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