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December 2018

Quantum Gravity Lesson 7

Recall that discrete simplices come from paths on a torus, or rather, discrete cubes. There are 2 easy ways to count 27 paths, using qutrits.

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Here the blue numbers count the noncommutative words in 3 letters, of length 3 or 4. By choosing one digit out of four, we select the neutrino source vertex on Cohl Furey’s parity cube of charges for Standard Model states. We must make the choice to get a 3d cube: a cube on each of the 3 sides of the triangle.

And for fun, here is the ancient seal with the 72 names of God in the center (aka e6). Discrete blowups for a magic plane require discrete simplices. Yes, there’s some serious history revision that the Patriarchy doesn’t want you to know about ...

878F671F-DD9F-4B23-86B4-1A0FA75719E4


Quantum Gravity Lesson 5

The Jordan algebra theorists have been studying the broken Jacobi rule in the algebras of exceptional periodicity, but forgot to mention the important polytope of length 3 words: the two dimensional permutoassociahedron.

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Here the zero terms are included. Taking 2 adjacent zeroes (two plus signs in a bracket) we can think of the braiding arrow in between as a zero. Then the remaining 11 edges give the new Jacobi rule. The associators act as minus signs and the gammas as plus signs. There are 2 additional zeroes, but it works. Recall that the 3d permutoassociahedron has eight of these 12-gons, and 120 vertices.

arxiv/1811.11202

In it’s usual form, the 12-gon appears here:

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Note the additional edges for the braiding of bracketed objects. Here I was discussing the 8n dimensions of nested cubes and the powers of 2 associated to spinors.


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