I’ve been following an interesting paper titled “Nested polytopes with non-crystallographic symmetry as projected orbits of extended Coxeter groups” which has used my E8 to H4 folding matrix as a basis for not only understanding Lie Algebras/Groups and hyper-dimensional geometry, but also the genetic protein / viral structures of life (very cool)!
The Nested Polytopes paper was first put into Arxiv in Nov of 2014 at about the same time I submitted my related paper on E8 to H4 folding to Vixra. I created this paper in response to discovering that my Rhombic Triacontahedron / QuasiCrystal (D6 projected to 3D using the E8 to H4 Folding Matrix to E8 to H4 folding) work on Wikipedia and this website was being used by Pierre-Philippe Dechant, John Baez and Greg Egan.
The Nested Polytopes paper has since undergone 4 revisions. The first three seemed to be typical (even minor) tweaks, but with a different author list/order in each. Yet, the latest (V4) seems to have a massive change, different author list and a completely different title “Orbits of crystallographic embedding of non-crystallographic groups and applications to virology”.
While I KNOW they were aware of my work, I wasn’t really surprised they never referenced it – as it isn’t published in academic press. I AM a bit surprised by the extensive changes to a single paper on arxiv. They have removed some of the E8 /H4 references (ref: Koca) and added completely different sources. Makes you wonder what’s up with that?
The recent announcement for the potential LHC realization of composite particle resonance of the pentaquark (or meson-baryon molecule) is interesting. This, along with a prior confirmation of the dimeson tetraquark Z(4430), and prognostications for hexaquarks (or dibaryons), expand the “zoo” of composite particles now numbering in the thousands.
If by chance we can use these new discoveries to discern the mathematical pattern (symmetry) well enough to predict the particle masses, lifetimes, branching ratios and CKM (quark) PMNS (neutrino) mixing matrix ratios – that would be COOL!
Yet, given the current size of this zoo of particles, it seems that adding a few more bags of quarks to the mix may not do the trick, but I am always hopeful.
IMNSHO (In My Not So Humble Opinion ;-)… it is more a task of “naming the animals”.
or in Ernest Rutherford’s words:
“All science is either physics or stamp collecting.”
“The pentaquark search may be physics’ version of ‘stamp collecting'”. JGM
Please note, this is about the GEOMETRY used in what has come to be called “Sacred Geometry”. Upon further investigation, along with the Kabbalah’s “Tree of Life”, it seems even the Jewish “Star of David” (Solomon) is medieval and may not be sourced in authentic ancient Abrahamic theology.
As it stands, the so-called “sacred” origin of these, including the pentagon that shows up in the icosahedral/dodecahedral Platonic solids due to the Sqrt(5) Golden Ratio (Phi) relationship within my E8 to H4 folding, is likely medieval and mostly pagan. I am merely pointing out that E8 contains the geometry that many find “interesting” for whatever reason, and am not promoting the underlying cults that use them.
Video (Best in HD):
Copyright J Gregory Moxness 2015
Rectified E8 and F4 Triality (Original Work)
WikiMedia Commons source images:
Metatron’s Cube (User:Barfly2001)
Flower of Life (User:Life_of_Riley)
Tree of Life (User:AnonMoos)
I’ve integrated a few more demonstrations, see below for descriptions and pics..
The #13 pane (Chords) will address the psychology of the mathematical beauty of music. The 2D pane presents and s Pythagorean Meantone And Equal Temperament Musical Scales, while the 3D pane shows ’s 3D .
The #14 pane (Gematria) will address Theological Number Theory in the form of Hebrew gematria, H4, and Tori. This sociology pane deals with the idea of Old Testament Hebrew and New Testament Koine Greek Gematria. The histogram shows the distribution of words used in the Bible according to their gematria value in Hebrew or Greek. Each word in each verse is selectable and shown in the distribution. Each word in the verse is colored by their value in Hebrew (if Old Testament), Greek and English.
Note: Hebrew is properly presented from right to left.
These are more personal interest than hard math/science as the other panes – but they are, IMO, interesting asides.
The sociology pane deals with the idea of Old Testament Hebrew and New Testament Koine Greek Gematria. The histogram shows the distribution of words used in the Bible according to their gematria value in Hebrew or Greek. Each word in each verse is selectable and shown in the distribution. Each word in the verse is colored by their value in Hebrew (if Old Testament), Greek and English.
Note: Hebrew is properly presented from right to left.
The psychology pane deals with the idea of the mathematical beauty of music.
The list of 18 panes is now:
1) Math:____ Chaos/Fibr/Fractal/Surface: Navier Stokes/Hopf/MandelBulb/Klein
2) Math:____ Number Theory:_________ Mod 2-9 Pascal and Sierpinski Triangle
3) Math:____ Geometric Calculus:______ Octonion Fano Plane-Cubic Visualize
4) Math:____ Group Theory:__________ Dynkin Diagram Algebra Create
5) Math:____ Representation Theory:___ E8 Lie Algebra Subgroups Visualize
6) Physics:__ Quantum Elements:______ Fundamental Quantum Element Select
7) Physics:__ Particle Theory:_________ CKM(q)-PMNS(ν) Mix CPT Unitarity
8) Physics:__ Hadronic Elements:______ Composite Quark-Gluon Select Decays
9) Physics:__ Relativistic Cosmology:___ N-Body Bohmian GR-QM Simulation
10) Chemistry: Atomic Elements:_______ 4D Periodic Table Element Select
11) Chemistry:Molecular Crystallography: 4D Molecule Visualization Select
12) Biology:_ Genetic Crystallography:___ 4D Protein/DNA/RNA E8-H4 Folding
13) Biology:_ Human Neurology:________ OrchOR Quantum Consciousness
14) Psychology:Music Theory & Cognition: Chords, Lambdoma, H4, and Tori
15) Sociology: Theological Number Theory: Ancient Sacred Text Gematria
16) CompSci: Quantum Computing:______ Poincare-Bloch Sphere /Qubit Fourier
17) CompSci: Artificial Intelligence:_______ nD Conway’s Game Of Life
18) CompSci: Human/Machine Interfaces:_ nD Human Machine Interface
It contains photo albums with pics from various sources.
I found some Mathematica code for color mapping of complex functions here.