A Theory of Everything Visualizer:
J. Gregory Moxness
Latest: 05/30/2022 (135 Mb).
This is a link to the newer version of the ToE_Demonstration.nb.
This is a Mathematica version 13 notebook that 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).
I decided to integrate some chemistry/biology/CompSci panes to the math/physics of the VisibLie_E8 tool. This uses some great demonstrations that begin to address (but are by no means complete regarding) the connections between algebra/geometry/math/physics to chemistry/biology/CompSci and even consciousness connection of the mind/brain/neurons-axons (e.g. the Penrose/Hameroff Orchestrated Objective Reduction (OrchOR) of quantum microtubules.
A Theory of Everything Visualizer, with links to free Cloud based Interactive Demonstrations:
4) Math: Group Theory: Dynkin Diagram Algebra Create (cloud simple) or local .nb with Quaternion Weyl Orbit Generated 3D Geometry (requires Mathematica license)
10) Chemistry: Atomic Elements: 4D Periodic Table Element Select
11) Chemistry: Molecular Crystallography: 4D Molecule Visualization Select
13) Biology: Human Neurology: OrchOR Quantum Consciousness
14) Psychology: Music Theory & Cognition: Chords, Lambdoma, CA MIDI,& Tori
15) Sociology: Theological Number Theory: Ancient Sacred Text Gematria
17) CompSci: Artificial Intelligence: 3D Conway’s Game Of Life
18) CompSci: Human/Machine Interfaces: nD Human Machine Interface
This demonstration combines five original demonstrations by the author (#1-5 Fano, Pascal, Dynkin, E8, and Particle and an OpenCL based N-Body Universal history simulation #8). It combines and integrates many other author’s Wolfram demonstrations with significant original value added to each. All of these are in some way related to fundamental mathematical symmetries. Most are also theoretically related to and integrated with an extended Standard Model (SM) originated by A.G. Lisi and modified by the author. It visualizes, among other things, the math and physics of “An Exceptionally Simple Theory of Everything“ as well as myToE as a basis for understanding the relationships between the fundamental constants, (C)harge, (T)ime, and space or spin (P)arity.
The resulting combination of 18 panes brings the user from the mathematical abstractions of geometry and algebra, through particle and nuclear physics, adds a universal history simulation engine, including quantum mechanics and general relativity of cosmological N-body gravitation and Big Bang physics, and goes on to visualize the chemistry of the atoms, molecules, and proteins, as well as speculation about the quantum brain-mind connection of neurons/axons as it relates to Orchestrated Objective Reductions (OrchOR).
The #1 pane (Chaos) is taken largely from several great Wolfram Demonstrations of Zeleny’s Five Mode Truncation Of The Navier-Stokes Equations, A Collection Of Chaotic Attractors and Hennegan’s Rotating The Hopf Fibration. It now includes 2D and 3D visualizations of these equations. It also adds an OpenCL based visualization of 3D and 4D Fractals (e.g. the Menger Sponge and MandelBulb) and surfaces (e.g. the Boy surface, a rose and others from Paul Nylander, more from Zeleny, and Hanson’s 6D Calabi-Yau in String Theory).
Navier-Stokes is not only useful in Computational Fluid Dynamics (CFD) and weather prediction, these visualizations are useful in understanding alternate theories of Quantum Gravity’s space-time structure. These OpenCL codes are only available with the Mathematica Source for this module (available by request). For those w/o OpenCL capability, I’ve integrated and extended Yu-Sung Chang‘s excellent interactive surface visualizations from ContoursOfAlgebraicSurfaces.
