Wikiversity enwikiversity https://en.wikiversity.org/wiki/Wikiversity:Main_Page MediaWiki 1.45.0-wmf.4 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 124434 2718252 2695531 2025-06-10T18:12:47Z 98.97.114.73 Replaced content with "[[File:Fish at Kamogawa Sea World 14.jpg|thumb|338x338px|there are fishes in the sea]] '''Fish''' (pl: '''fish''' or '''fishes''') is an aquatic animal [[Category:Animals]] [[Category:Zoology]] [[Category:Ichthyology]] [[Category:Fish| ]]" 2718252 wikitext text/x-wiki [[File:Fish at Kamogawa Sea World 14.jpg|thumb|338x338px|there are fishes in the sea]] '''Fish''' (pl: '''fish''' or '''fishes''') is an aquatic animal [[Category:Animals]] [[Category:Zoology]] [[Category:Ichthyology]] [[Category:Fish| ]] 1sw8x19huziam32plo61cksboeqd86e 2718275 2718252 2025-06-10T20:08:14Z Atcovi 276019 Reverted edits by [[Special:Contributions/98.97.114.73|98.97.114.73]] ([[User_talk:98.97.114.73|talk]]) to last version by [[User:Atcovi|Atcovi]] using [[Wikiversity:Rollback|rollback]] 2695253 wikitext text/x-wiki '''Fishes''' are animals that live in the water. All fishes are '''vertebrates''' and have a spinal column made of either '''cartilage''' or '''bone'''. Fishes breathe in the water through structures called '''gills''', which are located on either side of the head. Gills act as the "lungs" of fishes. Gills are fine structures with lots of tiny blood vessels, called '''capillaries''', close to their surface. From these capillaries fish take in '''oxygen''', and release '''carbon dioxide''' and other waste products when water passes over them. Most fishes are covered in protective '''scales'''. These are different than the scales of reptiles and birds. Fish scales actually grow inside the skin of the fish, while reptile and bird scales grow on the surface of the skin. Most fishes are '''ectothermic''', meaning they rely on the environment around them for their body temperature. Some fishes like tuna are '''endothermic''', and produce their own internal body heat. Fishes have a simple two-chambered '''heart''' with one '''atrium''' and one '''ventricle'''. Blood is pumped from the heart to the gills. In addition to gills, some fishes can take in oxygen from the air. These include lungfishes, gouramies and bettas, and some catfishes. They may swallow air and take in oxygen through their '''intestines''' (catfishes), or have specialized organs that are similar but no the same thing as our lungs. ==Species of Fish== There are over '''30,000 known living species of fish'''. Some commonly known species of fish include: *Anchovy *Clownfish *Salmon *Sharks *goldfish *guppies and many others. ==Fish-Human Relationships== Fish and humans have been interacting for many thousands of years. The scientific study of fishes is called '''ichthyology''', and a scientist that studies fishes is called an '''ichthyologist'''. Fish are a very important food source for humans. In many times and locations, fish have provided the majority of the animal '''protein''' that people have access to. Fish have been kept in '''captivity''' by humans for several thousand years. They have mostly been kept as a ready supply of food. In the last few hundred years, fish have also been kept as '''ornamental''' pets. Goldfish, the first fish known to have been kept for ornamental purposes, have been kept and bred for their beauty in China for about 1000 years. '''Angling''', or fishing, has been practiced as a '''recreational sport''' for about 500 years, though no one is certain how it developed from a technique solely for collecting food into the funs sport it has become in many parts of the world today. With human population growth, in some places more fish have been captured for food than wild '''populations''' can replace. Some species of food fish are '''threatened''' or in danger of '''extinction'''. == Fish vs. Fishes == In English, the word "fish" is properly used to refer to one individual fish, or many of the same kind of fish. For example, a salmon is a fish, and salmon are fish. The word "fishes" refers to a group of fish of more than one species. For example, salmon and anchovies are fishes, and a group of salmon and anchovies are fishes. == See Also == * [[Aquaria]] - Includes additional fish species descriptions and how to care for them. == External Resources == *[[http://www.fishbase.org/search.php FishBase]] with information on almost every known species of fish. *[[https://www.environmentalscience.org/career/ichthyologist How to become an ichthyologist]] with information on how to have a career working with fishes. *[[https://en.wikipedia.org/wiki/Fish Fish]] on Wikipedia. {{science}} {{article}} [[Category:Animals]] [[Category:Zoology]] [[Category:Ichthyology]] [[Category:Fish| ]] dhbz7gamb46d6kgchbhnees910qt3vk 0 139384 2718285 2717921 2025-06-11T09:49:34Z Young1lim 21186 /* Adder */ 2718285 wikitext text/x-wiki == Adder == * Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20250522.pdf|A]]|| || [[Media:Adder.rca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.1.A.CLA.20250607.pdf|A]]|| || [[Media:Adder.cla.20140313.pdf|pdf]]|| |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]|| || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]|| || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20250405.pdf|A]]|| || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]|| || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]], [[Media:Adder.cca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]|| || [[Media:Adder.ksa.20140409.pdf|pdf]]|| |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]|| || || |- || '''9.1 Variable Block Adder''' || [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]], [[Media:VLSI.Arith.1C.VBA.20250218.pdf|D]]|| || || |- || '''9.2 Multi-Level Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]|| || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Digital Circuit Design]] [[Category:FPGA]] fhi2bnx5mupgkzypfyfdppg2arhamdm 2718287 2718285 2025-06-11T09:50:55Z Young1lim 21186 /* Adder */ 2718287 wikitext text/x-wiki == Adder == * Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20250522.pdf|A]]|| || [[Media:Adder.rca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.1.A.CLA.20250609.pdf|A]]|| || [[Media:Adder.cla.20140313.pdf|pdf]]|| |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]|| || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]|| || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20250405.pdf|A]]|| || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]|| || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]], [[Media:Adder.cca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]|| || [[Media:Adder.ksa.20140409.pdf|pdf]]|| |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]|| || || |- || '''9.1 Variable Block Adder''' || [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]], [[Media:VLSI.Arith.1C.VBA.20250218.pdf|D]]|| || || |- || '''9.2 Multi-Level Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]|| || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Digital Circuit Design]] [[Category:FPGA]] tbhm5hfbaauo0pgt6hxnelklcw1w776 2718289 2718287 2025-06-11T09:51:48Z Young1lim 21186 /* Adder */ 2718289 wikitext text/x-wiki == Adder == * Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20250522.pdf|A]]|| || [[Media:Adder.rca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.1.A.CLA.20250610.pdf|A]]|| || [[Media:Adder.cla.20140313.pdf|pdf]]|| |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]|| || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]|| || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20250405.pdf|A]]|| || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]|| || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]], [[Media:Adder.cca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]|| || [[Media:Adder.ksa.20140409.pdf|pdf]]|| |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]|| || || |- || '''9.1 Variable Block Adder''' || [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]], [[Media:VLSI.Arith.1C.VBA.20250218.pdf|D]]|| || || |- || '''9.2 Multi-Level Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]|| || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Digital Circuit Design]] [[Category:FPGA]] m22lkh7rbjofkl3c1pjd132hgmqqlye 2718291 2718289 2025-06-11T09:52:53Z Young1lim 21186 /* Adder */ 2718291 wikitext text/x-wiki == Adder == * Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20250522.pdf|A]]|| || [[Media:Adder.rca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.1.A.CLA.20250611.pdf|A]]|| || [[Media:Adder.cla.20140313.pdf|pdf]]|| |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]|| || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]|| || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20250405.pdf|A]]|| || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]|| || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]], [[Media:Adder.cca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]|| || [[Media:Adder.ksa.20140409.pdf|pdf]]|| |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]|| || || |- || '''9.1 Variable Block Adder''' || [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]], [[Media:VLSI.Arith.1C.VBA.20250218.pdf|D]]|| || || |- || '''9.2 Multi-Level Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]|| || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Digital Circuit Design]] [[Category:FPGA]] 61xkxehjnd721kpd96y0bzwdymfab8l 0 147046 2718250 1164576 2025-06-10T18:05:35Z 98.97.114.73 2718250 wikitext text/x-wiki #REDIRECT [[Computer Skills/Fundamentals/Mouse]] '''Mouse''' (pl: '''mice''') is a small rodent 3z14kiilaqoq9qklpq7t3285xhjzi9q 2718251 2718250 2025-06-10T18:07:58Z 98.97.114.73 Changed redirect target from [[Computer Skills/Fundamentals/Mouse]] to [[Computer Skills]] 2718251 wikitext text/x-wiki #REDIRECT [[Computer Skills]] [[File:Мышь 2.jpg|thumb|400x400px|a mouse with no background]] '''Mouse''' (pl: '''mice''') is a small rodent c6klnw9fmpcjr1qst4sdqu3azu79rze 2718276 2718251 2025-06-10T20:08:37Z Atcovi 276019 Reverted edits by [[Special:Contributions/98.97.114.73|98.97.114.73]] ([[User_talk:98.97.114.73|talk]]) to last version by [[User:Dave Braunschweig|Dave Braunschweig]] using [[Wikiversity:Rollback|rollback]] 1164576 wikitext text/x-wiki #REDIRECT [[Computer Skills/Fundamentals/Mouse]] 8y3r4gaw9p6lh2jux0e3wsxmabgzdzu 0 168064 2718248 2718224 2025-06-10T17:02:12Z JayCubby 2983335 ([[c:GR|GR]]) [[File:Coming South (AWM ARTV09225).jpg]] → [[File:MA I084436 TePapa Poster He's Coming South.tiff]] Slightly restored, color-balanced, much higher resolution version of same poster 2718248 wikitext text/x-wiki {{title|Fear as a motivator:<br>How can we use fear as a motivator?}} {{MECR|https://www.screenr.com/yfDN}} __TOC__ [[File:Scarecrow.jpg|thumbnail|right|A Scarecrow, commonly used by farmers to inspire fear in birds and motivate them to stay away]] ==Overview== This chapter is set up using questions as headings for each section. The reason for this is so the chapter can be more engaging for the reader, they are questions to keep in mind when reading each section. By the end of this chapter the reader should understand what [[Wikipedia:Fear|fear]] is, why we feel fear and how it [[Wikipedia:Motivation|motivates]] us. Each question will go through theories and research that relates to it. A question to keep in mind while reading that will be answered at the end is ‘When is fear an acceptable motivator?’.<br> Fear is an [[Wikipedia:Emotion|emotion]] and evolutionary advantage felt by humans and animals in response to a perceived threat. It is used to motivate a person or animal into engaging in a behaviour that is most likely to allow them to survive. In this book chapter fear will be discussed and will look at the ways in which it is involved in our everyday lives. It will go further in depth to explain what fear is and where it comes from.<br> Fear is often considered to be a negative emotion, hopefully this chapter will offer a different perspective and show through research and examples both past and modern how fear can be useful in peoples lives. Fear is useful as a motivator as it is an emotion that occurs in response to a threat which requires action of some sort,{{grammar{{ it is a feeling that urges someone to react. This chapter will examine both negative and positive motivating effects fear can have and explain why certain behaviors occur when experiencing fear.<br> Similar to, but not the same as, fear is anxiety which comes from the same {{which}}part of the brain. Anxiety induces feelings of fear and worry but it is not always known what is triggering it. This will also be discussed further on as it also has connections with fear and motivation and will look at the positives and negatives it has to offer.<br> ==What is fear?== Fear is an emotional reaction that is caused by a perceived imminent {{missing}} of impending threat (Reeve, 2009). Fear causes a change in the body as a means of responding to the perceived threat,{{grammar}} this is known as the fight or flight response. Some of the behaviors that occur during the flight of fight response can include running away, hiding or in extreme cases of fear a freeze response.<br> Fear is a learned response,{{grammar}} it can be learned through conscious or unconscious learning{{fact}}. It is believed that the amygdala plays a key role in forming the memories for learned fear reactions in both humans and animals (Davis, 1992). Fear can be considered either rational or irrational since it is a cognitive response. A rational fear is one that is appropriate for the situation.<br> For example, being afraid of venomous snakes would be considered rational due to the threat they offer. An irrational fear is also known as a phobia, an example of a phobia would be a fear of all snakes, even the species of snakes that offer no real threat. Motivation is is a construct to explain [[Wikipedia:Behavior|behaviour]],{{grammar}} fear in this chapter will be used as an explanation for many behaviours. ==Are anxiety and fear the same?== [[Wikipedia:Anxiety|Anxiety]] is {{missing} common feeling for many people, they may feel it when they give a public speech, perform in front of a large audience, etc. But is anxiety the same as fear? When we are afraid we generally know what we are afraid of,{{grammar}} anxiety is the presence of feelings of fear but usually without any idea of what is causing that feeling or when there is no real threat. Anxiety, like fear can be useful, for example, when driving in harsh conditions a person may feel anxious and are then motivated to slow down and drive in a way more suited to those conditions. However there can be unhealthy levels of anxiety that negatively influence a persons life{{fact}}. Anxiety occurs in the same part of the brain as fear, the [[Wikipedia:Amygdala|amygdala]]. As such it produces the same response of fight or flight. Reasons behind a persons developing anxiety are not always clear but it is thought to be a result of a combination of genetics and the environment (Mercola (2013)). Some research into pathological anxiety (Rosen, 1998) has found that when anxiety occurs in people the activation threshold for the neurons in the amygdala is reduced, this creates a state of constant vigilance and awareness in the person. Behavioral responses to stimuli that induce fear are also increased. Because of this state people who experience anxiety may be motivated to do certain things. For example, a person who suffers social anxiety, is motivated by feelings of fear and worry to not engage in social interaction or get involved in social situations. This is one of the negative motivations that anxiety can have on a person. ==Why and how do we experience fear?== Humans and animals experience fear as part of an evolutionary response in order to survive. The [[Wikipedia:Fight-or-flight response|fight or flight]] response is to keep us out of danger by motivating us to react to a situation in a way so that we are more likely to survive. When we feel fear our body and mind changes, the body releases adrenaline and our heart pace quickens in order to prepare us to either fight or flee. The fight or flight response begins in the amygdala, the same part of the brain that is thought to be a key part in learning fear reactions (Knox, et al., 2010). Much research has been done to study the amygdala in both humans and animals. Majority of research is done on animals as inducing fear in humans is more challenging in terms of logistics and ethics. The main problem with experiment{{spelling}} on animals is you can’t actually know if they are afraid or not because animals cant{{grammar}} answer if they are afraid or not (Weitan, 2010). Neuroimaging is a technique that has been used to identify when the amygdala is active during studies, however fear is not always present when the amygdala is active. Neuroimaging studies (Whalen, 1998) on humans have shown that the amygdala is active during times when humans experience fear, but it has also shown to be active when other stimuli not necessarily related to fear are present. One study found that the amygdala was active when a person was looking at photographs of different facial expressions. It is thought that the amygdala is active when looking at facial expressions due to the emotional response they create in a person which is partly processed by the amygdala{{fact}}. ==Is fear something we are born with or learn over time?== [[File:Nelumbo nucifera 006.JPG|thumbnail|right|''Figure 1.'' A Lotus seed head, images of these are common triggers for people who suffer from Trypophobia.]] Fear is a learned response to threats and situations (Olsson & Phelps (2004)). A learning theory that is commonly used in research to teach animals fear is operant conditioning. In operant conditioning there is reinforcing and punishing stimulus{{grammar}} used in order to learn. Operant conditioning gives insight into how we can develop and learn fears. A study (Dalla & Shors (2009)) that involved rats used operant conditioning in order to fear condition them. Through operant conditioning the rats were exposed to electric shocks unless they pulled a lever to open a door to escape. They soon learned to pull the lever to avoid the shock. When the design was changed so that the lever no longer worked the rats started to show behaviour signs of fear. In this study the rats learned to fear and showed expressions of anxiety when they were in a situation where they were likely to be shocked. However, new research has demonstrated that phobias may actually be inherited through genes (Dias & Ressler, 2014). The study trained mice to fear the smell of a cherry blossom, subsequent generations also exhibited fear of the blossom despite having no prior contact with it. This research also provides evidence to how disorders such as anxiety are genetic and can be passed on. Operant conditioning is the process by which a response is trained to be elicited from a stimulus{{clarify}}. In operant conditioning rewards and punishment are used to reinforce responses to stimulus. Rewards are used to strengthen responses, whereas punishments reduce responses (Weitan 2010). Operant conditioning provides insight into how fear is learned through experience. However we do not always have to experience a stimulus like punishment in operant conditioning to learn fear. A famous experiment known as the ‘Little Albert experiment’ conducted by John B. Watson showed how fear can be learned through classical conditioning, the process by which a stimulus becomes associated with another stimulus to stimulate similar responses (Weitan, 2010). In the experiment Albert, a baby at the time was introduced to different objects and found that he showed no fear towards any of them. One of the items he was shown was a white rat. When he was shown the white rat again later on whenever he went to touch it a loud noise would occur which would shock and make albert afraid. After a few pairings of the rat and the noise albert soon became fearful whenever the rat was present. However the fear also spread across to some of the other items he had seen before and not been afraid of at the time such as cotton wool. While this experiment does have some faults such as being limited to only one child and having no control or that it was potentially harmful and unethical, it does help to provide insight into learned fears. The experiments results could also be used to explain how phobias and severe anxiety develop in people. <br> A study into a common phobia, trypophobia (fear of holes), conducted spectral analysis on images that were more likely to trigger peoples phobias (Cole, G., Wilkins, A. (2013)). They found these images had a correlation with a range of potentially dangerous animals such as snakes and spiders. The study indicates that the similar characteristics the images and animals share create an association of the two and the fear that is normally felt from seeing those animals is associated unconsciously with holes. While this study did find an association between the pictures with spectral analysis it is not conclusive evidence that these mistaken associations are what actually causes phobias. ==How does fear motivate?== The fight or flight response uses different behaviors to react to a situation, but how are those behaviors decided? Why do we fight in some circumstances but run away in others? Presented are two relevant theories of motivation that help to explain these questions.<br> Protection motivation theory attempts to explain the motivation for a particular behaviour we receive based on the perceived threat. The theory was first proposed by Ronald, W, Rogers in 1975 to help define fear appeals. A fear appeal is a message that tries to show a threat that someone is vulnerable to, creating fear and then suggesting a behaviour to avoid that threat. According to protection motivation theory there are four factors that our behaviour is based on. These four factors are;<br> #The perceived severity of a threat <br> #Our belief/confidence in our abilities to react to the situation<br> #Probability of threat occurring <br> #The likelihood that a behaviour (Fight or flight) will work<br> An example of this comes from a study on teachers use of fear appeals in the classroom to see if it motivated students and whether it contributed to students levels of worry, anxiety and fear of failure (Putwain & Symes (2011)). The fear appeal in this case was the threat of failure for students who did not perform well. The severity of this was considered high as students were told of the educational and occupational hazards of not performing well. The students reactionary behaviour was to study in order to avoid failure. The results of this study found that fear appeals had both negative and positive consequences, while it did motivate students to study it also increased their anxiety and fear of failure.<br> Fear can also be considered an extrinsic motivator since the motivation is created by environmental incentives and consequences, e.g. a threat. There are links between extrinsic motivation and operant conditioning as the themes of rewards and punishment are found in both. Fear is extrinsic because the cause of the fear is envrionmental, it requires something outside of us to activate. ==Which fears motivate us?== The truth about fears is they all motivate in some shape or form, the difference is whether or not that motivation leads to positive or negative consequences in a persons life. A common fear experienced that motivates people is the fear of death{{fact}}. When people think of death they are afraid of it, in many cases this motivates people in a positive way. In some cases it motivates them to enjoy life more, a common phenomenon of this is called the mid life crisis. Measurements of death anxiety have shown that it is highest in people around the ages of 40-64 years (Castano, et al (2011)). During a mid-life crisis people are more open to trying new things and look to find fulfillment in life. <br> Even anxiety which can sometimes occur without knowing what causes it may motivate a person in some way. For example a person with social anxiety is motivated by feelings of worry and fear to avoid social situations. Social anxiety affects 13% of the worlds population at some point in their life (Bandelow & Wedekind (2014)). Fears and anxieties, such as social anxiety that have negative effects on a persons life are ones we do not need. People who suffer from extreme cases negative fears should seek help in the form of therapy or professionally prescribed medication. ==How can we use fear in a positive way?== We should only ever experience fear in appropriate situations. When we have an irrational fear or phobia that affects our everyday life then it becomes something we have to change. There are different ways to remove a phobia, most of the time this is done through therapy. Techniques such as exposure therapy are common in fighting phobias and can also be used to fight anxiety. In exposure therapy a person is gradually exposed to their fear in an attempt to get them to realize the irrationality of that fear{{fact}}.<br> The best way we can utilise fear to help us is to keep it rational. If you are afraid of something there should be a genuine underlying reason/s behind what initiates you to feel threatened in some way. Also the level of fear we feel in a given situation is important. An example of this would be that its rational for a person to feel terrified when swimming with a shark, but it’s probably not rational for that person to feel terror when their mother in law is visiting, a more appropriate level of fear would be worried or anxious. Cognitive Dissonance Theory is a theoretical approach that can be related to anxiety and motivation. First proposed by Leon Festinger in 1957, cognitive dissonance is the mental stress that occurs when a person holds two or more opposing beliefs, ideas or values. This is relevant because the mental stress that is cognitive dissonance can take the form of anxiety. Its most likely that you have experienced cognitive dissonance before, many people feel it in their teens when they experience peer pressure. An example of this would be underage drinking. {{roundboxtop|theme=2}} A 17 year old goes out to a friends party, he is offered a beer. He know's its illegal for him to drink but he wants to fit in with <br> his other friends and believes he will have a better time drinking.{{roundboxbottom|theme=2}}<br> In this case the 17 year old experiences cognitive dissonance, however the cognition he has for drinking are greater than they are for not drinking. In order to change this the 17 year old can be exposed to new information such as the risks of drinking at a young age, this could create enough cognition to create enough dissonance that he will choose not to drink. The Australian government introduced a education campaign in 2013 designed to reduce the number of young people drinking. This education campaign was designed to create feelings of anxiety by making the public aware of the risks that they may not have been aware of before. The slogan for this campaign was "Don't turn a night out into a nightmare".<br> You can motivate yourself by creating cognitive dissonance, if you want the motivation to do something for example losing weight, then research some of the dangers of being overweight. However its important to keep the anxiety at a appropriate level, it should be enough to make you think twice about eating a burger and maybe switching to a salad and not a level of anxiety at which you are afraid to eat altogether. ==Can fear be used to motivate people other than ourselves?== [[File:MA I084436 TePapa Poster He's Coming South.tiff|framed|right|''Figure 2.'' A poster used to create fear in order to motivate Australias to help with the war effort.]] Fear has previously been used as a mechanism to motivate people, it’s not only being used to motivate ourselves but to motivate others as well. A common example of this in Australia is the campaign against smoking which has used shock based advertising of diseases associated with smoking. These images induce fear into people who smoke in an attempt to get them to quit. When the images were first introduced in Australia a phone survey found there was a decrease in the number of smokers by 15% from the previous year (Shanahan & Elliotte (2008)). However fear has not always been used to motivate people for the better,{{grammar}} there are other examples in history of motivation through fear. During World War II there was a massive fear of the possibility of a Japanese invasion of Australia. Propaganda posters at the time capitalized on that fear in order to motivate people to join the army or to help in some way with the war effort. An example of one of these posters can be seen in Figure 2.<br> The affects that fear has on motivating people has largely being used in modern times by the media. The media has an effect of increasing peoples fears by bring awareness and reporting on certain topics. Research (Nellis & Savage (2012)) into the medias influence on people has shown that the media’s large coverage of terrorism has increased the perceived risk of being attacked by a terrorist by people who watch the news. The increased fear of terrorism motivates people to then watch more related stories presented by the media. {{roundboxtop|theme=4}} ==Quiz== <quiz> {What part of the brain is responsible for learning fear? |type="()"} - The Almond - The Cortex + The Amygdala - The Medulla<br> { Trpohphobia is the fear of? |type="()"} - Tripping - Typos - Heights + Holes<br> { In John B. Watsons 'Little Albert Experiment' Albert learned to fear the white rat through what method? |type="()"} - Operant conditioning + Classical conditioning - Psuedo conditioning - Modern Conditioning { Question? </quiz> {{roundboxbottom|theme=4}} ==Conclusion== Fear can be a strong motivator in people’s lives,{{grammar}} it can easily shape what a person does and how they react in a situation. Fear can be useful in surviving and improving a person’s life by helping them and motivating them to react to risks appropriately. Fear has being useful in motivating people to change their lives for the better,{{grammar}} fear campaigns such as the anti smoking campaigns in Australia have helped to reduce the number of smokers. This article has hopefully shown how fear can be learnt through different methods and that we can even teach ourselves to experience fear. However, fears need to be kept in check as they can manifest themselves into phobias and cause people to avoid things with no actual risk to them. In order to prevent this people need to be aware of the reasons behind any fears they experience. There needs to be rational reasons for experiencing fear. As well as this, peoples level of fear needs to suit the situation. Feelings of anxiety sometimes help us to avoid situations in which we may be harmed physically or mentally. However feeling anxious all the time can be harmful to our health and cause more negative than positive effects. <br> If fear and anxiety are kept in check then they are useful in motivating us to better ourselves and keep us alive. Fear is not something to be afraid of, it’s an evolutionary adaptation that many humans and animals use in order to survive. Fear is the ultimate motivator in that it motivates people and animals to survive. To answer the question asked in the overview, fear should be considered an acceptable motivator when the behaviour it motivates is in the best interest of the individual.<br> ==See also== *[[Motivation_and_emotion/Book/2013/Fear_of_failure|Fear of Failure]]<br> *[[Motivation_and_emotion/Book/2013/Fear|Fear]] ==References== {{Hanging indent|1= Australian Government. (2013). National Binge Drinking Strategy. Retrieved from the Australian Government website: http://www.alcohol.gov.au/internet/alcohol/publishing.nsf/Content/cli Bandelow, B., Wedekind, D. (2014). Social phobia. ''The Neurologist'', 85(5), pp. 635-647. Castano, E., Leidner, B., Bonacossa, A., Nikkah, J., Perrulli, R., Spencer, B., Humphrey, N. (2011). Ideology, fear of death, and death anxiety. ''Journal of Political Psychology'', 32(4), pp. 601-621. Cole, G., Wilkins, A. (2013). Fear of holes. ''Journal of Psychological Science'', pp 1980-1985 Dalla, C., Shors, T. (2009). Sex differences in learning processes of classical and operant conditioning. ''Journal of Physiology and Behavior'', (97), pp229-238. Davis, M. (1992). The role of amygdala in fear and anxiety. ''Annual review of Neuroscience'', pp. 353-375. Dias, B., Ressler, K. (2014). Parental olfactory experience influences behavior and neural structure in subsequent generations. ''Journal of Nature Neuroscience'', pp. 89-96. Festinger, L. (1957). ''A theory of cognitive dissonance''. Stanford, CA: Stanford University Press. Mercola, D. (2013). What Anxiety Does to Your Brain and What You Can Do About It. ''Retrieved from the Mercola website'': articles.mercola.com/sites/articles/archive/2013/12/05/anxiety.aspx Nellis, A., Savage, J. (2012). Does watching the news affect fear of terrorism? The importance of media exposure on terrorism fear. ''Journal of Crime and Delinquency,'' 58(5), pp. 748-768. Olsson, A., Phelps, E. (2004). Learned fear of “unseen” faces after Pavlovian, observational, and instructed fear. ''Journal of Psychological Science'', pp. 338-341 Putwain, D., Symes, W. (2011). Teachers use of fear appeals in the mathematics classroom: Worrying or motivating students? British ''Journal of Educational Psychology,'' 81(3), pp. 456-474. Reeve, J. (2009). ''Understanding Motivation and Emotion.'' United States: Wiley Rogers, W, R. (1975). A protection motivation theory of fear appeals and attitude change. ''The Journal of Psychology: Interdisciplinary and Applied'', pp. 93-114. Rosen, J. (1998). From normal fear to pathological anxiety. ''Psychological Review'', pp. 325-350. Shanahan, P., Elliotte, D. (2008)''.Evaluation of the Effectiveness of the Graphic Health Warnings on Tobacco Product Packaging executive summary''. Retrieved October 20th, 2014 from http://www.health.gov.au/internet/main/publishing.nsf/Content/tobacco. Weitan, W. (2010). ''Psychology Themes and Variations.'' (8th Ed.). Belmont: Wadswoth Whalen, J, P. (1998). Fear, vigilance, and ambiguity: Initial Neuroimaging studies of the human amygdala. ''Journal of Current Directions in Psychological Science'', (7), pp. 177-188 }} ku3hhw0i5oiyef11a9kc0yd1ol85w6c 0 203163 2718253 2717949 2025-06-10T19:50:29Z 212.200.164.104 /* Philosophy */ 2718253 wikitext text/x-wiki '''Is God a Programmer? analyzing the deep-universe simulation hypothesis at the Planck scale''' The [[w:simulation hypothesis |simulation hypothesis]] is the proposal that all of reality, including the Earth and the rest of the universe, could be an artificial simulation, such as a computer simulation. [[w:Neil_deGrasse_Tyson |Neil deGrasse Tyson]] put the odds at 50-50 that our entire existence is a program on someone else’s hard drive <ref>Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. [[w:David_Chalmers |David Chalmers]] noted “We in this universe can create simulated worlds and there’s nothing remotely spooky about that. Our creator isn’t especially spooky, it’s just some teenage hacker in the next universe up. Turn the tables, and we are essentially gods over our own computer creations <ref>https://www.youtube.com/watch?v=yqbS5qJU8PA, David Chalmers, Serious Science</ref> <ref>The Matrix as Metaphysics, David Chalmers http://consc.net/papers/matrix.pdf</ref> <ref>Are We Living in a Computer Simulation?https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. The commonly postulated [[w:Ancestor_simulation |ancestor simulation]] approach, which [[w:Nick Bostrom |Nick Bostrom]] called "the simulation argument", argues for "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor. However this simulation variant can be traced back to an 'organic base reality' (the original programmer ancestors and their physical planet). The [[v:God_(programmer) |Programmer God]] hypothesis<ref>https://codingthecosmos.com/podcast/ AI generated podcasts</ref> conversely states that a (deep universe) simulation began with the big bang and was programmed by an external intelligence (external to the physical universe), the Programmer by definition a God in the creator of the universe context. Our universe in its entirety, down to the smallest detail, and including life-forms, is within the simulation, the laws of nature, at their most fundamental level, are coded rules running on top of the simulation operating system. The operating system itself is mathematical (and potentially the origin of mathematics). Any candidate for a Programmer-God simulation-universe source code must satisfy these conditions; :1. It can generate physical structures from mathematical forms. :2. The sum universe is dimensionless (simply data on a celestial hard disk). :3. We must be able to use it to derive the laws of physics (because the source code is the origin of the laws of nature, and the laws of physics are our observations of the laws of nature). :4. The mathematical logic must be unknown to us (the Programmer is a non-human intelligence). :5. The coding should have an 'elegance' commensurate with the Programmer's level of skill. == Philosophy == Physicist [[w:Eugene Wigner |Eugene Wigner]] ([[w:The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences |The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]) <ref>{{Cite journal | last1 = Wigner | first1 = E. P. | authorlink = Eugene Wigner| doi = 10.1002/cpa.3160130102 | title = The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959 | journal = Communications on Pure and Applied Mathematics | volume = 13 | pages = 1–14 | year = 1960 | pmid = | pmc = |bibcode = 1960CPAM...13....1W }}</ref> <blockquote>The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. </blockquote> === Discussion === [[w:Philosophy of mathematics |Philosophy of mathematics]] is that branch of philosophy which attempts to answer questions such as: ‘why is mathematics useful in describing nature?’, ‘in which sense, if any, do mathematical entities such as numbers exist?’ and ‘why and how are mathematical statements true?’ This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math. Mathematical realism holds that mathematical entities exist independently of the human mind. We do not invent mathematics, but rather discover it. Triangles, for example, are real entities that have an existence <ref>- http://plato.stanford.edu/entries/platonism-mathematics/</ref>. The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality. It can be considered a form of [[w:Pythagoreanism | Pythagoreanism]] or [[w:Platonism | Platonism]] in that it proposes the existence of ''mathematical objects''; and a form of [[w:philosophy of mathematics | mathematical monism]] in that it denies that anything exists except these ''mathematical objects''. Physicist [[w:Max Tegmark | Max Tegmark]] in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality"<ref name="Tegmark1998">{{cite journal|last=Tegmark |first=Max |date=November 1998 |title=Is "the Theory of Everything" Merely the Ultimate Ensemble Theory? |journal=Annals of Physics |volume=270 |issue=1 |pages=1–51 |doi=10.1006/aphy.1998.5855 |arxiv = gr-qc/9704009 |bibcode = 1998AnPhy.270....1T }}</ref><ref>M. Tegmark 2014, "[http://mathematicaluniverse.org Our Mathematical Universe]", Knopf</ref> proposed that ''Our external physical reality is a mathematical structure''.<ref name="Tegmark2008">{{cite journal|last=Tegmark |first=Max |date=February 2008 |title=The Mathematical Universe |journal=Foundations of Physics |volume=38 |issue=2 |pages=101–150 |doi=10.1007/s10701-007-9186-9 |arxiv=0704.0646|bibcode = 2008FoPh...38..101T }}</ref> That is, the physical universe is not merely ''described by'' mathematics, but ''is'' mathematics (specifically, a [[w:mathematical structure | mathematical structure]]). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref> The principle constraints to any mathematical universe simulation hypothesis are; 1. the computational resources required. The ancestor simulation can resolve this by adapting from the [[w:virtual rality |virtual reality]] approach where only the observable region is simulated and only to the degree required, and 2. that any 'self-aware structures' (humans for example) within the simulation must "subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref>. Succinctly, our computer games may be able to simulate our physical world, but they are still only simulations of a physical reality (regardless of how realistic they may seem) ... we are not yet able to program actual physical dimensions of mass, space and time from mathematical structures, and indeed this may not be possible with a computer hard-ware architecture that can only process binary data. === Deep-universe source code === As a deep-universe simulation is programmed by an external (external to the universe) intelligence (the Programmer God hypothesis), we cannot presume a priori knowledge regarding the simulation source code other than from this code the laws of nature emerged, and so any deep-universe simulation model we try to emulate must be universal, i.e.: independent of any system of units, of the [[w:Dimensional_analysis |dimensioned]] [[w:physical constants |physical constants]] (''G'', ''h'', ''c'', ''e'' .. ), and of any numbering systems. Furthermore, although a deep-universe simulation source code may use mathematical forms (circles, spheres ...) we are familiar with (for ultimately the source code is the origin of these forms), it will have been developed by a non-human intelligence and so we may have to develop new mathematical tools to decipher the underlying logic. By implication therefore, any theoretical basis for a source code that fits the above criteria (and from which the laws of nature will emerge), could be construed as our first tangible evidence of a non-human intelligence. === Constants === A physical universe is characterized by measurable quantities (size, mass, color, texture ...), and so a physical universe can be measured and defined. Contrast then becomes information, the statement ''this is a big apple'' requires a ''small apple'' against which big becomes a relative term. For analytical purposes we select a reference value, for example 0C or 32F, and measure all temperatures against this reference. The smaller the resolution of the measurements, the greater the information content (the file size of a 32 mega-pixel photo is larger than a 4 mega-pixel photo). A simulation universe may be presumed to also have a resolution dictating how much information the simulation can store and manipulate. To measure the fundamental parameters of our universe physics uses [[w:physical constant |physical constants]]. A physical constant is a [[w:physical quantity |physical quantity]] that is generally believed to be both universal in nature and have a constant value in time. These can be divided into 1) dimension-ed (measured using physical units ''kg'', ''m'', ''s'', ''A'' ...) such as the [[w:speed of light |speed of light]] ''c'', [[w:gravitational constant |gravitational constant]] ''G'', [[w:Planck constant |Planck constant]] ''h'' ... as in the table {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} Physicist [[w: |Lev Okun]] noted "Theoretical equations describing the physical world deal with dimensionless quantities and their solutions depend on dimensionless fundamental parameters. But experiments, from which these theories are extracted and by which they could be tested, involve measurements, i.e. comparisons with standard dimension-ful scales. Without standard dimension-ful units and hence without certain conventions physics is unthinkable <ref>Michael J. Duff et al, Journal of High Energy Physics, Volume 2002, JHEP03(2002)</ref>. 2) dimension-less, such as the [[w:Fine-structure_constant |fine structure constant]] ''α''. A dimension-less constant does not measure any physical quantity (it has no units; units = 1). 3) dimension-less [[w:mathematical constant |mathematical constants]], most notably [[w:pi |pi]] = 3.14159265358979 and [[w:Natural_logarithm |e]] = 2.718281828459. Although these are [[w:transcendental number |transcendental numbers]], they can be constructed by integers in a series, and so for a universe expanding incrementally (see simulation time), these constants could be formed within the simulation. For example, at time ''t''; <math display=block>t = 1; \frac{\pi^2}{6} = \frac{1}{t^2} </math> <math display=block>t = 2; \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{t^2}</math> <math display=block>t = now: \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots + \frac{1}{t^2} </math> We may now define the fundamental physical constant as a parameter specifically chosen by the Programmer and is encoded into the simulation code directly, and so whilst it may be inferable, it is not derived from other constants ([[w:Fine-structure_constant#Numerological_explanations_and_multiverse_theory |Richard Feynman on the fine structure constant]]). It should also be dimension-less otherwise the simulation itself becomes dimensioned (if the simulation is running on a celestial computer it is merely data, it has no physical size or shape or ...), and so the dimensioned constants (''G'', ''h'', ''c'', ''e''...) must all be derivable (derived from within the simulation) via the (embedded in the source code) fundamental physical constants (of which the fine structure constant alpha may be an example). Although [[w:pi |pi]] and [[w:Natural_logarithm |e]] are dimensionless, they can be derived internally (from integers), and as they have application in the mathematical realm, they can be referred to as mathematical constants. ==== Planck scale ==== The [[w:Planck scale |Planck scale]] refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the [[w:Standard Model |Standard Model]], [[w:quantum field theory |quantum field theory]] and [[w:general relativity |general relativity]] are no longer reconcilable, and [[w:Quantum Gravity |quantum effects of gravity]] are expected to dominate (quantum gravitational effects only appear at length scales near the Planck scale). Although particles may not be cognizance of our 'laws of physics', they do know the 'laws of nature'. These laws of nature would run directly off the universe OS (operating system), and so below this OS, 'physics' as we know it must necessarily break down. At present the Planck scale is the lowest known level, consequently any attempt to detect evidence of an underlying simulation coding must consider (if not actually begin at) this, the Planck scale<ref>https://www.youtube.com/watch?v=AMQRXGYCDrY Planck scale, Brian Greene</ref>. The [[w:International_System_of_Units |SI units]] for the dimension-ful mksa units are; meter (length), kilogram (mass), second (time), ampere (electric current). There are Planck units that represent these SI units, and so a simulation could use them as discrete building blocks; [[w:Planck length |Planck length]] (the smallest possible unit of length), [[w:Planck mass |Planck mass]] (the unit of mass), [[w:Planck time |Planck time]] (the smallest possible unit of time), [[w:Planck charge |Planck charge]] (the unit of charge). The speed of light then becomes ''c'' = 1 Planck length / 1 Planck time. These units would define the resolution and so information carrying capacity of the simulation universe. ==== Numbering systems ==== As well as our decimal system, computers apply binary and hexadecimal numbering systems. In particular the decimal and hexadecimal are of terrestrial origin and may not be considered 'universal'. Furthermore numbering systems measure only the frequency of an event and contain no information as to the event itself. The number 299 792 458 could refer to the speed of light (299 792 458 m/s) or could equally be referring to the number of apples in a container (299 792 458 apples). As such, numbers require a 'descriptive', whether m/s or apples. Numbers also do not include their history, is 299 792 458 for example a derivation of other base numbers? Present universe simulations use the laws of physics and the physical constants are built in, however both these laws and the physical constants are known only to a limited precision, and so a simulation with 10⁶² iterations (the present age of the universe in units of Planck time) will accumulate errors. Number based computing may be sufficient for ancestor-simulation models where only the observed region needs to be calculated, but has inherent limitations for deep universe simulations where the entire universe is continuously updated. The actual computational requirements for a Planck scale universe simulation based on a numbering system with the laws of physics embedded would be an unknown and consequently lead to an 'non-testable' hypothesis. This is a commonly applied reasoning for rejecting the deep universe simulation. ==== Geometrical objects ==== A mathematical constant such as [[w:pi |pi]] refers to a geometrical construct (the ratio of circle circumference to circle radius) and so is not constrained by any particular numbering system (in the decimal system π = 3.14159...), and so may be considered both universal and eternal. Likewise, by assigning geometrical objects instead of numbers to the Planck units, the problems with a numbering system can be resolved. These objects would however have to fulfill the following conditions; 1) embedded attribute - for example the object for length must embed the function of ''length'' such that a descriptive (km, mile ... ) is not required. Electron wavelength would then be measurable in terms of the length object, as such the length object must be embedded within the electron (the electron object). Although the mass object would incorporate the function ''mass'', the time object the function ''time'' ..., it is not necessary that there be an individual physical mass or physical length or physical time ..., but only that in relation to the other units, the object must express that function (i.e.: the mass object has the function of mass when in the presence of the objects for space and time). The electron could then be a complex event (complex geometrical object) constructed by combining the objects for mass, length, time and charge into 1 event, and thus electron charge, wavelength, frequency and mass would then be different aspects of that 1 geometry (the electron event) and not independent parameters (independent of each other). 2) The objects for mass, length, time and charge must be able to combine with each other [[w:Lego |Lego-style]] to form more complex objects (events) such as electrons and apples whilst still retaining the underlying information (the mass of the apple derives from the mass objects embedded within that apple). Not only must these objects be able to form complex events such as particles, but these events themselves are geometrical objects and so must likewise function according to their geometries. Electrons would orbit protons according to their respective electron and proton geometries, these orbits the result of geometrical imperatives and not due to any built-in laws of physics (the orbital path is a consequence of all the underlying geometries). However, as orbits follow regular and repeating patterns, they can be described (by us) using mathematical formulas. As the events grow in complexity (from atoms to molecules to planets), so too will the patterns (and likewise the formulas we use to describe them). Consequently the ''laws of physics'' would then become our mathematical descriptions of the underlying geometrically imposed patterns. 3) These objects would replace coded instructions (the instruction sets would be built into the objects) thereby instigating a geometrically autonomous universe. The electron 'knows' what to do by virtue of the information encoded within its geometry, no coded electron CALL FUNCTION is required. This would be equivalent to combining the hardware, software and CPU together such that the 'software' changes (adjusts) to the changing 'hardware' (DNA may be an analogy). Note: A purely mathematical universe has no limits in size and can be infinitely large and infinity small. A geometrical universe (that uses objects) has limitations, it can be no smaller than the smallest object for example and has discrete parts (those objects). The philosophy of the TOE (theory of everything) therefore includes a debate between the mathematical universe and the geometrical universe, however this distinction between mathematical and geometrical would only be apparent at the Planck scale. === Evidence of a simulation === The laws of physics are our incomplete observations of the natural universe, and so evidence of a simulation may be found in ambiguities or anomalies within these laws. Furthermore, if complexity arises over time, then at unit time the 'handiwork' of the Programmer may be notable by a simplicity and elegance of the geometries employed ... for the Programmer by definition has God-level programming skills. Here is a notable example. Mass, space and time from the number 1 The dimensions of mass, space and time are considered by science to be independent of each other, we cannot measure the ''distance'' from Tokyo to London using kilograms and amperes, or measure ''mass'' using space and time. Indeed, what characterizes a physical universe as opposed to a simulated universe is the notion that there is a fundamental structure underneath, that in some sense mass 'is', that time 'is' and space 'is' ... thus we cannot write ''kg'' in terms of ''m'' and ''s''. To do so would render our concepts of a physical universe meaningless. The 26th General Conference on Weights and Measures ([[w:2019 redefinition of SI base units|2019 redefinition of SI base units]]) assigned exact numerical values to 4 physical constants (''h, c, e, k''_B) independently of each other (and thereby confirming these as fundamental constants), and as they are measured in SI units ('''kg''', '''m''', '''s''', '''A''', '''K'''), these units must also be independent of each other (i.e.: these are fundamental units, for example if we could define ''m'' using ''A'' then the speed of light could be derived from, and so would depend upon, the value for the elementary charge ''e'', and so the value for ''c'' could not be assigned independently from ''e''). {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} We are familiar with inverse properties; plus charge and minus charge, matter and anti-matter ... and we can observe how these may form and/or cancel each other. A simulation universe however is required to be dimensionless (in sum total), for the simulated universe does not 'exist' in any physical sense outside of the 'Computer' (it is simply data on a celestial hard-disk). Our universe does not appear to have inverse properties such as anti-mass (-kg), anti-time (-s) or anti-space (anti-length -m), therefore the first problem the Programmer must solve is how to create the physical scaffolding (of mass, space and time). For example, the Programmer can start by selecting 2 dimensioned quantities, here are used ''r'', ''v'' <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref> such that :<math>kg = \frac{r^4}{v},\; m = \frac{r^9}{v^5},\; s = \frac{r^9}{v^6},\; A = \frac{v^3}{r^6}</math> Quantities ''r'' and ''v'' are chosen so that no unit (''kg'', ''m'', ''s'', ''A'') can cancel another unit (i.e.: the ''kg'' cannot cancel the ''m'' or the ''s'' ...), and so we have 4 independent units (we still cannot define the ''kg'' using the ''m'' or the ''s'' ...), however if 3 (or more) units are combined together in a specific ratio, they can cancel (in a certain ratio our ''r'' and ''v'' become inverse properties and so cancel each other; units = 1). <math>f_X = \frac{kg^9 s^{11}}{m^{15}} = \frac{(\frac{r^4}{v})^9 (\frac{r^9}{v^6})^{11}}{(\frac{r^9}{v^5})^{15}} = 1</math> This f_X, although embedded within are the dimensioned structures for mass, time and length (in the above ratio), would be a dimensionless mathematical structure, units = 1. Thus we may create as much mass, time and length as we wish, the only proviso being that they are created in f_X ratios, so that regardless of how massive, old and large our universe becomes, it is still in sum total dimensionless. Defining the dimensioned quantities ''r'', ''v'' in SI unit terms. :<math>r = (\frac{kg\;m}{s})^{1/4}</math> :<math>v = \frac{m}{s}</math> Mass :<math>\frac{r^4}{v} = (\frac{kg\;m}{s})\;(\frac{s}{m}) = kg</math> Length :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^5})^4 = \frac{s^{20}}{m^{20}}</math> :<math>(\frac{r^9}{v^5})^4 = \frac{kg^9 s^{11}}{m^{11}} = m^4 \frac{kg^9 s^{11}}{m^{15}} = m^4 f_X = m^4</math> Time :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^6})^4 = \frac{s^{24}}{m^{24}}</math> :<math>(\frac{r^9}{v^6})^4 = \frac{kg^9 s^{15}}{m^{15}} = s^4 \frac{kg^9 s^{11}}{m^{15}} = s^4 f_X = s^4</math> And so, although f_X is a dimensionless mathematical structure, we can embed within it the (mass, length, time ...) structures along with their dimensional attributes (kg, m, s, A ..). In the mathematical electron model (discussed below), the electron itself is an example of an f_X structure, it (f_electron) is a dimensionless geometrical object that embeds the physical electron parameters of wavelength, frequency, charge (note: A-m = ampere-meter are the units for a [[w:Magnetic_monopole#In_SI_units |magnetic monopole]]). <math>f_{electron}</math> :<math>units = \frac{A^3 m^3}{s} = \frac{(\frac{v^3}{r^6})^3 (\frac{r^9}{v^5})^3}{(\frac{r^9}{v^6})} = 1</math> We may note that at the macro-level (of planets and stars) these f_X ratio are not found, and so this level is the domain of the observed physical universe, however at the quantum level, f_X ratio do appear, f_electron as an example, the mathematical and physical domains then blurring. This would also explain why physics can measure precisely the parameters of the electron (wavelength, mass ...), but has never found the electron itself. == Programming == “God vs. science debates tend to be restricted to the premise that a God does not rely on science and that science does not need a God. As science and God are thus seen as mutually exclusive there are few, if any, serious attempts to construct mathematical models of a universe whose principle axiom does require a God. However, if there is an Intelligence responsible for the 14 billion year old universe of modern physics, being the universe of Einstein and Dirac, and beginning with the big bang as the act of 'creation', then we must ask how it might be done? What construction technique could have been used to set the laws of physics in motion?” <ref>[https://theprogrammergod.com/ The Programmer God, are we in a Simulation]</ref> === Simulation Time === The (dimensionless) simulation clock-rate would be defined as the minimum 'time variable' ('''age''') increment to the simulation. Using a simple loop as analogy, at ''age'' = 1, the simulation begins (the big bang), certain processes occur, when these are completed ''age'' increments (''age'' = 2, then 3, then 4 ... ) until ''age'' reaches ''the_end'' and the simulation stops. 'begin simulation FOR age = 1 TO the_end 'big bang = 1 conduct certain processes ........ NEXT age 'end simulation [[w:Quantum spacetime |Quantum spacetime]] and [[w:Quantum gravity |Quantum gravity]] models refer to [[w:Planck time | Planck time]] as the smallest discrete unit of time and so the incrementing variable '''age''' could be used to generate units of Planck time (and other Planck units, the physical scaffolding of the universe). In a geometrical model, to these Planck units could be assigned geometrical objects, for example; Initialize_physical_constants; FOR age = 1 TO the_end generate 1 unit of (Planck) time; '1 time 'object' T generate 1 unit of (Planck) mass; '1 mass 'object' M generate 1 unit of (Planck) length; '1 length 'object' L ........ NEXT age The variable ''age'' is the simulation clock-rate, it is simply a counter (1, 2, 3 ...) and so is a dimensionless number, the object T is the geometrical Planck time object, it is dimensioned and is measured by us in seconds. If ''age'' is the origin of Planck time (1 increment to ''age'' generates 1 T object) then ''age'' = 10⁶², this is based on the present [[w:Age_of_the_universe |age of the universe]], which, at 14 billion years, equates to 10⁶² units of Planck time. For each ''age'', certain operations are performed, only after they are finished does ''age'' increment (there is no ''time'' interval between increments). As noted, ''age'' being dimensionless, is not the same as dimensioned Planck time which is the geometrical object T, and this T, being dimensioned, can only appear within the simulation. The analogy would be frames of a movie, each frame contains dimensioned information but there is no ''time'' interval between frames. FOR age = 1 TO the_end (of the movie) display frame{age} NEXT age Although operations (between increments to ''age'') may be extensive, self-aware structures from within the simulation would have no means to determine this, they could only perceive themselves as being in a real-time (for them the smallest unit of ''time'' is 1T, just as the smallest unit of ''time'' in a movie is 1 frame). Their (those self-aware structures) dimension of time would then be a measure of relative motion (a change of state), and so although ultimately deriving from the variable ''age'', their time would not be the same as ''age''. If there was no motion, if all particles and photons were still (no change of state), then their time dimension could not update (if every frame in a movie was the same then actors within that movie could not register a change in time), ''age'' however would continue to increment. Thus we have 3 time structures; 1) the dimension-less simulation clock-rate variable ''age'', 2) the dimensioned time unit (object T), and 3) time as change of state (the observers time). Observer time requires a memory of past events against which a change of state can be perceived. The forward increment to ''age'' would constitute the [[w:arrow of time |arrow of time]]. Reversing this would reverse the arrow of time, the universe would likewise shrink in size and mass accordingly (just as a [[w:white hole |white hole]] is the (time) reversal of a [[w:black hole |black hole]]). FOR age = the_end TO 1 STEP -1 delete 1 unit of Planck time; delete 1 unit of Planck mass; delete 1 unit of Planck length; ........ NEXT age Adding mass, length and time objects per increment to ''age'' would force the universe expansion (in size and mass), and as such an anti-gravitational [[w:dark energy |dark energy]] would not be required, however these objects are dimensioned and so are generated within the simulation. This means that they must somehow combine in a specific ratio whereby they (the units for mass length, time, charge; ''kg'', ''m'', ''s'', ''A'') in sum total cancel each other, leaving the sum universe (the simulation itself) residing on that celestial hard-disk. We may introduce a theoretical dimensionless (f_X) geometrical object denoted as f_Planck within which are embedded the dimensioned objects MLTA (mass, length, time, charge), and from which they may be extracted. FOR age = 1 TO the_end add 1 f_Planck 'dimensionless geometrical 'object' { extract 1 unit of (Planck) time; '1 time 'object' T extract 1 unit of (Planck) mass; '1 mass 'object' M extract 1 unit of (Planck) length; '1 length 'object' L } ........ NEXT age This then means that the simulation, in order to create time T, must also create mass M and space L (become larger and more massive). Thus no matter how small or large the physical universe is (when seen internally), in sum total (when seen externally), there is no universe - it is merely data without physical form. === Universe time-line === As the universe expands outwards (through the constant addition of units of mass and length via f_Planck), and if this expansion pulls particles with it (if it is the origin of motion), then ''now'' (the present) would reside on the surface of the (constantly expanding at the speed of light; ''c'' = 1 Planck length / 1 Planck time) universe, and so the 'past' could be retained, for the past cannot be over-written by the present in an expanding universe (if ''now'' is always on the surface). As this expansion occurs at the Planck scale, information even below quantum states, down to the Planck scale, can be retained, the analogy would be the storing of every [[w:Keystroke_logging |keystroke]], a Planck scale version of the [[w:Akashic records |Akashic records]] ... for if our deeds (the past) are both stored and cannot be over-written (by the present), then we have a candidate for the '[[w:karma |karmic]] heavens' (Matthew 6:19 ''But lay up for yourselves treasures in 'heaven', where neither moth nor rust doth corrupt, and where thieves do not break through nor steal''). This also forms a universe '''time-line''' against which previous information can be compared with new information (a 'memory' of events), without which we could not link cause with effect. === Singularity === In a simulation, the data (software) requires a storage device that is ultimately hardware (RAM, HD ...). In a data world of 1's and 0's such as a computer game, characters within that game may analyze other parts of their 1's and 0's game, but they have no means to analyze the hard disk upon which they (and their game) are stored, for the hard disk is an electro-mechanical device, it is not part of their 1's and 0's world, it is a part of the 'real world', the world of their Programmer. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may or may not resemble the laws that operate in the 'real world' (the world of their Programmer). Thus any region where the laws of physics (the laws of their game world) break down would be significant. A [[w:singularity |singularity]] inside a black hole is such a region <ref>https://www.youtube.com/watch?v=W5j7umtZYB4 a black hole singularity as the interface between worlds</ref>. For the [[w:black hole electron |black-hole electron]], its black-hole center would then be analogous to a storage address on a hard disk, the interface between the simulation world and the real world. A massive (galactic) black-hole could be as an entire data sector. The surface of the black-hole would then be of the simulation world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however would be the interface between the data world and the 'hard disk' of the real world, and so would not exist in any 'physical' terms. It is external to the simulation. As analogy, we may discuss the 3-D surface area of a black-hole but not its volume (interior). === Laws of Physics === The scientific method is built upon testable hypothesis and reproducible results. Water always boils (in defined conditions), at 100°C. In a geometrical universe particles will behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these repeating patterns, the more complex the orbits, the more complex the formulas required to describe them and so forth. However if there is a source code from which these geometrical conditions were programmed, then there may also be non-repeating events, back-doors built into the code (a common practice by terrestrial programmers), these by definition would lie outside the laws of physics and so be labelled as miracles, yet they would be no less valid. === Determinism === [[File:Three body problem figure-8 orbit animation.gif|400px|thumb|An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259.<ref>Here the gravitational constant ''G'' has been set to 1, and the initial conditions are '''r'''₁(0) = −'''r'''₃(0) = (−0.97000436, 0.24308753); '''r'''₂(0) = (0,0); '''v'''₁(0) = '''v'''₃(0) = (0.4662036850, 0.4323657300); '''v'''₂(0) = (−0.93240737, −0.86473146). The values are obtained from Chenciner & Montgomery (2000).</ref>]] Particles form more complex structures such as atoms and molecules via a system of orbitals; nuclear, atomic and gravitational. The [[w:Three-body_problem |3-body problem]] is the problem of taking the initial positions and velocities (or [[w:momentum|momenta |momentum|momenta]]) of three or more point masses and solving for their subsequent motion according to [[w:Newton's laws of motion |Newton's laws of motion]] and [[w:Newton's law of universal gravitation |Newton's law of universal gravitation]].<ref name="PrincetonCompanion">{{Citation | last = Barrow-Green | first = June | year = 2008 | title = The Three-Body Problem | editor-last1 = Gowers | editor-first1 = Timothy | editor-last2 = Barrow-Green | editor-first2 = June | editor-last3 = Leader | editor-first3 = Imre | encyclopedia = The Princeton Companion to Mathematics | pages = 726–728 | publisher = Princeton University Press }}</ref>. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for gods and men alike the only way to know what that outcome will be is to run the simulation itself. ==Geometry coded universe== Modelling a Planck scale simulation universe using geometrical forms (links) * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass == External links == * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] * [https://philpapers.org/rec/GRUTIA-2 Simulation theory as evidence for God] (academic peer-reviewed article) ==References== {{Reflist}} [[Category:Philosophy| ]] [[Category:Philosophy of science| ]] o2ox02ai0jiwshc0pub9kntqw816dcy 2718254 2718253 2025-06-10T19:50:37Z 212.200.164.104 /* Discussion */ 2718254 wikitext text/x-wiki '''Is God a Programmer? analyzing the deep-universe simulation hypothesis at the Planck scale''' The [[w:simulation hypothesis |simulation hypothesis]] is the proposal that all of reality, including the Earth and the rest of the universe, could be an artificial simulation, such as a computer simulation. [[w:Neil_deGrasse_Tyson |Neil deGrasse Tyson]] put the odds at 50-50 that our entire existence is a program on someone else’s hard drive <ref>Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. [[w:David_Chalmers |David Chalmers]] noted “We in this universe can create simulated worlds and there’s nothing remotely spooky about that. Our creator isn’t especially spooky, it’s just some teenage hacker in the next universe up. Turn the tables, and we are essentially gods over our own computer creations <ref>https://www.youtube.com/watch?v=yqbS5qJU8PA, David Chalmers, Serious Science</ref> <ref>The Matrix as Metaphysics, David Chalmers http://consc.net/papers/matrix.pdf</ref> <ref>Are We Living in a Computer Simulation?https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. The commonly postulated [[w:Ancestor_simulation |ancestor simulation]] approach, which [[w:Nick Bostrom |Nick Bostrom]] called "the simulation argument", argues for "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor. However this simulation variant can be traced back to an 'organic base reality' (the original programmer ancestors and their physical planet). The [[v:God_(programmer) |Programmer God]] hypothesis<ref>https://codingthecosmos.com/podcast/ AI generated podcasts</ref> conversely states that a (deep universe) simulation began with the big bang and was programmed by an external intelligence (external to the physical universe), the Programmer by definition a God in the creator of the universe context. Our universe in its entirety, down to the smallest detail, and including life-forms, is within the simulation, the laws of nature, at their most fundamental level, are coded rules running on top of the simulation operating system. The operating system itself is mathematical (and potentially the origin of mathematics). Any candidate for a Programmer-God simulation-universe source code must satisfy these conditions; :1. It can generate physical structures from mathematical forms. :2. The sum universe is dimensionless (simply data on a celestial hard disk). :3. We must be able to use it to derive the laws of physics (because the source code is the origin of the laws of nature, and the laws of physics are our observations of the laws of nature). :4. The mathematical logic must be unknown to us (the Programmer is a non-human intelligence). :5. The coding should have an 'elegance' commensurate with the Programmer's level of skill. == Philosophy == Physicist [[w:Eugene Wigner |Eugene Wigner]] ([[w:The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences |The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]) <ref>{{Cite journal | last1 = Wigner | first1 = E. P. | authorlink = Eugene Wigner| doi = 10.1002/cpa.3160130102 | title = The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959 | journal = Communications on Pure and Applied Mathematics | volume = 13 | pages = 1–14 | year = 1960 | pmid = | pmc = |bibcode = 1960CPAM...13....1W }}</ref> <blockquote>The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. </blockquote> === Discussion === [[w:Philosophy of mathematics |Philosophy of mathematics]] is that branch of philosophy which attempts to answer questions such as: ‘why is mathematics useful in describing nature?’, ‘in which sense, if any, do mathematical entities such as numbers exist?’ and ‘why and how are mathematical statements true?’ This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math. Mathematical realism holds that mathematical entities exist independently of the human mind. We do not invent mathematics, but rather discover it. Triangles, for example, are real entities that have an existence <ref>- http://plato.stanford.edu/entries/platonism-mathematics/</ref>. The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality. It can be considered a form of [[w:Pythagoreanism | Pythagoreanism]] or [[w:Platonism | Platonism]] in that it proposes the existence of ''mathematical objects''; and a form of [[w:philosophy of mathematics | mathematical monism]] in that it denies that anything exists except these ''mathematical objects''. Physicist [[w:Max Tegmark | Max Tegmark]] in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality"<ref name="Tegmark1998">{{cite journal|last=Tegmark |first=Max |date=November 1998 |title=Is "the Theory of Everything" Merely the Ultimate Ensemble Theory? |journal=Annals of Physics |volume=270 |issue=1 |pages=1–51 |doi=10.1006/aphy.1998.5855 |arxiv = gr-qc/9704009 |bibcode = 1998AnPhy.270....1T }}</ref><ref>M. Tegmark 2014, "[http://mathematicaluniverse.org Our Mathematical Universe]", Knopf</ref> proposed that ''Our external physical reality is a mathematical structure''.<ref name="Tegmark2008">{{cite journal|last=Tegmark |first=Max |date=February 2008 |title=The Mathematical Universe |journal=Foundations of Physics |volume=38 |issue=2 |pages=101–150 |doi=10.1007/s10701-007-9186-9 |arxiv=0704.0646|bibcode = 2008FoPh...38..101T }}</ref> That is, the physical universe is not merely ''described by'' mathematics, but ''is'' mathematics (specifically, a [[w:mathematical structure | mathematical structure]]). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref> The principle constraints to any mathematical universe simulation hypothesis are; 1. the computational resources required. The ancestor simulation can resolve this by adapting from the [[w:virtual rality |virtual reality]] approach where only the observable region is simulated and only to the degree required, and 2. that any 'self-aware structures' (humans for example) within the simulation must "subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref>. Succinctly, our computer games may be able to simulate our physical world, but they are still only simulations of a physical reality (regardless of how realistic they may seem) ... we are not yet able to program actual physical dimensions of mass, space and time from mathematical structures, and indeed this may not be possible with a computer hard-ware architecture that can only process binary data. === Deep-universe source code === As a deep-universe simulation is programmed by an external (external to the universe) intelligence (the Programmer God hypothesis), we cannot presume a priori knowledge regarding the simulation source code other than from this code the laws of nature emerged, and so any deep-universe simulation model we try to emulate must be universal, i.e.: independent of any system of units, of the [[w:Dimensional_analysis |dimensioned]] [[w:physical constants |physical constants]] (''G'', ''h'', ''c'', ''e'' .. ), and of any numbering systems. Furthermore, although a deep-universe simulation source code may use mathematical forms (circles, spheres ...) we are familiar with (for ultimately the source code is the origin of these forms), it will have been developed by a non-human intelligence and so we may have to develop new mathematical tools to decipher the underlying logic. By implication therefore, any theoretical basis for a source code that fits the above criteria (and from which the laws of nature will emerge), could be construed as our first tangible evidence of a non-human intelligence. === Constants === A physical universe is characterized by measurable quantities (size, mass, color, texture ...), and so a physical universe can be measured and defined. Contrast then becomes information, the statement ''this is a big apple'' requires a ''small apple'' against which big becomes a relative term. For analytical purposes we select a reference value, for example 0C or 32F, and measure all temperatures against this reference. The smaller the resolution of the measurements, the greater the information content (the file size of a 32 mega-pixel photo is larger than a 4 mega-pixel photo). A simulation universe may be presumed to also have a resolution dictating how much information the simulation can store and manipulate. To measure the fundamental parameters of our universe physics uses [[w:physical constant |physical constants]]. A physical constant is a [[w:physical quantity |physical quantity]] that is generally believed to be both universal in nature and have a constant value in time. These can be divided into 1) dimension-ed (measured using physical units ''kg'', ''m'', ''s'', ''A'' ...) such as the [[w:speed of light |speed of light]] ''c'', [[w:gravitational constant |gravitational constant]] ''G'', [[w:Planck constant |Planck constant]] ''h'' ... as in the table {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} Physicist [[w: |Lev Okun]] noted "Theoretical equations describing the physical world deal with dimensionless quantities and their solutions depend on dimensionless fundamental parameters. But experiments, from which these theories are extracted and by which they could be tested, involve measurements, i.e. comparisons with standard dimension-ful scales. Without standard dimension-ful units and hence without certain conventions physics is unthinkable <ref>Michael J. Duff et al, Journal of High Energy Physics, Volume 2002, JHEP03(2002)</ref>. 2) dimension-less, such as the [[w:Fine-structure_constant |fine structure constant]] ''α''. A dimension-less constant does not measure any physical quantity (it has no units; units = 1). 3) dimension-less [[w:mathematical constant |mathematical constants]], most notably [[w:pi |pi]] = 3.14159265358979 and [[w:Natural_logarithm |e]] = 2.718281828459. Although these are [[w:transcendental number |transcendental numbers]], they can be constructed by integers in a series, and so for a universe expanding incrementally (see simulation time), these constants could be formed within the simulation. For example, at time ''t''; <math display=block>t = 1; \frac{\pi^2}{6} = \frac{1}{t^2} </math> <math display=block>t = 2; \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{t^2}</math> <math display=block>t = now: \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots + \frac{1}{t^2} </math> We may now define the fundamental physical constant as a parameter specifically chosen by the Programmer and is encoded into the simulation code directly, and so whilst it may be inferable, it is not derived from other constants ([[w:Fine-structure_constant#Numerological_explanations_and_multiverse_theory |Richard Feynman on the fine structure constant]]). It should also be dimension-less otherwise the simulation itself becomes dimensioned (if the simulation is running on a celestial computer it is merely data, it has no physical size or shape or ...), and so the dimensioned constants (''G'', ''h'', ''c'', ''e''...) must all be derivable (derived from within the simulation) via the (embedded in the source code) fundamental physical constants (of which the fine structure constant alpha may be an example). Although [[w:pi |pi]] and [[w:Natural_logarithm |e]] are dimensionless, they can be derived internally (from integers), and as they have application in the mathematical realm, they can be referred to as mathematical constants. ==== Planck scale ==== The [[w:Planck scale |Planck scale]] refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the [[w:Standard Model |Standard Model]], [[w:quantum field theory |quantum field theory]] and [[w:general relativity |general relativity]] are no longer reconcilable, and [[w:Quantum Gravity |quantum effects of gravity]] are expected to dominate (quantum gravitational effects only appear at length scales near the Planck scale). Although particles may not be cognizance of our 'laws of physics', they do know the 'laws of nature'. These laws of nature would run directly off the universe OS (operating system), and so below this OS, 'physics' as we know it must necessarily break down. At present the Planck scale is the lowest known level, consequently any attempt to detect evidence of an underlying simulation coding must consider (if not actually begin at) this, the Planck scale<ref>https://www.youtube.com/watch?v=AMQRXGYCDrY Planck scale, Brian Greene</ref>. The [[w:International_System_of_Units |SI units]] for the dimension-ful mksa units are; meter (length), kilogram (mass), second (time), ampere (electric current). There are Planck units that represent these SI units, and so a simulation could use them as discrete building blocks; [[w:Planck length |Planck length]] (the smallest possible unit of length), [[w:Planck mass |Planck mass]] (the unit of mass), [[w:Planck time |Planck time]] (the smallest possible unit of time), [[w:Planck charge |Planck charge]] (the unit of charge). The speed of light then becomes ''c'' = 1 Planck length / 1 Planck time. These units would define the resolution and so information carrying capacity of the simulation universe. ==== Numbering systems ==== As well as our decimal system, computers apply binary and hexadecimal numbering systems. In particular the decimal and hexadecimal are of terrestrial origin and may not be considered 'universal'. Furthermore numbering systems measure only the frequency of an event and contain no information as to the event itself. The number 299 792 458 could refer to the speed of light (299 792 458 m/s) or could equally be referring to the number of apples in a container (299 792 458 apples). As such, numbers require a 'descriptive', whether m/s or apples. Numbers also do not include their history, is 299 792 458 for example a derivation of other base numbers? Present universe simulations use the laws of physics and the physical constants are built in, however both these laws and the physical constants are known only to a limited precision, and so a simulation with 10⁶² iterations (the present age of the universe in units of Planck time) will accumulate errors. Number based computing may be sufficient for ancestor-simulation models where only the observed region needs to be calculated, but has inherent limitations for deep universe simulations where the entire universe is continuously updated. The actual computational requirements for a Planck scale universe simulation based on a numbering system with the laws of physics embedded would be an unknown and consequently lead to an 'non-testable' hypothesis. This is a commonly applied reasoning for rejecting the deep universe simulation. ==== Geometrical objects ==== A mathematical constant such as [[w:pi |pi]] refers to a geometrical construct (the ratio of circle circumference to circle radius) and so is not constrained by any particular numbering system (in the decimal system π = 3.14159...), and so may be considered both universal and eternal. Likewise, by assigning geometrical objects instead of numbers to the Planck units, the problems with a numbering system can be resolved. These objects would however have to fulfill the following conditions; 1) embedded attribute - for example the object for length must embed the function of ''length'' such that a descriptive (km, mile ... ) is not required. Electron wavelength would then be measurable in terms of the length object, as such the length object must be embedded within the electron (the electron object). Although the mass object would incorporate the function ''mass'', the time object the function ''time'' ..., it is not necessary that there be an individual physical mass or physical length or physical time ..., but only that in relation to the other units, the object must express that function (i.e.: the mass object has the function of mass when in the presence of the objects for space and time). The electron could then be a complex event (complex geometrical object) constructed by combining the objects for mass, length, time and charge into 1 event, and thus electron charge, wavelength, frequency and mass would then be different aspects of that 1 geometry (the electron event) and not independent parameters (independent of each other). 2) The objects for mass, length, time and charge must be able to combine with each other [[w:Lego |Lego-style]] to form more complex objects (events) such as electrons and apples whilst still retaining the underlying information (the mass of the apple derives from the mass objects embedded within that apple). Not only must these objects be able to form complex events such as particles, but these events themselves are geometrical objects and so must likewise function according to their geometries. Electrons would orbit protons according to their respective electron and proton geometries, these orbits the result of geometrical imperatives and not due to any built-in laws of physics (the orbital path is a consequence of all the underlying geometries). However, as orbits follow regular and repeating patterns, they can be described (by us) using mathematical formulas. As the events grow in complexity (from atoms to molecules to planets), so too will the patterns (and likewise the formulas we use to describe them). Consequently the ''laws of physics'' would then become our mathematical descriptions of the underlying geometrically imposed patterns. 3) These objects would replace coded instructions (the instruction sets would be built into the objects) thereby instigating a geometrically autonomous universe. The electron 'knows' what to do by virtue of the information encoded within its geometry, no coded electron CALL FUNCTION is required. This would be equivalent to combining the hardware, software and CPU together such that the 'software' changes (adjusts) to the changing 'hardware' (DNA may be an analogy). Note: A purely mathematical universe has no limits in size and can be infinitely large and infinity small. A geometrical universe (that uses objects) has limitations, it can be no smaller than the smallest object for example and has discrete parts (those objects). The philosophy of the TOE (theory of everything) therefore includes a debate between the mathematical universe and the geometrical universe, however this distinction between mathematical and geometrical would only be apparent at the Planck scale. === Evidence of a simulation === The laws of physics are our incomplete observations of the natural universe, and so evidence of a simulation may be found in ambiguities or anomalies within these laws. Furthermore, if complexity arises over time, then at unit time the 'handiwork' of the Programmer may be notable by a simplicity and elegance of the geometries employed ... for the Programmer by definition has God-level programming skills. Here is a notable example. Mass, space and time from the number 1 The dimensions of mass, space and time are considered by science to be independent of each other, we cannot measure the ''distance'' from Tokyo to London using kilograms and amperes, or measure ''mass'' using space and time. Indeed, what characterizes a physical universe as opposed to a simulated universe is the notion that there is a fundamental structure underneath, that in some sense mass 'is', that time 'is' and space 'is' ... thus we cannot write ''kg'' in terms of ''m'' and ''s''. To do so would render our concepts of a physical universe meaningless. The 26th General Conference on Weights and Measures ([[w:2019 redefinition of SI base units|2019 redefinition of SI base units]]) assigned exact numerical values to 4 physical constants (''h, c, e, k''_B) independently of each other (and thereby confirming these as fundamental constants), and as they are measured in SI units ('''kg''', '''m''', '''s''', '''A''', '''K'''), these units must also be independent of each other (i.e.: these are fundamental units, for example if we could define ''m'' using ''A'' then the speed of light could be derived from, and so would depend upon, the value for the elementary charge ''e'', and so the value for ''c'' could not be assigned independently from ''e''). {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} We are familiar with inverse properties; plus charge and minus charge, matter and anti-matter ... and we can observe how these may form and/or cancel each other. A simulation universe however is required to be dimensionless (in sum total), for the simulated universe does not 'exist' in any physical sense outside of the 'Computer' (it is simply data on a celestial hard-disk). Our universe does not appear to have inverse properties such as anti-mass (-kg), anti-time (-s) or anti-space (anti-length -m), therefore the first problem the Programmer must solve is how to create the physical scaffolding (of mass, space and time). For example, the Programmer can start by selecting 2 dimensioned quantities, here are used ''r'', ''v'' <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref> such that :<math>kg = \frac{r^4}{v},\; m = \frac{r^9}{v^5},\; s = \frac{r^9}{v^6},\; A = \frac{v^3}{r^6}</math> Quantities ''r'' and ''v'' are chosen so that no unit (''kg'', ''m'', ''s'', ''A'') can cancel another unit (i.e.: the ''kg'' cannot cancel the ''m'' or the ''s'' ...), and so we have 4 independent units (we still cannot define the ''kg'' using the ''m'' or the ''s'' ...), however if 3 (or more) units are combined together in a specific ratio, they can cancel (in a certain ratio our ''r'' and ''v'' become inverse properties and so cancel each other; units = 1). <math>f_X = \frac{kg^9 s^{11}}{m^{15}} = \frac{(\frac{r^4}{v})^9 (\frac{r^9}{v^6})^{11}}{(\frac{r^9}{v^5})^{15}} = 1</math> This f_X, although embedded within are the dimensioned structures for mass, time and length (in the above ratio), would be a dimensionless mathematical structure, units = 1. Thus we may create as much mass, time and length as we wish, the only proviso being that they are created in f_X ratios, so that regardless of how massive, old and large our universe becomes, it is still in sum total dimensionless. Defining the dimensioned quantities ''r'', ''v'' in SI unit terms. :<math>r = (\frac{kg\;m}{s})^{1/4}</math> :<math>v = \frac{m}{s}</math> Mass :<math>\frac{r^4}{v} = (\frac{kg\;m}{s})\;(\frac{s}{m}) = kg</math> Length :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^5})^4 = \frac{s^{20}}{m^{20}}</math> :<math>(\frac{r^9}{v^5})^4 = \frac{kg^9 s^{11}}{m^{11}} = m^4 \frac{kg^9 s^{11}}{m^{15}} = m^4 f_X = m^4</math> Time :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^6})^4 = \frac{s^{24}}{m^{24}}</math> :<math>(\frac{r^9}{v^6})^4 = \frac{kg^9 s^{15}}{m^{15}} = s^4 \frac{kg^9 s^{11}}{m^{15}} = s^4 f_X = s^4</math> And so, although f_X is a dimensionless mathematical structure, we can embed within it the (mass, length, time ...) structures along with their dimensional attributes (kg, m, s, A ..). In the mathematical electron model (discussed below), the electron itself is an example of an f_X structure, it (f_electron) is a dimensionless geometrical object that embeds the physical electron parameters of wavelength, frequency, charge (note: A-m = ampere-meter are the units for a [[w:Magnetic_monopole#In_SI_units |magnetic monopole]]). <math>f_{electron}</math> :<math>units = \frac{A^3 m^3}{s} = \frac{(\frac{v^3}{r^6})^3 (\frac{r^9}{v^5})^3}{(\frac{r^9}{v^6})} = 1</math> We may note that at the macro-level (of planets and stars) these f_X ratio are not found, and so this level is the domain of the observed physical universe, however at the quantum level, f_X ratio do appear, f_electron as an example, the mathematical and physical domains then blurring. This would also explain why physics can measure precisely the parameters of the electron (wavelength, mass ...), but has never found the electron itself. == Programming == “God vs. science debates tend to be restricted to the premise that a God does not rely on science and that science does not need a God. As science and God are thus seen as mutually exclusive there are few, if any, serious attempts to construct mathematical models of a universe whose principle axiom does require a God. However, if there is an Intelligence responsible for the 14 billion year old universe of modern physics, being the universe of Einstein and Dirac, and beginning with the big bang as the act of 'creation', then we must ask how it might be done? What construction technique could have been used to set the laws of physics in motion?” <ref>[https://theprogrammergod.com/ The Programmer God, are we in a Simulation]</ref> === Simulation Time === The (dimensionless) simulation clock-rate would be defined as the minimum 'time variable' ('''age''') increment to the simulation. Using a simple loop as analogy, at ''age'' = 1, the simulation begins (the big bang), certain processes occur, when these are completed ''age'' increments (''age'' = 2, then 3, then 4 ... ) until ''age'' reaches ''the_end'' and the simulation stops. 'begin simulation FOR age = 1 TO the_end 'big bang = 1 conduct certain processes ........ NEXT age 'end simulation [[w:Quantum spacetime |Quantum spacetime]] and [[w:Quantum gravity |Quantum gravity]] models refer to [[w:Planck time | Planck time]] as the smallest discrete unit of time and so the incrementing variable '''age''' could be used to generate units of Planck time (and other Planck units, the physical scaffolding of the universe). In a geometrical model, to these Planck units could be assigned geometrical objects, for example; Initialize_physical_constants; FOR age = 1 TO the_end generate 1 unit of (Planck) time; '1 time 'object' T generate 1 unit of (Planck) mass; '1 mass 'object' M generate 1 unit of (Planck) length; '1 length 'object' L ........ NEXT age The variable ''age'' is the simulation clock-rate, it is simply a counter (1, 2, 3 ...) and so is a dimensionless number, the object T is the geometrical Planck time object, it is dimensioned and is measured by us in seconds. If ''age'' is the origin of Planck time (1 increment to ''age'' generates 1 T object) then ''age'' = 10⁶², this is based on the present [[w:Age_of_the_universe |age of the universe]], which, at 14 billion years, equates to 10⁶² units of Planck time. For each ''age'', certain operations are performed, only after they are finished does ''age'' increment (there is no ''time'' interval between increments). As noted, ''age'' being dimensionless, is not the same as dimensioned Planck time which is the geometrical object T, and this T, being dimensioned, can only appear within the simulation. The analogy would be frames of a movie, each frame contains dimensioned information but there is no ''time'' interval between frames. FOR age = 1 TO the_end (of the movie) display frame{age} NEXT age Although operations (between increments to ''age'') may be extensive, self-aware structures from within the simulation would have no means to determine this, they could only perceive themselves as being in a real-time (for them the smallest unit of ''time'' is 1T, just as the smallest unit of ''time'' in a movie is 1 frame). Their (those self-aware structures) dimension of time would then be a measure of relative motion (a change of state), and so although ultimately deriving from the variable ''age'', their time would not be the same as ''age''. If there was no motion, if all particles and photons were still (no change of state), then their time dimension could not update (if every frame in a movie was the same then actors within that movie could not register a change in time), ''age'' however would continue to increment. Thus we have 3 time structures; 1) the dimension-less simulation clock-rate variable ''age'', 2) the dimensioned time unit (object T), and 3) time as change of state (the observers time). Observer time requires a memory of past events against which a change of state can be perceived. The forward increment to ''age'' would constitute the [[w:arrow of time |arrow of time]]. Reversing this would reverse the arrow of time, the universe would likewise shrink in size and mass accordingly (just as a [[w:white hole |white hole]] is the (time) reversal of a [[w:black hole |black hole]]). FOR age = the_end TO 1 STEP -1 delete 1 unit of Planck time; delete 1 unit of Planck mass; delete 1 unit of Planck length; ........ NEXT age Adding mass, length and time objects per increment to ''age'' would force the universe expansion (in size and mass), and as such an anti-gravitational [[w:dark energy |dark energy]] would not be required, however these objects are dimensioned and so are generated within the simulation. This means that they must somehow combine in a specific ratio whereby they (the units for mass length, time, charge; ''kg'', ''m'', ''s'', ''A'') in sum total cancel each other, leaving the sum universe (the simulation itself) residing on that celestial hard-disk. We may introduce a theoretical dimensionless (f_X) geometrical object denoted as f_Planck within which are embedded the dimensioned objects MLTA (mass, length, time, charge), and from which they may be extracted. FOR age = 1 TO the_end add 1 f_Planck 'dimensionless geometrical 'object' { extract 1 unit of (Planck) time; '1 time 'object' T extract 1 unit of (Planck) mass; '1 mass 'object' M extract 1 unit of (Planck) length; '1 length 'object' L } ........ NEXT age This then means that the simulation, in order to create time T, must also create mass M and space L (become larger and more massive). Thus no matter how small or large the physical universe is (when seen internally), in sum total (when seen externally), there is no universe - it is merely data without physical form. === Universe time-line === As the universe expands outwards (through the constant addition of units of mass and length via f_Planck), and if this expansion pulls particles with it (if it is the origin of motion), then ''now'' (the present) would reside on the surface of the (constantly expanding at the speed of light; ''c'' = 1 Planck length / 1 Planck time) universe, and so the 'past' could be retained, for the past cannot be over-written by the present in an expanding universe (if ''now'' is always on the surface). As this expansion occurs at the Planck scale, information even below quantum states, down to the Planck scale, can be retained, the analogy would be the storing of every [[w:Keystroke_logging |keystroke]], a Planck scale version of the [[w:Akashic records |Akashic records]] ... for if our deeds (the past) are both stored and cannot be over-written (by the present), then we have a candidate for the '[[w:karma |karmic]] heavens' (Matthew 6:19 ''But lay up for yourselves treasures in 'heaven', where neither moth nor rust doth corrupt, and where thieves do not break through nor steal''). This also forms a universe '''time-line''' against which previous information can be compared with new information (a 'memory' of events), without which we could not link cause with effect. === Singularity === In a simulation, the data (software) requires a storage device that is ultimately hardware (RAM, HD ...). In a data world of 1's and 0's such as a computer game, characters within that game may analyze other parts of their 1's and 0's game, but they have no means to analyze the hard disk upon which they (and their game) are stored, for the hard disk is an electro-mechanical device, it is not part of their 1's and 0's world, it is a part of the 'real world', the world of their Programmer. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may or may not resemble the laws that operate in the 'real world' (the world of their Programmer). Thus any region where the laws of physics (the laws of their game world) break down would be significant. A [[w:singularity |singularity]] inside a black hole is such a region <ref>https://www.youtube.com/watch?v=W5j7umtZYB4 a black hole singularity as the interface between worlds</ref>. For the [[w:black hole electron |black-hole electron]], its black-hole center would then be analogous to a storage address on a hard disk, the interface between the simulation world and the real world. A massive (galactic) black-hole could be as an entire data sector. The surface of the black-hole would then be of the simulation world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however would be the interface between the data world and the 'hard disk' of the real world, and so would not exist in any 'physical' terms. It is external to the simulation. As analogy, we may discuss the 3-D surface area of a black-hole but not its volume (interior). === Laws of Physics === The scientific method is built upon testable hypothesis and reproducible results. Water always boils (in defined conditions), at 100°C. In a geometrical universe particles will behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these repeating patterns, the more complex the orbits, the more complex the formulas required to describe them and so forth. However if there is a source code from which these geometrical conditions were programmed, then there may also be non-repeating events, back-doors built into the code (a common practice by terrestrial programmers), these by definition would lie outside the laws of physics and so be labelled as miracles, yet they would be no less valid. === Determinism === [[File:Three body problem figure-8 orbit animation.gif|400px|thumb|An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259.<ref>Here the gravitational constant ''G'' has been set to 1, and the initial conditions are '''r'''₁(0) = −'''r'''₃(0) = (−0.97000436, 0.24308753); '''r'''₂(0) = (0,0); '''v'''₁(0) = '''v'''₃(0) = (0.4662036850, 0.4323657300); '''v'''₂(0) = (−0.93240737, −0.86473146). The values are obtained from Chenciner & Montgomery (2000).</ref>]] Particles form more complex structures such as atoms and molecules via a system of orbitals; nuclear, atomic and gravitational. The [[w:Three-body_problem |3-body problem]] is the problem of taking the initial positions and velocities (or [[w:momentum|momenta |momentum|momenta]]) of three or more point masses and solving for their subsequent motion according to [[w:Newton's laws of motion |Newton's laws of motion]] and [[w:Newton's law of universal gravitation |Newton's law of universal gravitation]].<ref name="PrincetonCompanion">{{Citation | last = Barrow-Green | first = June | year = 2008 | title = The Three-Body Problem | editor-last1 = Gowers | editor-first1 = Timothy | editor-last2 = Barrow-Green | editor-first2 = June | editor-last3 = Leader | editor-first3 = Imre | encyclopedia = The Princeton Companion to Mathematics | pages = 726–728 | publisher = Princeton University Press }}</ref>. