooti'' Arnold, 1937 (South Africa) ''Psammoderes longicollis'' Arnold, 1937 (Democratic Republic of Congo) ''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) ''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) ''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) ''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''<u>Tachypompilus</u>'' ''<u>ignitus</u>''] (Smith, 1855) (South Africa, Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''<u>Tachypompilus</u>'' ''<u>ovambo</u>''] (Arnold, 1937) (Namibia) ''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''<u>Tachypompilus</u>''] ''<u>vitripennis</u>'' (Arnold, 1937) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== tpxvcmeveco31q9ybn6fkrmdctjc6nf 2719933 2719932 2025-06-28T12:38:25Z Alandmanson 1669821 /* Genus Psammoderes Haupt, 1929 */ 2719933 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>'''] === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === ''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) ''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== ''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) ''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== ''Pompilioides braunsi'' Kohl, 1894 (Cameroon) ''Pompilioides decipiens'' Arnold, 1936 (South Africa) ''Pompilioides latifrons'' Arnold, 1936 (South Africa) ''Pompilioides pruinosus'' Smith, 1855 (South Africa, Zimbabwe) ''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) ''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) ''Pompilioides validus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== ''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) ''Psammoderes collaris'' Saussure, 1891 (Madagascar) ''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) ''Psammoderes lightfooti'' Arnold, 1937 (South Africa) ''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) ''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) ''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) ''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) ''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''<u>Tachypompilus</u>'' ''<u>ignitus</u>''] (Smith, 1855) (South Africa, Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''<u>Tachypompilus</u>'' ''<u>ovambo</u>''] (Arnold, 1937) (Namibia) ''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''<u>Tachypompilus</u>''] ''<u>vitripennis</u>'' (Arnold, 1937) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== oaeuzruzrynyaqzpciib84jbbww89yp 2719934 2719933 2025-06-28T12:39:31Z Alandmanson 1669821 /* Genus Psammoderes Haupt, 1929 */ 2719934 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>'''] === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === ''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) ''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== ''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) ''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== ''Pompilioides braunsi'' Kohl, 1894 (Cameroon) ''Pompilioides decipiens'' Arnold, 1936 (South Africa) ''Pompilioides latifrons'' Arnold, 1936 (South Africa) ''Pompilioides pruinosus'' Smith, 1855 (South Africa, Zimbabwe) ''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) ''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) ''Pompilioides validus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''<u>Tachypompilus</u>'' ''<u>ignitus</u>''] (Smith, 1855) (South Africa, Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''<u>Tachypompilus</u>'' ''<u>ovambo</u>''] (Arnold, 1937) (Namibia) ''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''<u>Tachypompilus</u>''] ''<u>vitripennis</u>'' (Arnold, 1937) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== 2a1if02qg67plhqjycjzwln8paqhw1u 2719935 2719934 2025-06-28T12:40:47Z Alandmanson 1669821 /* Genus Psammoderes Haupt, 1929 */ 2719935 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>'''] === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === ''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) ''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== ''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) ''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== ''Pompilioides braunsi'' Kohl, 1894 (Cameroon) ''Pompilioides decipiens'' Arnold, 1936 (South Africa) ''Pompilioides latifrons'' Arnold, 1936 (South Africa) ''Pompilioides pruinosus'' Smith, 1855 (South Africa, Zimbabwe) ''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) ''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) ''Pompilioides validus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''<u>Tachypompilus</u>'' ''<u>ignitus</u>''] (Smith, 1855) (South Africa, Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''<u>Tachypompilus</u>'' ''<u>ovambo</u>''] (Arnold, 1937) (Namibia) ''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''<u>Tachypompilus</u>''] ''<u>vitripennis</u>'' (Arnold, 1937) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== r1r1n54toyuczmtad40r86mrawuvxs7 2719939 2719935 2025-06-28T12:53:58Z Alandmanson 1669821 /* Genus Tachypompilus Ashmead, 1902 */ 2719939 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>'''] === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === ''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) ''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== ''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) ''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== ''Pompilioides braunsi'' Kohl, 1894 (Cameroon) ''Pompilioides decipiens'' Arnold, 1936 (South Africa) ''Pompilioides latifrons'' Arnold, 1936 (South Africa) ''Pompilioides pruinosus'' Smith, 1855 (South Africa, Zimbabwe) ''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) ''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) ''Pompilioides validus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== 8w0uhywmcdlqlsjb6nabqpg1eos72r9 2719940 2719939 2025-06-28T12:57:19Z Alandmanson 1669821 /* Genus Aetheopompilus Arnold, 1934 */ 2719940 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>'''] === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === ''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) ''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== ''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) ''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== ''Pompilioides braunsi'' Kohl, 1894 (Cameroon) ''Pompilioides decipiens'' Arnold, 1936 (South Africa) ''Pompilioides latifrons'' Arnold, 1936 (South Africa) ''Pompilioides pruinosus'' Smith, 1855 (South Africa, Zimbabwe) ''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) ''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) ''Pompilioides validus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== 94843ao26wrrhhp5dt4dgjfbsgcvgyh 2719941 2719940 2025-06-28T13:01:08Z Alandmanson 1669821 /* Genus Pompilioides Radley, 1887 */ 2719941 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>'''] === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === ''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) ''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== ''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) ''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== m8qdqdrknxboa0rtyjnxgmb6xm4undz 2719942 2719941 2025-06-28T13:13:11Z Alandmanson 1669821 /* Afrotropical Pompilinae */ 2719942 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75 includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === ''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) ''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== ''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) ''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== 42shgjvrlf15jm1m8vaurq76l7kdt06 2719943 2719942 2025-06-28T13:13:32Z Alandmanson 1669821 /* Afrotropical Pompilinae */ 2719943 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === ''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) ''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== ''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) ''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== 2wydx8bdd756bk7s8uuci2c63d6bzz3 2719944 2719943 2025-06-28T13:14:18Z Alandmanson 1669821 /* Afrotropical Pompilinae */ 2719944 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === ''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) ''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== ''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) ''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== 71b468ibkob5j7mxbqbtbj1qnrwhwsl 2719945 2719944 2025-06-28T13:14:47Z Alandmanson 1669821 /* Genus Aeluropetrus Arnold, 1936 */ 2719945 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== ''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) ''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== 33si154wn9j0idx1oayupufi5yg6bsl 2719946 2719945 2025-06-28T13:15:26Z Alandmanson 1669821 /* Genus Apareia Haupt, 1929 */ 2719946 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== ''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== gma4lre5biga244u3alhf16i8ffvrgg 2719947 2719946 2025-06-28T13:15:42Z Alandmanson 1669821 /* Genus Aporinellus Banks, 1911 */ 2719947 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== ''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== szmcueconwow3oll7y52zs6hglsltjc 