The main change was an improved association of the 120 periodic table elements to the 120 root vectors weighted by their simple root grading. See the full 241 page reference here.

# Tag Archives: Fano

# The 480 octonions, their Fano planes and multiplication tables

I am pleased to announce the availability of Fano.pdf, a 241 page pdf file with the 480 octonion permutations (with Fano planes and multiplication tables). These are organized into “flipped” and “non-flipped” pairs associated with the 240 assigned particles to E8 vertices (sorted by Fano plane index or fPi). For each split real even E8 vertex, the algebra root, weight and height are listed along with the Clifford/Pascal binary and physics rotation coordinates. On each page, the E8 particle number, symbol, and assigned 2D/3D shape are shown along with the (a)nti, (p)Type, (s)pin, (c)olor, (g)eneration bitwise quantum assignments. Also included is the particle experimental mass and lifetime along with my ToE theoretically calculated mass. (30MB)

I believe this is the only comprehensive presentation of all 480 Fano planes with their multiplication tables available.

# Update: Quaternions, Octonions, Time, Particle Mass/Charge and Reality

I am improving and tightening the octonion to E8 to particle symmetry assignments which should inform the particle mass/charge assignment (prediction).

Keep looking at the .CDF .NB or interactive pages – it is always up to date.

I am thinking about how the quaternion trialities within the non-associative algebra of octonions relate to time (and differentiate particles). So it is less about E8 and more about how octonions (linked to E8) affect our 4D reality.

# Octonions, Quaternions and the Fano plane mnemonic – Conquered!

See:

http://theoryofeverything.org/TOE/JGM/ToE_Demonstration.cdf

Of course, it requires the free Mathematica CDF plugin.