From df1d1038048c1db7e1f7c2436993c3017de2542a Mon Sep 17 00:00:00 2001 From: bnewbold Date: Fri, 16 Jan 2009 04:29:16 -0500 Subject: initial import of existing content --- sicm-fall08.html | 127 +++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 127 insertions(+) create mode 100644 sicm-fall08.html (limited to 'sicm-fall08.html') diff --git a/sicm-fall08.html b/sicm-fall08.html new file mode 100644 index 0000000..db6c70e --- /dev/null +++ b/sicm-fall08.html @@ -0,0 +1,127 @@ + +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