2719948 2719947 2025-06-28T13:31:26Z Alandmanson 1669821 /* Genus Aporoideus Ashmead, 1902 */ 2719948 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== ''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== bsrm8bf3ifyp4fua3hwv0kdl0p7emk3 2719949 2719948 2025-06-28T13:31:40Z Alandmanson 1669821 /* Genus Arachnospila Kincaid, 1900 */ 2719949 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== km196pwc2r4p9muq7rijm840ikjwbge 2719950 2719949 2025-06-28T13:31:59Z Alandmanson 1669821 /* Genus Bambesa Arnold, 1936 */ 2719950 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== ''Batozonus bipunctatus'' Banks, 1940 (Madagascar) ''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== 6fuib6vcmjfhk22hz6iweg28dfjzbqx 2719951 2719950 2025-06-28T13:32:38Z Alandmanson 1669821 /* Genus Batozonus Ashmead, 1902 */ 2719951 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== *''Batozonus bipunctatus'' Banks, 1940 (Madagascar) *''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== ''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== 7z5eav1mlk2ff077217tfy5i0miowg4 2719952 2719951 2025-06-28T13:33:12Z Alandmanson 1669821 /* Genus Cliochares Banks, 1940 */ 2719952 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== *''Batozonus bipunctatus'' Banks, 1940 (Madagascar) *''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== *''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== ''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) ''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) ''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) ''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) ''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) ''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) ''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== ka5vnwn1ff1bdrbsplf4if0pr248x0a 2719953 2719952 2025-06-28T13:33:52Z Alandmanson 1669821 /* Genus Cordyloscelis Arnold, 1935 */ 2719953 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== *''Batozonus bipunctatus'' Banks, 1940 (Madagascar) *''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== *''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== *''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) *''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) *''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) *''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) *''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) *''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) *''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== ''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== 3p33xaa21rbsqq9chboyg9tlwr4g1mn 2719954 2719953 2025-06-28T13:34:18Z Alandmanson 1669821 /* Genus Ctenagenia Saussure, 1892 */ 2719954 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== *''Batozonus bipunctatus'' Banks, 1940 (Madagascar) *''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== *''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== *''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) *''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) *''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) *''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) *''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) *''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) *''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== *''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === ''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) ''Dromochares fumipennis'' Arnold, 1935 (South Africa) ''Dromochares premnopterus'' Kohl, 1900 (South Africa) ''Dromochares rufipes'' Arnold, 1935 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''<u>Dromochares transvaalensis</u>''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== n8nvdo3hb3wp6p5q4wdmoy92kgrsg4v 2719955 2719954 2025-06-28T13:35:27Z Alandmanson 1669821 /* Genus Dromochares Haupt, 1930 */ 2719955 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== *''Batozonus bipunctatus'' Banks, 1940 (Madagascar) *''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== *''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== *''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) *''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) *''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) *''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) *''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) *''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) *''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== *''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === *''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) *''Dromochares fumipennis'' Arnold, 1935 (South Africa) *''Dromochares premnopterus'' Kohl, 1900 (South Africa) *''Dromochares rufipes'' Arnold, 1935 (South Africa) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''Dromochares transvaalensis''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== ''Epiclinotus capensis'' Arnold, 1959 (South Africa) ''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) ''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== 0tmmiww16rog8zm8rzjncd0t82uwgqf 2719956 2719955 2025-06-28T13:37:03Z Alandmanson 1669821 /* Genus Epiclinotus Haupt, 1929 */ 2719956 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== *''Batozonus bipunctatus'' Banks, 1940 (Madagascar) *''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== *''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== *''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) *''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) *''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) *''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) *''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) *''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) *''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== *''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === *''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) *''Dromochares fumipennis'' Arnold, 1935 (South Africa) *''Dromochares premnopterus'' Kohl, 1900 (South Africa) *''Dromochares rufipes'' Arnold, 1935 (South Africa) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''Dromochares transvaalensis''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== *''Epiclinotus capensis'' Arnold, 1959 (South Africa) *''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) *''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== ''Episyron argillaceus'' Arnold, 1936 (Zambia) ''Episyron bequaerti'' Arnold, 1936 (Liberia) ''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) ''Episyron braunsii'' Arnold, 1936 (South Africa) ''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) ''Episyron gryps'' Saussure, 1890 (Madagascar) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''<u>Episyron histrio</u>''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) ''Episyron pedunculatus'' Arnold, 1936 (Liberia) ''Episyron solitaneum'' Kohl, 1906 (Yemen) ''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) ''Episyron turneri'' Arnold, 1936 (South Africa) ''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) ''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== 0b0itcz15weyuq2qsgb2wy5hk0qk3sb 2719957 2719956 2025-06-28T13:38:01Z Alandmanson 1669821 /* Genus Episyron Schiødte, 1837 */ 2719957 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== *''Batozonus bipunctatus'' Banks, 1940 (Madagascar) *''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== *''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== *''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) *''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) *''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) *''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) *''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) *''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) *''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== *''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === *''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) *''Dromochares fumipennis'' Arnold, 1935 (South Africa) *''Dromochares premnopterus'' Kohl, 1900 (South Africa) *''Dromochares rufipes'' Arnold, 1935 (South Africa) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''Dromochares transvaalensis''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== *''Epiclinotus capensis'' Arnold, 1959 (South Africa) *''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) *''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== *''Episyron argillaceus'' Arnold, 1936 (Zambia) *''Episyron bequaerti'' Arnold, 1936 (Liberia) *''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) *''Episyron braunsii'' Arnold, 1936 (South Africa) *''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) *''Episyron gryps'' Saussure, 1890 (Madagascar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''Episyron histrio''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) *''Episyron pedunculatus'' Arnold, 1936 (Liberia) *''Episyron solitaneum'' Kohl, 1906 (Yemen) *''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) *''Episyron turneri'' Arnold, 1936 (South