On Mon, Jul 27, 2009 at 10:59 PM, Steve Witham<sw@tiac.net> wrote:

it looks like the only kind of symmetries it applies to are transformations that you can have continuous versions of, like translation and rotation.  Is this true?  It makes me sad!

No.

I would have liked a conservation law to pop out of *every* kind of symmetry!

James Gilliam did his thesis on "discrete mechanics", a generalization of classical mechanics in which both the phase space and time are discrete. There's a lot of work on mechanics in which time takes integer values, so the real novelty here was adapting the use of calculus in physics to situations where the phase space is also discrete. It turns out that the Euler-Lagrange equation, Noether's theorem, and the symplectic structure on phase space all generalize to this context. http://www.math.ucr.edu/home/baez/thesis_gilliam.pdf -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com