From 474f620ecc069600b82c22c753c11fbe46494055 Mon Sep 17 00:00:00 2001 From: bnewbold Date: Fri, 16 Jan 2009 18:59:40 -0500 Subject: moved some files --- sicm-fall08.html | 127 ------------------------------------------------------- 1 file changed, 127 deletions(-) delete mode 100644 sicm-fall08.html (limited to 'sicm-fall08.html') diff --git a/sicm-fall08.html b/sicm-fall08.html deleted file mode 100644 index db6c70e..0000000 --- a/sicm-fall08.html +++ /dev/null @@ -1,127 +0,0 @@ - -SICM Material Fall 2008 - -

Functional Relativity, Symbolic Geometry, et al

-Bryan Newbold, bnewbold@mit.edu
- -http://web.mit.edu/bnewbold/Public/sicm-fall08.html - -

Informal Background

-For the fall of 2008 I'm very interested in investigating gravitation and -other physical theories using functional programming techniques. I find that -formalizing physical systems into a computer model is the best way to solidify -my understanding of the system; using functional languages and techniques -makes the conceptual wall between mathematical abstraction and programming -implementation much lower; the result is a more reusable and general model -well suited for experimentation and exploration. -

-I am planning on getting my undergraduate physics degree in spring 2009, for -which I will need a thesis. I am hoping to develop skills and tools this fall -with which to accomplish Real Live Science over IAP and in the early spring. -

-The stimulus for this course of study was the class -Classical -Mechanics: A Computational Approach taught by G. Sussman and J. Wisdom -at MIT. I had trouble with the later sections -of the book/course and am hoping that now with an eta of math under my belt I -can chip away at it. - -

Potential Fall Projects

- -Integration of mit-scheme and scmutils into Sage -(yes) -
The Sage math system is an open-source -alternative to Mathematica, Maple, etc. It provides an easy to learn html -notebook interface (as well as command line) and is bundled with a plethora -of high performance libraries (like PARI, GMP, MAXIMA, SINGULAR, see this -list).
-A number of other packages (including common lisp) already have interfaces -based around a fake TTY device; this should be easy with mit-scheme. Or a more -complete object-style interface could be implemented. There is documentation -for writing interfaces -here and here -
-There is a public demo server at sagenb.org, -but it's usually slow. Try this -server instead (user: -ableseaman, password: bottlerum, if you don't want to fill out the form). -Sage has been used in math classes at MIT already; Tim Abbot is working -on "debianizing" the whole system, after which it should be on Athena. -

- -Exploration of "higher order dynamics" -(possible) -
-I'd like to play with systems involving "higher order dynamics", aka {jerk, -yank, snap, crackle, pop}. These dynamics have become interesting to cosmologists? -
See arxiv one, two, other chaotic pdf. -

- -General Relativity Simulations: compact bodies, inspirals, precession -(possible) -
Should talk with Lee Finn -@penn, pranesh@mit? Go to -mki journal club. -

- -Modified Newtonian Dynamics -(possible) -
MOND -was originally proposed to explain the galactic rotation curve -problem; it has been extended as a relativistic field theory as -TeVeS -(Tensor-vector-scalar gravity, described in 2004). -
-I think it would be interesting to implement and play with MOND or other -alternative gravitational theories in a symbolic computation framework. -Assumptions could be checked quickly and easily (eg, behaves like X in the -short distance limit, behaves like Y in the high stress-energy limit). -The process of formalization could also be a good test; if the theory can't -be coded, is it a valid theory? Would also demonstrate that programming tools -are general and can be used to explore non-physical theories. -
See also Henon-Heiles. -

- -Action Minimization Problems -(possible) -
-Minimization of action over path integrals is a classic hammer in the physics -toolbox (everything looks like an oscillating nail). It might be fun to -play with some old classics like optics or Ohm-ic resistance. -

- -Basic Quantum Mechanics -(unlikely) -
Methods with Wilkson-Sommerfeld quantization? I don't know enough -QM to go beyond simple, introductory quantum systems, but might be interesting. -

- -Quantum Computation -(unlikely) -
There is already extensive work done here; see -http://tph.tuwien.ac.at/~oemer/qcl.html

- - -

Resources

-The SICM text book is free online; -so is the SICP book. -
-There is an unofficial SICM mailing list.
-
-Papers to read? (download) - - - - -- cgit v1.2.3