Africa) *''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) *''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm <u>Euclavelia</u>]'' Arnold, 1932=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''<u>Euclavelia fasciata</u>''] Arnold, 1932 (South Africa) ''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== hyqcpslyy1m8hkdktui3t4abjd3kqaq 2719958 2719957 2025-06-28T13:38:44Z Alandmanson 1669821 /* Genus Euclavelia Arnold, 1932 */ 2719958 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== *''Batozonus bipunctatus'' Banks, 1940 (Madagascar) *''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== *''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== *''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) *''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) *''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) *''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) *''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) *''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) *''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== *''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === *''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) *''Dromochares fumipennis'' Arnold, 1935 (South Africa) *''Dromochares premnopterus'' Kohl, 1900 (South Africa) *''Dromochares rufipes'' Arnold, 1935 (South Africa) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''Dromochares transvaalensis''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== *''Epiclinotus capensis'' Arnold, 1959 (South Africa) *''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) *''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== *''Episyron argillaceus'' Arnold, 1936 (Zambia) *''Episyron bequaerti'' Arnold, 1936 (Liberia) *''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) *''Episyron braunsii'' Arnold, 1936 (South Africa) *''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) *''Episyron gryps'' Saussure, 1890 (Madagascar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''Episyron histrio''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) *''Episyron pedunculatus'' Arnold, 1936 (Liberia) *''Episyron solitaneum'' Kohl, 1906 (Yemen) *''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) *''Episyron turneri'' Arnold, 1936 (South Africa) *''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) *''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm Euclavelia]'' Arnold, 1932=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''Euclavelia fasciata''] Arnold, 1932 (South Africa) *''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== ''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== hw4mtiwnw6nro3ooexgr3gp7l5ecqnb 2719959 2719958 2025-06-28T13:39:22Z Alandmanson 1669821 /* Genus Ferreola Lepeletier, 1845 */ 2719959 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== *''Batozonus bipunctatus'' Banks, 1940 (Madagascar) *''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== *''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== *''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) *''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) *''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) *''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) *''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) *''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) *''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== *''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === *''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) *''Dromochares fumipennis'' Arnold, 1935 (South Africa) *''Dromochares premnopterus'' Kohl, 1900 (South Africa) *''Dromochares rufipes'' Arnold, 1935 (South Africa) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''Dromochares transvaalensis''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== *''Epiclinotus capensis'' Arnold, 1959 (South Africa) *''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) *''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== *''Episyron argillaceus'' Arnold, 1936 (Zambia) *''Episyron bequaerti'' Arnold, 1936 (Liberia) *''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) *''Episyron braunsii'' Arnold, 1936 (South Africa) *''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) *''Episyron gryps'' Saussure, 1890 (Madagascar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''Episyron histrio''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) *''Episyron pedunculatus'' Arnold, 1936 (Liberia) *''Episyron solitaneum'' Kohl, 1906 (Yemen) *''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) *''Episyron turneri'' Arnold, 1936 (South Africa) *''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) *''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm Euclavelia]'' Arnold, 1932=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''Euclavelia fasciata''] Arnold, 1932 (South Africa) *''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== *''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== ''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) ''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== b4o6l2k6hqamvgjo0tavqv9wyiprn09 2719960 2719959 2025-06-28T13:39:36Z Alandmanson 1669821 /* Genus Ferreoloides Haupt, 1919 */ 2719960 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== *''Batozonus bipunctatus'' Banks, 1940 (Madagascar) *''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== *''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== *''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) *''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) *''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) *''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) *''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) *''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) *''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== *''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === *''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) *''Dromochares fumipennis'' Arnold, 1935 (South Africa) *''Dromochares premnopterus'' Kohl, 1900 (South Africa) *''Dromochares rufipes'' Arnold, 1935 (South Africa) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''Dromochares transvaalensis''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== *''Epiclinotus capensis'' Arnold, 1959 (South Africa) *''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) *''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== *''Episyron argillaceus'' Arnold, 1936 (Zambia) *''Episyron bequaerti'' Arnold, 1936 (Liberia) *''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) *''Episyron braunsii'' Arnold, 1936 (South Africa) *''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) *''Episyron gryps'' Saussure, 1890 (Madagascar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''Episyron histrio''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) *''Episyron pedunculatus'' Arnold, 1936 (Liberia) *''Episyron solitaneum'' Kohl, 1906 (Yemen) *''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) *''Episyron turneri'' Arnold, 1936 (South Africa) *''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) *''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm Euclavelia]'' Arnold, 1932=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''Euclavelia fasciata''] Arnold, 1932 (South Africa) *''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== *''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== *''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) *''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== ''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== cwkedela9yp129bt8azzq60ab9ao0w4 2719961 2719960 2025-06-28T13:40:32Z Alandmanson 1669821 /* Genus Guichardia Arnold, 1951 */ 2719961 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== *''Batozonus bipunctatus'' Banks, 1940 (Madagascar) *''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== *''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== *''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) *''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) *''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) *''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) *''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) *''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) *''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== *''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === *''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) *''Dromochares fumipennis'' Arnold, 1935 (South Africa) *''Dromochares premnopterus'' Kohl, 1900 (South Africa) *''Dromochares rufipes'' Arnold, 1935 (South Africa) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''Dromochares transvaalensis''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== *''Epiclinotus capensis'' Arnold, 1959 (South Africa) *''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) *''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== *''Episyron argillaceus'' Arnold, 1936 (Zambia) *''Episyron bequaerti'' Arnold, 1936 (Liberia) *''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) *''Episyron braunsii'' Arnold, 1936 (South Africa) *''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) *''Episyron gryps'' Saussure, 1890 (Madagascar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''Episyron histrio''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) *''Episyron pedunculatus'' Arnold, 1936 (Liberia) *''Episyron solitaneum'' Kohl, 1906 (Yemen) *''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) *''Episyron turneri'' Arnold, 1936 (South Africa) *''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) *''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm Euclavelia]'' Arnold, 1932=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''Euclavelia fasciata''] Arnold, 1932 (South Africa) *''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== *''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== *''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) *''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== *''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== ''Hadropompilus braunsi'' Arnold, 1934 (South Africa) ''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== a684crk7ng661f9quhvyk5ivkc9mzrx 2719962 2719961 2025-06-28T13:40:54Z Alandmanson 1669821 /* Genus Hadropompilus Arnold, 1934 */ 2719962 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== *''Batozonus bipunctatus'' Banks, 1940 (Madagascar) *''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== *''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== *''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) *''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) *''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) *''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) *''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) *''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) *''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== *''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === *''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) *''Dromochares fumipennis'' Arnold, 1935 (South Africa) *''Dromochares premnopterus'' Kohl, 1900 (South Africa) *''Dromochares rufipes'' Arnold, 1935 (South Africa) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''Dromochares transvaalensis''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== *''Epiclinotus capensis'' Arnold, 1959 (South Africa) *''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) *''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== *''Episyron argillaceus'' Arnold, 1936 (Zambia) *''Episyron bequaerti'' Arnold, 1936 (Liberia) *''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) *''Episyron braunsii'' Arnold, 1936 (South Africa) *''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) *''Episyron gryps'' Saussure, 1890 (Madagascar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''Episyron histrio''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) *''Episyron pedunculatus'' Arnold, 1936 (Liberia) *''Episyron solitaneum'' Kohl, 1906 (Yemen) *''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) *''Episyron turneri'' Arnold, 1936 (South Africa) *''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) *''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm Euclavelia]'' Arnold, 1932=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''Euclavelia fasciata''] Arnold, 1932 (South Africa) *''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== *''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== *''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) *''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== *''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== *''Hadropompilus braunsi'' Arnold, 1934 (South Africa) *''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== ''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== gt1t001sta0m212ww9vfufwtubyqc0a 2719963 2719962 2025-06-28T13:41:11Z Alandmanson 1669821 /* Genus Hauptiella Arnold, 1936 */ 2719963 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== *''Batozonus bipunctatus'' Banks, 1940 (Madagascar) *''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== *''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== *''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) *''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) *''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) *''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) *''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) *''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) *''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== *''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === *''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) *''Dromochares fumipennis'' Arnold, 1935 (South Africa) *''Dromochares premnopterus'' Kohl, 1900 (South Africa) *''Dromochares rufipes'' Arnold, 1935 (South Africa) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''Dromochares transvaalensis''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== *''Epiclinotus capensis'' Arnold, 1959 (South Africa) *''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) *''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== *''Episyron argillaceus'' Arnold, 1936 (Zambia) *''Episyron bequaerti'' Arnold, 1936 (Liberia) *''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) *''Episyron braunsii'' Arnold, 1936 (South Africa) *''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) *''Episyron gryps'' Saussure, 1890 (Madagascar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''Episyron histrio''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) *''Episyron pedunculatus'' Arnold, 1936 (Liberia) *''Episyron solitaneum'' Kohl, 1906 (Yemen) *''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) *''Episyron turneri'' Arnold, 1936 (South Africa) *''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) *''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm Euclavelia]'' Arnold, 1932=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''Euclavelia fasciata''] Arnold, 1932 (South Africa) *''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== *''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== *''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) *''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== *''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== *''Hadropompilus braunsi'' Arnold, 1934 (South Africa) *''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== *''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''<u>Herpetosphex</u>''] Arnold, 1940=== [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''<u>Herpetosphex staphylinoides</u>''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== iw6b88l5fw35p11e3uafz5of7fbssew 2719964 2719963 2025-06-28T13:41:51Z Alandmanson 1669821 /* Genus Herpetosphex Arnold, 1940 */ 2719964 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== *''Batozonus bipunctatus'' Banks, 1940 (Madagascar) *''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== *''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== *''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) *''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) *''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) *''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) *''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) *''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) *''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== *''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === *''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) *''Dromochares fumipennis'' Arnold, 1935 (South Africa) *''Dromochares premnopterus'' Kohl, 1900 (South Africa) *''Dromochares rufipes'' Arnold, 1935 (South Africa) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''Dromochares transvaalensis''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== *''Epiclinotus capensis'' Arnold, 1959 (South Africa) *''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) *''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== *''Episyron argillaceus'' Arnold, 1936 (Zambia) *''Episyron bequaerti'' Arnold, 1936 (Liberia) *''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) *''Episyron braunsii'' Arnold, 1936 (South Africa) *''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) *''Episyron gryps'' Saussure, 1890 (Madagascar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''Episyron histrio''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) *''Episyron pedunculatus'' Arnold, 1936 (Liberia) *''Episyron solitaneum'' Kohl, 1906 (Yemen) *''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) *''Episyron turneri'' Arnold, 1936 (South Africa) *''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) *''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm Euclavelia]'' Arnold, 1932=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''Euclavelia fasciata''] Arnold, 1932 (South Africa) *''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== *''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== *''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) *''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== *''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== *''Hadropompilus braunsi'' Arnold, 1934 (South Africa) *''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== *''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''Herpetosphex''] Arnold, 1940=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''Herpetosphex