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for gods and men alike the only way to know what that outcome will be is to run the simulation itself. ==Geometry coded universe== Modelling a Planck scale simulation universe using geometrical forms (links) * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass == External links == * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] * [https://philpapers.org/rec/GRUTIA-2 Simulation theory as evidence for God] (academic peer-reviewed article) ==References== {{Reflist}} [[Category:Philosophy| ]] [[Category:Philosophy of science| ]] 2rt6klau7udtok5pj8671ch4fmcfa0b 2718255 2718254 2025-06-10T19:50:48Z 212.200.164.104 /* Deep-universe source code */ 2718255 wikitext text/x-wiki '''Is God a Programmer? analyzing the deep-universe simulation hypothesis at the Planck scale''' The [[w:simulation hypothesis |simulation hypothesis]] is the proposal that all of reality, including the Earth and the rest of the universe, could be an artificial simulation, such as a computer simulation. [[w:Neil_deGrasse_Tyson |Neil deGrasse Tyson]] put the odds at 50-50 that our entire existence is a program on someone else’s hard drive <ref>Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. [[w:David_Chalmers |David Chalmers]] noted “We in this universe can create simulated worlds and there’s nothing remotely spooky about that. Our creator isn’t especially spooky, it’s just some teenage hacker in the next universe up. Turn the tables, and we are essentially gods over our own computer creations <ref>https://www.youtube.com/watch?v=yqbS5qJU8PA, David Chalmers, Serious Science</ref> <ref>The Matrix as Metaphysics, David Chalmers http://consc.net/papers/matrix.pdf</ref> <ref>Are We Living in a Computer Simulation?https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. The commonly postulated [[w:Ancestor_simulation |ancestor simulation]] approach, which [[w:Nick Bostrom |Nick Bostrom]] called "the simulation argument", argues for "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor. However this simulation variant can be traced back to an 'organic base reality' (the original programmer ancestors and their physical planet). The [[v:God_(programmer) |Programmer God]] hypothesis<ref>https://codingthecosmos.com/podcast/ AI generated podcasts</ref> conversely states that a (deep universe) simulation began with the big bang and was programmed by an external intelligence (external to the physical universe), the Programmer by definition a God in the creator of the universe context. Our universe in its entirety, down to the smallest detail, and including life-forms, is within the simulation, the laws of nature, at their most fundamental level, are coded rules running on top of the simulation operating system. The operating system itself is mathematical (and potentially the origin of mathematics). Any candidate for a Programmer-God simulation-universe source code must satisfy these conditions; :1. It can generate physical structures from mathematical forms. :2. The sum universe is dimensionless (simply data on a celestial hard disk). :3. We must be able to use it to derive the laws of physics (because the source code is the origin of the laws of nature, and the laws of physics are our observations of the laws of nature). :4. The mathematical logic must be unknown to us (the Programmer is a non-human intelligence). :5. The coding should have an 'elegance' commensurate with the Programmer's level of skill. == Philosophy == Physicist [[w:Eugene Wigner |Eugene Wigner]] ([[w:The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences |The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]) <ref>{{Cite journal | last1 = Wigner | first1 = E. P. | authorlink = Eugene Wigner| doi = 10.1002/cpa.3160130102 | title = The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959 | journal = Communications on Pure and Applied Mathematics | volume = 13 | pages = 1–14 | year = 1960 | pmid = | pmc = |bibcode = 1960CPAM...13....1W }}</ref> <blockquote>The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. </blockquote> === Discussion === [[w:Philosophy of mathematics |Philosophy of mathematics]] is that branch of philosophy which attempts to answer questions such as: ‘why is mathematics useful in describing nature?’, ‘in which sense, if any, do mathematical entities such as numbers exist?’ and ‘why and how are mathematical statements true?’ This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math. Mathematical realism holds that mathematical entities exist independently of the human mind. We do not invent mathematics, but rather discover it. Triangles, for example, are real entities that have an existence <ref>- http://plato.stanford.edu/entries/platonism-mathematics/</ref>. The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality. It can be considered a form of [[w:Pythagoreanism | Pythagoreanism]] or [[w:Platonism | Platonism]] in that it proposes the existence of ''mathematical objects''; and a form of [[w:philosophy of mathematics | mathematical monism]] in that it denies that anything exists except these ''mathematical objects''. Physicist [[w:Max Tegmark | Max Tegmark]] in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality"<ref name="Tegmark1998">{{cite journal|last=Tegmark |first=Max |date=November 1998 |title=Is "the Theory of Everything" Merely the Ultimate Ensemble Theory? |journal=Annals of Physics |volume=270 |issue=1 |pages=1–51 |doi=10.1006/aphy.1998.5855 |arxiv = gr-qc/9704009 |bibcode = 1998AnPhy.270....1T }}</ref><ref>M. Tegmark 2014, "[http://mathematicaluniverse.org Our Mathematical Universe]", Knopf</ref> proposed that ''Our external physical reality is a mathematical structure''.<ref name="Tegmark2008">{{cite journal|last=Tegmark |first=Max |date=February 2008 |title=The Mathematical Universe |journal=Foundations of Physics |volume=38 |issue=2 |pages=101–150 |doi=10.1007/s10701-007-9186-9 |arxiv=0704.0646|bibcode = 2008FoPh...38..101T }}</ref> That is, the physical universe is not merely ''described by'' mathematics, but ''is'' mathematics (specifically, a [[w:mathematical structure | mathematical structure]]). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref> The principle constraints to any mathematical universe simulation hypothesis are; 1. the computational resources required. The ancestor simulation can resolve this by adapting from the [[w:virtual rality |virtual reality]] approach where only the observable region is simulated and only to the degree required, and 2. that any 'self-aware structures' (humans for example) within the simulation must "subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref>. Succinctly, our computer games may be able to simulate our physical world, but they are still only simulations of a physical reality (regardless of how realistic they may seem) ... we are not yet able to program actual physical dimensions of mass, space and time from mathematical structures, and indeed this may not be possible with a computer hard-ware architecture that can only process binary data. === Deep-universe source code === As a deep-universe simulation is programmed by an external (external to the universe) intelligence (the Programmer God hypothesis), we cannot presume a priori knowledge regarding the simulation source code other than from this code the laws of nature emerged, and so any deep-universe simulation model we try to emulate must be universal, i.e.: independent of any system of units, of the [[w:Dimensional_analysis |dimensioned]] [[w:physical constants |physical constants]] (''G'', ''h'', ''c'', ''e'' .. ), and of any numbering systems. Furthermore, although a deep-universe simulation source code may use mathematical forms (circles, spheres ...) we are familiar with (for ultimately the source code is the origin of these forms), it will have been developed by a non-human intelligence and so we may have to develop new mathematical tools to decipher the underlying logic. By implication therefore, any theoretical basis for a source code that fits the above criteria (and from which the laws of nature will emerge), could be construed as our first tangible evidence of a non-human intelligence. === Constants === A physical universe is characterized by measurable quantities (size, mass, color, texture ...), and so a physical universe can be measured and defined. Contrast then becomes information, the statement ''this is a big apple'' requires a ''small apple'' against which big becomes a relative term. For analytical purposes we select a reference value, for example 0C or 32F, and measure all temperatures against this reference. The smaller the resolution of the measurements, the greater the information content (the file size of a 32 mega-pixel photo is larger than a 4 mega-pixel photo). A simulation universe may be presumed to also have a resolution dictating how much information the simulation can store and manipulate. To measure the fundamental parameters of our universe physics uses [[w:physical constant |physical constants]]. A physical constant is a [[w:physical quantity |physical quantity]] that is generally believed to be both universal in nature and have a constant value in time. These can be divided into 1) dimension-ed (measured using physical units ''kg'', ''m'', ''s'', ''A'' ...) such as the [[w:speed of light |speed of light]] ''c'', [[w:gravitational constant |gravitational constant]] ''G'', [[w:Planck constant |Planck constant]] ''h'' ... as in the table {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} Physicist [[w: |Lev Okun]] noted "Theoretical equations describing the physical world deal with dimensionless quantities and their solutions depend on dimensionless fundamental parameters. But experiments, from which these theories are extracted and by which they could be tested, involve measurements, i.e. comparisons with standard dimension-ful scales. Without standard dimension-ful units and hence without certain conventions physics is unthinkable <ref>Michael J. Duff et al, Journal of High Energy Physics, Volume 2002, JHEP03(2002)</ref>. 2) dimension-less, such as the [[w:Fine-structure_constant |fine structure constant]] ''α''. A dimension-less constant does not measure any physical quantity (it has no units; units = 1). 3) dimension-less [[w:mathematical constant |mathematical constants]], most notably [[w:pi |pi]] = 3.14159265358979 and [[w:Natural_logarithm |e]] = 2.718281828459. Although these are [[w:transcendental number |transcendental numbers]], they can be constructed by integers in a series, and so for a universe expanding incrementally (see simulation time), these constants could be formed within the simulation. For example, at time ''t''; <math display=block>t = 1; \frac{\pi^2}{6} = \frac{1}{t^2} </math> <math display=block>t = 2; \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{t^2}</math> <math display=block>t = now: \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots + \frac{1}{t^2} </math> We may now define the fundamental physical constant as a parameter specifically chosen by the Programmer and is encoded into the simulation code directly, and so whilst it may be inferable, it is not derived from other constants ([[w:Fine-structure_constant#Numerological_explanations_and_multiverse_theory |Richard Feynman on the fine structure constant]]). It should also be dimension-less otherwise the simulation itself becomes dimensioned (if the simulation is running on a celestial computer it is merely data, it has no physical size or shape or ...), and so the dimensioned constants (''G'', ''h'', ''c'', ''e''...) must all be derivable (derived from within the simulation) via the (embedded in the source code) fundamental physical constants (of which the fine structure constant alpha may be an example). Although [[w:pi |pi]] and [[w:Natural_logarithm |e]] are dimensionless, they can be derived internally (from integers), and as they have application in the mathematical realm, they can be referred to as mathematical constants. ==== Planck scale ==== The [[w:Planck scale |Planck scale]] refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the [[w:Standard Model |Standard Model]], [[w:quantum field theory |quantum field theory]] and [[w:general relativity |general relativity]] are no longer reconcilable, and [[w:Quantum Gravity |quantum effects of gravity]] are expected to dominate (quantum gravitational effects only appear at length scales near the Planck scale). Although particles may not be cognizance of our 'laws of physics', they do know the 'laws of nature'. These laws of nature would run directly off the universe OS (operating system), and so below this OS, 'physics' as we know it must necessarily break down. At present the Planck scale is the lowest known level, consequently any attempt to detect evidence of an underlying simulation coding must consider (if not actually begin at) this, the Planck scale<ref>https://www.youtube.com/watch?v=AMQRXGYCDrY Planck scale, Brian Greene</ref>. The [[w:International_System_of_Units |SI units]] for the dimension-ful mksa units are; meter (length), kilogram (mass), second (time), ampere (electric current). There are Planck units that represent these SI units, and so a simulation could use them as discrete building blocks; [[w:Planck length |Planck length]] (the smallest possible unit of length), [[w:Planck mass |Planck mass]] (the unit of mass), [[w:Planck time |Planck time]] (the smallest possible unit of time), [[w:Planck charge |Planck charge]] (the unit of charge). The speed of light then becomes ''c'' = 1 Planck length / 1 Planck time. These units would define the resolution and so information carrying capacity of the simulation universe. ==== Numbering systems ==== As well as our decimal system, computers apply binary and hexadecimal numbering systems. In particular the decimal and hexadecimal are of terrestrial origin and may not be considered 'universal'. Furthermore numbering systems measure only the frequency of an event and contain no information as to the event itself. The number 299 792 458 could refer to the speed of light (299 792 458 m/s) or could equally be referring to the number of apples in a container (299 792 458 apples). As such, numbers require a 'descriptive', whether m/s or apples. Numbers also do not include their history, is 299 792 458 for example a derivation of other base numbers? Present universe simulations use the laws of physics and the physical constants are built in, however both these laws and the physical constants are known only to a limited precision, and so a simulation with 10⁶² iterations (the present age of the universe in units of Planck time) will accumulate errors. Number based computing may be sufficient for ancestor-simulation models where only the observed region needs to be calculated, but has inherent limitations for deep universe simulations where the entire universe is continuously updated. The actual computational requirements for a Planck scale universe simulation based on a numbering system with the laws of physics embedded would be an unknown and consequently lead to an 'non-testable' hypothesis. This is a commonly applied reasoning for rejecting the deep universe simulation. ==== Geometrical objects ==== A mathematical constant such as [[w:pi |pi]] refers to a geometrical construct (the ratio of circle circumference to circle radius) and so is not constrained by any particular numbering system (in the decimal system π = 3.14159...), and so may be considered both universal and eternal. Likewise, by assigning geometrical objects instead of numbers to the Planck units, the problems with a numbering system can be resolved. These objects would however have to fulfill the following conditions; 1) embedded attribute - for example the object for length must embed the function of ''length'' such that a descriptive (km, mile ... ) is not required. Electron wavelength would then be measurable in terms of the length object, as such the length object must be embedded within the electron (the electron object). Although the mass object would incorporate the function ''mass'', the time object the function ''time'' ..., it is not necessary that there be an individual physical mass or physical length or physical time ..., but only that in relation to the other units, the object must express that function (i.e.: the mass object has the function of mass when in the presence of the objects for space and time). The electron could then be a complex event (complex geometrical object) constructed by combining the objects for mass, length, time and charge into 1 event, and thus electron charge, wavelength, frequency and mass would then be different aspects of that 1 geometry (the electron event) and not independent parameters (independent of each other). 2) The objects for mass, length, time and charge must be able to combine with each other [[w:Lego |Lego-style]] to form more complex objects (events) such as electrons and apples whilst still retaining the underlying information (the mass of the apple derives from the mass objects embedded within that apple). Not only must these objects be able to form complex events such as particles, but these events themselves are geometrical objects and so must likewise function according to their geometries. Electrons would orbit protons according to their respective electron and proton geometries, these orbits the result of geometrical imperatives and not due to any built-in laws of physics (the orbital path is a consequence of all the underlying geometries). However, as orbits follow regular and repeating patterns, they can be described (by us) using mathematical formulas. As the events grow in complexity (from atoms to molecules to planets), so too will the patterns (and likewise the formulas we use to describe them). Consequently the ''laws of physics'' would then become our mathematical descriptions of the underlying geometrically imposed patterns. 3) These objects would replace coded instructions (the instruction sets would be built into the objects) thereby instigating a geometrically autonomous universe. The electron 'knows' what to do by virtue of the information encoded within its geometry, no coded electron CALL FUNCTION is required. This would be equivalent to combining the hardware, software and CPU together such that the 'software' changes (adjusts) to the changing 'hardware' (DNA may be an analogy). Note: A purely mathematical universe has no limits in size and can be infinitely large and infinity small. A geometrical universe (that uses objects) has limitations, it can be no smaller than the smallest object for example and has discrete parts (those objects). The philosophy of the TOE (theory of everything) therefore includes a debate between the mathematical universe and the geometrical universe, however this distinction between mathematical and geometrical would only be apparent at the Planck scale. === Evidence of a simulation === The laws of physics are our incomplete observations of the natural universe, and so evidence of a simulation may be found in ambiguities or anomalies within these laws. Furthermore, if complexity arises over time, then at unit time the 'handiwork' of the Programmer may be notable by a simplicity and elegance of the geometries employed ... for the Programmer by definition has God-level programming skills. Here is a notable example. Mass, space and time from the number 1 The dimensions of mass, space and time are considered by science to be independent of each other, we cannot measure the ''distance'' from Tokyo to London using kilograms and amperes, or measure ''mass'' using space and time. Indeed, what characterizes a physical universe as opposed to a simulated universe is the notion that there is a fundamental structure underneath, that in some sense mass 'is', that time 'is' and space 'is' ... thus we cannot write ''kg'' in terms of ''m'' and ''s''. To do so would render our concepts of a physical universe meaningless. The 26th General Conference on Weights and Measures ([[w:2019 redefinition of SI base units|2019 redefinition of SI base units]]) assigned exact numerical values to 4 physical constants (''h, c, e, k''_B) independently of each other (and thereby confirming these as fundamental constants), and as they are measured in SI units ('''kg''', '''m''', '''s''', '''A''', '''K'''), these units must also be independent of each other (i.e.: these are fundamental units, for example if we could define ''m'' using ''A'' then the speed of light could be derived from, and so would depend upon, the value for the elementary charge ''e'', and so the value for ''c'' could not be assigned independently from ''e''). {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} We are familiar with inverse properties; plus charge and minus charge, matter and anti-matter ... and we can observe how these may form and/or cancel each other. A simulation universe however is required to be dimensionless (in sum total), for the simulated universe does not 'exist' in any physical sense outside of the 'Computer' (it is simply data on a celestial hard-disk). Our universe does not appear to have inverse properties such as anti-mass (-kg), anti-time (-s) or anti-space (anti-length -m), therefore the first problem the Programmer must solve is how to create the physical scaffolding (of mass, space and time). For example, the Programmer can start by selecting 2 dimensioned quantities, here are used ''r'', ''v'' <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref> such that :<math>kg = \frac{r^4}{v},\; m = \frac{r^9}{v^5},\; s = \frac{r^9}{v^6},\; A = \frac{v^3}{r^6}</math> Quantities ''r'' and ''v'' are chosen so that no unit (''kg'', ''m'', ''s'', ''A'') can cancel another unit (i.e.: the ''kg'' cannot cancel the ''m'' or the ''s'' ...), and so we have 4 independent units (we still cannot define the ''kg'' using the ''m'' or the ''s'' ...), however if 3 (or more) units are combined together in a specific ratio, they can cancel (in a certain ratio our ''r'' and ''v'' become inverse properties and so cancel each other; units = 1). <math>f_X = \frac{kg^9 s^{11}}{m^{15}} = \frac{(\frac{r^4}{v})^9 (\frac{r^9}{v^6})^{11}}{(\frac{r^9}{v^5})^{15}} = 1</math> This f_X, although embedded within are the dimensioned structures for mass, time and length (in the above ratio), would be a dimensionless mathematical structure, units = 1. Thus we may create as much mass, time and length as we wish, the only proviso being that they are created in f_X ratios, so that regardless of how massive, old and large our universe becomes, it is still in sum total dimensionless. Defining the dimensioned quantities ''r'', ''v'' in SI unit terms. :<math>r = (\frac{kg\;m}{s})^{1/4}</math> :<math>v = \frac{m}{s}</math> Mass :<math>\frac{r^4}{v} = (\frac{kg\;m}{s})\;(\frac{s}{m}) = kg</math> Length :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^5})^4 = \frac{s^{20}}{m^{20}}</math> :<math>(\frac{r^9}{v^5})^4 = \frac{kg^9 s^{11}}{m^{11}} = m^4 \frac{kg^9 s^{11}}{m^{15}} = m^4 f_X = m^4</math> Time :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^6})^4 = \frac{s^{24}}{m^{24}}</math> :<math>(\frac{r^9}{v^6})^4 = \frac{kg^9 s^{15}}{m^{15}} = s^4 \frac{kg^9 s^{11}}{m^{15}} = s^4 f_X = s^4</math> And so, although f_X is a dimensionless mathematical structure, we can embed within it the (mass, length, time ...) structures along with their dimensional attributes (kg, m, s, A ..). In the mathematical electron model (discussed below), the electron itself is an example of an f_X structure, it (f_electron) is a dimensionless geometrical object that embeds the physical electron parameters of wavelength, frequency, charge (note: A-m = ampere-meter are the units for a [[w:Magnetic_monopole#In_SI_units |magnetic monopole]]). <math>f_{electron}</math> :<math>units = \frac{A^3 m^3}{s} = \frac{(\frac{v^3}{r^6})^3 (\frac{r^9}{v^5})^3}{(\frac{r^9}{v^6})} = 1</math> We may note that at the macro-level (of planets and stars) these f_X ratio are not found, and so this level is the domain of the observed physical universe, however at the quantum level, f_X ratio do appear, f_electron as an example, the mathematical and physical domains then blurring. This would also explain why physics can measure precisely the parameters of the electron (wavelength, mass ...), but has never found the electron itself. == Programming == “God vs. science debates tend to be restricted to the premise that a God does not rely on science and that science does not need a God. As science and God are thus seen as mutually exclusive there are few, if any, serious attempts to construct mathematical models of a universe whose principle axiom does require a God. However, if there is an Intelligence responsible for the 14 billion year old universe of modern physics, being the universe of Einstein and Dirac, and beginning with the big bang as the act of 'creation', then we must ask how it might be done? What construction technique could have been used to set the laws of physics in motion?” <ref>[https://theprogrammergod.com/ The Programmer God, are we in a Simulation]</ref> === Simulation Time === The (dimensionless) simulation clock-rate would be defined as the minimum 'time variable' ('''age''') increment to the simulation. Using a simple loop as analogy, at ''age'' = 1, the simulation begins (the big bang), certain processes occur, when these are completed ''age'' increments (''age'' = 2, then 3, then 4 ... ) until ''age'' reaches ''the_end'' and the simulation stops. 'begin simulation FOR age = 1 TO the_end 'big bang = 1 conduct certain processes ........ NEXT age 'end simulation [[w:Quantum spacetime |Quantum spacetime]] and [[w:Quantum gravity |Quantum gravity]] models refer to [[w:Planck time | Planck time]] as the smallest discrete unit of time and so the incrementing variable '''age''' could be used to generate units of Planck time (and other Planck units, the physical scaffolding of the universe). In a geometrical model, to these Planck units could be assigned geometrical objects, for example; Initialize_physical_constants; FOR age = 1 TO the_end generate 1 unit of (Planck) time; '1 time 'object' T generate 1 unit of (Planck) mass; '1 mass 'object' M generate 1 unit of (Planck) length; '1 length 'object' L ........ NEXT age The variable ''age'' is the simulation clock-rate, it is simply a counter (1, 2, 3 ...) and so is a dimensionless number, the object T is the geometrical Planck time object, it is dimensioned and is measured by us in seconds. If ''age'' is the origin of Planck time (1 increment to ''age'' generates 1 T object) then ''age'' = 10⁶², this is based on the present [[w:Age_of_the_universe |age of the universe]], which, at 14 billion years, equates to 10⁶² units of Planck time. For each ''age'', certain operations are performed, only after they are finished does ''age'' increment (there is no ''time'' interval between increments). As noted, ''age'' being dimensionless, is not the same as dimensioned Planck time which is the geometrical object T, and this T, being dimensioned, can only appear within the simulation. The analogy would be frames of a movie, each frame contains dimensioned information but there is no ''time'' interval between frames. FOR age = 1 TO the_end (of the movie) display frame{age} NEXT age Although operations (between increments to ''age'') may be extensive, self-aware structures from within the simulation would have no means to determine this, they could only perceive themselves as being in a real-time (for them the smallest unit of ''time'' is 1T, just as the smallest unit of ''time'' in a movie is 1 frame). Their (those self-aware structures) dimension of time would then be a measure of relative motion (a change of state), and so although ultimately deriving from the variable ''age'', their time would not be the same as ''age''. If there was no motion, if all particles and photons were still (no change of state), then their time dimension could not update (if every frame in a movie was the same then actors within that movie could not register a change in time), ''age'' however would continue to increment. Thus we have 3 time structures; 1) the dimension-less simulation clock-rate variable ''age'', 2) the dimensioned time unit (object T), and 3) time as change of state (the observers time). Observer time requires a memory of past events against which a change of state can be perceived. The forward increment to ''age'' would constitute the [[w:arrow of time |arrow of time]]. Reversing this would reverse the arrow of time, the universe would likewise shrink in size and mass accordingly (just as a [[w:white hole |white hole]] is the (time) reversal of a [[w:black hole |black hole]]). FOR age = the_end TO 1 STEP -1 delete 1 unit of Planck time; delete 1 unit of Planck mass; delete 1 unit of Planck length; ........ NEXT age Adding mass, length and time objects per increment to ''age'' would force the universe expansion (in size and mass), and as such an anti-gravitational [[w:dark energy |dark energy]] would not be required, however these objects are dimensioned and so are generated within the simulation. This means that they must somehow combine in a specific ratio whereby they (the units for mass length, time, charge; ''kg'', ''m'', ''s'', ''A'') in sum total cancel each other, leaving the sum universe (the simulation itself) residing on that celestial hard-disk. We may introduce a theoretical dimensionless (f_X) geometrical object denoted as f_Planck within which are embedded the dimensioned objects MLTA (mass, length, time, charge), and from which they may be extracted. FOR age = 1 TO the_end add 1 f_Planck 'dimensionless geometrical 'object' { extract 1 unit of (Planck) time; '1 time 'object' T extract 1 unit of (Planck) mass; '1 mass 'object' M extract 1 unit of (Planck) length; '1 length 'object' L } ........ NEXT age This then means that the simulation, in order to create time T, must also create mass M and space L (become larger and more massive). Thus no matter how small or large the physical universe is (when seen internally), in sum total (when seen externally), there is no universe - it is merely data without physical form. === Universe time-line === As the universe expands outwards (through the constant addition of units of mass and length via f_Planck), and if this expansion pulls particles with it (if it is the origin of motion), then ''now'' (the present) would reside on the surface of the (constantly expanding at the speed of light; ''c'' = 1 Planck length / 1 Planck time) universe, and so the 'past' could be retained, for the past cannot be over-written by the present in an expanding universe (if ''now'' is always on the surface). As this expansion occurs at the Planck scale, information even below quantum states, down to the Planck scale, can be retained, the analogy would be the storing of every [[w:Keystroke_logging |keystroke]], a Planck scale version of the [[w:Akashic records |Akashic records]] ... for if our deeds (the past) are both stored and cannot be over-written (by the present), then we have a candidate for the '[[w:karma |karmic]] heavens' (Matthew 6:19 ''But lay up for yourselves treasures in 'heaven', where neither moth nor rust doth corrupt, and where thieves do not break through nor steal''). This also forms a universe '''time-line''' against which previous information can be compared with new information (a 'memory' of events), without which we could not link cause with effect. === Singularity === In a simulation, the data (software) requires a storage device that is ultimately hardware (RAM, HD ...). In a data world of 1's and 0's such as a computer game, characters within that game may analyze other parts of their 1's and 0's game, but they have no means to analyze the hard disk upon which they (and their game) are stored, for the hard disk is an electro-mechanical device, it is not part of their 1's and 0's world, it is a part of the 'real world', the world of their Programmer. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may or may not resemble the laws that operate in the 'real world' (the world of their Programmer). Thus any region where the laws of physics (the laws of their game world) break down would be significant. A [[w:singularity |singularity]] inside a black hole is such a region <ref>https://www.youtube.com/watch?v=W5j7umtZYB4 a black hole singularity as the interface between worlds</ref>. For the [[w:black hole electron |black-hole electron]], its black-hole center would then be analogous to a storage address on a hard disk, the interface between the simulation world and the real world. A massive (galactic) black-hole could be as an entire data sector. The surface of the black-hole would then be of the simulation world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however would be the interface between the data world and the 'hard disk' of the real world, and so would not exist in any 'physical' terms. It is external to the simulation. As analogy, we may discuss the 3-D surface area of a black-hole but not its volume (interior). === Laws of Physics === The scientific method is built upon testable hypothesis and reproducible results. Water always boils (in defined conditions), at 100°C. In a geometrical universe particles will behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these repeating patterns, the more complex the orbits, the more complex the formulas required to describe them and so forth. However if there is a source code from which these geometrical conditions were programmed, then there may also be non-repeating events, back-doors built into the code (a common practice by terrestrial programmers), these by definition would lie outside the laws of physics and so be labelled as miracles, yet they would be no less valid. === Determinism === [[File:Three body problem figure-8 orbit animation.gif|400px|thumb|An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259.<ref>Here the gravitational constant ''G'' has been set to 1, and the initial conditions are '''r'''₁(0) = −'''r'''₃(0) = (−0.97000436, 0.24308753); '''r'''₂(0) = (0,0); '''v'''₁(0) = '''v'''₃(0) = (0.4662036850, 0.4323657300); '''v'''₂(0) = (−0.93240737, −0.86473146). The values are obtained from Chenciner & Montgomery (2000).</ref>]] Particles form more complex structures such as atoms and molecules via a system of orbitals; nuclear, atomic and gravitational. The [[w:Three-body_problem |3-body problem]] is the problem of taking the initial positions and velocities (or [[w:momentum|momenta |momentum|momenta]]) of three or more point masses and solving for their subsequent motion according to [[w:Newton's laws of motion |Newton's laws of motion]] and [[w:Newton's law of universal gravitation |Newton's law of universal gravitation]].<ref name="PrincetonCompanion">{{Citation | last = Barrow-Green | first = June | year = 2008 | title = The Three-Body Problem | editor-last1 = Gowers | editor-first1 = Timothy | editor-last2 = Barrow-Green | editor-first2 = June | editor-last3 = Leader | editor-first3 = Imre | encyclopedia = The Princeton Companion to Mathematics | pages = 726–728 | publisher = Princeton University Press }}</ref>. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for gods and men alike the only way to know what that outcome will be is to run the simulation itself. ==Geometry coded universe== Modelling a Planck scale simulation universe using geometrical forms (links) * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass == External links == * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] * [https://philpapers.org/rec/GRUTIA-2 Simulation theory as evidence for God] (academic peer-reviewed article) ==References== {{Reflist}} [[Category:Philosophy| ]] [[Category:Philosophy of science| ]] be7zn8v7summ4kasfsioiu0zbrsizhv 2718256 2718255 2025-06-10T19:50:56Z 212.200.164.104 /* Constants */ 2718256 wikitext text/x-wiki '''Is God a Programmer? analyzing the deep-universe simulation hypothesis at the Planck scale''' The [[w:simulation hypothesis |simulation hypothesis]] is the proposal that all of reality, including the Earth and the rest of the universe, could be an artificial simulation, such as a computer simulation. [[w:Neil_deGrasse_Tyson |Neil deGrasse Tyson]] put the odds at 50-50 that our entire existence is a program on someone else’s hard drive <ref>Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. [[w:David_Chalmers |David Chalmers]] noted “We in this universe can create simulated worlds and there’s nothing remotely spooky about that. Our creator isn’t especially spooky, it’s just some teenage hacker in the next universe up. Turn the tables, and we are essentially gods over our own computer creations <ref>https://www.youtube.com/watch?v=yqbS5qJU8PA, David Chalmers, Serious Science</ref> <ref>The Matrix as Metaphysics, David Chalmers http://consc.net/papers/matrix.pdf</ref> <ref>Are We Living in a Computer Simulation?https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. The commonly postulated [[w:Ancestor_simulation |ancestor simulation]] approach, which [[w:Nick Bostrom |Nick Bostrom]] called "the simulation argument", argues for "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor. However this simulation variant can be traced back to an 'organic base reality' (the original programmer ancestors and their physical planet). The [[v:God_(programmer) |Programmer God]] hypothesis<ref>https://codingthecosmos.com/podcast/ AI generated podcasts</ref> conversely states that a (deep universe) simulation began with the big bang and was programmed by an external intelligence (external to the physical universe), the Programmer by definition a God in the creator of the universe context. Our universe in its entirety, down to the smallest detail, and including life-forms, is within the simulation, the laws of nature, at their most fundamental level, are coded rules running on top of the simulation operating system. The operating system itself is mathematical (and potentially the origin of mathematics). Any candidate for a Programmer-God simulation-universe source code must satisfy these conditions; :1. It can generate physical structures from mathematical forms. :2. The sum universe is dimensionless (simply data on a celestial hard disk). :3. We must be able to use it to derive the laws of physics (because the source code is the origin of the laws of nature, and the laws of physics are our observations of the laws of nature). :4. The mathematical logic must be unknown to us (the Programmer is a non-human intelligence). :5. The coding should have an 'elegance' commensurate with the Programmer's level of skill. == Philosophy == Physicist [[w:Eugene Wigner |Eugene Wigner]] ([[w:The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences |The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]) <ref>{{Cite journal | last1 = Wigner | first1 = E. P. | authorlink = Eugene Wigner| doi = 10.1002/cpa.3160130102 | title = The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959 | journal = Communications on Pure and Applied Mathematics | volume = 13 | pages = 1–14 | year = 1960 | pmid = | pmc = |bibcode = 1960CPAM...13....1W }}</ref> <blockquote>The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. </blockquote> === Discussion === [[w:Philosophy of mathematics |Philosophy of mathematics]] is that branch of philosophy which attempts to answer questions such as: ‘why is mathematics useful in describing nature?’, ‘in which sense, if any, do mathematical entities such as numbers exist?’ and ‘why and how are mathematical statements true?’ This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math. Mathematical realism holds that mathematical entities exist independently of the human mind. We do not invent mathematics, but rather discover it. Triangles, for example, are real entities that have an existence <ref>- http://plato.stanford.edu/entries/platonism-mathematics/</ref>. The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality. It can be considered a form of [[w:Pythagoreanism | Pythagoreanism]] or [[w:Platonism | Platonism]] in that it proposes the existence of ''mathematical objects''; and a form of [[w:philosophy of mathematics | mathematical monism]] in that it denies that anything exists except these ''mathematical objects''. Physicist [[w:Max Tegmark | Max Tegmark]] in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality"<ref name="Tegmark1998">{{cite journal|last=Tegmark |first=Max |date=November 1998 |title=Is "the Theory of Everything" Merely the Ultimate Ensemble Theory? |journal=Annals of Physics |volume=270 |issue=1 |pages=1–51 |doi=10.1006/aphy.1998.5855 |arxiv = gr-qc/9704009 |bibcode = 1998AnPhy.270....1T }}</ref><ref>M. Tegmark 2014, "[http://mathematicaluniverse.org Our Mathematical Universe]", Knopf</ref> proposed that ''Our external physical reality is a mathematical structure''.<ref name="Tegmark2008">{{cite journal|last=Tegmark |first=Max |date=February 2008 |title=The Mathematical Universe |journal=Foundations of Physics |volume=38 |issue=2 |pages=101–150 |doi=10.1007/s10701-007-9186-9 |arxiv=0704.0646|bibcode = 2008FoPh...38..101T }}</ref> That is, the physical universe is not merely ''described by'' mathematics, but ''is'' mathematics (specifically, a [[w:mathematical structure | mathematical structure]]). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref> The principle constraints to any mathematical universe simulation hypothesis are; 1. the computational resources required. The ancestor simulation can resolve this by adapting from the [[w:virtual rality |virtual reality]] approach where only the observable region is simulated and only to the degree required, and 2. that any 'self-aware structures' (humans for example) within the simulation must "subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref>. Succinctly, our computer games may be able to simulate our physical world, but they are still only simulations of a physical reality (regardless of how realistic they may seem) ... we are not yet able to program actual physical dimensions of mass, space and time from mathematical structures, and indeed this may not be possible with a computer hard-ware architecture that can only process binary data. === Deep-universe source code === As a deep-universe simulation is programmed by an external (external to the universe) intelligence (the Programmer God hypothesis), we cannot presume a priori knowledge regarding the simulation source code other than from this code the laws of nature emerged, and so any deep-universe simulation model we try to emulate must be universal, i.e.: independent of any system of units, of the [[w:Dimensional_analysis |dimensioned]] [[w:physical constants |physical constants]] (''G'', ''h'', ''c'', ''e'' .. ), and of any numbering systems. Furthermore, although a deep-universe simulation source code may use mathematical forms (circles, spheres ...) we are familiar with (for ultimately the source code is the origin of these forms), it will have been developed by a non-human intelligence and so we may have to develop new mathematical tools to decipher the underlying logic. By implication therefore, any theoretical basis for a source code that fits the above criteria (and from which the laws of nature will emerge), could be construed as our first tangible evidence of a non-human intelligence. === Constants === A physical universe is characterized by measurable quantities (size, mass, color, texture ...), and so a physical universe can be measured and defined. Contrast then becomes information, the statement ''this is a big apple'' requires a ''small apple'' against which big becomes a relative term. For analytical purposes we select a reference value, for example 0C or 32F, and measure all temperatures against this reference. The smaller the resolution of the measurements, the greater the information content (the file size of a 32 mega-pixel photo is larger than a 4 mega-pixel photo). A simulation universe may be presumed to also have a resolution dictating how much information the simulation can store and manipulate. To measure the fundamental parameters of our universe physics uses [[w:physical constant |physical constants]]. A physical constant is a [[w:physical quantity |physical quantity]] that is generally believed to be both universal in nature and have a constant value in time. These can be divided into 1) dimension-ed (measured using physical units ''kg'', ''m'', ''s'', ''A'' ...) such as the [[w:speed of light |speed of light]] ''c'', [[w:gravitational constant |gravitational constant]] ''G'', [[w:Planck constant |Planck constant]] ''h'' ... as in the table {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} Physicist [[w: |Lev Okun]] noted "Theoretical equations describing the physical world deal with dimensionless quantities and their solutions depend on dimensionless fundamental parameters. But experiments, from which these theories are extracted and by which they could be tested, involve measurements, i.e. comparisons with standard dimension-ful scales. Without standard dimension-ful units and hence without certain conventions physics is unthinkable <ref>Michael J. Duff et al, Journal of High Energy Physics, Volume 2002, JHEP03(2002)</ref>. 2) dimension-less, such as the [[w:Fine-structure_constant |fine structure constant]] ''α''. A dimension-less constant does not measure any physical quantity (it has no units; units = 1). 3) dimension-less [[w:mathematical constant |mathematical constants]], most notably [[w:pi |pi]] = 3.14159265358979 and [[w:Natural_logarithm |e]] = 2.718281828459. Although these are [[w:transcendental number |transcendental numbers]], they can be constructed by integers in a series, and so for a universe expanding incrementally (see simulation time), these constants could be formed within the simulation. For example, at time ''t''; <math display=block>t = 1; \frac{\pi^2}{6} = \frac{1}{t^2} </math> <math display=block>t = 2; \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{t^2}</math> <math display=block>t = now: \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots + \frac{1}{t^2} </math> We may now define the fundamental physical constant as a parameter specifically chosen by the Programmer and is encoded into the simulation code directly, and so whilst it may be inferable, it is not derived from other constants ([[w:Fine-structure_constant#Numerological_explanations_and_multiverse_theory |Richard Feynman on the fine structure constant]]). It should also be dimension-less otherwise the simulation itself becomes dimensioned (if the simulation is running on a celestial computer it is merely data, it has no physical size or shape or ...), and so the dimensioned constants (''G'', ''h'', ''c'', ''e''...) must all be derivable (derived from within the simulation) via the (embedded in the source code) fundamental physical constants (of which the fine structure constant alpha may be an example). Although [[w:pi |pi]] and [[w:Natural_logarithm |e]] are dimensionless, they can be derived internally (from integers), and as they have application in the mathematical realm, they can be referred to as mathematical constants. ==== Planck scale ==== The [[w:Planck scale |Planck scale]] refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the [[w:Standard Model |Standard Model]], [[w:quantum field theory |quantum field theory]] and [[w:general relativity |general relativity]] are no longer reconcilable, and [[w:Quantum Gravity |quantum effects of gravity]] are expected to dominate (quantum gravitational effects only appear at length scales near the Planck scale). Although particles may not be cognizance of our 'laws of physics', they do know the 'laws of nature'. These laws of nature would run directly off the universe OS (operating system), and so below this OS, 'physics' as we know it must necessarily break down. At present the Planck scale is the lowest known level, consequently any attempt to detect evidence of an underlying simulation coding must consider (if not actually begin at) this, the Planck scale<ref>https://www.youtube.com/watch?v=AMQRXGYCDrY Planck scale, Brian Greene</ref>. The [[w:International_System_of_Units |SI units]] for the dimension-ful mksa units are; meter (length), kilogram (mass), second (time), ampere (electric current). There are Planck units that represent these SI units, and so a simulation could use them as discrete building blocks; [[w:Planck length |Planck length]] (the smallest possible unit of length), [[w:Planck mass |Planck mass]] (the unit of mass), [[w:Planck time |Planck time]] (the smallest possible unit of time), [[w:Planck charge |Planck charge]] (the unit of charge). The speed of light then becomes ''c'' = 1 Planck length / 1 Planck time. These units would define the resolution and so information carrying capacity of the simulation universe. ==== Numbering systems ==== As well as our decimal system, computers apply binary and hexadecimal numbering systems. In particular the decimal and hexadecimal are of terrestrial origin and may not be considered 'universal'. Furthermore numbering systems measure only the frequency of an event and contain no information as to the event itself. The number 299 792 458 could refer to the speed of light (299 792 458 m/s) or could equally be referring to the number of apples in a container (299 792 458 apples). As such, numbers require a 'descriptive', whether m/s or apples. Numbers also do not include their history, is 299 792 458 for example a derivation of other base numbers? Present universe simulations use the laws of physics and the physical constants are built in, however both these laws and the physical constants are known only to a limited precision, and so a simulation with 10⁶² iterations (the present age of the universe in units of Planck time) will accumulate errors. Number based computing may be sufficient for ancestor-simulation models where only the observed region needs to be calculated, but has inherent limitations for deep universe simulations where the entire universe is continuously updated. The actual computational requirements for a Planck scale universe simulation based on a numbering system with the laws of physics embedded would be an unknown and consequently lead to an 'non-testable' hypothesis. This is a commonly applied reasoning for rejecting the deep universe simulation. ==== Geometrical objects ==== A mathematical constant such as [[w:pi |pi]] refers to a geometrical construct (the ratio of circle circumference to circle radius) and so is not constrained by any particular numbering system (in the decimal system π = 3.14159...), and so may be considered both universal and eternal. Likewise, by assigning geometrical objects instead of numbers to the Planck units, the problems with a numbering system can be resolved. These objects would however have to fulfill the following conditions; 1) embedded attribute - for example the object for length must embed the function of ''length'' such that a descriptive (km, mile ... ) is not required. Electron wavelength would then be measurable in terms of the length object, as such the length object must be embedded within the electron (the electron object). Although the mass object would incorporate the function ''mass'', the time object the function ''time'' ..., it is not necessary that there be an individual physical mass or physical length or physical time ..., but only that in relation to the other units, the object must express that function (i.e.: the mass object has the function of mass when in the presence of the objects for space and time). The electron could then be a complex event (complex geometrical object) constructed by combining the objects for mass, length, time and charge into 1 event, and thus electron charge, wavelength, frequency and mass would then be different aspects of that 1 geometry (the electron event) and not independent parameters (independent of each other). 2) The objects for mass, length, time and charge must be able to combine with each other [[w:Lego |Lego-style]] to form more complex objects (events) such as electrons and apples whilst still retaining the underlying information (the mass of the apple derives from the mass objects embedded within that apple). Not only must these objects be able to form complex events such as particles, but these events themselves are geometrical objects and so must likewise function according to their geometries. Electrons would orbit protons according to their respective electron and proton geometries, these orbits the result of geometrical imperatives and not due to any built-in laws of physics (the orbital path is a consequence of all the underlying geometries). However, as orbits follow regular and repeating patterns, they can be described (by us) using mathematical formulas. As the events grow in complexity (from atoms to molecules to planets), so too will the patterns (and likewise the formulas we use to describe them). Consequently the ''laws of physics'' would then become our mathematical descriptions of the underlying geometrically imposed patterns. 3) These objects would replace coded instructions (the instruction sets would be built into the objects) thereby instigating a geometrically autonomous universe. The electron 'knows' what to do by virtue of the information encoded within its geometry, no coded electron CALL FUNCTION is required. This would be equivalent to combining the hardware, software and CPU together such that the 'software' changes (adjusts) to the changing 'hardware' (DNA may be an analogy). Note: A purely mathematical universe has no limits in size and can be infinitely large and infinity small. A geometrical universe (that uses objects) has limitations, it can be no smaller than the smallest object for example and has discrete parts (those objects). The philosophy of the TOE (theory of everything) therefore includes a debate between the mathematical universe and the geometrical universe, however this distinction between mathematical and geometrical would only be apparent at the Planck scale. === Evidence of a simulation === The laws of physics are our incomplete observations of the natural universe, and so evidence of a simulation may be found in ambiguities or anomalies within these laws. Furthermore, if complexity arises over time, then at unit time the 'handiwork' of the Programmer may be notable by a simplicity and elegance of the geometries employed ... for the Programmer by definition has God-level programming skills. Here is a notable example. Mass, space and time from the number 1 The dimensions of mass, space and time are considered by science to be independent of each other, we cannot measure the ''distance'' from Tokyo to London using kilograms and amperes, or measure ''mass'' using space and time. Indeed, what characterizes a physical universe as opposed to a simulated universe is the notion that there is a fundamental structure underneath, that in some sense mass 'is', that time 'is' and space 'is' ... thus we cannot write ''kg'' in terms of ''m'' and ''s''. To do so would render our concepts of a physical universe meaningless. The 26th General Conference on Weights and Measures ([[w:2019 redefinition of SI base units|2019 redefinition of SI base units]]) assigned exact numerical values to 4 physical constants (''h, c, e, k''_B) independently of each other (and thereby confirming these as fundamental constants), and as they are measured in SI units ('''kg''', '''m''', '''s''', '''A''', '''K'''), these units must also be independent of each other (i.e.: these are fundamental units, for example if we could define ''m'' using ''A'' then the speed of light could be derived from, and so would depend upon, the value for the elementary charge ''e'', and so the value for ''c'' could not be assigned independently from ''e''). {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} We are familiar with inverse properties; plus charge and minus charge, matter and anti-matter ... and we can observe how these may form and/or cancel each other. A simulation universe however is required to be dimensionless (in sum total), for the simulated universe does not 'exist' in any physical sense outside of the 'Computer' (it is simply data on a celestial hard-disk). Our universe does not appear to have inverse properties such as anti-mass (-kg), anti-time (-s) or anti-space (anti-length -m), therefore the first problem the Programmer must solve is how to create the physical scaffolding (of mass, space and time). For example, the Programmer can start by selecting 2 dimensioned quantities, here are used ''r'', ''v'' <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref> such that :<math>kg = \frac{r^4}{v},\; m = \frac{r^9}{v^5},\; s = \frac{r^9}{v^6},\; A = \frac{v^3}{r^6}</math> Quantities ''r'' and ''v'' are chosen so that no unit (''kg'', ''m'', ''s'', ''A'') can cancel another unit (i.e.: the ''kg'' cannot cancel the ''m'' or the ''s'' ...), and so we have 4 independent units (we still cannot define the ''kg'' using the ''m'' or the ''s'' ...), however if 3 (or more) units are combined together in a specific ratio, they can cancel (in a certain ratio our ''r'' and ''v'' become inverse properties and so cancel each other; units = 1). <math>f_X = \frac{kg^9 s^{11}}{m^{15}} = \frac{(\frac{r^4}{v})^9 (\frac{r^9}{v^6})^{11}}{(\frac{r^9}{v^5})^{15}} = 1</math> This f_X, although embedded within are the dimensioned structures for mass, time and length (in the above ratio), would be a dimensionless mathematical structure, units = 1. Thus we may create as much mass, time and length as we wish, the only proviso being that they are created in f_X ratios, so that regardless of how massive, old and large our universe becomes, it is still in sum total dimensionless. Defining the dimensioned quantities ''r'', ''v'' in SI unit terms. :<math>r = (\frac{kg\;m}{s})^{1/4}</math> :<math>v = \frac{m}{s}</math> Mass :<math>\frac{r^4}{v} = (\frac{kg\;m}{s})\;(\frac{s}{m}) = kg</math> Length :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^5})^4 = \frac{s^{20}}{m^{20}}</math> :<math>(\frac{r^9}{v^5})^4 = \frac{kg^9 s^{11}}{m^{11}} = m^4 \frac{kg^9 s^{11}}{m^{15}} = m^4 f_X = m^4</math> Time :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^6})^4 = \frac{s^{24}}{m^{24}}</math> :<math>(\frac{r^9}{v^6})^4 = \frac{kg^9 s^{15}}{m^{15}} = s^4 \frac{kg^9 s^{11}}{m^{15}} = s^4 f_X = s^4</math> And so, although f_X is a dimensionless mathematical structure, we can embed within it the (mass, length, time ...) structures along with their dimensional attributes (kg, m, s, A ..). In the mathematical electron model (discussed below), the electron itself is an example of an f_X structure, it (f_electron) is a dimensionless geometrical object that embeds the physical electron parameters of wavelength, frequency, charge (note: A-m = ampere-meter are the units for a [[w:Magnetic_monopole#In_SI_units |magnetic monopole]]). <math>f_{electron}</math> :<math>units = \frac{A^3 m^3}{s} = \frac{(\frac{v^3}{r^6})^3 (\frac{r^9}{v^5})^3}{(\frac{r^9}{v^6})} = 1</math> We may note that at the macro-level (of planets and stars) these f_X ratio are not found, and so this level is the domain of the observed physical universe, however at the quantum level, f_X ratio do appear, f_electron as an example, the mathematical and physical domains then blurring. This would also explain why physics can measure precisely the parameters of the electron (wavelength, mass ...), but has never found the electron itself. == Programming == “God vs. science debates tend to be restricted to the premise that a God does not rely on science and that science does not need a God. As science and God are thus seen as mutually exclusive there are few, if any, serious attempts to construct mathematical models of a universe whose principle axiom does require a God. However, if there is an Intelligence responsible for the 14 billion year old universe of modern physics, being the universe of Einstein and Dirac, and beginning with the big bang as the act of 'creation', then we must ask how it might be done? What construction technique could have been used to set the laws of physics in motion?” <ref>[https://theprogrammergod.com/ The Programmer God, are we in a Simulation]</ref> === Simulation Time === The (dimensionless) simulation clock-rate would be defined as the minimum 'time variable' ('''age''') increment to the simulation. Using a simple loop as analogy, at ''age'' = 1, the simulation begins (the big bang), certain processes occur, when these are completed ''age'' increments (''age'' = 2, then 3, then 4 ... ) until ''age'' reaches ''the_end'' and the simulation stops. 'begin simulation FOR age = 1 TO the_end 'big bang = 1 conduct certain processes ........ NEXT age 'end simulation [[w:Quantum spacetime |Quantum spacetime]] and [[w:Quantum gravity |Quantum gravity]] models refer to [[w:Planck time | Planck time]] as the smallest discrete unit of time and so the incrementing variable '''age''' could be used to generate units of Planck time (and other Planck units, the physical scaffolding of the universe). In a geometrical model, to these Planck units could be assigned geometrical objects, for example; Initialize_physical_constants; FOR age = 1 TO the_end generate 1 unit of (Planck) time; '1 time 'object' T generate 1 unit of (Planck) mass; '1 mass 'object' M generate 1 unit of (Planck) length; '1 length 'object' L ........ NEXT age The variable ''age'' is the simulation clock-rate, it is simply a counter (1, 2, 3 ...) and so is a dimensionless number, the object T is the geometrical Planck time object, it is dimensioned and is measured by us in seconds. If ''age'' is the origin of Planck time (1 increment to ''age'' generates 1 T object) then ''age'' = 10⁶², this is based on the present [[w:Age_of_the_universe |age of the universe]], which, at 14 billion years, equates to 10⁶² units of Planck time. For each ''age'', certain operations are performed, only after they are finished does ''age'' increment (there is no ''time'' interval between increments). As noted, ''age'' being dimensionless, is not the same as dimensioned Planck time which is the geometrical object T, and this T, being dimensioned, can only appear within the simulation. The analogy would be frames of a movie, each frame contains dimensioned information but there is no ''time'' interval between frames. FOR age = 1 TO the_end (of the movie) display frame{age} NEXT age Although operations (between increments to ''age'') may be extensive, self-aware structures from within the simulation would have no means to determine this, they could only perceive themselves as being in a real-time (for them the smallest unit of ''time'' is 1T, just as the smallest unit of ''time'' in a movie is 1 frame). Their (those self-aware structures) dimension of time would then be a measure of relative motion (a change of state), and so although ultimately deriving from the variable ''age'', their time would not be the same as ''age''. If there was no motion, if all particles and photons were still (no change of state), then their time dimension could not update (if every frame in a movie was the same then actors within that movie could not register a change in time), ''age'' however would continue to increment. Thus we have 3 time structures; 1) the dimension-less simulation clock-rate variable ''age'', 2) the dimensioned time unit (object T), and 3) time as change of state (the observers time). Observer time requires a memory of past events against which a change of state can be perceived. The forward increment to ''age'' would constitute the [[w:arrow of time |arrow of time]]. Reversing this would reverse the arrow of time, the universe would likewise shrink in size and mass accordingly (just as a [[w:white hole |white hole]] is the (time) reversal of a [[w:black hole |black hole]]). FOR age = the_end TO 1 STEP -1 delete 1 unit of Planck time; delete 1 unit of Planck mass; delete 1 unit of Planck length; ........ NEXT age Adding mass, length and time objects per increment to ''age'' would force the universe expansion (in size and mass), and as such an anti-gravitational [[w:dark energy |dark energy]] would not be required, however these objects are dimensioned and so are generated within the simulation. This means that they must somehow combine in a specific ratio whereby they (the units for mass length, time, charge; ''kg'', ''m'', ''s'', ''A'') in sum total cancel each other, leaving the sum universe (the simulation itself) residing on that celestial hard-disk. We may introduce a theoretical dimensionless (f_X) geometrical object denoted as f_Planck within which are embedded the dimensioned objects MLTA (mass, length, time, charge), and from which they may be extracted. FOR age = 1 TO the_end add 1 f_Planck 'dimensionless geometrical 'object' { extract 1 unit of (Planck) time; '1 time 'object' T extract 1 unit of (Planck) mass; '1 mass 'object' M extract 1 unit of (Planck) length; '1 length 'object' L } ........ NEXT age This then means that the simulation, in order to create time T, must also create mass M and space L (become larger and more massive). Thus no matter how small or large the physical universe is (when seen internally), in sum total (when seen externally), there is no universe - it is merely data without physical form. === Universe time-line === As the universe expands outwards (through the constant addition of units of mass and length via f_Planck), and if this expansion pulls particles with it (if it is the origin of motion), then ''now'' (the present) would reside on the surface of the (constantly expanding at the speed of light; ''c'' = 1 Planck length / 1 Planck time) universe, and so the 'past' could be retained, for the past cannot be over-written by the present in an expanding universe (if ''now'' is always on the surface). As this expansion occurs at the Planck scale, information even below quantum states, down to the Planck scale, can be retained, the analogy would be the storing of every [[w:Keystroke_logging |keystroke]], a Planck scale version of the [[w:Akashic records |Akashic records]] ... for if our deeds (the past) are both stored and cannot be over-written (by the present), then we have a candidate for the '[[w:karma |karmic]] heavens' (Matthew 6:19 ''But lay up for yourselves treasures in 'heaven', where neither moth nor rust doth corrupt, and where thieves do not break through nor steal''). This also forms a universe '''time-line''' against which previous information can be compared with new information (a 'memory' of events), without which we could not link cause with effect. === Singularity === In a simulation, the data (software) requires a storage device that is ultimately hardware (RAM, HD ...). In a data world of 1's and 0's such as a computer game, characters within that game may analyze other parts of their 1's and 0's game, but they have no means to analyze the hard disk upon which they (and their game) are stored, for the hard disk is an electro-mechanical device, it is not part of their 1's and 0's world, it is a part of the 'real world', the world of their Programmer. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may or may not resemble the laws that operate in the 'real world' (the world of their Programmer). Thus any region where the laws of physics (the laws of their game world) break down would be significant. A [[w:singularity |singularity]] inside a black hole is such a region <ref>https://www.youtube.com/watch?v=W5j7umtZYB4 a black hole singularity as the interface between worlds</ref>. For the [[w:black hole electron |black-hole electron]], its black-hole center would then be analogous to a storage address on a hard disk, the interface between the simulation world and the real world. A massive (galactic) black-hole could be as an entire data sector. The surface of the black-hole would then be of the simulation world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however would be the interface between the data world and the 'hard disk' of the real world, and so would not exist in any 'physical' terms. It is external to the simulation. As analogy, we may discuss the 3-D surface area of a black-hole but not its volume (interior). === Laws of Physics === The scientific method is built upon testable hypothesis and reproducible results. Water always boils (in defined conditions), at 100°C. In a geometrical universe particles will behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these repeating patterns, the more complex the orbits, the more complex the formulas required to describe them and so forth. However if there is a source code from which these geometrical conditions were programmed, then there may also be non-repeating events, back-doors built into the code (a common practice by terrestrial programmers), these by definition would lie outside the laws of physics and so be labelled as miracles, yet they would be no less valid. === Determinism === [[File:Three body problem figure-8 orbit animation.gif|400px|thumb|An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259.<ref>Here the gravitational constant ''G'' has been set to 1, and the initial conditions are '''r'''₁(0) = −'''r'''₃(0) = (−0.97000436, 0.24308753); '''r'''₂(0) = (0,0); '''v'''₁(0) = '''v'''₃(0) = (0.4662036850, 0.4323657300); '''v'''₂(0) = (−0.93240737, −0.86473146). The values are obtained from Chenciner & Montgomery (2000).</ref>]] Particles form more complex structures such as atoms and molecules via a system of orbitals; nuclear, atomic and gravitational. The [[w:Three-body_problem |3-body problem]] is the problem of taking the initial positions and velocities (or [[w:momentum|momenta |momentum|momenta]]) of three or more point masses and solving for their subsequent motion according to [[w:Newton's laws of motion |Newton's laws of motion]] and [[w:Newton's law of universal gravitation |Newton's law of universal gravitation]].<ref name="PrincetonCompanion">{{Citation | last = Barrow-Green | first = June | year = 2008 | title = The Three-Body Problem | editor-last1 = Gowers | editor-first1 = Timothy | editor-last2 = Barrow-Green | editor-first2 = June | editor-last3 = Leader | editor-first3 = Imre | encyclopedia = The Princeton Companion to Mathematics | pages = 726–728 | publisher = Princeton University Press }}</ref>. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for gods and men alike the only way to know what that outcome will be is to run the simulation itself. ==Geometry coded universe== Modelling a Planck scale simulation universe using geometrical forms (links) * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass == External links == * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] * [https://philpapers.org/rec/GRUTIA-2 Simulation theory as evidence for God] (academic peer-reviewed article) ==References== {{Reflist}} [[Category:Philosophy| ]] [[Category:Philosophy of science| ]] 45y8bkvc1o7nl22vwj2aluwkxsx75h0 2718257 2718256 2025-06-10T19:51:10Z 212.200.164.104 /* Planck scale */ 2718257 wikitext text/x-wiki '''Is God a Programmer? analyzing the deep-universe simulation hypothesis at the Planck scale''' The [[w:simulation hypothesis |simulation hypothesis]] is the proposal that all of reality, including the Earth and the rest of the universe, could be an artificial simulation, such as a computer simulation. [[w:Neil_deGrasse_Tyson |Neil deGrasse Tyson]] put the odds at 50-50 that our entire existence is a program on someone else’s hard drive <ref>Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. [[w:David_Chalmers |David Chalmers]] noted “We in this universe can create simulated worlds and there’s nothing remotely spooky about that. Our creator isn’t especially spooky, it’s just some teenage hacker in the next universe up. Turn the tables, and we are essentially gods over our own computer creations <ref>https://www.youtube.com/watch?v=yqbS5qJU8PA, David Chalmers, Serious Science</ref> <ref>The Matrix as Metaphysics, David Chalmers http://consc.net/papers/matrix.pdf</ref> <ref>Are We Living in a Computer Simulation?https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. The commonly postulated [[w:Ancestor_simulation |ancestor simulation]] approach, which [[w:Nick Bostrom |Nick Bostrom]] called "the simulation argument", argues for "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor. However this simulation variant can be traced back to an 'organic base reality' (the original programmer ancestors and their physical planet). The [[v:God_(programmer) |Programmer God]] hypothesis<ref>https://codingthecosmos.com/podcast/ AI generated podcasts</ref> conversely states that a (deep universe) simulation began with the big bang and was programmed by an external intelligence (external to the physical universe), the Programmer by definition a God in the creator of the universe context. Our universe in its entirety, down to the smallest detail, and including life-forms, is within the simulation, the laws of nature, at their most fundamental level, are coded rules running on top of the simulation operating system. The operating system itself is mathematical (and potentially the origin of mathematics). Any candidate for a Programmer-God simulation-universe source code must satisfy these conditions; :1. It can generate physical structures from mathematical forms. :2. The sum universe is dimensionless (simply data on a celestial hard disk). :3. We must be able to use it to derive the laws of physics (because the source code is the origin of the laws of nature, and the laws of physics are our observations of the laws of nature). :4. The mathematical logic must be unknown to us (the Programmer is a non-human intelligence). :5. The coding should have an 'elegance' commensurate with the Programmer's level of skill. == Philosophy == Physicist [[w:Eugene Wigner |Eugene Wigner]] ([[w:The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences |The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]) <ref>{{Cite journal | last1 = Wigner | first1 = E. P. | authorlink = Eugene Wigner| doi = 10.1002/cpa.3160130102 | title = The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959 | journal = Communications on Pure and Applied Mathematics | volume = 13 | pages = 1–14 | year = 1960 | pmid = | pmc = |bibcode = 1960CPAM...13....1W }}</ref> <blockquote>The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. </blockquote> === Discussion === [[w:Philosophy of mathematics |Philosophy of mathematics]] is that branch of philosophy which attempts to answer questions such as: ‘why is mathematics useful in describing nature?’, ‘in which sense, if any, do mathematical entities such as numbers exist?’ and ‘why and how are mathematical statements true?’ This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math. Mathematical realism holds that mathematical entities exist independently of the human mind. We do not invent mathematics, but rather discover it. Triangles, for example, are real entities that have an existence <ref>- http://plato.stanford.edu/entries/platonism-mathematics/</ref>. The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality. It can be considered a form of [[w:Pythagoreanism | Pythagoreanism]] or [[w:Platonism | Platonism]] in that it proposes the existence of ''mathematical objects''; and a form of [[w:philosophy of mathematics | mathematical monism]] in that it denies that anything exists except these ''mathematical objects''. Physicist [[w:Max Tegmark | Max Tegmark]] in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality"<ref name="Tegmark1998">{{cite journal|last=Tegmark |first=Max |date=November 1998 |title=Is "the Theory of Everything" Merely the Ultimate Ensemble Theory? |journal=Annals of Physics |volume=270 |issue=1 |pages=1–51 |doi=10.1006/aphy.1998.5855 |arxiv = gr-qc/9704009 |bibcode = 1998AnPhy.270....1T }}</ref><ref>M. Tegmark 2014, "[http://mathematicaluniverse.org Our Mathematical Universe]", Knopf</ref> proposed that ''Our external physical reality is a mathematical structure''.<ref name="Tegmark2008">{{cite journal|last=Tegmark |first=Max |date=February 2008 |title=The Mathematical Universe |journal=Foundations of Physics |volume=38 |issue=2 |pages=101–150 |doi=10.1007/s10701-007-9186-9 |arxiv=0704.0646|bibcode = 2008FoPh...38..101T }}</ref> That is, the physical universe is not merely ''described by'' mathematics, but ''is'' mathematics (specifically, a [[w:mathematical structure | mathematical structure]]). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref> The principle constraints to any mathematical universe simulation hypothesis are; 1. the computational resources required. The ancestor simulation can resolve this by adapting from the [[w:virtual rality |virtual reality]] approach where only the observable region is simulated and only to the degree required, and 2. that any 'self-aware structures' (humans for example) within the simulation must "subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref>. Succinctly, our computer games may be able to simulate our physical world, but they are still only simulations of a physical reality (regardless of how realistic they may seem) ... we are not yet able to program actual physical dimensions of mass, space and time from mathematical structures, and indeed this may not be possible with a computer hard-ware architecture that can only process binary data. === Deep-universe source code === As a deep-universe simulation is programmed by an external (external to the universe) intelligence (the Programmer God hypothesis), we cannot presume a priori knowledge regarding the simulation source code other than from this code the laws of nature emerged, and so any deep-universe simulation model we try to emulate must be universal, i.e.: independent of any system of units, of the [[w:Dimensional_analysis |dimensioned]] [[w:physical constants |physical constants]] (''G'', ''h'', ''c'', ''e'' .. ), and of any numbering systems. Furthermore, although a deep-universe simulation source code may use mathematical forms (circles, spheres ...) we are familiar with (for ultimately the source code is the origin of these forms), it will have been developed by a non-human intelligence and so we may have to develop new mathematical tools to decipher the underlying logic. By implication therefore, any theoretical basis for a source code that fits the above criteria (and from which the laws of nature will emerge), could be construed as our first tangible evidence of a non-human intelligence. === Constants === A physical universe is characterized by measurable quantities (size, mass, color, texture ...), and so a physical universe can be measured and defined. Contrast then becomes information, the statement ''this is a big apple'' requires a ''small apple'' against which big becomes a relative term. For analytical purposes we select a reference value, for example 0C or 32F, and measure all temperatures against this reference. The smaller the resolution of the measurements, the greater the information content (the file size of a 32 mega-pixel photo is larger than a 4 mega-pixel photo). A simulation universe may be presumed to also have a resolution dictating how much information the simulation can store and manipulate. To measure the fundamental parameters of our universe physics uses [[w:physical constant |physical constants]]. A physical constant is a [[w:physical quantity |physical quantity]] that is generally believed to be both universal in nature and have a constant value in time. These can be divided into 1) dimension-ed (measured using physical units ''kg'', ''m'', ''s'', ''A'' ...) such as the [[w:speed of light |speed of light]] ''c'', [[w:gravitational constant |gravitational constant]] ''G'', [[w:Planck constant |Planck constant]] ''h'' ... as in the table {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} Physicist [[w: |Lev Okun]] noted "Theoretical equations describing the physical world deal with dimensionless quantities and their solutions depend on dimensionless fundamental parameters. But experiments, from which these theories are extracted and by which they could be tested, involve measurements, i.e. comparisons with standard dimension-ful scales. Without standard dimension-ful units and hence without certain conventions physics is unthinkable <ref>Michael J. Duff et al, Journal of High Energy Physics, Volume 2002, JHEP03(2002)</ref>. 2) dimension-less, such as the [[w:Fine-structure_constant |fine structure constant]] ''α''. A dimension-less constant does not measure any physical quantity (it has no units; units = 1). 3) dimension-less [[w:mathematical constant |mathematical constants]], most notably [[w:pi |pi]] = 3.14159265358979 and [[w:Natural_logarithm |e]] = 2.718281828459. Although these are [[w:transcendental number |transcendental numbers]], they can be constructed by integers in a series, and so for a universe expanding incrementally (see simulation time), these constants could be formed within the simulation. For example, at time ''t''; <math display=block>t = 1; \frac{\pi^2}{6} = \frac{1}{t^2} </math> <math display=block>t = 2; \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{t^2}</math> <math display=block>t = now: \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots + \frac{1}{t^2} </math> We may now define the fundamental physical constant as a parameter specifically chosen by the Programmer and is encoded into the simulation code directly, and so whilst it may be inferable, it is not derived from other constants ([[w:Fine-structure_constant#Numerological_explanations_and_multiverse_theory |Richard Feynman on the fine structure constant]]). It should also be dimension-less otherwise the simulation itself becomes dimensioned (if the simulation is running on a celestial computer it is merely data, it has no physical size or shape or ...), and so the dimensioned constants (''G'', ''h'', ''c'', ''e''...) must all be derivable (derived from within the simulation) via the (embedded in the source code) fundamental physical constants (of which the fine structure constant alpha may be an example). Although [[w:pi |pi]] and [[w:Natural_logarithm |e]] are dimensionless, they can be derived internally (from integers), and as they have application in the mathematical realm, they can be referred to as mathematical constants. ==== Planck scale ==== The [[w:Planck scale |Planck scale]] refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the [[w:Standard Model |Standard Model]], [[w:quantum field theory |quantum field theory]] and [[w:general relativity |general relativity]] are no longer reconcilable, and [[w:Quantum Gravity |quantum effects of gravity]] are expected to dominate (quantum gravitational effects only appear at length scales near the Planck scale). Although particles may not be cognizance of our 'laws of physics', they do know the 'laws of nature'. These laws of nature would run directly off the universe OS (operating system), and so below this OS, 'physics' as we know it must necessarily break down. At present the Planck scale is the lowest known level, consequently any attempt to detect evidence of an underlying simulation coding must consider (if not actually begin at) this, the Planck scale<ref>https://www.youtube.com/watch?v=AMQRXGYCDrY Planck scale, Brian Greene</ref>. The [[w:International_System_of_Units |SI units]] for the dimension-ful mksa units are; meter (length), kilogram (mass), second (time), ampere (electric current). There are Planck units that represent these SI units, and so a simulation could use them as discrete building blocks; [[w:Planck length |Planck length]] (the smallest possible unit of length), [[w:Planck mass |Planck mass]] (the unit of mass), [[w:Planck time |Planck time]] (the smallest possible unit of time), [[w:Planck charge |Planck charge]] (the unit of charge). The speed of light then becomes ''c'' = 1 Planck length / 1 Planck time. These units would define the resolution and so information carrying capacity of the simulation universe. ==== Numbering systems ==== As well as our decimal system, computers apply binary and hexadecimal numbering systems. In particular the decimal and hexadecimal are of terrestrial origin and may not be considered 'universal'. Furthermore numbering systems measure only the frequency of an event and contain no information as to the event itself. The number 299 792 458 could refer to the speed of light (299 792 458 m/s) or could equally be referring to the number of apples in a container (299 792 458 apples). As such, numbers require a 'descriptive', whether m/s or apples. Numbers also do not include their history, is 299 792 458 for example a derivation of other base numbers? Present universe simulations use the laws of physics and the physical constants are built in, however both these laws and the physical constants are known only to a limited precision, and so a simulation with 10⁶² iterations (the present age of the universe in units of Planck time) will accumulate errors. Number based computing may be sufficient for ancestor-simulation models where only the observed region needs to be calculated, but has inherent limitations for deep universe simulations where the entire universe is continuously updated. The actual computational requirements for a Planck scale universe simulation based on a numbering system with the laws of physics embedded would be an unknown and consequently lead to an 'non-testable' hypothesis. This is a commonly applied reasoning for rejecting the deep universe simulation. ==== Geometrical objects ==== A mathematical constant such as [[w:pi |pi]] refers to a geometrical construct (the ratio of circle circumference to circle radius) and so is not constrained by any particular numbering system (in the decimal system π = 3.14159...), and so may be considered both universal and eternal. Likewise, by assigning geometrical objects instead of numbers to the Planck units, the problems with a numbering system can be resolved. These objects would however have to fulfill the following conditions; 1) embedded attribute - for example the object for length must embed the function of ''length'' such that a descriptive (km, mile ... ) is not required. Electron wavelength would then be measurable in terms of the length object, as such the length object must be embedded within the electron (the electron object). Although the mass object would incorporate the function ''mass'', the time object the function ''time'' ..., it is not necessary that there be an individual physical mass or physical length or physical time ..., but only that in relation to the other units, the object must express that function (i.e.: the mass object has the function of mass when in the presence of the objects for space and time). The electron could then be a complex event (complex geometrical object) constructed by combining the objects for mass, length, time and charge into 1 event, and thus electron charge, wavelength, frequency and mass would then be different aspects of that 1 geometry (the electron event) and not independent parameters (independent of each other). 2) The objects for mass, length, time and charge must be able to combine with each other [[w:Lego |Lego-style]] to form more complex objects (events) such as electrons and apples whilst still retaining the underlying information (the mass of the apple derives from the mass objects embedded within that apple). Not only must these objects be able to form complex events such as particles, but these events themselves are geometrical objects and so must likewise function according to their geometries. Electrons would orbit protons according to their respective electron and proton geometries, these orbits the result of geometrical imperatives and not due to any built-in laws of physics (the orbital path is a consequence of all the underlying geometries). However, as orbits follow regular and repeating patterns, they can be described (by us) using mathematical formulas. As the events grow in complexity (from atoms to molecules to planets), so too will the patterns (and likewise the formulas we use to describe them). Consequently the ''laws of physics'' would then become our mathematical descriptions of the underlying geometrically imposed patterns. 3) These objects would replace coded instructions (the instruction sets would be built into the objects) thereby instigating a geometrically autonomous universe. The electron 'knows' what to do by virtue of the information encoded within its geometry, no coded electron CALL FUNCTION is required. This would be equivalent to combining the hardware, software and CPU together such that the 'software' changes (adjusts) to the changing 'hardware' (DNA may be an analogy). Note: A purely mathematical universe has no limits in size and can be infinitely large and infinity small. A geometrical universe (that uses objects) has limitations, it can be no smaller than the smallest object for example and has discrete parts (those objects). The philosophy of the TOE (theory of everything) therefore includes a debate between the mathematical universe and the geometrical universe, however this distinction between mathematical and geometrical would only be apparent at the Planck scale. === Evidence of a simulation === The laws of physics are our incomplete observations of the natural universe, and so evidence of a simulation may be found in ambiguities or anomalies within these laws. Furthermore, if complexity arises over time, then at unit time the 'handiwork' of the Programmer may be notable by a simplicity and elegance of the geometries employed ... for the Programmer by definition has God-level programming skills. Here is a notable example. Mass, space and time from the number 1 The dimensions of mass, space and time are considered by science to be independent of each other, we cannot measure the ''distance'' from Tokyo to London using kilograms and amperes, or measure ''mass'' using space and time. Indeed, what characterizes a physical universe as opposed to a simulated universe is the notion that there is a fundamental structure underneath, that in some sense mass 'is', that time 'is' and space 'is' ... thus we cannot write ''kg'' in terms of ''m'' and ''s''. To do so would render our concepts of a physical universe meaningless. The 26th General Conference on Weights and Measures ([[w:2019 redefinition of SI base units|2019 redefinition of SI base units]]) assigned exact numerical values to 4 physical constants (''h, c, e, k''_B) independently of each other (and thereby confirming these as fundamental constants), and as they are measured in SI units ('''kg''', '''m''', '''s''', '''A''', '''K'''), these units must also be independent of each other (i.e.: these are fundamental units, for example if we could define ''m'' using ''A'' then the speed of light could be derived from, and so would depend upon, the value for the elementary charge ''e'', and so the value for ''c'' could not be assigned independently from ''e''). {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} We are familiar with inverse properties; plus charge and minus charge, matter and anti-matter ... and we can observe how these may form and/or cancel each other. A simulation universe however is required to be dimensionless (in sum total), for the simulated universe does not 'exist' in any physical sense outside of the 'Computer' (it is simply data on a celestial hard-disk). Our universe does not appear to have inverse properties such as anti-mass (-kg), anti-time (-s) or anti-space (anti-length -m), therefore the first problem the Programmer must solve is how to create the physical scaffolding (of mass, space and time). For example, the Programmer can start by selecting 2 dimensioned quantities, here are used ''r'', ''v'' <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref> such that :<math>kg = \frac{r^4}{v},\; m = \frac{r^9}{v^5},\; s = \frac{r^9}{v^6},\; A = \frac{v^3}{r^6}</math> Quantities ''r'' and ''v'' are chosen so that no unit (''kg'', ''m'', ''s'', ''A'') can cancel another unit (i.e.: the ''kg'' cannot cancel the ''m'' or the ''s'' ...), and so we have 4 independent units (we still cannot define the ''kg'' using the ''m'' or the ''s'' ...), however if 3 (or more) units are combined together in a specific ratio, they can cancel (in a certain ratio our ''r'' and ''v'' become inverse properties and so cancel each other; units = 1). <math>f_X = \frac{kg^9 s^{11}}{m^{15}} = \frac{(\frac{r^4}{v})^9 (\frac{r^9}{v^6})^{11}}{(\frac{r^9}{v^5})^{15}} = 1</math> This f_X, although embedded within are the dimensioned structures for mass, time and length (in the above ratio), would be a dimensionless mathematical structure, units = 1. Thus we may create as much mass, time and length as we wish, the only proviso being that they are created in f_X ratios, so that regardless of how massive, old and large our universe becomes, it is still in sum total dimensionless. Defining the dimensioned quantities ''r'', ''v'' in SI unit terms. :<math>r = (\frac{kg\;m}{s})^{1/4}</math> :<math>v = \frac{m}{s}</math> Mass :<math>\frac{r^4}{v} = (\frac{kg\;m}{s})\;(\frac{s}{m}) = kg</math> Length :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^5})^4 = \frac{s^{20}}{m^{20}}</math> :<math>(\frac{r^9}{v^5})^4 = \frac{kg^9 s^{11}}{m^{11}} = m^4 \frac{kg^9 s^{11}}{m^{15}} = m^4 f_X = m^4</math> Time :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^6})^4 = \frac{s^{24}}{m^{24}}</math> :<math>(\frac{r^9}{v^6})^4 = \frac{kg^9 s^{15}}{m^{15}} = s^4 \frac{kg^9 s^{11}}{m^{15}} = s^4 f_X = s^4</math> And so, although f_X is a dimensionless mathematical structure, we can embed within it the (mass, length, time ...) structures along with their dimensional attributes (kg, m, s, A ..). In the mathematical electron model (discussed below), the electron itself is an example of an f_X structure, it (f_electron) is a dimensionless geometrical object that embeds the physical electron parameters of wavelength, frequency, charge (note: A-m = ampere-meter are the units for a [[w:Magnetic_monopole#In_SI_units |magnetic monopole]]). <math>f_{electron}</math> :<math>units = \frac{A^3 m^3}{s} = \frac{(\frac{v^3}{r^6})^3 (\frac{r^9}{v^5})^3}{(\frac{r^9}{v^6})} = 1</math> We may note that at the macro-level (of planets and stars) these f_X ratio are not found, and so this level is the domain of the observed physical universe, however at the quantum level, f_X ratio do appear, f_electron as an example, the mathematical and physical domains then blurring. This would also explain why physics can measure precisely the parameters of the electron (wavelength, mass ...), but has never found the electron itself. == Programming == “God vs. science debates tend to be restricted to the premise that a God does not rely on science and that science does not need a God. As science and God are thus seen as mutually exclusive there are few, if any, serious attempts to construct mathematical models of a universe whose principle axiom does require a God. However, if there is an Intelligence responsible for the 14 billion year old universe of modern physics, being the universe of Einstein and Dirac, and beginning with the big bang as the act of 'creation', then we must ask how it might be done? What construction technique could have been used to set the laws of physics in motion?” <ref>[https://theprogrammergod.com/ The Programmer God, are we in a Simulation]</ref> === Simulation Time === The (dimensionless) simulation clock-rate would be defined as the minimum 'time variable' ('''age''') increment to the simulation. Using a simple loop as analogy, at ''age'' = 1, the simulation begins (the big bang), certain processes occur, when these are completed ''age'' increments (''age'' = 2, then 3, then 4 ... ) until ''age'' reaches ''the_end'' and the simulation stops. 'begin simulation FOR age = 1 TO the_end 'big bang = 1 conduct certain processes ........ NEXT age 'end simulation [[w:Quantum spacetime |Quantum spacetime]] and [[w:Quantum gravity |Quantum gravity]] models refer to [[w:Planck time | Planck time]] as the smallest discrete unit of time and so the incrementing variable '''age''' could be used to generate units of Planck time (and other Planck units, the physical scaffolding of the universe). In a geometrical model, to these Planck units could be assigned geometrical objects, for example; Initialize_physical_constants; FOR age = 1 TO the_end generate 1 unit of (Planck) time; '1 time 'object' T generate 1 unit of (Planck) mass; '1 mass 'object' M generate 1 unit of (Planck) length; '1 length 'object' L ........ NEXT age The variable ''age'' is the simulation clock-rate, it is simply a counter (1, 2, 3 ...) and so is a dimensionless number, the object T is the geometrical Planck time object, it is dimensioned and is measured by us in seconds. If ''age'' is the origin of Planck time (1 increment to ''age'' generates 1 T object) then ''age'' = 10⁶², this is based on the present [[w:Age_of_the_universe |age of the universe]], which, at 14 billion years, equates to 10⁶² units of Planck time. For each ''age'', certain operations are performed, only after they are finished does ''age'' increment (there is no ''time'' interval between increments). As noted, ''age'' being dimensionless, is not the same as dimensioned Planck time which is the geometrical object T, and this T, being dimensioned, can only appear within the simulation. The analogy would be frames of a movie, each frame contains dimensioned information but there is no ''time'' interval between frames. FOR age = 1 TO the_end (of the movie) display frame{age} NEXT age Although operations (between increments to ''age'') may be extensive, self-aware structures from within the simulation would have no means to determine this, they could only perceive themselves as being in a real-time (for them the smallest unit of ''time'' is 1T, just as the smallest unit of ''time'' in a movie is 1 frame). Their (those self-aware structures) dimension of time would then be a measure of relative motion (a change of state), and so although ultimately deriving from the variable ''age'', their time would not be the same as ''age''. If there was no motion, if all particles and photons were still (no change of state), then their time dimension could not update (if every frame in a movie was the same then actors within that movie could not register a change in time), ''age'' however would continue to increment. Thus we have 3 time structures; 1) the dimension-less simulation clock-rate variable ''age'', 2) the dimensioned time unit (object T), and 3) time as change of state (the observers time). Observer time requires a memory of past events against which a change of state can be perceived. The forward increment to ''age'' would constitute the [[w:arrow of time |arrow of time]]. Reversing this would reverse the arrow of time, the universe would likewise shrink in size and mass accordingly (just as a [[w:white hole |white hole]] is the (time) reversal of a [[w:black hole |black hole]]). FOR age = the_end TO 1 STEP -1 delete 1 unit of Planck time; delete 1 unit of Planck mass; delete 1 unit of Planck length; ........ NEXT age Adding mass, length and time objects per increment to ''age'' would force the universe expansion (in size and mass), and as such an anti-gravitational [[w:dark energy |dark energy]] would not be required, however these objects are dimensioned and so are generated within the simulation. This means that they must somehow combine in a specific ratio whereby they (the units for mass length, time, charge; ''kg'', ''m'', ''s'', ''A'') in sum total cancel each other, leaving the sum universe (the simulation itself) residing on that celestial hard-disk. We may introduce a theoretical dimensionless (f_X) geometrical object denoted as f_Planck within which are embedded the dimensioned objects MLTA (mass, length, time, charge), and from which they may be extracted. FOR age = 1 TO the_end add 1 f_Planck 'dimensionless geometrical 'object' { extract 1 unit of (Planck) time; '1 time 'object' T extract 1 unit of (Planck) mass; '1 mass 'object' M extract 1 unit of (Planck) length; '1 length 'object' L } ........ NEXT age This then means that the simulation, in order to create time T, must also create mass M and space L (become larger and more massive). Thus no matter how small or large the physical universe is (when seen internally), in sum total (when seen externally), there is no universe - it is merely data without physical form. === Universe time-line === As the universe expands outwards (through the constant addition of units of mass and length via f_Planck), and if this expansion pulls particles with it (if it is the origin of motion), then ''now'' (the present) would reside on the surface of the (constantly expanding at the speed of light; ''c'' = 1 Planck length / 1 Planck time) universe, and so the 'past' could be retained, for the past cannot be over-written by the present in an expanding universe (if ''now'' is always on the surface). As this expansion occurs at the Planck scale, information even below quantum states, down to the Planck scale, can be retained, the analogy would be the storing of every [[w:Keystroke_logging |keystroke]], a Planck scale version of the [[w:Akashic records |Akashic records]] ... for if our deeds (the past) are both stored and cannot be over-written (by the present), then we have a candidate for the '[[w:karma |karmic]] heavens' (Matthew 6:19 ''But lay up for yourselves treasures in 'heaven', where neither moth nor rust doth corrupt, and where thieves do not break through nor steal''). This also forms a universe '''time-line''' against which previous information can be compared with new information (a 'memory' of events), without which we could not link cause with effect. === Singularity === In a simulation, the data (software) requires a storage device that is ultimately hardware (RAM, HD ...). In a data world of 1's and 0's such as a computer game, characters within that game may analyze other parts of their 1's and 0's game, but they have no means to analyze the hard disk upon which they (and their game) are stored, for the hard disk is an electro-mechanical device, it is not part of their 1's and 0's world, it is a part of the 'real world', the world of their Programmer. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may or may not resemble the laws that operate in the 'real world' (the world of their Programmer). Thus any region where the laws of physics (the laws of their game world) break down would be significant. A [[w:singularity |singularity]] inside a black hole is such a region <ref>https://www.youtube.com/watch?v=W5j7umtZYB4 a black hole singularity as the interface between worlds</ref>. For the [[w:black hole electron |black-hole electron]], its black-hole center would then be analogous to a storage address on a hard disk, the interface between the simulation world and the real world. A massive (galactic) black-hole could be as an entire data sector. The surface of the black-hole would then be of the simulation world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however would be the interface between the data world and the 'hard disk' of the real world, and so would not exist in any 'physical' terms. It is external to the simulation. As analogy, we may discuss the 3-D surface area of a black-hole but not its volume (interior). === Laws of Physics === The scientific method is built upon testable hypothesis and reproducible results. Water always boils (in defined conditions), at 100°C. In a geometrical universe particles will behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these repeating patterns, the more complex the orbits, the more complex the formulas required to describe them and so forth. However if there is a source code from which these geometrical conditions were programmed, then there may also be non-repeating events, back-doors built into the code (a common practice by terrestrial programmers), these by definition would lie outside the laws of physics and so be labelled as miracles, yet they would be no less valid. === Determinism === [[File:Three body problem figure-8 orbit animation.gif|400px|thumb|An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259.<ref>Here the gravitational constant ''G'' has been set to 1, and the initial conditions are '''r'''₁(0) = −'''r'''₃(0) = (−0.97000436, 0.24308753); '''r'''₂(0) = (0,0); '''v'''₁(0) = '''v'''₃(0) = (0.4662036850, 0.4323657300); '''v'''₂(0) = (−0.93240737, −0.86473146). The values are obtained from Chenciner & Montgomery (2000).</ref>]] Particles form more complex structures such as atoms and molecules via a system of orbitals; nuclear, atomic and gravitational. The [[w:Three-body_problem |3-body problem]] is the problem of taking the initial positions and velocities (or [[w:momentum|momenta |momentum|momenta]]) of three or more point masses and solving for their subsequent motion according to [[w:Newton's laws of motion |Newton's laws of motion]] and [[w:Newton's law of universal gravitation |Newton's law of universal gravitation]].<ref name="PrincetonCompanion">{{Citation | last = Barrow-Green | first = June | year = 2008 | title = The Three-Body Problem | editor-last1 = Gowers | editor-first1 = Timothy | editor-last2 = Barrow-Green | editor-first2 = June | editor-last3 = Leader | editor-first3 = Imre | encyclopedia = The Princeton Companion to Mathematics | pages = 726–728 | publisher = Princeton University Press }}</ref>. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for gods and men alike the only way to know what that outcome will be is to run the simulation itself. ==Geometry coded universe== Modelling a Planck scale simulation universe using geometrical forms (links) * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass == External links == * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] * [https://philpapers.org/rec/GRUTIA-2 Simulation theory as evidence for God] (academic peer-reviewed article) ==References== {{Reflist}} [[Category:Philosophy| ]] [[Category:Philosophy of science| ]] nldnrrebk5q9nahpxlnqylf1js2r2vv 2718258 2718257 2025-06-10T19:51:19Z 212.200.164.104 /* Numbering systems */ 2718258 wikitext text/x-wiki '''Is God a Programmer? analyzing the deep-universe simulation hypothesis at the Planck scale''' The [[w:simulation hypothesis |simulation hypothesis]] is the proposal that all of reality, including the Earth and the rest of the universe, could be an artificial simulation, such as a computer simulation. [[w:Neil_deGrasse_Tyson |Neil deGrasse Tyson]] put the odds at 50-50 that our entire existence is a program on someone else’s hard drive <ref>Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. [[w:David_Chalmers |David Chalmers]] noted “We in this universe can create simulated worlds and there’s nothing remotely spooky about that. Our creator isn’t especially spooky, it’s just some teenage hacker in the next universe up. Turn the tables, and we are essentially gods over our own computer creations <ref>https://www.youtube.com/watch?v=yqbS5qJU8PA, David Chalmers, Serious Science</ref> <ref>The Matrix as Metaphysics, David Chalmers http://consc.net/papers/matrix.pdf</ref> <ref>Are We Living in a Computer Simulation?https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. The commonly postulated [[w:Ancestor_simulation |ancestor simulation]] approach, which [[w:Nick Bostrom |Nick Bostrom]] called "the simulation argument", argues for "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor. However this simulation variant can be traced back to an 'organic base reality' (the original programmer ancestors and their physical planet). The [[v:God_(programmer) |Programmer God]] hypothesis<ref>https://codingthecosmos.com/podcast/ AI generated podcasts</ref> conversely states that a (deep universe) simulation began with the big bang and was programmed by an external intelligence (external to the physical universe), the Programmer by definition a God in the creator of the universe context. Our universe in its entirety, down to the smallest detail, and including life-forms, is within the simulation, the laws of nature, at their most fundamental level, are coded rules running on top of the simulation operating system. The operating system itself is mathematical (and potentially the origin of mathematics). Any candidate for a Programmer-God simulation-universe source code must satisfy these conditions; :1. It can generate physical structures from mathematical forms. :2. The sum universe is dimensionless (simply data on a celestial hard disk). :3. We must be able to use it to derive the laws of physics (because the source code is the origin of the laws of nature, and the laws of physics are our observations of the laws of nature). :4. The mathematical logic must be unknown to us (the Programmer is a non-human intelligence). :5. The coding should have an 'elegance' commensurate with the Programmer's level of skill. == Philosophy == Physicist [[w:Eugene Wigner |Eugene Wigner]] ([[w:The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences |The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]) <ref>{{Cite journal | last1 = Wigner | first1 = E. P. | authorlink = Eugene Wigner| doi = 10.1002/cpa.3160130102 | title = The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959 | journal = Communications on Pure and Applied Mathematics | volume = 13 | pages = 1–14 | year = 1960 | pmid = | pmc = |bibcode = 1960CPAM...13....1W }}</ref> <blockquote>The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. </blockquote> === Discussion === [[w:Philosophy of mathematics |Philosophy of mathematics]] is that branch of philosophy which attempts to answer questions such as: ‘why is mathematics useful in describing nature?’, ‘in which sense, if any, do mathematical entities such as numbers exist?’ and ‘why and how are mathematical statements true?’ This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math. Mathematical realism holds that mathematical entities exist independently of the human mind. We do not invent mathematics, but rather discover it. Triangles, for example, are real entities that have an existence <ref>- http://plato.stanford.edu/entries/platonism-mathematics/</ref>. The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality. It can be considered a form of [[w:Pythagoreanism | Pythagoreanism]] or [[w:Platonism | Platonism]] in that it proposes the existence of ''mathematical objects''; and a form of [[w:philosophy of mathematics | mathematical monism]] in that it denies that anything exists except these ''mathematical objects''. Physicist [[w:Max Tegmark | Max Tegmark]] in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality"<ref name="Tegmark1998">{{cite journal|last=Tegmark |first=Max |date=November 1998 |title=Is "the Theory of Everything" Merely the Ultimate Ensemble Theory? |journal=Annals of Physics |volume=270 |issue=1 |pages=1–51 |doi=10.1006/aphy.1998.5855 |arxiv = gr-qc/9704009 |bibcode = 1998AnPhy.270....1T }}</ref><ref>M. Tegmark 2014, "[http://mathematicaluniverse.org Our Mathematical Universe]", Knopf</ref> proposed that ''Our external physical reality is a mathematical structure''.<ref name="Tegmark2008">{{cite journal|last=Tegmark |first=Max |date=February 2008 |title=The Mathematical Universe |journal=Foundations of Physics |volume=38 |issue=2 |pages=101–150 |doi=10.1007/s10701-007-9186-9 |arxiv=0704.0646|bibcode = 2008FoPh...38..101T }}</ref> That is, the physical universe is not merely ''described by'' mathematics, but ''is'' mathematics (specifically, a [[w:mathematical structure | mathematical structure]]). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref> The principle constraints to any mathematical universe simulation hypothesis are; 1. the computational resources required. The ancestor simulation can resolve this by adapting from the [[w:virtual rality |virtual reality]] approach where only the observable region is simulated and only to the degree required, and 2. that any 'self-aware structures' (humans for example) within the simulation must "subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref>. Succinctly, our computer games may be able to simulate our physical world, but they are still only simulations of a physical reality (regardless of how realistic they may seem) ... we are not yet able to program actual physical dimensions of mass, space and time from mathematical structures, and indeed this may not be possible with a computer hard-ware architecture that can only process binary data. === Deep-universe source code === As a deep-universe simulation is programmed by an external (external to the universe) intelligence (the Programmer God hypothesis), we cannot presume a priori knowledge regarding the simulation source code other than from this code the laws of nature emerged, and so any deep-universe simulation model we try to emulate must be universal, i.e.: independent of any system of units, of the [[w:Dimensional_analysis |dimensioned]] [[w:physical constants |physical constants]] (''G'', ''h'', ''c'', ''e'' .. ), and of any numbering systems. Furthermore, although a deep-universe simulation source code may use mathematical forms (circles, spheres ...) we are familiar with (for ultimately the source code is the origin of these forms), it will have been developed by a non-human intelligence and so we may have to develop new mathematical tools to decipher the underlying logic. By implication therefore, any theoretical basis for a source code that fits the above criteria (and from which the laws of nature will emerge), could be construed as our first tangible evidence of a non-human intelligence. === Constants === A physical universe is characterized by measurable quantities (size, mass, color, texture ...), and so a physical universe can be measured and defined. Contrast then becomes information, the statement ''this is a big apple'' requires a ''small apple'' against which big becomes a relative term. For analytical purposes we select a reference value, for example 0C or 32F, and measure all temperatures against this reference. The smaller the resolution of the measurements, the greater the information content (the file size of a 32 mega-pixel photo is larger than a 4 mega-pixel photo). A simulation universe may be presumed to also have a resolution dictating how much information the simulation can store and manipulate. To measure the fundamental parameters of our universe physics uses [[w:physical constant |physical constants]]. A physical constant is a [[w:physical quantity |physical quantity]] that is generally believed to be both universal in nature and have a constant value in time. These can be divided into 1) dimension-ed (measured using physical units ''kg'', ''m'', ''s'', ''A'' ...) such as the [[w:speed of light |speed of light]] ''c'', [[w:gravitational constant |gravitational constant]] ''G'', [[w:Planck constant |Planck constant]] ''h'' ... as in the table {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} Physicist [[w: |Lev Okun]] noted "Theoretical equations describing the physical world deal with dimensionless quantities and their solutions depend on dimensionless fundamental parameters. But experiments, from which these theories are extracted and by which they could be tested, involve measurements, i.e. comparisons with standard dimension-ful scales. Without standard dimension-ful units and hence without certain conventions physics is unthinkable <ref>Michael J. Duff et al, Journal of High Energy Physics, Volume 2002, JHEP03(2002)</ref>. 2) dimension-less, such as the [[w:Fine-structure_constant |fine structure constant]] ''α''. A dimension-less constant does not measure any physical quantity (it has no units; units = 1). 3) dimension-less [[w:mathematical constant |mathematical constants]], most notably [[w:pi |pi]] = 3.14159265358979 and [[w:Natural_logarithm |e]] = 2.718281828459. Although these are [[w:transcendental number |transcendental numbers]], they can be constructed by integers in a series, and so for a universe expanding incrementally (see simulation time), these constants could be formed within the simulation. For example, at time ''t''; <math display=block>t = 1; \frac{\pi^2}{6} = \frac{1}{t^2} </math> <math display=block>t = 2; \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{t^2}</math> <math display=block>t = now: \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots + \frac{1}{t^2} </math> We may now define the fundamental physical constant as a parameter specifically chosen by the Programmer and is encoded into the simulation code directly, and so whilst it may be inferable, it is not derived from other constants ([[w:Fine-structure_constant#Numerological_explanations_and_multiverse_theory |Richard Feynman on the fine structure constant]]). It should also be dimension-less otherwise the simulation itself becomes dimensioned (if the simulation is running on a celestial computer it is merely data, it has no physical size or shape or ...), and so the dimensioned constants (''G'', ''h'', ''c'', ''e''...) must all be derivable (derived from within the simulation) via the (embedded in the source code) fundamental physical constants (of which the fine structure constant alpha may be an example). Although [[w:pi |pi]] and [[w:Natural_logarithm |e]] are dimensionless, they can be derived internally (from integers), and as they have application in the mathematical realm, they can be referred to as mathematical constants. ==== Planck scale ==== The [[w:Planck scale |Planck scale]] refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the [[w:Standard Model |Standard Model]], [[w:quantum field theory |quantum field theory]] and [[w:general relativity |general relativity]] are no longer reconcilable, and [[w:Quantum Gravity |quantum effects of gravity]] are expected to dominate (quantum gravitational effects only appear at length scales near the Planck scale). Although particles may not be cognizance of our 'laws of physics', they do know the 'laws of nature'. These laws of nature would run directly off the universe OS (operating system), and so below this OS, 'physics' as we know it must necessarily break down. At present the Planck scale is the lowest known level, consequently any attempt to detect evidence of an underlying simulation coding must consider (if not actually begin at) this, the Planck scale<ref>https://www.youtube.com/watch?v=AMQRXGYCDrY Planck scale, Brian Greene</ref>. The [[w:International_System_of_Units |SI units]] for the dimension-ful mksa units are; meter (length), kilogram (mass), second (time), ampere (electric current). There are Planck units that represent these SI units, and so a simulation could use them as discrete building blocks; [[w:Planck length |Planck length]] (the smallest possible unit of length), [[w:Planck mass |Planck mass]] (the unit of mass), [[w:Planck time |Planck time]] (the smallest possible unit of time), [[w:Planck charge |Planck charge]] (the unit of charge). The speed of light then becomes ''c'' = 1 Planck length / 1 Planck time. These units would define the resolution and so information carrying capacity of the simulation universe. ==== Numbering systems ==== As well as our decimal system, computers apply binary and hexadecimal numbering systems. In particular the decimal and hexadecimal are of terrestrial origin and may not be considered 'universal'. Furthermore numbering systems measure only the frequency of an event and contain no information as to the event itself. The number 299 792 458 could refer to the speed of light (299 792 458 m/s) or could equally be referring to the number of apples in a container (299 792 458 apples). As such, numbers require a 'descriptive', whether m/s or apples. Numbers also do not include their history, is 299 792 458 for example a derivation of other base numbers? Present universe simulations use the laws of physics and the physical constants are built in, however both these laws and the physical constants are known only to a limited precision, and so a simulation with 10⁶² iterations (the present age of the universe in units of Planck time) will accumulate errors. Number based computing may be sufficient for ancestor-simulation models where only the observed region needs to be calculated, but has inherent limitations for deep universe simulations where the entire universe is continuously updated. The actual computational requirements for a Planck scale universe simulation based on a numbering system with the laws of physics embedded would be an unknown and consequently lead to an 'non-testable' hypothesis. This is a commonly applied reasoning for rejecting the deep universe simulation. ==== Geometrical objects ==== A mathematical constant such as [[w:pi |pi]] refers to a geometrical construct (the ratio of circle circumference to circle radius) and so is not constrained by any particular numbering system (in the decimal system π = 3.14159...), and so may be considered both universal and eternal. Likewise, by assigning geometrical objects instead of numbers to the Planck units, the problems with a numbering system can be resolved. These objects would however have to fulfill the following conditions; 1) embedded attribute - for example the object for length must embed the function of ''length'' such that a descriptive (km, mile ... ) is not required. Electron wavelength would then be measurable in terms of the length object, as such the length object must be embedded within the electron (the electron object). Although the mass object would incorporate the function ''mass'', the time object the function ''time'' ..., it is not necessary that there be an individual physical mass or physical length or physical time ..., but only that in relation to the other units, the object must express that function (i.e.: the mass object has the function of mass when in the presence of the objects for space and time). The electron could then be a complex event (complex geometrical object) constructed by combining the objects for mass, length, time and charge into 1 event, and thus electron charge, wavelength, frequency and mass would then be different aspects of that 1 geometry (the electron event) and not independent parameters (independent of each other). 2) The objects for mass, length, time and charge must be able to combine with each other [[w:Lego |Lego-style]] to form more complex objects (events) such as electrons and apples whilst still retaining the underlying information (the mass of the apple derives from the mass objects embedded within that apple). Not only must these objects be able to form complex events such as particles, but these events themselves are geometrical objects and so must likewise function according to their geometries. Electrons would orbit protons according to their respective electron and proton geometries, these orbits the result of geometrical imperatives and not due to any built-in laws of physics (the orbital path is a consequence of all the underlying geometries). However, as orbits follow regular and repeating patterns, they can be described (by us) using mathematical formulas. As the events grow in complexity (from atoms to molecules to planets), so too will the patterns (and likewise the formulas we use to describe them). Consequently the ''laws of physics'' would then become our mathematical descriptions of the underlying geometrically imposed patterns. 3) These objects would replace coded instructions (the instruction sets would be built into the objects) thereby instigating a geometrically autonomous universe. The electron 'knows' what to do by virtue of the information encoded within its geometry, no coded electron CALL FUNCTION is required. This would be equivalent to combining the hardware, software and CPU together such that the 'software' changes (adjusts) to the changing 'hardware' (DNA may be an analogy). Note: A purely mathematical universe has no limits in size and can be infinitely large and infinity small. A geometrical universe (that uses objects) has limitations, it can be no smaller than the smallest object for example and has discrete parts (those objects). The philosophy of the TOE (theory of everything) therefore includes a debate between the mathematical universe and the geometrical universe, however this distinction between mathematical and geometrical would only be apparent at the Planck scale. === Evidence of a simulation === The laws of physics are our incomplete observations of the natural universe, and so evidence of a simulation may be found in ambiguities or anomalies within these laws. Furthermore, if complexity arises over time, then at unit time the 'handiwork' of the Programmer may be notable by a simplicity and elegance of the geometries employed ... for the Programmer by definition has God-level programming skills. Here is a notable example. Mass, space and time from the number 1 The dimensions of mass, space and time are considered by science to be independent of each other, we cannot measure the ''distance'' from Tokyo to London using kilograms and amperes, or measure ''mass'' using space and time. Indeed, what characterizes a physical universe as opposed to a simulated universe is the notion that there is a fundamental structure underneath, that in some sense mass 'is', that time 'is' and space 'is' ... thus we cannot write ''kg'' in terms of ''m'' and ''s''. To do so would render our concepts of a physical universe meaningless. The 26th General Conference on Weights and Measures ([[w:2019 redefinition of SI base units|2019 redefinition of SI base units]]) assigned exact numerical values to 4 physical constants (''h, c, e, k''_B) independently of each other (and thereby confirming these as fundamental constants), and as they are measured in SI units ('''kg''', '''m''', '''s''', '''A''', '''K'''), these units must also be independent of each other (i.e.: these are fundamental units, for example if we could define ''m'' using ''A'' then the speed of light could be derived from, and so would depend upon, the value for the elementary charge ''e'', and so the value for ''c'' could not be assigned independently from ''e''). {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} We are familiar with inverse properties; plus charge and minus charge, matter and anti-matter ... and we can observe how these may form and/or cancel each other. A simulation universe however is required to be dimensionless (in sum total), for the simulated universe does not 'exist' in any physical sense outside of the 'Computer' (it is simply data on a celestial hard-disk). Our universe does not appear to have inverse properties such as anti-mass (-kg), anti-time (-s) or anti-space (anti-length -m), therefore the first problem the Programmer must solve is how to create the physical scaffolding (of mass, space and time). For example, the Programmer can start by selecting 2 dimensioned quantities, here are used ''r'', ''v'' <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref> such that :<math>kg = \frac{r^4}{v},\; m = \frac{r^9}{v^5},\; s = \frac{r^9}{v^6},\; A = \frac{v^3}{r^6}</math> Quantities ''r'' and ''v'' are chosen so that no unit (''kg'', ''m'', ''s'', ''A'') can cancel another unit (i.e.: the ''kg'' cannot cancel the ''m'' or the ''s'' ...), and so we have 4 independent units (we still cannot define the ''kg'' using the ''m'' or the ''s'' ...), however if 3 (or more) units are combined together in a specific ratio, they can cancel (in a certain ratio our ''r'' and ''v'' become inverse properties and so cancel each other; units = 1). <math>f_X = \frac{kg^9 s^{11}}{m^{15}} = \frac{(\frac{r^4}{v})^9 (\frac{r^9}{v^6})^{11}}{(\frac{r^9}{v^5})^{15}} = 1</math> This f_X, although embedded within are the dimensioned structures for mass, time and length (in the above ratio), would be a dimensionless mathematical structure, units = 1. Thus we may create as much mass, time and length as we wish, the only proviso being that they are created in f_X ratios, so that regardless of how massive, old and large our universe becomes, it is still in sum total dimensionless. Defining the dimensioned quantities ''r'', ''v'' in SI unit terms. :<math>r = (\frac{kg\;m}{s})^{1/4}</math> :<math>v = \frac{m}{s}</math> Mass :<math>\frac{r^4}{v} = (\frac{kg\;m}{s})\;(\frac{s}{m}) = kg</math> Length :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^5})^4 = \frac{s^{20}}{m^{20}}</math> :<math>(\frac{r^9}{v^5})^4 = \frac{kg^9 s^{11}}{m^{11}} = m^4 \frac{kg^9 s^{11}}{m^{15}} = m^4 f_X = m^4</math> Time :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^6})^4 = \frac{s^{24}}{m^{24}}</math> :<math>(\frac{r^9}{v^6})^4 = \frac{kg^9 s^{15}}{m^{15}} = s^4 \frac{kg^9 s^{11}}{m^{15}} = s^4 f_X = s^4</math> And so, although f_X is a dimensionless mathematical structure, we can embed within it the (mass, length, time ...) structures along with their dimensional attributes (kg, m, s, A ..). In the mathematical electron model (discussed below), the electron itself is an example of an f_X structure, it (f_electron) is a dimensionless geometrical object that embeds the physical electron parameters of wavelength, frequency, charge (note: A-m = ampere-meter are the units for a [[w:Magnetic_monopole#In_SI_units |magnetic monopole]]). <math>f_{electron}</math> :<math>units = \frac{A^3 m^3}{s} = \frac{(\frac{v^3}{r^6})^3 (\frac{r^9}{v^5})^3}{(\frac{r^9}{v^6})} = 1</math> We may note that at the macro-level (of planets and stars) these f_X ratio are not found, and so this level is the domain of the observed physical universe, however at the quantum level, f_X ratio do appear, f_electron as an example, the mathematical and physical domains then blurring. This would also explain why physics can measure precisely the parameters of the electron (wavelength, mass ...), but has never found the electron itself. == Programming == “God vs. science debates tend to be restricted to the premise that a God does not rely on science and that science does not need a God. As science and God are thus seen as mutually exclusive there are few, if any, serious attempts to construct mathematical models of a universe whose principle axiom does require a God. However, if there is an Intelligence responsible for the 14 billion year old universe of modern physics, being the universe of Einstein and Dirac, and beginning with the big bang as the act of 'creation', then we must ask how it might be done? What construction technique could have been used to set the laws of physics in motion?” <ref>[https://theprogrammergod.com/ The Programmer God, are we in a Simulation]</ref> === Simulation Time === The (dimensionless) simulation clock-rate would be defined as the minimum 'time variable' ('''age''') increment to the simulation. Using a simple loop as analogy, at ''age'' = 1, the simulation begins (the big bang), certain processes occur, when these are completed ''age'' increments (''age'' = 2, then 3, then 4 ... ) until ''age'' reaches ''the_end'' and the simulation stops. 'begin simulation FOR age = 1 TO the_end 'big bang = 1 conduct certain processes ........ NEXT age 'end simulation [[w:Quantum spacetime |Quantum spacetime]] and [[w:Quantum gravity |Quantum gravity]] models refer to [[w:Planck time | Planck time]] as the smallest discrete unit of time and so the incrementing variable '''age''' could be used to generate units of Planck time (and other Planck units, the physical scaffolding of the universe). In a geometrical model, to these Planck units could be assigned geometrical objects, for example; Initialize_physical_constants; FOR age = 1 TO the_end generate 1 unit of (Planck) time; '1 time 'object' T generate 1 unit of (Planck) mass; '1 mass 'object' M generate 1 unit of (Planck) length; '1 length 'object' L ........ NEXT age The variable ''age'' is the simulation clock-rate, it is simply a counter (1, 2, 3 ...) and so is a dimensionless number, the object T is the geometrical Planck time object, it is dimensioned and is measured by us in seconds. If ''age'' is the origin of Planck time (1 increment to ''age'' generates 1 T object) then ''age'' = 10⁶², this is based on the present [[w:Age_of_the_universe |age of the universe]], which, at 14 billion years, equates to 10⁶² units of Planck time. For each ''age'', certain operations are performed, only after they are finished does ''age'' increment (there is no ''time'' interval between increments). As noted, ''age'' being dimensionless, is not the same as dimensioned Planck time which is the geometrical object T, and this T, being dimensioned, can only appear within the simulation. The analogy would be frames of a movie, each frame contains dimensioned information but there is no ''time'' interval between frames. FOR age = 1 TO the_end (of the movie) display frame{age} NEXT age Although operations (between increments to ''age'') may be extensive, self-aware structures from within the simulation would have no means to determine this, they could only perceive themselves as being in a real-time (for them the smallest unit of ''time'' is 1T, just as the smallest unit of ''time'' in a movie is 1 frame). Their (those self-aware structures) dimension of time would then be a measure of relative motion (a change of state), and so although ultimately deriving from the variable ''age'', their time would not be the same as ''age''. If there was no motion, if all particles and photons were still (no change of state), then their time dimension could not update (if every frame in a movie was the same then actors within that movie could not register a change in time), ''age'' however would continue to increment. Thus we have 3 time structures; 1) the dimension-less simulation clock-rate variable ''age'', 2) the dimensioned time unit (object T), and 3) time as change of state (the observers time). Observer time requires a memory of past events against which a change of state can be perceived. The forward increment to ''age'' would constitute the [[w:arrow of time |arrow of time]]. Reversing this would reverse the arrow of time, the universe would likewise shrink in size and mass accordingly (just as a [[w:white hole |white hole]] is the (time) reversal of a [[w:black hole |black hole]]). FOR age = the_end TO 1 STEP -1 delete 1 unit of Planck time; delete 1 unit of Planck mass; delete 1 unit of Planck length; ........ NEXT age Adding mass, length and time objects per increment to ''age'' would force the universe expansion (in size and mass), and as such an anti-gravitational [[w:dark energy |dark energy]] would not be required, however these objects are dimensioned and so are generated within the simulation. This means that they must somehow combine in a specific ratio whereby they (the units for mass length, time, charge; ''kg'', ''m'', ''s'', ''A'') in sum total cancel each other, leaving the sum universe (the simulation itself) residing on that celestial hard-disk. We may introduce a theoretical dimensionless (f_X) geometrical object denoted as f_Planck within which are embedded the dimensioned objects MLTA (mass, length, time, charge), and from which they may be extracted. FOR age = 1 TO the_end add 1 f_Planck 'dimensionless geometrical 'object' { extract 1 unit of (Planck) time; '1 time 'object' T extract 1 unit of (Planck) mass; '1 mass 'object' M extract 1 unit of (Planck) length; '1 length 'object' L } ........ NEXT age This then means that the simulation, in order to create time T, must also create mass M and space L (become larger and more massive). Thus no matter how small or large the physical universe is (when seen internally), in sum total (when seen externally), there is no universe - it is merely data without physical form. === Universe time-line === As the universe expands outwards (through the constant addition of units of mass and length via f_Planck), and if this expansion pulls particles with it (if it is the origin of motion), then ''now'' (the present) would reside on the surface of the (constantly expanding at the speed of light; ''c'' = 1 Planck length / 1 Planck time) universe, and so the 'past' could be retained, for the past cannot be over-written by the present in an expanding universe (if ''now'' is always on the surface). As this expansion occurs at the Planck scale, information even below quantum states, down to the Planck scale, can be retained, the analogy would be the storing of every [[w:Keystroke_logging |keystroke]], a Planck scale version of the [[w:Akashic records |Akashic records]] ... for if our deeds (the past) are both stored and cannot be over-written (by the present), then we have a candidate for the '[[w:karma |karmic]] heavens' (Matthew 6:19 ''But lay up for yourselves treasures in 'heaven', where neither moth nor rust doth corrupt, and where thieves do not break through nor steal''). This also forms a universe '''time-line''' against which previous information can be compared with new information (a 'memory' of events), without which we could not link cause with effect. === Singularity === In a simulation, the data (software) requires a storage device that is ultimately hardware (RAM, HD ...). In a data world of 1's and 0's such as a computer game, characters within that game may analyze other parts of their 1's and 0's game, but they have no means to analyze the hard disk upon which they (and their game) are stored, for the hard disk is an electro-mechanical device, it is not part of their 1's and 0's world, it is a part of the 'real world', the world of their Programmer. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may or may not resemble the laws that operate in the 'real world' (the world of their Programmer). Thus any region where the laws of physics (the laws of their game world) break down would be significant. A [[w:singularity |singularity]] inside a black hole is such a region <ref>https://www.youtube.com/watch?v=W5j7umtZYB4 a black hole singularity as the interface between worlds</ref>. For the [[w:black hole electron |black-hole electron]], its black-hole center would then be analogous to a storage address on a hard disk, the interface between the simulation world and the real world. A massive (galactic) black-hole could be as an entire data sector. The surface of the black-hole would then be of the simulation world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however would be the interface between the data world and the 'hard disk' of the real world, and so would not exist in any 'physical' terms. It is external to the simulation. As analogy, we may discuss the 3-D surface area of a black-hole but not its volume (interior). === Laws of Physics === The scientific method is built upon testable hypothesis and reproducible results. Water always boils (in defined conditions), at 100°C. In a geometrical universe particles will behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these repeating patterns, the more complex the orbits, the more complex the formulas required to describe them and so forth. However if there is a source code from which these geometrical conditions were programmed, then there may also be non-repeating events, back-doors built into the code (a common practice by terrestrial programmers), these by definition would lie outside the laws of physics and so be labelled as miracles, yet they would be no less valid. === Determinism === [[File:Three body problem figure-8 orbit animation.gif|400px|thumb|An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259.<ref>Here the gravitational constant ''G'' has been set to 1, and the initial conditions are '''r'''₁(0) = −'''r'''₃(0) = (−0.97000436, 0.24308753); '''r'''₂(0) = (0,0); '''v'''₁(0) = '''v'''₃(0) = (0.4662036850, 0.4323657300); '''v'''₂(0) = (−0.93240737, −0.86473146). The values are obtained from Chenciner & Montgomery (2000).</ref>]] Particles form more complex structures such as atoms and molecules via a system of orbitals; nuclear, atomic and gravitational. The [[w:Three-body_problem |3-body problem]] is the problem of taking the initial positions and velocities (or [[w:momentum|momenta |momentum|momenta]]) of three or more point masses and solving for their subsequent motion according to [[w:Newton's laws of motion |Newton's laws of motion]] and [[w:Newton's law of universal gravitation |Newton's law of universal gravitation]].<ref name="PrincetonCompanion">{{Citation | last = Barrow-Green | first = June | year = 2008 | title = The Three-Body Problem | editor-last1 = Gowers | editor-first1 = Timothy | editor-last2 = Barrow-Green | editor-first2 = June | editor-last3 = Leader | editor-first3 = Imre | encyclopedia = The Princeton Companion to Mathematics | pages = 726–728 | publisher = Princeton University Press }}</ref>. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for gods and men alike the only way to know what that outcome will be is to run the simulation itself. ==Geometry coded universe== Modelling a Planck scale simulation universe using geometrical forms (links) * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass == External links == * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] * [https://philpapers.org/rec/GRUTIA-2 Simulation theory as evidence for God] (academic peer-reviewed article) ==References== {{Reflist}} [[Category:Philosophy| ]] [[Category:Philosophy of science| ]] c9ytjzkeckyzkvys8m8dz3qzl3cph83 2718259 2718258 2025-06-10T19:51:55Z 212.200.164.104 /* Programming */ 2718259 wikitext text/x-wiki '''Is God a Programmer? analyzing the deep-universe simulation hypothesis at the Planck scale''' The [[w:simulation hypothesis |simulation hypothesis]] is the proposal that all of reality, including the Earth and the rest of the universe, could be an artificial simulation, such as a computer simulation. [[w:Neil_deGrasse_Tyson |Neil deGrasse Tyson]] put the odds at 50-50 that our entire existence is a program on someone else’s hard drive <ref>Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. [[w:David_Chalmers |David Chalmers]] noted “We in this universe can create simulated worlds and there’s nothing remotely spooky about that. Our creator isn’t especially spooky, it’s just some teenage hacker in the next universe up. Turn the tables, and we are essentially gods over our own computer creations <ref>https://www.youtube.com/watch?v=yqbS5qJU8PA, David Chalmers, Serious Science</ref> <ref>The Matrix as Metaphysics, David Chalmers http://consc.net/papers/matrix.pdf</ref> <ref>Are We Living in a Computer Simulation?https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. The commonly postulated [[w:Ancestor_simulation |ancestor simulation]] approach, which [[w:Nick Bostrom |Nick Bostrom]] called "the simulation argument", argues for "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor. However this simulation variant can be traced back to an 'organic base reality' (the original programmer ancestors and their physical planet). The [[v:God_(programmer) |Programmer God]] hypothesis<ref>https://codingthecosmos.com/podcast/ AI generated podcasts</ref> conversely states that a (deep universe) simulation began with the big bang and was programmed by an external intelligence (external to the physical universe), the Programmer by definition a God in the creator of the universe context. Our universe in its entirety, down to the smallest detail, and including life-forms, is within the simulation, the laws of nature, at their most fundamental level, are coded rules running on top of the simulation operating system. The operating system itself is mathematical (and potentially the origin of mathematics). Any candidate for a Programmer-God simulation-universe source code must satisfy these conditions; :1. It can generate physical structures from mathematical forms. :2. The sum universe is dimensionless (simply data on a celestial hard disk). :3. We must be able to use it to derive the laws of physics (because the source code is the origin of the laws of nature, and the laws of physics are our observations of the laws of nature). :4. The mathematical logic must be unknown to us (the Programmer is a non-human intelligence). :5. The coding should have an 'elegance' commensurate with the Programmer's level of skill. == Philosophy == Physicist [[w:Eugene Wigner |Eugene Wigner]] ([[w:The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences |The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]) <ref>{{Cite journal | last1 = Wigner | first1 = E. P. | authorlink = Eugene Wigner| doi = 10.1002/cpa.3160130102 | title = The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959 | journal = Communications on Pure and Applied Mathematics | volume = 13 | pages = 1–14 | year = 1960 | pmid = | pmc = |bibcode = 1960CPAM...13....1W }}</ref> <blockquote>The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. </blockquote> === Discussion === [[w:Philosophy of mathematics |Philosophy of mathematics]] is that branch of philosophy which attempts to answer questions such as: ‘why is mathematics useful in describing nature?’, ‘in which sense, if any, do mathematical entities such as numbers exist?’ and ‘why and how are mathematical statements true?’ This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math. Mathematical realism holds that mathematical entities exist independently of the human mind. We do not invent mathematics, but rather discover it. Triangles, for example, are real entities that have an existence <ref>- http://plato.stanford.edu/entries/platonism-mathematics/</ref>. The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality. It can be considered a form of [[w:Pythagoreanism | Pythagoreanism]] or [[w:Platonism | Platonism]] in that it proposes the existence of ''mathematical objects''; and a form of [[w:philosophy of mathematics | mathematical monism]] in that it denies that anything exists except these ''mathematical objects''. Physicist [[w:Max Tegmark | Max Tegmark]] in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality"<ref name="Tegmark1998">{{cite journal|last=Tegmark |first=Max |date=November 1998 |title=Is "the Theory of Everything" Merely the Ultimate Ensemble Theory? |journal=Annals of Physics |volume=270 |issue=1 |pages=1–51 |doi=10.1006/aphy.1998.5855 |arxiv = gr-qc/9704009 |bibcode = 1998AnPhy.270....1T }}</ref><ref>M. Tegmark 2014, "[http://mathematicaluniverse.org Our Mathematical Universe]", Knopf</ref> proposed that ''Our external physical reality is a mathematical structure''.<ref name="Tegmark2008">{{cite journal|last=Tegmark |first=Max |date=February 2008 |title=The Mathematical Universe |journal=Foundations of Physics |volume=38 |issue=2 |pages=101–150 |doi=10.1007/s10701-007-9186-9 |arxiv=0704.0646|bibcode = 2008FoPh...38..101T }}</ref> That is, the physical universe is not merely ''described by'' mathematics, but ''is'' mathematics (specifically, a [[w:mathematical structure | mathematical structure]]). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref> The principle constraints to any mathematical universe simulation hypothesis are; 1. the computational resources required. The ancestor simulation can resolve this by adapting from the [[w:virtual rality |virtual reality]] approach where only the observable region is simulated and only to the degree required, and 2. that any 'self-aware structures' (humans for example) within the simulation must "subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref>. Succinctly, our computer games may be able to simulate our physical world, but they are still only simulations of a physical reality (regardless of how realistic they may seem) ... we are not yet able to program actual physical dimensions of mass, space and time from mathematical structures, and indeed this may not be possible with a computer hard-ware architecture that can only process binary data. === Deep-universe source code === As a deep-universe simulation is programmed by an external (external to the universe) intelligence (the Programmer God hypothesis), we cannot presume a priori knowledge regarding the simulation source code other than from this code the laws of nature emerged, and so any deep-universe simulation model we try to emulate must be universal, i.e.: independent of any system of units, of the [[w:Dimensional_analysis |dimensioned]] [[w:physical constants |physical constants]] (''G'', ''h'', ''c'', ''e'' .. ), and of any numbering systems. Furthermore, although a deep-universe simulation source code may use mathematical forms (circles, spheres ...) we are familiar with (for ultimately the source code is the origin of these forms), it will have been developed by a non-human intelligence and so we may have to develop new mathematical tools to decipher the underlying logic. By implication therefore, any theoretical basis for a source code that fits the above criteria (and from which the laws of nature will emerge), could be construed as our first tangible evidence of a non-human intelligence. === Constants === A physical universe is characterized by measurable quantities (size, mass, color, texture ...), and so a physical universe can be measured and defined. Contrast then becomes information, the statement ''this is a big apple'' requires a ''small apple'' against which big becomes a relative term. For analytical purposes we select a reference value, for example 0C or 32F, and measure all temperatures against this reference. The smaller the resolution of the measurements, the greater the information content (the file size of a 32 mega-pixel photo is larger than a 4 mega-pixel photo). A simulation universe may be presumed to also have a resolution dictating how much information the simulation can store and manipulate. To measure the fundamental parameters of our universe physics uses [[w:physical constant |physical constants]]. A physical constant is a [[w:physical quantity |physical quantity]] that is generally believed to be both universal in nature and have a constant value in time. These can be divided into 1) dimension-ed (measured using physical units ''kg'', ''m'', ''s'', ''A'' ...) such as the [[w:speed of light |speed of light]] ''c'', [[w:gravitational constant |gravitational constant]] ''G'', [[w:Planck constant |Planck constant]] ''h'' ... as in the table {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} Physicist [[w: |Lev Okun]] noted "Theoretical equations describing the physical world deal with dimensionless quantities and their solutions depend on dimensionless fundamental parameters. But experiments, from which these theories are extracted and by which they could be tested, involve measurements, i.e. comparisons with standard dimension-ful scales. Without standard dimension-ful units and hence without certain conventions physics is unthinkable <ref>Michael J. Duff et al, Journal of High Energy Physics, Volume 2002, JHEP03(2002)</ref>. 2) dimension-less, such as the [[w:Fine-structure_constant |fine structure constant]] ''α''. A dimension-less constant does not measure any physical quantity (it has no units; units = 1). 3) dimension-less [[w:mathematical constant |mathematical constants]], most notably [[w:pi |pi]] = 3.14159265358979 and [[w:Natural_logarithm |e]] = 2.718281828459. Although these are [[w:transcendental number |transcendental numbers]], they can be constructed by integers in a series, and so for a universe expanding incrementally (see simulation time), these constants could be formed within the simulation. For example, at time ''t''; <math display=block>t = 1; \frac{\pi^2}{6} = \frac{1}{t^2} </math> <math display=block>t = 2; \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{t^2}</math> <math display=block>t = now: \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots + \frac{1}{t^2} </math> We may now define the fundamental physical constant as a parameter specifically chosen by the Programmer and is encoded into the simulation code directly, and so whilst it may be inferable, it is not derived from other constants ([[w:Fine-structure_constant#Numerological_explanations_and_multiverse_theory |Richard Feynman on the fine structure constant]]). It should also be dimension-less otherwise the simulation itself becomes dimensioned (if the simulation is running on a celestial computer it is merely data, it has no physical size or shape or ...), and so the dimensioned constants (''G'', ''h'', ''c'', ''e''...) must all be derivable (derived from within the simulation) via the (embedded in the source code) fundamental physical constants (of which the fine structure constant alpha may be an example). Although [[w:pi |pi]] and [[w:Natural_logarithm |e]] are dimensionless, they can be derived internally (from integers), and as they have application in the mathematical realm, they can be referred to as mathematical constants. ==== Planck scale ==== The [[w:Planck scale |Planck scale]] refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the [[w:Standard Model |Standard Model]], [[w:quantum field theory |quantum field theory]] and [[w:general relativity |general relativity]] are no longer reconcilable, and [[w:Quantum Gravity |quantum effects of gravity]] are expected to dominate (quantum gravitational effects only appear at length scales near the Planck scale). Although particles may not be cognizance of our 'laws of physics', they do know the 'laws of nature'. These laws of nature would run directly off the universe OS (operating system), and so below this OS, 'physics' as we know it must necessarily break down. At present the Planck scale is the lowest known level, consequently any attempt to detect evidence of an underlying simulation coding must consider (if not actually begin at) this, the Planck scale<ref>https://www.youtube.com/watch?v=AMQRXGYCDrY Planck scale, Brian Greene</ref>. The [[w:International_System_of_Units |SI units]] for the dimension-ful mksa units are; meter (length), kilogram (mass), second (time), ampere (electric current). There are Planck units that represent these SI units, and so a simulation could use them as discrete building blocks; [[w:Planck length |Planck length]] (the smallest possible unit of length), [[w:Planck mass |Planck mass]] (the unit of mass), [[w:Planck time |Planck time]] (the smallest possible unit of time), [[w:Planck charge |Planck charge]] (the unit of charge). The speed of light then becomes ''c'' = 1 Planck length / 1 Planck time. These units would define the resolution and so information carrying capacity of the simulation universe. ==== Numbering systems ==== As well as our decimal system, computers apply binary and hexadecimal numbering systems. In particular the decimal and hexadecimal are of terrestrial origin and may not be considered 'universal'. Furthermore numbering systems measure only the frequency of an event and contain no information as to the event itself. The number 299 792 458 could refer to the speed of light (299 792 458 m/s) or could equally be referring to the number of apples in a container (299 792 458 apples). As such, numbers require a 'descriptive', whether m/s or apples. Numbers also do not include their history, is 299 792 458 for example a derivation of other base numbers? Present universe simulations use the laws of physics and the physical constants are built in, however both these laws and the physical constants are known only to a limited precision, and so a simulation with 10⁶² iterations (the present age of the universe in units of Planck time) will accumulate errors. Number based computing may be sufficient for ancestor-simulation models where only the observed region needs to be calculated, but has inherent limitations for deep universe simulations where the entire universe is continuously updated. The actual computational requirements for a Planck scale universe simulation based on a numbering system with the laws of physics embedded would be an unknown and consequently lead to an 'non-testable' hypothesis. This is a commonly applied reasoning for rejecting the deep universe simulation. ==== Geometrical objects ==== A mathematical constant such as [[w:pi |pi]] refers to a geometrical construct (the ratio of circle circumference to circle radius) and so is not constrained by any particular numbering system (in the decimal system π = 3.14159...), and so may be considered both universal and eternal. Likewise, by assigning geometrical objects instead of numbers to the Planck units, the problems with a numbering system can be resolved. These objects would however have to fulfill the following conditions; 1) embedded attribute - for example the object for length must embed the function of ''length'' such that a descriptive (km, mile ... ) is not required. Electron wavelength would then be measurable in terms of the length object, as such the length object must be embedded within the electron (the electron object). Although the mass object would incorporate the function ''mass'', the time object the function ''time'' ..., it is not necessary that there be an individual physical mass or physical length or physical time ..., but only that in relation to the other units, the object must express that function (i.e.: the mass object has the function of mass when in the presence of the objects for space and time). The electron could then be a complex event (complex geometrical object) constructed by combining the objects for mass, length, time and charge into 1 event, and thus electron charge, wavelength, frequency and mass would then be different aspects of that 1 geometry (the electron event) and not independent parameters (independent of each other). 2) The objects for mass, length, time and charge must be able to combine with each other [[w:Lego |Lego-style]] to form more complex objects (events) such as electrons and apples whilst still retaining the underlying information (the mass of the apple derives from the mass objects embedded within that apple). Not only must these objects be able to form complex events such as particles, but these events themselves are geometrical objects and so must likewise function according to their geometries. Electrons would orbit protons according to their respective electron and proton geometries, these orbits the result of geometrical imperatives and not due to any built-in laws of physics (the orbital path is a consequence of all the underlying geometries). However, as orbits follow regular and repeating patterns, they can be described (by us) using mathematical formulas. As the events grow in complexity (from atoms to molecules to planets), so too will the patterns (and likewise the formulas we use to describe them). Consequently the ''laws of physics'' would then become our mathematical descriptions of the underlying geometrically imposed patterns. 3) These objects would replace coded instructions (the instruction sets would be built into the objects) thereby instigating a geometrically autonomous universe. The electron 'knows' what to do by virtue of the information encoded within its geometry, no coded electron CALL FUNCTION is required. This would be equivalent to combining the hardware, software and CPU together such that the 'software' changes (adjusts) to the changing 'hardware' (DNA may be an analogy). Note: A purely mathematical universe has no limits in size and can be infinitely large and infinity small. A geometrical universe (that uses objects) has limitations, it can be no smaller than the smallest object for example and has discrete parts (those objects). The philosophy of the TOE (theory of everything) therefore includes a debate between the mathematical universe and the geometrical universe, however this distinction between mathematical and geometrical would only be apparent at the Planck scale. === Evidence of a simulation === The laws of physics are our incomplete observations of the natural universe, and so evidence of a simulation may be found in ambiguities or anomalies within these laws. Furthermore, if complexity arises over time, then at unit time the 'handiwork' of the Programmer may be notable by a simplicity and elegance of the geometries employed ... for the Programmer by definition has God-level programming skills. Here is a notable example. Mass, space and time from the number 1 The dimensions of mass, space and time are considered by science to be independent of each other, we cannot measure the ''distance'' from Tokyo to London using kilograms and amperes, or measure ''mass'' using space and time. Indeed, what characterizes a physical universe as opposed to a simulated universe is the notion that there is a fundamental structure underneath, that in some sense mass 'is', that time 'is' and space 'is' ... thus we cannot write ''kg'' in terms of ''m'' and ''s''. To do so would render our concepts of a physical universe meaningless. The 26th General Conference on Weights and Measures ([[w:2019 redefinition of SI base units|2019 redefinition of SI base units]]) assigned exact numerical values to 4 physical constants (''h, c, e, k''_B) independently of each other (and thereby confirming these as fundamental constants), and as they are measured in SI units ('''kg''', '''m''', '''s''', '''A''', '''K'''), these units must also be independent of each other (i.e.: these are fundamental units, for example if we could define ''m'' using ''A'' then the speed of light could be derived from, and so would depend upon, the value for the elementary charge ''e'', and so the value for ''c'' could not be assigned independently from ''e''). {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} We are familiar with inverse properties; plus charge and minus charge, matter and anti-matter ... and we can observe how these may form and/or cancel each other. A simulation universe however is required to be dimensionless (in sum total), for the simulated universe does not 'exist' in any physical sense outside of the 'Computer' (it is simply data on a celestial hard-disk). Our universe does not appear to have inverse properties such as anti-mass (-kg), anti-time (-s) or anti-space (anti-length -m), therefore the first problem the Programmer must solve is how to create the physical scaffolding (of mass, space and time). For example, the Programmer can start by selecting 2 dimensioned quantities, here are used ''r'', ''v'' <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref> such that :<math>kg = \frac{r^4}{v},\; m = \frac{r^9}{v^5},\; s = \frac{r^9}{v^6},\; A = \frac{v^3}{r^6}</math> Quantities ''r'' and ''v'' are chosen so that no unit (''kg'', ''m'', ''s'', ''A'') can cancel another unit (i.e.: the ''kg'' cannot cancel the ''m'' or the ''s'' ...), and so we have 4 independent units (we still cannot define the ''kg'' using the ''m'' or the ''s'' ...), however if 3 (or more) units are combined together in a specific ratio, they can cancel (in a certain ratio our ''r'' and ''v'' become inverse properties and so cancel each other; units = 1). <math>f_X = \frac{kg^9 s^{11}}{m^{15}} = \frac{(\frac{r^4}{v})^9 (\frac{r^9}{v^6})^{11}}{(\frac{r^9}{v^5})^{15}} = 1</math> This f_X, although embedded within are the dimensioned structures for mass, time and length (in the above ratio), would be a dimensionless mathematical structure, units = 1. Thus we may create as much mass, time and length as we wish, the only proviso being that they are created in f_X ratios, so that regardless of how massive, old and large our universe becomes, it is still in sum total dimensionless. Defining the dimensioned quantities ''r'', ''v'' in SI unit terms. :<math>r = (\frac{kg\;m}{s})^{1/4}</math> :<math>v = \frac{m}{s}</math> Mass :<math>\frac{r^4}{v} = (\frac{kg\;m}{s})\;(\frac{s}{m}) = kg</math> Length :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^5})^4 = \frac{s^{20}}{m^{20}}</math> :<math>(\frac{r^9}{v^5})^4 = \frac{kg^9 s^{11}}{m^{11}} = m^4 \frac{kg^9 s^{11}}{m^{15}} = m^4 f_X = m^4</math> Time :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^6})^4 = \frac{s^{24}}{m^{24}}</math> :<math>(\frac{r^9}{v^6})^4 = \frac{kg^9 s^{15}}{m^{15}} = s^4 \frac{kg^9 s^{11}}{m^{15}} = s^4 f_X = s^4</math> And so, although f_X is a dimensionless mathematical structure, we can embed within it the (mass, length, time ...) structures along with their dimensional attributes (kg, m, s, A ..). In the mathematical electron model (discussed below), the electron itself is an example of an f_X structure, it (f_electron) is a dimensionless geometrical object that embeds the physical electron parameters of wavelength, frequency, charge (note: A-m = ampere-meter are the units for a [[w:Magnetic_monopole#In_SI_units |magnetic monopole]]). <math>f_{electron}</math> :<math>units = \frac{A^3 m^3}{s} = \frac{(\frac{v^3}{r^6})^3 (\frac{r^9}{v^5})^3}{(\frac{r^9}{v^6})} = 1</math> We may note that at the macro-level (of planets and stars) these f_X ratio are not found, and so this level is the domain of the observed physical universe, however at the quantum level, f_X ratio do appear, f_electron as an example, the mathematical and physical domains then blurring. This would also explain why physics can measure precisely the parameters of the electron (wavelength, mass ...), but has never found the electron itself. == Programming == “God vs. science debates tend to be restricted to the premise that a God does not rely on science and that science does not need a God. As science and God are thus seen as mutually exclusive there are few, if any, serious attempts to construct mathematical models of a universe whose principle axiom does require a God. However, if there is an Intelligence responsible for the 14 billion year old universe of modern physics, being the universe of Einstein and Dirac, and beginning with the big bang as the act of 'creation', then we must ask how it might be done? What construction technique could have been used to set the laws of physics in motion?” <ref>[https://theprogrammergod.com/ The Programmer God, are we in a Simulation]</ref> === Simulation Time === The (dimensionless) simulation clock-rate would be defined as the minimum 'time variable' ('''age''') increment to the simulation. Using a simple loop as analogy, at ''age'' = 1, the simulation begins (the big bang), certain processes occur, when these are completed ''age'' increments (''age'' = 2, then 3, then 4 ... ) until ''age'' reaches ''the_end'' and the simulation stops. 'begin simulation FOR age = 1 TO the_end 'big bang = 1 conduct certain processes ........ NEXT age 'end simulation [[w:Quantum spacetime |Quantum spacetime]] and [[w:Quantum gravity |Quantum gravity]] models refer to [[w:Planck time | Planck time]] as the smallest discrete unit of time and so the incrementing variable '''age''' could be used to generate units of Planck time (and other Planck units, the physical scaffolding of the universe). In a geometrical model, to these Planck units could be assigned geometrical objects, for example; Initialize_physical_constants; FOR age = 1 TO the_end generate 1 unit of (Planck) time; '1 time 'object' T generate 1 unit of (Planck) mass; '1 mass 'object' M generate 1 unit of (Planck) length; '1 length 'object' L ........ NEXT age The variable ''age'' is the simulation clock-rate, it is simply a counter (1, 2, 3 ...) and so is a dimensionless number, the object T is the geometrical Planck time object, it is dimensioned and is measured by us in seconds. If ''age'' is the origin of Planck time (1 increment to ''age'' generates 1 T object) then ''age'' = 10⁶², this is based on the present [[w:Age_of_the_universe |age of the universe]], which, at 14 billion years, equates to 10⁶² units of Planck time. For each ''age'', certain operations are performed, only after they are finished does ''age'' increment (there is no ''time'' interval between increments). As noted, ''age'' being dimensionless, is not the same as dimensioned Planck time which is the geometrical object T, and this T, being dimensioned, can only appear within the simulation. The analogy would be frames of a movie, each frame contains dimensioned information but there is no ''time'' interval between frames. FOR age = 1 TO the_end (of the movie) display frame{age} NEXT age Although operations (between increments to ''age'') may be extensive, self-aware structures from within the simulation would have no means to determine this, they could only perceive themselves as being in a real-time (for them the smallest unit of ''time'' is 1T, just as the smallest unit of ''time'' in a movie is 1 frame). Their (those self-aware structures) dimension of time would then be a measure of relative motion (a change of state), and so although ultimately deriving from the variable ''age'', their time would not be the same as ''age''. If there was no motion, if all particles and photons were still (no change of state), then their time dimension could not update (if every frame in a movie was the same then actors within that movie could not register a change in time), ''age'' however would continue to increment. Thus we have 3 time structures; 1) the dimension-less simulation clock-rate variable ''age'', 2) the dimensioned time unit (object T), and 3) time as change of state (the observers time). Observer time requires a memory of past events against which a change of state can be perceived. The forward increment to ''age'' would constitute the [[w:arrow of time |arrow of time]]. Reversing this would reverse the arrow of time, the universe would likewise shrink in size and mass accordingly (just as a [[w:white hole |white hole]] is the (time) reversal of a [[w:black hole |black hole]]). FOR age = the_end TO 1 STEP -1 delete 1 unit of Planck time; delete 1 unit of Planck mass; delete 1 unit of Planck length; ........ NEXT age Adding mass, length and time objects per increment to ''age'' would force the universe expansion (in size and mass), and as such an anti-gravitational [[w:dark energy |dark energy]] would not be required, however these objects are dimensioned and so are generated within the simulation. This means that they must somehow combine in a specific ratio whereby they (the units for mass length, time, charge; ''kg'', ''m'', ''s'', ''A'') in sum total cancel each other, leaving the sum universe (the simulation itself) residing on that celestial hard-disk. We may introduce a theoretical dimensionless (f_X) geometrical object denoted as f_Planck within which are embedded the dimensioned objects MLTA (mass, length, time, charge), and from which they may be extracted. FOR age = 1 TO the_end add 1 f_Planck 'dimensionless geometrical 'object' { extract 1 unit of (Planck) time; '1 time 'object' T extract 1 unit of (Planck) mass; '1 mass 'object' M extract 1 unit of (Planck) length; '1 length 'object' L } ........ NEXT age This then means that the simulation, in order to create time T, must also create mass M and space L (become larger and more massive). Thus no matter how small or large the physical universe is (when seen internally), in sum total (when seen externally), there is no universe - it is merely data without physical form. === Universe time-line === As the universe expands outwards (through the constant addition of units of mass and length via f_Planck), and if this expansion pulls particles with it (if it is the origin of motion), then ''now'' (the present) would reside on the surface of the (constantly expanding at the speed of light; ''c'' = 1 Planck length / 1 Planck time) universe, and so the 'past' could be retained, for the past cannot be over-written by the present in an expanding universe (if ''now'' is always on the surface). As this expansion occurs at the Planck scale, information even below quantum states, down to the Planck scale, can be retained, the analogy would be the storing of every [[w:Keystroke_logging |keystroke]], a Planck scale version of the [[w:Akashic records |Akashic records]] ... for if our deeds (the past) are both stored and cannot be over-written (by the present), then we have a candidate for the '[[w:karma |karmic]] heavens' (Matthew 6:19 ''But lay up for yourselves treasures in 'heaven', where neither moth nor rust doth corrupt, and where thieves do not break through nor steal''). This also forms a universe '''time-line''' against which previous information can be compared with new information (a 'memory' of events), without which we could not link cause with effect. === Singularity === In a simulation, the data (software) requires a storage device that is ultimately hardware (RAM, HD ...). In a data world of 1's and 0's such as a computer game, characters within that game may analyze other parts of their 1's and 0's game, but they have no means to analyze the hard disk upon which they (and their game) are stored, for the hard disk is an electro-mechanical device, it is not part of their 1's and 0's world, it is a part of the 'real world', the world of their Programmer. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may or may not resemble the laws that operate in the 'real world' (the world of their Programmer). Thus any region where the laws of physics (the laws of their game world) break down would be significant. A [[w:singularity |singularity]] inside a black hole is such a region <ref>https://www.youtube.com/watch?v=W5j7umtZYB4 a black hole singularity as the interface between worlds</ref>. For the [[w:black hole electron |black-hole electron]], its black-hole center would then be analogous to a storage address on a hard disk, the interface between the simulation world and the real world. A massive (galactic) black-hole could be as an entire data sector. The surface of the black-hole would then be of the simulation world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however would be the interface between the data world and the 'hard disk' of the real world, and so would not exist in any 'physical' terms. It is external to the simulation. As analogy, we may discuss the 3-D surface area of a black-hole but not its volume (interior). === Laws of Physics === The scientific method is built upon testable hypothesis and reproducible results. Water always boils (in defined conditions), at 100°C. In a geometrical universe particles will behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these repeating patterns, the more complex the orbits, the more complex the formulas required to describe them and so forth. However if there is a source code from which these geometrical conditions were programmed, then there may also be non-repeating events, back-doors built into the code (a common practice by terrestrial programmers), these by definition would lie outside the laws of physics and so be labelled as miracles, yet they would be no less valid. === Determinism === [[File:Three body problem figure-8 orbit animation.gif|400px|thumb|An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259.<ref>Here the gravitational constant ''G'' has been set to 1, and the initial conditions are '''r'''₁(0) = −'''r'''₃(0) = (−0.97000436, 0.24308753); '''r'''₂(0) = (0,0); '''v'''₁(0) = '''v'''₃(0) = (0.4662036850, 0.4323657300); '''v'''₂(0) = (−0.93240737, −0.86473146). The values are obtained from Chenciner & Montgomery (2000).</ref>]] Particles form more complex structures such as atoms and molecules via a system of orbitals; nuclear, atomic and gravitational. The [[w:Three-body_problem |3-body problem]] is the problem of taking the initial positions and velocities (or [[w:momentum|momenta |momentum|momenta]]) of three or more point masses and solving for their subsequent motion according to [[w:Newton's laws of motion |Newton's laws of motion]] and [[w:Newton's law of universal gravitation |Newton's law of universal gravitation]].<ref name="PrincetonCompanion">{{Citation | last = Barrow-Green | first = June | year = 2008 | title = The Three-Body Problem | editor-last1 = Gowers | editor-first1 = Timothy | editor-last2 = Barrow-Green | editor-first2 = June | editor-last3 = Leader | editor-first3 = Imre | encyclopedia = The Princeton Companion to Mathematics | pages = 726–728 | publisher = Princeton University Press }}</ref>. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for gods and men alike the only way to know what that outcome will be is to run the simulation itself. ==Geometry coded universe== Modelling a Planck scale simulation universe using geometrical forms (links) * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass == External links == * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] * [https://philpapers.org/rec/GRUTIA-2 Simulation theory as evidence for God] (academic peer-reviewed article) ==References== {{Reflist}} [[Category:Philosophy| ]] [[Category:Philosophy of science| ]] gdaj5wtgxu76koo2f1wlkj2x6t92voe 2718260 2718259 2025-06-10T19:52:01Z 212.200.164.104 /* Simulation Time */ 2718260 wikitext text/x-wiki '''Is God a Programmer? analyzing the deep-universe simulation hypothesis at the Planck scale''' The [[w:simulation hypothesis |simulation hypothesis]] is the proposal that all of reality, including the Earth and the rest of the universe, could be an artificial simulation, such as a computer simulation. [[w:Neil_deGrasse_Tyson |Neil deGrasse Tyson]] put the odds at 50-50 that our entire existence is a program on someone else’s hard drive <ref>Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. [[w:David_Chalmers |David Chalmers]] noted “We in this universe can create simulated worlds and there’s nothing remotely spooky about that. Our creator isn’t especially spooky, it’s just some teenage hacker in the next universe up. Turn the tables, and we are essentially gods over our own computer creations <ref>https://www.youtube.com/watch?v=yqbS5qJU8PA, David Chalmers, Serious Science</ref> <ref>The Matrix as Metaphysics, David Chalmers http://consc.net/papers/matrix.pdf</ref> <ref>Are We Living in a Computer Simulation?https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. The commonly postulated [[w:Ancestor_simulation |ancestor simulation]] approach, which [[w:Nick Bostrom |Nick Bostrom]] called "the simulation argument", argues for "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor. However this simulation variant can be traced back to an 'organic base reality' (the original programmer ancestors and their physical planet). The [[v:God_(programmer) |Programmer God]] hypothesis<ref>https://codingthecosmos.com/podcast/ AI generated podcasts</ref> conversely states that a (deep universe) simulation began with the big bang and was programmed by an external intelligence (external to the physical universe), the Programmer by definition a God in the creator of the universe context. Our universe in its entirety, down to the smallest detail, and including life-forms, is within the simulation, the laws of nature, at their most fundamental level, are coded rules running on top of the simulation operating system. The operating system itself is mathematical (and potentially the origin of mathematics). Any candidate for a Programmer-God simulation-universe source code must satisfy these conditions; :1. It can generate physical structures from mathematical forms. :2. The sum universe is dimensionless (simply data on a celestial hard disk). :3. We must be able to use it to derive the laws of physics (because the source code is the origin of the laws of nature, and the laws of physics are our observations of the laws of nature). :4. The mathematical logic must be unknown to us (the Programmer is a non-human intelligence). :5. The coding should have an 'elegance' commensurate with the Programmer's level of skill. == Philosophy == Physicist [[w:Eugene Wigner |Eugene Wigner]] ([[w:The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences |The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]) <ref>{{Cite journal | last1 = Wigner | first1 = E. P. | authorlink = Eugene Wigner| doi = 10.1002/cpa.3160130102 | title = The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959 | journal = Communications on Pure and Applied Mathematics | volume = 13 | pages = 1–14 | year = 1960 | pmid = | pmc = |bibcode = 1960CPAM...13....1W }}</ref> <blockquote>The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. </blockquote> === Discussion === [[w:Philosophy of mathematics |Philosophy of mathematics]] is that branch of philosophy which attempts to answer questions such as: ‘why is mathematics useful in describing nature?’, ‘in which sense, if any, do mathematical entities such as numbers exist?’ and ‘why and how are mathematical statements true?’ This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math. Mathematical realism holds that mathematical entities exist independently of the human mind. We do not invent mathematics, but rather discover it. Triangles, for example, are real entities that have an existence <ref>- http://plato.stanford.edu/entries/platonism-mathematics/</ref>. The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality. It can be considered a form of [[w:Pythagoreanism | Pythagoreanism]] or [[w:Platonism | Platonism]] in that it proposes the existence of ''mathematical objects''; and a form of [[w:philosophy of mathematics | mathematical monism]] in that it denies that anything exists except these ''mathematical objects''. Physicist [[w:Max Tegmark | Max Tegmark]] in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality"<ref name="Tegmark1998">{{cite journal|last=Tegmark |first=Max |date=November 1998 |title=Is "the Theory of Everything" Merely the Ultimate Ensemble Theory? |journal=Annals of Physics |volume=270 |issue=1 |pages=1–51 |doi=10.1006/aphy.1998.5855 |arxiv = gr-qc/9704009 |bibcode = 1998AnPhy.270....1T }}</ref><ref>M. Tegmark 2014, "[http://mathematicaluniverse.org Our Mathematical Universe]", Knopf</ref> proposed that ''Our external physical reality is a mathematical structure''.<ref name="Tegmark2008">{{cite journal|last=Tegmark |first=Max |date=February 2008 |title=The Mathematical Universe |journal=Foundations of Physics |volume=38 |issue=2 |pages=101–150 |doi=10.1007/s10701-007-9186-9 |arxiv=0704.0646|bibcode = 2008FoPh...38..101T }}</ref> That is, the physical universe is not merely ''described by'' mathematics, but ''is'' mathematics (specifically, a [[w:mathematical structure | mathematical structure]]). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref> The principle constraints to any mathematical universe simulation hypothesis are; 1. the computational resources required. The ancestor simulation can resolve this by adapting from the [[w:virtual rality |virtual reality]] approach where only the observable region is simulated and only to the degree required, and 2. that any 'self-aware structures' (humans for example) within the simulation must "subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref>. Succinctly, our computer games may be able to simulate our physical world, but they are still only simulations of a physical reality (regardless of how realistic they may seem) ... we are not yet able to program actual physical dimensions of mass, space and time from mathematical structures, and indeed this may not be possible with a computer hard-ware architecture that can only process binary data. === Deep-universe source code === As a deep-universe simulation is programmed by an external (external to the universe) intelligence (the Programmer God hypothesis), we cannot presume a priori knowledge regarding the simulation source code other than from this code the laws of nature emerged, and so any deep-universe simulation model we try to emulate must be universal, i.e.: independent of any system of units, of the [[w:Dimensional_analysis |dimensioned]] [[w:physical constants |physical constants]] (''G'', ''h'', ''c'', ''e'' .. ), and of any numbering systems. Furthermore, although a deep-universe simulation source code may use mathematical forms (circles, spheres ...) we are familiar with (for ultimately the source code is the origin of these forms), it will have been developed by a non-human intelligence and so we may have to develop new mathematical tools to decipher the underlying logic. By implication therefore, any theoretical basis for a source code that fits the above criteria (and from which the laws of nature will emerge), could be construed as our first tangible evidence of a non-human intelligence. === Constants === A physical universe is characterized by measurable quantities (size, mass, color, texture ...), and so a physical universe can be measured and defined. Contrast then becomes information, the statement ''this is a big apple'' requires a ''small apple'' against which big becomes a relative term. For analytical purposes we select a reference value, for example 0C or 32F, and measure all temperatures against this reference. The smaller the resolution of the measurements, the greater the information content (the file size of a 32 mega-pixel photo is larger than a 4 mega-pixel photo). A simulation universe may be presumed to also have a resolution dictating how much information the simulation can store and manipulate. To measure the fundamental parameters of our universe physics uses [[w:physical constant |physical constants]]. A physical constant is a [[w:physical quantity |physical quantity]] that is generally believed to be both universal in nature and have a constant value in time. These can be divided into 1) dimension-ed (measured using physical units ''kg'', ''m'', ''s'', ''A'' ...) such as the [[w:speed of light |speed of light]] ''c'', [[w:gravitational constant |gravitational constant]] ''G'', [[w:Planck constant |Planck constant]] ''h'' ... as in the table {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} Physicist [[w: |Lev Okun]] noted "Theoretical equations describing the physical world deal with dimensionless quantities and their solutions depend on dimensionless fundamental parameters. But experiments, from which these theories are extracted and by which they could be tested, involve measurements, i.e. comparisons with standard dimension-ful scales. Without standard dimension-ful units and hence without certain conventions physics is unthinkable <ref>Michael J. Duff et al, Journal of High Energy Physics, Volume 2002, JHEP03(2002)</ref>. 2) dimension-less, such as the [[w:Fine-structure_constant |fine structure constant]] ''α''. A dimension-less constant does not measure any physical quantity (it has no units; units = 1). 3) dimension-less [[w:mathematical constant |mathematical constants]], most notably [[w:pi |pi]] = 3.14159265358979 and [[w:Natural_logarithm |e]] = 2.718281828459. Although these are [[w:transcendental number |transcendental numbers]], they can be constructed by integers in a series, and so for a universe expanding incrementally (see simulation time), these constants could be formed within the simulation. For example, at time ''t''; <math display=block>t = 1; \frac{\pi^2}{6} = \frac{1}{t^2} </math> <math display=block>t = 2; \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{t^2}</math> <math display=block>t = now: \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots + \frac{1}{t^2} </math> We may now define the fundamental physical constant as a parameter specifically chosen by the Programmer and is encoded into the simulation code directly, and so whilst it may be inferable, it is not derived from other constants ([[w:Fine-structure_constant#Numerological_explanations_and_multiverse_theory |Richard Feynman on the fine structure constant]]). It should also be dimension-less otherwise the simulation itself becomes dimensioned (if the simulation is running on a celestial computer it is merely data, it has no physical size or shape or ...), and so the dimensioned constants (''G'', ''h'', ''c'', ''e''...) must all be derivable (derived from within the simulation) via the (embedded in the source code) fundamental physical constants (of which the fine structure constant alpha may be an example). Although [[w:pi |pi]] and [[w:Natural_logarithm |e]] are dimensionless, they can be derived internally (from integers), and as they have application in the mathematical realm, they can be referred to as mathematical constants. ==== Planck scale ==== The [[w:Planck scale |Planck scale]] refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the [[w:Standard Model |Standard Model]], [[w:quantum field theory |quantum field theory]] and [[w:general relativity |general relativity]] are no longer reconcilable, and [[w:Quantum Gravity |quantum effects of gravity]] are expected to dominate (quantum gravitational effects only appear at length scales near the Planck scale). Although particles may not be cognizance of our 'laws of physics', they do know the 'laws of nature'. These laws of nature would run directly off the universe OS (operating system), and so below this OS, 'physics' as we know it must necessarily break down. At present the Planck scale is the lowest known level, consequently any attempt to detect evidence of an underlying simulation coding must consider (if not actually begin at) this, the Planck scale<ref>https://www.youtube.com/watch?v=AMQRXGYCDrY Planck scale, Brian Greene</ref>. The [[w:International_System_of_Units |SI units]] for the dimension-ful mksa units are; meter (length), kilogram (mass), second (time), ampere (electric current). There are Planck units that represent these SI units, and so a simulation could use them as discrete building blocks; [[w:Planck length |Planck length]] (the smallest possible unit of length), [[w:Planck mass |Planck mass]] (the unit of mass), [[w:Planck time |Planck time]] (the smallest possible unit of time), [[w:Planck charge |Planck charge]] (the unit of charge). The speed of light then becomes ''c'' = 1 Planck length / 1 Planck time. These units would define the resolution and so information carrying capacity of the simulation universe. ==== Numbering systems ==== As well as our decimal system, computers apply binary and hexadecimal numbering systems. In particular the decimal and hexadecimal are of terrestrial origin and may not be considered 'universal'. Furthermore numbering systems measure only the frequency of an event and contain no information as to the event itself. The number 299 792 458 could refer to the speed of light (299 792 458 m/s) or could equally be referring to the number of apples in a container (299 792 458 apples). As such, numbers require a 'descriptive', whether m/s or apples. Numbers also do not include their history, is 299 792 458 for example a derivation of other base numbers? Present universe simulations use the laws of physics and the physical constants are built in, however both these laws and the physical constants are known only to a limited precision, and so a simulation with 10⁶² iterations (the present age of the universe in units of Planck time) will accumulate errors. Number based computing may be sufficient for ancestor-simulation models where only the observed region needs to be calculated, but has inherent limitations for deep universe simulations where the entire universe is continuously updated. The actual computational requirements for a Planck scale universe simulation based on a numbering system with the laws of physics embedded would be an unknown and consequently lead to an 'non-testable' hypothesis. This is a commonly applied reasoning for rejecting the deep universe simulation. ==== Geometrical objects ==== A mathematical constant such as [[w:pi |pi]] refers to a geometrical construct (the ratio of circle circumference to circle radius) and so is not constrained by any particular numbering system (in the decimal system π = 3.14159...), and so may be considered both universal and eternal. Likewise, by assigning geometrical objects instead of numbers to the Planck units, the problems with a numbering system can be resolved. These objects would however have to fulfill the following conditions; 1) embedded attribute - for example the object for length must embed the function of ''length'' such that a descriptive (km, mile ... ) is not required. Electron wavelength would then be measurable in terms of the length object, as such the length object must be embedded within the electron (the electron object). Although the mass object would incorporate the function ''mass'', the time object the function ''time'' ..., it is not necessary that there be an individual physical mass or physical length or physical time ..., but only that in relation to the other units, the object must express that function (i.e.: the mass object has the function of mass when in the presence of the objects for space and time). The electron could then be a complex event (complex geometrical object) constructed by combining the objects for mass, length, time and charge into 1 event, and thus electron charge, wavelength, frequency and mass would then be different aspects of that 1 geometry (the electron event) and not independent parameters (independent of each other). 2) The objects for mass, length, time and charge must be able to combine with each other [[w:Lego |Lego-style]] to form more complex objects (events) such as electrons and apples whilst still retaining the underlying information (the mass of the apple derives from the mass objects embedded within that apple). Not only must these objects be able to form complex events such as particles, but these events themselves are geometrical objects and so must likewise function according to their geometries. Electrons would orbit protons according to their respective electron and proton geometries, these orbits the result of geometrical imperatives and not due to any built-in laws of physics (the orbital path is a consequence of all the underlying geometries). However, as orbits follow regular and repeating patterns, they can be described (by us) using mathematical formulas. As the events grow in complexity (from atoms to molecules to planets), so too will the patterns (and likewise the formulas we use to describe them). Consequently the ''laws of physics'' would then become our mathematical descriptions of the underlying geometrically imposed patterns. 3) These objects would replace coded instructions (the instruction sets would be built into the objects) thereby instigating a geometrically autonomous universe. The electron 'knows' what to do by virtue of the information encoded within its geometry, no coded electron CALL FUNCTION is required. This would be equivalent to combining the hardware, software and CPU together such that the 'software' changes (adjusts) to the changing 'hardware' (DNA may be an analogy). Note: A purely mathematical universe has no limits in size and can be infinitely large and infinity small. A geometrical universe (that uses objects) has limitations, it can be no smaller than the smallest object for example and has discrete parts (those objects). The philosophy of the TOE (theory of everything) therefore includes a debate between the mathematical universe and the geometrical universe, however this distinction between mathematical and geometrical would only be apparent at the Planck scale. === Evidence of a simulation === The laws of physics are our incomplete observations of the natural universe, and so evidence of a simulation may be found in ambiguities or anomalies within these laws. Furthermore, if complexity arises over time, then at unit time the 'handiwork' of the Programmer may be notable by a simplicity and elegance of the geometries employed ... for the Programmer by definition has God-level programming skills. Here is a notable example. Mass, space and time from the number 1 The dimensions of mass, space and time are considered by science to be independent of each other, we cannot measure the ''distance'' from Tokyo to London using kilograms and amperes, or measure ''mass'' using space and time. Indeed, what characterizes a physical universe as opposed to a simulated universe is the notion that there is a fundamental structure underneath, that in some sense mass 'is', that time 'is' and space 'is' ... thus we cannot write ''kg'' in terms of ''m'' and ''s''. To do so would render our concepts of a physical universe meaningless. The 26th General Conference on Weights and Measures ([[w:2019 redefinition of SI base units|2019 redefinition of SI base units]]) assigned exact numerical values to 4 physical constants (''h, c, e, k''_B) independently of each other (and thereby confirming these as fundamental constants), and as they are measured in SI units ('''kg''', '''m''', '''s''', '''A''', '''K'''), these units must also be independent of each other (i.e.: these are fundamental units, for example if we could define ''m'' using ''A'' then the speed of light could be derived from, and so would depend upon, the value for the elementary charge ''e'', and so the value for ''c'' could not be assigned independently from ''e''). {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} We are familiar with inverse properties; plus charge and minus charge, matter and anti-matter ... and we can observe how these may form and/or cancel each other. A simulation universe however is required to be dimensionless (in sum total), for the simulated universe does not 'exist' in any physical sense outside of the 'Computer' (it is simply data on a celestial hard-disk). Our universe does not appear to have inverse properties such as anti-mass (-kg), anti-time (-s) or anti-space (anti-length -m), therefore the first problem the Programmer must solve is how to create the physical scaffolding (of mass, space and time). For example, the Programmer can start by selecting 2 dimensioned quantities, here are used ''r'', ''v'' <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref> such that :<math>kg = \frac{r^4}{v},\; m = \frac{r^9}{v^5},\; s = \frac{r^9}{v^6},\; A = \frac{v^3}{r^6}</math> Quantities ''r'' and ''v'' are chosen so that no unit (''kg'', ''m'', ''s'', ''A'') can cancel another unit (i.e.: the ''kg'' cannot cancel the ''m'' or the ''s'' ...), and so we have 4 independent units (we still cannot define the ''kg'' using the ''m'' or the ''s'' ...), however if 3 (or more) units are combined together in a specific ratio, they can cancel (in a certain ratio our ''r'' and ''v'' become inverse properties and so cancel each other; units = 1). <math>f_X = \frac{kg^9 s^{11}}{m^{15}} = \frac{(\frac{r^4}{v})^9 (\frac{r^9}{v^6})^{11}}{(\frac{r^9}{v^5})^{15}} = 1</math> This f_X, although embedded within are the dimensioned structures for mass, time and length (in the above ratio), would be a dimensionless mathematical structure, units = 1. Thus we may create as much mass, time and length as we wish, the only proviso being that they are created in f_X ratios, so that regardless of how massive, old and large our universe becomes, it is still in sum total dimensionless. Defining the dimensioned quantities ''r'', ''v'' in SI unit terms. :<math>r = (\frac{kg\;m}{s})^{1/4}</math> :<math>v = \frac{m}{s}</math> Mass :<math>\frac{r^4}{v} = (\frac{kg\;m}{s})\;(\frac{s}{m}) = kg</math> Length :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^5})^4 = \frac{s^{20}}{m^{20}}</math> :<math>(\frac{r^9}{v^5})^4 = \frac{kg^9 s^{11}}{m^{11}} = m^4 \frac{kg^9 s^{11}}{m^{15}} = m^4 f_X = m^4</math> Time :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^6})^4 = \frac{s^{24}}{m^{24}}</math> :<math>(\frac{r^9}{v^6})^4 = \frac{kg^9 s^{15}}{m^{15}} = s^4 \frac{kg^9 s^{11}}{m^{15}} = s^4 f_X = s^4</math> And so, although f_X is a dimensionless mathematical structure, we can embed within it the (mass, length, time ...) structures along with their dimensional attributes (kg, m, s, A ..). In the mathematical electron model (discussed below), the electron itself is an example of an f_X structure, it (f_electron) is a dimensionless geometrical object that embeds the physical electron parameters of wavelength, frequency, charge (note: A-m = ampere-meter are the units for a [[w:Magnetic_monopole#In_SI_units |magnetic monopole]]). <math>f_{electron}</math> :<math>units = \frac{A^3 m^3}{s} = \frac{(\frac{v^3}{r^6})^3 (\frac{r^9}{v^5})^3}{(\frac{r^9}{v^6})} = 1</math> We may note that at the macro-level (of planets and stars) these f_X ratio are not found, and so this level is the domain of the observed physical universe, however at the quantum level, f_X ratio do appear, f_electron as an example, the mathematical and physical domains then blurring. This would also explain why physics can measure precisely the parameters of the electron (wavelength, mass ...), but has never found the electron itself. == Programming == “God vs. science debates tend to be restricted to the premise that a God does not rely on science and that science does not need a God. As science and God are thus seen as mutually exclusive there are few, if any, serious attempts to construct mathematical models of a universe whose principle axiom does require a God. However, if there is an Intelligence responsible for the 14 billion year old universe of modern physics, being the universe of Einstein and Dirac, and beginning with the big bang as the act of 'creation', then we must ask how it might be done? What construction technique could have been used to set the laws of physics in motion?” <ref>[https://theprogrammergod.com/ The Programmer God, are we in a Simulation]</ref> === Simulation Time === The (dimensionless) simulation clock-rate would be defined as the minimum 'time variable' ('''age''') increment to the simulation. Using a simple loop as analogy, at ''age'' = 1, the simulation begins (the big bang), certain processes occur, when these are completed ''age'' increments (''age'' = 2, then 3, then 4 ... ) until ''age'' reaches ''the_end'' and the simulation stops. 'begin simulation FOR age = 1 TO the_end 'big bang = 1 conduct certain processes ........ NEXT age 'end simulation [[w:Quantum spacetime |Quantum spacetime]] and [[w:Quantum gravity |Quantum gravity]] models refer to [[w:Planck time | Planck time]] as the smallest discrete unit of time and so the incrementing variable '''age''' could be used to generate units of Planck time (and other Planck units, the physical scaffolding of the universe). In a geometrical model, to these Planck units could be assigned geometrical objects, for example; Initialize_physical_constants; FOR age = 1 TO the_end generate 1 unit of (Planck) time; '1 time 'object' T generate 1 unit of (Planck) mass; '1 mass 'object' M generate 1 unit of (Planck) length; '1 length 'object' L ........ NEXT age The variable ''age'' is the simulation clock-rate, it is simply a counter (1, 2, 3 ...) and so is a dimensionless number, the object T is the geometrical Planck time object, it is dimensioned and is measured by us in seconds. If ''age'' is the origin of Planck time (1 increment to ''age'' generates 1 T object) then ''age'' = 10⁶², this is based on the present [[w:Age_of_the_universe |age of the universe]], which, at 14 billion years, equates to 10⁶² units of Planck time. For each ''age'', certain operations are performed, only after they are finished does ''age'' increment (there is no ''time'' interval between increments). As noted, ''age'' being dimensionless, is not the same as dimensioned Planck time which is the geometrical object T, and this T, being dimensioned, can only appear within the simulation. The analogy would be frames of a movie, each frame contains dimensioned information but there is no ''time'' interval between frames. FOR age = 1 TO the_end (of the movie) display frame{age} NEXT age Although operations (between increments to ''age'') may be extensive, self-aware structures from within the simulation would have no means to determine this, they could only perceive themselves as being in a real-time (for them the smallest unit of ''time'' is 1T, just as the smallest unit of ''time'' in a movie is 1 frame). Their (those self-aware structures) dimension of time would then be a measure of relative motion (a change of state), and so although ultimately deriving from the variable ''age'', their time would not be the same as ''age''. If there was no motion, if all particles and photons were still (no change of state), then their time dimension could not update (if every frame in a movie was the same then actors within that movie could not register a change in time), ''age'' however would continue to increment. Thus we have 3 time structures; 1) the dimension-less simulation clock-rate variable ''age'', 2) the dimensioned time unit (object T), and 3) time as change of state (the observers time). Observer time requires a memory of past events against which a change of state can be perceived. The forward increment to ''age'' would constitute the [[w:arrow of time |arrow of time]]. Reversing this would reverse the arrow of time, the universe would likewise shrink in size and mass accordingly (just as a [[w:white hole |white hole]] is the (time) reversal of a [[w:black hole |black hole]]). FOR age = the_end TO 1 STEP -1 delete 1 unit of Planck time; delete 1 unit of Planck mass; delete 1 unit of Planck length; ........ NEXT age Adding mass, length and time objects per increment to ''age'' would force the universe expansion (in size and mass), and as such an anti-gravitational [[w:dark energy |dark energy]] would not be required, however these objects are dimensioned and so are generated within the simulation. This means that they must somehow combine in a specific ratio whereby they (the units for mass length, time, charge; ''kg'', ''m'', ''s'', ''A'') in sum total cancel each other, leaving the sum universe (the simulation itself) residing on that celestial hard-disk. We may introduce a theoretical dimensionless (f_X) geometrical object denoted as f_Planck within which are embedded the dimensioned objects MLTA (mass, length, time, charge), and from which they may be extracted. FOR age = 1 TO the_end add 1 f_Planck 'dimensionless geometrical 'object' { extract 1 unit of (Planck) time; '1 time 'object' T extract 1 unit of (Planck) mass; '1 mass 'object' M extract 1 unit of (Planck) length; '1 length 'object' L } ........ NEXT age This then means that the simulation, in order to create time T, must also create mass M and space L (become larger and more massive). Thus no matter how small or large the physical universe is (when seen internally), in sum total (when seen externally), there is no universe - it is merely data without physical form. === Universe time-line === As the universe expands outwards (through the constant addition of units of mass and length via f_Planck), and if this expansion pulls particles with it (if it is the origin of motion), then ''now'' (the present) would reside on the surface of the (constantly expanding at the speed of light; ''c'' = 1 Planck length / 1 Planck time) universe, and so the 'past' could be retained, for the past cannot be over-written by the present in an expanding universe (if ''now'' is always on the surface). As this expansion occurs at the Planck scale, information even below quantum states, down to the Planck scale, can be retained, the analogy would be the storing of every [[w:Keystroke_logging |keystroke]], a Planck scale version of the [[w:Akashic records |Akashic records]] ... for if our deeds (the past) are both stored and cannot be over-written (by the present), then we have a candidate for the '[[w:karma |karmic]] heavens' (Matthew 6:19 ''But lay up for yourselves treasures in 'heaven', where neither moth nor rust doth corrupt, and where thieves do not break through nor steal''). This also forms a universe '''time-line''' against which previous information can be compared with new information (a 'memory' of events), without which we could not link cause with effect. === Singularity === In a simulation, the data (software) requires a storage device that is ultimately hardware (RAM, HD ...). In a data world of 1's and 0's such as a computer game, characters within that game may analyze other parts of their 1's and 0's game, but they have no means to analyze the hard disk upon which they (and their game) are stored, for the hard disk is an electro-mechanical device, it is not part of their 1's and 0's world, it is a part of the 'real world', the world of their Programmer. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may or may not resemble the laws that operate in the 'real world' (the world of their Programmer). Thus any region where the laws of physics (the laws of their game world) break down would be significant. A [[w:singularity |singularity]] inside a black hole is such a region <ref>https://www.youtube.com/watch?v=W5j7umtZYB4 a black hole singularity as the interface between worlds</ref>. For the [[w:black hole electron |black-hole electron]], its black-hole center would then be analogous to a storage address on a hard disk, the interface between the simulation world and the real world. A massive (galactic) black-hole could be as an entire data sector. The surface of the black-hole would then be of the simulation world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however would be the interface between the data world and the 'hard disk' of the real world, and so would not exist in any 'physical' terms. It is external to the simulation. As analogy, we may discuss the 3-D surface area of a black-hole but not its volume (interior). === Laws of Physics === The scientific method is built upon testable hypothesis and reproducible results. Water always boils (in defined conditions), at 100°C. In a geometrical universe particles will behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these repeating patterns, the more complex the orbits, the more complex the formulas required to describe them and so forth. However if there is a source code from which these geometrical conditions were programmed, then there may also be non-repeating events, back-doors built into the code (a common practice by terrestrial programmers), these by definition would lie outside the laws of physics and so be labelled as miracles, yet they would be no less valid. === Determinism === [[File:Three body problem figure-8 orbit animation.gif|400px|thumb|An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259.<ref>Here the gravitational constant ''G'' has been set to 1, and the initial conditions are '''r'''₁(0) = −'''r'''₃(0) = (−0.97000436, 0.24308753); '''r'''₂(0) = (0,0); '''v'''₁(0) = '''v'''₃(0) = (0.4662036850, 0.4323657300); '''v'''₂(0) = (−0.93240737, −0.86473146). The values are obtained from Chenciner & Montgomery (2000).</ref>]] Particles form more complex structures such as atoms and molecules via a system of orbitals; nuclear, atomic and gravitational. The [[w:Three-body_problem |3-body problem]] is the problem of taking the initial positions and velocities (or [[w:momentum|momenta |momentum|momenta]]) of three or more point masses and solving for their subsequent motion according to [[w:Newton's laws of motion |Newton's laws of motion]] and [[w:Newton's law of universal gravitation |Newton's law of universal gravitation]].<ref name="PrincetonCompanion">{{Citation | last = Barrow-Green | first = June | year = 2008 | title = The Three-Body Problem | editor-last1 = Gowers | editor-first1 = Timothy | editor-last2 = Barrow-Green | editor-first2 = June | editor-last3 = Leader | editor-first3 = Imre | encyclopedia = The Princeton Companion to Mathematics | pages = 726–728 | publisher = Princeton University Press }}</ref>. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for gods and men alike the only way to know what that outcome will be is to run the simulation itself. ==Geometry coded universe== Modelling a Planck scale simulation universe using geometrical forms (links) * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass == External links == * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] * [https://philpapers.org/rec/GRUTIA-2 Simulation theory as evidence for God] (academic peer-reviewed article) ==References== {{Reflist}} [[Category:Philosophy| ]] [[Category:Philosophy of science| ]] iekx13bb8w408jjkne17q1ixtjo2zum 2718261 2718260 2025-06-10T19:52:18Z 212.200.164.104 /* Universe time-line */ 2718261 wikitext text/x-wiki '''Is God a Programmer? analyzing the deep-universe simulation hypothesis at the Planck scale''' The [[w:simulation hypothesis |simulation hypothesis]] is the proposal that all of reality, including the Earth and the rest of the universe, could be an artificial simulation, such as a computer simulation. [[w:Neil_deGrasse_Tyson |Neil deGrasse Tyson]] put the odds at 50-50 that our entire existence is a program on someone else’s hard drive <ref>Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. [[w:David_Chalmers |David Chalmers]] noted “We in this universe can create simulated worlds and there’s nothing remotely spooky about that. Our creator isn’t especially spooky, it’s just some teenage hacker in the next universe up. Turn the tables, and we are essentially gods over our own computer creations <ref>https://www.youtube.com/watch?v=yqbS5qJU8PA, David Chalmers, Serious Science</ref> <ref>The Matrix as Metaphysics, David Chalmers http://consc.net/papers/matrix.pdf</ref> <ref>Are We Living in a Computer Simulation?https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. The commonly postulated [[w:Ancestor_simulation |ancestor simulation]] approach, which [[w:Nick Bostrom |Nick Bostrom]] called "the simulation argument", argues for "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor. However this simulation variant can be traced back to an 'organic base reality' (the original programmer ancestors and their physical planet). The [[v:God_(programmer) |Programmer God]] hypothesis<ref>https://codingthecosmos.com/podcast/ AI generated podcasts</ref> conversely states that a (deep universe) simulation began with the big bang and was programmed by an external intelligence (external to the physical universe), the Programmer by definition a God in the creator of the universe context. Our universe in its entirety, down to the smallest detail, and including life-forms, is within the simulation, the laws of nature, at their most fundamental level, are coded rules running on top of the simulation operating system. The operating system itself is mathematical (and potentially the origin of mathematics). Any candidate for a Programmer-God simulation-universe source code must satisfy these conditions; :1. It can generate physical structures from mathematical forms. :2. The sum universe is dimensionless (simply data on a celestial hard disk). :3. We must be able to use it to derive the laws of physics (because the source code is the origin of the laws of nature, and the laws of physics are our observations of the laws of nature). :4. The mathematical logic must be unknown to us (the Programmer is a non-human intelligence). :5. The coding should have an 'elegance' commensurate with the Programmer's level of skill. == Philosophy == Physicist [[w:Eugene Wigner |Eugene Wigner]] ([[w:The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences |The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]) <ref>{{Cite journal | last1 = Wigner | first1 = E. P. | authorlink = Eugene Wigner| doi = 10.1002/cpa.3160130102 | title = The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959 | journal = Communications on Pure and Applied Mathematics | volume = 13 | pages = 1–14 | year = 1960 | pmid = | pmc = |bibcode = 1960CPAM...13....1W }}</ref> <blockquote>The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. </blockquote> === Discussion === [[w:Philosophy of mathematics |Philosophy of mathematics]] is that branch of philosophy which attempts to answer questions such as: ‘why is mathematics useful in describing nature?’, ‘in which sense, if any, do mathematical entities such as numbers exist?’ and ‘why and how are mathematical statements true?’ This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math. Mathematical realism holds that mathematical entities exist independently of the human mind. We do not invent mathematics, but rather discover it. Triangles, for example, are real entities that have an existence <ref>- http://plato.stanford.edu/entries/platonism-mathematics/</ref>. The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality. It can be considered a form of [[w:Pythagoreanism | Pythagoreanism]] or [[w:Platonism | Platonism]] in that it proposes the existence of ''mathematical objects''; and a form of [[w:philosophy of mathematics | mathematical monism]] in that it denies that anything exists except these ''mathematical objects''. Physicist [[w:Max Tegmark | Max Tegmark]] in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality"<ref name="Tegmark1998">{{cite journal|last=Tegmark |first=Max |date=November 1998 |title=Is "the Theory of Everything" Merely the Ultimate Ensemble Theory? |journal=Annals of Physics |volume=270 |issue=1 |pages=1–51 |doi=10.1006/aphy.1998.5855 |arxiv = gr-qc/9704009 |bibcode = 1998AnPhy.270....1T }}</ref><ref>M. Tegmark 2014, "[http://mathematicaluniverse.org Our Mathematical Universe]", Knopf</ref> proposed that ''Our external physical reality is a mathematical structure''.<ref name="Tegmark2008">{{cite journal|last=Tegmark |first=Max |date=February 2008 |title=The Mathematical Universe |journal=Foundations of Physics |volume=38 |issue=2 |pages=101–150 |doi=10.1007/s10701-007-9186-9 |arxiv=0704.0646|bibcode = 2008FoPh...38..101T }}</ref> That is, the physical universe is not merely ''described by'' mathematics, but ''is'' mathematics (specifically, a [[w:mathematical structure | mathematical structure]]). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref> The principle constraints to any mathematical universe simulation hypothesis are; 1. the computational resources required. The ancestor simulation can resolve this by adapting from the [[w:virtual rality |virtual reality]] approach where only the observable region is simulated and only to the degree required, and 2. that any 'self-aware structures' (humans for example) within the simulation must "subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref>. Succinctly, our computer games may be able to simulate our physical world, but they are still only simulations of a physical reality (regardless of how realistic they may seem) ... we are not yet able to program actual physical dimensions of mass, space and time from mathematical structures, and indeed this may not be possible with a computer hard-ware architecture that can only process binary data. === Deep-universe source code === As a deep-universe simulation is programmed by an external (external to the universe) intelligence (the Programmer God hypothesis), we cannot presume a priori knowledge regarding the simulation source code other than from this code the laws of nature emerged, and so any deep-universe simulation model we try to emulate must be universal, i.e.: independent of any system of units, of the [[w:Dimensional_analysis |dimensioned]] [[w:physical constants |physical constants]] (''G'', ''h'', ''c'', ''e'' .. ), and of any numbering systems. Furthermore, although a deep-universe simulation source code may use mathematical forms (circles, spheres ...) we are familiar with (for ultimately the source code is the origin of these forms), it will have been developed by a non-human intelligence and so we may have to develop new mathematical tools to decipher the underlying logic. By implication therefore, any theoretical basis for a source code that fits the above criteria (and from which the laws of nature will emerge), could be construed as our first tangible evidence of a non-human intelligence. === Constants === A physical universe is characterized by measurable quantities (size, mass, color, texture ...), and so a physical universe can be measured and defined. Contrast then becomes information, the statement ''this is a big apple'' requires a ''small apple'' against which big becomes a relative term. For analytical purposes we select a reference value, for example 0C or 32F, and measure all temperatures against this reference. The smaller the resolution of the measurements, the greater the information content (the file size of a 32 mega-pixel photo is larger than a 4 mega-pixel photo). A simulation universe may be presumed to also have a resolution dictating how much information the simulation can store and manipulate. To measure the fundamental parameters of our universe physics uses [[w:physical constant |physical constants]]. A physical constant is a [[w:physical quantity |physical quantity]] that is generally believed to be both universal in nature and have a constant value in time. These can be divided into 1) dimension-ed (measured using physical units ''kg'', ''m'', ''s'', ''A'' ...) such as the [[w:speed of light |speed of light]] ''c'', [[w:gravitational constant |gravitational constant]] ''G'', [[w:Planck constant |Planck constant]] ''h'' ... as in the table {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} Physicist [[w: |Lev Okun]] noted "Theoretical equations describing the physical world deal with dimensionless quantities and their solutions depend on dimensionless fundamental parameters. But experiments, from which these theories are extracted and by which they could be tested, involve measurements, i.e. comparisons with standard dimension-ful scales. Without standard dimension-ful units and hence without certain conventions physics is unthinkable <ref>Michael J. Duff et al, Journal of High Energy Physics, Volume 2002, JHEP03(2002)</ref>. 2) dimension-less, such as the [[w:Fine-structure_constant |fine structure constant]] ''α''. A dimension-less constant does not measure any physical quantity (it has no units; units = 1). 3) dimension-less [[w:mathematical constant |mathematical constants]], most notably [[w:pi |pi]] = 3.14159265358979 and [[w:Natural_logarithm |e]] = 2.718281828459. Although these are [[w:transcendental number |transcendental numbers]], they can be constructed by integers in a series, and so for a universe expanding incrementally (see simulation time), these constants could be formed within the simulation. For example, at time ''t''; <math display=block>t = 1; \frac{\pi^2}{6} = \frac{1}{t^2} </math> <math display=block>t = 2; \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{t^2}</math> <math display=block>t = now: \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots + \frac{1}{t^2} </math> We may now define the fundamental physical constant as a parameter specifically chosen by the Programmer and is encoded into the simulation code directly, and so whilst it may be inferable, it is not derived from other constants ([[w:Fine-structure_constant#Numerological_explanations_and_multiverse_theory |Richard Feynman on the fine structure constant]]). It should also be dimension-less otherwise the simulation itself becomes dimensioned (if the simulation is running on a celestial computer it is merely data, it has no physical size or shape or ...), and so the dimensioned constants (''G'', ''h'', ''c'', ''e''...) must all be derivable (derived from within the simulation) via the (embedded in the source code) fundamental physical constants (of which the fine structure constant alpha may be an example). Although [[w:pi |pi]] and [[w:Natural_logarithm |e]] are dimensionless, they can be derived internally (from integers), and as they have application in the mathematical realm, they can be referred to as mathematical constants. ==== Planck scale ==== The [[w:Planck scale |Planck scale]] refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the [[w:Standard Model |Standard Model]], [[w:quantum field theory |quantum field theory]] and [[w:general relativity |general relativity]] are no longer reconcilable, and [[w:Quantum Gravity |quantum effects of gravity]] are expected to dominate (quantum gravitational effects only appear at length scales near the Planck scale). Although particles may not be cognizance of our 'laws of physics', they do know the 'laws of nature'. These laws of nature would run directly off the universe OS (operating system), and so below this OS, 'physics' as we know it must necessarily break down. At present the Planck scale is the lowest known level, consequently any attempt to detect evidence of an underlying simulation coding must consider (if not actually begin at) this, the Planck scale<ref>https://www.youtube.com/watch?v=AMQRXGYCDrY Planck scale, Brian Greene</ref>. The [[w:International_System_of_Units |SI units]] for the dimension-ful mksa units are; meter (length), kilogram (mass), second (time), ampere (electric current). There are Planck units that represent these SI units, and so a simulation could use them as discrete building blocks; [[w:Planck length |Planck length]] (the smallest possible unit of length), [[w:Planck mass |Planck mass]] (the unit of mass), [[w:Planck time |Planck time]] (the smallest possible unit of time), [[w:Planck charge |Planck charge]] (the unit of charge). The speed of light then becomes ''c'' = 1 Planck length / 1 Planck time. These units would define the resolution and so information carrying capacity of the simulation universe. ==== Numbering systems ==== As well as our decimal system, computers apply binary and hexadecimal numbering systems. In particular the decimal and hexadecimal are of terrestrial origin and may not be considered 'universal'. Furthermore numbering systems measure only the frequency of an event and contain no information as to the event itself. The number 299 792 458 could refer to the speed of light (299 792 458 m/s) or could equally be referring to the number of apples in a container (299 792 458 apples). As such, numbers require a 'descriptive', whether m/s or apples. Numbers also do not include their history, is 299 792 458 for example a derivation of other base numbers? Present universe simulations use the laws of physics and the physical constants are built in, however both these laws and the physical constants are known only to a limited precision, and so a simulation with 10⁶² iterations (the present age of the universe in units of Planck time) will accumulate errors. Number based computing may be sufficient for ancestor-simulation models where only the observed region needs to be calculated, but has inherent limitations for deep universe simulations where the entire universe is continuously updated. The actual computational requirements for a Planck scale universe simulation based on a numbering system with the laws of physics embedded would be an unknown and consequently lead to an 'non-testable' hypothesis. This is a commonly applied reasoning for rejecting the deep universe simulation. ==== Geometrical objects ==== A mathematical constant such as [[w:pi |pi]] refers to a geometrical construct (the ratio of circle circumference to circle radius) and so is not constrained by any particular numbering system (in the decimal system π = 3.14159...), and so may be considered both universal and eternal. Likewise, by assigning geometrical objects instead of numbers to the Planck units, the problems with a numbering system can be resolved. These objects would however have to fulfill the following conditions; 1) embedded attribute - for example the object for length must embed the function of ''length'' such that a descriptive (km, mile ... ) is not required. Electron wavelength would then be measurable in terms of the length object, as such the length object must be embedded within the electron (the electron object). Although the mass object would incorporate the function ''mass'', the time object the function ''time'' ..., it is not necessary that there be an individual physical mass or physical length or physical time ..., but only that in relation to the other units, the object must express that function (i.e.: the mass object has the function of mass when in the presence of the objects for space and time). The electron could then be a complex event (complex geometrical object) constructed by combining the objects for mass, length, time and charge into 1 event, and thus electron charge, wavelength, frequency and mass would then be different aspects of that 1 geometry (the electron event) and not independent parameters (independent of each other). 2) The objects for mass, length, time and charge must be able to combine with each other [[w:Lego |Lego-style]] to form more complex objects (events) such as electrons and apples whilst still retaining the underlying information (the mass of the apple derives from the mass objects embedded within that apple). Not only must these objects be able to form complex events such as particles, but these events themselves are geometrical objects and so must likewise function according to their geometries. Electrons would orbit protons according to their respective electron and proton geometries, these orbits the result of geometrical imperatives and not due to any built-in laws of physics (the orbital path is a consequence of all the underlying geometries). However, as orbits follow regular and repeating patterns, they can be described (by us) using mathematical formulas. As the events grow in complexity (from atoms to molecules to planets), so too will the patterns (and likewise the formulas we use to describe them). Consequently the ''laws of physics'' would then become our mathematical descriptions of the underlying geometrically imposed patterns. 3) These objects would replace coded instructions (the instruction sets would be built into the objects) thereby instigating a geometrically autonomous universe. The electron 'knows' what to do by virtue of the information encoded within its geometry, no coded electron CALL FUNCTION is required. This would be equivalent to combining the hardware, software and CPU together such that the 'software' changes (adjusts) to the changing 'hardware' (DNA may be an analogy). Note: A purely mathematical universe has no limits in size and can be infinitely large and infinity small. A geometrical universe (that uses objects) has limitations, it can be no smaller than the smallest object for example and has discrete parts (those objects). The philosophy of the TOE (theory of everything) therefore includes a debate between the mathematical universe and the geometrical universe, however this distinction between mathematical and geometrical would only be apparent at the Planck scale. === Evidence of a simulation === The laws of physics are our incomplete observations of the natural universe, and so evidence of a simulation may be found in ambiguities or anomalies within these laws. Furthermore, if complexity arises over time, then at unit time the 'handiwork' of the Programmer may be notable by a simplicity and elegance of the geometries employed ... for the Programmer by definition has God-level programming skills. Here is a notable example. Mass, space and time from the number 1 The dimensions of mass, space and time are considered by science to be independent of each other, we cannot measure the ''distance'' from Tokyo to London using kilograms and amperes, or measure ''mass'' using space and time. Indeed, what characterizes a physical universe as opposed to a simulated universe is the notion that there is a fundamental structure underneath, that in some sense mass 'is', that time 'is' and space 'is' ... thus we cannot write ''kg'' in terms of ''m'' and ''s''. To do so would render our concepts of a physical universe meaningless. The 26th General Conference on Weights and Measures ([[w:2019 redefinition of SI base units|2019 redefinition of SI base units]]) assigned exact numerical values to 4 physical constants (''h, c, e, k''_B) independently of each other (and thereby confirming these as fundamental constants), and as they are measured in SI units ('''kg''', '''m''', '''s''', '''A''', '''K'''), these units must also be independent of each other (i.e.: these are fundamental units, for example if we could define ''m'' using ''A'' then the speed of light could be derived from, and so would depend upon, the value for the elementary charge ''e'', and so the value for ''c'' could not be assigned independently from ''e''). {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} We are familiar with inverse properties; plus charge and minus charge, matter and anti-matter ... and we can observe how these may form and/or cancel each other. A simulation universe however is required to be dimensionless (in sum total), for the simulated universe does not 'exist' in any physical sense outside of the 'Computer' (it is simply data on a celestial hard-disk). Our universe does not appear to have inverse properties such as anti-mass (-kg), anti-time (-s) or anti-space (anti-length -m), therefore the first problem the Programmer must solve is how to create the physical scaffolding (of mass, space and time). For example, the Programmer can start by selecting 2 dimensioned quantities, here are used ''r'', ''v'' <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref> such that :<math>kg = \frac{r^4}{v},\; m = \frac{r^9}{v^5},\; s = \frac{r^9}{v^6},\; A = \frac{v^3}{r^6}</math> Quantities ''r'' and ''v'' are chosen so that no unit (''kg'', ''m'', ''s'', ''A'') can cancel another unit (i.e.: the ''kg'' cannot cancel the ''m'' or the ''s'' ...), and so we have 4 independent units (we still cannot define the ''kg'' using the ''m'' or the ''s'' ...), however if 3 (or more) units are combined together in a specific ratio, they can cancel (in a certain ratio our ''r'' and ''v'' become inverse properties and so cancel each other; units = 1). <math>f_X = \frac{kg^9 s^{11}}{m^{15}} = \frac{(\frac{r^4}{v})^9 (\frac{r^9}{v^6})^{11}}{(\frac{r^9}{v^5})^{15}} = 1</math> This f_X, although embedded within are the dimensioned structures for mass, time and length (in the above ratio), would be a dimensionless mathematical structure, units = 1. Thus we may create as much mass, time and length as we wish, the only proviso being that they are created in f_X ratios, so that regardless of how massive, old and large our universe becomes, it is still in sum total dimensionless. Defining the dimensioned quantities ''r'', ''v'' in SI unit terms. :<math>r = (\frac{kg\;m}{s})^{1/4}</math> :<math>v = \frac{m}{s}</math> Mass :<math>\frac{r^4}{v} = (\frac{kg\;m}{s})\;(\frac{s}{m}) = kg</math> Length :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^5})^4 = \frac{s^{20}}{m^{20}}</math> :<math>(\frac{r^9}{v^5})^4 = \frac{kg^9 s^{11}}{m^{11}} = m^4 \frac{kg^9 s^{11}}{m^{15}} = m^4 f_X = m^4</math> Time :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^6})^4 = \frac{s^{24}}{m^{24}}</math> :<math>(\frac{r^9}{v^6})^4 = \frac{kg^9 s^{15}}{m^{15}} = s^4 \frac{kg^9 s^{11}}{m^{15}} = s^4 f_X = s^4</math> And so, although f_X is a dimensionless mathematical structure, we can embed within it the (mass, length, time ...) structures along with their dimensional attributes (kg, m, s, A ..). In the mathematical electron model (discussed below), the electron itself is an example of an f_X structure, it (f_electron) is a dimensionless geometrical object that embeds the physical electron parameters of wavelength, frequency, charge (note: A-m = ampere-meter are the units for a [[w:Magnetic_monopole#In_SI_units |magnetic monopole]]). <math>f_{electron}</math> :<math>units = \frac{A^3 m^3}{s} = \frac{(\frac{v^3}{r^6})^3 (\frac{r^9}{v^5})^3}{(\frac{r^9}{v^6})} = 1</math> We may note that at the macro-level (of planets and stars) these f_X ratio are not found, and so this level is the domain of the observed physical universe, however at the quantum level, f_X ratio do appear, f_electron as an example, the mathematical and physical domains then blurring. This would also explain why physics can measure precisely the parameters of the electron (wavelength, mass ...), but has never found the electron itself. == Programming == “God vs. science debates tend to be restricted to the premise that a God does not rely on science and that science does not need a God. As science and God are thus seen as mutually exclusive there are few, if any, serious attempts to construct mathematical models of a universe whose principle axiom does require a God. However, if there is an Intelligence responsible for the 14 billion year old universe of modern physics, being the universe of Einstein and Dirac, and beginning with the big bang as the act of 'creation', then we must ask how it might be done? What construction technique could have been used to set the laws of physics in motion?” <ref>[https://theprogrammergod.com/ The Programmer God, are we in a Simulation]</ref> === Simulation Time === The (dimensionless) simulation clock-rate would be defined as the minimum 'time variable' ('''age''') increment to the simulation. Using a simple loop as analogy, at ''age'' = 1, the simulation begins (the big bang), certain processes occur, when these are completed ''age'' increments (''age'' = 2, then 3, then 4 ... ) until ''age'' reaches ''the_end'' and the simulation stops. 'begin simulation FOR age = 1 TO the_end 'big bang = 1 conduct certain processes ........ NEXT age 'end simulation [[w:Quantum spacetime |Quantum spacetime]] and [[w:Quantum gravity |Quantum gravity]] models refer to [[w:Planck time | Planck time]] as the smallest discrete unit of time and so the incrementing variable '''age''' could be used to generate units of Planck time (and other Planck units, the physical scaffolding of the universe). In a geometrical model, to these Planck units could be assigned geometrical objects, for example; Initialize_physical_constants; FOR age = 1 TO the_end generate 1 unit of (Planck) time; '1 time 'object' T generate 1 unit of (Planck) mass; '1 mass 'object' M generate 1 unit of (Planck) length; '1 length 'object' L ........ NEXT age The variable ''age'' is the simulation clock-rate, it is simply a counter (1, 2, 3 ...) and so is a dimensionless number, the object T is the geometrical Planck time object, it is dimensioned and is measured by us in seconds. If ''age'' is the origin of Planck time (1 increment to ''age'' generates 1 T object) then ''age'' = 10⁶², this is based on the present [[w:Age_of_the_universe |age of the universe]], which, at 14 billion years, equates to 10⁶² units of Planck time. For each ''age'', certain operations are performed, only after they are finished does ''age'' increment (there is no ''time'' interval between increments). As noted, ''age'' being dimensionless, is not the same as dimensioned Planck time which is the geometrical object T, and this T, being dimensioned, can only appear within the simulation. The analogy would be frames of a movie, each frame contains dimensioned information but there is no ''time'' interval between frames. FOR age = 1 TO the_end (of the movie) display frame{age} NEXT age Although operations (between increments to ''age'') may be extensive, self-aware structures from within the simulation would have no means to determine this, they could only perceive themselves as being in a real-time (for them the smallest unit of ''time'' is 1T, just as the smallest unit of ''time'' in a movie is 1 frame). Their (those self-aware structures) dimension of time would then be a measure of relative motion (a change of state), and so although ultimately deriving from the variable ''age'', their time would not be the same as ''age''. If there was no motion, if all particles and photons were still (no change of state), then their time dimension could not update (if every frame in a movie was the same then actors within that movie could not register a change in time), ''age'' however would continue to increment. Thus we have 3 time structures; 1) the dimension-less simulation clock-rate variable ''age'', 2) the dimensioned time unit (object T), and 3) time as change of state (the observers time). Observer time requires a memory of past events against which a change of state can be perceived. The forward increment to ''age'' would constitute the [[w:arrow of time |arrow of time]]. Reversing this would reverse the arrow of time, the universe would likewise shrink in size and mass accordingly (just as a [[w:white hole |white hole]] is the (time) reversal of a [[w:black hole |black hole]]). FOR age = the_end TO 1 STEP -1 delete 1 unit of Planck time; delete 1 unit of Planck mass; delete 1 unit of Planck length; ........ NEXT age Adding mass, length and time objects per increment to ''age'' would force the universe expansion (in size and mass), and as such an anti-gravitational [[w:dark energy |dark energy]] would not be required, however these objects are dimensioned and so are generated within the simulation. This means that they must somehow combine in a specific ratio whereby they (the units for mass length, time, charge; ''kg'', ''m'', ''s'', ''A'') in sum total cancel each other, leaving the sum universe (the simulation itself) residing on that celestial hard-disk. We may introduce a theoretical dimensionless (f_X) geometrical object denoted as f_Planck within which are embedded the dimensioned objects MLTA (mass, length, time, charge), and from which they may be extracted. FOR age = 1 TO the_end add 1 f_Planck 'dimensionless geometrical 'object' { extract 1 unit of (Planck) time; '1 time 'object' T extract 1 unit of (Planck) mass; '1 mass 'object' M extract 1 unit of (Planck) length; '1 length 'object' L } ........ NEXT age This then means that the simulation, in order to create time T, must also create mass M and space L (become larger and more massive). Thus no matter how small or large the physical universe is (when seen internally), in sum total (when seen externally), there is no universe - it is merely data without physical form. === Universe time-line === As the universe expands outwards (through the constant addition of units of mass and length via f_Planck), and if this expansion pulls particles with it (if it is the origin of motion), then ''now'' (the present) would reside on the surface of the (constantly expanding at the speed of light; ''c'' = 1 Planck length / 1 Planck time) universe, and so the 'past' could be retained, for the past cannot be over-written by the present in an expanding universe (if ''now'' is always on the surface). As this expansion occurs at the Planck scale, information even below quantum states, down to the Planck scale, can be retained, the analogy would be the storing of every [[w:Keystroke_logging |keystroke]], a Planck scale version of the [[w:Akashic records |Akashic records]] ... for if our deeds (the past) are both stored and cannot be over-written (by the present), then we have a candidate for the '[[w:karma |karmic]] heavens' (Matthew 6:19 ''But lay up for yourselves treasures in 'heaven', where neither moth nor rust doth corrupt, and where thieves do not break through nor steal''). This also forms a universe '''time-line''' against which previous information can be compared with new information (a 'memory' of events), without which we could not link cause with effect. === Singularity === In a simulation, the data (software) requires a storage device that is ultimately hardware (RAM, HD ...). In a data world of 1's and 0's such as a computer game, characters within that game may analyze other parts of their 1's and 0's game, but they have no means to analyze the hard disk upon which they (and their game) are stored, for the hard disk is an electro-mechanical device, it is not part of their 1's and 0's world, it is a part of the 'real world', the world of their Programmer. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may or may not resemble the laws that operate in the 'real world' (the world of their Programmer). Thus any region where the laws of physics (the laws of their game world) break down would be significant. A [[w:singularity |singularity]] inside a black hole is such a region <ref>https://www.youtube.com/watch?v=W5j7umtZYB4 a black hole singularity as the interface between worlds</ref>. For the [[w:black hole electron |black-hole electron]], its black-hole center would then be analogous to a storage address on a hard disk, the interface between the simulation world and the real world. A massive (galactic) black-hole could be as an entire data sector. The surface of the black-hole would then be of the simulation world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however would be the interface between the data world and the 'hard disk' of the real world, and so would not exist in any 'physical' terms. It is external to the simulation. As analogy, we may discuss the 3-D surface area of a black-hole but not its volume (interior). === Laws of Physics === The scientific method is built upon testable hypothesis and reproducible results. Water always boils (in defined conditions), at 100°C. In a geometrical universe particles will behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these repeating patterns, the more complex the orbits, the more complex the formulas required to describe them and so forth. However if there is a source code from which these geometrical conditions were programmed, then there may also be non-repeating events, back-doors built into the code (a common practice by terrestrial programmers), these by definition would lie outside the laws of physics and so be labelled as miracles, yet they would be no less valid. === Determinism === [[File:Three body problem figure-8 orbit animation.gif|400px|thumb|An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259.<ref>Here the gravitational constant ''G'' has been set to 1, and the initial conditions are '''r'''₁(0) = −'''r'''₃(0) = (−0.97000436, 0.24308753); '''r'''₂(0) = (0,0); '''v'''₁(0) = '''v'''₃(0) = (0.4662036850, 0.4323657300); '''v'''₂(0) = (−0.93240737, −0.86473146). The values are obtained from Chenciner & Montgomery (2000).</ref>]] Particles form more complex structures such as atoms and molecules via a system of orbitals; nuclear, atomic and gravitational. The [[w:Three-body_problem |3-body problem]] is the problem of taking the initial positions and velocities (or [[w:momentum|momenta |momentum|momenta]]) of three or more point masses and solving for their subsequent motion according to [[w:Newton's laws of motion |Newton's laws of motion]] and [[w:Newton's law of universal gravitation |Newton's law of universal gravitation]].<ref name="PrincetonCompanion">{{Citation | last = Barrow-Green | first = June | year = 2008 | title = The Three-Body Problem | editor-last1 = Gowers | editor-first1 = Timothy | editor-last2 = Barrow-Green | editor-first2 = June | editor-last3 = Leader | editor-first3 = Imre | encyclopedia = The Princeton Companion to Mathematics | pages = 726–728 | publisher = Princeton University Press }}</ref>. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for gods and men alike the only way to know what that outcome will be is to run the simulation itself. ==Geometry coded universe== Modelling a Planck scale simulation universe using geometrical forms (links) * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass == External links == * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] * [https://philpapers.org/rec/GRUTIA-2 Simulation theory as evidence for God] (academic peer-reviewed article) ==References== {{Reflist}} [[Category:Philosophy| ]] [[Category:Philosophy of science| ]] cncte3carzu0n0njutuyg9m7yyw22nb 2718262 2718261 2025-06-10T19:52:26Z 212.200.164.104 /* Singularity */ 2718262 wikitext text/x-wiki '''Is God a Programmer? analyzing the deep-universe simulation hypothesis at the Planck scale''' The [[w:simulation hypothesis |simulation hypothesis]] is the proposal that all of reality, including the Earth and the rest of the universe, could be an artificial simulation, such as a computer simulation. [[w:Neil_deGrasse_Tyson |Neil deGrasse Tyson]] put the odds at 50-50 that our entire existence is a program on someone else’s hard drive <ref>Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. [[w:David_Chalmers |David Chalmers]] noted “We in this universe can create simulated worlds and there’s nothing remotely spooky about that. Our creator isn’t especially spooky, it’s just some teenage hacker in the next universe up. Turn the tables, and we are essentially gods over our own computer creations <ref>https://www.youtube.com/watch?v=yqbS5qJU8PA, David Chalmers, Serious Science</ref> <ref>The Matrix as Metaphysics, David Chalmers http://consc.net/papers/matrix.pdf</ref> <ref>Are We Living in a Computer Simulation?https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. The commonly postulated [[w:Ancestor_simulation |ancestor simulation]] approach, which [[w:Nick Bostrom |Nick Bostrom]] called "the simulation argument", argues for "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor. However this simulation variant can be traced back to an 'organic base reality' (the original programmer ancestors and their physical planet). The [[v:God_(programmer) |Programmer God]] hypothesis<ref>https://codingthecosmos.com/podcast/ AI generated podcasts</ref> conversely states that a (deep universe) simulation began with the big bang and was programmed by an external intelligence (external to the physical universe), the Programmer by definition a God in the creator of the universe context. Our universe in its entirety, down to the smallest detail, and including life-forms, is within the simulation, the laws of nature, at their most fundamental level, are coded rules running on top of the simulation operating system. The operating system itself is mathematical (and potentially the origin of mathematics). Any candidate for a Programmer-God simulation-universe source code must satisfy these conditions; :1. It can generate physical structures from mathematical forms. :2. The sum universe is dimensionless (simply data on a celestial hard disk). :3. We must be able to use it to derive the laws of physics (because the source code is the origin of the laws of nature, and the laws of physics are our observations of the laws of nature). :4. The mathematical logic must be unknown to us (the Programmer is a non-human intelligence). :5. The coding should have an 'elegance' commensurate with the Programmer's level of skill. == Philosophy == Physicist [[w:Eugene Wigner |Eugene Wigner]] ([[w:The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences |The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]) <ref>{{Cite journal | last1 = Wigner | first1 = E. P. | authorlink = Eugene Wigner| doi = 10.1002/cpa.3160130102 | title = The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959 | journal = Communications on Pure and Applied Mathematics | volume = 13 | pages = 1–14 | year = 1960 | pmid = | pmc = |bibcode = 1960CPAM...13....1W }}</ref> <blockquote>The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. </blockquote> === Discussion === [[w:Philosophy of mathematics |Philosophy of mathematics]] is that branch of philosophy which attempts to answer questions such as: ‘why is mathematics useful in describing nature?’, ‘in which sense, if any, do mathematical entities such as numbers exist?’ and ‘why and how are mathematical statements true?’ This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math. Mathematical realism holds that mathematical entities exist independently of the human mind. We do not invent mathematics, but rather discover it. Triangles, for example, are real entities that have an existence <ref>- http://plato.stanford.edu/entries/platonism-mathematics/</ref>. The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality. It can be considered a form of [[w:Pythagoreanism | Pythagoreanism]] or [[w:Platonism | Platonism]] in that it proposes the existence of ''mathematical objects''; and a form of [[w:philosophy of mathematics | mathematical monism]] in that it denies that anything exists except these ''mathematical objects''. Physicist [[w:Max Tegmark | Max Tegmark]] in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality"<ref name="Tegmark1998">{{cite journal|last=Tegmark |first=Max |date=November 1998 |title=Is "the Theory of Everything" Merely the Ultimate Ensemble Theory? |journal=Annals of Physics |volume=270 |issue=1 |pages=1–51 |doi=10.1006/aphy.1998.5855 |arxiv = gr-qc/9704009 |bibcode = 1998AnPhy.270....1T }}</ref><ref>M. Tegmark 2014, "[http://mathematicaluniverse.org Our Mathematical Universe]", Knopf</ref> proposed that ''Our external physical reality is a mathematical structure''.<ref name="Tegmark2008">{{cite journal|last=Tegmark |first=Max |date=February 2008 |title=The Mathematical Universe |journal=Foundations of Physics |volume=38 |issue=2 |pages=101–150 |doi=10.1007/s10701-007-9186-9 |arxiv=0704.0646|bibcode = 2008FoPh...38..101T }}</ref> That is, the physical universe is not merely ''described by'' mathematics, but ''is'' mathematics (specifically, a [[w:mathematical structure | mathematical structure]]). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref> The principle constraints to any mathematical universe simulation hypothesis are; 1. the computational resources required. The ancestor simulation can resolve this by adapting from the [[w:virtual rality |virtual reality]] approach where only the observable region is simulated and only to the degree required, and 2. that any 'self-aware structures' (humans for example) within the simulation must "subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref>. Succinctly, our computer games may be able to simulate our physical world, but they are still only simulations of a physical reality (regardless of how realistic they may seem) ... we are not yet able to program actual physical dimensions of mass, space and time from mathematical structures, and indeed this may not be possible with a computer hard-ware architecture that can only process binary data. === Deep-universe source code === As a deep-universe simulation is programmed by an external (external to the universe) intelligence (the Programmer God hypothesis), we cannot presume a priori knowledge regarding the simulation source code other than from this code the laws of nature emerged, and so any deep-universe simulation model we try to emulate must be universal, i.e.: independent of any system of units, of the [[w:Dimensional_analysis |dimensioned]] [[w:physical constants |physical constants]] (''G'', ''h'', ''c'', ''e'' .. ), and of any numbering systems. Furthermore, although a deep-universe simulation source code may use mathematical forms (circles, spheres ...) we are familiar with (for ultimately the source code is the origin of these forms), it will have been developed by a non-human intelligence and so we may have to develop new mathematical tools to decipher the underlying logic. By implication therefore, any theoretical basis for a source code that fits the above criteria (and from which the laws of nature will emerge), could be construed as our first tangible evidence of a non-human intelligence. === Constants === A physical universe is characterized by measurable quantities (size, mass, color, texture ...), and so a physical universe can be measured and defined. Contrast then becomes information, the statement ''this is a big apple'' requires a ''small apple'' against which big becomes a relative term. For analytical purposes we select a reference value, for example 0C or 32F, and measure all temperatures against this reference. The smaller the resolution of the measurements, the greater the information content (the file size of a 32 mega-pixel photo is larger than a 4 mega-pixel photo). A simulation universe may be presumed to also have a resolution dictating how much information the simulation can store and manipulate. To measure the fundamental parameters of our universe physics uses [[w:physical constant |physical constants]]. A physical constant is a [[w:physical quantity |physical quantity]] that is generally believed to be both universal in nature and have a constant value in time. These can be divided into 1) dimension-ed (measured using physical units ''kg'', ''m'', ''s'', ''A'' ...) such as the [[w:speed of light |speed of light]] ''c'', [[w:gravitational constant |gravitational constant]] ''G'', [[w:Planck constant |Planck constant]] ''h'' ... as in the table {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} Physicist [[w: |Lev Okun]] noted "Theoretical equations describing the physical world deal with dimensionless quantities and their solutions depend on dimensionless fundamental parameters. But experiments, from which these theories are extracted and by which they could be tested, involve measurements, i.e. comparisons with standard dimension-ful scales. Without standard dimension-ful units and hence without certain conventions physics is unthinkable <ref>Michael J. Duff et al, Journal of High Energy Physics, Volume 2002, JHEP03(2002)</ref>. 2) dimension-less, such as the [[w:Fine-structure_constant |fine structure constant]] ''α''. A dimension-less constant does not measure any physical quantity (it has no units; units = 1). 3) dimension-less [[w:mathematical constant |mathematical constants]], most notably [[w:pi |pi]] = 3.14159265358979 and [[w:Natural_logarithm |e]] = 2.718281828459. Although these are [[w:transcendental number |transcendental numbers]], they can be constructed by integers in a series, and so for a universe expanding incrementally (see simulation time), these constants could be formed within the simulation. For example, at time ''t''; <math display=block>t = 1; \frac{\pi^2}{6} = \frac{1}{t^2} </math> <math display=block>t = 2; \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{t^2}</math> <math display=block>t = now: \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots + \frac{1}{t^2} </math> We may now define the fundamental physical constant as a parameter specifically chosen by the Programmer and is encoded into the simulation code directly, and so whilst it may be inferable, it is not derived from other constants ([[w:Fine-structure_constant#Numerological_explanations_and_multiverse_theory |Richard Feynman on the fine structure constant]]). It should also be dimension-less otherwise the simulation itself becomes dimensioned (if the simulation is running on a celestial computer it is merely data, it has no physical size or shape or ...), and so the dimensioned constants (''G'', ''h'', ''c'', ''e''...) must all be derivable (derived from within the simulation) via the (embedded in the source code) fundamental physical constants (of which the fine structure constant alpha may be an example). Although [[w:pi |pi]] and [[w:Natural_logarithm |e]] are dimensionless, they can be derived internally (from integers), and as they have application in the mathematical realm, they can be referred to as mathematical constants. ==== Planck scale ==== The [[w:Planck scale |Planck scale]] refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the [[w:Standard Model |Standard Model]], [[w:quantum field theory |quantum field theory]] and [[w:general relativity |general relativity]] are no longer reconcilable, and [[w:Quantum Gravity |quantum effects of gravity]] are expected to dominate (quantum gravitational effects only appear at length scales near the Planck scale). Although particles may not be cognizance of our 'laws of physics', they do know the 'laws of nature'. These laws of nature would run directly off the universe OS (operating system), and so below this OS, 'physics' as we know it must necessarily break down. At present the Planck scale is the lowest known level, consequently any attempt to detect evidence of an underlying simulation coding must consider (if not actually begin at) this, the Planck scale<ref>https://www.youtube.com/watch?v=AMQRXGYCDrY Planck scale, Brian Greene</ref>. The [[w:International_System_of_Units |SI units]] for the dimension-ful mksa units are; meter (length), kilogram (mass), second (time), ampere (electric current). There are Planck units that represent these SI units, and so a simulation could use them as discrete building blocks; [[w:Planck length |Planck length]] (the smallest possible unit of length), [[w:Planck mass |Planck mass]] (the unit of mass), [[w:Planck time |Planck time]] (the smallest possible unit of time), [[w:Planck charge |Planck charge]] (the unit of charge). The speed of light then becomes ''c'' = 1 Planck length / 1 Planck time. These units would define the resolution and so information carrying capacity of the simulation universe. ==== Numbering systems ==== As well as our decimal system, computers apply binary and hexadecimal numbering systems. In particular the decimal and hexadecimal are of terrestrial origin and may not be considered 'universal'. Furthermore numbering systems measure only the frequency of an event and contain no information as to the event itself. The number 299 792 458 could refer to the speed of light (299 792 458 m/s) or could equally be referring to the number of apples in a container (299 792 458 apples). As such, numbers require a 'descriptive', whether m/s or apples. Numbers also do not include their history, is 299 792 458 for example a derivation of other base numbers? Present universe simulations use the laws of physics and the physical constants are built in, however both these laws and the physical constants are known only to a limited precision, and so a simulation with 10⁶² iterations (the present age of the universe in units of Planck time) will accumulate errors. Number based computing may be sufficient for ancestor-simulation models where only the observed region needs to be calculated, but has inherent limitations for deep universe simulations where the entire universe is continuously updated. The actual computational requirements for a Planck scale universe simulation based on a numbering system with the laws of physics embedded would be an unknown and consequently lead to an 'non-testable' hypothesis. This is a commonly applied reasoning for rejecting the deep universe simulation. ==== Geometrical objects ==== A mathematical constant such as [[w:pi |pi]] refers to a geometrical construct (the ratio of circle circumference to circle radius) and so is not constrained by any particular numbering system (in the decimal system π = 3.14159...), and so may be considered both universal and eternal. Likewise, by assigning geometrical objects instead of numbers to the Planck units, the problems with a numbering system can be resolved. These objects would however have to fulfill the following conditions; 1) embedded attribute - for example the object for length must embed the function of ''length'' such that a descriptive (km, mile ... ) is not required. Electron wavelength would then be measurable in terms of the length object, as such the length object must be embedded within the electron (the electron object). Although the mass object would incorporate the function ''mass'', the time object the function ''time'' ..., it is not necessary that there be an individual physical mass or physical length or physical time ..., but only that in relation to the other units, the object must express that function (i.e.: the mass object has the function of mass when in the presence of the objects for space and time). The electron could then be a complex event (complex geometrical object) constructed by combining the objects for mass, length, time and charge into 1 event, and thus electron charge, wavelength, frequency and mass would then be different aspects of that 1 geometry (the electron event) and not independent parameters (independent of each other). 2) The objects for mass, length, time and charge must be able to combine with each other [[w:Lego |Lego-style]] to form more complex objects (events) such as electrons and apples whilst still retaining the underlying information (the mass of the apple derives from the mass objects embedded within that apple). Not only must these objects be able to form complex events such as particles, but these events themselves are geometrical objects and so must likewise function according to their geometries. Electrons would orbit protons according to their respective electron and proton geometries, these orbits the result of geometrical imperatives and not due to any built-in laws of physics (the orbital path is a consequence of all the underlying geometries). However, as orbits follow regular and repeating patterns, they can be described (by us) using mathematical formulas. As the events grow in complexity (from atoms to molecules to planets), so too will the patterns (and likewise the formulas we use to describe them). Consequently the ''laws of physics'' would then become our mathematical descriptions of the underlying geometrically imposed patterns. 3) These objects would replace coded instructions (the instruction sets would be built into the objects) thereby instigating a geometrically autonomous universe. The electron 'knows' what to do by virtue of the information encoded within its geometry, no coded electron CALL FUNCTION is required. This would be equivalent to combining the hardware, software and CPU together such that the 'software' changes (adjusts) to the changing 'hardware' (DNA may be an analogy). Note: A purely mathematical universe has no limits in size and can be infinitely large and infinity small. A geometrical universe (that uses objects) has limitations, it can be no smaller than the smallest object for example and has discrete parts (those objects). The philosophy of the TOE (theory of everything) therefore includes a debate between the mathematical universe and the geometrical universe, however this distinction between mathematical and geometrical would only be apparent at the Planck scale. === Evidence of a simulation === The laws of physics are our incomplete observations of the natural universe, and so evidence of a simulation may be found in ambiguities or anomalies within these laws. Furthermore, if complexity arises over time, then at unit time the 'handiwork' of the Programmer may be notable by a simplicity and elegance of the geometries employed ... for the Programmer by definition has God-level programming skills. Here is a notable example. Mass, space and time from the number 1 The dimensions of mass, space and time are considered by science to be independent of each other, we cannot measure the ''distance'' from Tokyo to London using kilograms and amperes, or measure ''mass'' using space and time. Indeed, what characterizes a physical universe as opposed to a simulated universe is the notion that there is a fundamental structure underneath, that in some sense mass 'is', that time 'is' and space 'is' ... thus we cannot write ''kg'' in terms of ''m'' and ''s''. To do so would render our concepts of a physical universe meaningless. The 26th General Conference on Weights and Measures ([[w:2019 redefinition of SI base units|2019 redefinition of SI base units]]) assigned exact numerical values to 4 physical constants (''h, c, e, k''_B) independently of each other (and thereby confirming these as fundamental constants), and as they are measured in SI units ('''kg''', '''m''', '''s''', '''A''', '''K'''), these units must also be independent of each other (i.e.: these are fundamental units, for example if we could define ''m'' using ''A'' then the speed of light could be derived from, and so would depend upon, the value for the elementary charge ''e'', and so the value for ''c'' could not be assigned independently from ''e''). {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} We are familiar with inverse properties; plus charge and minus charge, matter and anti-matter ... and we can observe how these may form and/or cancel each other. A simulation universe however is required to be dimensionless (in sum total), for the simulated universe does not 'exist' in any physical sense outside of the 'Computer' (it is simply data on a celestial hard-disk). Our universe does not appear to have inverse properties such as anti-mass (-kg), anti-time (-s) or anti-space (anti-length -m), therefore the first problem the Programmer must solve is how to create the physical scaffolding (of mass, space and time). For example, the Programmer can start by selecting 2 dimensioned quantities, here are used ''r'', ''v'' <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref> such that :<math>kg = \frac{r^4}{v},\; m = \frac{r^9}{v^5},\; s = \frac{r^9}{v^6},\; A = \frac{v^3}{r^6}</math> Quantities ''r'' and ''v'' are chosen so that no unit (''kg'', ''m'', ''s'', ''A'') can cancel another unit (i.e.: the ''kg'' cannot cancel the ''m'' or the ''s'' ...), and so we have 4 independent units (we still cannot define the ''kg'' using the ''m'' or the ''s'' ...), however if 3 (or more) units are combined together in a specific ratio, they can cancel (in a certain ratio our ''r'' and ''v'' become inverse properties and so cancel each other; units = 1). <math>f_X = \frac{kg^9 s^{11}}{m^{15}} = \frac{(\frac{r^4}{v})^9 (\frac{r^9}{v^6})^{11}}{(\frac{r^9}{v^5})^{15}} = 1</math> This f_X, although embedded within are the dimensioned structures for mass, time and length (in the above ratio), would be a dimensionless mathematical structure, units = 1. Thus we may create as much mass, time and length as we wish, the only proviso being that they are created in f_X ratios, so that regardless of how massive, old and large our universe becomes, it is still in sum total dimensionless. Defining the dimensioned quantities ''r'', ''v'' in SI unit terms. :<math>r = (\frac{kg\;m}{s})^{1/4}</math> :<math>v = \frac{m}{s}</math> Mass :<math>\frac{r^4}{v} = (\frac{kg\;m}{s})\;(\frac{s}{m}) = kg</math> Length :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^5})^4 = \frac{s^{20}}{m^{20}}</math> :<math>(\frac{r^9}{v^5})^4 = \frac{kg^9 s^{11}}{m^{11}} = m^4 \frac{kg^9 s^{11}}{m^{15}} = m^4 f_X = m^4</math> Time :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^6})^4 = \frac{s^{24}}{m^{24}}</math> :<math>(\frac{r^9}{v^6})^4 = \frac{kg^9 s^{15}}{m^{15}} = s^4 \frac{kg^9 s^{11}}{m^{15}} = s^4 f_X = s^4</math> And so, although f_X is a dimensionless mathematical structure, we can embed within it the (mass, length, time ...) structures along with their dimensional attributes (kg, m, s, A ..). In the mathematical electron model (discussed below), the electron itself is an example of an f_X structure, it (f_electron) is a dimensionless geometrical object that embeds the physical electron parameters of wavelength, frequency, charge (note: A-m = ampere-meter are the units for a [[w:Magnetic_monopole#In_SI_units |magnetic monopole]]). <math>f_{electron}</math> :<math>units = \frac{A^3 m^3}{s} = \frac{(\frac{v^3}{r^6})^3 (\frac{r^9}{v^5})^3}{(\frac{r^9}{v^6})} = 1</math> We may note that at the macro-level (of planets and stars) these f_X ratio are not found, and so this level is the domain of the observed physical universe, however at the quantum level, f_X ratio do appear, f_electron as an example, the mathematical and physical domains then blurring. This would also explain why physics can measure precisely the parameters of the electron (wavelength, mass ...), but has never found the electron itself. == Programming == “God vs. science debates tend to be restricted to the premise that a God does not rely on science and that science does not need a God. As science and God are thus seen as mutually exclusive there are few, if any, serious attempts to construct mathematical models of a universe whose principle axiom does require a God. However, if there is an Intelligence responsible for the 14 billion year old universe of modern physics, being the universe of Einstein and Dirac, and beginning with the big bang as the act of 'creation', then we must ask how it might be done? What construction technique could have been used to set the laws of physics in motion?” <ref>[https://theprogrammergod.com/ The Programmer God, are we in a Simulation]</ref> === Simulation Time === The (dimensionless) simulation clock-rate would be defined as the minimum 'time variable' ('''age''') increment to the simulation. Using a simple loop as analogy, at ''age'' = 1, the simulation begins (the big bang), certain processes occur, when these are completed ''age'' increments (''age'' = 2, then 3, then 4 ... ) until ''age'' reaches ''the_end'' and the simulation stops. 'begin simulation FOR age = 1 TO the_end 'big bang = 1 conduct certain processes ........ NEXT age 'end simulation [[w:Quantum spacetime |Quantum spacetime]] and [[w:Quantum gravity |Quantum gravity]] models refer to [[w:Planck time | Planck time]] as the smallest discrete unit of time and so the incrementing variable '''age''' could be used to generate units of Planck time (and other Planck units, the physical scaffolding of the universe). In a geometrical model, to these Planck units could be assigned geometrical objects, for example; Initialize_physical_constants; FOR age = 1 TO the_end generate 1 unit of (Planck) time; '1 time 'object' T generate 1 unit of (Planck) mass; '1 mass 'object' M generate 1 unit of (Planck) length; '1 length 'object' L ........ NEXT age The variable ''age'' is the simulation clock-rate, it is simply a counter (1, 2, 3 ...) and so is a dimensionless number, the object T is the geometrical Planck time object, it is dimensioned and is measured by us in seconds. If ''age'' is the origin of Planck time (1 increment to ''age'' generates 1 T object) then ''age'' = 10⁶², this is based on the present [[w:Age_of_the_universe |age of the universe]], which, at 14 billion years, equates to 10⁶² units of Planck time. For each ''age'', certain operations are performed, only after they are finished does ''age'' increment (there is no ''time'' interval between increments). As noted, ''age'' being dimensionless, is not the same as dimensioned Planck time which is the geometrical object T, and this T, being dimensioned, can only appear within the simulation. The analogy would be frames of a movie, each frame contains dimensioned information but there is no ''time'' interval between frames. FOR age = 1 TO the_end (of the movie) display frame{age} NEXT age Although operations (between increments to ''age'') may be extensive, self-aware structures from within the simulation would have no means to determine this, they could only perceive themselves as being in a real-time (for them the smallest unit of ''time'' is 1T, just as the smallest unit of ''time'' in a movie is 1 frame). Their (those self-aware structures) dimension of time would then be a measure of relative motion (a change of state), and so although ultimately deriving from the variable ''age'', their time would not be the same as ''age''. If there was no motion, if all particles and photons were still (no change of state), then their time dimension could not update (if every frame in a movie was the same then actors within that movie could not register a change in time), ''age'' however would continue to increment. Thus we have 3 time structures; 1) the dimension-less simulation clock-rate variable ''age'', 2) the dimensioned time unit (object T), and 3) time as change of state (the observers time). Observer time requires a memory of past events against which a change of state can be perceived. The forward increment to ''age'' would constitute the [[w:arrow of time |arrow of time]]. Reversing this would reverse the arrow of time, the universe would likewise shrink in size and mass accordingly (just as a [[w:white hole |white hole]] is the (time) reversal of a [[w:black hole |black hole]]). FOR age = the_end TO 1 STEP -1 delete 1 unit of Planck time; delete 1 unit of Planck mass; delete 1 unit of Planck length; ........ NEXT age Adding mass, length and time objects per increment to ''age'' would force the universe expansion (in size and mass), and as such an anti-gravitational [[w:dark energy |dark energy]] would not be required, however these objects are dimensioned and so are generated within the simulation. This means that they must somehow combine in a specific ratio whereby they (the units for mass length, time, charge; ''kg'', ''m'', ''s'', ''A'') in sum total cancel each other, leaving the sum universe (the simulation itself) residing on that celestial hard-disk. We may introduce a theoretical dimensionless (f_X) geometrical object denoted as f_Planck within which are embedded the dimensioned objects MLTA (mass, length, time, charge), and from which they may be extracted. FOR age = 1 TO the_end add 1 f_Planck 'dimensionless geometrical 'object' { extract 1 unit of (Planck) time; '1 time 'object' T extract 1 unit of (Planck) mass; '1 mass 'object' M extract 1 unit of (Planck) length; '1 length 'object' L } ........ NEXT age This then means that the simulation, in order to create time T, must also create mass M and space L (become larger and more massive). Thus no matter how small or large the physical universe is (when seen internally), in sum total (when seen externally), there is no universe - it is merely data without physical form. === Universe time-line === As the universe expands outwards (through the constant addition of units of mass and length via f_Planck), and if this expansion pulls particles with it (if it is the origin of motion), then ''now'' (the present) would reside on the surface of the (constantly expanding at the speed of light; ''c'' = 1 Planck length / 1 Planck time) universe, and so the 'past' could be retained, for the past cannot be over-written by the present in an expanding universe (if ''now'' is always on the surface). As this expansion occurs at the Planck scale, information even below quantum states, down to the Planck scale, can be retained, the analogy would be the storing of every [[w:Keystroke_logging |keystroke]], a Planck scale version of the [[w:Akashic records |Akashic records]] ... for if our deeds (the past) are both stored and cannot be over-written (by the present), then we have a candidate for the '[[w:karma |karmic]] heavens' (Matthew 6:19 ''But lay up for yourselves treasures in 'heaven', where neither moth nor rust doth corrupt, and where thieves do not break through nor steal''). This also forms a universe '''time-line''' against which previous information can be compared with new information (a 'memory' of events), without which we could not link cause with effect. === Singularity === In a simulation, the data (software) requires a storage device that is ultimately hardware (RAM, HD ...). In a data world of 1's and 0's such as a computer game, characters within that game may analyze other parts of their 1's and 0's game, but they have no means to analyze the hard disk upon which they (and their game) are stored, for the hard disk is an electro-mechanical device, it is not part of their 1's and 0's world, it is a part of the 'real world', the world of their Programmer. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may or may not resemble the laws that operate in the 'real world' (the world of their Programmer). Thus any region where the laws of physics (the laws of their game world) break down would be significant. A [[w:singularity |singularity]] inside a black hole is such a region <ref>https://www.youtube.com/watch?v=W5j7umtZYB4 a black hole singularity as the interface between worlds</ref>. For the [[w:black hole electron |black-hole electron]], its black-hole center would then be analogous to a storage address on a hard disk, the interface between the simulation world and the real world. A massive (galactic) black-hole could be as an entire data sector. The surface of the black-hole would then be of the simulation world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however would be the interface between the data world and the 'hard disk' of the real world, and so would not exist in any 'physical' terms. It is external to the simulation. As analogy, we may discuss the 3-D surface area of a black-hole but not its volume (interior). === Laws of Physics === The scientific method is built upon testable hypothesis and reproducible results. Water always boils (in defined conditions), at 100°C. In a geometrical universe particles will behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these repeating patterns, the more complex the orbits, the more complex the formulas required to describe them and so forth. However if there is a source code from which these geometrical conditions were programmed, then there may also be non-repeating events, back-doors built into the code (a common practice by terrestrial programmers), these by definition would lie outside the laws of physics and so be labelled as miracles, yet they would be no less valid. === Determinism === [[File:Three body problem figure-8 orbit animation.gif|400px|thumb|An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259.<ref>Here the gravitational constant ''G'' has been set to 1, and the initial conditions are '''r'''₁(0) = −'''r'''₃(0) = (−0.97000436, 0.24308753); '''r'''₂(0) = (0,0); '''v'''₁(0) = '''v'''₃(0) = (0.4662036850, 0.4323657300); '''v'''₂(0) = (−0.93240737, −0.86473146). The values are obtained from Chenciner & Montgomery (2000).</ref>]] Particles form more complex structures such as atoms and molecules via a system of orbitals; nuclear, atomic and gravitational. The [[w:Three-body_problem |3-body problem]] is the problem of taking the initial positions and velocities (or [[w:momentum|momenta |momentum|momenta]]) of three or more point masses and solving for their subsequent motion according to [[w:Newton's laws of motion |Newton's laws of motion]] and [[w:Newton's law of universal gravitation |Newton's law of universal gravitation]].<ref name="PrincetonCompanion">{{Citation | last = Barrow-Green | first = June | year = 2008 | title = The Three-Body Problem | editor-last1 = Gowers | editor-first1 = Timothy | editor-last2 = Barrow-Green | editor-first2 = June | editor-last3 = Leader | editor-first3 = Imre | encyclopedia = The Princeton Companion to Mathematics | pages = 726–728 | publisher = Princeton University Press }}</ref>. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for gods and men alike the only way to know what that outcome will be is to run the simulation itself. ==Geometry coded universe== Modelling a Planck scale simulation universe using geometrical forms (links) * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass == External links == * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] * [https://philpapers.org/rec/GRUTIA-2 Simulation theory as evidence for God] (academic peer-reviewed article) ==References== {{Reflist}} [[Category:Philosophy| ]] [[Category:Philosophy of science| ]] 7iqsbl7rj9bhy1raudkmm4i7gs5bfh6 2718263 2718262 2025-06-10T19:52:34Z 212.200.164.104 /* Laws of Physics */ 2718263 wikitext text/x-wiki '''Is God a Programmer? analyzing the deep-universe simulation hypothesis at the Planck scale''' The [[w:simulation hypothesis |simulation hypothesis]] is the proposal that all of reality, including the Earth and the rest of the universe, could be an artificial simulation, such as a computer simulation. [[w:Neil_deGrasse_Tyson |Neil deGrasse Tyson]] put the odds at 50-50 that our entire existence is a program on someone else’s hard drive <ref>Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. [[w:David_Chalmers |David Chalmers]] noted “We in this universe can create simulated worlds and there’s nothing remotely spooky about that. Our creator isn’t especially spooky, it’s just some teenage hacker in the next universe up. Turn the tables, and we are essentially gods over our own computer creations <ref>https://www.youtube.com/watch?v=yqbS5qJU8PA, David Chalmers, Serious Science</ref> <ref>The Matrix as Metaphysics, David Chalmers http://consc.net/papers/matrix.pdf</ref> <ref>Are We Living in a Computer Simulation?https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. The commonly postulated [[w:Ancestor_simulation |ancestor simulation]] approach, which [[w:Nick Bostrom |Nick Bostrom]] called "the simulation argument", argues for "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor. However this simulation variant can be traced back to an 'organic base reality' (the original programmer ancestors and their physical planet). The [[v:God_(programmer) |Programmer God]] hypothesis<ref>https://codingthecosmos.com/podcast/ AI generated podcasts</ref> conversely states that a (deep universe) simulation began with the big bang and was programmed by an external intelligence (external to the physical universe), the Programmer by definition a God in the creator of the universe context. Our universe in its entirety, down to the smallest detail, and including life-forms, is within the simulation, the laws of nature, at their most fundamental level, are coded rules running on top of the simulation operating system. The operating system itself is mathematical (and potentially the origin of mathematics). Any candidate for a Programmer-God simulation-universe source code must satisfy these conditions; :1. It can generate physical structures from mathematical forms. :2. The sum universe is dimensionless (simply data on a celestial hard disk). :3. We must be able to use it to derive the laws of physics (because the source code is the origin of the laws of nature, and the laws of physics are our observations of the laws of nature). :4. The mathematical logic must be unknown to us (the Programmer is a non-human intelligence). :5. The coding should have an 'elegance' commensurate with the Programmer's level of skill. == Philosophy == Physicist [[w:Eugene Wigner |Eugene Wigner]] ([[w:The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences |The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]) <ref>{{Cite journal | last1 = Wigner | first1 = E. P. | authorlink = Eugene Wigner| doi = 10.1002/cpa.3160130102 | title = The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959 | journal = Communications on Pure and Applied Mathematics | volume = 13 | pages = 1–14 | year = 1960 | pmid = | pmc = |bibcode = 1960CPAM...13....1W }}</ref> <blockquote>The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. </blockquote> === Discussion === [[w:Philosophy of mathematics |Philosophy of mathematics]] is that branch of philosophy which attempts to answer questions such as: ‘why is mathematics useful in describing nature?’, ‘in which sense, if any, do mathematical entities such as numbers exist?’ and ‘why and how are mathematical statements true?’ This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math. Mathematical realism holds that mathematical entities exist independently of the human mind. We do not invent mathematics, but rather discover it. Triangles, for example, are real entities that have an existence <ref>- http://plato.stanford.edu/entries/platonism-mathematics/</ref>. The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality. It can be considered a form of [[w:Pythagoreanism | Pythagoreanism]] or [[w:Platonism | Platonism]] in that it proposes the existence of ''mathematical objects''; and a form of [[w:philosophy of mathematics | mathematical monism]] in that it denies that anything exists except these ''mathematical objects''. Physicist [[w:Max Tegmark | Max Tegmark]] in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality"<ref name="Tegmark1998">{{cite journal|last=Tegmark |first=Max |date=November 1998 |title=Is "the Theory of Everything" Merely the Ultimate Ensemble Theory? |journal=Annals of Physics |volume=270 |issue=1 |pages=1–51 |doi=10.1006/aphy.1998.5855 |arxiv = gr-qc/9704009 |bibcode = 1998AnPhy.270....1T }}</ref><ref>M. Tegmark 2014, "[http://mathematicaluniverse.org Our Mathematical Universe]", Knopf</ref> proposed that ''Our external physical reality is a mathematical structure''.<ref name="Tegmark2008">{{cite journal|last=Tegmark |first=Max |date=February 2008 |title=The Mathematical Universe |journal=Foundations of Physics |volume=38 |issue=2 |pages=101–150 |doi=10.1007/s10701-007-9186-9 |arxiv=0704.0646|bibcode = 2008FoPh...38..101T }}</ref> That is, the physical universe is not merely ''described by'' mathematics, but ''is'' mathematics (specifically, a [[w:mathematical structure | mathematical structure]]). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref> The principle constraints to any mathematical universe simulation hypothesis are; 1. the computational resources required. The ancestor simulation can resolve this by adapting from the [[w:virtual rality |virtual reality]] approach where only the observable region is simulated and only to the degree required, and 2. that any 'self-aware structures' (humans for example) within the simulation must "subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref>. Succinctly, our computer games may be able to simulate our physical world, but they are still only simulations of a physical reality (regardless of how realistic they may seem) ... we are not yet able to program actual physical dimensions of mass, space and time from mathematical structures, and indeed this may not be possible with a computer hard-ware architecture that can only process binary data. === Deep-universe source code === As a deep-universe simulation is programmed by an external (external to the universe) intelligence (the Programmer God hypothesis), we cannot presume a priori knowledge regarding the simulation source code other than from this code the laws of nature emerged, and so any deep-universe simulation model we try to emulate must be universal, i.e.: independent of any system of units, of the [[w:Dimensional_analysis |dimensioned]] [[w:physical constants |physical constants]] (''G'', ''h'', ''c'', ''e'' .. ), and of any numbering systems. Furthermore, although a deep-universe simulation source code may use mathematical forms (circles, spheres ...) we are familiar with (for ultimately the source code is the origin of these forms), it will have been developed by a non-human intelligence and so we may have to develop new mathematical tools to decipher the underlying logic. By implication therefore, any theoretical basis for a source code that fits the above criteria (and from which the laws of nature will emerge), could be construed as our first tangible evidence of a non-human intelligence. === Constants === A physical universe is characterized by measurable quantities (size, mass, color, texture ...), and so a physical universe can be measured and defined. Contrast then becomes information, the statement ''this is a big apple'' requires a ''small apple'' against which big becomes a relative term. For analytical purposes we select a reference value, for example 0C or 32F, and measure all temperatures against this reference. The smaller the resolution of the measurements, the greater the information content (the file size of a 32 mega-pixel photo is larger than a 4 mega-pixel photo). A simulation universe may be presumed to also have a resolution dictating how much information the simulation can store and manipulate. To measure the fundamental parameters of our universe physics uses [[w:physical constant |physical constants]]. A physical constant is a [[w:physical quantity |physical quantity]] that is generally believed to be both universal in nature and have a constant value in time. These can be divided into 1) dimension-ed (measured using physical units ''kg'', ''m'', ''s'', ''A'' ...) such as the [[w:speed of light |speed of light]] ''c'', [[w:gravitational constant |gravitational constant]] ''G'', [[w:Planck constant |Planck constant]] ''h'' ... as in the table {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} Physicist [[w: |Lev Okun]] noted "Theoretical equations describing the physical world deal with dimensionless quantities and their solutions depend on dimensionless fundamental parameters. But experiments, from which these theories are extracted and by which they could be tested, involve measurements, i.e. comparisons with standard dimension-ful scales. Without standard dimension-ful units and hence without certain conventions physics is unthinkable <ref>Michael J. Duff et al, Journal of High Energy Physics, Volume 2002, JHEP03(2002)</ref>. 2) dimension-less, such as the [[w:Fine-structure_constant |fine structure constant]] ''α''. A dimension-less constant does not measure any physical quantity (it has no units; units = 1). 3) dimension-less [[w:mathematical constant |mathematical constants]], most notably [[w:pi |pi]] = 3.14159265358979 and [[w:Natural_logarithm |e]] = 2.718281828459. Although these are [[w:transcendental number |transcendental numbers]], they can be constructed by integers in a series, and so for a universe expanding incrementally (see simulation time), these constants could be formed within the simulation. For example, at time ''t''; <math display=block>t = 1; \frac{\pi^2}{6} = \frac{1}{t^2} </math> <math display=block>t = 2; \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{t^2}</math> <math display=block>t = now: \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots + \frac{1}{t^2} </math> We may now define the fundamental physical constant as a parameter specifically chosen by the Programmer and is encoded into the simulation code directly, and so whilst it may be inferable, it is not derived from other constants ([[w:Fine-structure_constant#Numerological_explanations_and_multiverse_theory |Richard Feynman on the fine structure constant]]). It should also be dimension-less otherwise the simulation itself becomes dimensioned (if the simulation is running on a celestial computer it is merely data, it has no physical size or shape or ...), and so the dimensioned constants (''G'', ''h'', ''c'', ''e''...) must all be derivable (derived from within the simulation) via the (embedded in the source code) fundamental physical constants (of which the fine structure constant alpha may be an example). Although [[w:pi |pi]] and [[w:Natural_logarithm |e]] are dimensionless, they can be derived internally (from integers), and as they have application in the mathematical realm, they can be referred to as mathematical constants. ==== Planck scale ==== The [[w:Planck scale |Planck scale]] refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the [[w:Standard Model |Standard Model]], [[w:quantum field theory |quantum field theory]] and [[w:general relativity |general relativity]] are no longer reconcilable, and [[w:Quantum Gravity |quantum effects of gravity]] are expected to dominate (quantum gravitational effects only appear at length scales near the Planck scale). Although particles may not be cognizance of our 'laws of physics', they do know the 'laws of nature'. These laws of nature would run directly off the universe OS (operating system), and so below this OS, 'physics' as we know it must necessarily break down. At present the Planck scale is the lowest known level, consequently any attempt to detect evidence of an underlying simulation coding must consider (if not actually begin at) this, the Planck scale<ref>https://www.youtube.com/watch?v=AMQRXGYCDrY Planck scale, Brian Greene</ref>. The [[w:International_System_of_Units |SI units]] for the dimension-ful mksa units are; meter (length), kilogram (mass), second (time), ampere (electric current). There are Planck units that represent these SI units, and so a simulation could use them as discrete building blocks; [[w:Planck length |Planck length]] (the smallest possible unit of length), [[w:Planck mass |Planck mass]] (the unit of mass), [[w:Planck time |Planck time]] (the smallest possible unit of time), [[w:Planck charge |Planck charge]] (the unit of charge). The speed of light then becomes ''c'' = 1 Planck length / 1 Planck time. These units would define the resolution and so information carrying capacity of the simulation universe. ==== Numbering systems ==== As well as our decimal system, computers apply binary and hexadecimal numbering systems. In particular the decimal and hexadecimal are of terrestrial origin and may not be considered 'universal'. Furthermore numbering systems measure only the frequency of an event and contain no information as to the event itself. The number 299 792 458 could refer to the speed of light (299 792 458 m/s) or could equally be referring to the number of apples in a container (299 792 458 apples). As such, numbers require a 'descriptive', whether m/s or apples. Numbers also do not include their history, is 299 792 458 for example a derivation of other base numbers? Present universe simulations use the laws of physics and the physical constants are built in, however both these laws and the physical constants are known only to a limited precision, and so a simulation with 10⁶² iterations (the present age of the universe in units of Planck time) will accumulate errors. Number based computing may be sufficient for ancestor-simulation models where only the observed region needs to be calculated, but has inherent limitations for deep universe simulations where the entire universe is continuously updated. The actual computational requirements for a Planck scale universe simulation based on a numbering system with the laws of physics embedded would be an unknown and consequently lead to an 'non-testable' hypothesis. This is a commonly applied reasoning for rejecting the deep universe simulation. ==== Geometrical objects ==== A mathematical constant such as [[w:pi |pi]] refers to a geometrical construct (the ratio of circle circumference to circle radius) and so is not constrained by any particular numbering system (in the decimal system π = 3.14159...), and so may be considered both universal and eternal. Likewise, by assigning geometrical objects instead of numbers to the Planck units, the problems with a numbering system can be resolved. These objects would however have to fulfill the following conditions; 1) embedded attribute - for example the object for length must embed the function of ''length'' such that a descriptive (km, mile ... ) is not required. Electron wavelength would then be measurable in terms of the length object, as such the length object must be embedded within the electron (the electron object). Although the mass object would incorporate the function ''mass'', the time object the function ''time'' ..., it is not necessary that there be an individual physical mass or physical length or physical time ..., but only that in relation to the other units, the object must express that function (i.e.: the mass object has the function of mass when in the presence of the objects for space and time). The electron could then be a complex event (complex geometrical object) constructed by combining the objects for mass, length, time and charge into 1 event, and thus electron charge, wavelength, frequency and mass would then be different aspects of that 1 geometry (the electron event) and not independent parameters (independent of each other). 2) The objects for mass, length, time and charge must be able to combine with each other [[w:Lego |Lego-style]] to form more complex objects (events) such as electrons and apples whilst still retaining the underlying information (the mass of the apple derives from the mass objects embedded within that apple). Not only must these objects be able to form complex events such as particles, but these events themselves are geometrical objects and so must likewise function according to their geometries. Electrons would orbit protons according to their respective electron and proton geometries, these orbits the result of geometrical imperatives and not due to any built-in laws of physics (the orbital path is a consequence of all the underlying geometries). However, as orbits follow regular and repeating patterns, they can be described (by us) using mathematical formulas. As the events grow in complexity (from atoms to molecules to planets), so too will the patterns (and likewise the formulas we use to describe them). Consequently the ''laws of physics'' would then become our mathematical descriptions of the underlying geometrically imposed patterns. 3) These objects would replace coded instructions (the instruction sets would be built into the objects) thereby instigating a geometrically autonomous universe. The electron 'knows' what to do by virtue of the information encoded within its geometry, no coded electron CALL FUNCTION is required. This would be equivalent to combining the hardware, software and CPU together such that the 'software' changes (adjusts) to the changing 'hardware' (DNA may be an analogy). Note: A purely mathematical universe has no limits in size and can be infinitely large and infinity small. A geometrical universe (that uses objects) has limitations, it can be no smaller than the smallest object for example and has discrete parts (those objects). The philosophy of the TOE (theory of everything) therefore includes a debate between the mathematical universe and the geometrical universe, however this distinction between mathematical and geometrical would only be apparent at the Planck scale. === Evidence of a simulation === The laws of physics are our incomplete observations of the natural universe, and so evidence of a simulation may be found in ambiguities or anomalies within these laws. Furthermore, if complexity arises over time, then at unit time the 'handiwork' of the Programmer may be notable by a simplicity and elegance of the geometries employed ... for the Programmer by definition has God-level programming skills. Here is a notable example. Mass, space and time from the number 1 The dimensions of mass, space and time are considered by science to be independent of each other, we cannot measure the ''distance'' from Tokyo to London using kilograms and amperes, or measure ''mass'' using space and time. Indeed, what characterizes a physical universe as opposed to a simulated universe is the notion that there is a fundamental structure underneath, that in some sense mass 'is', that time 'is' and space 'is' ... thus we cannot write ''kg'' in terms of ''m'' and ''s''. To do so would render our concepts of a physical universe meaningless. The 26th General Conference on Weights and Measures ([[w:2019 redefinition of SI base units|2019 redefinition of SI base units]]) assigned exact numerical values to 4 physical constants (''h, c, e, k''_B) independently of each other (and thereby confirming these as fundamental constants), and as they are measured in SI units ('''kg''', '''m''', '''s''', '''A''', '''K'''), these units must also be independent of each other (i.e.: these are fundamental units, for example if we could define ''m'' using ''A'' then the speed of light could be derived from, and so would depend upon, the value for the elementary charge ''e'', and so the value for ''c'' could not be assigned independently from ''e''). {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} We are familiar with inverse properties; plus charge and minus charge, matter and anti-matter ... and we can observe how these may form and/or cancel each other. A simulation universe however is required to be dimensionless (in sum total), for the simulated universe does not 'exist' in any physical sense outside of the 'Computer' (it is simply data on a celestial hard-disk). Our universe does not appear to have inverse properties such as anti-mass (-kg), anti-time (-s) or anti-space (anti-length -m), therefore the first problem the Programmer must solve is how to create the physical scaffolding (of mass, space and time). For example, the Programmer can start by selecting 2 dimensioned quantities, here are used ''r'', ''v'' <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref> such that :<math>kg = \frac{r^4}{v},\; m = \frac{r^9}{v^5},\; s = \frac{r^9}{v^6},\; A = \frac{v^3}{r^6}</math> Quantities ''r'' and ''v'' are chosen so that no unit (''kg'', ''m'', ''s'', ''A'') can cancel another unit (i.e.: the ''kg'' cannot cancel the ''m'' or the ''s'' ...), and so we have 4 independent units (we still cannot define the ''kg'' using the ''m'' or the ''s'' ...), however if 3 (or more) units are combined together in a specific ratio, they can cancel (in a certain ratio our ''r'' and ''v'' become inverse properties and so cancel each other; units = 1). <math>f_X = \frac{kg^9 s^{11}}{m^{15}} = \frac{(\frac{r^4}{v})^9 (\frac{r^9}{v^6})^{11}}{(\frac{r^9}{v^5})^{15}} = 1</math> This f_X, although embedded within are the dimensioned structures for mass, time and length (in the above ratio), would be a dimensionless mathematical structure, units = 1. Thus we may create as much mass, time and length as we wish, the only proviso being that they are created in f_X ratios, so that regardless of how massive, old and large our universe becomes, it is still in sum total dimensionless. Defining the dimensioned quantities ''r'', ''v'' in SI unit terms. :<math>r = (\frac{kg\;m}{s})^{1/4}</math> :<math>v = \frac{m}{s}</math> Mass :<math>\frac{r^4}{v} = (\frac{kg\;m}{s})\;(\frac{s}{m}) = kg</math> Length :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^5})^4 = \frac{s^{20}}{m^{20}}</math> :<math>(\frac{r^9}{v^5})^4 = \frac{kg^9 s^{11}}{m^{11}} = m^4 \frac{kg^9 s^{11}}{m^{15}} = m^4 f_X = m^4</math> Time :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^6})^4 = \frac{s^{24}}{m^{24}}</math> :<math>(\frac{r^9}{v^6})^4 = \frac{kg^9 s^{15}}{m^{15}} = s^4 \frac{kg^9 s^{11}}{m^{15}} = s^4 f_X = s^4</math> And so, although f_X is a dimensionless mathematical structure, we can embed within it the (mass, length, time ...) structures along with their dimensional attributes (kg, m, s, A ..). In the mathematical electron model (discussed below), the electron itself is an example of an f_X structure, it (f_electron) is a dimensionless geometrical object that embeds the physical electron parameters of wavelength, frequency, charge (note: A-m = ampere-meter are the units for a [[w:Magnetic_monopole#In_SI_units |magnetic monopole]]). <math>f_{electron}</math> :<math>units = \frac{A^3 m^3}{s} = \frac{(\frac{v^3}{r^6})^3 (\frac{r^9}{v^5})^3}{(\frac{r^9}{v^6})} = 1</math> We may note that at the macro-level (of planets and stars) these f_X ratio are not found, and so this level is the domain of the observed physical universe, however at the quantum level, f_X ratio do appear, f_electron as an example, the mathematical and physical domains then blurring. This would also explain why physics can measure precisely the parameters of the electron (wavelength, mass ...), but has never found the electron itself. == Programming == “God vs. science debates tend to be restricted to the premise that a God does not rely on science and that science does not need a God. As science and God are thus seen as mutually exclusive there are few, if any, serious attempts to construct mathematical models of a universe whose principle axiom does require a God. However, if there is an Intelligence responsible for the 14 billion year old universe of modern physics, being the universe of Einstein and Dirac, and beginning with the big bang as the act of 'creation', then we must ask how it might be done? What construction technique could have been used to set the laws of physics in motion?” <ref>[https://theprogrammergod.com/ The Programmer God, are we in a Simulation]</ref> === Simulation Time === The (dimensionless) simulation clock-rate would be defined as the minimum 'time variable' ('''age''') increment to the simulation. Using a simple loop as analogy, at ''age'' = 1, the simulation begins (the big bang), certain processes occur, when these are completed ''age'' increments (''age'' = 2, then 3, then 4 ... ) until ''age'' reaches ''the_end'' and the simulation stops. 'begin simulation FOR age = 1 TO the_end 'big bang = 1 conduct certain processes ........ NEXT age 'end simulation [[w:Quantum spacetime |Quantum spacetime]] and [[w:Quantum gravity |Quantum gravity]] models refer to [[w:Planck time | Planck time]] as the smallest discrete unit of time and so the incrementing variable '''age''' could be used to generate units of Planck time (and other Planck units, the physical scaffolding of the universe). In a geometrical model, to these Planck units could be assigned geometrical objects, for example; Initialize_physical_constants; FOR age = 1 TO the_end generate 1 unit of (Planck) time; '1 time 'object' T generate 1 unit of (Planck) mass; '1 mass 'object' M generate 1 unit of (Planck) length; '1 length 'object' L ........ NEXT age The variable ''age'' is the simulation clock-rate, it is simply a counter (1, 2, 3 ...) and so is a dimensionless number, the object T is the geometrical Planck time object, it is dimensioned and is measured by us in seconds. If ''age'' is the origin of Planck time (1 increment to ''age'' generates 1 T object) then ''age'' = 10⁶², this is based on the present [[w:Age_of_the_universe |age of the universe]], which, at 14 billion years, equates to 10⁶² units of Planck time. For each ''age'', certain operations are performed, only after they are finished does ''age'' increment (there is no ''time'' interval between increments). As noted, ''age'' being dimensionless, is not the same as dimensioned Planck time which is the geometrical object T, and this T, being dimensioned, can only appear within the simulation. The analogy would be frames of a movie, each frame contains dimensioned information but there is no ''time'' interval between frames. FOR age = 1 TO the_end (of the movie) display frame{age} NEXT age Although operations (between increments to ''age'') may be extensive, self-aware structures from within the simulation would have no means to determine this, they could only perceive themselves as being in a real-time (for them the smallest unit of ''time'' is 1T, just as the smallest unit of ''time'' in a movie is 1 frame). Their (those self-aware structures) dimension of time would then be a measure of relative motion (a change of state), and so although ultimately deriving from the variable ''age'', their time would not be the same as ''age''. If there was no motion, if all particles and photons were still (no change of state), then their time dimension could not update (if every frame in a movie was the same then actors within that movie could not register a change in time), ''age'' however would continue to increment. Thus we have 3 time structures; 1) the dimension-less simulation clock-rate variable ''age'', 2) the dimensioned time unit (object T), and 3) time as change of state (the observers time). Observer time requires a memory of past events against which a change of state can be perceived. The forward increment to ''age'' would constitute the [[w:arrow of time |arrow of time]]. Reversing this would reverse the arrow of time, the universe would likewise shrink in size and mass accordingly (just as a [[w:white hole |white hole]] is the (time) reversal of a [[w:black hole |black hole]]). FOR age = the_end TO 1 STEP -1 delete 1 unit of Planck time; delete 1 unit of Planck mass; delete 1 unit of Planck length; ........ NEXT age Adding mass, length and time objects per increment to ''age'' would force the universe expansion (in size and mass), and as such an anti-gravitational [[w:dark energy |dark energy]] would not be required, however these objects are dimensioned and so are generated within the simulation. This means that they must somehow combine in a specific ratio whereby they (the units for mass length, time, charge; ''kg'', ''m'', ''s'', ''A'') in sum total cancel each other, leaving the sum universe (the simulation itself) residing on that celestial hard-disk. We may introduce a theoretical dimensionless (f_X) geometrical object denoted as f_Planck within which are embedded the dimensioned objects MLTA (mass, length, time, charge), and from which they may be extracted. FOR age = 1 TO the_end add 1 f_Planck 'dimensionless geometrical 'object' { extract 1 unit of (Planck) time; '1 time 'object' T extract 1 unit of (Planck) mass; '1 mass 'object' M extract 1 unit of (Planck) length; '1 length 'object' L } ........ NEXT age This then means that the simulation, in order to create time T, must also create mass M and space L (become larger and more massive). Thus no matter how small or large the physical universe is (when seen internally), in sum total (when seen externally), there is no universe - it is merely data without physical form. === Universe time-line === As the universe expands outwards (through the constant addition of units of mass and length via f_Planck), and if this expansion pulls particles with it (if it is the origin of motion), then ''now'' (the present) would reside on the surface of the (constantly expanding at the speed of light; ''c'' = 1 Planck length / 1 Planck time) universe, and so the 'past' could be retained, for the past cannot be over-written by the present in an expanding universe (if ''now'' is always on the surface). As this expansion occurs at the Planck scale, information even below quantum states, down to the Planck scale, can be retained, the analogy would be the storing of every [[w:Keystroke_logging |keystroke]], a Planck scale version of the [[w:Akashic records |Akashic records]] ... for if our deeds (the past) are both stored and cannot be over-written (by the present), then we have a candidate for the '[[w:karma |karmic]] heavens' (Matthew 6:19 ''But lay up for yourselves treasures in 'heaven', where neither moth nor rust doth corrupt, and where thieves do not break through nor steal''). This also forms a universe '''time-line''' against which previous information can be compared with new information (a 'memory' of events), without which we could not link cause with effect. === Singularity === In a simulation, the data (software) requires a storage device that is ultimately hardware (RAM, HD ...). In a data world of 1's and 0's such as a computer game, characters within that game may analyze other parts of their 1's and 0's game, but they have no means to analyze the hard disk upon which they (and their game) are stored, for the hard disk is an electro-mechanical device, it is not part of their 1's and 0's world, it is a part of the 'real world', the world of their Programmer. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may or may not resemble the laws that operate in the 'real world' (the world of their Programmer). Thus any region where the laws of physics (the laws of their game world) break down would be significant. A [[w:singularity |singularity]] inside a black hole is such a region <ref>https://www.youtube.com/watch?v=W5j7umtZYB4 a black hole singularity as the interface between worlds</ref>. For the [[w:black hole electron |black-hole electron]], its black-hole center would then be analogous to a storage address on a hard disk, the interface between the simulation world and the real world. A massive (galactic) black-hole could be as an entire data sector. The surface of the black-hole would then be of the simulation world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however would be the interface between the data world and the 'hard disk' of the real world, and so would not exist in any 'physical' terms. It is external to the simulation. As analogy, we may discuss the 3-D surface area of a black-hole but not its volume (interior). === Laws of Physics === The scientific method is built upon testable hypothesis and reproducible results. Water always boils (in defined conditions), at 100°C. In a geometrical universe particles will behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these repeating patterns, the more complex the orbits, the more complex the formulas required to describe them and so forth. However if there is a source code from which these geometrical conditions were programmed, then there may also be non-repeating events, back-doors built into the code (a common practice by terrestrial programmers), these by definition would lie outside the laws of physics and so be labelled as miracles, yet they would be no less valid. === Determinism === [[File:Three body problem figure-8 orbit animation.gif|400px|thumb|An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259.<ref>Here the gravitational constant ''G'' has been set to 1, and the initial conditions are '''r'''₁(0) = −'''r'''₃(0) = (−0.97000436, 0.24308753); '''r'''₂(0) = (0,0); '''v'''₁(0) = '''v'''₃(0) = (0.4662036850, 0.4323657300); '''v'''₂(0) = (−0.93240737, −0.86473146). The values are obtained from Chenciner & Montgomery (2000).</ref>]] Particles form more complex structures such as atoms and molecules via a system of orbitals; nuclear, atomic and gravitational. The [[w:Three-body_problem |3-body problem]] is the problem of taking the initial positions and velocities (or [[w:momentum|momenta |momentum|momenta]]) of three or more point masses and solving for their subsequent motion according to [[w:Newton's laws of motion |Newton's laws of motion]] and [[w:Newton's law of universal gravitation |Newton's law of universal gravitation]].