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<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.bnewbold.net/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>
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