staphylinoides''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? ''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) ''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) ''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) ''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) ''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) ''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) ''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) ''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) ''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) ''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) ''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) ''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== artq2uf6b5v7ex4fd54e2w2iywvsy0c 2719965 2719964 2025-06-28T13:42:38Z Alandmanson 1669821 /* Genus Homonotus Dahlbom, 1844 */ 2719965 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== *''Batozonus bipunctatus'' Banks, 1940 (Madagascar) *''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== *''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== *''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) *''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) *''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) *''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) *''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) *''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) *''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== *''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === *''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) *''Dromochares fumipennis'' Arnold, 1935 (South Africa) *''Dromochares premnopterus'' Kohl, 1900 (South Africa) *''Dromochares rufipes'' Arnold, 1935 (South Africa) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''Dromochares transvaalensis''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== *''Epiclinotus capensis'' Arnold, 1959 (South Africa) *''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) *''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== *''Episyron argillaceus'' Arnold, 1936 (Zambia) *''Episyron bequaerti'' Arnold, 1936 (Liberia) *''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) *''Episyron braunsii'' Arnold, 1936 (South Africa) *''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) *''Episyron gryps'' Saussure, 1890 (Madagascar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''Episyron histrio''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) *''Episyron pedunculatus'' Arnold, 1936 (Liberia) *''Episyron solitaneum'' Kohl, 1906 (Yemen) *''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) *''Episyron turneri'' Arnold, 1936 (South Africa) *''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) *''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm Euclavelia]'' Arnold, 1932=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''Euclavelia fasciata''] Arnold, 1932 (South Africa) *''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== *''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== *''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) *''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== *''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== *''Hadropompilus braunsi'' Arnold, 1934 (South Africa) *''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== *''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''Herpetosphex''] Arnold, 1940=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''Herpetosphex staphylinoides''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? *''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) *''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) *''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) *''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) *''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) *''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) *''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) *''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) *''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) *''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) *''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) *''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== ''Idopompilus algoensis'' Arnold, 1936 (South Africa) ''Idopompilus algoensis major'' Arnold, 1935 (South Africa) ''Idopompilus braunsi'' Kohl, 1899 (South Africa) ''Idopompilus brunnescens'' Arnold, 1936 (South Africa) ''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) ''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) ''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) ''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) ''Idopompilus handlirschii'' Arnold, 1936 (South Africa) ''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) ''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== 0n9eqld5r11xr1a2lsrdpldeyxsnjp4 2719966 2719965 2025-06-28T13:43:29Z Alandmanson 1669821 /* Genus Idopompilus Haupt, 1930 */ 2719966 wikitext text/x-wiki Done to Genus Euryzonotulus Description of genus and species in Arnold, 1937, p. 38. ==Afrotropical Ctenocerinae== - Key in Arnold, 1932 (Arnold, G. 1932. The Psammocharidae of the Ethiopian region. Part II. Subfamily Claveliinae, Haupt. Annals of the Transvaal Museum 15: 41-122.)<br> - Claveliinae corrected to Ctenocerinae in Arnold, G. 1934 pp.386-388<br> - Several new genera and species in Arnold, G. 1934 pp.388-399<br> <br> <br> ==Afrotropical Pepsinae== Pepsinae can be defined by: *sternite 2 with a distinct transverse groove; *mesofemur and metafemur without subapical spine-like setae set in grooves or pits; *metatibia with apical spine-like setae of uniform length, setae not splayed; and *vein Cu1 of fore wing is simple at its base, without any definite downward deflection, i.e. the second discal cell (2D) is without a ‘pocket’.<ref name=Waichert2015></ref><ref name=Brothers1993>Brothers, D. J. & Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. & Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143</ref> These spider wasps display a range of nesting behaviours: *using preexisting cavities; *using the immobilised spider’s burrow; *digging a burrow in soil; *building nests of mud; *parasitoids; and *kleptoparasites.<ref name=Waichert2015> Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., & Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287.</ref> ===Tribe Ageniellini (Mud-nesting Spider Wasps)=== Genus ''Arpactomorpha'' - One Afrotropical species (Uganda)<br> Genus ''Auplopus'' - Many Afrotropical species, 36 in SA. Many described as ''Pseudagenia'' in Arnold, 1934, pp. 290-364.<br> Genus ''Cyemagenia'' - 6 Afrotropical species, 3 in SA. (Arnold, 1934, pp. 380-385.)<br> Genus ''Dichragenia'' - 3 Afrotropical species, 2 in SA. (in waspweb; ''Pseudagenia'' in iNat).<br> *''D. pulchricoma'' = ''Pseudagenia pulchricoma'' Arnold, 1934, p. 337-340<br> *''D. neavei'' = ''Pseudagenia mygnimioides'' Arnold, 1934, pp.336-337 and ''Pseudagenia neavei'' Kohl 1913<br> Genus ''Phanagenia'' - 2 Afrotropical species (Madagascar)<br> Genus ''Poecilagenia'' - 8 Afrotropical species, 4 in SA. - Arnold, 1934, p. 373-377.<br> *also ''Poecilagenia spinosipes'' = ''Trachyglyptus spinosipes'' Arnold, 1934, p. 377-379<br> Also in Ageniellini are the genera ''Ageniella'', ''Eragenia'', ''Fabriogenia'', ''Machaerothrix'', ''Macromerella'', ''Paragenia'', ''Priocnemella'' - No Afrotropical spp. indicated in waspweb (2025) ===Other Afrotropical Pepsinae=== ''Cryptocheilus'' - Key in Arnold, 1932 p.370<br> ''Cyphononyx '' - Key in Arnold, 1932 p.370<br> ''Diplonyx'' (Madagascar)<br> ''Dipogon'' = ''Deuteragenia turneri'', ''D. dregei'', ''D. chirindensis'', ''D. bicolor'' (Arnold, 1934, p. 367-372.)<br> ''Hemipepsis'' - Key in Arnold, 1932 p.318<br> ''Hormopogonius'' (''Hormopogonius willowmorensis'' = ''Calicurgus willowmorensis'' Arnold, 1932 p.395); also ''H. tenuicornis'' Arnold, 1934, pp. 379-380<br> ''Java'' <br> ''Micragenia'' - Genus and 2 spp. described in Arnold, 1934 p.286-288.