**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Sun, 4 Apr 1999 20:33:15 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 155] Re: [time 154] Entropy, wholeness,dialogue, algebras"**Previous message:**Ben Goertzel: "[time 153] reading"**Next in thread:**Stephen P. King: "[time 155] Re: [time 154] Entropy, wholeness,dialogue, algebras"

On Sun, 4 Apr 1999, Ben Goertzel wrote:

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

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

association(;-)?

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