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
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
All that gives hope for finding the generalized statistics we need
on the (relative) histories or observer-moments (i.e, with AUDA,
Well... let us dream a bit... ;-)