<br> ''Monodontonyx'' <br> ''Phanagenia'' (Madagascar)<br> ''Priocnemis'' - Key in Arnold, 1932 p.379<br> *Also ''Priocnernis aterrimus'' Arnold, 1934, pp. 385-386. *''Priocnemis meridionalis'' Arnold, 1934, p. 386. ''Schistonyx'' <br> <br> <br> ==Afrotropical Pompilinae== List of genera and species from [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm '''<u>https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Classification/index.htm</u>''']<br> Arnold (1937, p. 75-81) includes a "Key to the tribes and genera of the subfamily Psammocharinae" (Pompilinae) === '''Genus''' ''Aeluropetrus'' Arnold, 1936 === *''Aeluropetrus braunsi'' Arnold, 1936 (South Africa) *''Aeluropetrus lugubris'' Arnold, 1936 (South Africa) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/index.htm ''<u>Aetheopompilus</u>''] Arnold, 1934 === *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Aetheopompilus/Aetheopompilus_obliquetruncatus.htm ''<u>Aetheopompilus obliquetruncatus</u>''] Arnold, 1934; descr. in Arnold, 1937, p. 73 (Mozambique) ==='''Genus''' ''Agenioideus'' Ashmead, 1902=== *''Agenioideus lascivus'' (Cameron, 1891) (?) Accepted species in https://www.catalogueoflife.org/data/taxon/5TS6V 2025-06-28 *''Agenioideus rutilus'' (Klug, 1834) (Yemen) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6M 2025-06-28 *''Agenioideus rufipes'' (Arnold, 1937) (Namibia) Accepted species in https://www.catalogueoflife.org/data/taxon/65S6L 2025-06-28 *''Agenioideus waltlii'' (Spinola, 1838)(Ghana, Zimbabwe) Accepted species in https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Agenioideus cinnamomeus'' (Arnold, 1937) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28 ** = ''Psammochares cinnamomeus'' (Arnold, 1937, p52) https://www.catalogueoflife.org/data/taxon/65S86 2025-06-28<br> ''Agenioideus brevis'' (Arnold, 1937) (South Africa) is a synonym of ''Psammochares brevis'' (https://www.catalogueoflife.org/data/taxon/4NBRN 2025-06-28)<br> ''Agenioideus decipiens'' (Bischoff, 1913) (South Africa) is an ambiguous synonym of ''Psammochares decipiens'' Bischoff, 1913 (https://www.catalogueoflife.org/data/taxon/4NBSZ 2025-06-28)<br> ''Agenioideus gibber'' (Arnold, 1937) is a synonym of ''Psammochares gibber''(https://www.catalogueoflife.org/data/taxon/6WBTC 2025-06-28)<br> ''Agenioideus nudatus'' (Smith, 1855) (?) is a synonym of ''Pompilus nudatus'' Smith, 1855<br> (https://www.catalogueoflife.org/data/taxon/4LSLC 2025-06-28) ''Agenioideus rotundilabris'' (Arnold, 1937) (South Africa) - should be ''Psammochares rotundilabris''(Arnold, 1937, p.53.)? ''A. rotundilabris'' is not in CoL 2025-06-28<br> ''Agenioideus varians'' (Arnold, 1937) is a synonym of ''Psammochares varians'' Arnold, 1937 (https://www.catalogueoflife.org/data/taxon/4NC29 2025-06-28)<br> ==='''Genus''' ''Amblyellus'' Day, 1981=== *''Amblyellus willowmorensis'' (Arnold, 1937) (Burkina Faso, Democratic Republic of Congo, Ivory Coast, Senegal, South Africa, Togo) **= ''Psammochares willowmorensis'' Arnold, 1937, p. 51. ==='''Genus''' ''Anoplius'' Dufour, 1834=== Description of genus and key to species in Arnold, 1937, p. 59. *''Anoplius aethiopicus'' Arnold, 1937, p. 62 (Democratic Republic of Congo, Ethiopia, Mozambique, Uganda) *''Anoplius alecto'' Arnold, 1959 (South Africa) *''Anoplius bifasciatus'' Tullgren, 1904; descr. Arnold, 1937, p.60 (Cameroon, Democratic Republic of Congo, Ethiopia, Uganda) *''Anoplius concinnus'' (Dahlbom, 1845) (Yemen) *''Anoplius fuscus'' L. 1761; descr. of several African varieties in Arnold, 1937, p. 65 (Ethiopia, Kenya, Lesotho, South Africa, Tanzania, Zimbabwe) **''Anoplius fuscus'' ''excelsior'' Arnold, 1950 (Tanzania) *''Anoplius montanus'' Haupt, 1950 (Benin, Cameroon, Democratic Republic of Congo, Gabon, Ivory Coast, Liberia, Malawi, Principe Island, Senegal, South Africa, Togo) *''Anoplius morosus'' Smith, 1855; descr. Arnold, 1937, p. 64 (Mozambique, South Africa, Zimbabwe) *''Anoplius octomaculatus'' Arnold, 1951 (Mali) *''Anoplius panmelas'' (Saussure, 1891) (Madagascar) *''Anoplius saegeri'' Arnold, 1937, p. 61 (Democratic Republic of Congo) *''Anoplius subfasciatus'' Arnold, 1937, p. 63 (Kenya, Malawi, South Africa, Uganda, Zimbabwe) *''Anoplius successor'' (Cameron, 1910) (Democratic Republic of Congo, Ethiopia, South Africa, Tanzania, Uganda, Zimbabwe) *''Anoplius viridicatus'' Smith, 1879; descr. Arnold, 1937, p. 62 (West Africa) ==='''Genus''' ''Apareia'' Haupt, 1929=== *''Apareia multipicta rufifemur'' Haupt, 1929; descr. Arnold, 1935, p.449 (Zimbabwe) *''Apareia oedipus'' Kohl, 1886; descr. (synonymized?) as ''A. multipicta'' by Arnold, 1935, p.449 (South Africa) ==='''Genus''' ''Aporinellus'' Banks, 1911=== *''Aporinellus bidens'' (Saussure, 1892) (Madagascar) ==='''Genus''' ''Aporoideus'' Ashmead, 1902=== *''Aporoideus clarus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Arachnospila'' Kincaid, 1900=== *''Arachnospila (Ammosphex) consobrina heringi'' (Haupt, 1928) (California, Canary Islands, Spain, Tanzania, Yemen) ==='''Genus''' ''Argyroclitus'' Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p. 26. *''Argyroclitus fasciatipennis'' Arnold, 1937, p. 27 (South Africa, Zimbabwe) *''Argyroclitus hyalinipennis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus longicollis'' Arnold, 1937, p. 29 (Zimbabwe) *''Argyroclitus rufipes'' Arnold, 1937, p. 28 (Zimbabwe) *''Argyroclitus ruwenzoriensis'' Arnold, 1937, p. 30 (Democratic Republic of the Congo) ==='''Genus''' ''Atelostegus'' Haupt, 1929=== *''Atelostegus thrinax'' (Kohl, 1909) (Madagascar) ==='''Genus''' ''Atopopompilus'' Arnold, 1937=== Description of genus in Arnold, 1937, p. 22. *''Atopompilus jacens'' (Bingham, 1912) (Cameroon, Democratic Republic of Congo, Kenya, Malawi, Nigeria, Senegal, Sierra Leone, South Africa, Sudan, Tanzania, Zaire, Zambia, Zimbabwe, Yemen) *''Atopompilus marshalli'' Arnold, 1937, p. 24 (South Africa, Zimbabwe) *''Atopopompilus venans mlanjiensis'' Arnold, 1937, p. 24 (Ghana) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/index.htm ''<u>Bambesa</u>''] Arnold, 1936=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Bambesa/Bambesa_grisea.htm ''<u>Bambesa grisea</u>''] Arnold, 1936 (Democratic Republic of Congo) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/index.htm ''<u>Batozonellus</u>''] Arnold, 1937=== Description of genus and key to species in Arnold, 1937, p.2. *''Batozonellus capensis'' (Dahlbom, 1843); descr. Arnold, 1937, p.6 (Ethiopia, South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Batozonellus/Batozonellus_fuliginosus.htm ''<u>Batozonellus fuliginosus</u>''] (Klug, 1834); descr. Arnold, 1937, p.3 (Central Africa, South Africa, Yemen, Zimbabwe) *''Batozonellus gowdeyi'' (Turner, 1916); descr. Arnold, 1937, p.7 (Sierra Leone, Uganda) *''Batozonellus madecassus'' (Saussure, 1887) (Madagascar) *''Batozonellus separabilis'' (Turner, 1916); descr. Arnold, 1937, p.9 (Malawi, South Africa, Zimbabwe) ==='''Genus''' ''Batozonus'' Ashmead, 1902=== *''Batozonus bipunctatus'' Banks, 1940 (Madagascar) *''Batozonus capensis'' Dahlbom, 1940 (Ethiopia, South Africa, Uganda) ==='''Genus''' ''Cliochares'' Banks, 1940=== *''Cliochares convexus'' Banks, 1940 (Madagascar) ==='''Genus''' ''Cordyloscelis'' Arnold, 1935=== *''Cordyloscelis bequaerti'' Arnold, 1935, p.420 (Democratic Republic of Congo) *''Cordyloscelis flavipennis'' Arnold, 1935, p.424 (South Africa) *''Cordyloscelis latipes'' Arnold, 1935, p.417 (South Africa) *''Cordyloscelis namaqua'' Arnold, 1935, p.423 (South Africa) *''Cordyloscelis nigerrimus'' Arnold, 1935, p.421 (South Africa) *''Cordyloscelis parallelus'' Arnold, 1946 (Zimbabwe) *''Cordyloscelis ugandensis'' Arnold, 1935, p.425 (Congo, Uganda) ==='''Genus''' ''Ctenagenia'' Saussure, 1892=== *''Ctenagenia vespiformis'' (Klug, 1834) (Djibouti, Egypt, Eritrea, Ethiopia, Greece, Israel, Lebanon, Madagascar, Niger, Nigeria, Portugal, Saudi Arabia, Somalia, Sudan, Syria, Turkey, Yemen) === '''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/index.htm ''<u>Dromochares</u>''] Haupt, 1930 === *''Dromochares clavipennis'' Arnold, 1935 (Zimbabwe) *''Dromochares fumipennis'' Arnold, 1935 (South Africa) *''Dromochares premnopterus'' Kohl, 1900 (South Africa) *''Dromochares rufipes'' Arnold, 1935 (South Africa) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Dromochares/Dromochares_transvaalensis.htm ''Dromochares transvaalensis''] Arnold, 1935 (South Africa) ==='''Genus''' ''Dicyrtomellus'' Gussakovskij, 1935=== Description of genus and key to species in Arnold, 1937, p.14. *''Dicyrtomellus anomalipes'' Arnold, 1937, p.20 (South Africa) *''Dicyrtomellus argenteodecoratus'' Cameron, 1904; descr. Arnold, 1937, p.21 (South Africa, Zimbabwe) *''Dicyrtomellus griseus'' Arnold, 1937, p.17 (Zimbabwe) *''Dicyrtomellus impressus'' Arnold, 1937, p.18 (South Africa, Zimbabwe) *''Dicyrtomellus leptacanthius'' Cameron, 1910; descr. Arnold, 1937, p.16 (Ethiopia, South Africa, Zimbabwe) *''Dicyrtomellus meruensis'' Cameron, 1910 (South Africa, Zimbabwe) *''Dicyrtomellus neavei'' Kohl, 1913; descr. Arnold, 1937, p.19 (Congo) *''Dicyrtomellus rufofemoratus'' Bischoff, 1913; descr. Arnold, 1937, p.17 (South Africa) *''Dicyrtomellus sexspinosus'' (Saunders, 1901) = ''Dicyrtomellus pectinatus'' Arnold, 1937, p.19 (Sudan) ==='''Genus''' ''Elaphrosyron'' Haupt, 1930=== Description of genus and species in Arnold, 1937, p. 40. *''Elaphrosyron insidiosus'' Smith, 1879; descr. Arnold, 1937, p.41 (Ethiopia, Mali, Senegal, South Africa, Zimbabwe) *''Elaphrosyron multipictus'' Arnold, 1937, p.42 (Uganda) *''Elaphrosyron pauperculus'' Arnold, 1959 (South Africa) ==='''Genus''' ''Epiclinotus'' Haupt, 1929=== *''Epiclinotus capensis'' Arnold, 1959 (South Africa) *''Epiclinotus erythrurus'' Haupt, 1929; descr. Arnold, 1935, p.465 (South Africa) *''Epiclinotus turneri'' Haupt, 1929; descr. Arnold, 1935, p.466 (South Africa) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/index.htm ''<u>Episyron</u>''] Schiødte, 1837=== *''Episyron argillaceus'' Arnold, 1936 (Zambia) *''Episyron bequaerti'' Arnold, 1936 (Liberia) *''Episyron bicinctus'' Bischoff, 1913 (South Africa, Zimbabwe) *''Episyron braunsii'' Arnold, 1936 (South Africa) *''Episyron crassicornis'' Arnold, 1936 (Democratic Republic of Congo, Mozambique, Uganda) *''Episyron gryps'' Saussure, 1890 (Madagascar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Episyron/Episyron_histrio.htm ''Episyron histrio''] Lepeletier, 1845 (Democratic Republic of Congo, Ethiopia, Mali, South