| 3D & 4D Solids using Quaternion Weyl Orbits from Coxeter-Dynkin Geometric Group Theory.pdf |
02/17/2023. A PowerPoint version is here, with a cloud based one here. 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->H4 folding matrix) from quaternions given their Weyl Orbits. |
| ToE_Demonstration.nb |
Latest: 05/30/2022 (135 Mb). This is a Mathematica version 13 demonstration (or as an interactive web page) (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 Mathematica CDF plugin. |
| ToE_Demonstration-Lite.nb |
Latest: 05/30/2022 (11 Mb). This is a lite version of the full Mathematica version 13 demonstration. It only loads the first 8 panes and the last UI pane which doesn’t require the larger file and load times. It requires the free Mathematica CDF plugin. |
| 3D_Polytope_Hulls_of_E8-421-241-142.pdf |
05/19/2020 (40 Mb). My latest ToE paper-3D Polytope Hulls of E8-4_21, 2_41, and 1_42 |
| Unimodular-Rotation-of-E8-to-H4.pdf |
10/19/2019 (4 Mb). A recent paper-Unimodular rotation of E8 to H4 600-cells |
| E8 Particle Assignment Symmetry |
03/24/2015. An .html version of a .ppt (or .pps or .pdf) that explains the detail of the particle assignment symmetries contained in MyToE. A complete algorithmically assigned particle list is here. |
| E8toH4fold.pdf |
Latest: 12/19/2014. This paper presents detail on the matrix I found several years ago (as shown on the Wikipedia Quasicrystal and Rhombic Triacontahedron 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. |
| Integrated E8, Binary, Octonion |
An .html version of a .ppt (or .pps or .pdf) (15MB) that explains the detail of the content of Fano.pdf. It outlines the relationships in the integration of E8 with Octonions, Binary, Particles, NKS, and the Periodic Table of Elements. |
| splitFano.pdf |
Latest: 12/25/2015. A 241 page pdf file (15MB) with the 480 octonion permutations with Fano planes and multiplication tables, including the split octonion. These are organized into “flipped” and “non-flipped” pairs associated with the 240 assigned particles to E8 vertices. octonionG2-nonNull.pdf is a 481 page (15MB) file available that adds the G2 automorphisms for each multiplication table (including splits). |
| Octonion.nb |
A small Mathematica notebook for octonion math. It also has the ability to compare/contrast the more limited Mathematica based Quaternion logic as it applies to using the Cayley-Dickson doubling procedure for octonions. |
| DynkinParticleReductions.pdf |
Fully interactive paper discussing the potential to reduce the Standard Model to 8 elemental particles. This requires the free Mathematica CDF plugin (50Mb). If you don’t want to use CDF, here is a DynkinParticleReductions.pdf (25Mb). |
| ToEsummary.pdf |
A .pdf of the Mathematica notebook 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 ’98-’07 which predict an expanding (Hubble) and accelerating universe, as well as the Higgs boson. |
| ToE.pdf |
My ToE paper – 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 ToEnb.pdf. Here is the same paper above validated w/Mathematica |
| VisibLie_E8 vs. EPE |
Feature set comparison of Lisi’s Elementary Particle Explorer (EPE) 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 ( |
| E8Favorites.pdf |
“E8 Math, Science and Art” Gallery Exhibit. (10Mb) or on the web at E8 Art Prints. See Gallery.pdf for more “E8 Math, Science and Art” Gallery images. (6Mb) |
| What time is it.pdf |
A TheoryOfEverything in one .ppt slide |
| My Tools of the Trade |
I modified FormCalc to work on WinTel Mathematica platforms |
| NewPhysicalConstants.zip |
Mathematica’s PhysicalConstants.m organized w/ascending sort priority for fundamental, defined, measured, then derived values. Updated to 2010 CODATA and with the latest Higgs discovery. Includes new Units.m and PhysicalConstantErrrors.m to define fundamental measured physical constant std. errors also w/ascending sort priority for defined and smaller errors. |
Really beautiful and complex multifaceted pictures. Generaly, simplification is the better course when defining a TOE. No matter what you may see out there the more convoluted it is the less accurate.
If, at the bare-bones-level it doesn’t make sense and cannot be defined in a few succinct paragraphs then chances are it’s wrong.
Sincerely,
Michael Gary Jordan
■ Grand Unified Theory: The New Natural Perspective in the Mathematical & Scientific Unification of 4 Forces of the Universe – Bernard Rementilla.
