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 -- > ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
