{"id":14,"date":"2008-08-15T10:38:35","date_gmt":"2008-08-15T17:38:35","guid":{"rendered":"http:\/\/theoryofeverything.org\/wordpress\/?page_id=14"},"modified":"2026-04-01T12:00:20","modified_gmt":"2026-04-01T19:00:20","slug":"jgms-toe-2","status":"publish","type":"page","link":"https:\/\/theoryofeverything.org\/theToE\/","title":{"rendered":"the ToE Framework"},"content":{"rendered":"<p><script src=\"http:\/\/www.google-analytics.com\/urchin.js\" type=\"text\/javascript\"><\/script><script type=\"text\/javascript\">\/\/ <![CDATA[\n\/\/ < ![CDATA[\n\/\/ < ![CDATA[ _uacct = \"UA-1725847-1\"; urchinTracker();\n\/\/ ]]><\/script><\/p>\n<h2>Some of the works on this site can be custom made into personalized artwork for sale. See the &#8220;E8 Math, Science and Art&#8221; Gallery Sales at:<br \/>\n<a href=\"https:\/\/theoryofeverything.com\/theToE\">theoryofeverything.com\u00a0<\/a><\/h2>\n<h5>Some info on my creative work is <a href=\"https:\/\/theoryofeverything.org\/theToE\/2023\/08\/04\/info-about-my-creative-work\/\">here<\/a>. See also my Nature, Abstract, and Astro Photography on <a href=\"https:\/\/www.flickr.com\/photos\/jgmoxness\/albums\">Flickr<\/a>.<\/h5>\n<table border=\"0\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/E8_and_H4_in_QM_and_QC.pdf\">E8_and_H4_in_QM_and_QC.pdf<\/a><\/td>\n<td>Latest: 12\/09\/2024 (17Mb). My latest ToE paper <a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/E8_and_H4_in_QM_and_QC.pdf\">here<\/a>, and associated Mathematica notebook <a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/E8_and_H4_in_QM_and_QC.nb\">here.<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/The_Isomorphism_of_3-Qubit_Hadamards_and_E8.pdf\">The_Isomorphism_of_3-Qubit_Hadamards_and_E8.pdf<br \/>\n<\/a><\/td>\n<td>Latest: 11\/20\/2023 (12Mb). My latest ToE paper <a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/The_Isomorphism_of_3-Qubit_Hadamards_and_E8.pdf\">here<\/a>, and associated Mathematica notebook <a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/The_Isomorphism_of_3-Qubit_Hadamards_and_E8.nb\">here<\/a>.<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/The_Isomorphism_of_H4_and_E8.pdf\">The_Isomorphism_of_H4_and_E8.pdf<\/a><\/td>\n<td>Latest: 10\/28\/2023 (28Mb). My latest ToE paper <a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/The_Isomorphism_of_H4_and_E8.pdf\">here<\/a>, and associated Mathematica notebook <a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/The_Isomorphism_of_H4_and_E8.nb\">here.<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/Quaternion%20Coxeter-Dynkin%20Geometric%20Group%20Theory-2b.pdf\">3D &amp; 4D Solids using\u200b Quaternion Weyl Orbits from Coxeter-Dynkin \u200bGeometric Group Theory\u200b.pdf<\/a><\/td>\n<td>Latest: 02\/17\/2023. (15Mb) A PowerPoint version is <a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/Quaternion%20Coxeter-Dynkin%20Geometric%20Group%20Theory-2b.pptx\">here<\/a>, with a cloud based one <a href=\"https:\/\/1drv.ms\/p\/s!Ah5BIzPGaCWlgadD4hHmlnuGPAfczA?e=kRO6TA\">here<\/a>. These show code and output from my VisibLie-E8 tool generating all Platonic, Archimedean and Catalan 3D solids (including known and a few new 4D polychora from my discovery of the E8-&gt;H4 folding matrix) from quaternions given their Weyl Orbits.<\/td>\n<\/tr>\n<tr>\n<td><a href=\"\/TOE\/JGM\/ToE_Demonstration.nb\">ToE_Demonstration.nb<\/a><\/td>\n<td>Latest: 05\/30\/2022 (135 Mb). This is a <em>Mathematica<\/em> version 13 demonstration (or as an <a title=\"Interactive Demonstration\" href=\"https:\/\/theoryofeverything.org\/theToE\/visualizations\/interactive\/\">interactive web page<\/a>) (130 Mb) takes you on an integrated visual journey from the abstract elements of hyper-dimensional geometry, algebra, particle and nuclear physics, Computational Fluid Dynamics (CFD) in Chaos Theory and Fractals, quantum relativistic cosmological N-Body simulations, and on to the atomic elements of chemistry (visualized as a 4D periodic table arranged by quantum numbers). It requires the free <em>Mathematica<\/em> <a title=\"CDF plugin\" href=\"http:\/\/www.wolfram.com\/cdf-player\/\" target=\"_blank\" rel=\"noopener noreferrer\">CDF plugin<\/a>.