<ref name="PrincetonCompanion">{{Citation | last = Barrow-Green | first = June | year = 2008 | title = The Three-Body Problem | editor-last1 = Gowers | editor-first1 = Timothy | editor-last2 = Barrow-Green | editor-first2 = June | editor-last3 = Leader | editor-first3 = Imre | encyclopedia = The Princeton Companion to Mathematics | pages = 726–728 | publisher = Princeton University Press }}</ref>. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for gods and men alike the only way to know what that outcome will be is to run the simulation itself. ==Geometry coded universe== Modelling a Planck scale simulation universe using geometrical forms (links) * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass == External links == * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] * [https://philpapers.org/rec/GRUTIA-2 Simulation theory as evidence for God] (academic peer-reviewed article) ==References== {{Reflist}} [[Category:Philosophy| ]] [[Category:Philosophy of science| ]] 1o2frdho0vn91hez91gvtpt1nwc95vj 2718264 2718263 2025-06-10T19:52:47Z 212.200.164.104 /* Geometry coded universe */ 2718264 wikitext text/x-wiki '''Is God a Programmer? analyzing the deep-universe simulation hypothesis at the Planck scale''' The [[w:simulation hypothesis |simulation hypothesis]] is the proposal that all of reality, including the Earth and the rest of the universe, could be an artificial simulation, such as a computer simulation. [[w:Neil_deGrasse_Tyson |Neil deGrasse Tyson]] put the odds at 50-50 that our entire existence is a program on someone else’s hard drive <ref>Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. [[w:David_Chalmers |David Chalmers]] noted “We in this universe can create simulated worlds and there’s nothing remotely spooky about that. Our creator isn’t especially spooky, it’s just some teenage hacker in the next universe up. Turn the tables, and we are essentially gods over our own computer creations <ref>https://www.youtube.com/watch?v=yqbS5qJU8PA, David Chalmers, Serious Science</ref> <ref>The Matrix as Metaphysics, David Chalmers http://consc.net/papers/matrix.pdf</ref> <ref>Are We Living in a Computer Simulation?https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. The commonly postulated [[w:Ancestor_simulation |ancestor simulation]] approach, which [[w:Nick Bostrom |Nick Bostrom]] called "the simulation argument", argues for "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor. However this simulation variant can be traced back to an 'organic base reality' (the original programmer ancestors and their physical planet). The [[v:God_(programmer) |Programmer God]] hypothesis<ref>https://codingthecosmos.com/podcast/ AI generated podcasts</ref> conversely states that a (deep universe) simulation began with the big bang and was programmed by an external intelligence (external to the physical universe), the Programmer by definition a God in the creator of the universe context. Our universe in its entirety, down to the smallest detail, and including life-forms, is within the simulation, the laws of nature, at their most fundamental level, are coded rules running on top of the simulation operating system. The operating system itself is mathematical (and potentially the origin of mathematics). Any candidate for a Programmer-God simulation-universe source code must satisfy these conditions; :1. It can generate physical structures from mathematical forms. :2. The sum universe is dimensionless (simply data on a celestial hard disk). :3. We must be able to use it to derive the laws of physics (because the source code is the origin of the laws of nature, and the laws of physics are our observations of the laws of nature). :4. The mathematical logic must be unknown to us (the Programmer is a non-human intelligence). :5. The coding should have an 'elegance' commensurate with the Programmer's level of skill. == Philosophy == Physicist [[w:Eugene Wigner |Eugene Wigner]] ([[w:The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences |The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]) <ref>{{Cite journal | last1 = Wigner | first1 = E. P. | authorlink = Eugene Wigner| doi = 10.1002/cpa.3160130102 | title = The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959 | journal = Communications on Pure and Applied Mathematics | volume = 13 | pages = 1–14 | year = 1960 | pmid = | pmc = |bibcode = 1960CPAM...13....1W }}</ref> <blockquote>The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. </blockquote> === Discussion === [[w:Philosophy of mathematics |Philosophy of mathematics]] is that branch of philosophy which attempts to answer questions such as: ‘why is mathematics useful in describing nature?’, ‘in which sense, if any, do mathematical entities such as numbers exist?’ and ‘why and how are mathematical statements true?’ This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math. Mathematical realism holds that mathematical entities exist independently of the human mind. We do not invent mathematics, but rather discover it. Triangles, for example, are real entities that have an existence <ref>- http://plato.stanford.edu/entries/platonism-mathematics/</ref>. The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality. It can be considered a form of [[w:Pythagoreanism | Pythagoreanism]] or [[w:Platonism | Platonism]] in that it proposes the existence of ''mathematical objects''; and a form of [[w:philosophy of mathematics | mathematical monism]] in that it denies that anything exists except these ''mathematical objects''. Physicist [[w:Max Tegmark | Max Tegmark]] in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality"<ref name="Tegmark1998">{{cite journal|last=Tegmark |first=Max |date=November 1998 |title=Is "the Theory of Everything" Merely the Ultimate Ensemble Theory? |journal=Annals of Physics |volume=270 |issue=1 |pages=1–51 |doi=10.1006/aphy.1998.5855 |arxiv = gr-qc/9704009 |bibcode = 1998AnPhy.270....1T }}</ref><ref>M. Tegmark 2014, "[http://mathematicaluniverse.org Our Mathematical Universe]", Knopf</ref> proposed that ''Our external physical reality is a mathematical structure''.<ref name="Tegmark2008">{{cite journal|last=Tegmark |first=Max |date=February 2008 |title=The Mathematical Universe |journal=Foundations of Physics |volume=38 |issue=2 |pages=101–150 |doi=10.1007/s10701-007-9186-9 |arxiv=0704.0646|bibcode = 2008FoPh...38..101T }}</ref> That is, the physical universe is not merely ''described by'' mathematics, but ''is'' mathematics (specifically, a [[w:mathematical structure | mathematical structure]]). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref> The principle constraints to any mathematical universe simulation hypothesis are; 1. the computational resources required. The ancestor simulation can resolve this by adapting from the [[w:virtual rality |virtual reality]] approach where only the observable region is simulated and only to the degree required, and 2. that any 'self-aware structures' (humans for example) within the simulation must "subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref>. Succinctly, our computer games may be able to simulate our physical world, but they are still only simulations of a physical reality (regardless of how realistic they may seem) ... we are not yet able to program actual physical dimensions of mass, space and time from mathematical structures, and indeed this may not be possible with a computer hard-ware architecture that can only process binary data. === Deep-universe source code === As a deep-universe simulation is programmed by an external (external to the universe) intelligence (the Programmer God hypothesis), we cannot presume a priori knowledge regarding the simulation source code other than from this code the laws of nature emerged, and so any deep-universe simulation model we try to emulate must be universal, i.e.: independent of any system of units, of the [[w:Dimensional_analysis |dimensioned]] [[w:physical constants |physical constants]] (''G'', ''h'', ''c'', ''e'' .. ), and of any numbering systems. Furthermore, although a deep-universe simulation source code may use mathematical forms (circles, spheres ...) we are familiar with (for ultimately the source code is the origin of these forms), it will have been developed by a non-human intelligence and so we may have to develop new mathematical tools to decipher the underlying logic. By implication therefore, any theoretical basis for a source code that fits the above criteria (and from which the laws of nature will emerge), could be construed as our first tangible evidence of a non-human intelligence. === Constants === A physical universe is characterized by measurable quantities (size, mass, color, texture ...), and so a physical universe can be measured and defined. Contrast then becomes information, the statement ''this is a big apple'' requires a ''small apple'' against which big becomes a relative term. For analytical purposes we select a reference value, for example 0C or 32F, and measure all temperatures against this reference. The smaller the resolution of the measurements, the greater the information content (the file size of a 32 mega-pixel photo is larger than a 4 mega-pixel photo). A simulation universe may be presumed to also have a resolution dictating how much information the simulation can store and manipulate. To measure the fundamental parameters of our universe physics uses [[w:physical constant |physical constants]]. A physical constant is a [[w:physical quantity |physical quantity]] that is generally believed to be both universal in nature and have a constant value in time. These can be divided into 1) dimension-ed (measured using physical units ''kg'', ''m'', ''s'', ''A'' ...) such as the [[w:speed of light |speed of light]] ''c'', [[w:gravitational constant |gravitational constant]] ''G'', [[w:Planck constant |Planck constant]] ''h'' ... as in the table {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} Physicist [[w: |Lev Okun]] noted "Theoretical equations describing the physical world deal with dimensionless quantities and their solutions depend on dimensionless fundamental parameters. But experiments, from which these theories are extracted and by which they could be tested, involve measurements, i.e. comparisons with standard dimension-ful scales. Without standard dimension-ful units and hence without certain conventions physics is unthinkable <ref>Michael J. Duff et al, Journal of High Energy Physics, Volume 2002, JHEP03(2002)</ref>. 2) dimension-less, such as the [[w:Fine-structure_constant |fine structure constant]] ''α''. A dimension-less constant does not measure any physical quantity (it has no units; units = 1). 3) dimension-less [[w:mathematical constant |mathematical constants]], most notably [[w:pi |pi]] = 3.14159265358979 and [[w:Natural_logarithm |e]] = 2.718281828459. Although these are [[w:transcendental number |transcendental numbers]], they can be constructed by integers in a series, and so for a universe expanding incrementally (see simulation time), these constants could be formed within the simulation. For example, at time ''t''; <math display=block>t = 1; \frac{\pi^2}{6} = \frac{1}{t^2} </math> <math display=block>t = 2; \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{t^2}</math> <math display=block>t = now: \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots + \frac{1}{t^2} </math> We may now define the fundamental physical constant as a parameter specifically chosen by the Programmer and is encoded into the simulation code directly, and so whilst it may be inferable, it is not derived from other constants ([[w:Fine-structure_constant#Numerological_explanations_and_multiverse_theory |Richard Feynman on the fine structure constant]]). It should also be dimension-less otherwise the simulation itself becomes dimensioned (if the simulation is running on a celestial computer it is merely data, it has no physical size or shape or ...), and so the dimensioned constants (''G'', ''h'', ''c'', ''e''...) must all be derivable (derived from within the simulation) via the (embedded in the source code) fundamental physical constants (of which the fine structure constant alpha may be an example). Although [[w:pi |pi]] and [[w:Natural_logarithm |e]] are dimensionless, they can be derived internally (from integers), and as they have application in the mathematical realm, they can be referred to as mathematical constants. ==== Planck scale ==== The [[w:Planck scale |Planck scale]] refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the [[w:Standard Model |Standard Model]], [[w:quantum field theory |quantum field theory]] and [[w:general relativity |general relativity]] are no longer reconcilable, and [[w:Quantum Gravity |quantum effects of gravity]] are expected to dominate (quantum gravitational effects only appear at length scales near the Planck scale). Although particles may not be cognizance of our 'laws of physics', they do know the 'laws of nature'. These laws of nature would run directly off the universe OS (operating system), and so below this OS, 'physics' as we know it must necessarily break down. At present the Planck scale is the lowest known level, consequently any attempt to detect evidence of an underlying simulation coding must consider (if not actually begin at) this, the Planck scale<ref>https://www.youtube.com/watch?v=AMQRXGYCDrY Planck scale, Brian Greene</ref>. The [[w:International_System_of_Units |SI units]] for the dimension-ful mksa units are; meter (length), kilogram (mass), second (time), ampere (electric current). There are Planck units that represent these SI units, and so a simulation could use them as discrete building blocks; [[w:Planck length |Planck length]] (the smallest possible unit of length), [[w:Planck mass |Planck mass]] (the unit of mass), [[w:Planck time |Planck time]] (the smallest possible unit of time), [[w:Planck charge |Planck charge]] (the unit of charge). The speed of light then becomes ''c'' = 1 Planck length / 1 Planck time. These units would define the resolution and so information carrying capacity of the simulation universe. ==== Numbering systems ==== As well as our decimal system, computers apply binary and hexadecimal numbering systems. In particular the decimal and hexadecimal are of terrestrial origin and may not be considered 'universal'. Furthermore numbering systems measure only the frequency of an event and contain no information as to the event itself. The number 299 792 458 could refer to the speed of light (299 792 458 m/s) or could equally be referring to the number of apples in a container (299 792 458 apples). As such, numbers require a 'descriptive', whether m/s or apples. Numbers also do not include their history, is 299 792 458 for example a derivation of other base numbers? Present universe simulations use the laws of physics and the physical constants are built in, however both these laws and the physical constants are known only to a limited precision, and so a simulation with 10⁶² iterations (the present age of the universe in units of Planck time) will accumulate errors. Number based computing may be sufficient for ancestor-simulation models where only the observed region needs to be calculated, but has inherent limitations for deep universe simulations where the entire universe is continuously updated. The actual computational requirements for a Planck scale universe simulation based on a numbering system with the laws of physics embedded would be an unknown and consequently lead to an 'non-testable' hypothesis. This is a commonly applied reasoning for rejecting the deep universe simulation. ==== Geometrical objects ==== A mathematical constant such as [[w:pi |pi]] refers to a geometrical construct (the ratio of circle circumference to circle radius) and so is not constrained by any particular numbering system (in the decimal system π = 3.14159...), and so may be considered both universal and eternal. Likewise, by assigning geometrical objects instead of numbers to the Planck units, the problems with a numbering system can be resolved. These objects would however have to fulfill the following conditions; 1) embedded attribute - for example the object for length must embed the function of ''length'' such that a descriptive (km, mile ... ) is not required. Electron wavelength would then be measurable in terms of the length object, as such the length object must be embedded within the electron (the electron object). Although the mass object would incorporate the function ''mass'', the time object the function ''time'' ..., it is not necessary that there be an individual physical mass or physical length or physical time ..., but only that in relation to the other units, the object must express that function (i.e.: the mass object has the function of mass when in the presence of the objects for space and time). The electron could then be a complex event (complex geometrical object) constructed by combining the objects for mass, length, time and charge into 1 event, and thus electron charge, wavelength, frequency and mass would then be different aspects of that 1 geometry (the electron event) and not independent parameters (independent of each other). 2) The objects for mass, length, time and charge must be able to combine with each other [[w:Lego |Lego-style]] to form more complex objects (events) such as electrons and apples whilst still retaining the underlying information (the mass of the apple derives from the mass objects embedded within that apple). Not only must these objects be able to form complex events such as particles, but these events themselves are geometrical objects and so must likewise function according to their geometries. Electrons would orbit protons according to their respective electron and proton geometries, these orbits the result of geometrical imperatives and not due to any built-in laws of physics (the orbital path is a consequence of all the underlying geometries). However, as orbits follow regular and repeating patterns, they can be described (by us) using mathematical formulas. As the events grow in complexity (from atoms to molecules to planets), so too will the patterns (and likewise the formulas we use to describe them). Consequently the ''laws of physics'' would then become our mathematical descriptions of the underlying geometrically imposed patterns. 3) These objects would replace coded instructions (the instruction sets would be built into the objects) thereby instigating a geometrically autonomous universe. The electron 'knows' what to do by virtue of the information encoded within its geometry, no coded electron CALL FUNCTION is required. This would be equivalent to combining the hardware, software and CPU together such that the 'software' changes (adjusts) to the changing 'hardware' (DNA may be an analogy). Note: A purely mathematical universe has no limits in size and can be infinitely large and infinity small. A geometrical universe (that uses objects) has limitations, it can be no smaller than the smallest object for example and has discrete parts (those objects). The philosophy of the TOE (theory of everything) therefore includes a debate between the mathematical universe and the geometrical universe, however this distinction between mathematical and geometrical would only be apparent at the Planck scale. === Evidence of a simulation === The laws of physics are our incomplete observations of the natural universe, and so evidence of a simulation may be found in ambiguities or anomalies within these laws. Furthermore, if complexity arises over time, then at unit time the 'handiwork' of the Programmer may be notable by a simplicity and elegance of the geometries employed ... for the Programmer by definition has God-level programming skills. Here is a notable example. Mass, space and time from the number 1 The dimensions of mass, space and time are considered by science to be independent of each other, we cannot measure the ''distance'' from Tokyo to London using kilograms and amperes, or measure ''mass'' using space and time. Indeed, what characterizes a physical universe as opposed to a simulated universe is the notion that there is a fundamental structure underneath, that in some sense mass 'is', that time 'is' and space 'is' ... thus we cannot write ''kg'' in terms of ''m'' and ''s''. To do so would render our concepts of a physical universe meaningless. The 26th General Conference on Weights and Measures ([[w:2019 redefinition of SI base units|2019 redefinition of SI base units]]) assigned exact numerical values to 4 physical constants (''h, c, e, k''_B) independently of each other (and thereby confirming these as fundamental constants), and as they are measured in SI units ('''kg''', '''m''', '''s''', '''A''', '''K'''), these units must also be independent of each other (i.e.: these are fundamental units, for example if we could define ''m'' using ''A'' then the speed of light could be derived from, and so would depend upon, the value for the elementary charge ''e'', and so the value for ''c'' could not be assigned independently from ''e''). {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} We are familiar with inverse properties; plus charge and minus charge, matter and anti-matter ... and we can observe how these may form and/or cancel each other. A simulation universe however is required to be dimensionless (in sum total), for the simulated universe does not 'exist' in any physical sense outside of the 'Computer' (it is simply data on a celestial hard-disk). Our universe does not appear to have inverse properties such as anti-mass (-kg), anti-time (-s) or anti-space (anti-length -m), therefore the first problem the Programmer must solve is how to create the physical scaffolding (of mass, space and time). For example, the Programmer can start by selecting 2 dimensioned quantities, here are used ''r'', ''v'' <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref> such that :<math>kg = \frac{r^4}{v},\; m = \frac{r^9}{v^5},\; s = \frac{r^9}{v^6},\; A = \frac{v^3}{r^6}</math> Quantities ''r'' and ''v'' are chosen so that no unit (''kg'', ''m'', ''s'', ''A'') can cancel another unit (i.e.: the ''kg'' cannot cancel the ''m'' or the ''s'' ...), and so we have 4 independent units (we still cannot define the ''kg'' using the ''m'' or the ''s'' ...), however if 3 (or more) units are combined together in a specific ratio, they can cancel (in a certain ratio our ''r'' and ''v'' become inverse properties and so cancel each other; units = 1). <math>f_X = \frac{kg^9 s^{11}}{m^{15}} = \frac{(\frac{r^4}{v})^9 (\frac{r^9}{v^6})^{11}}{(\frac{r^9}{v^5})^{15}} = 1</math> This f_X, although embedded within are the dimensioned structures for mass, time and length (in the above ratio), would be a dimensionless mathematical structure, units = 1. Thus we may create as much mass, time and length as we wish, the only proviso being that they are created in f_X ratios, so that regardless of how massive, old and large our universe becomes, it is still in sum total dimensionless. Defining the dimensioned quantities ''r'', ''v'' in SI unit terms. :<math>r = (\frac{kg\;m}{s})^{1/4}</math> :<math>v = \frac{m}{s}</math> Mass :<math>\frac{r^4}{v} = (\frac{kg\;m}{s})\;(\frac{s}{m}) = kg</math> Length :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^5})^4 = \frac{s^{20}}{m^{20}}</math> :<math>(\frac{r^9}{v^5})^4 = \frac{kg^9 s^{11}}{m^{11}} = m^4 \frac{kg^9 s^{11}}{m^{15}} = m^4 f_X = m^4</math> Time :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^6})^4 = \frac{s^{24}}{m^{24}}</math> :<math>(\frac{r^9}{v^6})^4 = \frac{kg^9 s^{15}}{m^{15}} = s^4 \frac{kg^9 s^{11}}{m^{15}} = s^4 f_X = s^4</math> And so, although f_X is a dimensionless mathematical structure, we can embed within it the (mass, length, time ...) structures along with their dimensional attributes (kg, m, s, A ..). In the mathematical electron model (discussed below), the electron itself is an example of an f_X structure, it (f_electron) is a dimensionless geometrical object that embeds the physical electron parameters of wavelength, frequency, charge (note: A-m = ampere-meter are the units for a [[w:Magnetic_monopole#In_SI_units |magnetic monopole]]). <math>f_{electron}</math> :<math>units = \frac{A^3 m^3}{s} = \frac{(\frac{v^3}{r^6})^3 (\frac{r^9}{v^5})^3}{(\frac{r^9}{v^6})} = 1</math> We may note that at the macro-level (of planets and stars) these f_X ratio are not found, and so this level is the domain of the observed physical universe, however at the quantum level, f_X ratio do appear, f_electron as an example, the mathematical and physical domains then blurring. This would also explain why physics can measure precisely the parameters of the electron (wavelength, mass ...), but has never found the electron itself. == Programming == “God vs. science debates tend to be restricted to the premise that a God does not rely on science and that science does not need a God. As science and God are thus seen as mutually exclusive there are few, if any, serious attempts to construct mathematical models of a universe whose principle axiom does require a God. However, if there is an Intelligence responsible for the 14 billion year old universe of modern physics, being the universe of Einstein and Dirac, and beginning with the big bang as the act of 'creation', then we must ask how it might be done? What construction technique could have been used to set the laws of physics in motion?” <ref>[https://theprogrammergod.com/ The Programmer God, are we in a Simulation]</ref> === Simulation Time === The (dimensionless) simulation clock-rate would be defined as the minimum 'time variable' ('''age''') increment to the simulation. Using a simple loop as analogy, at ''age'' = 1, the simulation begins (the big bang), certain processes occur, when these are completed ''age'' increments (''age'' = 2, then 3, then 4 ... ) until ''age'' reaches ''the_end'' and the simulation stops. 'begin simulation FOR age = 1 TO the_end 'big bang = 1 conduct certain processes ........ NEXT age 'end simulation [[w:Quantum spacetime |Quantum spacetime]] and [[w:Quantum gravity |Quantum gravity]] models refer to [[w:Planck time | Planck time]] as the smallest discrete unit of time and so the incrementing variable '''age''' could be used to generate units of Planck time (and other Planck units, the physical scaffolding of the universe). In a geometrical model, to these Planck units could be assigned geometrical objects, for example; Initialize_physical_constants; FOR age = 1 TO the_end generate 1 unit of (Planck) time; '1 time 'object' T generate 1 unit of (Planck) mass; '1 mass 'object' M generate 1 unit of (Planck) length; '1 length 'object' L ........ NEXT age The variable ''age'' is the simulation clock-rate, it is simply a counter (1, 2, 3 ...) and so is a dimensionless number, the object T is the geometrical Planck time object, it is dimensioned and is measured by us in seconds. If ''age'' is the origin of Planck time (1 increment to ''age'' generates 1 T object) then ''age'' = 10⁶², this is based on the present [[w:Age_of_the_universe |age of the universe]], which, at 14 billion years, equates to 10⁶² units of Planck time. For each ''age'', certain operations are performed, only after they are finished does ''age'' increment (there is no ''time'' interval between increments). As noted, ''age'' being dimensionless, is not the same as dimensioned Planck time which is the geometrical object T, and this T, being dimensioned, can only appear within the simulation. The analogy would be frames of a movie, each frame contains dimensioned information but there is no ''time'' interval between frames. FOR age = 1 TO the_end (of the movie) display frame{age} NEXT age Although operations (between increments to ''age'') may be extensive, self-aware structures from within the simulation would have no means to determine this, they could only perceive themselves as being in a real-time (for them the smallest unit of ''time'' is 1T, just as the smallest unit of ''time'' in a movie is 1 frame). Their (those self-aware structures) dimension of time would then be a measure of relative motion (a change of state), and so although ultimately deriving from the variable ''age'', their time would not be the same as ''age''. If there was no motion, if all particles and photons were still (no change of state), then their time dimension could not update (if every frame in a movie was the same then actors within that movie could not register a change in time), ''age'' however would continue to increment. Thus we have 3 time structures; 1) the dimension-less simulation clock-rate variable ''age'', 2) the dimensioned time unit (object T), and 3) time as change of state (the observers time). Observer time requires a memory of past events against which a change of state can be perceived. The forward increment to ''age'' would constitute the [[w:arrow of time |arrow of time]]. Reversing this would reverse the arrow of time, the universe would likewise shrink in size and mass accordingly (just as a [[w:white hole |white hole]] is the (time) reversal of a [[w:black hole |black hole]]). FOR age = the_end TO 1 STEP -1 delete 1 unit of Planck time; delete 1 unit of Planck mass; delete 1 unit of Planck length; ........ NEXT age Adding mass, length and time objects per increment to ''age'' would force the universe expansion (in size and mass), and as such an anti-gravitational [[w:dark energy |dark energy]] would not be required, however these objects are dimensioned and so are generated within the simulation. This means that they must somehow combine in a specific ratio whereby they (the units for mass length, time, charge; ''kg'', ''m'', ''s'', ''A'') in sum total cancel each other, leaving the sum universe (the simulation itself) residing on that celestial hard-disk. We may introduce a theoretical dimensionless (f_X) geometrical object denoted as f_Planck within which are embedded the dimensioned objects MLTA (mass, length, time, charge), and from which they may be extracted. FOR age = 1 TO the_end add 1 f_Planck 'dimensionless geometrical 'object' { extract 1 unit of (Planck) time; '1 time 'object' T extract 1 unit of (Planck) mass; '1 mass 'object' M extract 1 unit of (Planck) length; '1 length 'object' L } ........ NEXT age This then means that the simulation, in order to create time T, must also create mass M and space L (become larger and more massive). Thus no matter how small or large the physical universe is (when seen internally), in sum total (when seen externally), there is no universe - it is merely data without physical form. === Universe time-line === As the universe expands outwards (through the constant addition of units of mass and length via f_Planck), and if this expansion pulls particles with it (if it is the origin of motion), then ''now'' (the present) would reside on the surface of the (constantly expanding at the speed of light; ''c'' = 1 Planck length / 1 Planck time) universe, and so the 'past' could be retained, for the past cannot be over-written by the present in an expanding universe (if ''now'' is always on the surface). As this expansion occurs at the Planck scale, information even below quantum states, down to the Planck scale, can be retained, the analogy would be the storing of every [[w:Keystroke_logging |keystroke]], a Planck scale version of the [[w:Akashic records |Akashic records]] ... for if our deeds (the past) are both stored and cannot be over-written (by the present), then we have a candidate for the '[[w:karma |karmic]] heavens' (Matthew 6:19 ''But lay up for yourselves treasures in 'heaven', where neither moth nor rust doth corrupt, and where thieves do not break through nor steal''). This also forms a universe '''time-line''' against which previous information can be compared with new information (a 'memory' of events), without which we could not link cause with effect. === Singularity === In a simulation, the data (software) requires a storage device that is ultimately hardware (RAM, HD ...). In a data world of 1's and 0's such as a computer game, characters within that game may analyze other parts of their 1's and 0's game, but they have no means to analyze the hard disk upon which they (and their game) are stored, for the hard disk is an electro-mechanical device, it is not part of their 1's and 0's world, it is a part of the 'real world', the world of their Programmer. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may or may not resemble the laws that operate in the 'real world' (the world of their Programmer). Thus any region where the laws of physics (the laws of their game world) break down would be significant. A [[w:singularity |singularity]] inside a black hole is such a region <ref>https://www.youtube.com/watch?v=W5j7umtZYB4 a black hole singularity as the interface between worlds</ref>. For the [[w:black hole electron |black-hole electron]], its black-hole center would then be analogous to a storage address on a hard disk, the interface between the simulation world and the real world. A massive (galactic) black-hole could be as an entire data sector. The surface of the black-hole would then be of the simulation world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however would be the interface between the data world and the 'hard disk' of the real world, and so would not exist in any 'physical' terms. It is external to the simulation. As analogy, we may discuss the 3-D surface area of a black-hole but not its volume (interior). === Laws of Physics === The scientific method is built upon testable hypothesis and reproducible results. Water always boils (in defined conditions), at 100°C. In a geometrical universe particles will behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these repeating patterns, the more complex the orbits, the more complex the formulas required to describe them and so forth. However if there is a source code from which these geometrical conditions were programmed, then there may also be non-repeating events, back-doors built into the code (a common practice by terrestrial programmers), these by definition would lie outside the laws of physics and so be labelled as miracles, yet they would be no less valid. === Determinism === [[File:Three body problem figure-8 orbit animation.gif|400px|thumb|An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259.<ref>Here the gravitational constant ''G'' has been set to 1, and the initial conditions are '''r'''₁(0) = −'''r'''₃(0) = (−0.97000436, 0.24308753); '''r'''₂(0) = (0,0); '''v'''₁(0) = '''v'''₃(0) = (0.4662036850, 0.4323657300); '''v'''₂(0) = (−0.93240737, −0.86473146). The values are obtained from Chenciner & Montgomery (2000).</ref>]] Particles form more complex structures such as atoms and molecules via a system of orbitals; nuclear, atomic and gravitational. The [[w:Three-body_problem |3-body problem]] is the problem of taking the initial positions and velocities (or [[w:momentum|momenta |momentum|momenta]]) of three or more point masses and solving for their subsequent motion according to [[w:Newton's laws of motion |Newton's laws of motion]] and [[w:Newton's law of universal gravitation |Newton's law of universal gravitation]].<ref name="PrincetonCompanion">{{Citation | last = Barrow-Green | first = June | year = 2008 | title = The Three-Body Problem | editor-last1 = Gowers | editor-first1 = Timothy | editor-last2 = Barrow-Green | editor-first2 = June | editor-last3 = Leader | editor-first3 = Imre | encyclopedia = The Princeton Companion to Mathematics | pages = 726–728 | publisher = Princeton University Press }}</ref>. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for gods and men alike the only way to know what that outcome will be is to run the simulation itself. ==Geometry coded universe== Modelling a Planck scale simulation universe using geometrical forms (links) * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass == External links == * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] * [https://philpapers.org/rec/GRUTIA-2 Simulation theory as evidence for God] (academic peer-reviewed article) ==References== {{Reflist}} [[Category:Philosophy| ]] [[Category:Philosophy of science| ]] 71qj9m5b306b1jqtpu7wijef3ow4rfu 2718265 2718264 2025-06-10T19:52:53Z 212.200.164.104 /* External links */ 2718265 wikitext text/x-wiki '''Is God a Programmer? analyzing the deep-universe simulation hypothesis at the Planck scale''' The [[w:simulation hypothesis |simulation hypothesis]] is the proposal that all of reality, including the Earth and the rest of the universe, could be an artificial simulation, such as a computer simulation. [[w:Neil_deGrasse_Tyson |Neil deGrasse Tyson]] put the odds at 50-50 that our entire existence is a program on someone else’s hard drive <ref>Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. [[w:David_Chalmers |David Chalmers]] noted “We in this universe can create simulated worlds and there’s nothing remotely spooky about that. Our creator isn’t especially spooky, it’s just some teenage hacker in the next universe up. Turn the tables, and we are essentially gods over our own computer creations <ref>https://www.youtube.com/watch?v=yqbS5qJU8PA, David Chalmers, Serious Science</ref> <ref>The Matrix as Metaphysics, David Chalmers http://consc.net/papers/matrix.pdf</ref> <ref>Are We Living in a Computer Simulation?https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. The commonly postulated [[w:Ancestor_simulation |ancestor simulation]] approach, which [[w:Nick Bostrom |Nick Bostrom]] called "the simulation argument", argues for "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor. However this simulation variant can be traced back to an 'organic base reality' (the original programmer ancestors and their physical planet). The [[v:God_(programmer) |Programmer God]] hypothesis<ref>https://codingthecosmos.com/podcast/ AI generated podcasts</ref> conversely states that a (deep universe) simulation began with the big bang and was programmed by an external intelligence (external to the physical universe), the Programmer by definition a God in the creator of the universe context. Our universe in its entirety, down to the smallest detail, and including life-forms, is within the simulation, the laws of nature, at their most fundamental level, are coded rules running on top of the simulation operating system. The operating system itself is mathematical (and potentially the origin of mathematics). Any candidate for a Programmer-God simulation-universe source code must satisfy these conditions; :1. It can generate physical structures from mathematical forms. :2. The sum universe is dimensionless (simply data on a celestial hard disk). :3. We must be able to use it to derive the laws of physics (because the source code is the origin of the laws of nature, and the laws of physics are our observations of the laws of nature). :4. The mathematical logic must be unknown to us (the Programmer is a non-human intelligence). :5. The coding should have an 'elegance' commensurate with the Programmer's level of skill. == Philosophy == Physicist [[w:Eugene Wigner |Eugene Wigner]] ([[w:The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences |The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]) <ref>{{Cite journal | last1 = Wigner | first1 = E. P. | authorlink = Eugene Wigner| doi = 10.1002/cpa.3160130102 | title = The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959 | journal = Communications on Pure and Applied Mathematics | volume = 13 | pages = 1–14 | year = 1960 | pmid = | pmc = |bibcode = 1960CPAM...13....1W }}</ref> <blockquote>The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. </blockquote> === Discussion === [[w:Philosophy of mathematics |Philosophy of mathematics]] is that branch of philosophy which attempts to answer questions such as: ‘why is mathematics useful in describing nature?’, ‘in which sense, if any, do mathematical entities such as numbers exist?’ and ‘why and how are mathematical statements true?’ This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math. Mathematical realism holds that mathematical entities exist independently of the human mind. We do not invent mathematics, but rather discover it. Triangles, for example, are real entities that have an existence <ref>- http://plato.stanford.edu/entries/platonism-mathematics/</ref>. The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality. It can be considered a form of [[w:Pythagoreanism | Pythagoreanism]] or [[w:Platonism | Platonism]] in that it proposes the existence of ''mathematical objects''; and a form of [[w:philosophy of mathematics | mathematical monism]] in that it denies that anything exists except these ''mathematical objects''. Physicist [[w:Max Tegmark | Max Tegmark]] in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality"<ref name="Tegmark1998">{{cite journal|last=Tegmark |first=Max |date=November 1998 |title=Is "the Theory of Everything" Merely the Ultimate Ensemble Theory? |journal=Annals of Physics |volume=270 |issue=1 |pages=1–51 |doi=10.1006/aphy.1998.5855 |arxiv = gr-qc/9704009 |bibcode = 1998AnPhy.270....1T }}</ref><ref>M. Tegmark 2014, "[http://mathematicaluniverse.org Our Mathematical Universe]", Knopf</ref> proposed that ''Our external physical reality is a mathematical structure''.<ref name="Tegmark2008">{{cite journal|last=Tegmark |first=Max |date=February 2008 |title=The Mathematical Universe |journal=Foundations of Physics |volume=38 |issue=2 |pages=101–150 |doi=10.1007/s10701-007-9186-9 |arxiv=0704.0646|bibcode = 2008FoPh...38..101T }}</ref> That is, the physical universe is not merely ''described by'' mathematics, but ''is'' mathematics (specifically, a [[w:mathematical structure | mathematical structure]]). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref> The principle constraints to any mathematical universe simulation hypothesis are; 1. the computational resources required. The ancestor simulation can resolve this by adapting from the [[w:virtual rality |virtual reality]] approach where only the observable region is simulated and only to the degree required, and 2. that any 'self-aware structures' (humans for example) within the simulation must "subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref>. Succinctly, our computer games may be able to simulate our physical world, but they are still only simulations of a physical reality (regardless of how realistic they may seem) ... we are not yet able to program actual physical dimensions of mass, space and time from mathematical structures, and indeed this may not be possible with a computer hard-ware architecture that can only process binary data. === Deep-universe source code === As a deep-universe simulation is programmed by an external (external to the universe) intelligence (the Programmer God hypothesis), we cannot presume a priori knowledge regarding the simulation source code other than from this code the laws of nature emerged, and so any deep-universe simulation model we try to emulate must be universal, i.e.: independent of any system of units, of the [[w:Dimensional_analysis |dimensioned]] [[w:physical constants |physical constants]] (''G'', ''h'', ''c'', ''e'' .. ), and of any numbering systems. Furthermore, although a deep-universe simulation source code may use mathematical forms (circles, spheres ...) we are familiar with (for ultimately the source code is the origin of these forms), it will have been developed by a non-human intelligence and so we may have to develop new mathematical tools to decipher the underlying logic. By implication therefore, any theoretical basis for a source code that fits the above criteria (and from which the laws of nature will emerge), could be construed as our first tangible evidence of a non-human intelligence. === Constants === A physical universe is characterized by measurable quantities (size, mass, color, texture ...), and so a physical universe can be measured and defined. Contrast then becomes information, the statement ''this is a big apple'' requires a ''small apple'' against which big becomes a relative term. For analytical purposes we select a reference value, for example 0C or 32F, and measure all temperatures against this reference. The smaller the resolution of the measurements, the greater the information content (the file size of a 32 mega-pixel photo is larger than a 4 mega-pixel photo). A simulation universe may be presumed to also have a resolution dictating how much information the simulation can store and manipulate. To measure the fundamental parameters of our universe physics uses [[w:physical constant |physical constants]]. A physical constant is a [[w:physical quantity |physical quantity]] that is generally believed to be both universal in nature and have a constant value in time. These can be divided into 1) dimension-ed (measured using physical units ''kg'', ''m'', ''s'', ''A'' ...) such as the [[w:speed of light |speed of light]] ''c'', [[w:gravitational constant |gravitational constant]] ''G'', [[w:Planck constant |Planck constant]] ''h'' ... as in the table {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} Physicist [[w: |Lev Okun]] noted "Theoretical equations describing the physical world deal with dimensionless quantities and their solutions depend on dimensionless fundamental parameters. But experiments, from which these theories are extracted and by which they could be tested, involve measurements, i.e. comparisons with standard dimension-ful scales. Without standard dimension-ful units and hence without certain conventions physics is unthinkable <ref>Michael J. Duff et al, Journal of High Energy Physics, Volume 2002, JHEP03(2002)</ref>. 2) dimension-less, such as the [[w:Fine-structure_constant |fine structure constant]] ''α''. A dimension-less constant does not measure any physical quantity (it has no units; units = 1). 3) dimension-less [[w:mathematical constant |mathematical constants]], most notably [[w:pi |pi]] = 3.14159265358979 and [[w:Natural_logarithm |e]] = 2.718281828459. Although these are [[w:transcendental number |transcendental numbers]], they can be constructed by integers in a series, and so for a universe expanding incrementally (see simulation time), these constants could be formed within the simulation. For example, at time ''t''; <math display=block>t = 1; \frac{\pi^2}{6} = \frac{1}{t^2} </math> <math display=block>t = 2; \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{t^2}</math> <math display=block>t = now: \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots + \frac{1}{t^2} </math> We may now define the fundamental physical constant as a parameter specifically chosen by the Programmer and is encoded into the simulation code directly, and so whilst it may be inferable, it is not derived from other constants ([[w:Fine-structure_constant#Numerological_explanations_and_multiverse_theory |Richard Feynman on the fine structure constant]]). It should also be dimension-less otherwise the simulation itself becomes dimensioned (if the simulation is running on a celestial computer it is merely data, it has no physical size or shape or ...), and so the dimensioned constants (''G'', ''h'', ''c'', ''e''...) must all be derivable (derived from within the simulation) via the (embedded in the source code) fundamental physical constants (of which the fine structure constant alpha may be an example). Although [[w:pi |pi]] and [[w:Natural_logarithm |e]] are dimensionless, they can be derived internally (from integers), and as they have application in the mathematical realm, they can be referred to as mathematical constants. ==== Planck scale ==== The [[w:Planck scale |Planck scale]] refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the [[w:Standard Model |Standard Model]], [[w:quantum field theory |quantum field theory]] and [[w:general relativity |general relativity]] are no longer reconcilable, and [[w:Quantum Gravity |quantum effects of gravity]] are expected to dominate (quantum gravitational effects only appear at length scales near the Planck scale). Although particles may not be cognizance of our 'laws of physics', they do know the 'laws of nature'. These laws of nature would run directly off the universe OS (operating system), and so below this OS, 'physics' as we know it must necessarily break down. At present the Planck scale is the lowest known level, consequently any attempt to detect evidence of an underlying simulation coding must consider (if not actually begin at) this, the Planck scale<ref>https://www.youtube.com/watch?v=AMQRXGYCDrY Planck scale, Brian Greene</ref>. The [[w:International_System_of_Units |SI units]] for the dimension-ful mksa units are; meter (length), kilogram (mass), second (time), ampere (electric current). There are Planck units that represent these SI units, and so a simulation could use them as discrete building blocks; [[w:Planck length |Planck length]] (the smallest possible unit of length), [[w:Planck mass |Planck mass]] (the unit of mass), [[w:Planck time |Planck time]] (the smallest possible unit of time), [[w:Planck charge |Planck charge]] (the unit of charge). The speed of light then becomes ''c'' = 1 Planck length / 1 Planck time. These units would define the resolution and so information carrying capacity of the simulation universe. ==== Numbering systems ==== As well as our decimal system, computers apply binary and hexadecimal numbering systems. In particular the decimal and hexadecimal are of terrestrial origin and may not be considered 'universal'. Furthermore numbering systems measure only the frequency of an event and contain no information as to the event itself. The number 299 792 458 could refer to the speed of light (299 792 458 m/s) or could equally be referring to the number of apples in a container (299 792 458 apples). As such, numbers require a 'descriptive', whether m/s or apples. Numbers also do not include their history, is 299 792 458 for example a derivation of other base numbers? Present universe simulations use the laws of physics and the physical constants are built in, however both these laws and the physical constants are known only to a limited precision, and so a simulation with 10⁶² iterations (the present age of the universe in units of Planck time) will accumulate errors. Number based computing may be sufficient for ancestor-simulation models where only the observed region needs to be calculated, but has inherent limitations for deep universe simulations where the entire universe is continuously updated. The actual computational requirements for a Planck scale universe simulation based on a numbering system with the laws of physics embedded would be an unknown and consequently lead to an 'non-testable' hypothesis. This is a commonly applied reasoning for rejecting the deep universe simulation. ==== Geometrical objects ==== A mathematical constant such as [[w:pi |pi]] refers to a geometrical construct (the ratio of circle circumference to circle radius) and so is not constrained by any particular numbering system (in the decimal system π = 3.14159...), and so may be considered both universal and eternal. Likewise, by assigning geometrical objects instead of numbers to the Planck units, the problems with a numbering system can be resolved. These objects would however have to fulfill the following conditions; 1) embedded attribute - for example the object for length must embed the function of ''length'' such that a descriptive (km, mile ... ) is not required. Electron wavelength would then be measurable in terms of the length object, as such the length object must be embedded within the electron (the electron object). Although the mass object would incorporate the function ''mass'', the time object the function ''time'' ..., it is not necessary that there be an individual physical mass or physical length or physical time ..., but only that in relation to the other units, the object must express that function (i.e.: the mass object has the function of mass when in the presence of the objects for space and time). The electron could then be a complex event (complex geometrical object) constructed by combining the objects for mass, length, time and charge into 1 event, and thus electron charge, wavelength, frequency and mass would then be different aspects of that 1 geometry (the electron event) and not independent parameters (independent of each other). 2) The objects for mass, length, time and charge must be able to combine with each other [[w:Lego |Lego-style]] to form more complex objects (events) such as electrons and apples whilst still retaining the underlying information (the mass of the apple derives from the mass objects embedded within that apple). Not only must these objects be able to form complex events such as particles, but these events themselves are geometrical objects and so must likewise function according to their geometries. Electrons would orbit protons according to their respective electron and proton geometries, these orbits the result of geometrical imperatives and not due to any built-in laws of physics (the orbital path is a consequence of all the underlying geometries). However, as orbits follow regular and repeating patterns, they can be described (by us) using mathematical formulas. As the events grow in complexity (from atoms to molecules to planets), so too will the patterns (and likewise the formulas we use to describe them). Consequently the ''laws of physics'' would then become our mathematical descriptions of the underlying geometrically imposed patterns. 3) These objects would replace coded instructions (the instruction sets would be built into the objects) thereby instigating a geometrically autonomous universe. The electron 'knows' what to do by virtue of the information encoded within its geometry, no coded electron CALL FUNCTION is required. This would be equivalent to combining the hardware, software and CPU together such that the 'software' changes (adjusts) to the changing 'hardware' (DNA may be an analogy). Note: A purely mathematical universe has no limits in size and can be infinitely large and infinity small. A geometrical universe (that uses objects) has limitations, it can be no smaller than the smallest object for example and has discrete parts (those objects). The philosophy of the TOE (theory of everything) therefore includes a debate between the mathematical universe and the geometrical universe, however this distinction between mathematical and geometrical would only be apparent at the Planck scale. === Evidence of a simulation === The laws of physics are our incomplete observations of the natural universe, and so evidence of a simulation may be found in ambiguities or anomalies within these laws. Furthermore, if complexity arises over time, then at unit time the 'handiwork' of the Programmer may be notable by a simplicity and elegance of the geometries employed ... for the Programmer by definition has God-level programming skills. Here is a notable example. Mass, space and time from the number 1 The dimensions of mass, space and time are considered by science to be independent of each other, we cannot measure the ''distance'' from Tokyo to London using kilograms and amperes, or measure ''mass'' using space and time. Indeed, what characterizes a physical universe as opposed to a simulated universe is the notion that there is a fundamental structure underneath, that in some sense mass 'is', that time 'is' and space 'is' ... thus we cannot write ''kg'' in terms of ''m'' and ''s''. To do so would render our concepts of a physical universe meaningless. The 26th General Conference on Weights and Measures ([[w:2019 redefinition of SI base units|2019 redefinition of SI base units]]) assigned exact numerical values to 4 physical constants (''h, c, e, k''_B) independently of each other (and thereby confirming these as fundamental constants), and as they are measured in SI units ('''kg''', '''m''', '''s''', '''A''', '''K'''), these units must also be independent of each other (i.e.: these are fundamental units, for example if we could define ''m'' using ''A'' then the speed of light could be derived from, and so would depend upon, the value for the elementary charge ''e'', and so the value for ''c'' could not be assigned independently from ''e''). {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} We are familiar with inverse properties; plus charge and minus charge, matter and anti-matter ... and we can observe how these may form and/or cancel each other. A simulation universe however is required to be dimensionless (in sum total), for the simulated universe does not 'exist' in any physical sense outside of the 'Computer' (it is simply data on a celestial hard-disk). Our universe does not appear to have inverse properties such as anti-mass (-kg), anti-time (-s) or anti-space (anti-length -m), therefore the first problem the Programmer must solve is how to create the physical scaffolding (of mass, space and time). For example, the Programmer can start by selecting 2 dimensioned quantities, here are used ''r'', ''v'' <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref> such that :<math>kg = \frac{r^4}{v},\; m = \frac{r^9}{v^5},\; s = \frac{r^9}{v^6},\; A = \frac{v^3}{r^6}</math> Quantities ''r'' and ''v'' are chosen so that no unit (''kg'', ''m'', ''s'', ''A'') can cancel another unit (i.e.: the ''kg'' cannot cancel the ''m'' or the ''s'' ...), and so we have 4 independent units (we still cannot define the ''kg'' using the ''m'' or the ''s'' ...), however if 3 (or more) units are combined together in a specific ratio, they can cancel (in a certain ratio our ''r'' and ''v'' become inverse properties and so cancel each other; units = 1). <math>f_X = \frac{kg^9 s^{11}}{m^{15}} = \frac{(\frac{r^4}{v})^9 (\frac{r^9}{v^6})^{11}}{(\frac{r^9}{v^5})^{15}} = 1</math> This f_X, although embedded within are the dimensioned structures for mass, time and length (in the above ratio), would be a dimensionless mathematical structure, units = 1. Thus we may create as much mass, time and length as we wish, the only proviso being that they are created in f_X ratios, so that regardless of how massive, old and large our universe becomes, it is still in sum total dimensionless. Defining the dimensioned quantities ''r'', ''v'' in SI unit terms. :<math>r = (\frac{kg\;m}{s})^{1/4}</math> :<math>v = \frac{m}{s}</math> Mass :<math>\frac{r^4}{v} = (\frac{kg\;m}{s})\;(\frac{s}{m}) = kg</math> Length :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^5})^4 = \frac{s^{20}}{m^{20}}</math> :<math>(\frac{r^9}{v^5})^4 = \frac{kg^9 s^{11}}{m^{11}} = m^4 \frac{kg^9 s^{11}}{m^{15}} = m^4 f_X = m^4</math> Time :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^6})^4 = \frac{s^{24}}{m^{24}}</math> :<math>(\frac{r^9}{v^6})^4 = \frac{kg^9 s^{15}}{m^{15}} = s^4 \frac{kg^9 s^{11}}{m^{15}} = s^4 f_X = s^4</math> And so, although f_X is a dimensionless mathematical structure, we can embed within it the (mass, length, time ...) structures along with their dimensional attributes (kg, m, s, A ..). In the mathematical electron model (discussed below), the electron itself is an example of an f_X structure, it (f_electron) is a dimensionless geometrical object that embeds the physical electron parameters of wavelength, frequency, charge (note: A-m = ampere-meter are the units for a [[w:Magnetic_monopole#In_SI_units |magnetic monopole]]). <math>f_{electron}</math> :<math>units = \frac{A^3 m^3}{s} = \frac{(\frac{v^3}{r^6})^3 (\frac{r^9}{v^5})^3}{(\frac{r^9}{v^6})} = 1</math> We may note that at the macro-level (of planets and stars) these f_X ratio are not found, and so this level is the domain of the observed physical universe, however at the quantum level, f_X ratio do appear, f_electron as an example, the mathematical and physical domains then blurring. This would also explain why physics can measure precisely the parameters of the electron (wavelength, mass ...), but has never found the electron itself. == Programming == “God vs. science debates tend to be restricted to the premise that a God does not rely on science and that science does not need a God. As science and God are thus seen as mutually exclusive there are few, if any, serious attempts to construct mathematical models of a universe whose principle axiom does require a God. However, if there is an Intelligence responsible for the 14 billion year old universe of modern physics, being the universe of Einstein and Dirac, and beginning with the big bang as the act of 'creation', then we must ask how it might be done? What construction technique could have been used to set the laws of physics in motion?” <ref>[https://theprogrammergod.com/ The Programmer God, are we in a Simulation]</ref> === Simulation Time === The (dimensionless) simulation clock-rate would be defined as the minimum 'time variable' ('''age''') increment to the simulation. Using a simple loop as analogy, at ''age'' = 1, the simulation begins (the big bang), certain processes occur, when these are completed ''age'' increments (''age'' = 2, then 3, then 4 ... ) until ''age'' reaches ''the_end'' and the simulation stops. 'begin simulation FOR age = 1 TO the_end 'big bang = 1 conduct certain processes ........ NEXT age 'end simulation [[w:Quantum spacetime |Quantum spacetime]] and [[w:Quantum gravity |Quantum gravity]] models refer to [[w:Planck time | Planck time]] as the smallest discrete unit of time and so the incrementing variable '''age''' could be used to generate units of Planck time (and other Planck units, the physical scaffolding of the universe). In a geometrical model, to these Planck units could be assigned geometrical objects, for example; Initialize_physical_constants; FOR age = 1 TO the_end generate 1 unit of (Planck) time; '1 time 'object' T generate 1 unit of (Planck) mass; '1 mass 'object' M generate 1 unit of (Planck) length; '1 length 'object' L ........ NEXT age The variable ''age'' is the simulation clock-rate, it is simply a counter (1, 2, 3 ...) and so is a dimensionless number, the object T is the geometrical Planck time object, it is dimensioned and is measured by us in seconds. If ''age'' is the origin of Planck time (1 increment to ''age'' generates 1 T object) then ''age'' = 10⁶², this is based on the present [[w:Age_of_the_universe |age of the universe]], which, at 14 billion years, equates to 10⁶² units of Planck time. For each ''age'', certain operations are performed, only after they are finished does ''age'' increment (there is no ''time'' interval between increments). As noted, ''age'' being dimensionless, is not the same as dimensioned Planck time which is the geometrical object T, and this T, being dimensioned, can only appear within the simulation. The analogy would be frames of a movie, each frame contains dimensioned information but there is no ''time'' interval between frames. FOR age = 1 TO the_end (of the movie) display frame{age} NEXT age Although operations (between increments to ''age'') may be extensive, self-aware structures from within the simulation would have no means to determine this, they could only perceive themselves as being in a real-time (for them the smallest unit of ''time'' is 1T, just as the smallest unit of ''time'' in a movie is 1 frame). Their (those self-aware structures) dimension of time would then be a measure of relative motion (a change of state), and so although ultimately deriving from the variable ''age'', their time would not be the same as ''age''. If there was no motion, if all particles and photons were still (no change of state), then their time dimension could not update (if every frame in a movie was the same then actors within that movie could not register a change in time), ''age'' however would continue to increment. Thus we have 3 time structures; 1) the dimension-less simulation clock-rate variable ''age'', 2) the dimensioned time unit (object T), and 3) time as change of state (the observers time). Observer time requires a memory of past events against which a change of state can be perceived. The forward increment to ''age'' would constitute the [[w:arrow of time |arrow of time]]. Reversing this would reverse the arrow of time, the universe would likewise shrink in size and mass accordingly (just as a [[w:white hole |white hole]] is the (time) reversal of a [[w:black hole |black hole]]). FOR age = the_end TO 1 STEP -1 delete 1 unit of Planck time; delete 1 unit of Planck mass; delete 1 unit of Planck length; ........ NEXT age Adding mass, length and time objects per increment to ''age'' would force the universe expansion (in size and mass), and as such an anti-gravitational [[w:dark energy |dark energy]] would not be required, however these objects are dimensioned and so are generated within the simulation. This means that they must somehow combine in a specific ratio whereby they (the units for mass length, time, charge; ''kg'', ''m'', ''s'', ''A'') in sum total cancel each other, leaving the sum universe (the simulation itself) residing on that celestial hard-disk. We may introduce a theoretical dimensionless (f_X) geometrical object denoted as f_Planck within which are embedded the dimensioned objects MLTA (mass, length, time, charge), and from which they may be extracted. FOR age = 1 TO the_end add 1 f_Planck 'dimensionless geometrical 'object' { extract 1 unit of (Planck) time; '1 time 'object' T extract 1 unit of (Planck) mass; '1 mass 'object' M extract 1 unit of (Planck) length; '1 length 'object' L } ........ NEXT age This then means that the simulation, in order to create time T, must also create mass M and space L (become larger and more massive). Thus no matter how small or large the physical universe is (when seen internally), in sum total (when seen externally), there is no universe - it is merely data without physical form. === Universe time-line === As the universe expands outwards (through the constant addition of units of mass and length via f_Planck), and if this expansion pulls particles with it (if it is the origin of motion), then ''now'' (the present) would reside on the surface of the (constantly expanding at the speed of light; ''c'' = 1 Planck length / 1 Planck time) universe, and so the 'past' could be retained, for the past cannot be over-written by the present in an expanding universe (if ''now'' is always on the surface). As this expansion occurs at the Planck scale, information even below quantum states, down to the Planck scale, can be retained, the analogy would be the storing of every [[w:Keystroke_logging |keystroke]], a Planck scale version of the [[w:Akashic records |Akashic records]] ... for if our deeds (the past) are both stored and cannot be over-written (by the present), then we have a candidate for the '[[w:karma |karmic]] heavens' (Matthew 6:19 ''But lay up for yourselves treasures in 'heaven', where neither moth nor rust doth corrupt, and where thieves do not break through nor steal''). This also forms a universe '''time-line''' against which previous information can be compared with new information (a 'memory' of events), without which we could not link cause with effect. === Singularity === In a simulation, the data (software) requires a storage device that is ultimately hardware (RAM, HD ...). In a data world of 1's and 0's such as a computer game, characters within that game may analyze other parts of their 1's and 0's game, but they have no means to analyze the hard disk upon which they (and their game) are stored, for the hard disk is an electro-mechanical device, it is not part of their 1's and 0's world, it is a part of the 'real world', the world of their Programmer. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may or may not resemble the laws that operate in the 'real world' (the world of their Programmer). Thus any region where the laws of physics (the laws of their game world) break down would be significant. A [[w:singularity |singularity]] inside a black hole is such a region <ref>https://www.youtube.com/watch?v=W5j7umtZYB4 a black hole singularity as the interface between worlds</ref>. For the [[w:black hole electron |black-hole electron]], its black-hole center would then be analogous to a storage address on a hard disk, the interface between the simulation world and the real world. A massive (galactic) black-hole could be as an entire data sector. The surface of the black-hole would then be of the simulation world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however would be the interface between the data world and the 'hard disk' of the real world, and so would not exist in any 'physical' terms. It is external to the simulation. As analogy, we may discuss the 3-D surface area of a black-hole but not its volume (interior). === Laws of Physics === The scientific method is built upon testable hypothesis and reproducible results. Water always boils (in defined conditions), at 100°C. In a geometrical universe particles will behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these repeating patterns, the more complex the orbits, the more complex the formulas required to describe them and so forth. However if there is a source code from which these geometrical conditions were programmed, then there may also be non-repeating events, back-doors built into the code (a common practice by terrestrial programmers), these by definition would lie outside the laws of physics and so be labelled as miracles, yet they would be no less valid. === Determinism === [[File:Three body problem figure-8 orbit animation.gif|400px|thumb|An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259.<ref>Here the gravitational constant ''G'' has been set to 1, and the initial conditions are '''r'''₁(0) = −'''r'''₃(0) = (−0.97000436, 0.24308753); '''r'''₂(0) = (0,0); '''v'''₁(0) = '''v'''₃(0) = (0.4662036850, 0.4323657300); '''v'''₂(0) = (−0.93240737, −0.86473146). The values are obtained from Chenciner & Montgomery (2000).</ref>]] Particles form more complex structures such as atoms and molecules via a system of orbitals; nuclear, atomic and gravitational. The [[w:Three-body_problem |3-body problem]] is the problem of taking the initial positions and velocities (or [[w:momentum|momenta |momentum|momenta]]) of three or more point masses and solving for their subsequent motion according to [[w:Newton's laws of motion |Newton's laws of motion]] and [[w:Newton's law of universal gravitation |Newton's law of universal gravitation]].<ref name="PrincetonCompanion">{{Citation | last = Barrow-Green | first = June | year = 2008 | title = The Three-Body Problem | editor-last1 = Gowers | editor-first1 = Timothy | editor-last2 = Barrow-Green | editor-first2 = June | editor-last3 = Leader | editor-first3 = Imre | encyclopedia = The Princeton Companion to Mathematics | pages = 726–728 | publisher = Princeton University Press }}</ref>. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for gods and men alike the only way to know what that outcome will be is to run the simulation itself. ==Geometry coded universe== Modelling a Planck scale simulation universe using geometrical forms (links) * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass == External links == * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] * [https://philpapers.org/rec/GRUTIA-2 Simulation theory as evidence for God] (academic peer-reviewed article) ==References== {{Reflist}} [[Category:Philosophy| ]] [[Category:Philosophy of science| ]] bjxhovj99qssgqywrf58fo5p76il6vn 2718277 2718265 2025-06-10T20:09:15Z Atcovi 276019 Reverted edits by [[Special:Contributions/212.200.164.104|212.200.164.104]] ([[User_talk:212.200.164.104|talk]]) to last version by [[User:Platos Cave (physics)|Platos Cave (physics)]] using [[Wikiversity:Rollback|rollback]] 2717949 wikitext text/x-wiki '''Is God a Programmer? analyzing the deep-universe simulation hypothesis at the Planck scale''' The [[w:simulation hypothesis |simulation hypothesis]] is the proposal that all of reality, including the Earth and the rest of the universe, could be an artificial simulation, such as a computer simulation. [[w:Neil_deGrasse_Tyson |Neil deGrasse Tyson]] put the odds at 50-50 that our entire existence is a program on someone else’s hard drive <ref>Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. [[w:David_Chalmers |David Chalmers]] noted “We in this universe can create simulated worlds and there’s nothing remotely spooky about that. Our creator isn’t especially spooky, it’s just some teenage hacker in the next universe up. Turn the tables, and we are essentially gods over our own computer creations <ref>https://www.youtube.com/watch?v=yqbS5qJU8PA, David Chalmers, Serious Science</ref> <ref>The Matrix as Metaphysics, David Chalmers http://consc.net/papers/matrix.pdf</ref> <ref>Are We Living in a Computer Simulation?https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/</ref>. The commonly postulated [[w:Ancestor_simulation |ancestor simulation]] approach, which [[w:Nick Bostrom |Nick Bostrom]] called "the simulation argument", argues for "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor. However this simulation variant can be traced back to an 'organic base reality' (the original programmer ancestors and their physical planet). The [[v:God_(programmer) |Programmer God]] hypothesis<ref>https://codingthecosmos.com/podcast/ AI generated podcasts</ref> conversely states that a (deep universe) simulation began with the big bang and was programmed by an external intelligence (external to the physical universe), the Programmer by definition a God in the creator of the universe context. Our universe in its entirety, down to the smallest detail, and including life-forms, is within the simulation, the laws of nature, at their most fundamental level, are coded rules running on top of the simulation operating system. The operating system itself is mathematical (and potentially the origin of mathematics). Any candidate for a Programmer-God simulation-universe source code must satisfy these conditions; :1. It can generate physical structures from mathematical forms. :2. The sum universe is dimensionless (simply data on a celestial hard disk). :3. We must be able to use it to derive the laws of physics (because the source code is the origin of the laws of nature, and the laws of physics are our observations of the laws of nature). :4. The mathematical logic must be unknown to us (the Programmer is a non-human intelligence). :5. The coding should have an 'elegance' commensurate with the Programmer's level of skill. == Philosophy == Physicist [[w:Eugene Wigner |Eugene Wigner]] ([[w:The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences |The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]) <ref>{{Cite journal | last1 = Wigner | first1 = E. P. | authorlink = Eugene Wigner| doi = 10.1002/cpa.3160130102 | title = The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959 | journal = Communications on Pure and Applied Mathematics | volume = 13 | pages = 1–14 | year = 1960 | pmid = | pmc = |bibcode = 1960CPAM...13....1W }}</ref> <blockquote>The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. </blockquote> === Discussion === [[w:Philosophy of mathematics |Philosophy of mathematics]] is that branch of philosophy which attempts to answer questions such as: ‘why is mathematics useful in describing nature?’, ‘in which sense, if any, do mathematical entities such as numbers exist?’ and ‘why and how are mathematical statements true?’ This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math. Mathematical realism holds that mathematical entities exist independently of the human mind. We do not invent mathematics, but rather discover it. Triangles, for example, are real entities that have an existence <ref>- http://plato.stanford.edu/entries/platonism-mathematics/</ref>. The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality. It can be considered a form of [[w:Pythagoreanism | Pythagoreanism]] or [[w:Platonism | Platonism]] in that it proposes the existence of ''mathematical objects''; and a form of [[w:philosophy of mathematics | mathematical monism]] in that it denies that anything exists except these ''mathematical objects''. Physicist [[w:Max Tegmark | Max Tegmark]] in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality"<ref name="Tegmark1998">{{cite journal|last=Tegmark |first=Max |date=November 1998 |title=Is "the Theory of Everything" Merely the Ultimate Ensemble Theory? |journal=Annals of Physics |volume=270 |issue=1 |pages=1–51 |doi=10.1006/aphy.1998.5855 |arxiv = gr-qc/9704009 |bibcode = 1998AnPhy.270....1T }}</ref><ref>M. Tegmark 2014, "[http://mathematicaluniverse.org Our Mathematical Universe]", Knopf</ref> proposed that ''Our external physical reality is a mathematical structure''.<ref name="Tegmark2008">{{cite journal|last=Tegmark |first=Max |date=February 2008 |title=The Mathematical Universe |journal=Foundations of Physics |volume=38 |issue=2 |pages=101–150 |doi=10.1007/s10701-007-9186-9 |arxiv=0704.0646|bibcode = 2008FoPh...38..101T }}</ref> That is, the physical universe is not merely ''described by'' mathematics, but ''is'' mathematics (specifically, a [[w:mathematical structure | mathematical structure]]). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref> The principle constraints to any mathematical universe simulation hypothesis are; 1. the computational resources required. The ancestor simulation can resolve this by adapting from the [[w:virtual rality |virtual reality]] approach where only the observable region is simulated and only to the degree required, and 2. that any 'self-aware structures' (humans for example) within the simulation must "subjectively perceive themselves as existing in a physically 'real' world".<ref>Tegmark (1998), p. 1.</ref>. Succinctly, our computer games may be able to simulate our physical world, but they are still only simulations of a physical reality (regardless of how realistic they may seem) ... we are not yet able to program actual physical dimensions of mass, space and time from mathematical structures, and indeed this may not be possible with a computer hard-ware architecture that can only process binary data. === Deep-universe source code === As a deep-universe simulation is programmed by an external (external to the universe) intelligence (the Programmer God hypothesis), we cannot presume a priori knowledge regarding the simulation source code other than from this code the laws of nature emerged, and so any deep-universe simulation model we try to emulate must be universal, i.e.: independent of any system of units, of the [[w:Dimensional_analysis |dimensioned]] [[w:physical constants |physical constants]] (''G'', ''h'', ''c'', ''e'' .. ), and of any numbering systems. Furthermore, although a deep-universe simulation source code may use mathematical forms (circles, spheres ...) we are familiar with (for ultimately the source code is the origin of these forms), it will have been developed by a non-human intelligence and so we may have to develop new mathematical tools to decipher the underlying logic. By implication therefore, any theoretical basis for a source code that fits the above criteria (and from which the laws of nature will emerge), could be construed as our first tangible evidence of a non-human intelligence. === Constants === A physical universe is characterized by measurable quantities (size, mass, color, texture ...), and so a physical universe can be measured and defined. Contrast then becomes information, the statement ''this is a big apple'' requires a ''small apple'' against which big becomes a relative term. For analytical purposes we select a reference value, for example 0C or 32F, and measure all temperatures against this reference. The smaller the resolution of the measurements, the greater the information content (the file size of a 32 mega-pixel photo is larger than a 4 mega-pixel photo). A simulation universe may be presumed to also have a resolution dictating how much information the simulation can store and manipulate. To measure the fundamental parameters of our universe physics uses [[w:physical constant |physical constants]]. A physical constant is a [[w:physical quantity |physical quantity]] that is generally believed to be both universal in nature and have a constant value in time. These can be divided into 1) dimension-ed (measured using physical units ''kg'', ''m'', ''s'', ''A'' ...) such as the [[w:speed of light |speed of light]] ''c'', [[w:gravitational constant |gravitational constant]] ''G'', [[w:Planck constant |Planck constant]] ''h'' ... as in the table {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} Physicist [[w: |Lev Okun]] noted "Theoretical equations describing the physical world deal with dimensionless quantities and their solutions depend on dimensionless fundamental parameters. But experiments, from which these theories are extracted and by which they could be tested, involve measurements, i.e. comparisons with standard dimension-ful scales. Without standard dimension-ful units and hence without certain conventions physics is unthinkable <ref>Michael J. Duff et al, Journal of High Energy Physics, Volume 2002, JHEP03(2002)</ref>. 2) dimension-less, such as the [[w:Fine-structure_constant |fine structure constant]] ''α''. A dimension-less constant does not measure any physical quantity (it has no units; units = 1). 3) dimension-less [[w:mathematical constant |mathematical constants]], most notably [[w:pi |pi]] = 3.14159265358979 and [[w:Natural_logarithm |e]] = 2.718281828459. Although these are [[w:transcendental number |transcendental numbers]], they can be constructed by integers in a series, and so for a universe expanding incrementally (see simulation time), these constants could be formed within the simulation. For example, at time ''t''; <math display=block>t = 1; \frac{\pi^2}{6} = \frac{1}{t^2} </math> <math display=block>t = 2; \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{t^2}</math> <math display=block>t = now: \frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots + \frac{1}{t^2} </math> We may now define the fundamental physical constant as a parameter specifically chosen by the Programmer and is encoded into the simulation code directly, and so whilst it may be inferable, it is not derived from other constants ([[w:Fine-structure_constant#Numerological_explanations_and_multiverse_theory |Richard Feynman on the fine structure constant]]). It should also be dimension-less otherwise the simulation itself becomes dimensioned (if the simulation is running on a celestial computer it is merely data, it has no physical size or shape or ...), and so the dimensioned constants (''G'', ''h'', ''c'', ''e''...) must all be derivable (derived from within the simulation) via the (embedded in the source code) fundamental physical constants (of which the fine structure constant alpha may be an example). Although [[w:pi |pi]] and [[w:Natural_logarithm |e]] are dimensionless, they can be derived internally (from integers), and as they have application in the mathematical realm, they can be referred to as mathematical constants. ==== Planck scale ==== The [[w:Planck scale |Planck scale]] refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the [[w:Standard Model |Standard Model]], [[w:quantum field theory |quantum field theory]] and [[w:general relativity |general relativity]] are no longer reconcilable, and [[w:Quantum Gravity |quantum effects of gravity]] are expected to dominate (quantum gravitational effects only appear at length scales near the Planck scale). Although particles may not be cognizance of our 'laws of physics', they do know the 'laws of nature'. These laws of nature would run directly off the universe OS (operating system), and so below this OS, 'physics' as we know it must necessarily break down. At present the Planck scale is the lowest known level, consequently any attempt to detect evidence of an underlying simulation coding must consider (if not actually begin at) this, the Planck scale<ref>https://www.youtube.com/watch?v=AMQRXGYCDrY Planck scale, Brian Greene</ref>. The [[w:International_System_of_Units |SI units]] for the dimension-ful mksa units are; meter (length), kilogram (mass), second (time), ampere (electric current). There are Planck units that represent these SI units, and so a simulation could use them as discrete building blocks; [[w:Planck length |Planck length]] (the smallest possible unit of length), [[w:Planck mass |Planck mass]] (the unit of mass), [[w:Planck time |Planck time]] (the smallest possible unit of time), [[w:Planck charge |Planck charge]] (the unit of charge). The speed of light then becomes ''c'' = 1 Planck length / 1 Planck time. These units would define the resolution and so information carrying capacity of the simulation universe. ==== Numbering systems ==== As well as our decimal system, computers apply binary and hexadecimal numbering systems. In particular the decimal and hexadecimal are of terrestrial origin and may not be considered 'universal'. Furthermore numbering systems measure only the frequency of an event and contain no information as to the event itself. The number 299 792 458 could refer to the speed of light (299 792 458 m/s) or could equally be referring to the number of apples in a container (299 792 458 apples). As such, numbers require a 'descriptive', whether m/s or apples. Numbers also do not include their history, is 299 792 458 for example a derivation of other base numbers? Present universe simulations use the laws of physics and the physical constants are built in, however both these laws and the physical constants are known only to a limited precision, and so a simulation with 10⁶² iterations (the present age of the universe in units of Planck time) will accumulate errors. Number based computing may be sufficient for ancestor-simulation models where only the observed region needs to be calculated, but has inherent limitations for deep universe simulations where the entire universe is continuously updated. The actual computational requirements for a Planck scale universe simulation based on a numbering system with the laws of physics embedded would be an unknown and consequently lead to an 'non-testable' hypothesis. This is a commonly applied reasoning for rejecting the deep universe simulation. ==== Geometrical objects ==== A mathematical constant such as [[w:pi |pi]] refers to a geometrical construct (the ratio of circle circumference to circle radius) and so is not constrained by any particular numbering system (in the decimal system π = 3.14159...), and so may be considered both universal and eternal. Likewise, by assigning geometrical objects instead of numbers to the Planck units, the problems with a numbering system can be resolved. These objects would however have to fulfill the following conditions; 1) embedded attribute - for example the object for length must embed the function of ''length'' such that a descriptive (km, mile ... ) is not required. Electron wavelength would then be measurable in terms of the length object, as such the length object must be embedded within the electron (the electron object). Although the mass object would incorporate the function ''mass'', the time object the function ''time'' ..., it is not necessary that there be an individual physical mass or physical length or physical time ..., but only that in relation to the other units, the object must express that function (i.e.: the mass object has the function of mass when in the presence of the objects for space and time). The electron could then be a complex event (complex geometrical object) constructed by combining the objects for mass, length, time and charge into 1 event, and thus electron charge, wavelength, frequency and mass would then be different aspects of that 1 geometry (the electron event) and not independent parameters (independent of each other). 2) The objects for mass, length, time and charge must be able to combine with each other [[w:Lego |Lego-style]] to form more complex objects (events) such as electrons and apples whilst still retaining the underlying information (the mass of the apple derives from the mass objects embedded within that apple). Not only must these objects be able to form complex events such as particles, but these events themselves are geometrical objects and so must likewise function according to their geometries. Electrons would orbit protons according to their respective electron and proton geometries, these orbits the result of geometrical imperatives and not due to any built-in laws of physics (the orbital path is a consequence of all the underlying geometries). However, as orbits follow regular and repeating patterns, they can be described (by us) using mathematical formulas. As the events grow in complexity (from atoms to molecules to planets), so too will the patterns (and likewise the formulas we use to describe them). Consequently the ''laws of physics'' would then become our mathematical descriptions of the underlying geometrically imposed patterns. 3) These objects would replace coded instructions (the instruction sets would be built into the objects) thereby instigating a geometrically autonomous universe. The electron 'knows' what to do by virtue of the information encoded within its geometry, no coded electron CALL FUNCTION is required. This would be equivalent to combining the hardware, software and CPU together such that the 'software' changes (adjusts) to the changing 'hardware' (DNA may be an analogy). Note: A purely mathematical universe has no limits in size and can be infinitely large and infinity small. A geometrical universe (that uses objects) has limitations, it can be no smaller than the smallest object for example and has discrete parts (those objects). The philosophy of the TOE (theory of everything) therefore includes a debate between the mathematical universe and the geometrical universe, however this distinction between mathematical and geometrical would only be apparent at the Planck scale. === Evidence of a simulation === The laws of physics are our incomplete observations of the natural universe, and so evidence of a simulation may be found in ambiguities or anomalies within these laws. Furthermore, if complexity arises over time, then at unit time the 'handiwork' of the Programmer may be notable by a simplicity and elegance of the geometries employed ... for the Programmer by definition has God-level programming skills. Here is a notable example. Mass, space and time from the number 1 The dimensions of mass, space and time are considered by science to be independent of each other, we cannot measure the ''distance'' from Tokyo to London using kilograms and amperes, or measure ''mass'' using space and time. Indeed, what characterizes a physical universe as opposed to a simulated universe is the notion that there is a fundamental structure underneath, that in some sense mass 'is', that time 'is' and space 'is' ... thus we cannot write ''kg'' in terms of ''m'' and ''s''. To do so would render our concepts of a physical universe meaningless. The 26th General Conference on Weights and Measures ([[w:2019 redefinition of SI base units|2019 redefinition of SI base units]]) assigned exact numerical values to 4 physical constants (''h, c, e, k''_B) independently of each other (and thereby confirming these as fundamental constants), and as they are measured in SI units ('''kg''', '''m''', '''s''', '''A''', '''K'''), these units must also be independent of each other (i.e.: these are fundamental units, for example if we could define ''m'' using ''A'' then the speed of light could be derived from, and so would depend upon, the value for the elementary charge ''e'', and so the value for ''c'' could not be assigned independently from ''e''). {| class="wikitable" |+ Physical constants ! constant ! symbol ! SI units |- | [[w:Speed of light | Speed of light]] | ''c'' | <math>\frac{m}{s}</math> |- | [[w:Planck constant | Planck constant]] | ''h'' | <math>\frac{kg \;m^2}{s}</math> |- | [[w:Elementary charge |Elementary charge]] | ''e'' | <math>C = A s</math> |- | [[w:Boltzmann constant | Boltzmann constant]] | ''k''_B | <math>\frac{kg \;m^2}{s^2 \;K}</math> |} We are familiar with inverse properties; plus charge and minus charge, matter and anti-matter ... and we can observe how these may form and/or cancel each other. A simulation universe however is required to be dimensionless (in sum total), for the simulated universe does not 'exist' in any physical sense outside of the 'Computer' (it is simply data on a celestial hard-disk). Our universe does not appear to have inverse properties such as anti-mass (-kg), anti-time (-s) or anti-space (anti-length -m), therefore the first problem the Programmer must solve is how to create the physical scaffolding (of mass, space and time). For example, the Programmer can start by selecting 2 dimensioned quantities, here are used ''r'', ''v'' <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref> such that :<math>kg = \frac{r^4}{v},\; m = \frac{r^9}{v^5},\; s = \frac{r^9}{v^6},\; A = \frac{v^3}{r^6}</math> Quantities ''r'' and ''v'' are chosen so that no unit (''kg'', ''m'', ''s'', ''A'') can cancel another unit (i.e.: the ''kg'' cannot cancel the ''m'' or the ''s'' ...), and so we have 4 independent units (we still cannot define the ''kg'' using the ''m'' or the ''s'' ...), however if 3 (or more) units are combined together in a specific ratio, they can cancel (in a certain ratio our ''r'' and ''v'' become inverse properties and so cancel each other; units = 1). <math>f_X = \frac{kg^9 s^{11}}{m^{15}} = \frac{(\frac{r^4}{v})^9 (\frac{r^9}{v^6})^{11}}{(\frac{r^9}{v^5})^{15}} = 1</math> This f_X, although embedded within are the dimensioned structures for mass, time and length (in the above ratio), would be a dimensionless mathematical structure, units = 1. Thus we may create as much mass, time and length as we wish, the only proviso being that they are created in f_X ratios, so that regardless of how massive, old and large our universe becomes, it is still in sum total dimensionless. Defining the dimensioned quantities ''r'', ''v'' in SI unit terms. :<math>r = (\frac{kg\;m}{s})^{1/4}</math> :<math>v = \frac{m}{s}</math> Mass :<math>\frac{r^4}{v} = (\frac{kg\;m}{s})\;(\frac{s}{m}) = kg</math> Length :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^5})^4 = \frac{s^{20}}{m^{20}}</math> :<math>(\frac{r^9}{v^5})^4 = \frac{kg^9 s^{11}}{m^{11}} = m^4 \frac{kg^9 s^{11}}{m^{15}} = m^4 f_X = m^4</math> Time :<math>(r^9)^4 = \frac{kg^9\;m^9}{s^9} </math> :<math>(\frac{1}{v^6})^4 = \frac{s^{24}}{m^{24}}</math> :<math>(\frac{r^9}{v^6})^4 = \frac{kg^9 s^{15}}{m^{15}} = s^4 \frac{kg^9 s^{11}}{m^{15}} = s^4 f_X = s^4</math> And so, although f_X is a dimensionless mathematical structure, we can embed within it the (mass, length, time ...) structures along with their dimensional attributes (kg, m, s, A ..). In the mathematical electron model (discussed below), the electron itself is an example of an f_X structure, it (f_electron) is a dimensionless geometrical object that embeds the physical electron parameters of wavelength, frequency, charge (note: A-m = ampere-meter are the units for a [[w:Magnetic_monopole#In_SI_units |magnetic monopole]]). <math>f_{electron}</math> :<math>units = \frac{A^3 m^3}{s} = \frac{(\frac{v^3}{r^6})^3 (\frac{r^9}{v^5})^3}{(\frac{r^9}{v^6})} = 1</math> We may note that at the macro-level (of planets and stars) these f_X ratio are not found, and so this level is the domain of the observed physical universe, however at the quantum level, f_X ratio do appear, f_electron as an example, the mathematical and physical domains then blurring. This would also explain why physics can measure precisely the parameters of the electron (wavelength, mass ...), but has never found the electron itself. == Programming == “God vs. science debates tend to be restricted to the premise that a God does not rely on science and that science does not need a God. As science and God are thus seen as mutually exclusive there are few, if any, serious attempts to construct mathematical models of a universe whose principle axiom does require a God. However, if there is an Intelligence responsible for the 14 billion year old universe of modern physics, being the universe of Einstein and Dirac, and beginning with the big bang as the act of 'creation', then we must ask how it might be done? What construction technique could have been used to set the laws of physics in motion?” <ref>[https://theprogrammergod.com/ The Programmer God, are we in a Simulation]</ref> === Simulation Time === The (dimensionless) simulation clock-rate would be defined as the minimum 'time variable' ('''age''') increment to the simulation. Using a simple loop as analogy, at ''age'' = 1, the simulation begins (the big bang), certain processes occur, when these are completed ''age'' increments (''age'' = 2, then 3, then 4 ... ) until ''age'' reaches ''the_end'' and the simulation stops. 'begin simulation FOR age = 1 TO the_end 'big bang = 1 conduct certain processes ........ NEXT age 'end simulation [[w:Quantum spacetime |Quantum spacetime]] and [[w:Quantum gravity |Quantum gravity]] models refer to [[w:Planck time | Planck time]] as the smallest discrete unit of time and so the incrementing variable '''age''' could be used to generate units of Planck time (and other Planck units, the physical scaffolding of the universe). In a geometrical model, to these Planck units could be assigned geometrical objects, for example; Initialize_physical_constants; FOR age = 1 TO the_end generate 1 unit of (Planck) time; '1 time 'object' T generate 1 unit of (Planck) mass; '1 mass 'object' M generate 1 unit of (Planck) length; '1 length 'object' L ........ NEXT age The variable ''age'' is the simulation clock-rate, it is simply a counter (1, 2, 3 ...) and so is a dimensionless number, the object T is the geometrical Planck time object, it is dimensioned and is measured by us in seconds. If ''age'' is the origin of Planck time (1 increment to ''age'' generates 1 T object) then ''age'' = 10⁶², this is based on the present [[w:Age_of_the_universe |age of the universe]], which, at 14 billion years, equates to 10⁶² units of Planck time. For each ''age'', certain operations are performed, only after they are finished does ''age'' increment (there is no ''time'' interval between increments). As noted, ''age'' being dimensionless, is not the same as dimensioned Planck time which is the geometrical object T, and this T, being dimensioned, can only appear within the simulation. The analogy would be frames of a movie, each frame contains dimensioned information but there is no ''time'' interval between frames. FOR age = 1 TO the_end (of the movie) display frame{age} NEXT age Although operations (between increments to ''age'') may be extensive, self-aware structures from within the simulation would have no means to determine this, they could only perceive themselves as being in a real-time (for them the smallest unit of ''time'' is 1T, just as the smallest unit of ''time'' in a movie is 1 frame). Their (those self-aware structures) dimension of time would then be a measure of relative motion (a change of state), and so although ultimately deriving from the variable ''age'', their time would not be the same as ''age''. If there was no motion, if all particles and photons were still (no change of state), then their time dimension could not update (if every frame in a movie was the same then actors within that movie could not register a change in time), ''age'' however would continue to increment. Thus we have 3 time structures; 1) the dimension-less simulation clock-rate variable ''age'', 2) the dimensioned time unit (object T), and 3) time as change of state (the observers time). Observer time requires a memory of past events against which a change of state can be perceived. The forward increment to ''age'' would constitute the [[w:arrow of time |arrow of time]]. Reversing this would reverse the arrow of time, the universe would likewise shrink in size and mass accordingly (just as a [[w:white hole |white hole]] is the (time) reversal of a [[w:black hole |black hole]]). FOR age = the_end TO 1 STEP -1 delete 1 unit of Planck time; delete 1 unit of Planck mass; delete 1 unit of Planck length; ........ NEXT age Adding mass, length and time objects per increment to ''age'' would force the universe expansion (in size and mass), and as such an anti-gravitational [[w:dark energy |dark energy]] would not be required, however these objects are dimensioned and so are generated within the simulation. This means that they must somehow combine in a specific ratio whereby they (the units for mass length, time, charge; ''kg'', ''m'', ''s'', ''A'') in sum total cancel each other, leaving the sum universe (the simulation itself) residing on that celestial hard-disk. We may introduce a theoretical dimensionless (f_X) geometrical object denoted as f_Planck within which are embedded the dimensioned objects MLTA (mass, length, time, charge), and from which they may be extracted. FOR age = 1 TO the_end add 1 f_Planck 'dimensionless geometrical 'object' { extract 1 unit of (Planck) time; '1 time 'object' T extract 1 unit of (Planck) mass; '1 mass 'object' M extract 1 unit of (Planck) length; '1 length 'object' L } ........ NEXT age This then means that the simulation, in order to create time T, must also create mass M and space L (become larger and more massive). Thus no matter how small or large the physical universe is (when seen internally), in sum total (when seen externally), there is no universe - it is merely data without physical form. === Universe time-line === As the universe expands outwards (through the constant addition of units of mass and length via f_Planck), and if this expansion pulls particles with it (if it is the origin of motion), then ''now'' (the present) would reside on the surface of the (constantly expanding at the speed of light; ''c'' = 1 Planck length / 1 Planck time) universe, and so the 'past' could be retained, for the past cannot be over-written by the present in an expanding universe (if ''now'' is always on the surface). As this expansion occurs at the Planck scale, information even below quantum states, down to the Planck scale, can be retained, the analogy would be the storing of every [[w:Keystroke_logging |keystroke]], a Planck scale version of the [[w:Akashic records |Akashic records]] ... for if our deeds (the past) are both stored and cannot be over-written (by the present), then we have a candidate for the '[[w:karma |karmic]] heavens' (Matthew 6:19 ''But lay up for yourselves treasures in 'heaven', where neither moth nor rust doth corrupt, and where thieves do not break through nor steal''). This also forms a universe '''time-line''' against which previous information can be compared with new information (a 'memory' of events), without which we could not link cause with effect. === Singularity === In a simulation, the data (software) requires a storage device that is ultimately hardware (RAM, HD ...). In a data world of 1's and 0's such as a computer game, characters within that game may analyze other parts of their 1's and 0's game, but they have no means to analyze the hard disk upon which they (and their game) are stored, for the hard disk is an electro-mechanical device, it is not part of their 1's and 0's world, it is a part of the 'real world', the world of their Programmer. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may or may not resemble the laws that operate in the 'real world' (the world of their Programmer). Thus any region where the laws of physics (the laws of their game world) break down would be significant. A [[w:singularity |singularity]] inside a black hole is such a region <ref>https://www.youtube.com/watch?v=W5j7umtZYB4 a black hole singularity as the interface between worlds</ref>. For the [[w:black hole electron |black-hole electron]], its black-hole center would then be analogous to a storage address on a hard disk, the interface between the simulation world and the real world. A massive (galactic) black-hole could be as an entire data sector. The surface of the black-hole would then be of the simulation world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however would be the interface between the data world and the 'hard disk' of the real world, and so would not exist in any 'physical' terms. It is external to the simulation. As analogy, we may discuss the 3-D surface area of a black-hole but not its volume (interior). === Laws of Physics === The scientific method is built upon testable hypothesis and reproducible results. Water always boils (in defined conditions), at 100°C. In a geometrical universe particles will behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these repeating patterns, the more complex the orbits, the more complex the formulas required to describe them and so forth. However if there is a source code from which these geometrical conditions were programmed, then there may also be non-repeating events, back-doors built into the code (a common practice by terrestrial programmers), these by definition would lie outside the laws of physics and so be labelled as miracles, yet they would be no less valid. === Determinism === [[File:Three body problem figure-8 orbit animation.gif|400px|thumb|An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259.