Africa, Yemen, Zimbabwe) *''Episyron pedunculatus'' Arnold, 1936 (Liberia) *''Episyron solitaneum'' Kohl, 1906 (Yemen) *''Episyron tropicalis'' Arnold, 1936 (Democratic Republic of Congo) *''Episyron turneri'' Arnold, 1936 (South Africa) *''Episyron viduus'' Arnold, 1936 (Namibia, South Africa, Zimbabwe) *''Episyron vindex'' Smith, 1879 (Democratic Republic of Congo, Malawi, South Africa) ==='''Genus''' ''[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/index.htm Euclavelia]'' Arnold, 1932=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Euclavelia/Euclavelia_fasciata.htm ''Euclavelia fasciata''] Arnold, 1932 (South Africa) *''Euclavelia longicollis'' Arnold, 1934 (South Africa) ==='''Genus''' ''Euryzonotulus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 38. *''Euryzonotulus nigeriensis'' Arnold, 1937 (Nigeria, Democratic Republic of the Congo) ==='''Genus''' ''Ferreola'' Lepeletier, 1845=== *''Ferreola auranticornis'' Wahis, 2000 (Eritrea, Yemen) ==='''Genus''' ''Ferreoloides'' Haupt, 1919=== *''Ferreoloides basutorum'' Arnold, 1960 (Lesotho) *''Ferreoloides versutus'' Arnold, 1960 (Lesotho) ==='''Genus''' ''Galactopterus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 32. *''Galactopterus otaviensis'' Arnold, 1937, p. 33 (South Africa) *''Galactopterus rufipes'' Arnold, 1937, p. 32 (Namibia, South Africa) *''Galactopterus simillimus'' Arnold, 1937, p. 34 (South Africa) ==='''Genus''' ''Guichardia'' Arnold, 1951=== *''Guichardia macilenta'' Arnold, 1951 (Ghana, South Africa) ==='''Genus''' ''Hadropompilus'' Arnold, 1934=== *''Hadropompilus braunsi'' Arnold, 1934 (South Africa) *''Hadropompilus montanus'' Arnold, 1936 (South Africa) ==='''Genus''' ''Hauptiella'' Arnold, 1936=== *''Hauptiella multipicta'' Arnold, 1936 ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/index.htm ''Herpetosphex''] Arnold, 1940=== *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Herpetosphex/Herpetosphex_staphylinoides.htm ''Herpetosphex staphylinoides''] Arnold, 1940 (Zimbabwe) ==='''Genus''' ''Homonotus'' Dahlbom, 1844=== Dahlbom 1843 (https://www.biodiversitylibrary.org/page/15796238) or Dahlbom, 1844 (https://www.biodiversitylibrary.org/page/15796653)? *''Homonotus aegyptiacus'' Turner, 1917; descr. Arnold, 1935, p.469 (South Africa, Uganda, Zimbabwe) *''Homonotus coxalis'' Arnold, 1935, p.478 (South Africa) *''Homonotus disparilis'' Turner, 1917; descr. Arnold, 1935, p.473 (South Africa) *''Homonotus dispersus'' Arnold, 1935, p.477 (Namibia, South Africa, Zimbabwe) *''Homonotus dissectus'' Arnold, 1935, p.474 (South Africa) *''Homonotus excavatus'' Arnold, 1935, p.472 (South Africa) *''Homonotus fuscipes'' Arnold, 1935, p.475 (South Africa) *''Homonotus imitans'' Arnold, 1935, p.477 (Zimbabwe) *''Homonotus leptogaster'' Arnold, 1935, p.476 (South Africa) *''Homonotus ruficornis'' Cameron, 1905; descr. Arnold, 1935, p.472 (South Africa) *''Homonotus rukwaensis'' Arnold, 1946 (Tanzania) *''Homonotus sansibaricus'' Arnold, 1935, p.471 (Zanzibar) ==='''Genus''' ''Idopompilus'' Haupt, 1930=== *''Idopompilus algoensis'' Arnold, 1936 (South Africa) *''Idopompilus algoensis major'' Arnold, 1935 (South Africa) *''Idopompilus braunsi'' Kohl, 1899 (South Africa) *''Idopompilus brunnescens'' Arnold, 1936 (South Africa) *''Idopompilus handlirschi handlirschi'' Arnold, 1936 (?) *''Idopompilus handlirschi basutorum'' Arnold, 1959 (Lesotho, South Africa) *''Idopompilus fuliginosus'' Arnold, 1946 (Lesotho) *''Idopompilus gracilicornis'' Arnold, 1936 (South Africa) *''Idopompilus handlirschii'' Arnold, 1936 (South Africa) *''Idopompilus krugeri'' Haupt, 1930 (South Africa, Zimbabwe) *''Idopompilus quadrifasciatus'' Arnold, 1936 (Zimbabwe) ==='''Genus''' ''Kolposphex'' Arnold, 1959=== *''Kolposphex atronitens'' Arnold, 1959 (South Africa) ==='''Genus''' ''Kyphopompilus'' Arnold, 1960=== *''Kyphopompilus flavipes'' Arnold, 1960 (Zimbabwe) ==='''Genus''' ''Microdrapetes'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 30 *''Microdrapetes bellus'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' ''Microphadnus'' Cameron, 1904=== Description of genus in Arnold, 1937, p. 67. *''Microphadnus bicolor'' Cameron, 1905; descr. Arnold, 1937, p. 68 (South Africa) ==='''Genus''' ''Paracyphononyx'' Gribodo, 1884=== ''Paracyphononyx affinis'' Haupt, 1929 (Cameroon, Ghana, Uganda) ''Paracyphononyx africanus'' Rad., 1881 (Angola, Democratic Republic of Congo, Uganda, Zimbabwe) ''Paracyphononyx capensis'' Arnold, 1959 (South Africa) ''Paracyphononyx carinatus'' Rad., 1881 Angola, Sierra Leone, South Africa, Zimbabwe) ''Paracyphononyx coloratus'' Haupt, 1929 (Cameroon) ''Paracyphononyx difficilis'' Bischoff, 1913 (Malai, South Africa, Uganda, Zimbabwe) ''Paracyphononyx diversipes'' Arnold, 1962 (Zimbabwe) ''Paracyphononyx diversus'' Dahlbom, 1845 (Central and East Africa to South Africa, Yemen) ''Paracyphononyx elliotti'' Saussure, 1891 (Madagascar) ''Paracyphononyx frustratus'' Smith, 1879 (South Africa, Uganda, Zimbabwe) ''Paracyphononyx funebris'' Magretti, 1884 (Ethiopia) ''Paracyphononyx gemellus'' Arnold, 1936 (South Africa, Zimbabwe) ''Paracyphononyx laboriosus'' Arnold, 1936 (Ethiopia, South Africa) ''Paracyphononyx languidus'' Haupt, 1929 (South Africa, Zimbabwe) ''Paracyphononyx lukombensis'' Cameron, 1912 (Ethiopia, Kenya, Uganda, Zambia) ''Paracyphononyx metemmensis'' Magretti, 1884 (Ghana, Mali, South Africa, Zimbabwe) ''Paracyphononyx mombassicus'' R. Luc., 1898 (Kenya) ''Paracyphononyx montanus'' Arnold, 1960 (South Africa) ''Paracyphononyx parallelus'' Haupt, 1929 (Democratic Republic of Congo, South Africa) ''Paracyphononyx petiolaris'' Saussure, 1891 (Madagascar) ''Paracyphononyx plutonis'' Banks, 1940 (Madagascar) ''Paracyphononyx rotundinervis'' Cameron, 1910 (Ethiopia, Tanzania, Uganda) ''Paracyphononyx ruficrus'' Klug, 1834 (Asia Minor, Egypt, South Africa, Yemen, Zimbabwe) ''Paracyphononyx zonatus'' Illiger,1802 (Mali, South Africa, Zimbabwe) ==='''Genus''' ''Paraferreola'' Sustera, 1913=== ''Paraferreola melanostoma'' Cameron, 1904; descr. Arnold, 1935, p.439 (South Africa, Zimbabwe) ''Paraferreola spilopus'' Cameron, 1904; descr. Arnold, 1935, p.441 (South Africa) ''Paraferreola soleana'' Cameron, 1905; descr. Arnold, 1935, p.443 (South Africa) ==='''Genus''' ''Platyderes'' Guérin-Méneville, 1844=== ''Platyderes bicolor'' Smith, 1855; descr. Arnold, 1935, p.454 (South Africa) ''Platyderes chalybeus'' Saussure, 1892 (or Tasch. 1880?); descr. Arnold, 1935, p.456 (East Africa, South Africa) ''Platyderes drègii'' Brauns, 1899; descr. Arnold, 1935, p.457 (South Africa) ''Platyderes erythrocephalus'' Guerin, **** (Madagascar) ''Platyderes flavoscutellatus'' Arnold, 1960 (Zimbabwe) ''Platyderes oraniensis'' Arnold, 1935, p.456 (South Africa) ''Platyderes rhodesianus'' Bischoff, 1913; descr. Arnold, 1935, p.461 (Ethiopia, Zimbabwe) ''Platyderes saussurei'' Banks, 1940 (Madagascar) ''Platyderes spoliatus'' Cameron, 1910; descr. Arnold, 1935, p.462 (South Africa, Zimbabwe) ''Platyderes vicinus'' Arnold, 1935, p.460 (South Africa) ''Platyderes wasmanni'' Brauns, 1904; descr. Arnold, 1935, p.459 (South Africa) ==='''Genus''' ''Pompilus'' Fabricius=== ''Pompilus alpinus'' Arnold, 1960 (Democratic Republic of Congo) ''Pompilus anomalopterus'' Cameron, 1908 (Malawi, South Africa) ''Pompilus cinereus'' Fabricius, 1775 (Yemen) ''Pompilus contrarius'' Arnold, 1951 (Mali) ''Pompilus curvifrons'' Cameron, 1908 ( ''Pompilus erythrostomus'' Cameron, 1908 ( ''Pompilus exploratrix'' Cameron, 1908 ''('' ''Pompilus ignobilis'' Arnold, 1959 (South Africa) ''Pompilus levis'' Arnold, 1951 (Ghana) ''Pompilus masaiensis'' Cameron, 1908 ( ''Pompilus meruensis'' Cameron, 1908 ( ''Pompilus plumbeus'' Fabricius, 1787 (Widespread through Africa (Ethiopia, Ghana, Mali, Senegal, South Africa) also in China, Europe, India) ''Pompilus sacchii'' Magretti, 1898 ( ''Pompilus shirae'' Arnold, 1950 (Democratic Republic of Congo) ''Pompilus successor'' Cameron, 1908 ( ''Pompilus vanutelli'' Magretti, 1898 ( ''Pompilus willowmorensis'' Arnold, 1937 (South Africa) ''Pompilus yngvei'' Cameron, 1908 ( ==='''Genus''' ''Pompilioides'' Radley, 1887=== *''Pompilioides braunsi'' Kohl, 1894 (Cameroon) *''Pompilioides decipiens'' Arnold, 1936 (South Africa) *''Pompilioides latifrons'' Arnold, 1936 (South Africa) *''Pompilioides pruinosus'' Smith, 1855; descr. Arnold, 1937, p. 74 (South Africa, Zimbabwe) *''Pompilioides rhodesianus'' Bischoff, 1913 (Zimbabwe) *''Pompilioides trifasciatus'' Arnold, 1936 (South Africa) *''Pompilioides validus'' Arnold, 1936; descr. Arnold, 1937, p. 73 (Zimbabwe) ==='''Genus''' ''Psammochares'' Latreille, 1796=== Description of genus and key to species in Arnold, 1937, p. 43. *''Psammochares bilineatus'' Arnold, 1937, p. 50 (South Africa) *''Psammochares brevis'' Arnold, 1937, p. 50 (South Africa) ** = ''Agenioideus brevis'' (Arnold, 1937) *''Psammochares brunniventris'' Arnold, 1937, p. 54 (South Africa) *''Psammochares decipiens'' Bischoff, 1913; descr. Arnold, 1937, p.48 (Botswana, Zimbabwe) *''Psammochares gibber'' Arnold, 1937, p. 52 ** = ''Agenioideus gibber'' (Arnold, 1937) (https://www.catalogueoflife.org/data/taxon/6WBTC) *''Psammochares insidiosus'' Smith, 1879 (Ethiopia, Malawi, South Africa, Zimbabwe) *''Psammochares irpex'' Gerstaecker, 1859; descr. Arnold, 1937, p.48 (Zimbabwe) *''Psammochares