<\/td>\n<\/tr>\n<tr>\n<td><a href=\"\/TOE\/JGM\/ToE_Demonstration-Lite.nb\">ToE_Demonstration-Lite.nb<\/a><\/td>\n<td>Latest: 05\/30\/2022 (11 Mb). This is a lite version of the full <em>Mathematica<\/em> version 13 demonstration. It only loads the first 8 panes and the last UI pane which doesn&#8217;t require the larger file and load times. It requires the free<em> Mathematica<\/em> <a title=\"CDF plugin\" href=\"http:\/\/www.wolfram.com\/cdf-player\/\" target=\"_blank\" rel=\"noopener noreferrer\">CDF plugin<\/a>.<\/td>\n<\/tr>\n<tr>\n<td><a href=\"\/TOE\/JGM\/3D_Polytope_Hulls_of_E8-421-241-142.pdf\">3D_Polytope_Hulls_of_E8-421-241-142.pdf<\/a><\/td>\n<td>Latest: 05\/19\/2020 (40 Mb). 3D Polytope Hulls of E8-4_21, 2_41, and 1_42<\/td>\n<\/tr>\n<tr>\n<td><a href=\"\/TOE\/JGM\/Unimodular-Rotation-of-E8-to-H4.pdf\">Unimodular-Rotation-of-E8-to-H4.pdf<\/a><\/td>\n<td>Latest: 10\/19\/2019 (4 Mb). A recent paper-Unimodular rotation of E8 to H4 600-cells<\/td>\n<\/tr>\n<tr>\n<td><a href=\"\/TOE\/JGM\/Integrated E8, Binary, Octonion-web.htm\">Integrated E8, Binary, Octonion<\/a><\/td>\n<td>Latest: 03\/10\/2017.\u00a0 An .html version of a <a title=\"Integrated E8, Binary, Octonion\" href=\"\/TOE\/JGM\/Integrated E8, Binary, Octonion-web.pptx\">.ppt<\/a> (or <a title=\"Integrated E8, Binary, Octonion\" href=\"\/TOE\/JGM\/Integrated E8, Binary, Octonion-web.ppsx\">.pps<\/a> or <a title=\"Integrated E8 .pdf\" href=\"\/TOE\/JGM\/Integrated E8, Binary, Octonion-web.pdf\">.pdf) <\/a> (15MB) that explains the detail of the content of <a title=\"Fano.pdf\" href=\"http:\/\/TOE\/JGM\/Fano.pdf\">Fano.pdf<\/a>. It outlines the relationships in the integration of E8 with Octonions, Binary, Particles, NKS, and the Periodic Table of Elements.<\/td>\n<\/tr>\n<tr>\n<td><a href=\"\/TOE\/JGM\/ece2.html\">VisibLie_E8 vs. EPE<\/a><\/td>\n<td>Latest: 06\/21\/2016. Feature set comparison of<a href=\"http:\/\/deferentialgeometry.org\/epe\/EPE3.html\"> Lisi&#8217;s Elementary Particle Explorer (EPE)<\/a> and ToE_Demonstration (above, aka. VisibLie_E8, E8Viewer, or E8Flyer). This is also a good source of instruction for interacting with the main VisbLie E8 demo for pane 5- E8 Representation Theory (<\/td>\n<\/tr>\n<tr>\n<td><a href=\"\/TOE\/JGM\/splitFano.pdf\">splitFano.pdf<\/a><\/td>\n<td>Latest: 12\/25\/2015. A 241 page pdf file (15MB) with the 480 octonion permutations with Fano planes and multiplication tables, including the <a title=\"split octonion\" href=\"http:\/\/en.wikipedia.org\/wiki\/Split-octonion\">split octonion<\/a>. These are organized into &#8220;flipped&#8221; and &#8220;non-flipped&#8221; pairs associated with the 240 assigned particles to E8 vertices. <a title=\"octonionG2-nonNull.pdf\" href=\"http:\/\/theoryofeverything.org\/TOE\/JGM\/octonionG2-nonNull.pdf\">octonionG2-nonNull.pdf<\/a> is a 481 page (15MB) file available that adds the G2 automorphisms for each multiplication table (including splits).<\/td>\n<\/tr>\n<tr>\n<td><a href=\"\/TOE\/JGM\/E8 Particle Assignment Symmetry.htm\">E8 Particle Assignment Symmetry<\/a><\/td>\n<td>Latest: 03\/24\/2015. An .html version of a <a title=\"E8 Particle Assignment Symmetry\" href=\"\/TOE\/JGM\/E8 Particle Assignment Symmetry.ppt\">.ppt<\/a> (or <a title=\"E8 Particle Assignment Symmetry\" href=\"\/TOE\/JGM\/E8 Particle Assignment Symmetry.pps\">.pps<\/a> or <a title=\"E8 Particle Assignment Symmetry\" href=\"\/TOE\/JGM\/E8 Particle Assignment Symmetry.pdf\">.pdf) <\/a> that explains the detail of the particle assignment symmetries contained in MyToE. A complete algorithmically assigned particle list is <a href=\"http:\/\/theoryofeverything.org\/TOE\/JGM\/Appendix_B_Integrated_List.pdf\">here<\/a>.