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.

2 thoughts on “The 480 octonions, their Fano planes and multiplication tables”

  1. Hello JG-
    Congratulations on this fine accomplishment. I’m reminded of the World Champion Bridge player Alan Sontag. In one of his books, he wrote series after series after series of bidding sequences in his – and Peter Weichsel’s – Precision Bidding System. As he finished a description of one of these sequences, he wrote that, “This sequence has never come up but we still think it should be in the system…”.

    It’s a dirty job but somebody has to do it…

    So, I ask a variation of the question I first asked: “What’s left to do and is anyone else listening?” I assume that Lisi and Smolin would be aware of this advance or at least someone would! If SU(5) would generate a 50,000 gallon water experiment in an abandoned mine in Japan to test X-bosons, I can’t imagine that extending this Type of idea to Octonians and E8 would lead to a shoulder shrug and “So, What?”

    What’s left to do?
    Who else needs to know this?



  2. As for “what is left to do”, the answer for me is to be able to simply, accurately and elegantly predict the particle mass and charge characteristics for all experimentally known particles. I believe the mathematics involved in E8, Octonions, and Clifford algebras may lead me to this – and that is why I do it- to understand the nature of the Universe.

    If anyone wants to listen – great! If not – oh well, their loss. I agree, one would think it would be worth even a query from academia as to the algorithms used. I have tried to publish the source at Wolfram Demonstrations, but the editors (some of whom have worked in this area) take issue with its publication there. I suspect it is because I have found errors in their published work.

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