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From: Marchal Bruno <marchal.domain.name.hidden>

Date: Thu, 21 Nov 2002 12:19:31 +0100 (MET)

Tim May wrote

*>(I was struck by the point that the sequence "1, 2, 4, 8" is the only
*

*>sequence satisfying certain properties--the only "scalars, vectors,
*

*>quaternions, octonions" there can be--and that the sequence "3, 4, 6,
*

*>10," just 2 higher than the first sequence, is closely related to
*

*>allowable solutions in some superstring theories, and that these facts
*

*>are related.)
*

That's indeed what amazes me the more. I always thought that the dimension

justification in string theories was unconvincing, but with the octonion

apparition there, I must revised my opinion.

Needless to say I hope octonions will appear in the Z1* semantics!

(so we could extract string theory from comp directly).

Do you know that Majid found a monoidal category in which the octonions

would naturally live, even (quasi)-associatively, apparently.

I think the sedenions (16 dim) could play a role too, even if they do not

make a division algebra. cf the (not really easy) 1998 paper by Helena

Albuquerque and Shahn Majid "quasialgebra structure of the octonions".

For the paper and some other see http://arXiv.org/find/math/1/ti:+octonions/0/1/0/1998/0/1

All that gives hope for finding the generalized statistics we need

on the (relative) consistent histories or observer-moments

(i.e, with AUDA, a Z1* semantics).

Well... let us dream a bit... ;-)

Bruno

Received on Thu Nov 21 2002 - 06:19:52 PST

Date: Thu, 21 Nov 2002 12:19:31 +0100 (MET)

Tim May wrote

That's indeed what amazes me the more. I always thought that the dimension

justification in string theories was unconvincing, but with the octonion

apparition there, I must revised my opinion.

Needless to say I hope octonions will appear in the Z1* semantics!

(so we could extract string theory from comp directly).

Do you know that Majid found a monoidal category in which the octonions

would naturally live, even (quasi)-associatively, apparently.

I think the sedenions (16 dim) could play a role too, even if they do not

make a division algebra. cf the (not really easy) 1998 paper by Helena

Albuquerque and Shahn Majid "quasialgebra structure of the octonions".

For the paper and some other see http://arXiv.org/find/math/1/ti:+octonions/0/1/0/1998/0/1

All that gives hope for finding the generalized statistics we need

on the (relative) consistent histories or observer-moments

(i.e, with AUDA, a Z1* semantics).

Well... let us dream a bit... ;-)

Bruno

Received on Thu Nov 21 2002 - 06:19:52 PST

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