reading course in SICM

email sent to a few grad students and a professor:

I mentioned earlier the idea of a reading course in 'symbolic computational physics'. This is an explanation of what I meant by that, and also maybe a draft of an advertisement for wider circulation:

What I had in mind by "symbolic computational physics" is along the lines of one of Sussman[1] and Wisdom[2]'s projects at MIT. They have used the computer language Scheme[7] to create an environment for doing symbolic computations--sort of a free, open-source mini-Mathematica--and then they have applied this to, so far, classical mechanics[3] and metric differential geometry[4]. Their introduction to this whole project, emphasizing pedagogical motivation, is [5]; their advanced course in classical mechanics at MIT is taught using [3] ("SICM") as a textbook.

The goals are several: (1) by implementing the mathematics in a computer language, all possible ambiguities in the notation are eliminated, since the notation can be interpreted mechanically, by a computer; a major goal of this is pedagogical, to really cultivate understanding of the theoretical, formal underpinnings of some theory. (2) another benefit is that once you have the entire formulism for some physical theory implemented on the computer, you can use it to do symbolic calculations and numerical simulations mechanically.

I am not sure whether Sussman and Wisdom have actually used their system in 'production' research, though I would be interested in finding out whether they have or if they have any ideas. My own interest is largely in learning the underlying physics or math. My idea is to, next semester, alone or with other interested grad students, go through the classical mechanics (SICM) text and/or the differential geometry text. We could try to apply and extend the differential geometry framework to gravitation or perhaps statistical mechanics, perhaps culminating in a note "Structure and Interpretation of {Gravitation, Statistical Mechanics}."

With a background in computer science, their approach appeals to me strongly; I am not sure whether someone with a more traditional physics background would feel the same attraction. I am experienced user of the Lisp programming language and would be able to teach the relevant parts to anyone interested; the canonical textbook is [6], though that would be overkill. It's a fun and powerful language.

Anyone interested?

[1] http://www.swiss.csail.mit.edu/~gjs/gjs.html
[2] http://swiss.csail.mit.edu/users/wisdom/
[3] http://mitpress.mit.edu/SICM/book-Z-H-4.html
[4] http://swiss.csail.mit.edu/users/wisdom/AIM-2005-003.pdf
[5] ftp://publications.ai.mit.edu/ai-publications/2002/AIM-2002-018.ps
[6] http://mitpress.mit.edu/sicp/
[7] http://en.wikipedia.org/wiki/Scheme_programming_language

Tobin


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