The #2 pane (Pascal) for visualizing the Pascal and Sierpinski triangles, along with the Fibonacci and Lucas numbers. In addition to allowing the change in size of the triangle, it highlights the binomial functions and allows the changing the modulus of the numbers used. The number backgrounds are colorized in the selected gradient. This pane was created with ideas from Peter S.Williams’ Mod 9 Pascal Triangle Physics http://naturalnumber.com/
The #3 pane (Fano) for visualizing the octonions, the Fano plane and its cubic. It also allows the manipulation of the 480 different permutations of the octonion basis (calculated from converted C source code from Donald Chesley of Davidson Laboratories, Stevens Institute of Technology). These are shown to be integrated 2:1 with the 240 vertices of E8 and its subgroups. Selection of the split octonion via triad number is a recently added feature. This demonstration also combines and extends Wolfram demonstrations from Ed Pegg Jr. and Oleksandr Pavlik. It also includes the generation of sedenions from the octonions by application of the Cayley-Dickson doubling procedure. As in the animated Fano Cube, the sedenion display includes the generation of an animated Fano Tesseract mnemonic visualization which steps through highlighting the vertices/edges of the 34 sedenion triads.
The #4 pane (Dynkin) allows for the creation of Dynkin diagrams and their corresponding Cartan matrices which generate Lie Algebras. This second pane drives the vertex content in the third pane. There is now a checkbox for showing the detail root vector data and Hasse visualizations instead of the interactive Dynkin pane, which is built from SuperLie 2.07 by P. Grozman.
The #5 pane (E8) provides 2D and 3D visualizations of E8 Lie Algebra and it’s split real even sub group vertices. Each of these vertices are each assigned to fundamental physics particles.
In the #6 pane (Particle), the vertices as fundamental physics particles are individually selectable by their quantum parameters. It is an interactive E8 linked demonstration similar to the idea behind the first pane of S.M. Blinder’s “Combining Quarks Into Hadrons”.
The #7 pane (CKM) is an improved form of Balázs Meszéna’s demonstration on Neutrino Oscillations which presents the Unitarity of CP=T violations by combining the Lepton (Neutrino) Pontecorvo–Maki–Nakagawa–Sakata matrix (PMNS) with the Quark Cabibbo–Kobayashi–Maskawa (CKM) mixing matrix calculations through the Quark–Lepton Complementarity (QLC) . The plots show the probability of finding a 1 GeV particle in the different flavors as a function of the distance between the source and the detector. It also demonstrates the hierarchy of the particle masses and the flavor coefficients in each eigenstate.
The #8 pane (Hadron) is modified from Hadron demonstrations from both Blinder and Zeleny,which allows the visualization of the composite Quark particles and their decays. These demonstrations are extended here by allowing the selection of 2 Quark Mesons, 3 Quark Baryons and recently discovered 4 and 6 Quark Hadrons. This also drives the E8 sub group projection pane. The author has also added a query to show all experimentally discovered composite Meson/Baryon particles with the same quark content from the ParticleData Group curated data set (with decay modes shown with a button click).
The #9 pane (N-Body) General Relativity (GR) / N-Body gravitational Universal history simulations in 15 epochs across 60 orders of magnitude space, time, mass(energy/temperature) scales. Due to the compute intensive nature of gravitational simulation, this uses the Mathematica support for multi-core GPU / CUDA High Performance Computing (HPC) Open Computing Language (OpenCL) with example NBody.cl code combined with Richard Hennegan’s NBody.cl code from this post. Some simulations are incomplete.
I’ve added visualizations in the first “Big Bang” epoch from Klaus von Bloh’s DeBroglie-Bohm deterministic QM demonstrations, specifically the 2D particle-wave duality of the 2-slit experiment and 3D version of trajectories of a particle-in-a-box.
There are 9 more QM related epoch simulations related to fundamental particle interactions related to inflation(2), quark-gluon, electro-weak, meson, baryon, lepton, nucleon, photon-atoms.
There are 3 GR related epochs related to black hole centric quasar and galaxy formation, and the emergence of the Large Scale Structure (LSS) of the Universe.
For the last “Recombination” epoch, I’ve created a Solar system simulation which uses the AstronomicalData curated data sets to set the mass, radius and beginning positions of the Solar System objects in the simulation and combines demonstrations from Cedric Voisin, Jeff Bryant , Enrique Zeleny, and Andrew Moylan.
