This link to an Oersted Medal talk is indeed of great interest. The
author, the theoretical physicist David Hestenes, built on the
foundation laid by mathematicians in the 19th century and in an
important sense completed their work on what is called "Geometric
Algebra", a framework which unifies much of the math done by
physicists, by providing geometric representations in all areas that
complement the algebra.

An analogy: The introduction of vectors by Gibbs made many things
easier to do and to say. Not only were many things easier to do, more
importantly the vector concept provided powerful new ways of thinking.
GA is like that. Some things that are very effortful with vectors
become much easier with GA, but more importantly it opens up new ways
of thinking and, as mentioned above, unifies many maths (plural) that
are usually seen as completely separate. Incidentally, Hestenes feels
that it's unfortunate that Gibbs took a piece out of GA and missed the
full point, but it's only the Gibbs vectors that most physicists know
about. For example, in the Gibbs view there are two kinds of vectors,
the regular kind and "axial" vectors. In GA there's only one kind of
vector; what has been called an "axial" vector is actually a 2D
"bivector" representing a planar element whose magnitude is its area.
An example is the cross product of two vectors.

For me, a striking example of the unifying power of GA is this: The
Pauli spin matrices were taught to me as special 2x2 matrices, special
to quantum mechanics, for describing the spin state of an electron. In
the GA framework, these matrices pop out as just a natural part of
living in a 3D world! Nothing particularly to do with quantum
mechanics! Stunning.

There are additional GA links on my home page, http://www4.ncsu.edu/~basherwo/.

I hasten to say that I am alas not an expert on GA, just a fan
observing from a distance. Also, I've been told that something called
"differential forms" has much of the same flavor and power, and I know
absolutely nothing about that.

Bruce

On Mon, Jan 23, 2012 at 11:43 PM, Roger Critchlow <r...@elf.org> wrote:
> http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf
>
> -- rec --
>

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