Re: Why Octonions 1: Introduction
- From: tadchem <tadchem@xxxxxxxxxxx>
- Date: Tue, 12 Aug 2008 15:09:19 -0700 (PDT)
On Aug 9, 12:03 am, Rick <r...@xxxxxxxxxxxxx> wrote:
Why should anyone bother with Octonion Algebra? After all,
it has been dismissed by many intelligent people as being
a mathematically interesting algebra, but with little
practical application.
Geometric symmetry groups in 8 dimensions? - Could be VERY
interesting.
Some have called it a "lost cause"
in physics,
Superstring theory jumped from 4 dimensions straight to 10 dimensions,
skipping octonians entirely.
others have said they would not recommend it as
an area of study for a graduate thesis.
Most graduates would like to get jobs with a chance at a decent
paycheck, and academics positions are sparse. Unfortunately the
commercial world has little interest in 8-dimensional physics at the
moment.
Some have claimed a
suitable calculus on Octonions cannot be had because the
notions of complex regularity do not extend to either the
Quaternions or the Octonions.
But quaternions at least are useful in Minkowski space, where the game
of General Relativity is played.
Since Octonions are not an
associative algebra for multiplication,
Symmetry groups used in crystallography, molecular modeling, etc. rely
on rotations in 3 space which do not obey associative algebra.
<GTG>
Tom Davidson
Richmond, VA
.
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