[time 154] Re: [time 149] Re: [time 108] Re: [time 81] Entropy, wholeness, dialogue, algebras

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Sun, 4 Apr 1999 20:33:15 +0300 (EET DST)

On Sun, 4 Apr 1999, Ben Goertzel wrote:

> >[MP]
> >I think that octonions and quaternions and p-adicity are separate aspects
> >of theory.
> One nice feature of Tony Smith's theory is that particle interactions are
> described
> by the octonion multiplication table.
> Your theory presumably explains these same particle interactions, by a
> different
> mathematics.

Mathematics is Super Virasoros et related algebras at basic level.
At QFT limit mathematics is p-adic version of standard model with
some modifications. YM action appears as effective action. I think
that octonions might be important at much deeper level.

> Therefore, if we could isolate the part of your theory that explains
> particle interactions,
> we would be able to map the octonions onto your theory.

There might be something deep in induction of imbedding space
tangent space octonion structure to spacetime surface [octonion units
are projected to spacetime and their products which contain also
part normal to surface are projected to spacetime surface so that one
obtains tangent space projection Calphabetagamma of structure constant
tensor Cklm defined by IkIl = Ckl^mIm ]. But I do not know any idea about
what deep consequences this might have. Quaternions appear
in the construction of exact solutions of YM action (instantons): could
octonions appear in the construction of the absolute minima of Kahler
action if this construction is possible at all (just a free

> I.e., every theory that explains
> the particle interactions covered by the Standard Model ~implicitly~ has
> octonions in it;
> the question is whether it's worth making this explicit or not
> ben

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