Ars Mathematica

The best part about this site is that I can link to interesting articles that I don’t have time to read. One of the early inspirations for the study of dynamical systems was statistical mechanics, particularly the ergodic hypothesis. Things have now come full circle with applications of dynamical systems to statistical mechanics. Here’s a survey article on the subject by David Ruelle: Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics.

As a follow-up to yesterday’s post, I came across an entry on symmetry breaking at the Stanford Encyclopedia of Philosophy. It’s interesting to see philosophy directly engaging with the implications of modern physics.

They also have two entries on the philosophical underpinnings of statistical mechanics: a general entry, and a more specific one on Boltzmann. The actual justification for statistical mechanics and the reduction of thermodynamics to statistical mechanics is apparently fairly controversial.

Sean at Cosmic Variance has written a nice introduction to symmetry breaking, one of the oddest (and most successful) ideas in particle physics.

Al Zimmermann is running a programming competition to see who can:

Pack n non-overlapping circles with radii from 1 to n into as small a circle as possible.

You have until mid-January to come up with solutions for n between 5 and 50.

(via Lamba the Ultimate).