Tag Archives: Hopf

Mathematica Analysis of JLN’s TUFT

This post presents my independent analysis of Jenny Lorraine Nielsen’s (JLN’s) Topological Unified Field Theory (TUFT). It symbolically implements her equations related to the fundamental constants, General Relativity (GR) cosmological parameters, and Standard Model (SM) particle masses and magnetic gyrometric ratios and anomalous moments. It then calculates the values and compares them against the PDG CODATA from Wolfram’s curated data sets.

The structure of this analysis is shown (below) in PNG (click for SVG version) or see here for the full PDF of the analysis or here for the Mathematica Notebook (NB) version:

Outline of my Mathematica analysis of JLN’s TUFT predictive theoretical parameters
E8 Hopf Fibration
The Aizawa Chaotic Attractor

This is all also related to the Clifford algebra of Cl(9,0) with the Bott Periodicity clock showing the related algebras (click for SVG):

Bott Periodicity Clock of Cl(9,0) as it relates to the Hopf Fibration of CP4

The Bott periodicity clock uses a Mod 8 clock face with second hand mnemonics taken from the I-Ching with the real Clifford algebra of signature (p,q) denoted as Clp,q(R)=Cl(p,q). An animated (GIF) example is on the Bott Periodicity Wikipedia page.

E8 and H4 Hopf Fibrations with the Aizawa Chaotic Attractor

If you are working with topological field theoretic Hopf fibrations, chaotic attractors, and/or E8 and any of its extensive set of maximal subgroups, polytopes, lattices and codes or its folded (rotated) H4 family of polytopes (e.g. 600 and 120 cells in their vertex, cell, face, and edge orientations), VisibLie_E8 can group theoretically integrate all of these concepts visually!

Click on the PNG image to get the SVG version.

E8 Hopf Fibration
H4 600-cell Hopf Fibration
The H4 cell-first {5,3,3} 120-cell Hopf Fibration (with envelope of a Chamfered Dodecahedron)
The Aizawa Chaotic Attractor

This is all also related to the Clifford algebra of Cl(9,0) with the Bott Periodicity clock showing the related algebras (click for SVG):

Bott Periodicity Clock of Cl(9,0) as it relates to the Hopf Fibration of CP4

The Bott periodicity clock uses a Mod 8 clock face with second hand mnemonics taken from the I-Ching with the real Clifford algebra of signature (p,q) denoted as Clp,q(R)=Cl(p,q). An animated (GIF) example is on the Bott Periodicity Wikipedia page.

A few more Hopf geometries:

The envelope of the vertex first 600-cell aka. PentakisIcosidodecahedron
The envelope of the cell first 120-cell aka. Chamfered Dodecahedron
The Icosahedron @ quality 3