<\/td>\n<\/tr>\n<tr>\n<td><a href=\"\/TOE\/JGM\/E8toH4fold.pdf\">E8toH4fold.pdf<\/a><\/td>\n<td>Latest: 12\/19\/2014. This paper presents detail on the matrix <a href=\"http:\/\/theoryofeverything.org\/MyToE\/?p=1454\">I found<\/a> several years ago (as shown on the <a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:6Cube-QuasiCrystal.jpg\"> Wikipedia Quasicrystal and Rhombic Triacontahedron<\/a> pages), which relates the crystallographic E8 to the non-crystallographic H4 (600 cell). It also presents various techniques for visualizing a split real even E8 representation in 2 and 3 dimensions using this E8 to H4 folding matrix. It shows its importance in the analysis of theoretical physics models and grand unified theories that are related to these structures.<\/td>\n<\/tr>\n<tr>\n<td><a href=\"\/TOE\/JGM\/ToEsummary.pdf\">ToEsummary.pdf<\/a><\/td>\n<td>Latest: 06\/04\/2013. A .pdf of the <a title=\"ToE Summary Notebook\" href=\"\/TOE\/JGM\/ToEsummary.nb\">Mathematica notebook <\/a>that summarizes how my ToE integrates the latest results from both the Planck spacecraft survey and the LHC Higgs discovery. It highlights minor changes to the original papers from &#8217;98-&#8217;07 which predict an expanding (Hubble) and accelerating universe, as well as the Higgs boson.<\/td>\n<\/tr>\n<tr>\n<td><a href=\"\/TOE\/JGM\/DynkinParticleReductions.pdf\">DynkinParticleReductions.pdf<\/a><\/td>\n<td>Latest: 09\/03\/2011. Fully interactive paper discussing the potential to reduce the Standard Model to 8 elemental particles. This requires the free <em>Mathematica<\/em> CDF plugin (50Mb). If you don&#8217;t want to use CDF, here is a DynkinParticleReductions.pdf (25Mb).<\/td>\n<\/tr>\n<tr>\n<td><a href=\"\/TOE\/JGM\/E8Favorites.pdf\">E8Favorites.pdf<\/a><\/td>\n<td>Latest: 03\/27\/2011. &#8220;E8 Math, Science and Art&#8221; Gallery Exhibit. (10Mb) or on the web at <a href=\"\/TOE\/JGM\/E8ArtPrints\/E8ArtPrints.htm\">E8 Art Prints<\/a>. See <a href=\"\/TOE\/JGM\/gallery.pdf\">Gallery.pdf<\/a> for more &#8220;E8 Math, Science and Art&#8221; Gallery images. (6Mb)<\/td>\n<\/tr>\n<tr>\n<td><a href=\"\/TOE\/JGM\/ToE.pdf\">ToE.pdf<\/a><\/td>\n<td>Latest: 11\/22\/2007. My ToE paper &#8211; full detail of a framework for a ToE based on a new look at fundamental constants, units-of-measure, and the dimensionality of time, mass, and charge. This version <a href=\"\/TOE\/JGM\/ToEnb.pdf\">ToEnb.pdf<\/a>. Here is the same paper above validated w\/Mathematica<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Some of the works on this site can be custom made into personalized artwork for sale. See the &#8220;E8 Math, Science and Art&#8221; Gallery Sales at: theoryofeverything.com\u00a0 Some info on my creative work is here. See also my Nature, Abstract, and Astro Photography on Flickr. E8_and_H4_in_QM_and_QC.pdf Latest: 12\/09\/2024 (17Mb). My latest ToE paper here, and &hellip; <a href=\"https:\/\/theoryofeverything.org\/theToE\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">the ToE Framework<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":3626,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-14","page","type-page","status-publish","has-post-thumbnail","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/pages\/14","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/comments?post=14"}],"version-history":[{"count":53,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/pages\/14\/revisions"}],"predecessor-version":[{"id":7868,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/pages\/14\/revisions\/7868"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media\/3626"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=14"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}