A New GUT Scientific & Mathematical Configuration(s) – The Riemann-Rementilla Non-Euclidean [Vector Duality Field Hyperdensity Matrix] Mathematics! – Bernard Rementilla
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UPDATE GUT SECTION 2011 AD.
The New Mathematical Approach to Correct & Consistent GUT: The Riemann-Rementilla Vector Field HD Matrix [Non-Euclidean] Mathematics
This New Perspective of GUT [Its New Mathematical Configuration & Scientific Structuring ] as figured out briefly in this UPDATE Section, reconstructs the mathematical & scientific knowledge of current GUT Perspective into a complete, new Mathematical & Scientific Perspective(s) of a true GUT as exactly extracted from hidden laws of natural phenomena. The result is Theory of Everything (TOE). How? What? Why?
That is, this GUT & TOE combined scientific & mathematical works termed as Nature’s Blueprint by Bernard Rementilla, a research mechanical engineer & thermodynamics professor in the Philippines. This Nature’s Blueprint, according to him, is basically a reconstructive, technical quantitative approach to extend GF Bernhard Riemann’s Positive Non-Euclidean Geometry into a Vector Field (Hyperdensity N-dimension of Dual Function) Matrix Mathematics that can extra-polate a 52-dimension Nature’s space-time-energy of the whole Cosmos, which is the key to extract 2 fields of the Universe: Energy Field & Force Field & the NEW HIDDEN 13 field constants, respectively: 13 Field Constants of Energy Field & 13 Field Constants of Force Field, totaling new 26 Vector Field Constants. Nature has these hidden new 26 Constants merged & harmonized into a 52-dimension Universe of dual complex hyperdensity space-time-energy; and so on.
By Duality Law of Nature, these two major vector fields of Nature, & the 26 hidden new constants are the key to the correct path to the true GUT & TOE. The new extended version of GF Bernhard Riemann’s positve Non Euclidean Energy, termed the Riemann-Rementilla Vector Field (Hyperdensity-N-Dimension Dual Function) Matrix Non-Euclidean Mathematics, is what makes it technically, scientifically, & numerically possible by which the accurate formulation of the true Grand Unification Theory, & the exact configuration of the Theory of Everything are consistently integrated in the mathematically combined Energy Field & Force Field – embracing the totality of the Universe’s 52 dimensions that put life into every fundamental equation of Physics, Chemistry, & Biology. All of these are found & explained in the Nature’s Blueprint.
This new Grand Unification Theory Perspective is only & solely based on Rementilla’s new configuration of the Theory of Everything he termed “Nature’s Blueprint” & is mathematically possible <> on account of this Blueprint’s 26 new unifying field constants, mathematically integrating both energy field & force field – the result is the unification of four (4) forces of Nature: gravity, weak & strong forces, & emf.
Why Scientists & Mathematicians Fail to Configure the Correct GUT?
According to Rementilla, it is the complete absence of the Energy Field & Force Field & their combined NEW Nature’s 26 unifying constants in the works of the scientists & mathematicians that make them hardly see the accurate configuration & formulation of nature’s GUT, hence, they have failed.
What is the Value of this Nature’s Blueprint? Again, why all these new Perspective Approach to Understand a true GUT? Why?
It is the complete key to SOLVE the climate change phenomena on Earth. The Final Law is what is needed to SOLVE Climate Change & save us all from imminent 6th Global Mass Extinction on Earth … – BBR.
The true theory of everything must explain explain the universe, in terms of a collection of identical fundamental units, as the Ancient Greek philosophers suggested. Only Squish Theory does this. http://squishtheory.wordpress.com/
Until Gravity is understood, matter will not be defined. Gravity is not a ‘pull’, it is a ‘push’. It is an electro-dynamic response influenced by electromagnetism. It is a by-product of matter’s reality.
Nice!
http://physics.aps.org/synopsis-for/10.1103/PhysRevD.90.052004?referer=rss
CW
Hello, Gregory,
I downloaded your Mathematica program, and used it to create a 3D model of the Gossett polytope 4 21. (E8 roots projected from 8D to 3D). Unfortunately, the data points do not seem to be correct: there are distortions. I can email you an stl file and a screen shot showing the issue. Could you please contact me at rick-russell@sbcglobal.net?
You can see the model here in 3D: https://www.shapeways.com/product/JSSA7YHWJ/e8-root-system-polytope
Thanks, Rick R