jocaste'' Banks, 1940 (Madagascar) *''Psammochares latilabris'' Arnold, 1937, p. 47 (Malawi, Zimbabwe) *''Psammochares quadriguttatus'' Arnold, 1937 (Ethiopia, Tanzania) *''Psammochares rotundilabris''(Arnold, 1937, p.53.) (South Africa) ** = ''Agenioideus rotundilabris''? *''Psammochares rufigaster'' Arnold, 1937, p. 54 (South Africa) *''Psammochares rutilus'' Klug, 1834; descr. Arnold, 1937, p. 58 (Ethiopia, Mozambique, Nigeria, Sudan, Zimbabwe) *''Psammochares varians'' Arnold, 1937, p. 55 (South Africa) ''Psammochares gibber'' (= ''Agenioideus gibber'' (Arnold, 1937)?) Descr. Arnold, 1937, p. 52 ==='''Genus''' ''Psammoderes'' Haupt, 1929=== *''Psammoderes capensis'' Arnold, 1937, p. 70 (South Africa) *''Psammoderes collaris'' Saussure, 1891 (Madagascar) *''Psammoderes fuliginosus'' Arnold, 1935, p.438 (Zimbabwe) *''Psammoderes lightfooti'' Arnold, 1937, p. 71 (South Africa) *''Psammoderes longicollis'' Arnold, 1937, p. 69 (Democratic Republic of Congo) *''Psammoderes major'' Haupt, 1929; descr. Arnold, 1935, p.433 (South Africa) *''Psammoderes mimicus'' Haupt, 1929; descr. Arnold, 1935, p.434 (South Africa) *''Psammoderes semirufus'' Haupt, 1929; descr. Arnold, 1935, p.436 (South Africa, Zimbabwe) *''Psammoderes reputatus'' Kohl, 1913; descr. Arnold, 1935, p.437 (Congo, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/index.htm ''<u>Pseudoclavelia</u>''] Haupt, 1930=== ''Pseudoclavelia argenteosignata'' Arnold, 1936 (Botswana, Namibia) ''Pseudoclavelia bituberculata'' Arnold, 1962 (Zimbabwe) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_damarensis.htm <u>''Pseudoclavelia damarensis''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia jouberti'' Kohl, 1900 (South Africa) [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Pseudoclavelia/Pseudoclavelia_nitidula.htm <u>''Pseudoclavelia nitidula'' ''nitidula''</u>] Arnold, 1936 (Namibia) ''Pseudoclavelia nitidula bechuanae'' Arnold, 1959 (South Africa) ''Pseudoclavelia rhodesiana'' Arnold, 1936 (Zimbabwe) ''Pseudoclavelia rufescens'' Arnold, 1936 (South Africa) ''Pseudoclavelia willowmorensis'' Arnold, 1936 (South Africa) ==='''Genus''' ''Pseudopompilus'' Costa, 1887=== ''Pseudopompilus funereus'' Arnold, 1935, p.444 (Zimbabwe, Namibia) ''Pseudopompilus hyalinipennis'' Arnold, 1935, p.446 (South Africa) ''Pseudopompilus lacteipennis'' Arnold, 1935, p.446 (South Africa) ==='''Genus''' ''Psyllosphex'' Arnold, 1935=== ''Psyllosphex dentatus'' (Cameron, 1904); descr. Arnold, 1935, p.482 (South Africa) ''Psyllosphex myrmosaeformis'' Arnold, 1935, p.482 (Zimbabwe) ''Psyllosphex saltator'' Arnold, 1935, p.480 (South Africa) ==='''Genus''' ''Pygmachus'' Haupt, 1930=== ''Pygmachus compressus'' Saussure, 1892 (Madagascar) ''Pygmachus umbratus'' Haupt, 1930 (Guinea, South Africa, Zanzibar, Zimbabwe) ==='''Genus''' ''Rhynchopompilus'' Arnold, 1934=== Description of genus and species in Arnold, 1937, p. 37. ''Rhynchopompilus cursor'' Arnold, 1934 (Zimbabwe) ==='''Genus''' ''Schistonyx'' Saussure, 1887=== ''Schistonyx aterrimus'' Arnold, 1946 (South Africa) ''Schistonyx prismaticus'' Saussure, 1890 (Madagascar) ''Schistonyx sinuatus'' Bischoff, 1913; descr. Arnold, 1937, p.10 (South Africa) ''Schistonyx sheppardi'' Arnold, 1937, p.13 (Zimbabwe) ''Schistonyx umbrosus'' Klug, 1834; descr. Arnold, 1937, p.10 (Throughout Africa, Namibia, Senegal, South Africa, Syria, Zimbabwe) Most common pompilid in Zimbabwe (Arnold, 1937, p.12) ==='''Genus''' ''Schizanoplius'' Cameron, 1904=== ''Schizanoplius lutarius'' (Saussure, 1834)(Ghana, Mali, Madagascar) ''Schizanoplius violaceipennis'' Cameron, 1904 (South Africa) ==='''Genus''' ''Spuridiophorus'' Arnold, 1934=== ''Spuridiophorus capensis'' Arnold, 1934 (South Africa) ''Spuridiophorus inermis'' Arnold, 1934 (Zimbabwe) ''Spuridiophorus maculipennis'' Arnold, 1936 (Zimbabwe) ''Spuridiophorus turneri'' Arnold, 1936 (South Africa, Zimbabwe) ==='''Genus''' ''Syntomoclitus'' Arnold, 1937=== Description of genus and species in Arnold, 1937, p. 25. *''Syntomoclitus bicolor'' Arnold, 1937 (South Africa, Zimbabwe) ==='''Genus''' [https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/index.htm ''<u>Tachypompilus</u>''] Ashmead, 1902=== ''Tachypompilus ovambo'' and ''Tachypompilus vitripennis'' were described as ''Afropompilus'' Arnold, 1937, p. 71-72. *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ignitus.htm ''Tachypompilus ignitus''] (Smith, 1855) (South Africa, Zimbabwe) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_ovambo.htm ''Tachypompilus ovambo''] (Arnold, 1937, p. 71) (Namibia) *''Tachypompilus praepotens'' (Kohl, 1894) (South Africa, Mozambique, Zimbabwe, Zanzibar) *[https://www.waspweb.org/Pompiloidea/Pompilidae/Pompilinae/Tachypompilus/Tachypompilus_vitripennis.htm ''Tachypompilus vitripennis''] (Arnold, 1937, p. 72) (Malawi, Zimbabwe) ==='''Genus''' ''Telostegus'' Costa, 1887=== Description of genus and species in Arnold, 1937, p. 35. *''Telostegus capensis'' Arnold, 1937; descr. Arnold, 1937, p.37 (South Africa) *''Telostegus fuscipennis'' Cameron, 1905; descr. Arnold, 1937, p.35 (South Africa) *''Telostegus insidiosus'' (Smith, 1879) (Yemen) *''Telostegus sabulicola'' Priesner, 1955 (Algeria, Egypt, Marocco, Senegal, Yemen) ==References== gs8jy0n5r7en9qq69ijicyc14v94nij 2 322223 2719970 2719887 2025-06-28T14:37:29Z Senthilkumarafun 3003660 /* Pulavanur Kasi Vishveshwarar Temple, Pulavnur, Mayiladuthurai district, TamilNadu, India. */ 2719970 wikitext text/x-wiki = Pulavanur Kasi Vishveshwarar Temple, Pulavnur, Mayiladuthurai district, TamilNadu, India. = This small Shiva temple located in Pulavanur, (Scholar’s Village)Mayiladuthurai district, is renowned for its Lord Vishveshvara Shrine,(Kai Vishwanath) fondlingly called as Lord of the world. The temple has shrine built for Lord’s consort Goddess Visalakshi, Lord Murugan and Lord Vinayaga. The temple also has a small shrine for Goddess Gajalakshmi. The temple has also lots of faith when offered ablution to Huge Lingas that were consecrated during renovation process and is located at the back of the main shrine temple. This lingam is located between the shrines of Lord Murugan and Lord Vinayaga. Overall, The temple faces east and there is a small beautiful Nandi facing towards Lord, Visveswaraya and Goddess Visalakshi. A small temple Well along with a Sthalavriksham(Temple tree) lies opposite the Amman shrine. Currently, the temple is under renovation and is expected to perform Kumbabhishekam simultaneously during the Mahamakam festival that occurs once in 12 years with the next one supposedly in March of 2028. The temple can be reached from bus 1A from Mayiladuthurai bus stand. The nearest railway station is Vaitheeswaran Kovil, which is around 8km from the temple. Sithamalli, which is around 4kms from this place is renowned for its Soundara Narayana perumal temple and Kailasanathar temple. The river Coleroon(Kollidam) flow beyond Lord  Vishnu Temple. It is believed that on praying to the Lord, one attains happiness far beyond his thoughts in this life. bhrsqk5u3rqgdepdzi4f4upxq0yae4z 2719979 2719970 2025-06-28T15:09:06Z Senthilkumarafun 3003660 /* Pulavanur Kasi Vishveshwarar Temple, Pulavnur, Mayiladuthurai district, TamilNadu, India. */ 2719979 wikitext text/x-wiki = Pulavanur Kasi Vishveshwarar Temple, Pulavnur, Mayiladuthurai district, TamilNadu, India. = This small Shiva temple located in Pulavanur, (Scholar’s Village)Mayiladuthurai district, is renowned for its Lord Vishveshvara Shrine,(Kasi Vishwanath) fondlingly called as Lord of the world. The temple has shrine built for Lord’s consort Goddess Visalakshi, Lord Murugan and Lord Vinayaga. The temple also has a small shrine for Goddess Gajalakshmi. The temple has also lots of faith when offered ablution to Huge Lingas that were consecrated during renovation process and is located at the back of the main shrine temple. This lingam is located between the shrines of Lord Murugan and Lord Vinayaga. Overall, The temple faces east and there is a small beautiful Nandi facing towards Lord, Visveswaraya and Goddess Visalakshi. A small temple Well along with a Sthalavriksham(Temple tree) lies opposite the Amman shrine. Currently, the temple is under renovation and is expected to perform Kumbabhishekam simultaneously during the Mahamakam festival that occurs once in 12 years with the next one supposedly in March of 2028. The temple can be reached from bus 1A from Mayiladuthurai bus stand. The nearest railway station is Vaitheeswaran Kovil, which is around 8km from the temple. Sithamalli, which is around 4kms from this place is renowned for its Soundara Narayana perumal temple and Kailasanathar temple. The river Coleroon(Kollidam) flow beyond Lord  Vishnu Temple. It is believed that on praying to the Lord, family attains happiness far beyond their thoughts in this life. 8x6x7mgunmfajigiz34q8qu30yi6nqo 0 322224 2719997 2025-06-29T07:02:12Z Watchduck 137431 Watchduck moved page [[Tutor and mentor of Boolean functions]] to [[Lector and mentor of Boolean functions]] 2719997 wikitext text/x-wiki #REDIRECT [[Lector and mentor of Boolean functions]] r3am4xdo12pq64qpo2btge0jn2av01b 2719998 2719997 2025-06-29T07:02:30Z Watchduck 137431 Removed redirect to [[Lector and mentor of Boolean functions]] 2719998 wikitext text/x-wiki {{speedy|unneeded redirect}} 3a1ta73eeh41bvqvy6e73m3pidzlqqe