diff options
| author | bnewbold <bnewbold@eta.mit.edu> | 2009-01-16 04:29:16 -0500 |
|---|---|---|
| committer | bnewbold <bnewbold@eta.mit.edu> | 2009-01-16 04:29:16 -0500 |
| commit | df1d1038048c1db7e1f7c2436993c3017de2542a (patch) | |
| tree | f402fa51f4480437585e3363ff862f9c08bb7946 /sicm-fall08.html | |
| download | 8thesis-df1d1038048c1db7e1f7c2436993c3017de2542a.tar.gz 8thesis-df1d1038048c1db7e1f7c2436993c3017de2542a.zip | |
initial import of existing content
Diffstat (limited to 'sicm-fall08.html')
| -rw-r--r-- | sicm-fall08.html | 127 |
1 files changed, 127 insertions, 0 deletions
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 @@ +<html> +<head><title>SICM Material Fall 2008</title></head> +<body style="margin: 25px; font-family: helvetica;"> +<h1 style="border-bottom: 2px solid;">Functional Relativity, Symbolic Geometry, et al</h1> +<i>Bryan Newbold, <a href="mailto:bnewbold@mit.edu">bnewbold@mit.edu</a></i><br /> +<i><a href="http://web.mit.edu/bnewbold/Public/sicm-fall08.html"> +http://web.mit.edu/bnewbold/Public/sicm-fall08.html</a></i> + +<h2>Informal Background</h2> +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. +<br /> <br /> +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. +<br /><br /> +The stimulus for this course of study was the class +<a href="http://www-swiss.ai.mit.edu/~gjs/6946/index.html">Classical +Mechanics: A Computational Approach</a> taught by G. Sussman and J. Wisdom +at <a href="http://web.mit.edu">MIT</a>. 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. + +<h2>Potential Fall Projects</h2> + +<b>Integration of mit-scheme and scmutils into Sage</b> +<span style="font-weight:bold; color:#00CC00;">(yes)</span> +<br />The <a href="http://sagemath.org">Sage math system</a> 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 +<a href="http://www.sagemath.org/packages/standard/">list</a>). <br /> +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 <a href="http://www.sagemath.org/doc/prog/prog.html"> +here</a> and <a href="http://www.sagemath.org/doc/ref/node95.html">here</a> +<br /> +There is a public demo server at <a href="http://sagenb.org">sagenb.org</a>, +but it's usually slow. Try this +<a href="https://sage.math.washington.edu:8102/">server</a> 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. +<br /><br /> + +<b>Exploration of "higher order dynamics"</b> +<span style="font-weight:bold; color:orange;">(possible)</span> +<br /> +I'd like to play with systems involving "higher order dynamics", aka {jerk, +yank, <a href="http://sprott.physics.wisc.edu/pubs/paper229.pdf">snap, crackle, pop</a>}. These dynamics have become interesting to cosmologists? +<br />See arxiv <a href="http://arxiv.org/abs/gr-qc/0309109">one</a>, <a href="http://arxiv.org/abs/astro-ph/0408279">two</a>, other chaotic <a href="http://sprott.physics.wisc.edu/pubs/paper229.pdf">pdf</a>. +<br /><br /> + +<b>General Relativity Simulations: compact bodies, inspirals, precession</b> +<span style="font-weight:bold; color:orange;">(possible)</span> +<br />Should talk with <a href="http://gravity.psu.edu/people/LSF/">Lee Finn +</a>@penn, <a href="http://mit.edu/pranesh/www/">pranesh</a>@mit? Go to +<a href="http://space.mit.edu/journalclub/index.html">mki journal club</a>. +<br /> <br /> + +<b>Modified Newtonian Dynamics</b> +<span style="font-weight:bold; color:orange;">(possible)</span> +<br /><a href="http://en.wikipedia.org/wiki/Modified_Newtonian_dynamics">MOND</a> +was originally proposed to explain the galactic rotation curve +problem; it has been extended as a relativistic field theory as +<a href="http://en.wikipedia.org/wiki/Tensor-vector-scalar_gravity">TeVeS</a> +(Tensor-vector-scalar gravity, described in 2004). +<br /> +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. +<br />See also Henon-Heiles. +<br /> <br /> + +<b>Action Minimization Problems</b> +<span style="font-weight:bold; color:orange;">(possible)</span> +<br /> +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. +<br /><br /> + +<b>Basic Quantum Mechanics</b> +<span style="font-weight:bold; color:red;">(unlikely)</span> +<br />Methods with Wilkson-Sommerfeld quantization? I don't know enough +QM to go beyond simple, introductory quantum systems, but might be interesting. +<br /><br /> + +<b>Quantum Computation</b> +<span style="font-weight:bold; color:red;">(unlikely)</span> +<br />There is already extensive work done here; see +<a href="http://tph.tuwien.ac.at/~oemer/qcl.html">http://tph.tuwien.ac.at/~oemer/qcl.html</a><br /><br /> + + +<h2>Resources</h2> +The SICM text book is <a href="http://mitpress.mit.edu/SICM/">free online</a>; +so is the <a href="http://mitpress.mit.edu/sicp/">SICP book</a>. +</br /> +There is an unofficial <a href="http://groups.google.com/group/sicm">SICM mailing list</a>.<br /> +<br /> +<b>Papers to read?</b> (<a href="http://static.bryannewbold.com/toread/thought/">download</a>) +<ul> + <li /><u>The Dynamicist's Workbench: Automatic Preparation of Numerical Experiments</u>, H. Abelson and G. Sussman + <li /><u>Simulating Physics with Computers</u>, R. Feynman + <li /><u>Functional Differential Geometry</u>, G. Sussman and J. Wisdom (2005) + + <li /><u>Computer Programs for Calculating General-Relativistic Curvature Tensors</u>, J. Fletcher, R. Clemen, R. Matzner, K. Thorne, and B. Zimmerman (letter, 1967) + <li /><u>Intelligence in Scientific Computing</u>, H. Abelson, M. Eisenberg, M. Halfant, J. Katzenelson, E. Sacks, G. Sussman, J. Wisdom, and K. Yip + <li /><u>Abstraction in Numerical Methods</u>, M. Halfant and G. Sussman + <li /><u>The Role of Programming in the Formulation of Ideas</u>, G. Sussman and J. Wisdom + <li /><u>Scientific Comutation and Functional Programming</u>, J. Karczmarczuk (1999) + <li /><u>The Supercomputer Toolkit: A general framework for special-purpose computing</u>, H. Abelson, A. Berlin, J. Katzenelson, W. McAllister, G. Rozas, G. Sussman, and J. Wisdom (1991) + +</ul> +</body> +</html> + |