Look octonions (denizens of Octonia, which borders Philistia?) up in
'This Weeks Finds'....John Baez wrote on 'em a bit awhile back...
glen e. p. ropella wrote:
Thus spake Owen Densmore circa 09-10-10 08:26 PM:
Has anyone read this?
http://math.ucr.edu/home/baez/octonions/conway_smith/
I've not read enough Conway and I'm not sure where to start!
So, is it fair to say that octonions are a geometric algebra, even
though they aren't associative? I think I remember reading somewhere
that they were considered a geometric algebra... perhaps in Hestenes
book or in Penrose's Road to Reality.
But wikipedia claims that a geometric norm _must_ be associative and
that a geometric algebra must be over a vector space with an associative
norm. WTF? Is wikipedia oversimplifying? Or are octonions really not
considered a geometric algebra despite their deep relevance to geometry?
And, more importantly, why do my searches for Clifford fail in Adobe
Reader, but succeed in Evince, while reading the following file:
http://www.ams.org/bull/2002-39-02/S0273-0979-01-00934-X/S0273-0979-01-00934-X.pdf
???
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