<ref>Here the gravitational constant ''G'' has been set to 1, and the initial conditions are '''r'''₁(0) = −'''r'''₃(0) = (−0.97000436, 0.24308753); '''r'''₂(0) = (0,0); '''v'''₁(0) = '''v'''₃(0) = (0.4662036850, 0.4323657300); '''v'''₂(0) = (−0.93240737, −0.86473146). The values are obtained from Chenciner & Montgomery (2000).</ref>]] Particles form more complex structures such as atoms and molecules via a system of orbitals; nuclear, atomic and gravitational. The [[w:Three-body_problem |3-body problem]] is the problem of taking the initial positions and velocities (or [[w:momentum|momenta |momentum|momenta]]) of three or more point masses and solving for their subsequent motion according to [[w:Newton's laws of motion |Newton's laws of motion]] and [[w:Newton's law of universal gravitation |Newton's law of universal gravitation]].<ref name="PrincetonCompanion">{{Citation | last = Barrow-Green | first = June | year = 2008 | title = The Three-Body Problem | editor-last1 = Gowers | editor-first1 = Timothy | editor-last2 = Barrow-Green | editor-first2 = June | editor-last3 = Leader | editor-first3 = Imre | encyclopedia = The Princeton Companion to Mathematics | pages = 726–728 | publisher = Princeton University Press }}</ref>. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for gods and men alike the only way to know what that outcome will be is to run the simulation itself. ==Geometry coded universe== Modelling a Planck scale simulation universe using geometrical forms (links) * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass == External links == * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] * [https://philpapers.org/rec/GRUTIA-2 Simulation theory as evidence for God] (academic peer-reviewed article) ==References== {{Reflist}} [[Category:Philosophy| ]] [[Category:Philosophy of science| ]] jmsz7gwcwfodv2xpyhikh3z1h9hxqgz 0 246801 2718266 2717951 2025-06-10T19:53:16Z 212.200.164.104 /* Planck objects */ 2718266 wikitext text/x-wiki '''The mathematical electron model''' In the mathematical electron model <ref>Macleod, M.J. {{Cite journal |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>, the electron is a dimensionless geometrical formula (ψ). This formula ψ, which resembles the volume of a torus or surface of a 4-D hypersphere, is itself a complex geometry that is the construct of simpler geometries; the [[w:Planck_units |Planck units]]. In this model the Planck units are geometrical objects, the geometry of 2 dimensionless constants (the[[w:fine-structure constant | fine structure constant alpha]] and a mathematical constant[[v:Planck_units_(geometrical)#Omega | Omega]]). Although dimensionless, the function of the Planck unit is embedded within the geometry; the geometry of the Planck time object embeds the function 'time', the geometry of the Planck length object embeds the function 'length' ... and being geometrical objects they can combine to form more complex objects, from electrons to galaxies. This means that the electron parameters are defined in Planck units; electron wavelength is measured in units of Planck length, electron frequency is measured in units of Planck time ... It is this geometrical electron formula ψ that dictates the magnitude of the electron parameters; length of the wavelength = ψ * Planck length (ψ units of Planck length), frequency = ψ * Planck time ... This ψ thus not only embeds the Planck units required for the electron parameters, it also dictates the magnitude of these parameters, and so technically it is the electron. This suggests there is no physical electron (only physical parameters), and if the electron is therefore a mathematical particle, then so too are the other particles, and so the universe itself becomes a mathematical universe. The formula ψ is the geometry of 2 constants; the [[w:dimensionless physical constant | dimensionless physical constant]] (inverse) [[w:fine-structure constant | fine structure constant alpha ]] '''α''' = 137.035 999 139 (CODATA 2014) and [[v:Planck_units_(geometrical)#Omega | Omega]] '''Ω''' = 2.0071349496 (best fit) Omega has a potential solution in terms of pi and e and so may be a mathematical (not physical) constant :<math>\Omega = \sqrt{ \left(\pi^e e^{(1-e)}\right)} = 2.0071349543... </math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = 0.238954531\;x10^{23}</math>, units = 1 === Planck objects === {{main|Planck units (geometrical)}} For the Planck units, the model uses geometrical objects (the geometry of alpha and Omega) instead of a numbering system, this has the advantage in that the attribute can be embedded within the geometry (although the geometry itself is dimensionless). {| class="wikitable" |+table 1. Geometrical units ! Attribute ! Geometrical object ! Unit |- | mass | <math>M = (1)</math> | (kg) |- | time | <math>T = (\pi)</math> | (s) |- | velocity | <math>V = (2\pi\Omega^2)</math> | (m/s) |- | length | <math>L = (2\pi^2\Omega^2)</math> | (m) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | (A) |} As these objects have a geometrical form, we can combine them [[w:Lego |Lego]] style; the length object L can be combined with the time object T to form the velocity object V and so forth ... to create complex events such as electrons to apples to ... and so the apple has mass because embedded within it are the mass objects M, complex events thus retain all the underlying information. This however requires a relationship between the Planck unit geometries that defines how they may combine, this can be represented by assigning to each attribute a unit number '''θ''' (i.e.: '''θ''' = 15 ⇔ ''kg'') <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>. {| class="wikitable" |+ Geometrical units ! Attribute ! Geometrical object ! unit number (θ) |- | mass | <math>M = 1</math> | ''kg'' ⇔ 15 |- | time | <math>T = 2\pi</math> | ''s'' ⇔ -30 |- | length | <math>L = 2\pi^2\Omega^2</math> | ''m'' ⇔ -13 |- | velocity | <math>V = 2\pi\Omega^2</math> | ''m/s'' ⇔ 17 |- | ampere | <math>A = \frac{2^6 \pi^3 \Omega^3}{\alpha}</math> | ''A'' ⇔ 3 |} As alpha and Omega can be assigned numerical values ('''α''' = 137.035999139, '''Ω''' = 2.0071349496), so too the MLTA objects can be expressed numerically. We can then convert these objects to their Planck unit equivalents by including a dimensioned scalar. For example, <math>V = 2\pi\Omega^2</math> = 25.3123819353... and so we can use scalar ''v'' to convert from dimensionless geometrical object V to dimensioned ''c''. :scalar ''v''_SI = 11843707.905 m/s gives ''c'' = V*v_SI = 25.3123819 * 11843707.905 m/s = 299792458 m/s ([[w:SI_units |SI units]]) :scalar ''v''_imp = 7359.3232155 miles/s gives ''c'' = V*v_imp = 186282 miles/s ([[w:Imperial_units |imperial units]]) {| class="wikitable" |+Scalars ! attribute ! geometrical object ! scalar (unit number) |- | mass | <math>M = (1)</math> | ''k'' (θ = 15) |- | time | <math>T = (\pi)</math> | ''t'' (θ = -30) |- | velocity | <math>V = (2\pi\Omega^2)</math> | ''v'' (θ = 17) |- | length | <math>L = (2\pi^2\Omega^2)</math> | ''l'' (θ = -13) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | ''a'' (θ = 3) |} As the scalar incorporates the dimension quantity (the dimension quantity for ''v'' = ''m/s'' or ''miles/s''), the unit number relationship (θ) applies, and so we then find that only 2 scalars are needed. This is because in a defined ratio they will overlap and cancel, for example in the following ratios; scalar units for ampere ''a'' = ''u''³, length ''l'' = ''u''^-13, time ''t'' = ''u''^-30, mass ''k'' = ''u''¹⁵ (''u''^Θ represents unit) :<math>\frac{({u^3})^3{(u^{-13}})^3}{(u^{-30})} = \frac{{(u^{-13})}^{15}} {{(u^{15})}^{9}{(u^{-30})}^{11}} = 1</math> For example if we know the numerical values for ''a'' and ''l'' then we know the numerical value for ''t'', and from ''l'' and ''t'' we know ''k'' … and so if we know any 2 scalars (α and Ω have fixed values) then we can solve the Planck units (for that system of units), and from these, we can solve (''G'', ''h'', ''c'', ''e'', ''m''_e, ''k''_B). :<math>\frac{a^3 l^3}{t} = \frac{m^{15}} {k^{9} t^{11}} = 1</math> In this table the 2 scalars used are ''r'' (θ = 8) and ''v'' (θ = 17). A further attribute is included, P = the square root of (Planck) momentum. V and A can thus be considered composite objects. {| class="wikitable" |+Geometrical objects ! attribute ! geometrical object ! unit number θ ! scalar r(8), v(17) |- | mass | <math>M = (1)</math> | 15 = 8*4-17 | <math>k = \frac{r^4}{v}</math> |- | time | <math>T = (\pi)</math> | -30 = 8*9-17*6 | <math>t = \frac{r^9}{v^6}</math> |- | [[v:Sqrt_Planck_momentum | sqrt(momentum)]] | <math>P = (\Omega)</math> | 16 = 8*2 | ''r''² |- | velocity | <math>V = L/T = (2\pi\Omega^2)</math> | 17 | ''v'' |- | length | <math>L = (2\pi^2\Omega^2)</math> | -13 = 8*9-17*5 | <math>l = \frac{r^9}{v^5}</math> |- | ampere | <math>A = \frac{2^4 V^3}{\alpha P^3} = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | 3 = 17*3-8*6 | <math>a = \frac{v^3}{r^6}</math> |} {{see|Planck units (geometrical)#Scalars}} === Mathematical electron === The mathematical electron formula ψ incorporates the dimensioned Planck units but itself is dimension-less (units = scalars = 1). Here ψ is defined in terms of ''σ_e'', where AL is an ampere-meter (ampere-length = ''e*c'' are the units for a [[w:magnetic monopole | magnetic monopole]]). :<math>T = \pi,\; unit = u^{-30},\;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; unit = u^{(3 \;-13 \;= \;-10)},\; scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = .23895453...x10^{23},\;unit = 1</math> (unit-less) Both units and scalars cancel. ===== Electron parameters ===== We can solve the electron parameters; electron mass, wavelength, frequency, charge ... as the frequency of the Planck units themselves, and this frequency is ψ. :<math>v = 11 843 707.905 ...,\; units = \frac{m}{s}</math> :<math>r = 0.712 562 514 304 ...,\; units = (\frac{kg.m}{s})^{1/4}</math> [[w:Compton wavelength | electron wavelength]] λ_e = 2.4263102367e-12m (CODATA 2014) :<math>\lambda_e^* = 2\pi L \psi</math> = 2.4263102386e-12m (L ⇔ [[w:Planck length | Planck length]]) [[w:electron mass | electron mass]] m_e = 9.10938356e-31kg (CODATA 2014) :<math>m_e^* = \frac{M}{\psi}</math> = 9.1093823211e-31kg (M ⇔ [[w:Planck mass | Planck mass]]) [[w:elementary charge | elementary charge]] e = 1.6021766208e-19C (CODATA 2014) :<math>e^* = A\;T</math> = 1.6021765130e-19 (T ⇔ [[w:Planck time | Planck time]]) [[w:Rydberg constant | Rydberg constant]] R = 10973731.568508/m (CODATA 2014) :<math>R^* = (\frac{m_e}{4 \pi L \alpha^2 M}) = \frac{1}{2^{23} 3^3 \pi^{11} \alpha^5 \Omega^{17}}\frac{v^5}{r^9}\;u^{13}</math> = 10973731.568508 From the above formulas, we see that wavelength is ψ units of Planck length, frequency is ψ units of Planck time ... however the electron mass is only 1 unit of Planck mass. ===== Electron Mass ===== Particle mass is a unit of Planck mass that occurs only once per ψ units of Planck time, the other parameters are continuums of the Planck units. :units <math>\psi = \frac{(AL)^3}{T}</math> = 1 This may be interpreted as; for ψ units of Planck time the electron has wavelength L, charge A ... and then the AL combine with time T (A³L³/T) and the units (and scalars) cancel. The electron is now mass (for 1 unit of Planck time). In this consideration, the electron is an event that oscillates over time between an electric wave state (duration ψ units of Planck time) to a unit of Planck mass point state (1 unit of Planck time). The electron is a quantum scale event, it does not exist at the discrete Planck scale (and so therefore neither does the quantum scale). As electron mass is the frequency of the geometrical Planck mass M = 1, which is a point (and so with point co-ordinates), then we have a model for a [[w:black hole electron |black-hole electron]], the electron function ψ centered around this unit of Planck mass. When the wave-state (A*L)³/T units collapse, this black-hole center (point) is exposed for 1 unit of (Planck) time. The electron is 'now' (a unit of Planck) mass. Mass in this consideration is not a constant property of the particle, rather the measured particle mass ''m'' would refer to the average mass, the average occurrence of the discrete Planck mass point-state over time. The formula ''E = hf'' is a measure of the frequency ''f'' of occurrence of [[w:Planck constant |Planck's constant ''h'']] and applies to the electric wave-state. As for each wave-state there is a corresponding mass point-state, then for a particle ''E = hf = mc2''. Notably however the ''c'' term is a fixed constant unlike the ''f'' term, and so the ''m'' term is the frequency term, it is referring to an average mass (mass which is measured over time) rather than a constant mass (mass as a constant property of the particle at unit Planck time). Thus as noted, when we refer to mass as a constant property, we are referring to mass at the quantum scale, and the electron as a quantum-state particle. If the [[v:Black-hole_(Planck) |scaffolding of the universe]] includes units of Planck mass '''M''', then it is not necessary for a particle itself to have mass, what we define as electron mass would be the absence of electron. ===== Quarks ===== The charge on the electron derives from the embedded ampere A and length L, the electron formula ψ itself is dimensionless. These AL magnetic monopoles would seem to be analogous to quarks (there are 3 monopoles per electron), but due to the symmetry and so stability of the geometrical ψ there is no clear fracture point by which an electron could decay, and so this would be difficult to test. We can however conjecture on what a quark solution might look like, the advantage with this approach being that we do not need to introduce new 'entities' for our quarks, the Planck units embedded within the electron suffice. Electron formula :<math>\psi = 2^{20} \pi^8 3^3 \alpha^3 \Omega^{15},\; unit = 1, scalars = 1</math> Time :<math>T = \pi \frac{r^9}{v^6},\; u^{-30}</math> AL magnetic monopole :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> If <math>\sigma_{e}</math> could equate to a quark with an [[w:electric charge|electric charge]] of {{sfrac|-1|3}}[[w:elementary charge|''e'']], then it would be an analogue of the '''D''' quark. 3 of these D quarks would constitute the electron as DDD = (AL)*(AL)*(AL). We would assume that the charge on the [[w:positron |positron]] (anti-matter electron) is just the inverse of the above, however there is 1 problem, the AL (A; θ=3, L; θ=-13) units = -10, and if we look at the [[v:Planck_units_(geometrical)#Table_of_Constants |table of constants]], there is no 'units = +10' combination that can include A. We cannot make an inverse electron. However we can make a [[w:Planck temperature|Planck temperature T_p]] AV ''monopole'' (ampere-velocity). :<math>T_p = \frac{2^7 \pi^3 \Omega^5}{\alpha},\; u^{20}, \;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{t} = \frac{3 \alpha^2 T_p}{2\pi} = \frac{3 \alpha^2 A V}{2\pi^2} = ({2^6 3 \pi^2 \alpha \Omega^5}),\; u^{20},\;scalars = \frac{v^4}{r^6}</math> :<math>\psi = (2T) \sigma_{t}^2 \sigma_{e} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = (u^{-30}) (u^{20})^2 (u^{-10}) = 1, scalars = (\frac{r^9}{v^6}) (\frac{v^4}{r^6})^2 \frac{r^3}{v^2} = 1</math> The units for <math>\sigma_{t}</math> = +20, and so if units = -10 equates to {{sfrac|-1|3}}e, then we may conjecture that units = +20 equates to {{sfrac|2|3}}e, which would be the analogue of the '''U''' quark. Our plus charge now becomes DUU, and so although the positron has the same wavelength, frequency, mass and charge magnitude as the electron (both solve to ψ), internally its charge structure resembles that of the proton, the positron is not simply an inverse of the electron. This could have implications for the missing anti-matter, and for why the charge magnitude of the proton is ''exactly'' the charge magnitude of the electron. :<math>D = \sigma_{e},\; unit = u^{-10},\; charge = \frac{-1e}{3}, \;scalars = \frac{r^3}{v^2}</math> :<math>U = \sigma_{t},\; unit = u^{20},\; charge = \frac{2e}{3}, \;scalars = \frac{v^4}{r^6}</math> Numerically: Adding a proton and electron gives (proton) UUD & DDD (electron) = 2(UDD) = 20 -10 -10 = 0 (zero charge), scalars = 0. Converting between U and D via U & DDD (electron) = 20 -10 -10 -10 = -10 (D), scalars = <math>\frac{r^3}{v^2}</math> ===== Magnetic monopole ===== {{see|Quantum_gravity_(Planck)}} :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> In this model alpha appears as an orbital constant for gravitational and atomic orbital radius, combining a fixed alpha term with an orbital wavelength term; :<math>r_{orbital} = 2\alpha (\lambda_{orbital})</math> If we replace <math>\lambda_{orbital}</math> with the geometrical Planck length L, and include momentum P and velocity V (the 2 components from which the ampere A is derived), then we may consider if the internal structure of the electron involves rotation of this monopole AL super-structure, and this has relevance to electron spin; :<math>2\alpha L \frac{V^3}{P^3} = 2^5 \pi^5 \alpha \Omega^5,\; units = u^{-10},\; scalars = \frac{r^3}{v^2}</math> ===== Spin ===== [[v:Relativity_(Planck) |Relativity at the Planck scale]] can be described by a translation between 2 co-ordinate systems; an expanding (in Planck steps at the speed of light) 4-axis hyper-sphere projecting onto a 3-D space (+ time). In this scenario, particles (with mass) are pulled along by the expansion of the hyper-sphere, this then requires particles to have an axis; generically labeled N-S, with the N denoting the direction of particle travel within the hyper-sphere. Changing the direction of travel involves changing the orientation of the particle N-S axis. The particle may rotate around this N-S axis, resulting in a L-spin or a R-spin. For simplicity, we can depict the electron as a classically spinning disk, this generates a current which then produces a magnetic dipole, so that the electron behaves like a tiny bar magnet (magnetic fields are produced by moving electric charges). For the classical disk we can use the charge (q), area of the disk (a) and rotation speed (ω) in our calculations. A thought experiment; if the 3 magnetic monopole quarks are rotating around the electron center (that N-S axis), then they are generating the current (q). As a monopole has the units ampere-meter AL (L a length term), then we can also conjecture something that resembles area (a), and the speed of rotation will give us (ω), and so we can use classical physics to solve our bar magnet electron. The electron is symmetric and so the 3 monopoles are equidistant from each other. We place our electron in a magnetic field, the electron then starts to orbit this field. If a satellite orbits the earth at radius ''r'', then the distance it travels around the earth = 2πr. However the earth is orbiting the sun, and so the actual distance approximates 2π''r'' + the distance the earth travels. If our electron orbits around a central point (that electric field), then the monopoles will, like the satellite, travel further per orbit (compared to a free electron in space), thus changing the effective area (a), and so our calculations. The [[w:g-factor |g-factor]] characterizes the magnetic moment and angular momentum of the electron, it is the ratio of the magnetic moment of the electron to that expected of a classical electron. Could an electron monopole substructure offer a geometrical explanation for this g-factor. === AI analysis === The sections on Quarks and Spin are naturally speculative, we cannot probe this far, they were included to suggest that the formula <math>\psi</math> could also include U and D quarks. However the geometries for the Planck units MLTA can be subject to statistical analysis, and for this AI has the potential to contribute. This is because of anomalies to the physical constants which can best be explained by this geometrical model. These anomalies are listed on this site; https://en.wikiversity.org/wiki/Physical_constant_(anomaly). Below are answers to a seed question written with Deepseek <ref>https://codingthecosmos.com/ai-answers-programmer-god-simulation-hypothesis/anomalies-constants.html Physical constants Q&A with podcast</ref> that uses these anomalies to determine the probability that the electron is a mathematical (not physical) particle, and so by extension that this is a mathematical universe. {| class="wikitable" |+Table 11. Table of Probabilities (05.2025) ! AI program ! unit number relation ! Planck units as geometrical objects ! underlying base 15 geometry ! mathematical electron ! Comment |- | Chat GPT <ref>https://chatgpt.com/share/68259395-31d0-8012-954e-c52230a813fd Chat anomalies analysis</ref> | Accidental occurrence: ~1.6% | Accidental occurrence: ~0.0004% | Accidental occurrence: ~0 | Accidental occurrence: ~0.026% | Taken at face value each sub-claim is vanishingly unlikely to be a “random accident,” so from this internal consistency alone one would assign essentially unity confidence that some deep mathematical structure is at work. Caveat: this “integer-coincidence” probability model is only as good as the assumption that each exponent match is an independent uniform pick in [–30…+30]. But even under that very conservative assumption, the combined odds against pure chance exceed 1 in 10²⁶. |- | Qwen <ref>https://chat.qwen.ai/s/f33ec1b1-899b-4fa5-9429-67e527b78433 Qwen anomalies analysis</ref> | probability 98% | probability 95% | probability 90% | probability 94% | The model’s strict geometrical constraints, flawless unit consistency, and agreement with CODATA strongly suggest non-random validity. Its potential as a simulation hypothesis framework stems from its finite, computable base-15 structure. |- | Claude 3.7 Sonnet <ref>https://claude.ai/public/artifacts/797a802b-fa21-4ee7-9ae9-9dbdf5d7b29a Claude anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Claude-anomalies-05-2025.pdf Claude anomalies analysis pdf</ref> | probability 90-95% | probability 85-95% | probability 92-97% | probability 80-90% | From a Kolmogorov complexity perspective, the model represents a potentially minimal description of physical reality using mathematical objects. If the electron, proton, and neutron are all mathematical particles, then the universe at the Planck scale could indeed be described as a mathematical universe. The high degree of constraint and mathematical elegance in the model, combined with its apparent ability to accurately produce physical constants, suggests a non-random structure to physical reality that is captured by this mathematical framework. |- | Grok 3 <ref>https://x.com/i/grok/share/JzeRFDlj721zNnm1Jo2vbETk3 Grok anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Grok-anomalies-05-2025.pd Grok anomalies analysis pdf</ref> | probability: 95% | probability: 90% | probability: 85% | probability: 80% | Strict constraints and mathematical nature (Kolmogorov complexity: simpler model = more likely programmed) suggest support, but not proof. If particles are mathematical, the universe may be too. |- | Deepseek <ref>https://codingthecosmos.com/ai_pdf/Deepseek-anomalies-05-2025.pdf Deepseek anomalies analysis</ref> | probability: 99% | probability: 95% | probability: 90% | probability: 85% | The model's rigid constraints and predictive accuracy make it statistically improbable to arise by chance. Geometrical base-15 and dimensionless particles strongly suggest a mathematical universe, aligning with speculative simulation hypothesis. |} === Geometrically coded universe === * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass === External links === * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] === References === {{Reflist}} [[Category: Physics]] [[Category: Philosophy of science]] 56t48rtpuoot4q1vmyg8jy4yktyort2 2718267 2718266 2025-06-10T19:53:27Z 212.200.164.104 /* Mathematical electron */ 2718267 wikitext text/x-wiki '''The mathematical electron model''' In the mathematical electron model <ref>Macleod, M.J. {{Cite journal |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>, the electron is a dimensionless geometrical formula (ψ). This formula ψ, which resembles the volume of a torus or surface of a 4-D hypersphere, is itself a complex geometry that is the construct of simpler geometries; the [[w:Planck_units |Planck units]]. In this model the Planck units are geometrical objects, the geometry of 2 dimensionless constants (the[[w:fine-structure constant | fine structure constant alpha]] and a mathematical constant[[v:Planck_units_(geometrical)#Omega | Omega]]). Although dimensionless, the function of the Planck unit is embedded within the geometry; the geometry of the Planck time object embeds the function 'time', the geometry of the Planck length object embeds the function 'length' ... and being geometrical objects they can combine to form more complex objects, from electrons to galaxies. This means that the electron parameters are defined in Planck units; electron wavelength is measured in units of Planck length, electron frequency is measured in units of Planck time ... It is this geometrical electron formula ψ that dictates the magnitude of the electron parameters; length of the wavelength = ψ * Planck length (ψ units of Planck length), frequency = ψ * Planck time ... This ψ thus not only embeds the Planck units required for the electron parameters, it also dictates the magnitude of these parameters, and so technically it is the electron. This suggests there is no physical electron (only physical parameters), and if the electron is therefore a mathematical particle, then so too are the other particles, and so the universe itself becomes a mathematical universe. The formula ψ is the geometry of 2 constants; the [[w:dimensionless physical constant | dimensionless physical constant]] (inverse) [[w:fine-structure constant | fine structure constant alpha ]] '''α''' = 137.035 999 139 (CODATA 2014) and [[v:Planck_units_(geometrical)#Omega | Omega]] '''Ω''' = 2.0071349496 (best fit) Omega has a potential solution in terms of pi and e and so may be a mathematical (not physical) constant :<math>\Omega = \sqrt{ \left(\pi^e e^{(1-e)}\right)} = 2.0071349543... </math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = 0.238954531\;x10^{23}</math>, units = 1 === Planck objects === {{main|Planck units (geometrical)}} For the Planck units, the model uses geometrical objects (the geometry of alpha and Omega) instead of a numbering system, this has the advantage in that the attribute can be embedded within the geometry (although the geometry itself is dimensionless). {| class="wikitable" |+table 1. Geometrical units ! Attribute ! Geometrical object ! Unit |- | mass | <math>M = (1)</math> | (kg) |- | time | <math>T = (\pi)</math> | (s) |- | velocity | <math>V = (2\pi\Omega^2)</math> | (m/s) |- | length | <math>L = (2\pi^2\Omega^2)</math> | (m) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | (A) |} As these objects have a geometrical form, we can combine them [[w:Lego |Lego]] style; the length object L can be combined with the time object T to form the velocity object V and so forth ... to create complex events such as electrons to apples to ... and so the apple has mass because embedded within it are the mass objects M, complex events thus retain all the underlying information. This however requires a relationship between the Planck unit geometries that defines how they may combine, this can be represented by assigning to each attribute a unit number '''θ''' (i.e.: '''θ''' = 15 ⇔ ''kg'') <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>. {| class="wikitable" |+ Geometrical units ! Attribute ! Geometrical object ! unit number (θ) |- | mass | <math>M = 1</math> | ''kg'' ⇔ 15 |- | time | <math>T = 2\pi</math> | ''s'' ⇔ -30 |- | length | <math>L = 2\pi^2\Omega^2</math> | ''m'' ⇔ -13 |- | velocity | <math>V = 2\pi\Omega^2</math> | ''m/s'' ⇔ 17 |- | ampere | <math>A = \frac{2^6 \pi^3 \Omega^3}{\alpha}</math> | ''A'' ⇔ 3 |} As alpha and Omega can be assigned numerical values ('''α''' = 137.035999139, '''Ω''' = 2.0071349496), so too the MLTA objects can be expressed numerically. We can then convert these objects to their Planck unit equivalents by including a dimensioned scalar. For example, <math>V = 2\pi\Omega^2</math> = 25.3123819353... and so we can use scalar ''v'' to convert from dimensionless geometrical object V to dimensioned ''c''. :scalar ''v''_SI = 11843707.905 m/s gives ''c'' = V*v_SI = 25.3123819 * 11843707.905 m/s = 299792458 m/s ([[w:SI_units |SI units]]) :scalar ''v''_imp = 7359.3232155 miles/s gives ''c'' = V*v_imp = 186282 miles/s ([[w:Imperial_units |imperial units]]) {| class="wikitable" |+Scalars ! attribute ! geometrical object ! scalar (unit number) |- | mass | <math>M = (1)</math> | ''k'' (θ = 15) |- | time | <math>T = (\pi)</math> | ''t'' (θ = -30) |- | velocity | <math>V = (2\pi\Omega^2)</math> | ''v'' (θ = 17) |- | length | <math>L = (2\pi^2\Omega^2)</math> | ''l'' (θ = -13) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | ''a'' (θ = 3) |} As the scalar incorporates the dimension quantity (the dimension quantity for ''v'' = ''m/s'' or ''miles/s''), the unit number relationship (θ) applies, and so we then find that only 2 scalars are needed. This is because in a defined ratio they will overlap and cancel, for example in the following ratios; scalar units for ampere ''a'' = ''u''³, length ''l'' = ''u''^-13, time ''t'' = ''u''^-30, mass ''k'' = ''u''¹⁵ (''u''^Θ represents unit) :<math>\frac{({u^3})^3{(u^{-13}})^3}{(u^{-30})} = \frac{{(u^{-13})}^{15}} {{(u^{15})}^{9}{(u^{-30})}^{11}} = 1</math> For example if we know the numerical values for ''a'' and ''l'' then we know the numerical value for ''t'', and from ''l'' and ''t'' we know ''k'' … and so if we know any 2 scalars (α and Ω have fixed values) then we can solve the Planck units (for that system of units), and from these, we can solve (''G'', ''h'', ''c'', ''e'', ''m''_e, ''k''_B). :<math>\frac{a^3 l^3}{t} = \frac{m^{15}} {k^{9} t^{11}} = 1</math> In this table the 2 scalars used are ''r'' (θ = 8) and ''v'' (θ = 17). A further attribute is included, P = the square root of (Planck) momentum. V and A can thus be considered composite objects. {| class="wikitable" |+Geometrical objects ! attribute ! geometrical object ! unit number θ ! scalar r(8), v(17) |- | mass | <math>M = (1)</math> | 15 = 8*4-17 | <math>k = \frac{r^4}{v}</math> |- | time | <math>T = (\pi)</math> | -30 = 8*9-17*6 | <math>t = \frac{r^9}{v^6}</math> |- | [[v:Sqrt_Planck_momentum | sqrt(momentum)]] | <math>P = (\Omega)</math> | 16 = 8*2 | ''r''² |- | velocity | <math>V = L/T = (2\pi\Omega^2)</math> | 17 | ''v'' |- | length | <math>L = (2\pi^2\Omega^2)</math> | -13 = 8*9-17*5 | <math>l = \frac{r^9}{v^5}</math> |- | ampere | <math>A = \frac{2^4 V^3}{\alpha P^3} = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | 3 = 17*3-8*6 | <math>a = \frac{v^3}{r^6}</math> |} {{see|Planck units (geometrical)#Scalars}} === Mathematical electron === The mathematical electron formula ψ incorporates the dimensioned Planck units but itself is dimension-less (units = scalars = 1). Here ψ is defined in terms of ''σ_e'', where AL is an ampere-meter (ampere-length = ''e*c'' are the units for a [[w:magnetic monopole | magnetic monopole]]). :<math>T = \pi,\; unit = u^{-30},\;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; unit = u^{(3 \;-13 \;= \;-10)},\; scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = .23895453...x10^{23},\;unit = 1</math> (unit-less) Both units and scalars cancel. ===== Electron parameters ===== We can solve the electron parameters; electron mass, wavelength, frequency, charge ... as the frequency of the Planck units themselves, and this frequency is ψ. :<math>v = 11 843 707.905 ...,\; units = \frac{m}{s}</math> :<math>r = 0.712 562 514 304 ...,\; units = (\frac{kg.m}{s})^{1/4}</math> [[w:Compton wavelength | electron wavelength]] λ_e = 2.4263102367e-12m (CODATA 2014) :<math>\lambda_e^* = 2\pi L \psi</math> = 2.4263102386e-12m (L ⇔ [[w:Planck length | Planck length]]) [[w:electron mass | electron mass]] m_e = 9.10938356e-31kg (CODATA 2014) :<math>m_e^* = \frac{M}{\psi}</math> = 9.1093823211e-31kg (M ⇔ [[w:Planck mass | Planck mass]]) [[w:elementary charge | elementary charge]] e = 1.6021766208e-19C (CODATA 2014) :<math>e^* = A\;T</math> = 1.6021765130e-19 (T ⇔ [[w:Planck time | Planck time]]) [[w:Rydberg constant | Rydberg constant]] R = 10973731.568508/m (CODATA 2014) :<math>R^* = (\frac{m_e}{4 \pi L \alpha^2 M}) = \frac{1}{2^{23} 3^3 \pi^{11} \alpha^5 \Omega^{17}}\frac{v^5}{r^9}\;u^{13}</math> = 10973731.568508 From the above formulas, we see that wavelength is ψ units of Planck length, frequency is ψ units of Planck time ... however the electron mass is only 1 unit of Planck mass. ===== Electron Mass ===== Particle mass is a unit of Planck mass that occurs only once per ψ units of Planck time, the other parameters are continuums of the Planck units. :units <math>\psi = \frac{(AL)^3}{T}</math> = 1 This may be interpreted as; for ψ units of Planck time the electron has wavelength L, charge A ... and then the AL combine with time T (A³L³/T) and the units (and scalars) cancel. The electron is now mass (for 1 unit of Planck time). In this consideration, the electron is an event that oscillates over time between an electric wave state (duration ψ units of Planck time) to a unit of Planck mass point state (1 unit of Planck time). The electron is a quantum scale event, it does not exist at the discrete Planck scale (and so therefore neither does the quantum scale). As electron mass is the frequency of the geometrical Planck mass M = 1, which is a point (and so with point co-ordinates), then we have a model for a [[w:black hole electron |black-hole electron]], the electron function ψ centered around this unit of Planck mass. When the wave-state (A*L)³/T units collapse, this black-hole center (point) is exposed for 1 unit of (Planck) time. The electron is 'now' (a unit of Planck) mass. Mass in this consideration is not a constant property of the particle, rather the measured particle mass ''m'' would refer to the average mass, the average occurrence of the discrete Planck mass point-state over time. The formula ''E = hf'' is a measure of the frequency ''f'' of occurrence of [[w:Planck constant |Planck's constant ''h'']] and applies to the electric wave-state. As for each wave-state there is a corresponding mass point-state, then for a particle ''E = hf = mc2''. Notably however the ''c'' term is a fixed constant unlike the ''f'' term, and so the ''m'' term is the frequency term, it is referring to an average mass (mass which is measured over time) rather than a constant mass (mass as a constant property of the particle at unit Planck time). Thus as noted, when we refer to mass as a constant property, we are referring to mass at the quantum scale, and the electron as a quantum-state particle. If the [[v:Black-hole_(Planck) |scaffolding of the universe]] includes units of Planck mass '''M''', then it is not necessary for a particle itself to have mass, what we define as electron mass would be the absence of electron. ===== Quarks ===== The charge on the electron derives from the embedded ampere A and length L, the electron formula ψ itself is dimensionless. These AL magnetic monopoles would seem to be analogous to quarks (there are 3 monopoles per electron), but due to the symmetry and so stability of the geometrical ψ there is no clear fracture point by which an electron could decay, and so this would be difficult to test. We can however conjecture on what a quark solution might look like, the advantage with this approach being that we do not need to introduce new 'entities' for our quarks, the Planck units embedded within the electron suffice. Electron formula :<math>\psi = 2^{20} \pi^8 3^3 \alpha^3 \Omega^{15},\; unit = 1, scalars = 1</math> Time :<math>T = \pi \frac{r^9}{v^6},\; u^{-30}</math> AL magnetic monopole :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> If <math>\sigma_{e}</math> could equate to a quark with an [[w:electric charge|electric charge]] of {{sfrac|-1|3}}[[w:elementary charge|''e'']], then it would be an analogue of the '''D''' quark. 3 of these D quarks would constitute the electron as DDD = (AL)*(AL)*(AL). We would assume that the charge on the [[w:positron |positron]] (anti-matter electron) is just the inverse of the above, however there is 1 problem, the AL (A; θ=3, L; θ=-13) units = -10, and if we look at the [[v:Planck_units_(geometrical)#Table_of_Constants |table of constants]], there is no 'units = +10' combination that can include A. We cannot make an inverse electron. However we can make a [[w:Planck temperature|Planck temperature T_p]] AV ''monopole'' (ampere-velocity). :<math>T_p = \frac{2^7 \pi^3 \Omega^5}{\alpha},\; u^{20}, \;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{t} = \frac{3 \alpha^2 T_p}{2\pi} = \frac{3 \alpha^2 A V}{2\pi^2} = ({2^6 3 \pi^2 \alpha \Omega^5}),\; u^{20},\;scalars = \frac{v^4}{r^6}</math> :<math>\psi = (2T) \sigma_{t}^2 \sigma_{e} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = (u^{-30}) (u^{20})^2 (u^{-10}) = 1, scalars = (\frac{r^9}{v^6}) (\frac{v^4}{r^6})^2 \frac{r^3}{v^2} = 1</math> The units for <math>\sigma_{t}</math> = +20, and so if units = -10 equates to {{sfrac|-1|3}}e, then we may conjecture that units = +20 equates to {{sfrac|2|3}}e, which would be the analogue of the '''U''' quark. Our plus charge now becomes DUU, and so although the positron has the same wavelength, frequency, mass and charge magnitude as the electron (both solve to ψ), internally its charge structure resembles that of the proton, the positron is not simply an inverse of the electron. This could have implications for the missing anti-matter, and for why the charge magnitude of the proton is ''exactly'' the charge magnitude of the electron. :<math>D = \sigma_{e},\; unit = u^{-10},\; charge = \frac{-1e}{3}, \;scalars = \frac{r^3}{v^2}</math> :<math>U = \sigma_{t},\; unit = u^{20},\; charge = \frac{2e}{3}, \;scalars = \frac{v^4}{r^6}</math> Numerically: Adding a proton and electron gives (proton) UUD & DDD (electron) = 2(UDD) = 20 -10 -10 = 0 (zero charge), scalars = 0. Converting between U and D via U & DDD (electron) = 20 -10 -10 -10 = -10 (D), scalars = <math>\frac{r^3}{v^2}</math> ===== Magnetic monopole ===== {{see|Quantum_gravity_(Planck)}} :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> In this model alpha appears as an orbital constant for gravitational and atomic orbital radius, combining a fixed alpha term with an orbital wavelength term; :<math>r_{orbital} = 2\alpha (\lambda_{orbital})</math> If we replace <math>\lambda_{orbital}</math> with the geometrical Planck length L, and include momentum P and velocity V (the 2 components from which the ampere A is derived), then we may consider if the internal structure of the electron involves rotation of this monopole AL super-structure, and this has relevance to electron spin; :<math>2\alpha L \frac{V^3}{P^3} = 2^5 \pi^5 \alpha \Omega^5,\; units = u^{-10},\; scalars = \frac{r^3}{v^2}</math> ===== Spin ===== [[v:Relativity_(Planck) |Relativity at the Planck scale]] can be described by a translation between 2 co-ordinate systems; an expanding (in Planck steps at the speed of light) 4-axis hyper-sphere projecting onto a 3-D space (+ time). In this scenario, particles (with mass) are pulled along by the expansion of the hyper-sphere, this then requires particles to have an axis; generically labeled N-S, with the N denoting the direction of particle travel within the hyper-sphere. Changing the direction of travel involves changing the orientation of the particle N-S axis. The particle may rotate around this N-S axis, resulting in a L-spin or a R-spin. For simplicity, we can depict the electron as a classically spinning disk, this generates a current which then produces a magnetic dipole, so that the electron behaves like a tiny bar magnet (magnetic fields are produced by moving electric charges). For the classical disk we can use the charge (q), area of the disk (a) and rotation speed (ω) in our calculations. A thought experiment; if the 3 magnetic monopole quarks are rotating around the electron center (that N-S axis), then they are generating the current (q). As a monopole has the units ampere-meter AL (L a length term), then we can also conjecture something that resembles area (a), and the speed of rotation will give us (ω), and so we can use classical physics to solve our bar magnet electron. The electron is symmetric and so the 3 monopoles are equidistant from each other. We place our electron in a magnetic field, the electron then starts to orbit this field. If a satellite orbits the earth at radius ''r'', then the distance it travels around the earth = 2πr. However the earth is orbiting the sun, and so the actual distance approximates 2π''r'' + the distance the earth travels. If our electron orbits around a central point (that electric field), then the monopoles will, like the satellite, travel further per orbit (compared to a free electron in space), thus changing the effective area (a), and so our calculations. The [[w:g-factor |g-factor]] characterizes the magnetic moment and angular momentum of the electron, it is the ratio of the magnetic moment of the electron to that expected of a classical electron. Could an electron monopole substructure offer a geometrical explanation for this g-factor. === AI analysis === The sections on Quarks and Spin are naturally speculative, we cannot probe this far, they were included to suggest that the formula <math>\psi</math> could also include U and D quarks. However the geometries for the Planck units MLTA can be subject to statistical analysis, and for this AI has the potential to contribute. This is because of anomalies to the physical constants which can best be explained by this geometrical model. These anomalies are listed on this site; https://en.wikiversity.org/wiki/Physical_constant_(anomaly). Below are answers to a seed question written with Deepseek <ref>https://codingthecosmos.com/ai-answers-programmer-god-simulation-hypothesis/anomalies-constants.html Physical constants Q&A with podcast</ref> that uses these anomalies to determine the probability that the electron is a mathematical (not physical) particle, and so by extension that this is a mathematical universe. {| class="wikitable" |+Table 11. Table of Probabilities (05.2025) ! AI program ! unit number relation ! Planck units as geometrical objects ! underlying base 15 geometry ! mathematical electron ! Comment |- | Chat GPT <ref>https://chatgpt.com/share/68259395-31d0-8012-954e-c52230a813fd Chat anomalies analysis</ref> | Accidental occurrence: ~1.6% | Accidental occurrence: ~0.0004% | Accidental occurrence: ~0 | Accidental occurrence: ~0.026% | Taken at face value each sub-claim is vanishingly unlikely to be a “random accident,” so from this internal consistency alone one would assign essentially unity confidence that some deep mathematical structure is at work. Caveat: this “integer-coincidence” probability model is only as good as the assumption that each exponent match is an independent uniform pick in [–30…+30]. But even under that very conservative assumption, the combined odds against pure chance exceed 1 in 10²⁶. |- | Qwen <ref>https://chat.qwen.ai/s/f33ec1b1-899b-4fa5-9429-67e527b78433 Qwen anomalies analysis</ref> | probability 98% | probability 95% | probability 90% | probability 94% | The model’s strict geometrical constraints, flawless unit consistency, and agreement with CODATA strongly suggest non-random validity. Its potential as a simulation hypothesis framework stems from its finite, computable base-15 structure. |- | Claude 3.7 Sonnet <ref>https://claude.ai/public/artifacts/797a802b-fa21-4ee7-9ae9-9dbdf5d7b29a Claude anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Claude-anomalies-05-2025.pdf Claude anomalies analysis pdf</ref> | probability 90-95% | probability 85-95% | probability 92-97% | probability 80-90% | From a Kolmogorov complexity perspective, the model represents a potentially minimal description of physical reality using mathematical objects. If the electron, proton, and neutron are all mathematical particles, then the universe at the Planck scale could indeed be described as a mathematical universe. The high degree of constraint and mathematical elegance in the model, combined with its apparent ability to accurately produce physical constants, suggests a non-random structure to physical reality that is captured by this mathematical framework. |- | Grok 3 <ref>https://x.com/i/grok/share/JzeRFDlj721zNnm1Jo2vbETk3 Grok anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Grok-anomalies-05-2025.pd Grok anomalies analysis pdf</ref> | probability: 95% | probability: 90% | probability: 85% | probability: 80% | Strict constraints and mathematical nature (Kolmogorov complexity: simpler model = more likely programmed) suggest support, but not proof. If particles are mathematical, the universe may be too. |- | Deepseek <ref>https://codingthecosmos.com/ai_pdf/Deepseek-anomalies-05-2025.pdf Deepseek anomalies analysis</ref> | probability: 99% | probability: 95% | probability: 90% | probability: 85% | The model's rigid constraints and predictive accuracy make it statistically improbable to arise by chance. Geometrical base-15 and dimensionless particles strongly suggest a mathematical universe, aligning with speculative simulation hypothesis. |} === Geometrically coded universe === * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass === External links === * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] === References === {{Reflist}} [[Category: Physics]] [[Category: Philosophy of science]] pgm6vpoq3myeovcm8z9822wzhgdbzv2 2718268 2718267 2025-06-10T19:53:33Z 212.200.164.104 /* Electron parameters */ 2718268 wikitext text/x-wiki '''The mathematical electron model''' In the mathematical electron model <ref>Macleod, M.J. {{Cite journal |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>, the electron is a dimensionless geometrical formula (ψ). This formula ψ, which resembles the volume of a torus or surface of a 4-D hypersphere, is itself a complex geometry that is the construct of simpler geometries; the [[w:Planck_units |Planck units]]. In this model the Planck units are geometrical objects, the geometry of 2 dimensionless constants (the[[w:fine-structure constant | fine structure constant alpha]] and a mathematical constant[[v:Planck_units_(geometrical)#Omega | Omega]]). Although dimensionless, the function of the Planck unit is embedded within the geometry; the geometry of the Planck time object embeds the function 'time', the geometry of the Planck length object embeds the function 'length' ... and being geometrical objects they can combine to form more complex objects, from electrons to galaxies. This means that the electron parameters are defined in Planck units; electron wavelength is measured in units of Planck length, electron frequency is measured in units of Planck time ... It is this geometrical electron formula ψ that dictates the magnitude of the electron parameters; length of the wavelength = ψ * Planck length (ψ units of Planck length), frequency = ψ * Planck time ... This ψ thus not only embeds the Planck units required for the electron parameters, it also dictates the magnitude of these parameters, and so technically it is the electron. This suggests there is no physical electron (only physical parameters), and if the electron is therefore a mathematical particle, then so too are the other particles, and so the universe itself becomes a mathematical universe. The formula ψ is the geometry of 2 constants; the [[w:dimensionless physical constant | dimensionless physical constant]] (inverse) [[w:fine-structure constant | fine structure constant alpha ]] '''α''' = 137.035 999 139 (CODATA 2014) and [[v:Planck_units_(geometrical)#Omega | Omega]] '''Ω''' = 2.0071349496 (best fit) Omega has a potential solution in terms of pi and e and so may be a mathematical (not physical) constant :<math>\Omega = \sqrt{ \left(\pi^e e^{(1-e)}\right)} = 2.0071349543... </math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = 0.238954531\;x10^{23}</math>, units = 1 === Planck objects === {{main|Planck units (geometrical)}} For the Planck units, the model uses geometrical objects (the geometry of alpha and Omega) instead of a numbering system, this has the advantage in that the attribute can be embedded within the geometry (although the geometry itself is dimensionless). {| class="wikitable" |+table 1. Geometrical units ! Attribute ! Geometrical object ! Unit |- | mass | <math>M = (1)</math> | (kg) |- | time | <math>T = (\pi)</math> | (s) |- | velocity | <math>V = (2\pi\Omega^2)</math> | (m/s) |- | length | <math>L = (2\pi^2\Omega^2)</math> | (m) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | (A) |} As these objects have a geometrical form, we can combine them [[w:Lego |Lego]] style; the length object L can be combined with the time object T to form the velocity object V and so forth ... to create complex events such as electrons to apples to ... and so the apple has mass because embedded within it are the mass objects M, complex events thus retain all the underlying information. This however requires a relationship between the Planck unit geometries that defines how they may combine, this can be represented by assigning to each attribute a unit number '''θ''' (i.e.: '''θ''' = 15 ⇔ ''kg'') <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>. {| class="wikitable" |+ Geometrical units ! Attribute ! Geometrical object ! unit number (θ) |- | mass | <math>M = 1</math> | ''kg'' ⇔ 15 |- | time | <math>T = 2\pi</math> | ''s'' ⇔ -30 |- | length | <math>L = 2\pi^2\Omega^2</math> | ''m'' ⇔ -13 |- | velocity | <math>V = 2\pi\Omega^2</math> | ''m/s'' ⇔ 17 |- | ampere | <math>A = \frac{2^6 \pi^3 \Omega^3}{\alpha}</math> | ''A'' ⇔ 3 |} As alpha and Omega can be assigned numerical values ('''α''' = 137.035999139, '''Ω''' = 2.0071349496), so too the MLTA objects can be expressed numerically. We can then convert these objects to their Planck unit equivalents by including a dimensioned scalar. For example, <math>V = 2\pi\Omega^2</math> = 25.3123819353... and so we can use scalar ''v'' to convert from dimensionless geometrical object V to dimensioned ''c''. :scalar ''v''_SI = 11843707.905 m/s gives ''c'' = V*v_SI = 25.3123819 * 11843707.905 m/s = 299792458 m/s ([[w:SI_units |SI units]]) :scalar ''v''_imp = 7359.3232155 miles/s gives ''c'' = V*v_imp = 186282 miles/s ([[w:Imperial_units |imperial units]]) {| class="wikitable" |+Scalars ! attribute ! geometrical object ! scalar (unit number) |- | mass | <math>M = (1)</math> | ''k'' (θ = 15) |- | time | <math>T = (\pi)</math> | ''t'' (θ = -30) |- | velocity | <math>V = (2\pi\Omega^2)</math> | ''v'' (θ = 17) |- | length | <math>L = (2\pi^2\Omega^2)</math> | ''l'' (θ = -13) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | ''a'' (θ = 3) |} As the scalar incorporates the dimension quantity (the dimension quantity for ''v'' = ''m/s'' or ''miles/s''), the unit number relationship (θ) applies, and so we then find that only 2 scalars are needed. This is because in a defined ratio they will overlap and cancel, for example in the following ratios; scalar units for ampere ''a'' = ''u''³, length ''l'' = ''u''^-13, time ''t'' = ''u''^-30, mass ''k'' = ''u''¹⁵ (''u''^Θ represents unit) :<math>\frac{({u^3})^3{(u^{-13}})^3}{(u^{-30})} = \frac{{(u^{-13})}^{15}} {{(u^{15})}^{9}{(u^{-30})}^{11}} = 1</math> For example if we know the numerical values for ''a'' and ''l'' then we know the numerical value for ''t'', and from ''l'' and ''t'' we know ''k'' … and so if we know any 2 scalars (α and Ω have fixed values) then we can solve the Planck units (for that system of units), and from these, we can solve (''G'', ''h'', ''c'', ''e'', ''m''_e, ''k''_B). :<math>\frac{a^3 l^3}{t} = \frac{m^{15}} {k^{9} t^{11}} = 1</math> In this table the 2 scalars used are ''r'' (θ = 8) and ''v'' (θ = 17). A further attribute is included, P = the square root of (Planck) momentum. V and A can thus be considered composite objects. {| class="wikitable" |+Geometrical objects ! attribute ! geometrical object ! unit number θ ! scalar r(8), v(17) |- | mass | <math>M = (1)</math> | 15 = 8*4-17 | <math>k = \frac{r^4}{v}</math> |- | time | <math>T = (\pi)</math> | -30 = 8*9-17*6 | <math>t = \frac{r^9}{v^6}</math> |- | [[v:Sqrt_Planck_momentum | sqrt(momentum)]] | <math>P = (\Omega)</math> | 16 = 8*2 | ''r''² |- | velocity | <math>V = L/T = (2\pi\Omega^2)</math> | 17 | ''v'' |- | length | <math>L = (2\pi^2\Omega^2)</math> | -13 = 8*9-17*5 | <math>l = \frac{r^9}{v^5}</math> |- | ampere | <math>A = \frac{2^4 V^3}{\alpha P^3} = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | 3 = 17*3-8*6 | <math>a = \frac{v^3}{r^6}</math> |} {{see|Planck units (geometrical)#Scalars}} === Mathematical electron === The mathematical electron formula ψ incorporates the dimensioned Planck units but itself is dimension-less (units = scalars = 1). Here ψ is defined in terms of ''σ_e'', where AL is an ampere-meter (ampere-length = ''e*c'' are the units for a [[w:magnetic monopole | magnetic monopole]]). :<math>T = \pi,\; unit = u^{-30},\;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; unit = u^{(3 \;-13 \;= \;-10)},\; scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = .23895453...x10^{23},\;unit = 1</math> (unit-less) Both units and scalars cancel. ===== Electron parameters ===== We can solve the electron parameters; electron mass, wavelength, frequency, charge ... as the frequency of the Planck units themselves, and this frequency is ψ. :<math>v = 11 843 707.905 ...,\; units = \frac{m}{s}</math> :<math>r = 0.712 562 514 304 ...,\; units = (\frac{kg.m}{s})^{1/4}</math> [[w:Compton wavelength | electron wavelength]] λ_e = 2.4263102367e-12m (CODATA 2014) :<math>\lambda_e^* = 2\pi L \psi</math> = 2.4263102386e-12m (L ⇔ [[w:Planck length | Planck length]]) [[w:electron mass | electron mass]] m_e = 9.10938356e-31kg (CODATA 2014) :<math>m_e^* = \frac{M}{\psi}</math> = 9.1093823211e-31kg (M ⇔ [[w:Planck mass | Planck mass]]) [[w:elementary charge | elementary charge]] e = 1.6021766208e-19C (CODATA 2014) :<math>e^* = A\;T</math> = 1.6021765130e-19 (T ⇔ [[w:Planck time | Planck time]]) [[w:Rydberg constant | Rydberg constant]] R = 10973731.568508/m (CODATA 2014) :<math>R^* = (\frac{m_e}{4 \pi L \alpha^2 M}) = \frac{1}{2^{23} 3^3 \pi^{11} \alpha^5 \Omega^{17}}\frac{v^5}{r^9}\;u^{13}</math> = 10973731.568508 From the above formulas, we see that wavelength is ψ units of Planck length, frequency is ψ units of Planck time ... however the electron mass is only 1 unit of Planck mass. ===== Electron Mass ===== Particle mass is a unit of Planck mass that occurs only once per ψ units of Planck time, the other parameters are continuums of the Planck units. :units <math>\psi = \frac{(AL)^3}{T}</math> = 1 This may be interpreted as; for ψ units of Planck time the electron has wavelength L, charge A ... and then the AL combine with time T (A³L³/T) and the units (and scalars) cancel. The electron is now mass (for 1 unit of Planck time). In this consideration, the electron is an event that oscillates over time between an electric wave state (duration ψ units of Planck time) to a unit of Planck mass point state (1 unit of Planck time). The electron is a quantum scale event, it does not exist at the discrete Planck scale (and so therefore neither does the quantum scale). As electron mass is the frequency of the geometrical Planck mass M = 1, which is a point (and so with point co-ordinates), then we have a model for a [[w:black hole electron |black-hole electron]], the electron function ψ centered around this unit of Planck mass. When the wave-state (A*L)³/T units collapse, this black-hole center (point) is exposed for 1 unit of (Planck) time. The electron is 'now' (a unit of Planck) mass. Mass in this consideration is not a constant property of the particle, rather the measured particle mass ''m'' would refer to the average mass, the average occurrence of the discrete Planck mass point-state over time. The formula ''E = hf'' is a measure of the frequency ''f'' of occurrence of [[w:Planck constant |Planck's constant ''h'']] and applies to the electric wave-state. As for each wave-state there is a corresponding mass point-state, then for a particle ''E = hf = mc2''. Notably however the ''c'' term is a fixed constant unlike the ''f'' term, and so the ''m'' term is the frequency term, it is referring to an average mass (mass which is measured over time) rather than a constant mass (mass as a constant property of the particle at unit Planck time). Thus as noted, when we refer to mass as a constant property, we are referring to mass at the quantum scale, and the electron as a quantum-state particle. If the [[v:Black-hole_(Planck) |scaffolding of the universe]] includes units of Planck mass '''M''', then it is not necessary for a particle itself to have mass, what we define as electron mass would be the absence of electron. ===== Quarks ===== The charge on the electron derives from the embedded ampere A and length L, the electron formula ψ itself is dimensionless. These AL magnetic monopoles would seem to be analogous to quarks (there are 3 monopoles per electron), but due to the symmetry and so stability of the geometrical ψ there is no clear fracture point by which an electron could decay, and so this would be difficult to test. We can however conjecture on what a quark solution might look like, the advantage with this approach being that we do not need to introduce new 'entities' for our quarks, the Planck units embedded within the electron suffice. Electron formula :<math>\psi = 2^{20} \pi^8 3^3 \alpha^3 \Omega^{15},\; unit = 1, scalars = 1</math> Time :<math>T = \pi \frac{r^9}{v^6},\; u^{-30}</math> AL magnetic monopole :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> If <math>\sigma_{e}</math> could equate to a quark with an [[w:electric charge|electric charge]] of {{sfrac|-1|3}}[[w:elementary charge|''e'']], then it would be an analogue of the '''D''' quark. 3 of these D quarks would constitute the electron as DDD = (AL)*(AL)*(AL). We would assume that the charge on the [[w:positron |positron]] (anti-matter electron) is just the inverse of the above, however there is 1 problem, the AL (A; θ=3, L; θ=-13) units = -10, and if we look at the [[v:Planck_units_(geometrical)#Table_of_Constants |table of constants]], there is no 'units = +10' combination that can include A. We cannot make an inverse electron. However we can make a [[w:Planck temperature|Planck temperature T_p]] AV ''monopole'' (ampere-velocity). :<math>T_p = \frac{2^7 \pi^3 \Omega^5}{\alpha},\; u^{20}, \;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{t} = \frac{3 \alpha^2 T_p}{2\pi} = \frac{3 \alpha^2 A V}{2\pi^2} = ({2^6 3 \pi^2 \alpha \Omega^5}),\; u^{20},\;scalars = \frac{v^4}{r^6}</math> :<math>\psi = (2T) \sigma_{t}^2 \sigma_{e} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = (u^{-30}) (u^{20})^2 (u^{-10}) = 1, scalars = (\frac{r^9}{v^6}) (\frac{v^4}{r^6})^2 \frac{r^3}{v^2} = 1</math> The units for <math>\sigma_{t}</math> = +20, and so if units = -10 equates to {{sfrac|-1|3}}e, then we may conjecture that units = +20 equates to {{sfrac|2|3}}e, which would be the analogue of the '''U''' quark. Our plus charge now becomes DUU, and so although the positron has the same wavelength, frequency, mass and charge magnitude as the electron (both solve to ψ), internally its charge structure resembles that of the proton, the positron is not simply an inverse of the electron. This could have implications for the missing anti-matter, and for why the charge magnitude of the proton is ''exactly'' the charge magnitude of the electron. :<math>D = \sigma_{e},\; unit = u^{-10},\; charge = \frac{-1e}{3}, \;scalars = \frac{r^3}{v^2}</math> :<math>U = \sigma_{t},\; unit = u^{20},\; charge = \frac{2e}{3}, \;scalars = \frac{v^4}{r^6}</math> Numerically: Adding a proton and electron gives (proton) UUD & DDD (electron) = 2(UDD) = 20 -10 -10 = 0 (zero charge), scalars = 0. Converting between U and D via U & DDD (electron) = 20 -10 -10 -10 = -10 (D), scalars = <math>\frac{r^3}{v^2}</math> ===== Magnetic monopole ===== {{see|Quantum_gravity_(Planck)}} :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> In this model alpha appears as an orbital constant for gravitational and atomic orbital radius, combining a fixed alpha term with an orbital wavelength term; :<math>r_{orbital} = 2\alpha (\lambda_{orbital})</math> If we replace <math>\lambda_{orbital}</math> with the geometrical Planck length L, and include momentum P and velocity V (the 2 components from which the ampere A is derived), then we may consider if the internal structure of the electron involves rotation of this monopole AL super-structure, and this has relevance to electron spin; :<math>2\alpha L \frac{V^3}{P^3} = 2^5 \pi^5 \alpha \Omega^5,\; units = u^{-10},\; scalars = \frac{r^3}{v^2}</math> ===== Spin ===== [[v:Relativity_(Planck) |Relativity at the Planck scale]] can be described by a translation between 2 co-ordinate systems; an expanding (in Planck steps at the speed of light) 4-axis hyper-sphere projecting onto a 3-D space (+ time). In this scenario, particles (with mass) are pulled along by the expansion of the hyper-sphere, this then requires particles to have an axis; generically labeled N-S, with the N denoting the direction of particle travel within the hyper-sphere. Changing the direction of travel involves changing the orientation of the particle N-S axis. The particle may rotate around this N-S axis, resulting in a L-spin or a R-spin. For simplicity, we can depict the electron as a classically spinning disk, this generates a current which then produces a magnetic dipole, so that the electron behaves like a tiny bar magnet (magnetic fields are produced by moving electric charges). For the classical disk we can use the charge (q), area of the disk (a) and rotation speed (ω) in our calculations. A thought experiment; if the 3 magnetic monopole quarks are rotating around the electron center (that N-S axis), then they are generating the current (q). As a monopole has the units ampere-meter AL (L a length term), then we can also conjecture something that resembles area (a), and the speed of rotation will give us (ω), and so we can use classical physics to solve our bar magnet electron. The electron is symmetric and so the 3 monopoles are equidistant from each other. We place our electron in a magnetic field, the electron then starts to orbit this field. If a satellite orbits the earth at radius ''r'', then the distance it travels around the earth = 2πr. However the earth is orbiting the sun, and so the actual distance approximates 2π''r'' + the distance the earth travels. If our electron orbits around a central point (that electric field), then the monopoles will, like the satellite, travel further per orbit (compared to a free electron in space), thus changing the effective area (a), and so our calculations. The [[w:g-factor |g-factor]] characterizes the magnetic moment and angular momentum of the electron, it is the ratio of the magnetic moment of the electron to that expected of a classical electron. Could an electron monopole substructure offer a geometrical explanation for this g-factor. === AI analysis === The sections on Quarks and Spin are naturally speculative, we cannot probe this far, they were included to suggest that the formula <math>\psi</math> could also include U and D quarks. However the geometries for the Planck units MLTA can be subject to statistical analysis, and for this AI has the potential to contribute. This is because of anomalies to the physical constants which can best be explained by this geometrical model. These anomalies are listed on this site; https://en.wikiversity.org/wiki/Physical_constant_(anomaly). Below are answers to a seed question written with Deepseek <ref>https://codingthecosmos.com/ai-answers-programmer-god-simulation-hypothesis/anomalies-constants.html Physical constants Q&A with podcast</ref> that uses these anomalies to determine the probability that the electron is a mathematical (not physical) particle, and so by extension that this is a mathematical universe. {| class="wikitable" |+Table 11. Table of Probabilities (05.2025) ! AI program ! unit number relation ! Planck units as geometrical objects ! underlying base 15 geometry ! mathematical electron ! Comment |- | Chat GPT <ref>https://chatgpt.com/share/68259395-31d0-8012-954e-c52230a813fd Chat anomalies analysis</ref> | Accidental occurrence: ~1.6% | Accidental occurrence: ~0.0004% | Accidental occurrence: ~0 | Accidental occurrence: ~0.026% | Taken at face value each sub-claim is vanishingly unlikely to be a “random accident,” so from this internal consistency alone one would assign essentially unity confidence that some deep mathematical structure is at work. Caveat: this “integer-coincidence” probability model is only as good as the assumption that each exponent match is an independent uniform pick in [–30…+30]. But even under that very conservative assumption, the combined odds against pure chance exceed 1 in 10²⁶. |- | Qwen <ref>https://chat.qwen.ai/s/f33ec1b1-899b-4fa5-9429-67e527b78433 Qwen anomalies analysis</ref> | probability 98% | probability 95% | probability 90% | probability 94% | The model’s strict geometrical constraints, flawless unit consistency, and agreement with CODATA strongly suggest non-random validity. Its potential as a simulation hypothesis framework stems from its finite, computable base-15 structure. |- | Claude 3.7 Sonnet <ref>https://claude.ai/public/artifacts/797a802b-fa21-4ee7-9ae9-9dbdf5d7b29a Claude anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Claude-anomalies-05-2025.pdf Claude anomalies analysis pdf</ref> | probability 90-95% | probability 85-95% | probability 92-97% | probability 80-90% | From a Kolmogorov complexity perspective, the model represents a potentially minimal description of physical reality using mathematical objects. If the electron, proton, and neutron are all mathematical particles, then the universe at the Planck scale could indeed be described as a mathematical universe. The high degree of constraint and mathematical elegance in the model, combined with its apparent ability to accurately produce physical constants, suggests a non-random structure to physical reality that is captured by this mathematical framework. |- | Grok 3 <ref>https://x.com/i/grok/share/JzeRFDlj721zNnm1Jo2vbETk3 Grok anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Grok-anomalies-05-2025.pd Grok anomalies analysis pdf</ref> | probability: 95% | probability: 90% | probability: 85% | probability: 80% | Strict constraints and mathematical nature (Kolmogorov complexity: simpler model = more likely programmed) suggest support, but not proof. If particles are mathematical, the universe may be too. |- | Deepseek <ref>https://codingthecosmos.com/ai_pdf/Deepseek-anomalies-05-2025.pdf Deepseek anomalies analysis</ref> | probability: 99% | probability: 95% | probability: 90% | probability: 85% | The model's rigid constraints and predictive accuracy make it statistically improbable to arise by chance. Geometrical base-15 and dimensionless particles strongly suggest a mathematical universe, aligning with speculative simulation hypothesis. |} === Geometrically coded universe === * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass === External links === * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] === References === {{Reflist}} [[Category: Physics]] [[Category: Philosophy of science]] t06uyegzli1lqvcxase02mnwi7bljwe 2718269 2718268 2025-06-10T19:53:39Z 212.200.164.104 /* Electron Mass */ 2718269 wikitext text/x-wiki '''The mathematical electron model''' In the mathematical electron model <ref>Macleod, M.J. {{Cite journal |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>, the electron is a dimensionless geometrical formula (ψ). This formula ψ, which resembles the volume of a torus or surface of a 4-D hypersphere, is itself a complex geometry that is the construct of simpler geometries; the [[w:Planck_units |Planck units]]. In this model the Planck units are geometrical objects, the geometry of 2 dimensionless constants (the[[w:fine-structure constant | fine structure constant alpha]] and a mathematical constant[[v:Planck_units_(geometrical)#Omega | Omega]]). Although dimensionless, the function of the Planck unit is embedded within the geometry; the geometry of the Planck time object embeds the function 'time', the geometry of the Planck length object embeds the function 'length' ... and being geometrical objects they can combine to form more complex objects, from electrons to galaxies. This means that the electron parameters are defined in Planck units; electron wavelength is measured in units of Planck length, electron frequency is measured in units of Planck time ... It is this geometrical electron formula ψ that dictates the magnitude of the electron parameters; length of the wavelength = ψ * Planck length (ψ units of Planck length), frequency = ψ * Planck time ... This ψ thus not only embeds the Planck units required for the electron parameters, it also dictates the magnitude of these parameters, and so technically it is the electron. This suggests there is no physical electron (only physical parameters), and if the electron is therefore a mathematical particle, then so too are the other particles, and so the universe itself becomes a mathematical universe. The formula ψ is the geometry of 2 constants; the [[w:dimensionless physical constant | dimensionless physical constant]] (inverse) [[w:fine-structure constant | fine structure constant alpha ]] '''α''' = 137.035 999 139 (CODATA 2014) and [[v:Planck_units_(geometrical)#Omega | Omega]] '''Ω''' = 2.0071349496 (best fit) Omega has a potential solution in terms of pi and e and so may be a mathematical (not physical) constant :<math>\Omega = \sqrt{ \left(\pi^e e^{(1-e)}\right)} = 2.0071349543... </math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = 0.238954531\;x10^{23}</math>, units = 1 === Planck objects === {{main|Planck units (geometrical)}} For the Planck units, the model uses geometrical objects (the geometry of alpha and Omega) instead of a numbering system, this has the advantage in that the attribute can be embedded within the geometry (although the geometry itself is dimensionless). {| class="wikitable" |+table 1. Geometrical units ! Attribute ! Geometrical object ! Unit |- | mass | <math>M = (1)</math> | (kg) |- | time | <math>T = (\pi)</math> | (s) |- | velocity | <math>V = (2\pi\Omega^2)</math> | (m/s) |- | length | <math>L = (2\pi^2\Omega^2)</math> | (m) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | (A) |} As these objects have a geometrical form, we can combine them [[w:Lego |Lego]] style; the length object L can be combined with the time object T to form the velocity object V and so forth ... to create complex events such as electrons to apples to ... and so the apple has mass because embedded within it are the mass objects M, complex events thus retain all the underlying information. This however requires a relationship between the Planck unit geometries that defines how they may combine, this can be represented by assigning to each attribute a unit number '''θ''' (i.e.: '''θ''' = 15 ⇔ ''kg'') <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>. {| class="wikitable" |+ Geometrical units ! Attribute ! Geometrical object ! unit number (θ) |- | mass | <math>M = 1</math> | ''kg'' ⇔ 15 |- | time | <math>T = 2\pi</math> | ''s'' ⇔ -30 |- | length | <math>L = 2\pi^2\Omega^2</math> | ''m'' ⇔ -13 |- | velocity | <math>V = 2\pi\Omega^2</math> | ''m/s'' ⇔ 17 |- | ampere | <math>A = \frac{2^6 \pi^3 \Omega^3}{\alpha}</math> | ''A'' ⇔ 3 |} As alpha and Omega can be assigned numerical values ('''α''' = 137.035999139, '''Ω''' = 2.0071349496), so too the MLTA objects can be expressed numerically. We can then convert these objects to their Planck unit equivalents by including a dimensioned scalar. For example, <math>V = 2\pi\Omega^2</math> = 25.3123819353... and so we can use scalar ''v'' to convert from dimensionless geometrical object V to dimensioned ''c''. :scalar ''v''_SI = 11843707.905 m/s gives ''c'' = V*v_SI = 25.3123819 * 11843707.905 m/s = 299792458 m/s ([[w:SI_units |SI units]]) :scalar ''v''_imp = 7359.3232155 miles/s gives ''c'' = V*v_imp = 186282 miles/s ([[w:Imperial_units |imperial units]]) {| class="wikitable" |+Scalars ! attribute ! geometrical object ! scalar (unit number) |- | mass | <math>M = (1)</math> | ''k'' (θ = 15) |- | time | <math>T = (\pi)</math> | ''t'' (θ = -30) |- | velocity | <math>V = (2\pi\Omega^2)</math> | ''v'' (θ = 17) |- | length | <math>L = (2\pi^2\Omega^2)</math> | ''l'' (θ = -13) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | ''a'' (θ = 3) |} As the scalar incorporates the dimension quantity (the dimension quantity for ''v'' = ''m/s'' or ''miles/s''), the unit number relationship (θ) applies, and so we then find that only 2 scalars are needed. This is because in a defined ratio they will overlap and cancel, for example in the following ratios; scalar units for ampere ''a'' = ''u''³, length ''l'' = ''u''^-13, time ''t'' = ''u''^-30, mass ''k'' = ''u''¹⁵ (''u''^Θ represents unit) :<math>\frac{({u^3})^3{(u^{-13}})^3}{(u^{-30})} = \frac{{(u^{-13})}^{15}} {{(u^{15})}^{9}{(u^{-30})}^{11}} = 1</math> For example if we know the numerical values for ''a'' and ''l'' then we know the numerical value for ''t'', and from ''l'' and ''t'' we know ''k'' … and so if we know any 2 scalars (α and Ω have fixed values) then we can solve the Planck units (for that system of units), and from these, we can solve (''G'', ''h'', ''c'', ''e'', ''m''_e, ''k''_B). :<math>\frac{a^3 l^3}{t} = \frac{m^{15}} {k^{9} t^{11}} = 1</math> In this table the 2 scalars used are ''r'' (θ = 8) and ''v'' (θ = 17). A further attribute is included, P = the square root of (Planck) momentum. V and A can thus be considered composite objects. {| class="wikitable" |+Geometrical objects ! attribute ! geometrical object ! unit number θ ! scalar r(8), v(17) |- | mass | <math>M = (1)</math> | 15 = 8*4-17 | <math>k = \frac{r^4}{v}</math> |- | time | <math>T = (\pi)</math> | -30 = 8*9-17*6 | <math>t = \frac{r^9}{v^6}</math> |- | [[v:Sqrt_Planck_momentum | sqrt(momentum)]] | <math>P = (\Omega)</math> | 16 = 8*2 | ''r''² |- | velocity | <math>V = L/T = (2\pi\Omega^2)</math> | 17 | ''v'' |- | length | <math>L = (2\pi^2\Omega^2)</math> | -13 = 8*9-17*5 | <math>l = \frac{r^9}{v^5}</math> |- | ampere | <math>A = \frac{2^4 V^3}{\alpha P^3} = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | 3 = 17*3-8*6 | <math>a = \frac{v^3}{r^6}</math> |} {{see|Planck units (geometrical)#Scalars}} === Mathematical electron === The mathematical electron formula ψ incorporates the dimensioned Planck units but itself is dimension-less (units = scalars = 1). Here ψ is defined in terms of ''σ_e'', where AL is an ampere-meter (ampere-length = ''e*c'' are the units for a [[w:magnetic monopole | magnetic monopole]]). :<math>T = \pi,\; unit = u^{-30},\;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; unit = u^{(3 \;-13 \;= \;-10)},\; scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = .23895453...x10^{23},\;unit = 1</math> (unit-less) Both units and scalars cancel. ===== Electron parameters ===== We can solve the electron parameters; electron mass, wavelength, frequency, charge ... as the frequency of the Planck units themselves, and this frequency is ψ. :<math>v = 11 843 707.905 ...,\; units = \frac{m}{s}</math> :<math>r = 0.712 562 514 304 ...,\; units = (\frac{kg.m}{s})^{1/4}</math> [[w:Compton wavelength | electron wavelength]] λ_e = 2.4263102367e-12m (CODATA 2014) :<math>\lambda_e^* = 2\pi L \psi</math> = 2.4263102386e-12m (L ⇔ [[w:Planck length | Planck length]]) [[w:electron mass | electron mass]] m_e = 9.10938356e-31kg (CODATA 2014) :<math>m_e^* = \frac{M}{\psi}</math> = 9.1093823211e-31kg (M ⇔ [[w:Planck mass | Planck mass]]) [[w:elementary charge | elementary charge]] e = 1.6021766208e-19C (CODATA 2014) :<math>e^* = A\;T</math> = 1.6021765130e-19 (T ⇔ [[w:Planck time | Planck time]]) [[w:Rydberg constant | Rydberg constant]] R = 10973731.568508/m (CODATA 2014) :<math>R^* = (\frac{m_e}{4 \pi L \alpha^2 M}) = \frac{1}{2^{23} 3^3 \pi^{11} \alpha^5 \Omega^{17}}\frac{v^5}{r^9}\;u^{13}</math> = 10973731.568508 From the above formulas, we see that wavelength is ψ units of Planck length, frequency is ψ units of Planck time ... however the electron mass is only 1 unit of Planck mass. ===== Electron Mass ===== Particle mass is a unit of Planck mass that occurs only once per ψ units of Planck time, the other parameters are continuums of the Planck units. :units <math>\psi = \frac{(AL)^3}{T}</math> = 1 This may be interpreted as; for ψ units of Planck time the electron has wavelength L, charge A ... and then the AL combine with time T (A³L³/T) and the units (and scalars) cancel. The electron is now mass (for 1 unit of Planck time). In this consideration, the electron is an event that oscillates over time between an electric wave state (duration ψ units of Planck time) to a unit of Planck mass point state (1 unit of Planck time). The electron is a quantum scale event, it does not exist at the discrete Planck scale (and so therefore neither does the quantum scale). As electron mass is the frequency of the geometrical Planck mass M = 1, which is a point (and so with point co-ordinates), then we have a model for a [[w:black hole electron |black-hole electron]], the electron function ψ centered around this unit of Planck mass. When the wave-state (A*L)³/T units collapse, this black-hole center (point) is exposed for 1 unit of (Planck) time. The electron is 'now' (a unit of Planck) mass. Mass in this consideration is not a constant property of the particle, rather the measured particle mass ''m'' would refer to the average mass, the average occurrence of the discrete Planck mass point-state over time. The formula ''E = hf'' is a measure of the frequency ''f'' of occurrence of [[w:Planck constant |Planck's constant ''h'']] and applies to the electric wave-state. As for each wave-state there is a corresponding mass point-state, then for a particle ''E = hf = mc2''. Notably however the ''c'' term is a fixed constant unlike the ''f'' term, and so the ''m'' term is the frequency term, it is referring to an average mass (mass which is measured over time) rather than a constant mass (mass as a constant property of the particle at unit Planck time). Thus as noted, when we refer to mass as a constant property, we are referring to mass at the quantum scale, and the electron as a quantum-state particle. If the [[v:Black-hole_(Planck) |scaffolding of the universe]] includes units of Planck mass '''M''', then it is not necessary for a particle itself to have mass, what we define as electron mass would be the absence of electron. ===== Quarks ===== The charge on the electron derives from the embedded ampere A and length L, the electron formula ψ itself is dimensionless. These AL magnetic monopoles would seem to be analogous to quarks (there are 3 monopoles per electron), but due to the symmetry and so stability of the geometrical ψ there is no clear fracture point by which an electron could decay, and so this would be difficult to test. We can however conjecture on what a quark solution might look like, the advantage with this approach being that we do not need to introduce new 'entities' for our quarks, the Planck units embedded within the electron suffice. Electron formula :<math>\psi = 2^{20} \pi^8 3^3 \alpha^3 \Omega^{15},\; unit = 1, scalars = 1</math> Time :<math>T = \pi \frac{r^9}{v^6},\; u^{-30}</math> AL magnetic monopole :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> If <math>\sigma_{e}</math> could equate to a quark with an [[w:electric charge|electric charge]] of {{sfrac|-1|3}}[[w:elementary charge|''e'']], then it would be an analogue of the '''D''' quark. 3 of these D quarks would constitute the electron as DDD = (AL)*(AL)*(AL). We would assume that the charge on the [[w:positron |positron]] (anti-matter electron) is just the inverse of the above, however there is 1 problem, the AL (A; θ=3, L; θ=-13) units = -10, and if we look at the [[v:Planck_units_(geometrical)#Table_of_Constants |table of constants]], there is no 'units = +10' combination that can include A. We cannot make an inverse electron. However we can make a [[w:Planck temperature|Planck temperature T_p]] AV ''monopole'' (ampere-velocity). :<math>T_p = \frac{2^7 \pi^3 \Omega^5}{\alpha},\; u^{20}, \;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{t} = \frac{3 \alpha^2 T_p}{2\pi} = \frac{3 \alpha^2 A V}{2\pi^2} = ({2^6 3 \pi^2 \alpha \Omega^5}),\; u^{20},\;scalars = \frac{v^4}{r^6}</math> :<math>\psi = (2T) \sigma_{t}^2 \sigma_{e} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = (u^{-30}) (u^{20})^2 (u^{-10}) = 1, scalars = (\frac{r^9}{v^6}) (\frac{v^4}{r^6})^2 \frac{r^3}{v^2} = 1</math> The units for <math>\sigma_{t}</math> = +20, and so if units = -10 equates to {{sfrac|-1|3}}e, then we may conjecture that units = +20 equates to {{sfrac|2|3}}e, which would be the analogue of the '''U''' quark. Our plus charge now becomes DUU, and so although the positron has the same wavelength, frequency, mass and charge magnitude as the electron (both solve to ψ), internally its charge structure resembles that of the proton, the positron is not simply an inverse of the electron. This could have implications for the missing anti-matter, and for why the charge magnitude of the proton is ''exactly'' the charge magnitude of the electron. :<math>D = \sigma_{e},\; unit = u^{-10},\; charge = \frac{-1e}{3}, \;scalars = \frac{r^3}{v^2}</math> :<math>U = \sigma_{t},\; unit = u^{20},\; charge = \frac{2e}{3}, \;scalars = \frac{v^4}{r^6}</math> Numerically: Adding a proton and electron gives (proton) UUD & DDD (electron) = 2(UDD) = 20 -10 -10 = 0 (zero charge), scalars = 0. Converting between U and D via U & DDD (electron) = 20 -10 -10 -10 = -10 (D), scalars = <math>\frac{r^3}{v^2}</math> ===== Magnetic monopole ===== {{see|Quantum_gravity_(Planck)}} :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> In this model alpha appears as an orbital constant for gravitational and atomic orbital radius, combining a fixed alpha term with an orbital wavelength term; :<math>r_{orbital} = 2\alpha (\lambda_{orbital})</math> If we replace <math>\lambda_{orbital}</math> with the geometrical Planck length L, and include momentum P and velocity V (the 2 components from which the ampere A is derived), then we may consider if the internal structure of the electron involves rotation of this monopole AL super-structure, and this has relevance to electron spin; :<math>2\alpha L \frac{V^3}{P^3} = 2^5 \pi^5 \alpha \Omega^5,\; units = u^{-10},\; scalars = \frac{r^3}{v^2}</math> ===== Spin ===== [[v:Relativity_(Planck) |Relativity at the Planck scale]] can be described by a translation between 2 co-ordinate systems; an expanding (in Planck steps at the speed of light) 4-axis hyper-sphere projecting onto a 3-D space (+ time). In this scenario, particles (with mass) are pulled along by the expansion of the hyper-sphere, this then requires particles to have an axis; generically labeled N-S, with the N denoting the direction of particle travel within the hyper-sphere. Changing the direction of travel involves changing the orientation of the particle N-S axis. The particle may rotate around this N-S axis, resulting in a L-spin or a R-spin. For simplicity, we can depict the electron as a classically spinning disk, this generates a current which then produces a magnetic dipole, so that the electron behaves like a tiny bar magnet (magnetic fields are produced by moving electric charges). For the classical disk we can use the charge (q), area of the disk (a) and rotation speed (ω) in our calculations. A thought experiment; if the 3 magnetic monopole quarks are rotating around the electron center (that N-S axis), then they are generating the current (q). As a monopole has the units ampere-meter AL (L a length term), then we can also conjecture something that resembles area (a), and the speed of rotation will give us (ω), and so we can use classical physics to solve our bar magnet electron. The electron is symmetric and so the 3 monopoles are equidistant from each other. We place our electron in a magnetic field, the electron then starts to orbit this field. If a satellite orbits the earth at radius ''r'', then the distance it travels around the earth = 2πr. However the earth is orbiting the sun, and so the actual distance approximates 2π''r'' + the distance the earth travels. If our electron orbits around a central point (that electric field), then the monopoles will, like the satellite, travel further per orbit (compared to a free electron in space), thus changing the effective area (a), and so our calculations. The [[w:g-factor |g-factor]] characterizes the magnetic moment and angular momentum of the electron, it is the ratio of the magnetic moment of the electron to that expected of a classical electron. Could an electron monopole substructure offer a geometrical explanation for this g-factor. === AI analysis === The sections on Quarks and Spin are naturally speculative, we cannot probe this far, they were included to suggest that the formula <math>\psi</math> could also include U and D quarks. However the geometries for the Planck units MLTA can be subject to statistical analysis, and for this AI has the potential to contribute. This is because of anomalies to the physical constants which can best be explained by this geometrical model. These anomalies are listed on this site; https://en.wikiversity.org/wiki/Physical_constant_(anomaly). Below are answers to a seed question written with Deepseek <ref>https://codingthecosmos.com/ai-answers-programmer-god-simulation-hypothesis/anomalies-constants.html Physical constants Q&A with podcast</ref> that uses these anomalies to determine the probability that the electron is a mathematical (not physical) particle, and so by extension that this is a mathematical universe. {| class="wikitable" |+Table 11. Table of Probabilities (05.2025) ! AI program ! unit number relation ! Planck units as geometrical objects ! underlying base 15 geometry ! mathematical electron ! Comment |- | Chat GPT <ref>https://chatgpt.com/share/68259395-31d0-8012-954e-c52230a813fd Chat anomalies analysis</ref> | Accidental occurrence: ~1.6% | Accidental occurrence: ~0.0004% | Accidental occurrence: ~0 | Accidental occurrence: ~0.026% | Taken at face value each sub-claim is vanishingly unlikely to be a “random accident,” so from this internal consistency alone one would assign essentially unity confidence that some deep mathematical structure is at work. Caveat: this “integer-coincidence” probability model is only as good as the assumption that each exponent match is an independent uniform pick in [–30…+30]. But even under that very conservative assumption, the combined odds against pure chance exceed 1 in 10²⁶. |- | Qwen <ref>https://chat.qwen.ai/s/f33ec1b1-899b-4fa5-9429-67e527b78433 Qwen anomalies analysis</ref> | probability 98% | probability 95% | probability 90% | probability 94% | The model’s strict geometrical constraints, flawless unit consistency, and agreement with CODATA strongly suggest non-random validity. Its potential as a simulation hypothesis framework stems from its finite, computable base-15 structure. |- | Claude 3.7 Sonnet <ref>https://claude.ai/public/artifacts/797a802b-fa21-4ee7-9ae9-9dbdf5d7b29a Claude anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Claude-anomalies-05-2025.pdf Claude anomalies analysis pdf</ref> | probability 90-95% | probability 85-95% | probability 92-97% | probability 80-90% | From a Kolmogorov complexity perspective, the model represents a potentially minimal description of physical reality using mathematical objects. If the electron, proton, and neutron are all mathematical particles, then the universe at the Planck scale could indeed be described as a mathematical universe. The high degree of constraint and mathematical elegance in the model, combined with its apparent ability to accurately produce physical constants, suggests a non-random structure to physical reality that is captured by this mathematical framework. |- | Grok 3 <ref>https://x.com/i/grok/share/JzeRFDlj721zNnm1Jo2vbETk3 Grok anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Grok-anomalies-05-2025.pd Grok anomalies analysis pdf</ref> | probability: 95% | probability: 90% | probability: 85% | probability: 80% | Strict constraints and mathematical nature (Kolmogorov complexity: simpler model = more likely programmed) suggest support, but not proof. If particles are mathematical, the universe may be too. |- | Deepseek <ref>https://codingthecosmos.com/ai_pdf/Deepseek-anomalies-05-2025.pdf Deepseek anomalies analysis</ref> | probability: 99% | probability: 95% | probability: 90% | probability: 85% | The model's rigid constraints and predictive accuracy make it statistically improbable to arise by chance. Geometrical base-15 and dimensionless particles strongly suggest a mathematical universe, aligning with speculative simulation hypothesis. |} === Geometrically coded universe === * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass === External links === * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] === References === {{Reflist}} [[Category: Physics]] [[Category: Philosophy of science]] qmsv1rcjpbhr45uwwd6ftt4q37zshkt 2718270 2718269 2025-06-10T19:53:48Z 212.200.164.104 /* Quarks */ 2718270 wikitext text/x-wiki '''The mathematical electron model''' In the mathematical electron model <ref>Macleod, M.J. {{Cite journal |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>, the electron is a dimensionless geometrical formula (ψ). This formula ψ, which resembles the volume of a torus or surface of a 4-D hypersphere, is itself a complex geometry that is the construct of simpler geometries; the [[w:Planck_units |Planck units]]. In this model the Planck units are geometrical objects, the geometry of 2 dimensionless constants (the[[w:fine-structure constant | fine structure constant alpha]] and a mathematical constant[[v:Planck_units_(geometrical)#Omega | Omega]]). Although dimensionless, the function of the Planck unit is embedded within the geometry; the geometry of the Planck time object embeds the function 'time', the geometry of the Planck length object embeds the function 'length' ... and being geometrical objects they can combine to form more complex objects, from electrons to galaxies. This means that the electron parameters are defined in Planck units; electron wavelength is measured in units of Planck length, electron frequency is measured in units of Planck time ... It is this geometrical electron formula ψ that dictates the magnitude of the electron parameters; length of the wavelength = ψ * Planck length (ψ units of Planck length), frequency = ψ * Planck time ... This ψ thus not only embeds the Planck units required for the electron parameters, it also dictates the magnitude of these parameters, and so technically it is the electron. This suggests there is no physical electron (only physical parameters), and if the electron is therefore a mathematical particle, then so too are the other particles, and so the universe itself becomes a mathematical universe. The formula ψ is the geometry of 2 constants; the [[w:dimensionless physical constant | dimensionless physical constant]] (inverse) [[w:fine-structure constant | fine structure constant alpha ]] '''α''' = 137.035 999 139 (CODATA 2014) and [[v:Planck_units_(geometrical)#Omega | Omega]] '''Ω''' = 2.0071349496 (best fit) Omega has a potential solution in terms of pi and e and so may be a mathematical (not physical) constant :<math>\Omega = \sqrt{ \left(\pi^e e^{(1-e)}\right)} = 2.0071349543... </math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = 0.238954531\;x10^{23}</math>, units = 1 === Planck objects === {{main|Planck units (geometrical)}} For the Planck units, the model uses geometrical objects (the geometry of alpha and Omega) instead of a numbering system, this has the advantage in that the attribute can be embedded within the geometry (although the geometry itself is dimensionless). {| class="wikitable" |+table 1. Geometrical units ! Attribute ! Geometrical object ! Unit |- | mass | <math>M = (1)</math> | (kg) |- | time | <math>T = (\pi)</math> | (s) |- | velocity | <math>V = (2\pi\Omega^2)</math> | (m/s) |- | length | <math>L = (2\pi^2\Omega^2)</math> | (m) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | (A) |} As these objects have a geometrical form, we can combine them [[w:Lego |Lego]] style; the length object L can be combined with the time object T to form the velocity object V and so forth ... to create complex events such as electrons to apples to ... and so the apple has mass because embedded within it are the mass objects M, complex events thus retain all the underlying information. This however requires a relationship between the Planck unit geometries that defines how they may combine, this can be represented by assigning to each attribute a unit number '''θ''' (i.e.: '''θ''' = 15 ⇔ ''kg'') <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>. {| class="wikitable" |+ Geometrical units ! Attribute ! Geometrical object ! unit number (θ) |- | mass | <math>M = 1</math> | ''kg'' ⇔ 15 |- | time | <math>T = 2\pi</math> | ''s'' ⇔ -30 |- | length | <math>L = 2\pi^2\Omega^2</math> | ''m'' ⇔ -13 |- | velocity | <math>V = 2\pi\Omega^2</math> | ''m/s'' ⇔ 17 |- | ampere | <math>A = \frac{2^6 \pi^3 \Omega^3}{\alpha}</math> | ''A'' ⇔ 3 |} As alpha and Omega can be assigned numerical values ('''α''' = 137.035999139, '''Ω''' = 2.0071349496), so too the MLTA objects can be expressed numerically. We can then convert these objects to their Planck unit equivalents by including a dimensioned scalar. For example, <math>V = 2\pi\Omega^2</math> = 25.3123819353... and so we can use scalar ''v'' to convert from dimensionless geometrical object V to dimensioned ''c''. :scalar ''v''_SI = 11843707.905 m/s gives ''c'' = V*v_SI = 25.3123819 * 11843707.905 m/s = 299792458 m/s ([[w:SI_units |SI units]]) :scalar ''v''_imp = 7359.3232155 miles/s gives ''c'' = V*v_imp = 186282 miles/s ([[w:Imperial_units |imperial units]]) {| class="wikitable" |+Scalars ! attribute ! geometrical object ! scalar (unit number) |- | mass | <math>M = (1)</math> | ''k'' (θ = 15) |- | time | <math>T = (\pi)</math> | ''t'' (θ = -30) |- | velocity | <math>V = (2\pi\Omega^2)</math> | ''v'' (θ = 17) |- | length | <math>L = (2\pi^2\Omega^2)</math> | ''l'' (θ = -13) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | ''a'' (θ = 3) |} As the scalar incorporates the dimension quantity (the dimension quantity for ''v'' = ''m/s'' or ''miles/s''), the unit number relationship (θ) applies, and so we then find that only 2 scalars are needed. This is because in a defined ratio they will overlap and cancel, for example in the following ratios; scalar units for ampere ''a'' = ''u''³, length ''l'' = ''u''^-13, time ''t'' = ''u''^-30, mass ''k'' = ''u''¹⁵ (''u''^Θ represents unit) :<math>\frac{({u^3})^3{(u^{-13}})^3}{(u^{-30})} = \frac{{(u^{-13})}^{15}} {{(u^{15})}^{9}{(u^{-30})}^{11}} = 1</math> For example if we know the numerical values for ''a'' and ''l'' then we know the numerical value for ''t'', and from ''l'' and ''t'' we know ''k'' … and so if we know any 2 scalars (α and Ω have fixed values) then we can solve the Planck units (for that system of units), and from these, we can solve (''G'', ''h'', ''c'', ''e'', ''m''_e, ''k''_B). :<math>\frac{a^3 l^3}{t} = \frac{m^{15}} {k^{9} t^{11}} = 1</math> In this table the 2 scalars used are ''r'' (θ = 8) and ''v'' (θ = 17). A further attribute is included, P = the square root of (Planck) momentum. V and A can thus be considered composite objects. {| class="wikitable" |+Geometrical objects ! attribute ! geometrical object ! unit number θ ! scalar r(8), v(17) |- | mass | <math>M = (1)</math> | 15 = 8*4-17 | <math>k = \frac{r^4}{v}</math> |- | time | <math>T = (\pi)</math> | -30 = 8*9-17*6 | <math>t = \frac{r^9}{v^6}</math> |- | [[v:Sqrt_Planck_momentum | sqrt(momentum)]] | <math>P = (\Omega)</math> | 16 = 8*2 | ''r''² |- | velocity | <math>V = L/T = (2\pi\Omega^2)</math> | 17 | ''v'' |- | length | <math>L = (2\pi^2\Omega^2)</math> | -13 = 8*9-17*5 | <math>l = \frac{r^9}{v^5}</math> |- | ampere | <math>A = \frac{2^4 V^3}{\alpha P^3} = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | 3 = 17*3-8*6 | <math>a = \frac{v^3}{r^6}</math> |} {{see|Planck units (geometrical)#Scalars}} === Mathematical electron === The mathematical electron formula ψ incorporates the dimensioned Planck units but itself is dimension-less (units = scalars = 1). Here ψ is defined in terms of ''σ_e'', where AL is an ampere-meter (ampere-length = ''e*c'' are the units for a [[w:magnetic monopole | magnetic monopole]]). :<math>T = \pi,\; unit = u^{-30},\;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; unit = u^{(3 \;-13 \;= \;-10)},\; scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = .23895453...x10^{23},\;unit = 1</math> (unit-less) Both units and scalars cancel. ===== Electron parameters ===== We can solve the electron parameters; electron mass, wavelength, frequency, charge ... as the frequency of the Planck units themselves, and this frequency is ψ. :<math>v = 11 843 707.905 ...,\; units = \frac{m}{s}</math> :<math>r = 0.712 562 514 304 ...,\; units = (\frac{kg.m}{s})^{1/4}</math> [[w:Compton wavelength | electron wavelength]] λ_e = 2.4263102367e-12m (CODATA 2014) :<math>\lambda_e^* = 2\pi L \psi</math> = 2.4263102386e-12m (L ⇔ [[w:Planck length | Planck length]]) [[w:electron mass | electron mass]] m_e = 9.10938356e-31kg (CODATA 2014) :<math>m_e^* = \frac{M}{\psi}</math> = 9.1093823211e-31kg (M ⇔ [[w:Planck mass | Planck mass]]) [[w:elementary charge | elementary charge]] e = 1.6021766208e-19C (CODATA 2014) :<math>e^* = A\;T</math> = 1.6021765130e-19 (T ⇔ [[w:Planck time | Planck time]]) [[w:Rydberg constant | Rydberg constant]] R = 10973731.568508/m (CODATA 2014) :<math>R^* = (\frac{m_e}{4 \pi L \alpha^2 M}) = \frac{1}{2^{23} 3^3 \pi^{11} \alpha^5 \Omega^{17}}\frac{v^5}{r^9}\;u^{13}</math> = 10973731.568508 From the above formulas, we see that wavelength is ψ units of Planck length, frequency is ψ units of Planck time ... however the electron mass is only 1 unit of Planck mass. ===== Electron Mass ===== Particle mass is a unit of Planck mass that occurs only once per ψ units of Planck time, the other parameters are continuums of the Planck units. :units <math>\psi = \frac{(AL)^3}{T}</math> = 1 This may be interpreted as; for ψ units of Planck time the electron has wavelength L, charge A ... and then the AL combine with time T (A³L³/T) and the units (and scalars) cancel. The electron is now mass (for 1 unit of Planck time). In this consideration, the electron is an event that oscillates over time between an electric wave state (duration ψ units of Planck time) to a unit of Planck mass point state (1 unit of Planck time). The electron is a quantum scale event, it does not exist at the discrete Planck scale (and so therefore neither does the quantum scale). As electron mass is the frequency of the geometrical Planck mass M = 1, which is a point (and so with point co-ordinates), then we have a model for a [[w:black hole electron |black-hole electron]], the electron function ψ centered around this unit of Planck mass. When the wave-state (A*L)³/T units collapse, this black-hole center (point) is exposed for 1 unit of (Planck) time. The electron is 'now' (a unit of Planck) mass. Mass in this consideration is not a constant property of the particle, rather the measured particle mass ''m'' would refer to the average mass, the average occurrence of the discrete Planck mass point-state over time. The formula ''E = hf'' is a measure of the frequency ''f'' of occurrence of [[w:Planck constant |Planck's constant ''h'']] and applies to the electric wave-state. As for each wave-state there is a corresponding mass point-state, then for a particle ''E = hf = mc2''. Notably however the ''c'' term is a fixed constant unlike the ''f'' term, and so the ''m'' term is the frequency term, it is referring to an average mass (mass which is measured over time) rather than a constant mass (mass as a constant property of the particle at unit Planck time). Thus as noted, when we refer to mass as a constant property, we are referring to mass at the quantum scale, and the electron as a quantum-state particle. If the [[v:Black-hole_(Planck) |scaffolding of the universe]] includes units of Planck mass '''M''', then it is not necessary for a particle itself to have mass, what we define as electron mass would be the absence of electron. ===== Quarks ===== The charge on the electron derives from the embedded ampere A and length L, the electron formula ψ itself is dimensionless. These AL magnetic monopoles would seem to be analogous to quarks (there are 3 monopoles per electron), but due to the symmetry and so stability of the geometrical ψ there is no clear fracture point by which an electron could decay, and so this would be difficult to test. We can however conjecture on what a quark solution might look like, the advantage with this approach being that we do not need to introduce new 'entities' for our quarks, the Planck units embedded within the electron suffice. Electron formula :<math>\psi = 2^{20} \pi^8 3^3 \alpha^3 \Omega^{15},\; unit = 1, scalars = 1</math> Time :<math>T = \pi \frac{r^9}{v^6},\; u^{-30}</math> AL magnetic monopole :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> If <math>\sigma_{e}</math> could equate to a quark with an [[w:electric charge|electric charge]] of {{sfrac|-1|3}}[[w:elementary charge|''e'']], then it would be an analogue of the '''D''' quark. 