[Haskell-cafe] Geometric Algebra [Was: writing a function to make a correspondance between type-level integers and value-level integers]

[oleg at okmij.org]

> It seems very interesting, but I have not currently the time to make a 
> detailed comparison with vector/tensor algebra. Moreover I have not 

I would suggest the freely available
        Oersted Medal Lecture 2002
        by David Hestenes
        http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf
the person who discovered and developed the Geometric Algebra.

In particular, see Section V of the above paper. It talks about
vectors, geometric products, the coordinate-free representation for
`vector product' and the geometric meaning of the imaginary unit i.
Section 1 gives a good motivation for the Geometric Algebra. Other
sections of the paper develop physical applications, from classical
mechanics to electrodynamics to non-relativistic and relativistic
quantum mechanics.

Computer Scientists might then like
        http://www.geometricalgebra.net/
see the good and free introduction
        http://www.geometricalgebra.net/downloads/ga4cs_chapter1.pdf

Incidentally, David Hestenes said in the lecture that he has applied
for an NSF grant to work on Geometric Algebra TWELVE times in a row,
and was rejected every single time.