The #10 pane (Atom) uses Wolfram’s curated ElementData and builds off of Enrique Zeleny’s Alternative Periodic Table Wolfram Demonstration and creates a 2D/3D/4D (with s-p-d-f colors) Stowe-Janet-Scerri version of the Periodic Table. This replaces my older enhanced Theodore Gray’s “Properties of the Elements” demonstration (as well as options for showing the Shrodinger the spherical harmonic electron probability visualizations of Michael Trott and Steven Wolfram and Satya Mohapatra for each element). It has a clickable pane on the periodic table which adds the particles who’s ordered E8 algebra root is that atomic element number.It creates a clickable pane on the periodic table which adds the particles who’s ordered E8 algebra root is that atomic element number.
The #11 pane (Molecule) continues the journey up the chain of complexity to visualize the crystalographic symmetries of multiple atoms. It is an integration of molecule graph demonstrations from Jaime Rangel-Mondragon, as well as from Guenther Galler’s Molecular Point Groups and Orbitals, and Bianca Eifert’s Displaying Multiple Bonds. It also uses Wolfram’s curated ChemicalData.
The #12 pane (DNA) begins to address the quantum biological (non)crystalographic symmetries of living organism’s protein, RNA, and DNA triple tetrahelix (Boerdijk-Coxeter) structures. It visualizes Mark White’s “G – Ball, a New Icon for Codon Symmetry and the Genetic Code”. It currently integrates demonstrations of Paul-Jean Letourneau the “Protein Alignment Wheel” and Luca Zammataro’s “Analyzing The Crystallography Of The SH2 Domain And Its Residue Contact Map”, which uses the Protein Data Bank and Wolfram’s curated ProteinData as well as a bit of the Humane Genome Data set.
The #13 pane (OrchOR) will address highly speculative ideas about the neurology of the brain-mind connection through quantum consciousness. Specifically, the “Orchestrated Objective Reduction” of qubits in microtubules from Roger Penrose and Stuart Hameroff. It is currently an integration of demonstrations that use the Protein Data Bank and Wolfram’s curated ProteinData to compute the probability of brain neuron connections, as well as present Pedro Faria’s “Hodgkin-Huxley Equations For Transmission Of Electrical Impulses” between neurons and axons.
The #14 pane (Chords) will address the psychology of the mathematical beauty of music. The 2D pane presents Emmanuel Amiot and Fernand Brunschwig’s Pythagorean Meantone And Equal Temperament Musical Scales using pure frequency audio generation and Luca Zammataro’s Music from the Game of Life with full MIDI instrument selections for sound. The 3D pane shows Drew Lesso’s 3D Lambdoma matrix.
The #15 pane (Gematria) will address sociology in the form of theological number theory and the study of the ancient sacred texts. It includes Old Testament (OT) Hebrew and Koine Greek (OT/NT), as well as the Sanskrit Rig Veda, Chinese I-Ching, and (eventually) the Persian Avestan Avesta. The word histogram shows the distribution of words used in the sacred texts according to their gematria value. It also presents a clickable 3D graph of proper names related within verses, as well as a clickable “nearest word” graph. Each word in each book, chapter, verse are selectable by slider or clickable (as are the list of words with the same color coded gematria values). This combination of UI creates a powerful new way to navigate the texts. It makes use of Wolfram’s curated LanguageData/DictionaryLookup to get a Nearest Word Graph in Hebrew and English. Note: Hebrew and Sanskrit is properly presented from right to left. I’ve also added a mathematically perfect Sri Yantra in 2D/3D. In addition, in the Chinese language selection the 8 I-Ching trigrams are shown in relationship to the 64 concepts behind the hexagrams and how it relates to Clifford Algebra’s (modified from Simon Tyler’s Trigrams And Real Clifford Algebras.
The #16 pane (QC) will address Quantum Computing in the context of MyToE. It uses several demonstrations… Qubits On The Poincare-Bloch Sphere, Quantum Logic Gates Roots Exponents And Eigensystems and Quantum Fourier Transform Circuit by Rudolf Muradian
The #17 pane (AI) will address Artificial Intelligence, an nD version of Conway’s “Game of Life” and Cellular Automata in the context of MyToE. It is an integration of Daniel de Souza Carvalho’s demonstration
The #18 pane (HMI) extends the Human Machine Interface (HMI) for the third pane. It has a tongue-in-cheek label referring to the user as a biological human life form. This UI provides for manipulation of all of the variables used to create beautiful E8 projections/animations.