3 of these D quarks would constitute the electron as DDD = (AL)*(AL)*(AL). We would assume that the charge on the [[w:positron |positron]] (anti-matter electron) is just the inverse of the above, however there is 1 problem, the AL (A; θ=3, L; θ=-13) units = -10, and if we look at the [[v:Planck_units_(geometrical)#Table_of_Constants |table of constants]], there is no 'units = +10' combination that can include A. We cannot make an inverse electron. However we can make a [[w:Planck temperature|Planck temperature T_p]] AV ''monopole'' (ampere-velocity). :<math>T_p = \frac{2^7 \pi^3 \Omega^5}{\alpha},\; u^{20}, \;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{t} = \frac{3 \alpha^2 T_p}{2\pi} = \frac{3 \alpha^2 A V}{2\pi^2} = ({2^6 3 \pi^2 \alpha \Omega^5}),\; u^{20},\;scalars = \frac{v^4}{r^6}</math> :<math>\psi = (2T) \sigma_{t}^2 \sigma_{e} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = (u^{-30}) (u^{20})^2 (u^{-10}) = 1, scalars = (\frac{r^9}{v^6}) (\frac{v^4}{r^6})^2 \frac{r^3}{v^2} = 1</math> The units for <math>\sigma_{t}</math> = +20, and so if units = -10 equates to {{sfrac|-1|3}}e, then we may conjecture that units = +20 equates to {{sfrac|2|3}}e, which would be the analogue of the '''U''' quark. Our plus charge now becomes DUU, and so although the positron has the same wavelength, frequency, mass and charge magnitude as the electron (both solve to ψ), internally its charge structure resembles that of the proton, the positron is not simply an inverse of the electron. This could have implications for the missing anti-matter, and for why the charge magnitude of the proton is ''exactly'' the charge magnitude of the electron. :<math>D = \sigma_{e},\; unit = u^{-10},\; charge = \frac{-1e}{3}, \;scalars = \frac{r^3}{v^2}</math> :<math>U = \sigma_{t},\; unit = u^{20},\; charge = \frac{2e}{3}, \;scalars = \frac{v^4}{r^6}</math> Numerically: Adding a proton and electron gives (proton) UUD & DDD (electron) = 2(UDD) = 20 -10 -10 = 0 (zero charge), scalars = 0. Converting between U and D via U & DDD (electron) = 20 -10 -10 -10 = -10 (D), scalars = <math>\frac{r^3}{v^2}</math> ===== Magnetic monopole ===== {{see|Quantum_gravity_(Planck)}} :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> In this model alpha appears as an orbital constant for gravitational and atomic orbital radius, combining a fixed alpha term with an orbital wavelength term; :<math>r_{orbital} = 2\alpha (\lambda_{orbital})</math> If we replace <math>\lambda_{orbital}</math> with the geometrical Planck length L, and include momentum P and velocity V (the 2 components from which the ampere A is derived), then we may consider if the internal structure of the electron involves rotation of this monopole AL super-structure, and this has relevance to electron spin; :<math>2\alpha L \frac{V^3}{P^3} = 2^5 \pi^5 \alpha \Omega^5,\; units = u^{-10},\; scalars = \frac{r^3}{v^2}</math> ===== Spin ===== [[v:Relativity_(Planck) |Relativity at the Planck scale]] can be described by a translation between 2 co-ordinate systems; an expanding (in Planck steps at the speed of light) 4-axis hyper-sphere projecting onto a 3-D space (+ time). In this scenario, particles (with mass) are pulled along by the expansion of the hyper-sphere, this then requires particles to have an axis; generically labeled N-S, with the N denoting the direction of particle travel within the hyper-sphere. Changing the direction of travel involves changing the orientation of the particle N-S axis. The particle may rotate around this N-S axis, resulting in a L-spin or a R-spin. For simplicity, we can depict the electron as a classically spinning disk, this generates a current which then produces a magnetic dipole, so that the electron behaves like a tiny bar magnet (magnetic fields are produced by moving electric charges). For the classical disk we can use the charge (q), area of the disk (a) and rotation speed (ω) in our calculations. A thought experiment; if the 3 magnetic monopole quarks are rotating around the electron center (that N-S axis), then they are generating the current (q). As a monopole has the units ampere-meter AL (L a length term), then we can also conjecture something that resembles area (a), and the speed of rotation will give us (ω), and so we can use classical physics to solve our bar magnet electron. The electron is symmetric and so the 3 monopoles are equidistant from each other. We place our electron in a magnetic field, the electron then starts to orbit this field. If a satellite orbits the earth at radius ''r'', then the distance it travels around the earth = 2πr. However the earth is orbiting the sun, and so the actual distance approximates 2π''r'' + the distance the earth travels. If our electron orbits around a central point (that electric field), then the monopoles will, like the satellite, travel further per orbit (compared to a free electron in space), thus changing the effective area (a), and so our calculations. The [[w:g-factor |g-factor]] characterizes the magnetic moment and angular momentum of the electron, it is the ratio of the magnetic moment of the electron to that expected of a classical electron. Could an electron monopole substructure offer a geometrical explanation for this g-factor. === AI analysis === The sections on Quarks and Spin are naturally speculative, we cannot probe this far, they were included to suggest that the formula <math>\psi</math> could also include U and D quarks. However the geometries for the Planck units MLTA can be subject to statistical analysis, and for this AI has the potential to contribute. This is because of anomalies to the physical constants which can best be explained by this geometrical model. These anomalies are listed on this site; https://en.wikiversity.org/wiki/Physical_constant_(anomaly). Below are answers to a seed question written with Deepseek <ref>https://codingthecosmos.com/ai-answers-programmer-god-simulation-hypothesis/anomalies-constants.html Physical constants Q&A with podcast</ref> that uses these anomalies to determine the probability that the electron is a mathematical (not physical) particle, and so by extension that this is a mathematical universe. {| class="wikitable" |+Table 11. Table of Probabilities (05.2025) ! AI program ! unit number relation ! Planck units as geometrical objects ! underlying base 15 geometry ! mathematical electron ! Comment |- | Chat GPT <ref>https://chatgpt.com/share/68259395-31d0-8012-954e-c52230a813fd Chat anomalies analysis</ref> | Accidental occurrence: ~1.6% | Accidental occurrence: ~0.0004% | Accidental occurrence: ~0 | Accidental occurrence: ~0.026% | Taken at face value each sub-claim is vanishingly unlikely to be a “random accident,” so from this internal consistency alone one would assign essentially unity confidence that some deep mathematical structure is at work. Caveat: this “integer-coincidence” probability model is only as good as the assumption that each exponent match is an independent uniform pick in [–30…+30]. But even under that very conservative assumption, the combined odds against pure chance exceed 1 in 10²⁶. |- | Qwen <ref>https://chat.qwen.ai/s/f33ec1b1-899b-4fa5-9429-67e527b78433 Qwen anomalies analysis</ref> | probability 98% | probability 95% | probability 90% | probability 94% | The model’s strict geometrical constraints, flawless unit consistency, and agreement with CODATA strongly suggest non-random validity. Its potential as a simulation hypothesis framework stems from its finite, computable base-15 structure. |- | Claude 3.7 Sonnet <ref>https://claude.ai/public/artifacts/797a802b-fa21-4ee7-9ae9-9dbdf5d7b29a Claude anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Claude-anomalies-05-2025.pdf Claude anomalies analysis pdf</ref> | probability 90-95% | probability 85-95% | probability 92-97% | probability 80-90% | From a Kolmogorov complexity perspective, the model represents a potentially minimal description of physical reality using mathematical objects. If the electron, proton, and neutron are all mathematical particles, then the universe at the Planck scale could indeed be described as a mathematical universe. The high degree of constraint and mathematical elegance in the model, combined with its apparent ability to accurately produce physical constants, suggests a non-random structure to physical reality that is captured by this mathematical framework. |- | Grok 3 <ref>https://x.com/i/grok/share/JzeRFDlj721zNnm1Jo2vbETk3 Grok anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Grok-anomalies-05-2025.pd Grok anomalies analysis pdf</ref> | probability: 95% | probability: 90% | probability: 85% | probability: 80% | Strict constraints and mathematical nature (Kolmogorov complexity: simpler model = more likely programmed) suggest support, but not proof. If particles are mathematical, the universe may be too. |- | Deepseek <ref>https://codingthecosmos.com/ai_pdf/Deepseek-anomalies-05-2025.pdf Deepseek anomalies analysis</ref> | probability: 99% | probability: 95% | probability: 90% | probability: 85% | The model's rigid constraints and predictive accuracy make it statistically improbable to arise by chance. Geometrical base-15 and dimensionless particles strongly suggest a mathematical universe, aligning with speculative simulation hypothesis. |} === Geometrically coded universe === * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass === External links === * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] === References === {{Reflist}} [[Category: Physics]] [[Category: Philosophy of science]] 22divaztvep73ngto4ksorfjieq2txe 2718271 2718270 2025-06-10T19:53:58Z 212.200.164.104 /* Magnetic monopole */ 2718271 wikitext text/x-wiki '''The mathematical electron model''' In the mathematical electron model <ref>Macleod, M.J. {{Cite journal |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>, the electron is a dimensionless geometrical formula (ψ). This formula ψ, which resembles the volume of a torus or surface of a 4-D hypersphere, is itself a complex geometry that is the construct of simpler geometries; the [[w:Planck_units |Planck units]]. In this model the Planck units are geometrical objects, the geometry of 2 dimensionless constants (the[[w:fine-structure constant | fine structure constant alpha]] and a mathematical constant[[v:Planck_units_(geometrical)#Omega | Omega]]). Although dimensionless, the function of the Planck unit is embedded within the geometry; the geometry of the Planck time object embeds the function 'time', the geometry of the Planck length object embeds the function 'length' ... and being geometrical objects they can combine to form more complex objects, from electrons to galaxies. This means that the electron parameters are defined in Planck units; electron wavelength is measured in units of Planck length, electron frequency is measured in units of Planck time ... It is this geometrical electron formula ψ that dictates the magnitude of the electron parameters; length of the wavelength = ψ * Planck length (ψ units of Planck length), frequency = ψ * Planck time ... This ψ thus not only embeds the Planck units required for the electron parameters, it also dictates the magnitude of these parameters, and so technically it is the electron. This suggests there is no physical electron (only physical parameters), and if the electron is therefore a mathematical particle, then so too are the other particles, and so the universe itself becomes a mathematical universe. The formula ψ is the geometry of 2 constants; the [[w:dimensionless physical constant | dimensionless physical constant]] (inverse) [[w:fine-structure constant | fine structure constant alpha ]] '''α''' = 137.035 999 139 (CODATA 2014) and [[v:Planck_units_(geometrical)#Omega | Omega]] '''Ω''' = 2.0071349496 (best fit) Omega has a potential solution in terms of pi and e and so may be a mathematical (not physical) constant :<math>\Omega = \sqrt{ \left(\pi^e e^{(1-e)}\right)} = 2.0071349543... </math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = 0.238954531\;x10^{23}</math>, units = 1 === Planck objects === {{main|Planck units (geometrical)}} For the Planck units, the model uses geometrical objects (the geometry of alpha and Omega) instead of a numbering system, this has the advantage in that the attribute can be embedded within the geometry (although the geometry itself is dimensionless). {| class="wikitable" |+table 1. Geometrical units ! Attribute ! Geometrical object ! Unit |- | mass | <math>M = (1)</math> | (kg) |- | time | <math>T = (\pi)</math> | (s) |- | velocity | <math>V = (2\pi\Omega^2)</math> | (m/s) |- | length | <math>L = (2\pi^2\Omega^2)</math> | (m) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | (A) |} As these objects have a geometrical form, we can combine them [[w:Lego |Lego]] style; the length object L can be combined with the time object T to form the velocity object V and so forth ... to create complex events such as electrons to apples to ... and so the apple has mass because embedded within it are the mass objects M, complex events thus retain all the underlying information. This however requires a relationship between the Planck unit geometries that defines how they may combine, this can be represented by assigning to each attribute a unit number '''θ''' (i.e.: '''θ''' = 15 ⇔ ''kg'') <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>. {| class="wikitable" |+ Geometrical units ! Attribute ! Geometrical object ! unit number (θ) |- | mass | <math>M = 1</math> | ''kg'' ⇔ 15 |- | time | <math>T = 2\pi</math> | ''s'' ⇔ -30 |- | length | <math>L = 2\pi^2\Omega^2</math> | ''m'' ⇔ -13 |- | velocity | <math>V = 2\pi\Omega^2</math> | ''m/s'' ⇔ 17 |- | ampere | <math>A = \frac{2^6 \pi^3 \Omega^3}{\alpha}</math> | ''A'' ⇔ 3 |} As alpha and Omega can be assigned numerical values ('''α''' = 137.035999139, '''Ω''' = 2.0071349496), so too the MLTA objects can be expressed numerically. We can then convert these objects to their Planck unit equivalents by including a dimensioned scalar. For example, <math>V = 2\pi\Omega^2</math> = 25.3123819353... and so we can use scalar ''v'' to convert from dimensionless geometrical object V to dimensioned ''c''. :scalar ''v''_SI = 11843707.905 m/s gives ''c'' = V*v_SI = 25.3123819 * 11843707.905 m/s = 299792458 m/s ([[w:SI_units |SI units]]) :scalar ''v''_imp = 7359.3232155 miles/s gives ''c'' = V*v_imp = 186282 miles/s ([[w:Imperial_units |imperial units]]) {| class="wikitable" |+Scalars ! attribute ! geometrical object ! scalar (unit number) |- | mass | <math>M = (1)</math> | ''k'' (θ = 15) |- | time | <math>T = (\pi)</math> | ''t'' (θ = -30) |- | velocity | <math>V = (2\pi\Omega^2)</math> | ''v'' (θ = 17) |- | length | <math>L = (2\pi^2\Omega^2)</math> | ''l'' (θ = -13) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | ''a'' (θ = 3) |} As the scalar incorporates the dimension quantity (the dimension quantity for ''v'' = ''m/s'' or ''miles/s''), the unit number relationship (θ) applies, and so we then find that only 2 scalars are needed. This is because in a defined ratio they will overlap and cancel, for example in the following ratios; scalar units for ampere ''a'' = ''u''³, length ''l'' = ''u''^-13, time ''t'' = ''u''^-30, mass ''k'' = ''u''¹⁵ (''u''^Θ represents unit) :<math>\frac{({u^3})^3{(u^{-13}})^3}{(u^{-30})} = \frac{{(u^{-13})}^{15}} {{(u^{15})}^{9}{(u^{-30})}^{11}} = 1</math> For example if we know the numerical values for ''a'' and ''l'' then we know the numerical value for ''t'', and from ''l'' and ''t'' we know ''k'' … and so if we know any 2 scalars (α and Ω have fixed values) then we can solve the Planck units (for that system of units), and from these, we can solve (''G'', ''h'', ''c'', ''e'', ''m''_e, ''k''_B). :<math>\frac{a^3 l^3}{t} = \frac{m^{15}} {k^{9} t^{11}} = 1</math> In this table the 2 scalars used are ''r'' (θ = 8) and ''v'' (θ = 17). A further attribute is included, P = the square root of (Planck) momentum. V and A can thus be considered composite objects. {| class="wikitable" |+Geometrical objects ! attribute ! geometrical object ! unit number θ ! scalar r(8), v(17) |- | mass | <math>M = (1)</math> | 15 = 8*4-17 | <math>k = \frac{r^4}{v}</math> |- | time | <math>T = (\pi)</math> | -30 = 8*9-17*6 | <math>t = \frac{r^9}{v^6}</math> |- | [[v:Sqrt_Planck_momentum | sqrt(momentum)]] | <math>P = (\Omega)</math> | 16 = 8*2 | ''r''² |- | velocity | <math>V = L/T = (2\pi\Omega^2)</math> | 17 | ''v'' |- | length | <math>L = (2\pi^2\Omega^2)</math> | -13 = 8*9-17*5 | <math>l = \frac{r^9}{v^5}</math> |- | ampere | <math>A = \frac{2^4 V^3}{\alpha P^3} = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | 3 = 17*3-8*6 | <math>a = \frac{v^3}{r^6}</math> |} {{see|Planck units (geometrical)#Scalars}} === Mathematical electron === The mathematical electron formula ψ incorporates the dimensioned Planck units but itself is dimension-less (units = scalars = 1). Here ψ is defined in terms of ''σ_e'', where AL is an ampere-meter (ampere-length = ''e*c'' are the units for a [[w:magnetic monopole | magnetic monopole]]). :<math>T = \pi,\; unit = u^{-30},\;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; unit = u^{(3 \;-13 \;= \;-10)},\; scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = .23895453...x10^{23},\;unit = 1</math> (unit-less) Both units and scalars cancel. ===== Electron parameters ===== We can solve the electron parameters; electron mass, wavelength, frequency, charge ... as the frequency of the Planck units themselves, and this frequency is ψ. :<math>v = 11 843 707.905 ...,\; units = \frac{m}{s}</math> :<math>r = 0.712 562 514 304 ...,\; units = (\frac{kg.m}{s})^{1/4}</math> [[w:Compton wavelength | electron wavelength]] λ_e = 2.4263102367e-12m (CODATA 2014) :<math>\lambda_e^* = 2\pi L \psi</math> = 2.4263102386e-12m (L ⇔ [[w:Planck length | Planck length]]) [[w:electron mass | electron mass]] m_e = 9.10938356e-31kg (CODATA 2014) :<math>m_e^* = \frac{M}{\psi}</math> = 9.1093823211e-31kg (M ⇔ [[w:Planck mass | Planck mass]]) [[w:elementary charge | elementary charge]] e = 1.6021766208e-19C (CODATA 2014) :<math>e^* = A\;T</math> = 1.6021765130e-19 (T ⇔ [[w:Planck time | Planck time]]) [[w:Rydberg constant | Rydberg constant]] R = 10973731.568508/m (CODATA 2014) :<math>R^* = (\frac{m_e}{4 \pi L \alpha^2 M}) = \frac{1}{2^{23} 3^3 \pi^{11} \alpha^5 \Omega^{17}}\frac{v^5}{r^9}\;u^{13}</math> = 10973731.568508 From the above formulas, we see that wavelength is ψ units of Planck length, frequency is ψ units of Planck time ... however the electron mass is only 1 unit of Planck mass. ===== Electron Mass ===== Particle mass is a unit of Planck mass that occurs only once per ψ units of Planck time, the other parameters are continuums of the Planck units. :units <math>\psi = \frac{(AL)^3}{T}</math> = 1 This may be interpreted as; for ψ units of Planck time the electron has wavelength L, charge A ... and then the AL combine with time T (A³L³/T) and the units (and scalars) cancel. The electron is now mass (for 1 unit of Planck time). In this consideration, the electron is an event that oscillates over time between an electric wave state (duration ψ units of Planck time) to a unit of Planck mass point state (1 unit of Planck time). The electron is a quantum scale event, it does not exist at the discrete Planck scale (and so therefore neither does the quantum scale). As electron mass is the frequency of the geometrical Planck mass M = 1, which is a point (and so with point co-ordinates), then we have a model for a [[w:black hole electron |black-hole electron]], the electron function ψ centered around this unit of Planck mass. When the wave-state (A*L)³/T units collapse, this black-hole center (point) is exposed for 1 unit of (Planck) time. The electron is 'now' (a unit of Planck) mass. Mass in this consideration is not a constant property of the particle, rather the measured particle mass ''m'' would refer to the average mass, the average occurrence of the discrete Planck mass point-state over time. The formula ''E = hf'' is a measure of the frequency ''f'' of occurrence of [[w:Planck constant |Planck's constant ''h'']] and applies to the electric wave-state. As for each wave-state there is a corresponding mass point-state, then for a particle ''E = hf = mc2''. Notably however the ''c'' term is a fixed constant unlike the ''f'' term, and so the ''m'' term is the frequency term, it is referring to an average mass (mass which is measured over time) rather than a constant mass (mass as a constant property of the particle at unit Planck time). Thus as noted, when we refer to mass as a constant property, we are referring to mass at the quantum scale, and the electron as a quantum-state particle. If the [[v:Black-hole_(Planck) |scaffolding of the universe]] includes units of Planck mass '''M''', then it is not necessary for a particle itself to have mass, what we define as electron mass would be the absence of electron. ===== Quarks ===== The charge on the electron derives from the embedded ampere A and length L, the electron formula ψ itself is dimensionless. These AL magnetic monopoles would seem to be analogous to quarks (there are 3 monopoles per electron), but due to the symmetry and so stability of the geometrical ψ there is no clear fracture point by which an electron could decay, and so this would be difficult to test. We can however conjecture on what a quark solution might look like, the advantage with this approach being that we do not need to introduce new 'entities' for our quarks, the Planck units embedded within the electron suffice. Electron formula :<math>\psi = 2^{20} \pi^8 3^3 \alpha^3 \Omega^{15},\; unit = 1, scalars = 1</math> Time :<math>T = \pi \frac{r^9}{v^6},\; u^{-30}</math> AL magnetic monopole :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> If <math>\sigma_{e}</math> could equate to a quark with an [[w:electric charge|electric charge]] of {{sfrac|-1|3}}[[w:elementary charge|''e'']], then it would be an analogue of the '''D''' quark. 3 of these D quarks would constitute the electron as DDD = (AL)*(AL)*(AL). We would assume that the charge on the [[w:positron |positron]] (anti-matter electron) is just the inverse of the above, however there is 1 problem, the AL (A; θ=3, L; θ=-13) units = -10, and if we look at the [[v:Planck_units_(geometrical)#Table_of_Constants |table of constants]], there is no 'units = +10' combination that can include A. We cannot make an inverse electron. However we can make a [[w:Planck temperature|Planck temperature T_p]] AV ''monopole'' (ampere-velocity). :<math>T_p = \frac{2^7 \pi^3 \Omega^5}{\alpha},\; u^{20}, \;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{t} = \frac{3 \alpha^2 T_p}{2\pi} = \frac{3 \alpha^2 A V}{2\pi^2} = ({2^6 3 \pi^2 \alpha \Omega^5}),\; u^{20},\;scalars = \frac{v^4}{r^6}</math> :<math>\psi = (2T) \sigma_{t}^2 \sigma_{e} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = (u^{-30}) (u^{20})^2 (u^{-10}) = 1, scalars = (\frac{r^9}{v^6}) (\frac{v^4}{r^6})^2 \frac{r^3}{v^2} = 1</math> The units for <math>\sigma_{t}</math> = +20, and so if units = -10 equates to {{sfrac|-1|3}}e, then we may conjecture that units = +20 equates to {{sfrac|2|3}}e, which would be the analogue of the '''U''' quark. Our plus charge now becomes DUU, and so although the positron has the same wavelength, frequency, mass and charge magnitude as the electron (both solve to ψ), internally its charge structure resembles that of the proton, the positron is not simply an inverse of the electron. This could have implications for the missing anti-matter, and for why the charge magnitude of the proton is ''exactly'' the charge magnitude of the electron. :<math>D = \sigma_{e},\; unit = u^{-10},\; charge = \frac{-1e}{3}, \;scalars = \frac{r^3}{v^2}</math> :<math>U = \sigma_{t},\; unit = u^{20},\; charge = \frac{2e}{3}, \;scalars = \frac{v^4}{r^6}</math> Numerically: Adding a proton and electron gives (proton) UUD & DDD (electron) = 2(UDD) = 20 -10 -10 = 0 (zero charge), scalars = 0. Converting between U and D via U & DDD (electron) = 20 -10 -10 -10 = -10 (D), scalars = <math>\frac{r^3}{v^2}</math> ===== Magnetic monopole ===== {{see|Quantum_gravity_(Planck)}} :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> In this model alpha appears as an orbital constant for gravitational and atomic orbital radius, combining a fixed alpha term with an orbital wavelength term; :<math>r_{orbital} = 2\alpha (\lambda_{orbital})</math> If we replace <math>\lambda_{orbital}</math> with the geometrical Planck length L, and include momentum P and velocity V (the 2 components from which the ampere A is derived), then we may consider if the internal structure of the electron involves rotation of this monopole AL super-structure, and this has relevance to electron spin; :<math>2\alpha L \frac{V^3}{P^3} = 2^5 \pi^5 \alpha \Omega^5,\; units = u^{-10},\; scalars = \frac{r^3}{v^2}</math> ===== Spin ===== [[v:Relativity_(Planck) |Relativity at the Planck scale]] can be described by a translation between 2 co-ordinate systems; an expanding (in Planck steps at the speed of light) 4-axis hyper-sphere projecting onto a 3-D space (+ time). In this scenario, particles (with mass) are pulled along by the expansion of the hyper-sphere, this then requires particles to have an axis; generically labeled N-S, with the N denoting the direction of particle travel within the hyper-sphere. Changing the direction of travel involves changing the orientation of the particle N-S axis. The particle may rotate around this N-S axis, resulting in a L-spin or a R-spin. For simplicity, we can depict the electron as a classically spinning disk, this generates a current which then produces a magnetic dipole, so that the electron behaves like a tiny bar magnet (magnetic fields are produced by moving electric charges). For the classical disk we can use the charge (q), area of the disk (a) and rotation speed (ω) in our calculations. A thought experiment; if the 3 magnetic monopole quarks are rotating around the electron center (that N-S axis), then they are generating the current (q). As a monopole has the units ampere-meter AL (L a length term), then we can also conjecture something that resembles area (a), and the speed of rotation will give us (ω), and so we can use classical physics to solve our bar magnet electron. The electron is symmetric and so the 3 monopoles are equidistant from each other. We place our electron in a magnetic field, the electron then starts to orbit this field. If a satellite orbits the earth at radius ''r'', then the distance it travels around the earth = 2πr. However the earth is orbiting the sun, and so the actual distance approximates 2π''r'' + the distance the earth travels. If our electron orbits around a central point (that electric field), then the monopoles will, like the satellite, travel further per orbit (compared to a free electron in space), thus changing the effective area (a), and so our calculations. The [[w:g-factor |g-factor]] characterizes the magnetic moment and angular momentum of the electron, it is the ratio of the magnetic moment of the electron to that expected of a classical electron. Could an electron monopole substructure offer a geometrical explanation for this g-factor. === AI analysis === The sections on Quarks and Spin are naturally speculative, we cannot probe this far, they were included to suggest that the formula <math>\psi</math> could also include U and D quarks. However the geometries for the Planck units MLTA can be subject to statistical analysis, and for this AI has the potential to contribute. This is because of anomalies to the physical constants which can best be explained by this geometrical model. These anomalies are listed on this site; https://en.wikiversity.org/wiki/Physical_constant_(anomaly). Below are answers to a seed question written with Deepseek <ref>https://codingthecosmos.com/ai-answers-programmer-god-simulation-hypothesis/anomalies-constants.html Physical constants Q&A with podcast</ref> that uses these anomalies to determine the probability that the electron is a mathematical (not physical) particle, and so by extension that this is a mathematical universe. {| class="wikitable" |+Table 11. Table of Probabilities (05.2025) ! AI program ! unit number relation ! Planck units as geometrical objects ! underlying base 15 geometry ! mathematical electron ! Comment |- | Chat GPT <ref>https://chatgpt.com/share/68259395-31d0-8012-954e-c52230a813fd Chat anomalies analysis</ref> | Accidental occurrence: ~1.6% | Accidental occurrence: ~0.0004% | Accidental occurrence: ~0 | Accidental occurrence: ~0.026% | Taken at face value each sub-claim is vanishingly unlikely to be a “random accident,” so from this internal consistency alone one would assign essentially unity confidence that some deep mathematical structure is at work. Caveat: this “integer-coincidence” probability model is only as good as the assumption that each exponent match is an independent uniform pick in [–30…+30]. But even under that very conservative assumption, the combined odds against pure chance exceed 1 in 10²⁶. |- | Qwen <ref>https://chat.qwen.ai/s/f33ec1b1-899b-4fa5-9429-67e527b78433 Qwen anomalies analysis</ref> | probability 98% | probability 95% | probability 90% | probability 94% | The model’s strict geometrical constraints, flawless unit consistency, and agreement with CODATA strongly suggest non-random validity. Its potential as a simulation hypothesis framework stems from its finite, computable base-15 structure. |- | Claude 3.7 Sonnet <ref>https://claude.ai/public/artifacts/797a802b-fa21-4ee7-9ae9-9dbdf5d7b29a Claude anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Claude-anomalies-05-2025.pdf Claude anomalies analysis pdf</ref> | probability 90-95% | probability 85-95% | probability 92-97% | probability 80-90% | From a Kolmogorov complexity perspective, the model represents a potentially minimal description of physical reality using mathematical objects. If the electron, proton, and neutron are all mathematical particles, then the universe at the Planck scale could indeed be described as a mathematical universe. The high degree of constraint and mathematical elegance in the model, combined with its apparent ability to accurately produce physical constants, suggests a non-random structure to physical reality that is captured by this mathematical framework. |- | Grok 3 <ref>https://x.com/i/grok/share/JzeRFDlj721zNnm1Jo2vbETk3 Grok anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Grok-anomalies-05-2025.pd Grok anomalies analysis pdf</ref> | probability: 95% | probability: 90% | probability: 85% | probability: 80% | Strict constraints and mathematical nature (Kolmogorov complexity: simpler model = more likely programmed) suggest support, but not proof. If particles are mathematical, the universe may be too. |- | Deepseek <ref>https://codingthecosmos.com/ai_pdf/Deepseek-anomalies-05-2025.pdf Deepseek anomalies analysis</ref> | probability: 99% | probability: 95% | probability: 90% | probability: 85% | The model's rigid constraints and predictive accuracy make it statistically improbable to arise by chance. Geometrical base-15 and dimensionless particles strongly suggest a mathematical universe, aligning with speculative simulation hypothesis. |} === Geometrically coded universe === * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass === External links === * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] === References === {{Reflist}} [[Category: Physics]] [[Category: Philosophy of science]] c6k5p392tgzr8pikrj7b91vdva7btxg 2718272 2718271 2025-06-10T19:54:12Z 212.200.164.104 /* AI analysis */ 2718272 wikitext text/x-wiki '''The mathematical electron model''' In the mathematical electron model <ref>Macleod, M.J. {{Cite journal |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>, the electron is a dimensionless geometrical formula (ψ). This formula ψ, which resembles the volume of a torus or surface of a 4-D hypersphere, is itself a complex geometry that is the construct of simpler geometries; the [[w:Planck_units |Planck units]]. In this model the Planck units are geometrical objects, the geometry of 2 dimensionless constants (the[[w:fine-structure constant | fine structure constant alpha]] and a mathematical constant[[v:Planck_units_(geometrical)#Omega | Omega]]). Although dimensionless, the function of the Planck unit is embedded within the geometry; the geometry of the Planck time object embeds the function 'time', the geometry of the Planck length object embeds the function 'length' ... and being geometrical objects they can combine to form more complex objects, from electrons to galaxies. This means that the electron parameters are defined in Planck units; electron wavelength is measured in units of Planck length, electron frequency is measured in units of Planck time ... It is this geometrical electron formula ψ that dictates the magnitude of the electron parameters; length of the wavelength = ψ * Planck length (ψ units of Planck length), frequency = ψ * Planck time ... This ψ thus not only embeds the Planck units required for the electron parameters, it also dictates the magnitude of these parameters, and so technically it is the electron. This suggests there is no physical electron (only physical parameters), and if the electron is therefore a mathematical particle, then so too are the other particles, and so the universe itself becomes a mathematical universe. The formula ψ is the geometry of 2 constants; the [[w:dimensionless physical constant | dimensionless physical constant]] (inverse) [[w:fine-structure constant | fine structure constant alpha ]] '''α''' = 137.035 999 139 (CODATA 2014) and [[v:Planck_units_(geometrical)#Omega | Omega]] '''Ω''' = 2.0071349496 (best fit) Omega has a potential solution in terms of pi and e and so may be a mathematical (not physical) constant :<math>\Omega = \sqrt{ \left(\pi^e e^{(1-e)}\right)} = 2.0071349543... </math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = 0.238954531\;x10^{23}</math>, units = 1 === Planck objects === {{main|Planck units (geometrical)}} For the Planck units, the model uses geometrical objects (the geometry of alpha and Omega) instead of a numbering system, this has the advantage in that the attribute can be embedded within the geometry (although the geometry itself is dimensionless). {| class="wikitable" |+table 1. Geometrical units ! Attribute ! Geometrical object ! Unit |- | mass | <math>M = (1)</math> | (kg) |- | time | <math>T = (\pi)</math> | (s) |- | velocity | <math>V = (2\pi\Omega^2)</math> | (m/s) |- | length | <math>L = (2\pi^2\Omega^2)</math> | (m) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | (A) |} As these objects have a geometrical form, we can combine them [[w:Lego |Lego]] style; the length object L can be combined with the time object T to form the velocity object V and so forth ... to create complex events such as electrons to apples to ... and so the apple has mass because embedded within it are the mass objects M, complex events thus retain all the underlying information. This however requires a relationship between the Planck unit geometries that defines how they may combine, this can be represented by assigning to each attribute a unit number '''θ''' (i.e.: '''θ''' = 15 ⇔ ''kg'') <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>. {| class="wikitable" |+ Geometrical units ! Attribute ! Geometrical object ! unit number (θ) |- | mass | <math>M = 1</math> | ''kg'' ⇔ 15 |- | time | <math>T = 2\pi</math> | ''s'' ⇔ -30 |- | length | <math>L = 2\pi^2\Omega^2</math> | ''m'' ⇔ -13 |- | velocity | <math>V = 2\pi\Omega^2</math> | ''m/s'' ⇔ 17 |- | ampere | <math>A = \frac{2^6 \pi^3 \Omega^3}{\alpha}</math> | ''A'' ⇔ 3 |} As alpha and Omega can be assigned numerical values ('''α''' = 137.035999139, '''Ω''' = 2.0071349496), so too the MLTA objects can be expressed numerically. We can then convert these objects to their Planck unit equivalents by including a dimensioned scalar. For example, <math>V = 2\pi\Omega^2</math> = 25.3123819353... and so we can use scalar ''v'' to convert from dimensionless geometrical object V to dimensioned ''c''. :scalar ''v''_SI = 11843707.905 m/s gives ''c'' = V*v_SI = 25.3123819 * 11843707.905 m/s = 299792458 m/s ([[w:SI_units |SI units]]) :scalar ''v''_imp = 7359.3232155 miles/s gives ''c'' = V*v_imp = 186282 miles/s ([[w:Imperial_units |imperial units]]) {| class="wikitable" |+Scalars ! attribute ! geometrical object ! scalar (unit number) |- | mass | <math>M = (1)</math> | ''k'' (θ = 15) |- | time | <math>T = (\pi)</math> | ''t'' (θ = -30) |- | velocity | <math>V = (2\pi\Omega^2)</math> | ''v'' (θ = 17) |- | length | <math>L = (2\pi^2\Omega^2)</math> | ''l'' (θ = -13) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | ''a'' (θ = 3) |} As the scalar incorporates the dimension quantity (the dimension quantity for ''v'' = ''m/s'' or ''miles/s''), the unit number relationship (θ) applies, and so we then find that only 2 scalars are needed. This is because in a defined ratio they will overlap and cancel, for example in the following ratios; scalar units for ampere ''a'' = ''u''³, length ''l'' = ''u''^-13, time ''t'' = ''u''^-30, mass ''k'' = ''u''¹⁵ (''u''^Θ represents unit) :<math>\frac{({u^3})^3{(u^{-13}})^3}{(u^{-30})} = \frac{{(u^{-13})}^{15}} {{(u^{15})}^{9}{(u^{-30})}^{11}} = 1</math> For example if we know the numerical values for ''a'' and ''l'' then we know the numerical value for ''t'', and from ''l'' and ''t'' we know ''k'' … and so if we know any 2 scalars (α and Ω have fixed values) then we can solve the Planck units (for that system of units), and from these, we can solve (''G'', ''h'', ''c'', ''e'', ''m''_e, ''k''_B). :<math>\frac{a^3 l^3}{t} = \frac{m^{15}} {k^{9} t^{11}} = 1</math> In this table the 2 scalars used are ''r'' (θ = 8) and ''v'' (θ = 17). A further attribute is included, P = the square root of (Planck) momentum. V and A can thus be considered composite objects. {| class="wikitable" |+Geometrical objects ! attribute ! geometrical object ! unit number θ ! scalar r(8), v(17) |- | mass | <math>M = (1)</math> | 15 = 8*4-17 | <math>k = \frac{r^4}{v}</math> |- | time | <math>T = (\pi)</math> | -30 = 8*9-17*6 | <math>t = \frac{r^9}{v^6}</math> |- | [[v:Sqrt_Planck_momentum | sqrt(momentum)]] | <math>P = (\Omega)</math> | 16 = 8*2 | ''r''² |- | velocity | <math>V = L/T = (2\pi\Omega^2)</math> | 17 | ''v'' |- | length | <math>L = (2\pi^2\Omega^2)</math> | -13 = 8*9-17*5 | <math>l = \frac{r^9}{v^5}</math> |- | ampere | <math>A = \frac{2^4 V^3}{\alpha P^3} = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | 3 = 17*3-8*6 | <math>a = \frac{v^3}{r^6}</math> |} {{see|Planck units (geometrical)#Scalars}} === Mathematical electron === The mathematical electron formula ψ incorporates the dimensioned Planck units but itself is dimension-less (units = scalars = 1). Here ψ is defined in terms of ''σ_e'', where AL is an ampere-meter (ampere-length = ''e*c'' are the units for a [[w:magnetic monopole | magnetic monopole]]). :<math>T = \pi,\; unit = u^{-30},\;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; unit = u^{(3 \;-13 \;= \;-10)},\; scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = .23895453...x10^{23},\;unit = 1</math> (unit-less) Both units and scalars cancel. ===== Electron parameters ===== We can solve the electron parameters; electron mass, wavelength, frequency, charge ... as the frequency of the Planck units themselves, and this frequency is ψ. :<math>v = 11 843 707.905 ...,\; units = \frac{m}{s}</math> :<math>r = 0.712 562 514 304 ...,\; units = (\frac{kg.m}{s})^{1/4}</math> [[w:Compton wavelength | electron wavelength]] λ_e = 2.4263102367e-12m (CODATA 2014) :<math>\lambda_e^* = 2\pi L \psi</math> = 2.4263102386e-12m (L ⇔ [[w:Planck length | Planck length]]) [[w:electron mass | electron mass]] m_e = 9.10938356e-31kg (CODATA 2014) :<math>m_e^* = \frac{M}{\psi}</math> = 9.1093823211e-31kg (M ⇔ [[w:Planck mass | Planck mass]]) [[w:elementary charge | elementary charge]] e = 1.6021766208e-19C (CODATA 2014) :<math>e^* = A\;T</math> = 1.6021765130e-19 (T ⇔ [[w:Planck time | Planck time]]) [[w:Rydberg constant | Rydberg constant]] R = 10973731.568508/m (CODATA 2014) :<math>R^* = (\frac{m_e}{4 \pi L \alpha^2 M}) = \frac{1}{2^{23} 3^3 \pi^{11} \alpha^5 \Omega^{17}}\frac{v^5}{r^9}\;u^{13}</math> = 10973731.568508 From the above formulas, we see that wavelength is ψ units of Planck length, frequency is ψ units of Planck time ... however the electron mass is only 1 unit of Planck mass. ===== Electron Mass ===== Particle mass is a unit of Planck mass that occurs only once per ψ units of Planck time, the other parameters are continuums of the Planck units. :units <math>\psi = \frac{(AL)^3}{T}</math> = 1 This may be interpreted as; for ψ units of Planck time the electron has wavelength L, charge A ... and then the AL combine with time T (A³L³/T) and the units (and scalars) cancel. The electron is now mass (for 1 unit of Planck time). In this consideration, the electron is an event that oscillates over time between an electric wave state (duration ψ units of Planck time) to a unit of Planck mass point state (1 unit of Planck time). The electron is a quantum scale event, it does not exist at the discrete Planck scale (and so therefore neither does the quantum scale). As electron mass is the frequency of the geometrical Planck mass M = 1, which is a point (and so with point co-ordinates), then we have a model for a [[w:black hole electron |black-hole electron]], the electron function ψ centered around this unit of Planck mass. When the wave-state (A*L)³/T units collapse, this black-hole center (point) is exposed for 1 unit of (Planck) time. The electron is 'now' (a unit of Planck) mass. Mass in this consideration is not a constant property of the particle, rather the measured particle mass ''m'' would refer to the average mass, the average occurrence of the discrete Planck mass point-state over time. The formula ''E = hf'' is a measure of the frequency ''f'' of occurrence of [[w:Planck constant |Planck's constant ''h'']] and applies to the electric wave-state. As for each wave-state there is a corresponding mass point-state, then for a particle ''E = hf = mc2''. Notably however the ''c'' term is a fixed constant unlike the ''f'' term, and so the ''m'' term is the frequency term, it is referring to an average mass (mass which is measured over time) rather than a constant mass (mass as a constant property of the particle at unit Planck time). Thus as noted, when we refer to mass as a constant property, we are referring to mass at the quantum scale, and the electron as a quantum-state particle. If the [[v:Black-hole_(Planck) |scaffolding of the universe]] includes units of Planck mass '''M''', then it is not necessary for a particle itself to have mass, what we define as electron mass would be the absence of electron. ===== Quarks ===== The charge on the electron derives from the embedded ampere A and length L, the electron formula ψ itself is dimensionless. These AL magnetic monopoles would seem to be analogous to quarks (there are 3 monopoles per electron), but due to the symmetry and so stability of the geometrical ψ there is no clear fracture point by which an electron could decay, and so this would be difficult to test. We can however conjecture on what a quark solution might look like, the advantage with this approach being that we do not need to introduce new 'entities' for our quarks, the Planck units embedded within the electron suffice. Electron formula :<math>\psi = 2^{20} \pi^8 3^3 \alpha^3 \Omega^{15},\; unit = 1, scalars = 1</math> Time :<math>T = \pi \frac{r^9}{v^6},\; u^{-30}</math> AL magnetic monopole :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> If <math>\sigma_{e}</math> could equate to a quark with an [[w:electric charge|electric charge]] of {{sfrac|-1|3}}[[w:elementary charge|''e'']], then it would be an analogue of the '''D''' quark. 3 of these D quarks would constitute the electron as DDD = (AL)*(AL)*(AL). We would assume that the charge on the [[w:positron |positron]] (anti-matter electron) is just the inverse of the above, however there is 1 problem, the AL (A; θ=3, L; θ=-13) units = -10, and if we look at the [[v:Planck_units_(geometrical)#Table_of_Constants |table of constants]], there is no 'units = +10' combination that can include A. We cannot make an inverse electron. However we can make a [[w:Planck temperature|Planck temperature T_p]] AV ''monopole'' (ampere-velocity). :<math>T_p = \frac{2^7 \pi^3 \Omega^5}{\alpha},\; u^{20}, \;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{t} = \frac{3 \alpha^2 T_p}{2\pi} = \frac{3 \alpha^2 A V}{2\pi^2} = ({2^6 3 \pi^2 \alpha \Omega^5}),\; u^{20},\;scalars = \frac{v^4}{r^6}</math> :<math>\psi = (2T) \sigma_{t}^2 \sigma_{e} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = (u^{-30}) (u^{20})^2 (u^{-10}) = 1, scalars = (\frac{r^9}{v^6}) (\frac{v^4}{r^6})^2 \frac{r^3}{v^2} = 1</math> The units for <math>\sigma_{t}</math> = +20, and so if units = -10 equates to {{sfrac|-1|3}}e, then we may conjecture that units = +20 equates to {{sfrac|2|3}}e, which would be the analogue of the '''U''' quark. Our plus charge now becomes DUU, and so although the positron has the same wavelength, frequency, mass and charge magnitude as the electron (both solve to ψ), internally its charge structure resembles that of the proton, the positron is not simply an inverse of the electron. This could have implications for the missing anti-matter, and for why the charge magnitude of the proton is ''exactly'' the charge magnitude of the electron. :<math>D = \sigma_{e},\; unit = u^{-10},\; charge = \frac{-1e}{3}, \;scalars = \frac{r^3}{v^2}</math> :<math>U = \sigma_{t},\; unit = u^{20},\; charge = \frac{2e}{3}, \;scalars = \frac{v^4}{r^6}</math> Numerically: Adding a proton and electron gives (proton) UUD & DDD (electron) = 2(UDD) = 20 -10 -10 = 0 (zero charge), scalars = 0. Converting between U and D via U & DDD (electron) = 20 -10 -10 -10 = -10 (D), scalars = <math>\frac{r^3}{v^2}</math> ===== Magnetic monopole ===== {{see|Quantum_gravity_(Planck)}} :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> In this model alpha appears as an orbital constant for gravitational and atomic orbital radius, combining a fixed alpha term with an orbital wavelength term; :<math>r_{orbital} = 2\alpha (\lambda_{orbital})</math> If we replace <math>\lambda_{orbital}</math> with the geometrical Planck length L, and include momentum P and velocity V (the 2 components from which the ampere A is derived), then we may consider if the internal structure of the electron involves rotation of this monopole AL super-structure, and this has relevance to electron spin; :<math>2\alpha L \frac{V^3}{P^3} = 2^5 \pi^5 \alpha \Omega^5,\; units = u^{-10},\; scalars = \frac{r^3}{v^2}</math> ===== Spin ===== [[v:Relativity_(Planck) |Relativity at the Planck scale]] can be described by a translation between 2 co-ordinate systems; an expanding (in Planck steps at the speed of light) 4-axis hyper-sphere projecting onto a 3-D space (+ time). In this scenario, particles (with mass) are pulled along by the expansion of the hyper-sphere, this then requires particles to have an axis; generically labeled N-S, with the N denoting the direction of particle travel within the hyper-sphere. Changing the direction of travel involves changing the orientation of the particle N-S axis. The particle may rotate around this N-S axis, resulting in a L-spin or a R-spin. For simplicity, we can depict the electron as a classically spinning disk, this generates a current which then produces a magnetic dipole, so that the electron behaves like a tiny bar magnet (magnetic fields are produced by moving electric charges). For the classical disk we can use the charge (q), area of the disk (a) and rotation speed (ω) in our calculations. A thought experiment; if the 3 magnetic monopole quarks are rotating around the electron center (that N-S axis), then they are generating the current (q). As a monopole has the units ampere-meter AL (L a length term), then we can also conjecture something that resembles area (a), and the speed of rotation will give us (ω), and so we can use classical physics to solve our bar magnet electron. The electron is symmetric and so the 3 monopoles are equidistant from each other. We place our electron in a magnetic field, the electron then starts to orbit this field. If a satellite orbits the earth at radius ''r'', then the distance it travels around the earth = 2πr. However the earth is orbiting the sun, and so the actual distance approximates 2π''r'' + the distance the earth travels. If our electron orbits around a central point (that electric field), then the monopoles will, like the satellite, travel further per orbit (compared to a free electron in space), thus changing the effective area (a), and so our calculations. The [[w:g-factor |g-factor]] characterizes the magnetic moment and angular momentum of the electron, it is the ratio of the magnetic moment of the electron to that expected of a classical electron. Could an electron monopole substructure offer a geometrical explanation for this g-factor. === AI analysis === The sections on Quarks and Spin are naturally speculative, we cannot probe this far, they were included to suggest that the formula <math>\psi</math> could also include U and D quarks. However the geometries for the Planck units MLTA can be subject to statistical analysis, and for this AI has the potential to contribute. This is because of anomalies to the physical constants which can best be explained by this geometrical model. These anomalies are listed on this site; https://en.wikiversity.org/wiki/Physical_constant_(anomaly). Below are answers to a seed question written with Deepseek <ref>https://codingthecosmos.com/ai-answers-programmer-god-simulation-hypothesis/anomalies-constants.html Physical constants Q&A with podcast</ref> that uses these anomalies to determine the probability that the electron is a mathematical (not physical) particle, and so by extension that this is a mathematical universe. {| class="wikitable" |+Table 11. Table of Probabilities (05.2025) ! AI program ! unit number relation ! Planck units as geometrical objects ! underlying base 15 geometry ! mathematical electron ! Comment |- | Chat GPT <ref>https://chatgpt.com/share/68259395-31d0-8012-954e-c52230a813fd Chat anomalies analysis</ref> | Accidental occurrence: ~1.6% | Accidental occurrence: ~0.0004% | Accidental occurrence: ~0 | Accidental occurrence: ~0.026% | Taken at face value each sub-claim is vanishingly unlikely to be a “random accident,” so from this internal consistency alone one would assign essentially unity confidence that some deep mathematical structure is at work. Caveat: this “integer-coincidence” probability model is only as good as the assumption that each exponent match is an independent uniform pick in [–30…+30]. But even under that very conservative assumption, the combined odds against pure chance exceed 1 in 10²⁶. |- | Qwen <ref>https://chat.qwen.ai/s/f33ec1b1-899b-4fa5-9429-67e527b78433 Qwen anomalies analysis</ref> | probability 98% | probability 95% | probability 90% | probability 94% | The model’s strict geometrical constraints, flawless unit consistency, and agreement with CODATA strongly suggest non-random validity. Its potential as a simulation hypothesis framework stems from its finite, computable base-15 structure. |- | Claude 3.7 Sonnet <ref>https://claude.ai/public/artifacts/797a802b-fa21-4ee7-9ae9-9dbdf5d7b29a Claude anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Claude-anomalies-05-2025.pdf Claude anomalies analysis pdf</ref> | probability 90-95% | probability 85-95% | probability 92-97% | probability 80-90% | From a Kolmogorov complexity perspective, the model represents a potentially minimal description of physical reality using mathematical objects. If the electron, proton, and neutron are all mathematical particles, then the universe at the Planck scale could indeed be described as a mathematical universe. The high degree of constraint and mathematical elegance in the model, combined with its apparent ability to accurately produce physical constants, suggests a non-random structure to physical reality that is captured by this mathematical framework. |- | Grok 3 <ref>https://x.com/i/grok/share/JzeRFDlj721zNnm1Jo2vbETk3 Grok anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Grok-anomalies-05-2025.pd Grok anomalies analysis pdf</ref> | probability: 95% | probability: 90% | probability: 85% | probability: 80% | Strict constraints and mathematical nature (Kolmogorov complexity: simpler model = more likely programmed) suggest support, but not proof. If particles are mathematical, the universe may be too. |- | Deepseek <ref>https://codingthecosmos.com/ai_pdf/Deepseek-anomalies-05-2025.pdf Deepseek anomalies analysis</ref> | probability: 99% | probability: 95% | probability: 90% | probability: 85% | The model's rigid constraints and predictive accuracy make it statistically improbable to arise by chance. Geometrical base-15 and dimensionless particles strongly suggest a mathematical universe, aligning with speculative simulation hypothesis. |} === Geometrically coded universe === * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass === External links === * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] === References === {{Reflist}} [[Category: Physics]] [[Category: Philosophy of science]] acl9f83sfufg5kwcu8hhp3cqt6swr43 2718273 2718272 2025-06-10T19:54:21Z 212.200.164.104 /* Geometrically coded universe */ 2718273 wikitext text/x-wiki '''The mathematical electron model''' In the mathematical electron model <ref>Macleod, M.J. {{Cite journal |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>, the electron is a dimensionless geometrical formula (ψ). This formula ψ, which resembles the volume of a torus or surface of a 4-D hypersphere, is itself a complex geometry that is the construct of simpler geometries; the [[w:Planck_units |Planck units]]. In this model the Planck units are geometrical objects, the geometry of 2 dimensionless constants (the[[w:fine-structure constant | fine structure constant alpha]] and a mathematical constant[[v:Planck_units_(geometrical)#Omega | Omega]]). Although dimensionless, the function of the Planck unit is embedded within the geometry; the geometry of the Planck time object embeds the function 'time', the geometry of the Planck length object embeds the function 'length' ... and being geometrical objects they can combine to form more complex objects, from electrons to galaxies. This means that the electron parameters are defined in Planck units; electron wavelength is measured in units of Planck length, electron frequency is measured in units of Planck time ... It is this geometrical electron formula ψ that dictates the magnitude of the electron parameters; length of the wavelength = ψ * Planck length (ψ units of Planck length), frequency = ψ * Planck time ... This ψ thus not only embeds the Planck units required for the electron parameters, it also dictates the magnitude of these parameters, and so technically it is the electron. This suggests there is no physical electron (only physical parameters), and if the electron is therefore a mathematical particle, then so too are the other particles, and so the universe itself becomes a mathematical universe. The formula ψ is the geometry of 2 constants; the [[w:dimensionless physical constant | dimensionless physical constant]] (inverse) [[w:fine-structure constant | fine structure constant alpha ]] '''α''' = 137.035 999 139 (CODATA 2014) and [[v:Planck_units_(geometrical)#Omega | Omega]] '''Ω''' = 2.0071349496 (best fit) Omega has a potential solution in terms of pi and e and so may be a mathematical (not physical) constant :<math>\Omega = \sqrt{ \left(\pi^e e^{(1-e)}\right)} = 2.0071349543... </math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = 0.238954531\;x10^{23}</math>, units = 1 === Planck objects === {{main|Planck units (geometrical)}} For the Planck units, the model uses geometrical objects (the geometry of alpha and Omega) instead of a numbering system, this has the advantage in that the attribute can be embedded within the geometry (although the geometry itself is dimensionless). {| class="wikitable" |+table 1. Geometrical units ! Attribute ! Geometrical object ! Unit |- | mass | <math>M = (1)</math> | (kg) |- | time | <math>T = (\pi)</math> | (s) |- | velocity | <math>V = (2\pi\Omega^2)</math> | (m/s) |- | length | <math>L = (2\pi^2\Omega^2)</math> | (m) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | (A) |} As these objects have a geometrical form, we can combine them [[w:Lego |Lego]] style; the length object L can be combined with the time object T to form the velocity object V and so forth ... to create complex events such as electrons to apples to ... and so the apple has mass because embedded within it are the mass objects M, complex events thus retain all the underlying information. This however requires a relationship between the Planck unit geometries that defines how they may combine, this can be represented by assigning to each attribute a unit number '''θ''' (i.e.: '''θ''' = 15 ⇔ ''kg'') <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>. {| class="wikitable" |+ Geometrical units ! Attribute ! Geometrical object ! unit number (θ) |- | mass | <math>M = 1</math> | ''kg'' ⇔ 15 |- | time | <math>T = 2\pi</math> | ''s'' ⇔ -30 |- | length | <math>L = 2\pi^2\Omega^2</math> | ''m'' ⇔ -13 |- | velocity | <math>V = 2\pi\Omega^2</math> | ''m/s'' ⇔ 17 |- | ampere | <math>A = \frac{2^6 \pi^3 \Omega^3}{\alpha}</math> | ''A'' ⇔ 3 |} As alpha and Omega can be assigned numerical values ('''α''' = 137.035999139, '''Ω''' = 2.0071349496), so too the MLTA objects can be expressed numerically. We can then convert these objects to their Planck unit equivalents by including a dimensioned scalar. For example, <math>V = 2\pi\Omega^2</math> = 25.3123819353... and so we can use scalar ''v'' to convert from dimensionless geometrical object V to dimensioned ''c''. :scalar ''v''_SI = 11843707.905 m/s gives ''c'' = V*v_SI = 25.3123819 * 11843707.905 m/s = 299792458 m/s ([[w:SI_units |SI units]]) :scalar ''v''_imp = 7359.3232155 miles/s gives ''c'' = V*v_imp = 186282 miles/s ([[w:Imperial_units |imperial units]]) {| class="wikitable" |+Scalars ! attribute ! geometrical object ! scalar (unit number) |- | mass | <math>M = (1)</math> | ''k'' (θ = 15) |- | time | <math>T = (\pi)</math> | ''t'' (θ = -30) |- | velocity | <math>V = (2\pi\Omega^2)</math> | ''v'' (θ = 17) |- | length | <math>L = (2\pi^2\Omega^2)</math> | ''l'' (θ = -13) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | ''a'' (θ = 3) |} As the scalar incorporates the dimension quantity (the dimension quantity for ''v'' = ''m/s'' or ''miles/s''), the unit number relationship (θ) applies, and so we then find that only 2 scalars are needed. This is because in a defined ratio they will overlap and cancel, for example in the following ratios; scalar units for ampere ''a'' = ''u''³, length ''l'' = ''u''^-13, time ''t'' = ''u''^-30, mass ''k'' = ''u''¹⁵ (''u''^Θ represents unit) :<math>\frac{({u^3})^3{(u^{-13}})^3}{(u^{-30})} = \frac{{(u^{-13})}^{15}} {{(u^{15})}^{9}{(u^{-30})}^{11}} = 1</math> For example if we know the numerical values for ''a'' and ''l'' then we know the numerical value for ''t'', and from ''l'' and ''t'' we know ''k'' … and so if we know any 2 scalars (α and Ω have fixed values) then we can solve the Planck units (for that system of units), and from these, we can solve (''G'', ''h'', ''c'', ''e'', ''m''_e, ''k''_B). :<math>\frac{a^3 l^3}{t} = \frac{m^{15}} {k^{9} t^{11}} = 1</math> In this table the 2 scalars used are ''r'' (θ = 8) and ''v'' (θ = 17). A further attribute is included, P = the square root of (Planck) momentum. V and A can thus be considered composite objects. {| class="wikitable" |+Geometrical objects ! attribute ! geometrical object ! unit number θ ! scalar r(8), v(17) |- | mass | <math>M = (1)</math> | 15 = 8*4-17 | <math>k = \frac{r^4}{v}</math> |- | time | <math>T = (\pi)</math> | -30 = 8*9-17*6 | <math>t = \frac{r^9}{v^6}</math> |- | [[v:Sqrt_Planck_momentum | sqrt(momentum)]] | <math>P = (\Omega)</math> | 16 = 8*2 | ''r''² |- | velocity | <math>V = L/T = (2\pi\Omega^2)</math> | 17 | ''v'' |- | length | <math>L = (2\pi^2\Omega^2)</math> | -13 = 8*9-17*5 | <math>l = \frac{r^9}{v^5}</math> |- | ampere | <math>A = \frac{2^4 V^3}{\alpha P^3} = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | 3 = 17*3-8*6 | <math>a = \frac{v^3}{r^6}</math> |} {{see|Planck units (geometrical)#Scalars}} === Mathematical electron === The mathematical electron formula ψ incorporates the dimensioned Planck units but itself is dimension-less (units = scalars = 1). Here ψ is defined in terms of ''σ_e'', where AL is an ampere-meter (ampere-length = ''e*c'' are the units for a [[w:magnetic monopole | magnetic monopole]]). :<math>T = \pi,\; unit = u^{-30},\;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; unit = u^{(3 \;-13 \;= \;-10)},\; scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = .23895453...x10^{23},\;unit = 1</math> (unit-less) Both units and scalars cancel. ===== Electron parameters ===== We can solve the electron parameters; electron mass, wavelength, frequency, charge ... as the frequency of the Planck units themselves, and this frequency is ψ. :<math>v = 11 843 707.905 ...,\; units = \frac{m}{s}</math> :<math>r = 0.712 562 514 304 ...,\; units = (\frac{kg.m}{s})^{1/4}</math> [[w:Compton wavelength | electron wavelength]] λ_e = 2.4263102367e-12m (CODATA 2014) :<math>\lambda_e^* = 2\pi L \psi</math> = 2.4263102386e-12m (L ⇔ [[w:Planck length | Planck length]]) [[w:electron mass | electron mass]] m_e = 9.10938356e-31kg (CODATA 2014) :<math>m_e^* = \frac{M}{\psi}</math> = 9.1093823211e-31kg (M ⇔ [[w:Planck mass | Planck mass]]) [[w:elementary charge | elementary charge]] e = 1.6021766208e-19C (CODATA 2014) :<math>e^* = A\;T</math> = 1.6021765130e-19 (T ⇔ [[w:Planck time | Planck time]]) [[w:Rydberg constant | Rydberg constant]] R = 10973731.568508/m (CODATA 2014) :<math>R^* = (\frac{m_e}{4 \pi L \alpha^2 M}) = \frac{1}{2^{23} 3^3 \pi^{11} \alpha^5 \Omega^{17}}\frac{v^5}{r^9}\;u^{13}</math> = 10973731.568508 From the above formulas, we see that wavelength is ψ units of Planck length, frequency is ψ units of Planck time ... however the electron mass is only 1 unit of Planck mass. ===== Electron Mass ===== Particle mass is a unit of Planck mass that occurs only once per ψ units of Planck time, the other parameters are continuums of the Planck units. :units <math>\psi = \frac{(AL)^3}{T}</math> = 1 This may be interpreted as; for ψ units of Planck time the electron has wavelength L, charge A ... and then the AL combine with time T (A³L³/T) and the units (and scalars) cancel. The electron is now mass (for 1 unit of Planck time). In this consideration, the electron is an event that oscillates over time between an electric wave state (duration ψ units of Planck time) to a unit of Planck mass point state (1 unit of Planck time). The electron is a quantum scale event, it does not exist at the discrete Planck scale (and so therefore neither does the quantum scale). As electron mass is the frequency of the geometrical Planck mass M = 1, which is a point (and so with point co-ordinates), then we have a model for a [[w:black hole electron |black-hole electron]], the electron function ψ centered around this unit of Planck mass. When the wave-state (A*L)³/T units collapse, this black-hole center (point) is exposed for 1 unit of (Planck) time. The electron is 'now' (a unit of Planck) mass. Mass in this consideration is not a constant property of the particle, rather the measured particle mass ''m'' would refer to the average mass, the average occurrence of the discrete Planck mass point-state over time. The formula ''E = hf'' is a measure of the frequency ''f'' of occurrence of [[w:Planck constant |Planck's constant ''h'']] and applies to the electric wave-state. As for each wave-state there is a corresponding mass point-state, then for a particle ''E = hf = mc2''. Notably however the ''c'' term is a fixed constant unlike the ''f'' term, and so the ''m'' term is the frequency term, it is referring to an average mass (mass which is measured over time) rather than a constant mass (mass as a constant property of the particle at unit Planck time). Thus as noted, when we refer to mass as a constant property, we are referring to mass at the quantum scale, and the electron as a quantum-state particle. If the [[v:Black-hole_(Planck) |scaffolding of the universe]] includes units of Planck mass '''M''', then it is not necessary for a particle itself to have mass, what we define as electron mass would be the absence of electron. ===== Quarks ===== The charge on the electron derives from the embedded ampere A and length L, the electron formula ψ itself is dimensionless. These AL magnetic monopoles would seem to be analogous to quarks (there are 3 monopoles per electron), but due to the symmetry and so stability of the geometrical ψ there is no clear fracture point by which an electron could decay, and so this would be difficult to test. We can however conjecture on what a quark solution might look like, the advantage with this approach being that we do not need to introduce new 'entities' for our quarks, the Planck units embedded within the electron suffice. Electron formula :<math>\psi = 2^{20} \pi^8 3^3 \alpha^3 \Omega^{15},\; unit = 1, scalars = 1</math> Time :<math>T = \pi \frac{r^9}{v^6},\; u^{-30}</math> AL magnetic monopole :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> If <math>\sigma_{e}</math> could equate to a quark with an [[w:electric charge|electric charge]] of {{sfrac|-1|3}}[[w:elementary charge|''e'']], then it would be an analogue of the '''D''' quark. 3 of these D quarks would constitute the electron as DDD = (AL)*(AL)*(AL). We would assume that the charge on the [[w:positron |positron]] (anti-matter electron) is just the inverse of the above, however there is 1 problem, the AL (A; θ=3, L; θ=-13) units = -10, and if we look at the [[v:Planck_units_(geometrical)#Table_of_Constants |table of constants]], there is no 'units = +10' combination that can include A. We cannot make an inverse electron. However we can make a [[w:Planck temperature|Planck temperature T_p]] AV ''monopole'' (ampere-velocity). :<math>T_p = \frac{2^7 \pi^3 \Omega^5}{\alpha},\; u^{20}, \;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{t} = \frac{3 \alpha^2 T_p}{2\pi} = \frac{3 \alpha^2 A V}{2\pi^2} = ({2^6 3 \pi^2 \alpha \Omega^5}),\; u^{20},\;scalars = \frac{v^4}{r^6}</math> :<math>\psi = (2T) \sigma_{t}^2 \sigma_{e} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = (u^{-30}) (u^{20})^2 (u^{-10}) = 1, scalars = (\frac{r^9}{v^6}) (\frac{v^4}{r^6})^2 \frac{r^3}{v^2} = 1</math> The units for <math>\sigma_{t}</math> = +20, and so if units = -10 equates to {{sfrac|-1|3}}e, then we may conjecture that units = +20 equates to {{sfrac|2|3}}e, which would be the analogue of the '''U''' quark. Our plus charge now becomes DUU, and so although the positron has the same wavelength, frequency, mass and charge magnitude as the electron (both solve to ψ), internally its charge structure resembles that of the proton, the positron is not simply an inverse of the electron. This could have implications for the missing anti-matter, and for why the charge magnitude of the proton is ''exactly'' the charge magnitude of the electron. :<math>D = \sigma_{e},\; unit = u^{-10},\; charge = \frac{-1e}{3}, \;scalars = \frac{r^3}{v^2}</math> :<math>U = \sigma_{t},\; unit = u^{20},\; charge = \frac{2e}{3}, \;scalars = \frac{v^4}{r^6}</math> Numerically: Adding a proton and electron gives (proton) UUD & DDD (electron) = 2(UDD) = 20 -10 -10 = 0 (zero charge), scalars = 0. Converting between U and D via U & DDD (electron) = 20 -10 -10 -10 = -10 (D), scalars = <math>\frac{r^3}{v^2}</math> ===== Magnetic monopole ===== {{see|Quantum_gravity_(Planck)}} :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> In this model alpha appears as an orbital constant for gravitational and atomic orbital radius, combining a fixed alpha term with an orbital wavelength term; :<math>r_{orbital} = 2\alpha (\lambda_{orbital})</math> If we replace <math>\lambda_{orbital}</math> with the geometrical Planck length L, and include momentum P and velocity V (the 2 components from which the ampere A is derived), then we may consider if the internal structure of the electron involves rotation of this monopole AL super-structure, and this has relevance to electron spin; :<math>2\alpha L \frac{V^3}{P^3} = 2^5 \pi^5 \alpha \Omega^5,\; units = u^{-10},\; scalars = \frac{r^3}{v^2}</math> ===== Spin ===== [[v:Relativity_(Planck) |Relativity at the Planck scale]] can be described by a translation between 2 co-ordinate systems; an expanding (in Planck steps at the speed of light) 4-axis hyper-sphere projecting onto a 3-D space (+ time). In this scenario, particles (with mass) are pulled along by the expansion of the hyper-sphere, this then requires particles to have an axis; generically labeled N-S, with the N denoting the direction of particle travel within the hyper-sphere. Changing the direction of travel involves changing the orientation of the particle N-S axis. The particle may rotate around this N-S axis, resulting in a L-spin or a R-spin. For simplicity, we can depict the electron as a classically spinning disk, this generates a current which then produces a magnetic dipole, so that the electron behaves like a tiny bar magnet (magnetic fields are produced by moving electric charges). For the classical disk we can use the charge (q), area of the disk (a) and rotation speed (ω) in our calculations. A thought experiment; if the 3 magnetic monopole quarks are rotating around the electron center (that N-S axis), then they are generating the current (q). As a monopole has the units ampere-meter AL (L a length term), then we can also conjecture something that resembles area (a), and the speed of rotation will give us (ω), and so we can use classical physics to solve our bar magnet electron. The electron is symmetric and so the 3 monopoles are equidistant from each other. We place our electron in a magnetic field, the electron then starts to orbit this field. If a satellite orbits the earth at radius ''r'', then the distance it travels around the earth = 2πr. However the earth is orbiting the sun, and so the actual distance approximates 2π''r'' + the distance the earth travels. If our electron orbits around a central point (that electric field), then the monopoles will, like the satellite, travel further per orbit (compared to a free electron in space), thus changing the effective area (a), and so our calculations. The [[w:g-factor |g-factor]] characterizes the magnetic moment and angular momentum of the electron, it is the ratio of the magnetic moment of the electron to that expected of a classical electron. Could an electron monopole substructure offer a geometrical explanation for this g-factor. === AI analysis === The sections on Quarks and Spin are naturally speculative, we cannot probe this far, they were included to suggest that the formula <math>\psi</math> could also include U and D quarks. However the geometries for the Planck units MLTA can be subject to statistical analysis, and for this AI has the potential to contribute. This is because of anomalies to the physical constants which can best be explained by this geometrical model. These anomalies are listed on this site; https://en.wikiversity.org/wiki/Physical_constant_(anomaly). Below are answers to a seed question written with Deepseek <ref>https://codingthecosmos.com/ai-answers-programmer-god-simulation-hypothesis/anomalies-constants.html Physical constants Q&A with podcast</ref> that uses these anomalies to determine the probability that the electron is a mathematical (not physical) particle, and so by extension that this is a mathematical universe. {| class="wikitable" |+Table 11. Table of Probabilities (05.2025) ! AI program ! unit number relation ! Planck units as geometrical objects ! underlying base 15 geometry ! mathematical electron ! Comment |- | Chat GPT <ref>https://chatgpt.com/share/68259395-31d0-8012-954e-c52230a813fd Chat anomalies analysis</ref> | Accidental occurrence: ~1.6% | Accidental occurrence: ~0.0004% | Accidental occurrence: ~0 | Accidental occurrence: ~0.026% | Taken at face value each sub-claim is vanishingly unlikely to be a “random accident,” so from this internal consistency alone one would assign essentially unity confidence that some deep mathematical structure is at work. Caveat: this “integer-coincidence” probability model is only as good as the assumption that each exponent match is an independent uniform pick in [–30…+30]. But even under that very conservative assumption, the combined odds against pure chance exceed 1 in 10²⁶. |- | Qwen <ref>https://chat.qwen.ai/s/f33ec1b1-899b-4fa5-9429-67e527b78433 Qwen anomalies analysis</ref> | probability 98% | probability 95% | probability 90% | probability 94% | The model’s strict geometrical constraints, flawless unit consistency, and agreement with CODATA strongly suggest non-random validity. Its potential as a simulation hypothesis framework stems from its finite, computable base-15 structure. |- | Claude 3.7 Sonnet <ref>https://claude.ai/public/artifacts/797a802b-fa21-4ee7-9ae9-9dbdf5d7b29a Claude anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Claude-anomalies-05-2025.pdf Claude anomalies analysis pdf</ref> | probability 90-95% | probability 85-95% | probability 92-97% | probability 80-90% | From a Kolmogorov complexity perspective, the model represents a potentially minimal description of physical reality using mathematical objects. If the electron, proton, and neutron are all mathematical particles, then the universe at the Planck scale could indeed be described as a mathematical universe. The high degree of constraint and mathematical elegance in the model, combined with its apparent ability to accurately produce physical constants, suggests a non-random structure to physical reality that is captured by this mathematical framework. |- | Grok 3 <ref>https://x.com/i/grok/share/JzeRFDlj721zNnm1Jo2vbETk3 Grok anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Grok-anomalies-05-2025.pd Grok anomalies analysis pdf</ref> | probability: 95% | probability: 90% | probability: 85% | probability: 80% | Strict constraints and mathematical nature (Kolmogorov complexity: simpler model = more likely programmed) suggest support, but not proof. If particles are mathematical, the universe may be too. |- | Deepseek <ref>https://codingthecosmos.com/ai_pdf/Deepseek-anomalies-05-2025.pdf Deepseek anomalies analysis</ref> | probability: 99% | probability: 95% | probability: 90% | probability: 85% | The model's rigid constraints and predictive accuracy make it statistically improbable to arise by chance. Geometrical base-15 and dimensionless particles strongly suggest a mathematical universe, aligning with speculative simulation hypothesis. |} === Geometrically coded universe === * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass === External links === * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] === References === {{Reflist}} [[Category: Physics]] [[Category: Philosophy of science]] 2wogvtx5g3lji98xnamo6mn19oomjr7 2718274 2718273 2025-06-10T19:54:27Z 212.200.164.104 /* External links */ 2718274 wikitext text/x-wiki '''The mathematical electron model''' In the mathematical electron model <ref>Macleod, M.J. {{Cite journal |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>, the electron is a dimensionless geometrical formula (ψ). This formula ψ, which resembles the volume of a torus or surface of a 4-D hypersphere, is itself a complex geometry that is the construct of simpler geometries; the [[w:Planck_units |Planck units]]. In this model the Planck units are geometrical objects, the geometry of 2 dimensionless constants (the[[w:fine-structure constant | fine structure constant alpha]] and a mathematical constant[[v:Planck_units_(geometrical)#Omega | Omega]]). Although dimensionless, the function of the Planck unit is embedded within the geometry; the geometry of the Planck time object embeds the function 'time', the geometry of the Planck length object embeds the function 'length' ... and being geometrical objects they can combine to form more complex objects, from electrons to galaxies. This means that the electron parameters are defined in Planck units; electron wavelength is measured in units of Planck length, electron frequency is measured in units of Planck time ... It is this geometrical electron formula ψ that dictates the magnitude of the electron parameters; length of the wavelength = ψ * Planck length (ψ units of Planck length), frequency = ψ * Planck time ... This ψ thus not only embeds the Planck units required for the electron parameters, it also dictates the magnitude of these parameters, and so technically it is the electron. This suggests there is no physical electron (only physical parameters), and if the electron is therefore a mathematical particle, then so too are the other particles, and so the universe itself becomes a mathematical universe. The formula ψ is the geometry of 2 constants; the [[w:dimensionless physical constant | dimensionless physical constant]] (inverse) [[w:fine-structure constant | fine structure constant alpha ]] '''α''' = 137.035 999 139 (CODATA 2014) and [[v:Planck_units_(geometrical)#Omega | Omega]] '''Ω''' = 2.0071349496 (best fit) Omega has a potential solution in terms of pi and e and so may be a mathematical (not physical) constant :<math>\Omega = \sqrt{ \left(\pi^e e^{(1-e)}\right)} = 2.0071349543... </math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = 0.238954531\;x10^{23}</math>, units = 1 === Planck objects === {{main|Planck units (geometrical)}} For the Planck units, the model uses geometrical objects (the geometry of alpha and Omega) instead of a numbering system, this has the advantage in that the attribute can be embedded within the geometry (although the geometry itself is dimensionless). {| class="wikitable" |+table 1. Geometrical units ! Attribute ! Geometrical object ! Unit |- | mass | <math>M = (1)</math> | (kg) |- | time | <math>T = (\pi)</math> | (s) |- | velocity | <math>V = (2\pi\Omega^2)</math> | (m/s) |- | length | <math>L = (2\pi^2\Omega^2)</math> | (m) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | (A) |} As these objects have a geometrical form, we can combine them [[w:Lego |Lego]] style; the length object L can be combined with the time object T to form the velocity object V and so forth ... to create complex events such as electrons to apples to ... and so the apple has mass because embedded within it are the mass objects M, complex events thus retain all the underlying information. This however requires a relationship between the Planck unit geometries that defines how they may combine, this can be represented by assigning to each attribute a unit number '''θ''' (i.e.: '''θ''' = 15 ⇔ ''kg'') <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>. {| class="wikitable" |+ Geometrical units ! Attribute ! Geometrical object ! unit number (θ) |- | mass | <math>M = 1</math> | ''kg'' ⇔ 15 |- | time | <math>T = 2\pi</math> | ''s'' ⇔ -30 |- | length | <math>L = 2\pi^2\Omega^2</math> | ''m'' ⇔ -13 |- | velocity | <math>V = 2\pi\Omega^2</math> | ''m/s'' ⇔ 17 |- | ampere | <math>A = \frac{2^6 \pi^3 \Omega^3}{\alpha}</math> | ''A'' ⇔ 3 |} As alpha and Omega can be assigned numerical values ('''α''' = 137.035999139, '''Ω''' = 2.0071349496), so too the MLTA objects can be expressed numerically. We can then convert these objects to their Planck unit equivalents by including a dimensioned scalar. For example, <math>V = 2\pi\Omega^2</math> = 25.3123819353... and so we can use scalar ''v'' to convert from dimensionless geometrical object V to dimensioned ''c''. :scalar ''v''_SI = 11843707.905 m/s gives ''c'' = V*v_SI = 25.3123819 * 11843707.905 m/s = 299792458 m/s ([[w:SI_units |SI units]]) :scalar ''v''_imp = 7359.3232155 miles/s gives ''c'' = V*v_imp = 186282 miles/s ([[w:Imperial_units |imperial units]]) {| class="wikitable" |+Scalars ! attribute ! geometrical object ! scalar (unit number) |- | mass | <math>M = (1)</math> | ''k'' (θ = 15) |- | time | <math>T = (\pi)</math> | ''t'' (θ = -30) |- | velocity | <math>V = (2\pi\Omega^2)</math> | ''v'' (θ = 17) |- | length | <math>L = (2\pi^2\Omega^2)</math> | ''l'' (θ = -13) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | ''a'' (θ = 3) |} As the scalar incorporates the dimension quantity (the dimension quantity for ''v'' = ''m/s'' or ''miles/s''), the unit number relationship (θ) applies, and so we then find that only 2 scalars are needed. This is because in a defined ratio they will overlap and cancel, for example in the following ratios; scalar units for ampere ''a'' = ''u''³, length ''l'' = ''u''^-13, time ''t'' = ''u''^-30, mass ''k'' = ''u''¹⁵ (''u''^Θ represents unit) :<math>\frac{({u^3})^3{(u^{-13}})^3}{(u^{-30})} = \frac{{(u^{-13})}^{15}} {{(u^{15})}^{9}{(u^{-30})}^{11}} = 1</math> For example if we know the numerical values for ''a'' and ''l'' then we know the numerical value for ''t'', and from ''l'' and ''t'' we know ''k'' … and so if we know any 2 scalars (α and Ω have fixed values) then we can solve the Planck units (for that system of units), and from these, we can solve (''G'', ''h'', ''c'', ''e'', ''m''_e, ''k''_B). :<math>\frac{a^3 l^3}{t} = \frac{m^{15}} {k^{9} t^{11}} = 1</math> In this table the 2 scalars used are ''r'' (θ = 8) and ''v'' (θ = 17). A further attribute is included, P = the square root of (Planck) momentum. V and A can thus be considered composite objects. {| class="wikitable" |+Geometrical objects ! attribute ! geometrical object ! unit number θ ! scalar r(8), v(17) |- | mass | <math>M = (1)</math> | 15 = 8*4-17 | <math>k = \frac{r^4}{v}</math> |- | time | <math>T = (\pi)</math> | -30 = 8*9-17*6 | <math>t = \frac{r^9}{v^6}</math> |- | [[v:Sqrt_Planck_momentum | sqrt(momentum)]] | <math>P = (\Omega)</math> | 16 = 8*2 | ''r''² |- | velocity | <math>V = L/T = (2\pi\Omega^2)</math> | 17 | ''v'' |- | length | <math>L = (2\pi^2\Omega^2)</math> | -13 = 8*9-17*5 | <math>l = \frac{r^9}{v^5}</math> |- | ampere | <math>A = \frac{2^4 V^3}{\alpha P^3} = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | 3 = 17*3-8*6 | <math>a = \frac{v^3}{r^6}</math> |} {{see|Planck units (geometrical)#Scalars}} === Mathematical electron === The mathematical electron formula ψ incorporates the dimensioned Planck units but itself is dimension-less (units = scalars = 1). Here ψ is defined in terms of ''σ_e'', where AL is an ampere-meter (ampere-length = ''e*c'' are the units for a [[w:magnetic monopole | magnetic monopole]]). :<math>T = \pi,\; unit = u^{-30},\;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; unit = u^{(3 \;-13 \;= \;-10)},\; scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = .23895453...x10^{23},\;unit = 1</math> (unit-less) Both units and scalars cancel. ===== Electron parameters ===== We can solve the electron parameters; electron mass, wavelength, frequency, charge ... as the frequency of the Planck units themselves, and this frequency is ψ. :<math>v = 11 843 707.905 ...,\; units = \frac{m}{s}</math> :<math>r = 0.712 562 514 304 ...,\; units = (\frac{kg.m}{s})^{1/4}</math> [[w:Compton wavelength | electron wavelength]] λ_e = 2.4263102367e-12m (CODATA 2014) :<math>\lambda_e^* = 2\pi L \psi</math> = 2.4263102386e-12m (L ⇔ [[w:Planck length | Planck length]]) [[w:electron mass | electron mass]] m_e = 9.10938356e-31kg (CODATA 2014) :<math>m_e^* = \frac{M}{\psi}</math> = 9.1093823211e-31kg (M ⇔ [[w:Planck mass | Planck mass]]) [[w:elementary charge | elementary charge]] e = 1.6021766208e-19C (CODATA 2014) :<math>e^* = A\;T</math> = 1.6021765130e-19 (T ⇔ [[w:Planck time | Planck time]]) [[w:Rydberg constant | Rydberg constant]] R = 10973731.568508/m (CODATA 2014) :<math>R^* = (\frac{m_e}{4 \pi L \alpha^2 M}) = \frac{1}{2^{23} 3^3 \pi^{11} \alpha^5 \Omega^{17}}\frac{v^5}{r^9}\;u^{13}</math> = 10973731.568508 From the above formulas, we see that wavelength is ψ units of Planck length, frequency is ψ units of Planck time ... however the electron mass is only 1 unit of Planck mass. ===== Electron Mass ===== Particle mass is a unit of Planck mass that occurs only once per ψ units of Planck time, the other parameters are continuums of the Planck units. :units <math>\psi = \frac{(AL)^3}{T}</math> = 1 This may be interpreted as; for ψ units of Planck time the electron has wavelength L, charge A ... and then the AL combine with time T (A³L³/T) and the units (and scalars) cancel. The electron is now mass (for 1 unit of Planck time). In this consideration, the electron is an event that oscillates over time between an electric wave state (duration ψ units of Planck time) to a unit of Planck mass point state (1 unit of Planck time). The electron is a quantum scale event, it does not exist at the discrete Planck scale (and so therefore neither does the quantum scale). As electron mass is the frequency of the geometrical Planck mass M = 1, which is a point (and so with point co-ordinates), then we have a model for a [[w:black hole electron |black-hole electron]], the electron function ψ centered around this unit of Planck mass. When the wave-state (A*L)³/T units collapse, this black-hole center (point) is exposed for 1 unit of (Planck) time. The electron is 'now' (a unit of Planck) mass. Mass in this consideration is not a constant property of the particle, rather the measured particle mass ''m'' would refer to the average mass, the average occurrence of the discrete Planck mass point-state over time. The formula ''E = hf'' is a measure of the frequency ''f'' of occurrence of [[w:Planck constant |Planck's constant ''h'']] and applies to the electric wave-state. As for each wave-state there is a corresponding mass point-state, then for a particle ''E = hf = mc2''. Notably however the ''c'' term is a fixed constant unlike the ''f'' term, and so the ''m'' term is the frequency term, it is referring to an average mass (mass which is measured over time) rather than a constant mass (mass as a constant property of the particle at unit Planck time). Thus as noted, when we refer to mass as a constant property, we are referring to mass at the quantum scale, and the electron as a quantum-state particle. If the [[v:Black-hole_(Planck) |scaffolding of the universe]] includes units of Planck mass '''M''', then it is not necessary for a particle itself to have mass, what we define as electron mass would be the absence of electron. ===== Quarks ===== The charge on the electron derives from the embedded ampere A and length L, the electron formula ψ itself is dimensionless. These AL magnetic monopoles would seem to be analogous to quarks (there are 3 monopoles per electron), but due to the symmetry and so stability of the geometrical ψ there is no clear fracture point by which an electron could decay, and so this would be difficult to test. We can however conjecture on what a quark solution might look like, the advantage with this approach being that we do not need to introduce new 'entities' for our quarks, the Planck units embedded within the electron suffice. Electron formula :<math>\psi = 2^{20} \pi^8 3^3 \alpha^3 \Omega^{15},\; unit = 1, scalars = 1</math> Time :<math>T = \pi \frac{r^9}{v^6},\; u^{-30}</math> AL magnetic monopole :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> If <math>\sigma_{e}</math> could equate to a quark with an [[w:electric charge|electric charge]] of {{sfrac|-1|3}}[[w:elementary charge|''e'']], then it would be an analogue of the '''D''' quark. 3 of these D quarks would constitute the electron as DDD = (AL)*(AL)*(AL). We would assume that the charge on the [[w:positron |positron]] (anti-matter electron) is just the inverse of the above, however there is 1 problem, the AL (A; θ=3, L; θ=-13) units = -10, and if we look at the [[v:Planck_units_(geometrical)#Table_of_Constants |table of constants]], there is no 'units = +10' combination that can include A. We cannot make an inverse electron. However we can make a [[w:Planck temperature|Planck temperature T_p]] AV ''monopole'' (ampere-velocity). :<math>T_p = \frac{2^7 \pi^3 \Omega^5}{\alpha},\; u^{20}, \;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{t} = \frac{3 \alpha^2 T_p}{2\pi} = \frac{3 \alpha^2 A V}{2\pi^2} = ({2^6 3 \pi^2 \alpha \Omega^5}),\; u^{20},\;scalars = \frac{v^4}{r^6}</math> :<math>\psi = (2T) \sigma_{t}^2 \sigma_{e} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = (u^{-30}) (u^{20})^2 (u^{-10}) = 1, scalars = (\frac{r^9}{v^6}) (\frac{v^4}{r^6})^2 \frac{r^3}{v^2} = 1</math> The units for <math>\sigma_{t}</math> = +20, and so if units = -10 equates to {{sfrac|-1|3}}e, then we may conjecture that units = +20 equates to {{sfrac|2|3}}e, which would be the analogue of the '''U''' quark. Our plus charge now becomes DUU, and so although the positron has the same wavelength, frequency, mass and charge magnitude as the electron (both solve to ψ), internally its charge structure resembles that of the proton, the positron is not simply an inverse of the electron. This could have implications for the missing anti-matter, and for why the charge magnitude of the proton is ''exactly'' the charge magnitude of the electron. :<math>D = \sigma_{e},\; unit = u^{-10},\; charge = \frac{-1e}{3}, \;scalars = \frac{r^3}{v^2}</math> :<math>U = \sigma_{t},\; unit = u^{20},\; charge = \frac{2e}{3}, \;scalars = \frac{v^4}{r^6}</math> Numerically: Adding a proton and electron gives (proton) UUD & DDD (electron) = 2(UDD) = 20 -10 -10 = 0 (zero charge), scalars = 0. Converting between U and D via U & DDD (electron) = 20 -10 -10 -10 = -10 (D), scalars = <math>\frac{r^3}{v^2}</math> ===== Magnetic monopole ===== {{see|Quantum_gravity_(Planck)}} :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> In this model alpha appears as an orbital constant for gravitational and atomic orbital radius, combining a fixed alpha term with an orbital wavelength term; :<math>r_{orbital} = 2\alpha (\lambda_{orbital})</math> If we replace <math>\lambda_{orbital}</math> with the geometrical Planck length L, and include momentum P and velocity V (the 2 components from which the ampere A is derived), then we may consider if the internal structure of the electron involves rotation of this monopole AL super-structure, and this has relevance to electron spin; :<math>2\alpha L \frac{V^3}{P^3} = 2^5 \pi^5 \alpha \Omega^5,\; units = u^{-10},\; scalars = \frac{r^3}{v^2}</math> ===== Spin ===== [[v:Relativity_(Planck) |Relativity at the Planck scale]] can be described by a translation between 2 co-ordinate systems; an expanding (in Planck steps at the speed of light) 4-axis hyper-sphere projecting onto a 3-D space (+ time). In this scenario, particles (with mass) are pulled along by the expansion of the hyper-sphere, this then requires particles to have an axis; generically labeled N-S, with the N denoting the direction of particle travel within the hyper-sphere. Changing the direction of travel involves changing the orientation of the particle N-S axis. The particle may rotate around this N-S axis, resulting in a L-spin or a R-spin. For simplicity, we can depict the electron as a classically spinning disk, this generates a current which then produces a magnetic dipole, so that the electron behaves like a tiny bar magnet (magnetic fields are produced by moving electric charges). For the classical disk we can use the charge (q), area of the disk (a) and rotation speed (ω) in our calculations. A thought experiment; if the 3 magnetic monopole quarks are rotating around the electron center (that N-S axis), then they are generating the current (q). As a monopole has the units ampere-meter AL (L a length term), then we can also conjecture something that resembles area (a), and the speed of rotation will give us (ω), and so we can use classical physics to solve our bar magnet electron. The electron is symmetric and so the 3 monopoles are equidistant from each other. We place our electron in a magnetic field, the electron then starts to orbit this field. If a satellite orbits the earth at radius ''r'', then the distance it travels around the earth = 2πr. However the earth is orbiting the sun, and so the actual distance approximates 2π''r'' + the distance the earth travels. If our electron orbits around a central point (that electric field), then the monopoles will, like the satellite, travel further per orbit (compared to a free electron in space), thus changing the effective area (a), and so our calculations. The [[w:g-factor |g-factor]] characterizes the magnetic moment and angular momentum of the electron, it is the ratio of the magnetic moment of the electron to that expected of a classical electron. Could an electron monopole substructure offer a geometrical explanation for this g-factor. === AI analysis === The sections on Quarks and Spin are naturally speculative, we cannot probe this far, they were included to suggest that the formula <math>\psi</math> could also include U and D quarks. However the geometries for the Planck units MLTA can be subject to statistical analysis, and for this AI has the potential to contribute. This is because of anomalies to the physical constants which can best be explained by this geometrical model. These anomalies are listed on this site; https://en.wikiversity.org/wiki/Physical_constant_(anomaly). Below are answers to a seed question written with Deepseek <ref>https://codingthecosmos.com/ai-answers-programmer-god-simulation-hypothesis/anomalies-constants.html Physical constants Q&A with podcast</ref> that uses these anomalies to determine the probability that the electron is a mathematical (not physical) particle, and so by extension that this is a mathematical universe. {| class="wikitable" |+Table 11. Table of Probabilities (05.2025) ! AI program ! unit number relation ! Planck units as geometrical objects ! underlying base 15 geometry ! mathematical electron ! Comment |- | Chat GPT <ref>https://chatgpt.com/share/68259395-31d0-8012-954e-c52230a813fd Chat anomalies analysis</ref> | Accidental occurrence: ~1.6% | Accidental occurrence: ~0.0004% | Accidental occurrence: ~0 | Accidental occurrence: ~0.026% | Taken at face value each sub-claim is vanishingly unlikely to be a “random accident,” so from this internal consistency alone one would assign essentially unity confidence that some deep mathematical structure is at work. Caveat: this “integer-coincidence” probability model is only as good as the assumption that each exponent match is an independent uniform pick in [–30…+30]. But even under that very conservative assumption, the combined odds against pure chance exceed 1 in 10²⁶. |- | Qwen <ref>https://chat.qwen.ai/s/f33ec1b1-899b-4fa5-9429-67e527b78433 Qwen anomalies analysis</ref> | probability 98% | probability 95% | probability 90% | probability 94% | The model’s strict geometrical constraints, flawless unit consistency, and agreement with CODATA strongly suggest non-random validity. Its potential as a simulation hypothesis framework stems from its finite, computable base-15 structure. |- | Claude 3.7 Sonnet <ref>https://claude.ai/public/artifacts/797a802b-fa21-4ee7-9ae9-9dbdf5d7b29a Claude anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Claude-anomalies-05-2025.pdf Claude anomalies analysis pdf</ref> | probability 90-95% | probability 85-95% | probability 92-97% | probability 80-90% | From a Kolmogorov complexity perspective, the model represents a potentially minimal description of physical reality using mathematical objects. If the electron, proton, and neutron are all mathematical particles, then the universe at the Planck scale could indeed be described as a mathematical universe. The high degree of constraint and mathematical elegance in the model, combined with its apparent ability to accurately produce physical constants, suggests a non-random structure to physical reality that is captured by this mathematical framework. |- | Grok 3 <ref>https://x.com/i/grok/share/JzeRFDlj721zNnm1Jo2vbETk3 Grok anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Grok-anomalies-05-2025.pd Grok anomalies analysis pdf</ref> | probability: 95% | probability: 90% | probability: 85% | probability: 80% | Strict constraints and mathematical nature (Kolmogorov complexity: simpler model = more likely programmed) suggest support, but not proof. If particles are mathematical, the universe may be too. |- | Deepseek <ref>https://codingthecosmos.com/ai_pdf/Deepseek-anomalies-05-2025.pdf Deepseek anomalies analysis</ref> | probability: 99% | probability: 95% | probability: 90% | probability: 85% | The model's rigid constraints and predictive accuracy make it statistically improbable to arise by chance. Geometrical base-15 and dimensionless particles strongly suggest a mathematical universe, aligning with speculative simulation hypothesis. |} === Geometrically coded universe === * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass === External links === * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] === References === {{Reflist}} [[Category: Physics]] [[Category: Philosophy of science]] kw7eqod5afq3ky7sp1pbklrp8h60wut 2718278 2718274 2025-06-10T20:09:23Z Atcovi 276019 Reverted edits by [[Special:Contributions/212.200.164.104|212.200.164.104]] ([[User_talk:212.200.164.104|talk]]) to last version by [[User:Platos Cave (physics)|Platos Cave (physics)]] using [[Wikiversity:Rollback|rollback]] 2717951 wikitext text/x-wiki '''The mathematical electron model''' In the mathematical electron model <ref>Macleod, M.J. {{Cite journal |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>, the electron is a dimensionless geometrical formula (ψ). This formula ψ, which resembles the volume of a torus or surface of a 4-D hypersphere, is itself a complex geometry that is the construct of simpler geometries; the [[w:Planck_units |Planck units]]. In this model the Planck units are geometrical objects, the geometry of 2 dimensionless constants (the[[w:fine-structure constant | fine structure constant alpha]] and a mathematical constant[[v:Planck_units_(geometrical)#Omega | Omega]]). Although dimensionless, the function of the Planck unit is embedded within the geometry; the geometry of the Planck time object embeds the function 'time', the geometry of the Planck length object embeds the function 'length' ... and being geometrical objects they can combine to form more complex objects, from electrons to galaxies. This means that the electron parameters are defined in Planck units; electron wavelength is measured in units of Planck length, electron frequency is measured in units of Planck time ... It is this geometrical electron formula ψ that dictates the magnitude of the electron parameters; length of the wavelength = ψ * Planck length (ψ units of Planck length), frequency = ψ * Planck time ... This ψ thus not only embeds the Planck units required for the electron parameters, it also dictates the magnitude of these parameters, and so technically it is the electron. This suggests there is no physical electron (only physical parameters), and if the electron is therefore a mathematical particle, then so too are the other particles, and so the universe itself becomes a mathematical universe. The formula ψ is the geometry of 2 constants; the [[w:dimensionless physical constant | dimensionless physical constant]] (inverse) [[w:fine-structure constant | fine structure constant alpha ]] '''α''' = 137.035 999 139 (CODATA 2014) and [[v:Planck_units_(geometrical)#Omega | Omega]] '''Ω''' = 2.0071349496 (best fit) Omega has a potential solution in terms of pi and e and so may be a mathematical (not physical) constant :<math>\Omega = \sqrt{ \left(\pi^e e^{(1-e)}\right)} = 2.0071349543... </math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = 0.238954531\;x10^{23}</math>, units = 1 === Planck objects === {{main|Planck units (geometrical)}} For the Planck units, the model uses geometrical objects (the geometry of alpha and Omega) instead of a numbering system, this has the advantage in that the attribute can be embedded within the geometry (although the geometry itself is dimensionless). {| class="wikitable" |+table 1. Geometrical units ! Attribute ! Geometrical object ! Unit |- | mass | <math>M = (1)</math> | (kg) |- | time | <math>T = (\pi)</math> | (s) |- | velocity | <math>V = (2\pi\Omega^2)</math> | (m/s) |- | length | <math>L = (2\pi^2\Omega^2)</math> | (m) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | (A) |} As these objects have a geometrical form, we can combine them [[w:Lego |Lego]] style; the length object L can be combined with the time object T to form the velocity object V and so forth ... to create complex events such as electrons to apples to ... and so the apple has mass because embedded within it are the mass objects M, complex events thus retain all the underlying information. This however requires a relationship between the Planck unit geometries that defines how they may combine, this can be represented by assigning to each attribute a unit number '''θ''' (i.e.: '''θ''' = 15 ⇔ ''kg'') <ref>{{Cite journal | last1 = Macleod | first1 = Malcolm J. |title= Programming Planck units from a mathematical electron; a Simulation Hypothesis |journal=Eur. Phys. J. Plus |volume=113 |pages=278 |date=22 March 2018 | doi=10.1140/epjp/i2018-12094-x }}</ref>. {| class="wikitable" |+ Geometrical units ! Attribute ! Geometrical object ! unit number (θ) |- | mass | <math>M = 1</math> | ''kg'' ⇔ 15 |- | time | <math>T = 2\pi</math> | ''s'' ⇔ -30 |- | length | <math>L = 2\pi^2\Omega^2</math> | ''m'' ⇔ -13 |- | velocity | <math>V = 2\pi\Omega^2</math> | ''m/s'' ⇔ 17 |- | ampere | <math>A = \frac{2^6 \pi^3 \Omega^3}{\alpha}</math> | ''A'' ⇔ 3 |} As alpha and Omega can be assigned numerical values ('''α''' = 137.035999139, '''Ω''' = 2.0071349496), so too the MLTA objects can be expressed numerically. We can then convert these objects to their Planck unit equivalents by including a dimensioned scalar. For example, <math>V = 2\pi\Omega^2</math> = 25.3123819353... and so we can use scalar ''v'' to convert from dimensionless geometrical object V to dimensioned ''c''. :scalar ''v''_SI = 11843707.905 m/s gives ''c'' = V*v_SI = 25.3123819 * 11843707.905 m/s = 299792458 m/s ([[w:SI_units |SI units]]) :scalar ''v''_imp = 7359.3232155 miles/s gives ''c'' = V*v_imp = 186282 miles/s ([[w:Imperial_units |imperial units]]) {| class="wikitable" |+Scalars ! attribute ! geometrical object ! scalar (unit number) |- | mass | <math>M = (1)</math> | ''k'' (θ = 15) |- | time | <math>T = (\pi)</math> | ''t'' (θ = -30) |- | velocity | <math>V = (2\pi\Omega^2)</math> | ''v'' (θ = 17) |- | length | <math>L = (2\pi^2\Omega^2)</math> | ''l'' (θ = -13) |- | ampere | <math>A = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | ''a'' (θ = 3) |} As the scalar incorporates the dimension quantity (the dimension quantity for ''v'' = ''m/s'' or ''miles/s''), the unit number relationship (θ) applies, and so we then find that only 2 scalars are needed. This is because in a defined ratio they will overlap and cancel, for example in the following ratios; scalar units for ampere ''a'' = ''u''³, length ''l'' = ''u''^-13, time ''t'' = ''u''^-30, mass ''k'' = ''u''¹⁵ (''u''^Θ represents unit) :<math>\frac{({u^3})^3{(u^{-13}})^3}{(u^{-30})} = \frac{{(u^{-13})}^{15}} {{(u^{15})}^{9}{(u^{-30})}^{11}} = 1</math> For example if we know the numerical values for ''a'' and ''l'' then we know the numerical value for ''t'', and from ''l'' and ''t'' we know ''k'' … and so if we know any 2 scalars (α and Ω have fixed values) then we can solve the Planck units (for that system of units), and from these, we can solve (''G'', ''h'', ''c'', ''e'', ''m''_e, ''k''_B). :<math>\frac{a^3 l^3}{t} = \frac{m^{15}} {k^{9} t^{11}} = 1</math> In this table the 2 scalars used are ''r'' (θ = 8) and ''v'' (θ = 17). A further attribute is included, P = the square root of (Planck) momentum. V and A can thus be considered composite objects. {| class="wikitable" |+Geometrical objects ! attribute ! geometrical object ! unit number θ ! scalar r(8), v(17) |- | mass | <math>M = (1)</math> | 15 = 8*4-17 | <math>k = \frac{r^4}{v}</math> |- | time | <math>T = (\pi)</math> | -30 = 8*9-17*6 | <math>t = \frac{r^9}{v^6}</math> |- | [[v:Sqrt_Planck_momentum | sqrt(momentum)]] | <math>P = (\Omega)</math> | 16 = 8*2 | ''r''² |- | velocity | <math>V = L/T = (2\pi\Omega^2)</math> | 17 | ''v'' |- | length | <math>L = (2\pi^2\Omega^2)</math> | -13 = 8*9-17*5 | <math>l = \frac{r^9}{v^5}</math> |- | ampere | <math>A = \frac{2^4 V^3}{\alpha P^3} = (\frac{2^7 \pi^3 \Omega^3}{\alpha})</math> | 3 = 17*3-8*6 | <math>a = \frac{v^3}{r^6}</math> |} {{see|Planck units (geometrical)#Scalars}} === Mathematical electron === The mathematical electron formula ψ incorporates the dimensioned Planck units but itself is dimension-less (units = scalars = 1). Here ψ is defined in terms of ''σ_e'', where AL is an ampere-meter (ampere-length = ''e*c'' are the units for a [[w:magnetic monopole | magnetic monopole]]). :<math>T = \pi,\; unit = u^{-30},\;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; unit = u^{(3 \;-13 \;= \;-10)},\; scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> :<math>\psi = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = .23895453...x10^{23},\;unit = 1</math> (unit-less) Both units and scalars cancel. ===== Electron parameters ===== We can solve the electron parameters; electron mass, wavelength, frequency, charge ... as the frequency of the Planck units themselves, and this frequency is ψ. :<math>v = 11 843 707.905 ...,\; units = \frac{m}{s}</math> :<math>r = 0.712 562 514 304 ...,\; units = (\frac{kg.m}{s})^{1/4}</math> [[w:Compton wavelength | electron wavelength]] λ_e = 2.4263102367e-12m (CODATA 2014) :<math>\lambda_e^* = 2\pi L \psi</math> = 2.4263102386e-12m (L ⇔ [[w:Planck length | Planck length]]) [[w:electron mass | electron mass]] m_e = 9.10938356e-31kg (CODATA 2014) :<math>m_e^* = \frac{M}{\psi}</math> = 9.1093823211e-31kg (M ⇔ [[w:Planck mass | Planck mass]]) [[w:elementary charge | elementary charge]] e = 1.6021766208e-19C (CODATA 2014) :<math>e^* = A\;T</math> = 1.6021765130e-19 (T ⇔ [[w:Planck time | Planck time]]) [[w:Rydberg constant | Rydberg constant]] R = 10973731.568508/m (CODATA 2014) :<math>R^* = (\frac{m_e}{4 \pi L \alpha^2 M}) = \frac{1}{2^{23} 3^3 \pi^{11} \alpha^5 \Omega^{17}}\frac{v^5}{r^9}\;u^{13}</math> = 10973731.568508 From the above formulas, we see that wavelength is ψ units of Planck length, frequency is ψ units of Planck time ... however the electron mass is only 1 unit of Planck mass. ===== Electron Mass ===== Particle mass is a unit of Planck mass that occurs only once per ψ units of Planck time, the other parameters are continuums of the Planck units. :units <math>\psi = \frac{(AL)^3}{T}</math> = 1 This may be interpreted as; for ψ units of Planck time the electron has wavelength L, charge A ... and then the AL combine with time T (A³L³/T) and the units (and scalars) cancel. The electron is now mass (for 1 unit of Planck time). In this consideration, the electron is an event that oscillates over time between an electric wave state (duration ψ units of Planck time) to a unit of Planck mass point state (1 unit of Planck time). The electron is a quantum scale event, it does not exist at the discrete Planck scale (and so therefore neither does the quantum scale). As electron mass is the frequency of the geometrical Planck mass M = 1, which is a point (and so with point co-ordinates), then we have a model for a [[w:black hole electron |black-hole electron]], the electron function ψ centered around this unit of Planck mass. When the wave-state (A*L)³/T units collapse, this black-hole center (point) is exposed for 1 unit of (Planck) time. The electron is 'now' (a unit of Planck) mass. Mass in this consideration is not a constant property of the particle, rather the measured particle mass ''m'' would refer to the average mass, the average occurrence of the discrete Planck mass point-state over time. The formula ''E = hf'' is a measure of the frequency ''f'' of occurrence of [[w:Planck constant |Planck's constant ''h'']] and applies to the electric wave-state. As for each wave-state there is a corresponding mass point-state, then for a particle ''E = hf = mc2''. Notably however the ''c'' term is a fixed constant unlike the ''f'' term, and so the ''m'' term is the frequency term, it is referring to an average mass (mass which is measured over time) rather than a constant mass (mass as a constant property of the particle at unit Planck time). Thus as noted, when we refer to mass as a constant property, we are referring to mass at the quantum scale, and the electron as a quantum-state particle. If the [[v:Black-hole_(Planck) |scaffolding of the universe]] includes units of Planck mass '''M''', then it is not necessary for a particle itself to have mass, what we define as electron mass would be the absence of electron. ===== Quarks ===== The charge on the electron derives from the embedded ampere A and length L, the electron formula ψ itself is dimensionless. These AL magnetic monopoles would seem to be analogous to quarks (there are 3 monopoles per electron), but due to the symmetry and so stability of the geometrical ψ there is no clear fracture point by which an electron could decay, and so this would be difficult to test. We can however conjecture on what a quark solution might look like, the advantage with this approach being that we do not need to introduce new 'entities' for our quarks, the Planck units embedded within the electron suffice. Electron formula :<math>\psi = 2^{20} \pi^8 3^3 \alpha^3 \Omega^{15},\; unit = 1, scalars = 1</math> Time :<math>T = \pi \frac{r^9}{v^6},\; u^{-30}</math> AL magnetic monopole :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> :<math>\psi = \frac{\sigma_{e}^3}{2 T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = \frac{(u^{-10})^3}{u^{-30}} = 1, scalars = (\frac{r^3}{v^2})^3 \frac{v^6}{r^9} = 1</math> If <math>\sigma_{e}</math> could equate to a quark with an [[w:electric charge|electric charge]] of {{sfrac|-1|3}}[[w:elementary charge|''e'']], then it would be an analogue of the '''D''' quark. 