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!

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) histories or observer-moments (i.e, with AUDA, 
Z1* semantics). 
Well... let us dream a bit...  ;-)

Bruno
 

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