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<head><title>bnewbold thesis</title></head>
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<h1 style="border-bottom: 2px solid;">
Functional General Relativity in Scheme</h1>
<i>Bryan Newbold, <a href="mailto:bnewbold@mit.edu">bnewbold@mit.edu</a></i><br />
<i><a href="http://web.mit.edu/bnewbold/thesis/">
http://web.mit.edu/bnewbold/thesis/</a></i>
<br /><br />
<b>Title: </b> A Compuational Elucidation of Curved Spacetime<br />
<b>Advisor: </b> Prof. Gerald Sussman, EECS<br />
<b>Year: </b>2009<br />
<br />
The old version of this page is <a href="other/sicm-fall08.html">here</a>,
outlining what kind of projects I was interested in.
<h2>Quick Links</h2>
<ul>
<li /><a href="http://git.bryannewbold.com/">git repository</a>:
<a href="README">README file</a>, changelog, browse tree,
<a href="./">browse local</a>
<li />MIT/GNU Scheme: project, guide, installation
<li />R5RS
<li />SICM: textbook, scmutils
<li />My knowledge: scheme, math, physics
</ul>
<h2>Schedule</h2>
My course schedule etc can be found at <a href="http://bryannewbold.com/cal/">
bryannewbold.com/cal</a>.<br /><br />
<table style="border: solid black 1px; margin-left: 100px;" border="1" cellpadding="3" cellspacing="0">
<tr /><td /><b><u>When</u></b>
<td width="450px"/><b><u>What to do</u></b>
<tr /><td />Jan 16-22
<td />Self teach some more scheme and differential geometry, documenting
examples. Maybe work through 2 or 3 problems from SICM textbook
or implement some classic physics problems (eg current through
wire cross section, variational principle examples in Feynman
lectures, derivation of magnetism at the 8.022 level).
<br />Understand and document scmutils package and compiler
interactions (at least conceptually).
<br />If I'm going to put mit-scheme in sage, this is the time to
do it, after this point I shouldn't be focusing on the software
tools as much.
<tr /><td />Jan 19-26?
<td />Work through "Functional Differential Geometry", rewriting by hand
<tr /><td />Jan 31
<td />By this date have a proposed outline with length estimates so
I can sanity check with somebody in the physics department.
<tr /><td />Feb 28?
<td />Have something resembling a draft and be working out details,
getting comments from professors and other students. At least
one interesting application should be demonstrated.
<tr /><td />???
<td />Spring break week
<tr /><td />???
<td />Final due to department
</table>
<h2><a href="journal/">Journal Entries</a></h2>
<h2><a href="references.html">References</a></h2>
<h2>Summary/Abstract</h2>
<i>from proposal:</i>
<p />
I propose to implement a geometric formulation of curved space time in a
functional computer programming language, and to explore the space of
simulations
and manipulations made possible by such a formulation. A primary motivation
is to state the foundations of General Relativity in a non-ambiguous manner.
<p />
This work follows several attempts to formulate curved spacetime on
computers for the purpose of numerical calculations and algebraic manipulation.
Most of these packages are specially designed for the tasks of tensor analysis
and/or efficient numerical calculation, as is appropriate for use in
calculations.
A crucial difference of this proposed work will be to carefully build up the
geometric and analytical tools in a general purpose functional programing
language (mit-scheme). As a learning and reference tool, this will allow users
to explore
the inner workings and structure of the system, which I believe is essential to
understanding the system as a whole.
<p />
The frame field representation will be used to emphasize the geometric
properties of curved space time, as opposed to the more traditional coordinate
heavy tensor analysis approach.
<p />
The resulting work will include a full implementation with source code and
documentation, as well as example problems and qualitative comparisons with
existing packages and software systems.
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