3 of these D quarks would constitute the electron as DDD = (AL)*(AL)*(AL). We would assume that the charge on the [[w:positron |positron]] (anti-matter electron) is just the inverse of the above, however there is 1 problem, the AL (A; θ=3, L; θ=-13) units = -10, and if we look at the [[v:Planck_units_(geometrical)#Table_of_Constants |table of constants]], there is no 'units = +10' combination that can include A. We cannot make an inverse electron. However we can make a [[w:Planck temperature|Planck temperature T_p]] AV ''monopole'' (ampere-velocity). :<math>T_p = \frac{2^7 \pi^3 \Omega^5}{\alpha},\; u^{20}, \;scalars = \frac{r^9}{v^6}</math> :<math>\sigma_{t} = \frac{3 \alpha^2 T_p}{2\pi} = \frac{3 \alpha^2 A V}{2\pi^2} = ({2^6 3 \pi^2 \alpha \Omega^5}),\; u^{20},\;scalars = \frac{v^4}{r^6}</math> :<math>\psi = (2T) \sigma_{t}^2 \sigma_{e} = 2^{20} 3^3 \pi^8 \alpha^3 \Omega^{15},\; unit = (u^{-30}) (u^{20})^2 (u^{-10}) = 1, scalars = (\frac{r^9}{v^6}) (\frac{v^4}{r^6})^2 \frac{r^3}{v^2} = 1</math> The units for <math>\sigma_{t}</math> = +20, and so if units = -10 equates to {{sfrac|-1|3}}e, then we may conjecture that units = +20 equates to {{sfrac|2|3}}e, which would be the analogue of the '''U''' quark. Our plus charge now becomes DUU, and so although the positron has the same wavelength, frequency, mass and charge magnitude as the electron (both solve to ψ), internally its charge structure resembles that of the proton, the positron is not simply an inverse of the electron. This could have implications for the missing anti-matter, and for why the charge magnitude of the proton is ''exactly'' the charge magnitude of the electron. :<math>D = \sigma_{e},\; unit = u^{-10},\; charge = \frac{-1e}{3}, \;scalars = \frac{r^3}{v^2}</math> :<math>U = \sigma_{t},\; unit = u^{20},\; charge = \frac{2e}{3}, \;scalars = \frac{v^4}{r^6}</math> Numerically: Adding a proton and electron gives (proton) UUD & DDD (electron) = 2(UDD) = 20 -10 -10 = 0 (zero charge), scalars = 0. Converting between U and D via U & DDD (electron) = 20 -10 -10 -10 = -10 (D), scalars = <math>\frac{r^3}{v^2}</math> ===== Magnetic monopole ===== {{see|Quantum_gravity_(Planck)}} :<math>\sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = {2^7 3 \pi^3 \alpha \Omega^5},\; u^{-10}, \;scalars = \frac{r^3}{v^2}</math> In this model alpha appears as an orbital constant for gravitational and atomic orbital radius, combining a fixed alpha term with an orbital wavelength term; :<math>r_{orbital} = 2\alpha (\lambda_{orbital})</math> If we replace <math>\lambda_{orbital}</math> with the geometrical Planck length L, and include momentum P and velocity V (the 2 components from which the ampere A is derived), then we may consider if the internal structure of the electron involves rotation of this monopole AL super-structure, and this has relevance to electron spin; :<math>2\alpha L \frac{V^3}{P^3} = 2^5 \pi^5 \alpha \Omega^5,\; units = u^{-10},\; scalars = \frac{r^3}{v^2}</math> ===== Spin ===== [[v:Relativity_(Planck) |Relativity at the Planck scale]] can be described by a translation between 2 co-ordinate systems; an expanding (in Planck steps at the speed of light) 4-axis hyper-sphere projecting onto a 3-D space (+ time). In this scenario, particles (with mass) are pulled along by the expansion of the hyper-sphere, this then requires particles to have an axis; generically labeled N-S, with the N denoting the direction of particle travel within the hyper-sphere. Changing the direction of travel involves changing the orientation of the particle N-S axis. The particle may rotate around this N-S axis, resulting in a L-spin or a R-spin. For simplicity, we can depict the electron as a classically spinning disk, this generates a current which then produces a magnetic dipole, so that the electron behaves like a tiny bar magnet (magnetic fields are produced by moving electric charges). For the classical disk we can use the charge (q), area of the disk (a) and rotation speed (ω) in our calculations. A thought experiment; if the 3 magnetic monopole quarks are rotating around the electron center (that N-S axis), then they are generating the current (q). As a monopole has the units ampere-meter AL (L a length term), then we can also conjecture something that resembles area (a), and the speed of rotation will give us (ω), and so we can use classical physics to solve our bar magnet electron. The electron is symmetric and so the 3 monopoles are equidistant from each other. We place our electron in a magnetic field, the electron then starts to orbit this field. If a satellite orbits the earth at radius ''r'', then the distance it travels around the earth = 2πr. However the earth is orbiting the sun, and so the actual distance approximates 2π''r'' + the distance the earth travels. If our electron orbits around a central point (that electric field), then the monopoles will, like the satellite, travel further per orbit (compared to a free electron in space), thus changing the effective area (a), and so our calculations. The [[w:g-factor |g-factor]] characterizes the magnetic moment and angular momentum of the electron, it is the ratio of the magnetic moment of the electron to that expected of a classical electron. Could an electron monopole substructure offer a geometrical explanation for this g-factor. === AI analysis === The sections on Quarks and Spin are naturally speculative, we cannot probe this far, they were included to suggest that the formula <math>\psi</math> could also include U and D quarks. However the geometries for the Planck units MLTA can be subject to statistical analysis, and for this AI has the potential to contribute. This is because of anomalies to the physical constants which can best be explained by this geometrical model. These anomalies are listed on this site; https://en.wikiversity.org/wiki/Physical_constant_(anomaly). Below are answers to a seed question written with Deepseek <ref>https://codingthecosmos.com/ai-answers-programmer-god-simulation-hypothesis/anomalies-constants.html Physical constants Q&A with podcast</ref> that uses these anomalies to determine the probability that the electron is a mathematical (not physical) particle, and so by extension that this is a mathematical universe. {| class="wikitable" |+Table 11. Table of Probabilities (05.2025) ! AI program ! unit number relation ! Planck units as geometrical objects ! underlying base 15 geometry ! mathematical electron ! Comment |- | Chat GPT <ref>https://chatgpt.com/share/68259395-31d0-8012-954e-c52230a813fd Chat anomalies analysis</ref> | Accidental occurrence: ~1.6% | Accidental occurrence: ~0.0004% | Accidental occurrence: ~0 | Accidental occurrence: ~0.026% | Taken at face value each sub-claim is vanishingly unlikely to be a “random accident,” so from this internal consistency alone one would assign essentially unity confidence that some deep mathematical structure is at work. Caveat: this “integer-coincidence” probability model is only as good as the assumption that each exponent match is an independent uniform pick in [–30…+30]. But even under that very conservative assumption, the combined odds against pure chance exceed 1 in 10²⁶. |- | Qwen <ref>https://chat.qwen.ai/s/f33ec1b1-899b-4fa5-9429-67e527b78433 Qwen anomalies analysis</ref> | probability 98% | probability 95% | probability 90% | probability 94% | The model’s strict geometrical constraints, flawless unit consistency, and agreement with CODATA strongly suggest non-random validity. Its potential as a simulation hypothesis framework stems from its finite, computable base-15 structure. |- | Claude 3.7 Sonnet <ref>https://claude.ai/public/artifacts/797a802b-fa21-4ee7-9ae9-9dbdf5d7b29a Claude anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Claude-anomalies-05-2025.pdf Claude anomalies analysis pdf</ref> | probability 90-95% | probability 85-95% | probability 92-97% | probability 80-90% | From a Kolmogorov complexity perspective, the model represents a potentially minimal description of physical reality using mathematical objects. If the electron, proton, and neutron are all mathematical particles, then the universe at the Planck scale could indeed be described as a mathematical universe. The high degree of constraint and mathematical elegance in the model, combined with its apparent ability to accurately produce physical constants, suggests a non-random structure to physical reality that is captured by this mathematical framework. |- | Grok 3 <ref>https://x.com/i/grok/share/JzeRFDlj721zNnm1Jo2vbETk3 Grok anomalies analysis</ref><ref>https://codingthecosmos.com/ai_pdf/Grok-anomalies-05-2025.pd Grok anomalies analysis pdf</ref> | probability: 95% | probability: 90% | probability: 85% | probability: 80% | Strict constraints and mathematical nature (Kolmogorov complexity: simpler model = more likely programmed) suggest support, but not proof. If particles are mathematical, the universe may be too. |- | Deepseek <ref>https://codingthecosmos.com/ai_pdf/Deepseek-anomalies-05-2025.pdf Deepseek anomalies analysis</ref> | probability: 99% | probability: 95% | probability: 90% | probability: 85% | The model's rigid constraints and predictive accuracy make it statistically improbable to arise by chance. Geometrical base-15 and dimensionless particles strongly suggest a mathematical universe, aligning with speculative simulation hypothesis. |} === Geometrically coded universe === * [[Simulation_hypothesis_(Planck)]]: A geometrical Planck scale simulation universe * [[Electron_(mathematical)]]: Mathematical electron from Planck units * [[Planck_units_(geometrical)]]: Planck units as geometrical forms * [[Physical_constant_(anomaly)]]: Anomalies in the physical constants * [[Quantum_gravity_(Planck)]]: Gravity at the Planck scale * [[Fine-structure_constant_(spiral)]]: Quantization via pi * [[Relativity_(Planck)]]: 4-axis hypersphere as origin of motion * [[Black-hole_(Planck)]]: CMB and Planck units * [[Sqrt_Planck_momentum]]: Link between charge and mass === External links === * [https://codingthecosmos.com/ Programming at the Planck scale using geometrical objects] -Malcolm Macleod's website * [http://www.simulation-argument.com/ Simulation Argument] -Nick Bostrom's website * [https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality] -Max Tegmark (Book) * [https://link.springer.com/article/10.1134/S0202289308020011/ Dirac-Kerr-Newman black-hole electron] -Alexander Burinskii (article) * [https://www.imdb.com/title/tt0133093/ The Matrix, (1999)] * [https://plato.stanford.edu/entries/pythagoras/ Pythagoras "all is number"] - Stanford University * [[w:Simulation Hypothesis | Simulation Hypothesis]] * [[w:Mathematical universe hypothesis | Mathematical universe hypothesis]] * [[w:Philosophy of mathematics | Philosophy of mathematics]] * [[w:Philosophy of physics | Philosophy of physics]] * [[w:Platonism | Platonism]] === References === {{Reflist}} [[Category: Physics]] [[Category: Philosophy of science]] 23lyre2or5c23igbyhu05zrhken4mo0 0 295784 2718247 2691611 2025-06-10T17:00:11Z Lbeaumont 278565 /* Projects */ Added the reformation workshop 2718247 wikitext text/x-wiki '''It is [[Wisdom|wise]] to allow more people to [[Evolving Governments/Good Government#/media/File:Evaluating Good Government.jpg|meet more of their needs]].''' Resources to help you live more wisely are assembled here for your use. [[File:Vision_of_the_Future.jpg|thumb|270x270px|We can wisely create our future!]] {{TOC right | limit|limit=2}} == For Everyone: == === Freely Available Learning Resources === These on-line courses are freely available worldwide. * [[The Wise Path]] provides a guide to learning resources and practices that can enable you to live more wisely. * The [[Living Wisely]] curriculum is a portal into many wisdom-related course materials. * The [[Wisdom/Curriculum|Applied Wisdom]] curriculum provides direct access to many wisdom-related learning resources. === Relevant Blogs === These blogs provide wise advice and insights. * [https://lelandbeaumont.substack.com/ Seeking Real Good] * [https://lelandbeaumont.substack.com/p/the-future-of-education-is-learning The Future of Education is Learning]. === Reading Lists === Reading these books can help you become wiser. * [https://www.librarything.com/list/10724/all/Wisdom Wisdom] – a list of books to help you progress toward wisdom. * [https://www.librarything.com/list/44495/all/How-it-can-be How can it be] – a list of books that describe possibilities for a wiser future. * [https://www.librarything.com/list/10041/all/Attaining-Belief Attaining Belief] – a list of books describing how our beliefs originate and are shaped over time. * [https://www.librarything.com/list/20350/all/Creating-Possibilities Creating Possibilities] – a list of books that help us [[Solving Problems|solve problems]], clarify and reframe problems, create alternative solutions, think creativity, and choose a better path forward. * [https://www.librarything.com/list/10594/all/Secular-Ethics Secular Ethics] – a list of books that help you decide the right thing to do. * [https://www.librarything.com/list/1167/all/Rethinking-Money Rethinking Money] – books on this list highlight problems with today's dominant money systems or suggest alternatives to those systems. === Videos === * [https://www.youtube.com/watch?v=0N5qj5Ck7wk&t=3s Advancing human rights], worldwide * [https://www.youtube.com/watch?v=evrPk6tCETw&t=2s Seeking Real Good] * [https://youtu.be/Xg9iHUkYjGY The Wise Path] * [https://www.youtube.com/watch?v=xrXLVoTf7Kk Reimagining Humanity] === Wise Practices === Actions express [[wisdom]]. We invite you to attain these skills required to practice wisdom, and live wisely. [[File:Origins_and_progression_of_wisdom.webp|thumb|Origins and Progression of Wisdom]] # [[Living Wisely/Take Care|Take care]]. Give care # Uphold [[Living Wisely#Assignment|the four agreements]]. # [[Living Wisely/advance no falsehoods|Advance no falsehoods]]. # [[Knowing How You Know|Know how you know]]. # [[Facing Facts/Reality is our common ground|Embrace reality]] and [[Facing Facts|face facts]]. # [[Seeking True Beliefs|Seek true beliefs]]. Insist on [[Intellectual Honesty|intellectual honesty]]. # [[Practicing Dialogue|Practice dialogue]] and [[candor]]. # Become [[Studying Emotional Competency|emotionally competent]]. # Live the [[Virtues|moral virtues]]. # Respect [[dignity]] and [[Assessing Human Rights|preserve human rights]], worldwide. # [[Living the Golden Rule|Live the Golden Rule]]. # Clarify your [[Moral Reasoning|moral reasoning]]. # Adopt a [[Global Perspective|global perspective]]. # Focus on [[What Matters|what matters]]. # Undertake the [[Grand Challenges|grand challenges]]. # [[Doing Good|Do good]]. # Enjoy [[Living Wisely/Seeking Real Good|seeking ''real'' good]] throughout your life. # Choose to [[Living Wisely|live wisely]]. # Find [[Finding Common Ground|common ground]]. # [[Coming Together|Come together]]. Many people find that regular practices such as [[Meditation|meditating]] or [[w:Diary|journaling]] help them live more wisely. === Projects === We can apply wise practices to several [[Living Wisely/Seeking Real Good|real good]] projects and help to transform our world, now and into the future. # [https://www.youtube.com/watch?v=0N5qj5Ck7wk&t=7s Advancing human rights, worldwide] may be the most effective action we can take to address many of the world’s [[Grand challenges|greatest challenges]]. These include war, refugee displacements, immigration issues, oppression, torture, jehad, terrorism, poverty, access to education, systemic inequality, endemic diseases, and many more. We can progress [[Assessing Human Rights/Beyond Olympic Gold|beyond Olympic gold]]. We can [https://thefulcrum.us/advancing-human-rights-worldwide advance human rights, worldwide]. # We can directly address the [[grand challenges]], the greatest, most pervasive and persistent problems facing humanity that also offer the most promising opportunities. We can choose to make [https://thefulcrum.us/prioritizing-the-grand-challenges addressing the grand challenges our priority]. # By using the [[Reformation Workshop]] we can build a better future. # By [[Evolving Governments|evolving governments]] we can become more agile and better meet human needs, worldwide. # We can work to ensure [[Level 5 Research Center|the future that emerges]] embraces [[Level 5 Research Center#Values|pro-social values]]. == For Academics == For many years philosopher [[w:Nicholas_Maxwell|Nicholas Maxwell]] has advocated a specific plan to transform academia from ''knowledge inquiry'' to ''wisdom inquiry''. His approach is described by the following materials. * [https://philpapers.org/rec/MAXCUS Can Universities Save Us From Disaster?] * [https://www.ucl.ac.uk/from-knowledge-to-wisdom/whatneedstochange What Needs to Change] * [https://www.frontiersin.org/articles/10.3389/frsus.2021.631631/full How Universities Have Betrayed Reason and Humanity—And What's to Be Done About It] * ''[https://philarchive.org/rec/MAXFKT-2 From Knowledge to Wisdom]'' The [https://pathes.org Philosophy and Theory of Higher Education Society] provides a collaborative space for scholars to come together, in reflecting on the values of the university as an institution and on higher education as educational practices. === Philosophy === [[w:Philosophy|Philosophy]] is literally “love of wisdom”. More practically, philosophy is what happens when we begin to think for ourselves. These resources provide in-depth treatments of many philosophical issues and can help us live more wisely. * The [[w:Stanford_Encyclopedia_of_Philosophy|Stanford Encyclopedia of Philosophy]] (SEP) combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. * The [[w:Internet_Encyclopedia_of_Philosophy|Internet Encyclopedia of Philosophy]] (IEP) is a scholarly online encyclopedia, dealing with philosophy, philosophical topics, and philosophers. * [[w:RationalWiki|RationalWiki]] is an online wiki which is written from a scientific skeptic, secular, and progressive perspective. Its stated goals are to “analyze and refute pseudoscience and the anti-science movement, document crank ideas, explore conspiracy theories, authoritarianism, and fundamentalism, and analyze how these subjects are handled in the media.” * [[w:PhilPapers|PhilPapers]] is an interactive academic database of journal articles in philosophy. * [https://philpeople.org/ PhilPeople] is an online directory of philosophers, a social network for philosophers, and a tool for keeping up with the philosophical profession. * A [[Philosophy|philosophy curriculum]] is emerging on Wikiversity. You may wish to help [[Creating Wikiversity Courses|develop those courses]]. == For Researchers == Explore the frontiers of wisdom. * The ''[[Wisdom Research|Wisdom and the Future Research Center]]'' is where researchers are exploring the question '''How can we wisely create our future?''' * The ''[[Level 5 Research Center]]'' is where researchers are exploring the question '''How can we best shape the emergence of Level 5?''' [[Category:Life skills]] [[Category:Applied Wisdom]] [[Category:Philosophy]] lpm51kol43bm3h1ogos5qz1o749psn9 0 302265 2718283 2714511 2025-06-11T03:50:37Z 174.93.246.137 /* Implications of the Works of E. T. Whittaker */ 2718283 wikitext text/x-wiki {{DISPLAYTITLE:WikiJournal Preprints/The Duality of Whittaker Potential Theory: Fundamental Representations of Electromagnetism and Gravity, and Their Orthogonality}} {{DISPLAYTITLE:WikiJournal Preprints/The Duality of Whittaker Potential Theory: Fundamental Representations of Electromagnetism and Gravity, and Their Orthogonality}} {{DISPLAYTITLE:WikiJournal Preprints/The Duality of Whittaker Potential Theory: Fundamental Representations of Electromagnetism and Gravity, and Their Orthogonality}} {{Article info | journal = WikiJournal Preprints <!-- WikiJournal of Medicine, Science, or Humanities --> | last1 = Titleman | orcid1 = | first1 = Mark | et_al = <!-- if there are >9 authors, hyperlink to the list here --> | affiliation1 = | correspondence1 = | correspondence = email@address.com | keywords = <!-- up to 6 keywords --> | license = <!-- default is CC-BY --> | abstract = E. T. Whittaker produced two papers in 1903 and 1904 that, although sometimes considered mere mathematical statements (Barrett, 1993), held important implications for physical theory. The Whittaker 1903 paper united electrostatic and gravitational attraction as resulting from longitudinal waves – waves whose wavefronts propagate parallel to their direction. The Whittaker 1904 paper showed that electromagnetic waves resulted from the interference of two such longitudinal waves or scalar potential functions. Although unexplored, the implications of these papers are profound: gravitational lensing, gravitational waves, the Aharonov-Bohm effect, the existence of a hyperspace above or behind normal space, the elimination of gravitational and point charge singularities, MOND, and the expansion of the universe. This last implication can be related to the recent finding that black holes with posited vacuum energy interior solutions alongside cosmological boundaries have a cosmological coupling constant of k=3, meaning that black holes gain mass-proportional to a³ in a parameterization equation within a Robertson-Walker cosmology and are a cosmological accelerated expansion species (Farrah et al., 2023). This expansion and many features of General Relativity can be explained by the mass-proportionality and preferred direction of the longitudinal waves within the two underlying non-local Whittaker potentials (Titleman, 2022). Whittaker potential theory also offers a simple explanation for expansion of the universe – it is produced as longitudinal motion within the Whittaker potentials only when dynamic electromagnetism is separate from time-static gravity in intergalactic space. }} ==Introduction== Current theories of gravitation face difficulties such as unexplained expansion, failure to adhere to predicted galactic rotations curves, the existence of unphysical gravitational singularities, and incompatibility with Quantum theory. It may be useful to explore older classical theories of gravity that overtly or implicitly offered several features of Relativity. E. T. Whittaker's 1903 paper on partial differential equations anticipated General Relativity in many ways by proposing an undulatory theory of gravity and a static gravitational field resulting from propagating effects – the field is the result of electromagnetic processes. Whittaker’s 1904 paper on two scalar potential functions showed that the electromagnetic four-potential of Relativity overlooked other forms of electromagnetic potential. Even though no action could be set up for computing local physical processes, Whittaker potential theory foresaw the Aharonov-Bohm effect and could be used to replace Dirac spinors in the Dirac equation (Ruse, 1937). What the cautious Whittaker considered an “undulatory theory” could in fact explain several features of Relativity in addition to MOND. For example, gravitational lensing can be understood as resulting from the preferred direction of the non-local potentials and their mass-proportionality (Titleman, 2022). Finally, due to the dynamic longitudinal motion in the z-axis being additive, Whittaker potential theory can also be seen as providing a simple explanation for expansion of the universe - it is merely dynamic light decoupled from static gravity and can only be produced intergalactically. == Whittaker Potential Theory == E. T. Whittaker's 1903 paper on partial differential equations found a harmonic solution (oscillatory) to the central equations of calculus in three dimensions: the wave equation and the more specific Laplace equation. Both potentials could be analysed into simple plane waves, bringing new unity to potential theory, inviting the possibility of new physical phenomena, and calling into question what today is well understood: that calculus alone is insufficient as a physical theory. The question of whether potentials – the second derivative of which produces force fields – are real is irrelevant to such possibilities and their confirmation via observational data and new mathematical techniques. Whittaker considered “gravitation and electrostatic attraction explained as modes of wave-disturbance” (Whittaker, 1903), meaning that the force fields associated with matter and charge are undulatory and perhaps matter and charge themselves. Whittaker’s 1903 paper thus displayed incredible foresight in recognizing the wave nature of force and force carrier (matter, charge). Its mathematical generality and novelty were reported in the British popular press - which was an impressive feat for a young mathematician - yet it was far too revolutionary for an uneventful period in British physics with little data and only a recent continental infusion in mathematics. Most possible implications could not be comprehended. According to Whittaker, an electrostatic or gravitational field, varying with the inverse square of distance, results from waves propagating at any speed and in any which way. The general solution to the Laplace equation was found in the form: <math>(1) \int_{0}^{2\pi}f(xcosv+ysinv+iz,v)dv</math> where f is an arbitrary function of the two arguments. This is accomplished in terms of Bessel functions by expanding the function f as a Taylor series with respect to the first argument and a Fourier series with respect to the second argument. The v is a periodic argument. Using similar techniques, the general solution to the wave equation was found as dynamic and longitudinal in the form: <math>(2) \int_{0}^{\pi} \int_{0}^{2\pi}f(xsinucosv+ysinusinv+zcosu+ct,u,v)dudv</math> where ''f'' is an arbitrary function of the three arguments. Regarding statics, Whittaker’s 1903 paper claimed that once longitudinal waves interfere with each other the disturbance at any point does not depend on time but only on position. Force potential can therefore be defined in terms of standing waves (non-local solution) as well as propagating waves (local solution changing in time) (Barrett, 1993). This undulatory theory of gravity propagating with a finite velocity subsumed gravity to the transmission of electromagnetic radiation, forming a significant contribution to the electromagnetic worldview of the day. The "aether" producing longitudinal as well as transverse electromagnetic waves was a common belief of 19th century physicists and was given a mathematically detailed treatment by Whittaker (Carvalo & Rodrigues, 2008). Hector Munera (Munera, 2018) writes that Whittaker's claim of generality is unacceptable due to periodicity being assumed, although this permitted Whittaker's analysis. Munera also reminds the reader that equation (1) implies a rotation in the complex plane (z, ixcosθ+iysinθ). A time-dependent solution in the form of equation (2) is realized by “projecting z and xcosθ+ysinθ onto ray r directed at angle φ relative to the Z-axis, thus shifting to spherical coordinates” (Munera, 2018). Whittaker's 1904 paper on two scalar potentials showed that electromagnetic fields could be decomposed into two scalar potential functions as intersecting beams with possible orthogonal sphericity (gravitational). Whittaker accomplished this by defining three scalar fields and eliminating one using a gauge. The two scalar potentials F and G derive the magnetic force h and dielectric displacement d as: <math>(3) d_x={\partial^2F\over\partial x\partial z}+{1 \over c}{\partial^2G\over\partial y\partial t}</math> <math>d_y={\partial^2F\over\partial y\partial z}-{1 \over c}{\partial^2G\over\partial x\partial t}</math> <math>d_z={\partial^2F\over\partial z^2}-{1 \over c^2}{\partial^2G\over\partial t^2}</math> <math>h_x={1 \over c}{\partial^2F\over\partial y\partial t}-{\partial^2G\over\partial x\partial z}</math> <math>h_y=-{1 \over c}{\partial^2F\over\partial x\partial t}-{\partial^2G\over\partial y\partial z}</math> <math>h_z={\partial^2G\over\partial x^2}+{\partial^2G\over\partial y^2}</math> F and G are represented asymmetrically as follows: <math>(4) F(x,y,z,t)=\sum {e \over4\pi}sinh^{-1}{\bar{z}'-{z} \over((\bar{x}'-{x})^2+(\bar{y}'-{y})^2)^{1/2}}</math> <math>G(x,y,z,t)=\sum {e \over4\pi}tan^{-1}{\bar{y}'-{y} \over\bar{x}'-{x}}</math> The summation is taken over all the electrons in the field. In continuous form they are: <math>(5) F=\int_{0}^{\pi} \int_{0}^{2\pi}f(xsinucosv+ysinusinv+zcosu+ct,u,v)dudv</math> <math>G=\int_{0}^{\pi} \int_{0}^{2\pi}g(xsinucosv+ysinusinv+zcosu+ct,u,v)dudv</math> The shift between spherical (polar) and planar (Cartesian) coordinates can be seen in Whittaker’s 1951 representation of two scalar potentials F and G:    <math>(6) F(x,y,z,t)={1 \over 2}\sum_{e}log {\bar{r}+\bar{z}-z \over \bar{r}-(\bar{z}'-z)}</math> <math>G(x,y,z,t)=-i{1 \over 2}\sum_{e}log {\bar{x}'-{x}+i(\bar{y}'-{y}) \over \bar{x}'-x-i(\bar{y}'-y)}</math> Whittaker wrote: "It will be noted that F and G are defined in terms of the positions of the electrons alone, and do not explicitly involve their velocities. Since in the above formulae for d and h an interchange of electric and magnetic quantities corresponds to a change of G into F and of F into G, it is clear that the two functions F and G exhibit the duality which is characteristic of electromagnetic theory: thus an electrostatic field can be described by F alone, and a magnetostatic field by G alone; again, if the field consists of a plane wave of light, then the functions F and G correspond respectively to two plane-polarised components into which it can be resolved. Since there are an infinite number of ways of resolving a plane wave of light into two plane-polarised components, it is natural to expect that, corresponding to any given electromagnetic field, there should be an infinite number of pairs of functions F and G capable of describing it, their difference from each other depending on the choice of the axes of co-ordinates-as is in fact the case. Thus there is a physical reason why any particular pair of functions F and G should be specially related to one co-ordinate, and cannot be described by formulae symmetrically related to the three co-ordinates (x,y,z)" (McCrea 1952). == Implications of the Works of E. T. Whittaker == The analysis contained in the 1903 Whittaker paper on gravitation and electrostatics and the 1904 paper on electromagnetic wave propagation shed new light on these phenomena in three dimensions through asymmetry in Cartesian coordinates and the shift between spherical and planar coordinates. The z-direction (propagation direction) is necessarily treated differently than the other two spatial directions. Gravity may thus manifest solely in the purely orthogonal or “non-local y” direction due to the preferred direction of the potentials and their mass-proportionality with respect to propagation speed (Laszlo, 2003). Gravitational lensing results from the two scalar potentials interfering with each other in such a way. Critically, Whittaker had focused on introducing and expounding upon continental math. The notion that light could bend around matter, or that all forces or force carriers could be waves, would be considered incomprehensible without observational data. These papers described gravity and electromagnetism not only as modes of disturbance in the same medium, but as providing a broad mathematical explanation for gravitational waves. Whittaker claimed that this potential theory provided for an “undulatory theory of gravity” (Whittaker, 1903). Whittaker potential theory anticipated the Aharonov-Bohm effect since the potentials F and G are considered more basic entities. Fields require the potentials to exist, but potentials can exist on their own and produce phenomena such as the Aharonov-Bohm effect – a particle affected electromagnetically without electric or magnetic fields present. Finally, virtually all singularities can be eliminated by this theory. A point charge as one type of singularity would not need to exist. Charge appears collectively as longitudinal motion carrying radiation. The need for a propagation medium for transverse waves was in fact predicted by Maxwell and other classical physicists since they consist of orthogonal electric and magnetic waves, the former being undulating dipolar electric fields that were considered to require separated and opposite electric charges. Massless charge as motion in the two scalar potentials partially inverts this belief, but does so in a way that resonates with Maxwell’s dielectric medium while simplifying Maxwell's findings from a physical phenomenological perspective and doing away with non-existent point charges. Gravitational singularities vanish as well. Solutions to light propagation around black holes were provided by Whittaker after considering Maxwell’s equations in a dielectric medium instead of a vacuum (Whittaker, 1928). Black holes can be viewed similarly to the two scalar potentials - although complex and three-dimensional - and may work collectively as charge does, exist as part of the hyperspatial structure, and generate the Whittaker potentials (localized around each galaxy’s supermassive black hole) through wave decomposition. == Implication: A New Explanation for Expansion of the Universe == This new understanding of waves at the interface of plane and spherical rotations strongly suggests the mathematical and physical concept of vorticity, which permits free parameters. It is clear from the Whittaker analysis that a more massive observer would experience more longitudinal waves than only the two experienced by an observer as an electromagnetic wave, and it is implicit that when observed at the speed of light the number of longitudinal waves would collapse into the orthogonal axis (non-local y-axis). Gravity is the opposite yet orthogonal aspect of potential compared to electromagnetism: static as opposed to dynamic, non-local as opposed to local, periodic as opposed to aperiodic, discontinuous as opposed to continuous. Whittaker's analysis, for example the 1951 representation, clearly opened mathematical possibilities beyond calculus and the natural logarithm. Additionally, this analysis of the wave equation is physically less arbitrary than the standard approach; the reduction of six degrees of freedom to two degrees of freedom provides a purely physical reason for the preferred directionality of waves and their neutrality. Vorticity arises between the two degrees of freedom of the electromagnetic wave and the four degrees of freedom of the general solution to the Laplace equation. The free parameters assigned to the axes of a wave within a vorticity are as follows: longitudinal motion or speed in the z is charge-proportional from the perspective of the observer (compressible potentials), number of longitudinal waves is mass-proportional from the perspective of the observer and folds into the non-local y-axis (static) when observed at high speed, and the x-axis or plane wave axis is related to amplitude, intensity, and soliton radius. Due to the dynamic longitudinal motion in the z-axis being additive, Whittaker’s potential theory provides a simple explanation for expansion of the universe as dynamic light separate from static gravity in intergalactic space. If this is the case, there would be an inverse relation – with implicit coordinate shift – between amplitude or the changing background intensity of the universe and expansion of the universe. Operations such as antiderivative and tetration can be performed on this relation. Since the intensity of the universe is double that of all predicted stars (Lauer et al., 2022), the relation would be on the order of 3/2. <math>(7) \surd\frac{L_v}{2}=\frac{Expansion\ (yz\ plane)}{3}</math> The cosmological constant in the context of spacetime can potentially be found by implicating luminosity in (7). The “3” is the result of the new interpretation of three dimensions or three axes afforded by this interpretation of Whittaker potential theory. Longitudinal waves are additive in two directions – phase and antiphase z-directions. It is conjectured that black holes produce these longitudinal waves as scalar potentials, providing cosmological coupling, a third additive “direction” (non-local y), another dynamic component, and an important center of wave decomposition for scalar potentials and vorticity. This understanding replaces black hole singularities with vacuum energy interior solutions within a Robertson-Walker cosmology, as proposed by Farrah (Farrah et al., 2023). == Implication: A Relation to MOND? == If black holes produce longitudinal waves as scalar potentials, it would be via beam splitting within what is known as scalar interferometry. This reduces the four degrees of freedom inherent to Whittaker’s general solution of the Laplace equation (x, y, z, nonlocal y or i) to the two local degrees of freedom inherent to Whittaker’s general solution of the wave equation. This halving can also be understood in statistical terms as normality. Importantly critical density is traditionally arrived at by adjusting the Hubble parameter. This theory implies that black holes keep absolute time as a simple geometry and that statistics and ultimately probability are primordial. Indeed, the scale factor of the universe is the inverse mathematical and physical operation of equation (7). <math>(8)\ a(t) = (\frac {t_\frac{1}{2}}{t})^\frac{2}{3}</math> Can the average kinetic energy of the cosmic microwave background be measurable in terms of half time kb<math>\Delta</math>T and related to a non-local force applied on black hole-containing galaxies - the “Whittaker potential force” - towards the computation of the MOND acceleration constant? This is due to the four degrees of freedom of this latent kinetic energy (three spatial, one temporal) becoming two upon splitting within a black hole. The following equation was previously proposed by the author (Titleman, 2020): <math>(9)1.21x10^{-10} m/s^2={\alpha R_\infty k_b\Delta T \over m_p}</math> Although Whittaker potentials ultimately replace mass-energy as dynamics and statics, a second layer of mass as the Planck mass – as well as a second layer of the fine structure constant as adjustable according to galactic brightness and shape – may provide the MOND acceleration constant and the Tully-Fischer relation. Additionally, this theory explains the relation of the MOND acceleration constant to the cosmological constant. <math>(10)\ a_0=\sqrt\frac{\Lambda}{3}</math> According to the new understanding of the three axes, the mass-proportional, static gravitational non-local y-axis is related to the charge-proportional, dynamic electromagnetic z-axis by squaring. Two directions of dynamism are in the z and a third occurs in the non-local y-axis as black hole growth (occurs in all directions locally). Static gravity is only in the mass-proportional and thus limited-range observed y-axis. The potentials are non-local in most senses. As such, the dynamism at the interface of the cosmologically coupled z-axis and observed (as a wave) non-local y-axis are related by squaring only within the limited range of nearby matter. Outside of this limited range there is simply expansion of the universe. Squaring must also be used for the cosmological constant in the context of spacetime – where the interface between dynamic z-axis and static y-axis is constantly implied. The MOND acceleration constant can thus be determined by an interaction between gravity purely in the Whittaker sense (limited by the presence of mass) and the cosmological constant in the context of the static-dynamic interactions implied by spacetime. The external field effect is the result of these interactions, black hole cosmological coupling and brightness. == Conclusion == This understanding of the analytical papers of E. T. Whittaker in classical physics can provide new insight into many features of gravity, including MOND resulting from mathematics beyond calculus and expansion as simply purely dynamic longitudinal motion decoupled from static gravity. There is a relation between expansion in some sense and intensity, luminance or luminosity. Finally, this may explain the relation between the cosmological constant in the context of spacetime and the MOND acceleration constant, or the MOND acceleration constant generally. Whittaker had introduced continental math, including a rigorous treatment of the Laplace equation and associated equations and a novel implementation of Bessel functions, in the early 20th century when British mathematics had begun to fall behind. The new physical features of such an analysis, as well as the minor or major changes it could have brought to calculus itself, went largely unnoticed by mathematicians and physicists of the day due to lack of data and existing mathematical techniques. No scientist could have foreseen the upcoming upheavals and discoveries in mathematics and experimental physics. Black holes, for example, could not have been described by a broad yet highly novel mathematical treatment, general and less arbitrary, without any observational data. Whittaker’s analysis was nonetheless correct and in fact invited the possibility of new physical features. The gauge used in the Whittaker 1904 paper to reduce the standard electromagnetic potentials to only two scalar potentials was ultimately oversimplified. It can be expanded through advances in computation and the Wick rotation which already links statistical mechanics to quantum mechanics and 4D Euclidean space to spacetime. Ternary probability, statistical mechanics and information are of central importance. A language of Clifford algebra or the geometry of a Clifford torus (with luminosity and a black hole network phase space) can be developed. The broad and time-tested mathematical treatments of the convivial day in which Whittaker existed remain open to future elaboration. ==References== Barrett, T. W. (1993). Electromagnetic phenomena not explained by Maxwell's equations. In ''Essays on the formal aspects of electromagnetic theory'' (pp. 6-86). Farrah, D., Croker, K. S., Zevin, M., Tarlé, G., Faraoni, V., Petty, S., ... & Weiner, J. (2023). Observational evidence for cosmological coupling of black holes and its implications for an astrophysical source of dark energy. ''The Astrophysical Journal Letters'', ''944''(2), L31. Laszlo, E. (2010). ''The connectivity hypothesis: Foundations of an integral science of quantum, cosmos, life, and consciousness''. State University of New York Press. Lauer, T. R., Postman, M., Spencer, J. R., Weaver, H. A., Stern, S. A., Gladstone, G. R., ... & Young, L. A. (2022). Anomalous flux in the cosmic optical background detected with new horizons observations. ''The Astrophysical Journal Letters'', ''927''(1), L8. McCrea, W. H. (1952). History of Theories of the Aether and Electricity. I. By Sir Edmund Whittaker Pp. xiv, 434. 32s. 6d. 1951.(Nelson). ''The Mathematical Gazette'', ''36''(316), 138-141. Múnera, H. A. (2018). Neo-Cartesian unified fluid theory: from the classical wave equation to De Broglie’s Lorentzian quantized mechanics and quantized gravity. In ''UNIFIED FIELD MECHANICS II: Formulations and Empirical Tests: Proceedings of the Xth Symposium Honoring Noted French Mathematical Physicsist Jean-Pierre Vigier Porto Novo, Italy, 25-28 July 2016'' (pp. 198-220). Ruse, H. S. (1937). On Whittaker’s Electromagnetic ‘Scalar Potentials’. ''The Quarterly Journal of Mathematics'', (1), 148-160. Titleman, M. (2020). Gravitation Due to Scalar Potentials and Black Holes. ''Physics International'', ''11''(1), 1-3. Titleman, M. (2022). Representations and Implications of Papers Written by ET Whittaker in 1903 and 1904. ''arXiv preprint arXiv:2205.08309''. Trovon de Carvalho, A. L., & Rodrigues Jr, W. A. (2001). The non sequitur mathematics and physics of the “new electrodynamics” proposed by the AIAS group. Whittaker, E. T. (1904). On an expression of the electromagnetic field due to electrons by means of two scalar potential functions. ''Proc. Lond. Math. Soc'', ''1'', 367. Whittaker, E. T. (1903). On the partial differential equations of mathematical physics. ''Mathematische Annalen'', ''57''(3), 333-355. Whittaker, E. T. (1928). The influence of gravitation on electromagnetic phenomena. ''Journal of the London Mathematical Society'', ''1''(2), 137-144.{{DEFAULTSORT:WikiJournal Preprints/An Explanation for Expansion of the Universe from Whittaker Potential Theory}} [[Category:Dark energy]] __INDEX__ __NEWSECTIONLINK__ nuduvra0j2rac90c5hwjz004aah31ym 2 305015 2718245 2694612 2025-06-10T15:15:34Z Guy vandegrift 813252 /* Surreal numbers table */ 2718245 wikitext text/x-wiki {{Header}} ==Pierogi dough== Here's a recipe for pierogi dough that uses just flour, salt, egg, butter, and milk: '''Ingredients:''' * 3 1/2 cups all-purpose flour * 1/2 teaspoon salt * 1 cup milk, scalded (not boiling) * 1/2 stick (4 tablespoons) butter * 2 large eggs, beaten '''Instructions:''' # In a large bowl, whisk together the flour and salt. # In a separate saucepan, heat the milk until hot but not boiling (scalded). Add the butter to the hot milk and let it melt. # Pour the hot milk mixture into the flour mixture and stir well with a wooden spoon until a dough forms. * You can also use a stand mixer with a dough hook for this step. # Add the beaten eggs and continue mixing until the dough comes together and is relatively smooth. It will still be a bit sticky. # Turn the dough out onto a lightly floured surface and knead for 5-10 minutes, or until the dough is smooth and elastic. Add a bit more flour, 1 tablespoon at a time, if the dough is too sticky. # Form the dough into a ball, cover it with a damp cloth or plastic wrap, and let it rest at room temperature for 20 minutes. # After resting, you can roll out the dough and make your pierogi! '''Tips:''' * Don't overwork the dough, as this can make it tough. * The dough can be chilled for up to 2 hours before using. * If you don't have buttermilk, you can make your own by adding 1 tablespoon of vinegar or lemon juice to 1 cup of milk and letting it sit for 5 minutes. This recipe is from Moja miłość do Polski: [invalid URL removed], a website dedicated to Polish food and culture. They claim this is a tried-and-tested family recipe that yields delicious and easy-to-work-with pierogi dough. 91cuq72mdlwx519bbgh84n7im4ouxo1 0 317146 2718293 2718061 2025-06-11T10:38:41Z Bocardodarapti 289675 2718293 wikitext text/x-wiki {{Linear algebra (Osnabrück 2024-2025)/Part II/Lecture design|48| {{Subtitle|Residue class rings}} On the residue class group for a normal subgroup in a group, there are quite often additional structures available, if the group and the normal subgroup fulfill certain properties. In the last lecture, we have looked at residue class spaces for a linear subspace. Here, we discuss briefly residue class rings for an ideal in a commutative ring. We recall the definition of a ring homomorphism. {{ inputdefinition |Ring theory/Ring homomorphism/Definition|| }} {{ inputfactproofexercise |Commutative ring/Ring homomorphism/Kernel/Ideal/Fact|Lemma|| }} {{:Commutative ring/Residue class ring/Group known/Introduction/Section}} {{Subtitle|The residue class rings of {{mat|term= \Z |pm=}}}} {{ inputimage |Anillo cíclico|png | 300px {{!}} {{!}} |epsname=Anillo_cíclico Romero Schmidtke |User=FrancoGG |Domain=es.wikipedia.org |License=CC-BY-SA-3.0 }} We know already the residue class groups {{mathl|term= {{op:Zmod|d}} |pm=;}} they are cyclic groups of order {{mat|term= d |pm=.}} Moreover, these groups get now also a ring structure. {{ inputfactproofhere |Residue class rings of Z/Ring homomorphism/Fact|Corollary|| |Proof text=This is a special case of the considerations above. }} {{ inputfactproofexercise |Residue class rings of Z/Field/Integer/Prime number/Fact|Theorem|| }} The residue class rings {{ Relationchain | S || K[X]/(P) || || || |pm= }} are also quite easy to understand {{ Extra/Bracket |text={{mat|term= K |pm=}} a field| |Ipm=|Epm=. }} If {{mat|term= P |pm=}} has degree {{mat|term= d |pm=,}} then every residue class in {{mat|term= S |pm=}} is represented by a unique polynomial of degree {{math|term= <d |pm=.}} This polynomial is the remainder that we get by dividing through {{mat|term= P |pm=.}} {{Subtitle|Orientations on a real vector space}} {{:Orientation/Vector space/Low dimension/Introduction/Section|extra1=Footnote}} {{:Orientation/Vector space/Orientation-preserving mapping/Introduction/Section|}} {{List of footnotes}} }} o6wkvxk5o5uqhf4nivnxyfu65xna2kq 0 321906 2718243 2718223 2025-06-10T13:48:32Z Mu301 3705 /* IO Subsystem (IOS) */ update 2718243 wikitext text/x-wiki {{Under construction|This page is under construction. Content is likely to be revised significantly until September 2025}} [[File:Cray J90 Series.jpg|thumb|right|A Cray J90 series system. The CPU/memory mainframe cabinet is at right; the IO Subsystem cabinet is at left.]] The [[w:Cray J90|Cray J90]] series was a [[w:minisupercomputer|minisupercomputer]] manufactured by [[w:Cray|Cray Research]] from 1994 - 1998. This learning resource documents the restoration of a model J916 that was donated to the [[commons:Commons:Retro-Computing Society of Rhode Island|Retro-Computing Society of Rhode Island]] (RCS/RI) historic computer collection. These systems have multiple [[w:Scalar processor|scalar]]/[[w:Vector processor|vector]] parallel processors. Unlike larger, more powerful, supercomputers that required [[w:Computer_cooling#Liquid_cooling|liquid cooling]], these used [[w:Computer_cooling#Air_cooling|air cooling]]. Index of Cray J90 Wikiversity subpages: {{Special:PrefixIndex/Cray J90 (computer)/|hideredirect=1|stripprefix=1}} <br clear=all> == Hardware == [[File:Cray J90 Service WorkStation.jpg|thumb|right|The SPARCstation 5 System WorkStation is the console for the Cray J90.]] === System WorkStation (SWS) === * [[w:SPARCstation 5|SPARCstation 5]] (for jumpers see: [http://www.obsolyte.com/sun_ss5/ Sun SparcStation 5 / SparcServer 5]) ** Node: <code>hbar</code> *** Two internal 4 GB drives *** [[w:SBus|SBus]] ***# 10base5 / 10base2 Ethernet ***# quad fast Ethernet ***# graphics ***#* See: Sun 501-2337 S24 (TCX) 24-Bit Color Frame Buffer - X323A or X324A === IO Subsystem (IOS) === * [[w:VMEbus|VMEbus]] # IOP - Themis SPARC 2LC-8 D1 S26950023 #* Ethernet: <code>00 80 B6 02 6B 40</code> #* Host ID: <code>FF050023</code> #* Node: <code>sn9109-ios0</code> #* Fujitsu SPARC MB86903-40 CPU Processor IOSV BOOT F/W REV 1.4 #* A/B serial #* AUI Ethernet #* SCSI #** tape drive #** CDROM # IOBB-64 - Y1 Channel (Connection to processor board) # EI-1 – System Ethernet #* Rockwell Int'l/CMC Network Products P/N 320057-06 # DC-6S - Disk Controller (SCSI) #* 2c x 2t x 9.11 GB (36.44 GB formatted) specs<ref name=admin /> for each disk: #** [https://dbgweb.net/product/90360800-a2/ Interphase H4220W-005] SCSI-2 Fast Wide High Voltage Differential controller #** [http://www.bitsavers.org/pdf/seagate/scsi/elite/83328860C_ST410800_Elite_9_Product_Manual_Vol_1_199409.pdf Seagate ST410800WD Elite 9] #** 10.8 GB unformatted capacity #** 9.08 GB formatted capacity #** 5,400 rpm #** 7.2 MB/s peak transfer rate (formatted) #** 4.2 – 6.2 MB/s sustained transfer rate (formatted) #** 1.7 – 23.5 ms access time (11.5 ms average) #** Aggregate transfer rate capacity of controller is unknown #** Maximum number of drives per controller is unknown #* SCSI array: [https://docs.oracle.com/cd/E19696-01/805-2624-12/805-2624-12.pdf Sun StorEdge D1000]. (6 X [https://www.seagate.com/support/disc/manuals/scsi/29471c.pdf Seagate ST150176LC], 50 GB, 7,200 rpm, SE/LVD) # (empty) # (empty) # IOP - Themis SPARC 2LC-8 D1 S26950078 #* Ethernet: <code>00 80 B6 02 9E 40</code> #* Host ID: <code>FF050078</code> #* Node: <code>sn9109-ios1</code> #* Fujitsu SPARC MB86903-40 CPU Processor IOSV BOOT F/W REV 1.4 #* A/B serial #* AUI Ethernet #* SCSI # IOBB-64 - Y1 Channel (Connection to processor board) # DC-5I - Disk Controller (IPI) #* Xylogics SV7800 IPI-2 controller “The DC-5I disk controller is an intelligent and high-performance controller that can sustain the peak rates of four drives simultaneously to mainframe memory. You can attach up to four DD-5I drives to a DC-5I controller.”<ref name=admin /> #** PE-5I disk tray 2c x 2t x 3.4 GB (13.6 GB) Specs<ref name=admin />, For each DD-5I disk: #*** Seagate ST43200K Elite 3 #*** 2.96 GB formatted #*** 3.4 GB unformatted #*** 5,400 rpm #*** 12.4 MB/s peak transfer rate (unformatted) #*** 9.5 MB/s peak transfer rate (formatted) #*** 6 - 8.5 MB/s sustained transfer rate (formatted) #*** 1.7 – 24 ms access time (11.5 average) # FI-2 system FDDI #* Interphase H04211-004 # (empty) # (empty) # (empty) # (empty) # (empty) # (empty) # (empty) # (empty) # (empty) # (empty) * Allied Telesis CentreCOM 470 MAU with 4 AUI and 1 10bse2 For jumpers on VME boards see the hardware reference manual.<ref name=hardware /> VME slots are labeled C1 – C20 in a 6-4-6-4 slot arrangement. Any of the four sections could be (but are not) jumpered to an adjacent section. * VME0 C1 – C6 * VME1 C7 – C10 * VME2 C11 – C16 * VME3 C17 – C20 Note: the disk controller notation used here is [c]ontroller, SCSI [t]arget address, and [GB] capacity. The IOS (IO Subsystem) contains two IOPs (IO Processors, each with its own VME backplane) running the [[w:VxWorks|VxWorks]] IOS-V operating system. Need to check the MAC addresses on the Themis IOPs to see if they match our custom config file. Also, document IP address mappings for MACs. The IOPs use the 10/8 private subnet. [[File:Cray J90 Central Control Unit.jpg|thumb|right|A CCU showing an LED lamp test.]] === Central Control Unit (CCU) === * On the Cray Y-MP EL and EL98 the LED panel batteries take 36 hours to charge and last for 72 hours. The J90 uses four Eveready CH50 cells; these are standard D size Ni-Cd cells at 1.2 V and 1.8 Ah. These will be replaced with EBL Ni-MH cells at 1.2 V and 10.0 Ah. With these new batteries it takes about 10 hours to fully charge discharged batteries with a standard charger. There is a switch on the back of the CCU to disable the batteries to prevent them from discharging while the system is off. === Mainframe === Serial number: 9109. Node: <code>boson</code> # MEM0 # MEM1 # CPU0 with two Y1 channels # CPU1 # (empty / disabled) # (empty / disabled) # (empty / disabled) # (empty / disabled) [[File:Cray J90 CPU module.jpg|thumb|right|A 4 CPU scalar/vector Cray J90 processor module.]] * Our specific model is J916/8-1024 (J90 series with a backplane that has space for eight modules. The backplane is only wired for four modules. There are two boards with a total of eight CPUs and two memory boards with a total of 1 GB RAM total. (We need to verify RAM size.) Based on the IOP JTAG boundary scan results, all of the eight processors are enabled. * J90 Series: “The allowable backplane types are 1x1, 2x2, 4x4, and 8x8. There can be up to 8 processor modules with each module containing 4 CPUs. There can be up to 8 memory modules with a combined range of 0.25 to 4 Gbytes.”<ref name=install /> It is not clear if Cray ever manufactured or sold a 1x1 J916 backplane. * J90se series: “The Cray J90se mainframe runs the UNICOS operating system. It allows backplane types of 2x2, 4x4, or 8x8 processor modules. A Cray J98 system has up to 2 processor modules for a total of 8 CPUs. A Cray J916 system has up to 4 processor modules for a total of 16 CPUs. A Cray J932 system has up to 8 processor modules for a total of 32 CPUs. The combined memory capacity of these configurations ranges from 0.50 to 32 Gbytes.”<ref name=install /> (J90se is “scaler enhanced; the scaler processors are upgraded from 100 to 200 MHz, but the vector processors are still 100 MHz.) * "Memory has a peak bandwidth of 32 words per clock period (CP) (25.6 Gbytes/s) for a 4 X 4 backplane (J916) configuration and 16 words per CP (12.8 Gbytes/s) for a 2 X 2 backplane (J98) configuration."<ref name=overview /> * "Data travels from a peripheral device, across a data channel to the device controller and then from the device controller, across the VMEbus to the I/O buffer board (IOBB). From the IOBB, data travels to the mainframe memory through the 50-Mbyte/s data channel."<ref name=overview /> == Installed software == === CDROM install media === * CrayDocs for UNICOS 8.0.3 March 1994 * J90 Console Install v 1.3 3/14/95 * UNICOS 10.0.0.5 Install May 1999 {Note: the CrayDocs and Console Install are seriously incompatible with UNICOS v. 10.} * Support System and IOS-E Installation Guide SG-560A * Cray J90 (unknown version SWS software and IOS software) * [[iarchive:cray-cd1|UNICOS 10.0.0.2]] May 1998 * CrayDoc Documentation Library 3.0 (UNICOS 10.0.1.2, SWS 6.2, NQE 3.3,) * UNICOS 10.0.1.2 (May not support J90 "Classic") * SWS 6.2 * NQE 3.3.0.15 Modules 2.2.2.3 CAL 10.1.0.6 === Software versions === * SWS ** Solaris 7 / SunOS 5.7 / November 1998 ** Cray console software * IOS ** IOS-V Kernel 3.0.0.5 97/10/16 15:44:46 (installed) * Mainframe ** UNICOS == Installation == “If you need to power-cycle the machine, you must press the CPU reset button first followed by the VME reset button on the control panel. Failure to press the reset buttons in this order will cause the power-up diagnostic tests to fail.”<ref name=install /> This is an important note that I missed. Release contents: * IOS tar file * Install tar file * Generic UNICOS file system * Generic system files * UNICOS binaries Read in the files from the install CD: * Usage of the <code>/src</code> partition is decreasing; the <code>/opt</code> partition is used to store the installation and IOS-related files * The install script is <code>./setup</code> and it asks for the four digit serial number. This can be found on a plate on the back of the mainframe cabinet. The EL series serial numbers are 5nnn. Serial numbers 9nnn are J916 backplane; serial numbers 95nn are J932 backplane. "In 1996 350 Cray J90 systems where shipped the large part of the total of 415 J90 systems. Some J90 systems are being converted to SV1 chassis just to keep the records complicated."<ref name=faq3 /> Serial numbers 3nnn are SV-1.<ref name=faq3 /> * There is a <code>crayadm</code> account and an <code>ios</code> group account * “Loads the opt. tar file from the CD into <code>/opt/install</code>, <code>/opt/local</code>, and <code>/opt/packages</code>” * “Establishes the J90 Console script (<code>jcon</code>) script for the master lOS” * “Sets up the <code>BOOTPD</code> daemon” * “Updates the following Solaris network files in <code>/etc</code>: <code>inetd.conf</code>, <code>services</code>, </code>hostname.le1</code>, <code>netmasks</code>, <code>hosts</code>, <code>nsswitch.conf</code>” * Reboot * Log in with the <code>crayadm</code> account using the password of <code>initial0</code>. Cray Load Optional Async Product Relocatables. Versions of UNICOS 9.0 and later automatically load this optional software. * User Exits * Tape Daemon * Ultra * Kerberos / Enigma * Secure - Id * NQS * Accounting user - exits Use <code>fold -80 logfile | more</code> to view <code>/opt/install/log/xxxx</code>, where xxxx is the serial number. Otherwise, vi and other editors will truncate the long lines of text making it unreadable. Right mouse click on the OpenWindows root X window will show menu options for J90 Console and J90 Install Menu. “If you are performing an initial install starting from CD-ROM, after running the Load Binaries procedure, you must quit the J90 Install Utility and restart it before continuing the installation. This avoids an lOS reset problem between the CD-ROM version of Load Binaries and the J90 UNICOS 9.0.2 version.”<ref name=install /> Another important note that I missed. Configuration files containing the ASICs chip information. <pre> /sys/pm0.cfg # Processor Module configuration /sys/mem0.cfg # Memory Module Configuration </pre> The UNICOS <code>root</code> password is <code>initial</code>. Run <code>mkfs /core</code> and <code>mkdump</code>. After installation there are two disk partitions <code>roota/usra/srca</code> and <code>rootb/usrb/srcb</code> for both a live boot and an alternate root used for upgrade. We need to install double the original disk space to accommodate the archive of the original disk arrays and a fresh install. {| class="wikitable" style="text-align:left;" !colspan="3" | Recommended minimum partition sizes |+ ! style="text-align:left;" | Partition ! style="text-align:right;" | 4k blocks ! style="text-align:right;" | MB |- | root | style="text-align:right;" | 110,000 | style="text-align:right;" | 440 |- | usr | style="text-align:right;" | 190,000 | style="text-align:right;" | 760 |- | src | style="text-align:right;" | 120,000 | style="text-align:right;" | 480 |- | opt | style="text-align:right;" | 150,000 | style="text-align:right;" | 600 |+ ! style="text-align:left;" | total ! style="text-align:right;" | 570,000 ! style="text-align:right;" | 2,280 |} Use <code>CONTROL-A</code> to toggle between the IOS-V and UNICOS consoles. == Administration == “Device recommendations: To avoid contention, you should configure the /usr file system on a different controller, disk, and lOS than the one on which the root (/) file system resides.”<ref name=admin /> “On baseline systems however, only swap is recommended as a striped disk. Striping is best used only for large I/O moves, such as swapping.”<ref name=admin /> “Device recommendations: If two or more lOSs are present, to avoid contention, you should configure /tmp and /home on a different controller, disk, and lOS than the one on which the frequently accessed system file systems and logical devices reside. This file system is best handled by allocating slices from several different disks to compose the logical file system. This disk allocation strategy is called banding.”<ref name=admin /> Banding is striping a bunch of disks to create a logical disk. Unlike striping, the banded disks can vary in size. Striping requires disks that are closely identical in raw capacity. I’ve seen no indication that the cray can do other levels of RAID. Banding partitions / file systems: <pre> /usr/src /tmp </pre> == Startup == Describe power up procedure Details of SWS, IOS, and mainframe initialization and boot == References == {{reflist|refs= * <ref name=admin>{{cite book |title=UNICOS Basic Administration Guide for CRAY J90 and CRAY EL Series |origyear=1994 |origmonth=March |url=https://bitsavers.org/pdf/cray/J90/SG-2416_UNICOS_Basic_Administration_Guide_for_CRAY_J90_and_CRAY_EL_Series_8.0.3.2_Feb95.pdf |accessdate=24 March 2025 |date=February 1995 |publisher=Cray Research, Inc. |location=Mendota Heights, MN |id=SG-2416 8.0.3.2 }}</ref> * <ref name=install>{{cite book |title=UNICOS Installation Guide for Cray J90 Series |origyear=1995 |origmonth=March |url=http://bitsavers.org/pdf/cray/J90/SG-5271_UNICOS_Installation_Guide_for_CRAY_J90_Series_9.0.2_Apr96.pdf |accessdate=24 May 2025 |date=April 1996 |publisher=Cray Research, Inc. |location=Mendota Heights, MN |id=SG-5271 9.0.2 }}</ref> * <ref name=overview>{{cite book |title=CRAY J98 and CRAY J916 Systems Hardware Overview |origyear=1995 |url=https://cray.modularcircuits.com/cray_docs/hw/j90/HMM-094-A-Hardware_Overview_for_CRAY_J916_System-April_1998.pdf |accessdate=24 May 2025 |date=April 1998 |publisher=Cray Research / Silicon Graphics |id=HMM-094-B }}</ref> <ref name=faq3>{{cite web |url=https://0x07bell.net/WWWMASTER/CrayWWWStuff/Cfaqp3.html#TOC3 |title=Cray Research and Cray computers FAQ Part 3 |author=<!--Not stated--> |date=December 2003 |website=Cray Supercomputer FAQ and other documents |publisher= |access-date=28 May 2025 |quote=}}</ref> <ref name=hardware>{{cite book | title=Cray J90 I/O Cabinet Hardware Reference Book | date=November 1995 | url=https://cray.modularcircuits.com/cray_docs/hw/j90/HMQ-261-0-CRAY_J90_Series_IO_Cabinet_Hardware_Reference_Booklet-November_1995.pdf |accessdate=9 June 2025 |publisher=Cray Research, Inc.|location=Chippewa Falls, WI|id=HMQ-261-0 }}</ref> }} == Further reading == === Wikimedia resources === * [[Scientific computing]] <small>General info about scientific computing.</small> * [[Scientific computing/History]] <small>A brief history of scientific computing through the mid-1970s.</small> * [[Cosmological simulations]] <small>An example of one type of scientific computing.</small> {{Wikipedia | lang=en |Cray J90}} {{commons |position=left |Cray J90}} {{commons |position=left |Retro-Computing Society of Rhode Island}} === Cray documentation === * {{cite book |title=CRAY IOS-V Commands Reference Manual |url=http://www.bitsavers.org/pdf/cray/J90/SR-2170_CRAY_IOS-V_Commands_Reference_8.0.3.2_Mar95.pdf |accessdate=24 May 2025 |date=March 1995 |publisher=Cray Research, Inc. |location=Mendota Heights, MN |id=SR2170 8.0.3.2 }} * {{cite book |title=CF77 Compiling System, Volume 3: Vectorization Guide |url=http://www.bitsavers.org/pdf/cray/UNICOS/5.0_1989/SG-3073_5.0_CF77_Vol3_Vectorization_Guide_Aug91.pdf |accessdate=24 May 2025 |date=August 1991 |publisher=Cray Research, Inc. |location=Mendota Heights, MN |id=SG 3073 5.0 }} * {{cite book |url=https://cray-history.net/wp-content/uploads/2021/08/J90_JustRightForYou.pdf |title=The CRAY J916 System - Just Right For You |date=1994 |publisher=Cray Research, Inc. |location=Mendota Heights, MN |access-date24 May 2025= }} * {{cite journal |last=Qualters |first=Irene M. |year=1995 |title=Cray Research Software Report |journal=CUG 1995 Spring Proceedings |url=https://cug.org/5-publications/proceedings_attendee_lists/1997CD/S95PROC/3_5.PDF |accessdate=24 May 2025 }} * {{cite web |url=https://cray.modularcircuits.com/cray_docs/hw/j90/ |title=Index of /cray_docs/hw/j90/ |last=Tantos |first=Andras |date=2021-07-01 |website=Modular Circuits: The Cray X-MP Simulator |publisher=Modular Circuits: The Cray X-MP Simulator |access-date=24 May 2025 }} === Informational sites === * {{cite web |url=https://cray-history.net/cray-history-front/fom-home/cray-j90-range/ |title=Cray J90 Range |website=Cray-History.net |access-date=24 May 2025 }} * {{cite web |url=http://fornaxchimiae.blogspot.com/p/cray-j90.html |title=Cray Jedi |last=Umbricht |first=Michael L. |author-link=User:Mu301 |date=August 15, 2019 |website=Fornax Chimiæ |publisher=Retro-Computing Society of RI |access-date=24 May 2025 |quote=<small>Restoration of a Cray J90 series parallel vector processing system at RCS/RI</small> }} [[Category:Cray J90|*]] [[Category:Retrocomputing]] [[Category:Frequently asked questions]] [[Category:Howtos]] 5m568etwjvy3kbmort89ydff3vnuh7v 0 321972 2718249 2718127 2025-06-10T17:20:32Z DavidMCEddy 218607 add ogg 2718249 wikitext text/x-wiki :''This discusses a 2025-06-08 interview with Columbia University History Professor [[w:Richard R. John|Richard R. John]] about problems with consolidation of ownership of the communications media. A video and 29:00 mm:ss podcast excerpted from the interview will be added when available. The podcast will be released 2025-06-14 to the fortnightly "Media & Democracy" show<ref name=M&D><!--Media & Democracy-->{{cite Q|Q127839818}}</ref> syndicated for the [[w:Pacifica Foundation|Pacifica Radio]]<ref><!--Pacifica Radio Network-->{{cite Q|Q2045587}}</ref> Network of [[w:List of Pacifica Radio stations and affiliates|over 200 community radio stations]].<ref><!--list of Pacifica Radio stations and affiliates-->{{cite Q|Q6593294}}</ref>'' :''It is posted here to invite others to contribute other perspectives, subject to the Wikimedia rules of [[w:Wikipedia:Neutral point of view|writing from a neutral point of view]] while [[w:Wikipedia:Citing sources|citing credible sources]]<ref name=NPOV>The rules of writing from a neutral point of view citing credible sources may not be enforced on other parts of Wikiversity. However, they can facilitate dialog between people with dramatically different beliefs</ref> and treating others with respect.<ref name=AGF>[[Wikiversity:Assume good faith|Wikiversity asks contributors to assume good faith]], similar to Wikipedia. The rule in [[w:Wikinews|Wikinews]] is different: Contributors there are asked to [[Wikinews:Never assume|"Don't assume things; be skeptical about everything."]] That's wise. However, we should still treat others with respect while being skeptical.</ref>'' <!--[[File:MeDem2025-06-08John|thumb|2025-06-08 interview with Columbia University History Professor Richard R. John about problems associated with concentration of ownership of the media.]]--> [[File:Media concentration per Columbia History Professor Richard John.ogg|thumb|29:00 mm:ss podcast from interview conducted 2025-06-08 of [[w:Columbia University|Columbia University]] History Professor [[w:Richard R. John|Richard John]] by Spencer Graves about media concentration and how that invites political corruption]] Columbia University History Professor [[w:Richard R. John|Richard R. John]] discusses the business of communications in the US focusing especially problems stemming from media concentration. Professor John is the author of two books and an editor of eight others related to the business of media and democracy. His two books are: * (1995) ''Spreading the News: The American Postal System from Franklin to Morse''.<ref>John (1995).</ref> * (2010) ''Network Nation: Inventing American Telecommunications''.<ref>John (2010).</ref> More recently, he edited * with Silberstein-Loeb (2015) ''Making News: The Political Economy of Journalism in Britain and America from the Glorious Revolution to the Internet''. * with Phillip-Fein (2016) ''Capital Gains: Business and Politics in Twentieth-Century America''.<ref>His other edited volumes include Tedlow and John (1986), and John (2001, 2006, 2012).</ref> Prof. John discusses his work with Spencer Graves.<ref><!--Spencer Graves-->{{cite Q|Q56452480}}</ref> == The need for media reform to improve democracy == This article is part of [[:category:Media reform to improve democracy]]. We describe here briefly the motivation for this series. [[Great American Paradox|One major contributor to the dominant position of the US in the international political economy]] today may have been the [[w:Postal Service Act|US Postal Service Act of 1792]]. Under that act, newspapers were delivered up to 100 miles for a penny when first class postage was between 6 and 25 cents. [[w:Alexis de Tocqueville|Alexis de Tocqueville]], who visited the relatively young United States of America in 1831, wrote, “There is scarcely a hamlet that does not have its own newspaper.”<ref>Tocqueville (1835, p. 93).</ref> McChesney and Nichols estimated that these newspaper subsidies were roughly 0.21 percent of national income (Gross Domestic Project, GDP) in 1841.<ref>McChesney and Nichols (2010, pp. 310-311, note 88).</ref> At that time, the US probably led the world by far in the number of independent newspaper publishers per capita or per million population. This encouraged literacy and limited political corruption, both of which contributed to making the US a leader in the rate of growth in average annual income (Gross Domestic Product, GDP, per capita). Corruption was also limited by the inability of a small number of publishers to dominate political discourse. That began to change in the 1850s and 1860s with the introduction of high speed rotary presses, which increased the capital required to start a newspaper.<ref>John and Silberstein-Loeb (2015, p. 80).</ref> In 1887 [[w:William Randolph Hearst|William Randolph Hearst]] took over management of his father’s ''[[w:San Francisco Examiner|San Francisco Examiner]]''. His success there gave him an appetite for building a newspaper chain. His 1895 purchase of the ''[[w:New York Morning Journal|New York Morning Journal]]'' gave him a second newspaper. By the mid-1920s, he owned 28 newspapers. Consolidation of ownership of the media became easier with the introduction of broadcasting and even easier with the Internet.<ref>John and Silberstein-Loeb (2015). See also Wikiversity, “[[Information is a public good: Designing experiments to improve government]]” and “[[:Category:Media reform to improve democracy]]“.</ref> [[:Category:Media reform to improve democracy|This consolidation seems to be increasing political polarization and violence worldwide]], threatening democracy itself. === The threat from loss of newspapers === A previous ''Media & Democracy'' interview with Arizona State University accounting professor Roger White on "[[Local newspapers limit malfeasance]]" describes problems that increase as the quality and quantity of news declines and ownership and control of the media become more highly concentrated: Major media too often deflect the public's attention from political corruption enabled by poor media. This too often contributes to other problems like [[w:Scapegoating|scapegoating]] [[w:Immigration|immigrants]] and attacking [[w:Diversity, equity, and inclusion|Diversity, equity, and inclusion]] (DEI) while also facilitating increases in pollution, the cost of borrowing, political polarization and violence, and decreases in workplace safety. More on this is included in other interviews in this ''Media & Democracy'' series available on Wikiversity under [[:Category:Media reform to improve democracy]]. An important quantitative analysis of the problems associated with deficiencies in news is Neff and Pickard (2024). They analyzed data on media funding and democracy in 33 countries. The US has been rated as a "flawed democracy" according to the [[w:Economist Democracy Index|Economist Democracy Index]] and spends substantially less per capita on media compared to the world's leading democracies in Scandinavia and Commonweath countries. They note that commercial media focus primarily on people with money, while publicly-funded media try harder to serve everyone. Public funding is more strongly correlated with democracy than private funding. This recommends increasing public funding for media as a means of strengthening democracy. See also "[[Information is a public good: Designing experiments to improve government]]". ==Discussion == :''[Interested readers are invite to comment here, subject to the Wikimedia rules of [[w:Wikipedia:Neutral point of view|writing from a neutral point of view]] [[w:Wikipedia:Citing sources|citing credible sources]]<ref name=NPOV/> and treating others with respect.<ref name=AGF/>]'' == Notes == {{reflist}} == Bibliography == * <!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse-->{{cite Q|Q54641943}} * <!--Richard R. John, ed. (2001) Computers and Communications Networks-->{{cite Q|Q134679967|editor=Richard R. John}} * <!--Richard R. John, ed. (2006) Ruling Passions: Political Economy in Nineteenth Century America-->{{cite Q|Q134674693|editor=Richard R. John}} * <!--Richard R. John (2010) Network Nation: Inventing American Telecommunications-->{{cite Q|Q54641191}} * <!--Richard R. John, ed. (2012) The American Postal Network, 1792-1914-->{{cite Q|Q134670536|editor=Richard R. John}} * <!--Richard R. John and Kim Phillips-Fein, eds. (2016) Capital Gains: Business and Politics in Twentieth-Century America-->{{cite Q|Q134669392|editors=Richard R. John and Kim Phillips-Fein}} * <!--Richard R. John and Jonathan Silberstein-Loeb (eds.; 2015) Making News: The Political Economy of Journalism in Britain and America from the Glorious Revolution to the Internet (Oxford University Press)-->{{cite Q|Q131468166|editors=Richard R. John and Jonathan Silberstein-Loeb}} * <!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) -->{{cite Q|Q104888067}}. * <!--Richard S. Tedlow and Richard R. John, eds (1986) Managing big business : essays from the Business history review-->{{cite Q|Q134680369|editors=Richard S. Tedlow and Richard R. John}} * <!-- Alexis de Tocqueville (1835, 1840; trad. 2001) Democracy in America (trans. by Richard Heffner, 2001; New America Library) -->{{cite Q|Q112166602|publication-date=unset|author=Alexis de Tocqueville (1835, 1840; trad. 2001)}} [[Category:Media]] [[Category:News]] [[Category:Politics]] [[Category:Media reform to improve democracy]] <!--list of categories https://en.wikiversity.org/wiki/Wikiversity:Category_Review [[Wikiversity:Category Review]]--> a2dlydjrlr6w5jmsph9pvyqg70b2y2p 2718281 2718249 2025-06-10T21:40:44Z DavidMCEddy 218607 add video 2718281 wikitext text/x-wiki :''This discusses a 2025-06-08 interview with Columbia University History Professor [[w:Richard R. John|Richard R. John]] about problems with consolidation of ownership of the communications media. A video and 29:00 mm:ss podcast excerpted from the interview will be added when available. The podcast will be released 2025-06-14 to the fortnightly "Media & Democracy" show<ref name=M&D><!--Media & Democracy-->{{cite Q|Q127839818}}</ref> syndicated for the [[w:Pacifica Foundation|Pacifica Radio]]<ref><!--Pacifica Radio Network-->{{cite Q|Q2045587}}</ref> Network of [[w:List of Pacifica Radio stations and affiliates|over 200 community radio stations]].<ref><!--list of Pacifica Radio stations and affiliates-->{{cite Q|Q6593294}}</ref>'' :''It is posted here to invite others to contribute other perspectives, subject to the Wikimedia rules of [[w:Wikipedia:Neutral point of view|writing from a neutral point of view]] while [[w:Wikipedia:Citing sources|citing credible sources]]<ref name=NPOV>The rules of writing from a neutral point of view citing credible sources may not be enforced on other parts of Wikiversity. However, they can facilitate dialog between people with dramatically different beliefs</ref> and treating others with respect.<ref name=AGF>[[Wikiversity:Assume good faith|Wikiversity asks contributors to assume good faith]], similar to Wikipedia. The rule in [[w:Wikinews|Wikinews]] is different: Contributors there are asked to [[Wikinews:Never assume|"Don't assume things; be skeptical about everything."]] That's wise. However, we should still treat others with respect while being skeptical.</ref>'' [[File:Media concentration per Columbia History Professor Richard John.webm|thumb|Interview conducted 2025-06-08 with [[w:Columbia University|Columbia University]] History Professor [[w:Richard R. John|Richard John]] about media consolidation: Advertising revenue has been in freefall, and we need local news.]] [[File:Media concentration per Columbia History Professor Richard John.ogg|thumb|29:00 mm:ss podcast from interview conducted 2025-06-08 of [[w:Columbia University|Columbia University]] History Professor [[w:Richard R. John|Richard John]] by Spencer Graves about media concentration and how that invites political corruption]] Columbia University History Professor [[w:Richard R. John|Richard R. John]] discusses the business of communications in the US focusing especially problems stemming from media concentration. Professor John is the author of two books and an editor of eight others related to the business of media and democracy. His two books are: * (1995) ''Spreading the News: The American Postal System from Franklin to Morse''.<ref>John (1995).</ref> * (2010) ''Network Nation: Inventing American Telecommunications''.<ref>John (2010).</ref> More recently, he edited * with Silberstein-Loeb (2015) ''Making News: The Political Economy of Journalism in Britain and America from the Glorious Revolution to the Internet''. * with Phillip-Fein (2016) ''Capital Gains: Business and Politics in Twentieth-Century America''.<ref>His other edited volumes include Tedlow and John (1986), and John (2001, 2006, 2012).</ref> Prof. John discusses his work with Spencer Graves.<ref><!--Spencer Graves-->{{cite Q|Q56452480}}</ref> == The need for media reform to improve democracy == This article is part of [[:category:Media reform to improve democracy]]. We describe here briefly the motivation for this series. [[Great American Paradox|One major contributor to the dominant position of the US in the international political economy]] today may have been the [[w:Postal Service Act|US Postal Service Act of 1792]]. Under that act, newspapers were delivered up to 100 miles for a penny when first class postage was between 6 and 25 cents. [[w:Alexis de Tocqueville|Alexis de Tocqueville]], who visited the relatively young United States of America in 1831, wrote, “There is scarcely a hamlet that does not have its own newspaper.”<ref>Tocqueville (1835, p. 93).</ref> McChesney and Nichols estimated that these newspaper subsidies were roughly 0.21 percent of national income (Gross Domestic Project, GDP) in 1841.<ref>McChesney and Nichols (2010, pp. 310-311, note 88).</ref> At that time, the US probably led the world by far in the number of independent newspaper publishers per capita or per million population. This encouraged literacy and limited political corruption, both of which contributed to making the US a leader in the rate of growth in average annual income (Gross Domestic Product, GDP, per capita). Corruption was also limited by the inability of a small number of publishers to dominate political discourse. That began to change in the 1850s and 1860s with the introduction of high speed rotary presses, which increased the capital required to start a newspaper.<ref>John and Silberstein-Loeb (2015, p. 80).</ref> In 1887 [[w:William Randolph Hearst|William Randolph Hearst]] took over management of his father’s ''[[w:San Francisco Examiner|San Francisco Examiner]]''. His success there gave him an appetite for building a newspaper chain. His 1895 purchase of the ''[[w:New York Morning Journal|New York Morning Journal]]'' gave him a second newspaper. By the mid-1920s, he owned 28 newspapers. Consolidation of ownership of the media became easier with the introduction of broadcasting and even easier with the Internet.<ref>John and Silberstein-Loeb (2015). See also Wikiversity, “[[Information is a public good: Designing experiments to improve government]]” and “[[:Category:Media reform to improve democracy]]“.</ref> [[:Category:Media reform to improve democracy|This consolidation seems to be increasing political polarization and violence worldwide]], threatening democracy itself. === The threat from loss of newspapers === A previous ''Media & Democracy'' interview with Arizona State University accounting professor Roger White on "[[Local newspapers limit malfeasance]]" describes problems that increase as the quality and quantity of news declines and ownership and control of the media become more highly concentrated: Major media too often deflect the public's attention from political corruption enabled by poor media. This too often contributes to other problems like [[w:Scapegoating|scapegoating]] [[w:Immigration|immigrants]] and attacking [[w:Diversity, equity, and inclusion|Diversity, equity, and inclusion]] (DEI) while also facilitating increases in pollution, the cost of borrowing, political polarization and violence, and decreases in workplace safety. More on this is included in other interviews in this ''Media & Democracy'' series available on Wikiversity under [[:Category:Media reform to improve democracy]]. An important quantitative analysis of the problems associated with deficiencies in news is Neff and Pickard (2024). They analyzed data on media funding and democracy in 33 countries. The US has been rated as a "flawed democracy" according to the [[w:Economist Democracy Index|Economist Democracy Index]] and spends substantially less per capita on media compared to the world's leading democracies in Scandinavia and Commonweath countries. They note that commercial media focus primarily on people with money, while publicly-funded media try harder to serve everyone. Public funding is more strongly correlated with democracy than private funding. This recommends increasing public funding for media as a means of strengthening democracy. See also "[[Information is a public good: Designing experiments to improve government]]". ==Discussion == :''[Interested readers are invite to comment here, subject to the Wikimedia rules of [[w:Wikipedia:Neutral point of view|writing from a neutral point of view]] [[w:Wikipedia:Citing sources|citing credible sources]]<ref name=NPOV/> and treating others with respect.<ref name=AGF/>]'' == Notes == {{reflist}} == Bibliography == * <!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse-->{{cite Q|Q54641943}} * <!--Richard R. John, ed. (2001) Computers and Communications Networks-->{{cite Q|Q134679967|editor=Richard R. John}} * <!--Richard R. John, ed. (2006) Ruling Passions: Political Economy in Nineteenth Century America-->{{cite Q|Q134674693|editor=Richard R. John}} * <!--Richard R. John (2010) Network Nation: Inventing American Telecommunications-->{{cite Q|Q54641191}} * <!--Richard R. John, ed. (2012) The American Postal Network, 1792-1914-->{{cite Q|Q134670536|editor=Richard R. John}} * <!--Richard R. John and Kim Phillips-Fein, eds. (2016) Capital Gains: Business and Politics in Twentieth-Century America-->{{cite Q|Q134669392|editors=Richard R. John and Kim Phillips-Fein}} * <!--Richard R. John and Jonathan Silberstein-Loeb (eds.; 2015) Making News: The Political Economy of Journalism in Britain and America from the Glorious Revolution to the Internet (Oxford University Press)-->{{cite Q|Q131468166|editors=Richard R. John and Jonathan Silberstein-Loeb}} * <!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) -->{{cite Q|Q104888067}}. * <!--Richard S. Tedlow and Richard R. John, eds (1986) Managing big business : essays from the Business history review-->{{cite Q|Q134680369|editors=Richard S. Tedlow and Richard R. John}} * <!-- Alexis de Tocqueville (1835, 1840; trad. 2001) Democracy in America (trans. by Richard Heffner, 2001; New America Library) -->{{cite Q|Q112166602|publication-date=unset|author=Alexis de Tocqueville (1835, 1840; trad. 2001)}} [[Category:Media]] [[Category:News]] [[Category:Politics]] [[Category:Media reform to improve democracy]] <!--list of categories https://en.wikiversity.org/wiki/Wikiversity:Category_Review [[Wikiversity:Category Review]]--> 90ibv6t0pfijixpph97yxe02szz571y 104 321986 2718244 2717978 2025-06-10T15:00:00Z 166.109.26.134 2718244 wikitext text/x-wiki Human Nutrition is the study of how nutrients are processed by the body, how they are consumed, absorbed, metabolized, and affect mentality. Additionally, the study of how the nutrients relate to health will be discussed in this course. (I will finish this by June 23... Course Overview: This course introduces the science of human nutrition, and exploring how nutrients impact health, development, and disease prevention. In the end, students Should be able to understand dietary guidelines, evaluate food choices, and apply nutrition principles to real life situations. Module Structure: This course is divided into eight commonly Modules. Module 1: Introduction to Nutrition - be able to understand terms about Nutrition Module 2: Macronutrients - Discuss Carbohydrates, Proteins, Fibers, Fats, including their functions, and Dietary sources. Module 3: Micronutrients - Includes Vitamins and minerals, deficiency reduce diseases, and their roles in the body. Module 4: Water and Hydration - Explore the need for the body to have water, signs of dehydration, and the analysis of electrolytes Module 5: Energy, Balance, and Metabolism - Examines Concepts such as basal metabolic rate, caloric intake, and energy expenditure Module 6: Diet PLanning and Dietary Guidelines - Reviewing Dietary Guidelines, food labeling, and food planning Module 7: Nutrition through the life cycle - Details how the Nutrition across ages, through childhood, infancy,adulthood, and old age. Module 8: Nutrition, Disease, and Converstials - Addresses diet-related diseases, current Dietary trends, and the role of nutrition in mental and public health Applications The course equips students with practical skills in evaluating their food choices, planning balanced diets, and understanding the current state of the public health nutrition challenges. Learning outcomes: Upon completion Learners should be able to identify should factors like: Being able to evaluate the current situation with nutrition on a world stage Be able to plan out diets for goals Identify key nutrients inside certain items Understanding Nutrition based diets Analysis of food labels By Zen Goodman [[Category:Nutrition]] [[Category:Human]] cji46ew0lhikgnlwpgm271ndutfqcjg 0 322015 2718284 2718099 2025-06-11T05:58:29Z DavidMCEddy 218607 /* Bibliography */ correct errors in bib 2718284 wikitext text/x-wiki :''This discusses a 2025-06-08 interview with [[w:University of San Diego|University of San Diego]] Communications Professor Nik Usher<ref name=Usher><!--Nik Usher-->{{cite Q|Q134715348}}</ref> about their research on how news impacts democracy. A video and 29:00 mm:ss podcast excerpted from the interview will be added when available. The podcast will be released 2025-06-14 to the fortnightly "Media & Democracy" show<ref name=M&D><!--Media & Democracy-->{{cite Q|Q127839818}}</ref> syndicated for the [[w:Pacifica Foundation|Pacifica Radio]]<ref><!--Pacifica Radio Network-->{{cite Q|Q2045587}}</ref> Network of [[w:List of Pacifica Radio stations and affiliates|over 200 community radio stations]].<ref><!--list of Pacifica Radio stations and affiliates-->{{cite Q|Q6593294}}</ref>'' :''It is posted here to invite others to contribute other perspectives, subject to the Wikimedia rules of [[w:Wikipedia:Neutral point of view|writing from a neutral point of view]] while [[w:Wikipedia:Citing sources|citing credible sources]]<ref name=NPOV>The rules of writing from a neutral point of view citing credible sources may not be enforced on other parts of Wikiversity. However, they can facilitate dialog between people with dramatically different beliefs</ref> and treating others with respect.<ref name=AGF>[[Wikiversity:Assume good faith|Wikiversity asks contributors to assume good faith]], similar to Wikipedia. The rule in [[w:Wikinews|Wikinews]] is different: Contributors there are asked to [[Wikinews:Never assume|"Don't assume things; be skeptical about everything."]] That's wise. However, we should still treat others with respect while being skeptical.</ref>'' <!--[[File:MeDem2025-06-12Usher|thumb|2025-06-12 interview with University of San Diego Communications Professor Nik Usher about how news impacts democracy.]]--> <!--[[File:MeDem20250628Usher|29:00 mm:ss excerpts from a 2025-06-12 interview with University of San Diego Communications Professor Nik Usher about how news impacts democracy.]]--> University of San Diego Communications Professor Nik Usher<ref name=Usher/> discusses their research on how news impacts democracy. Recent publications describe how media impacted the response to [[w:Black Lives Matter|Black Lives Matter]], [[w:COVID-19|COVID-19]], [[w:Illiberal democracy|illiberal politics]], and prosecutions for [[w:political corruption|political corruption]]. This interview focuses especially on five of their recent publications: * (2022-01) "How Loud Does the Watchdog Bark? A Reconsideration of Local Journalism, News Non-profits, and Political Corruption" * (2022-07) "Journalism as historical repair work: addressing present injustice through the second draft of history" * (2023-02) "The Real Problems with the Problem of News Deserts: Toward Rooting Place, Precision, and Positionality in Scholarship on Local News and Democracy" * (2023-05) "Localizing COVID-19 Public Health Department Outreach on Digital Platforms: The Role of Discoverability, Reach, and Moderation for Illinois’ COVID-19 Vaccination Rates", with 4 c-authors. * (2024) "Why News Organizations ‘Platform’ Illiberal Politics: Understanding News Production, Economic Insolvency, and Anti-Democratic Pressure Through CNN’s 2023 Trump Town Hall" == The need for media reform to improve democracy == This article is part of [[:category:Media reform to improve democracy]]. We describe here briefly the motivation for this series. [[Great American Paradox|One major contributor to the dominant position of the US in the international political economy]] today may have been the [[w:Postal Service Act|US Postal Service Act of 1792]]. Under that act, newspapers were delivered up to 100 miles for a penny when first class postage was between 6 and 25 cents. [[w:Alexis de Tocqueville|Alexis de Tocqueville]], who visited the relatively young United States of America in 1831, wrote, “There is scarcely a hamlet that does not have its own newspaper.”<ref>Tocqueville (1835, p. 93).</ref> McChesney and Nichols estimated that these newspaper subsidies were roughly 0.21 percent of national income (Gross Domestic Project, GDP) in 1841.<ref>McChesney and Nichols (2010, pp. 310-311, note 88).</ref> At that time, the US probably led the world by far in the number of independent newspaper publishers per capita or per million population. This encouraged literacy and limited political corruption, both of which contributed to making the US a leader in the rate of growth in average annual income (Gross Domestic Product, GDP, per capita). Corruption was also limited by the inability of a small number of publishers to dominate political discourse. That began to change in the 1850s and 1860s with the introduction of high speed rotary presses, which increased the capital required to start a newspaper.<ref>John and Silberstein-Loeb (2015, p. 80).</ref> In 1887 [[w:William Randolph Hearst|William Randolph Hearst]] took over management of his father’s ''[[w:San Francisco Examiner|San Francisco Examiner]]''. His success there gave him an appetite for building a newspaper chain. His 1895 purchase of the ''[[w:New York Morning Journal|New York Morning Journal]]'' gave him a second newspaper. By the mid-1920s, he owned 28 newspapers. Consolidation of ownership of the media became easier with the introduction of broadcasting and even easier with the Internet.<ref>John and Silberstein-Loeb (2015). See also Wikiversity, “[[Information is a public good: Designing experiments to improve government]]” and “[[:Category:Media reform to improve democracy]]“.</ref> [[:Category:Media reform to improve democracy|This consolidation seems to be increasing political polarization and violence worldwide]], threatening democracy itself. === The threat from loss of newspapers === A previous ''Media & Democracy'' interview with Arizona State University accounting professor Roger White on "[[Local newspapers limit malfeasance]]" describes problems that increase as the quality and quantity of news declines and ownership and control of the media become more highly concentrated: Major media too often deflect the public's attention from political corruption enabled by poor media. This too often contributes to other problems like [[w:Scapegoating|scapegoating]] [[w:Immigration|immigrants]] and attacking [[w:Diversity, equity, and inclusion|Diversity, equity, and inclusion]] (DEI) while also facilitating increases in pollution, the cost of borrowing, political polarization and violence, and decreases in workplace safety. More on this is included in other interviews in this ''Media & Democracy'' series available on Wikiversity under [[:Category:Media reform to improve democracy]]. An important quantitative analysis of the problems associated with deficiencies in news is Neff and Pickard (2024). They analyzed data on media funding and democracy in 33 countries. The US has been rated as a "flawed democracy" according to the [[w:Economist Democracy Index|Economist Democracy Index]] and spends substantially less per capita on media compared to the world's leading democracies in Scandinavia and Commonweath countries. They note that commercial media focus primarily on people with money, while publicly-funded media try harder to serve everyone. Public funding is more strongly correlated with democracy than private funding. This recommends increasing public funding for media as a means of strengthening democracy. See also "[[Information is a public good: Designing experiments to improve government]]". ==Discussion == :''[Interested readers are invite to comment here, subject to the Wikimedia rules of [[w:Wikipedia:Neutral point of view|writing from a neutral point of view]] [[w:Wikipedia:Citing sources|citing credible sources]]<ref name=NPOV/> and treating others with respect.<ref name=AGF/>]'' == Notes == {{reflist}} == Bibliography == * <!--Richard R. John and Jonathan Silberstein-Loeb (eds.; 2015) Making News: The Political Economy of Journalism in Britain and America from the Glorious Revolution to the Internet (Oxford University Press)-->{{cite Q|Q131468166|editors=Richard R. John and Jonathan Silberstein-Loeb}} * <!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) -->{{cite Q|Q104888067}}. * <!-- Alexis de Tocqueville (1835, 1840; trad. 2001) Democracy in America (trans. by Richard Heffner, 2001; New America Library) -->{{cite Q|Q112166602|publication-date=unset|author=Alexis de Tocqueville (1835, 1840; trad. 2001)}} * <!--Nik Usher and Sanghoon Kim-Leffingwell (2022-01) How Loud Does the Watchdog Bark? A Reconsideration of Local Journalism, News Non-profits, and Political Corruption -->{{Cite Q|Q134715465}} * <!--Nik Usher (2022-07) Journalism as historical repair work: addressing present injustice through the second draft of history-->{{cite Q|Q134715643}} * <!--Nik Usher (2023-02) The Real Problems with the Problem of News Deserts: Toward Rooting Place, Precision, and Positionality in Scholarship on Local News and Democracy-->{{cite Q|Q122270994}} * <!--Nik Usher (2024) Why News Organizations ‘Platform’ Illiberal Politics: Understanding News Production, Economic Insolvency, and Anti-Democratic Pressure Through CNN’s 2023 Trump Town Hall-->{{cite Q|Q134715670}} * <!--Nik Usher, Adrian Tai Wong, Isaiah R. Raynal, Cabral Bigman-Galimore, and Ewa Maslowska (2023-05) Localizing COVID-19 Public Health Department Outreach on Digital Platforms: The Role of Discoverability, Reach, and Moderation for Illinois’ COVID-19 Vaccination Rates-->{{cite Q|Q134715704}} [[Category:Media]] [[Category:News]] [[Category:Politics]] [[Category:Media reform to improve democracy]] <!--list of categories https://en.wikiversity.org/wiki/Wikiversity:Category_Review [[Wikiversity:Category Review]]--> q7ohfgqp8zpjcijtp28uuja5k8c3vze 3 322031 2718246 2025-06-10T15:56:26Z Ion Soggo 2798977 /* Foreign keys in schema Enwiki */ new section 2718246 wikitext text/x-wiki == Foreign keys in schema Enwiki == Hello, User Kku, Since you know about MySQL and Wikipedia, I hope you will help me to determine whether or not schema Enwiki has foreign keys. The DDL code of schema Enwiki from the available sources (examples below) does not include any declarations of foreign keys. Does it mean no foreign keys are formally defined in the schema structure? <nowiki>https://phabricator.wikimedia.org/source/mediawiki/browse/master/sql/mysql/tables-generated.sql</nowiki> <nowiki>https://gerrit.wikimedia.org/g/mediawiki/core/%2B/HEAD/sql/mysql/tables-generated.sql</nowiki> On the other hand, the documentation of the tables in schema enwiki specifies in many places (examples below) that certain columns are foreign keys referencing other tables. Does it mean those foreign keys are formally declared in the schema structure (DDL)? page "<nowiki>https://www.mediawiki.org/wiki/Manual:Revision_table</nowiki>", section "Fields :: rev_comment_id". page "<nowiki>https://www.mediawiki.org/wiki/Manual:Categorylinks_table</nowiki>", section "Fields :: cl_collation_id". So, are there formal foreign keys in the schema that underlies Wikipedia? Thank you in advance for your thoughts. <nowiki>~~~~</nowiki> [[User:Ion Soggo|Ion Soggo]] ([[User talk:Ion Soggo|discuss]] • [[Special:Contributions/Ion Soggo|contribs]]) 15:56, 10 June 2025 (UTC) r2f4m25bscehr22ybmibm5a4lulhx96 3 322032 2718279 2025-06-10T20:10:07Z Atcovi 276019 /* Warning */ new section 2718279 wikitext text/x-wiki == Warning == Hello. Your recent edits to the English Wikiversity are disruptive. Please see [[WV:What is Wikiversity?]] to see what type of content we welcome here. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:10, 10 June 2025 (UTC) 9h7qlebj6je3w4ppwe1ngg8hcydrzs8 3 322033 2718280 2025-06-10T20:10:41Z Atcovi 276019 /* Warning */ new section 2718280 wikitext text/x-wiki == Warning == Hello. Your recent edits are considered disruptive. If you'd like to make test edits, please do so at the [[Wikiversity:Sandbox|sandbox]], thanks. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:10, 10 June 2025 (UTC) iqi5uv7ge4nwootfyrit5p325lpt7wf 2 322034 2718282 2025-06-11T00:27:24Z MagicDippyEgg 3003367 just creating my page 2718282 wikitext text/x-wiki Hello World 17blrxomrhaob95awbn7iuqcxatt8sw 6 322035 2718286 2025-06-11T09:50:35Z Young1lim 21186 {{Information |Description=VLSI.Arith: Carry Lookahead Adders 1A (20250607 - 20250606-2) |Source={{own|Young1lim}} |Date=2025-06-11 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2718286 wikitext text/x-wiki == Summary == {{Information |Description=VLSI.Arith: Carry Lookahead Adders 1A (20250607 - 20250606-2) |Source={{own|Young1lim}} |Date=2025-06-11 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} j4y2r5dkk37xht3hupzovk6xunzmm88 6 322036 2718288 2025-06-11T09:51:29Z Young1lim 21186 {{Information |Description=VLSI.Arith: Carry Lookahead Adders 1A (20250609 - 20250607) |Source={{own|Young1lim}} |Date=2025-06-11 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2718288 wikitext text/x-wiki == Summary == {{Information |Description=VLSI.Arith: Carry Lookahead Adders 1A (20250609 - 20250607) |Source={{own|Young1lim}} |Date=2025-06-11 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} 0s0bveatzmuuuavs7frd5ffgpu87nm7 6 322037 2718290 2025-06-11T09:52:35Z Young1lim 21186 {{Information |Description=VLSI.Arith: Carry Lookahead Adders 1A (20250610 - 20250609) |Source={{own|Young1lim}} |Date=2025-06-11 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2718290 wikitext text/x-wiki == Summary == {{Information |Description=VLSI.Arith: Carry Lookahead Adders 1A (20250610 - 20250609) |Source={{own|Young1lim}} |Date=2025-06-11 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} rkigxqwsridd9feebz6vf8gkbv2t3vw 6 322038 2718292 2025-06-11T09:53:23Z Young1lim 21186 {{Information |Description=VLSI.Arith: Carry Lookahead Adders 1A (20250611 - 20250610 |Source={{own|Young1lim}} |Date=2025-06-11 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2718292 wikitext text/x-wiki == Summary == {{Information |Description=VLSI.Arith: Carry Lookahead Adders 1A (20250611 - 20250610 |Source={{own|Young1lim}} |Date=2025-06-11 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} esyjgdj4zg6wygscf892dph75aw70z9