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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 />git repository:
<a href="README">README file</a>, <a href="http://git.bnewbold.net/?p=8thesis.git;a=log">changelog</a>, <a href="http://git.bnewbold.net/?p=8thesis.git;a=tree">browse tree</a>,
<a href="./">browse local</a>
<li />MIT/GNU Scheme: <a href="http://www.gnu.org/software/mit-scheme/">project</a>, <a href="http://www.gnu.org/software/mit-scheme/documentation/mit-scheme-user/index.html">user guide</a>, <a href="http://www.gnu.org/software/mit-scheme/documentation/mit-scheme-ref/index.html">reference</a>, <a href="http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-4.html#%_toc_start">SICP text</a>
<li />R5RS: <a href="http://www.schemers.org/Documents/Standards/R5RS/r5rs.pdf">pdf</a>, <a href="http://www.schemers.org/Documents/Standards/R5RS/HTML/">html</a>
<li />SICM: <a href="http://mitpress.mit.edu/SICM/book-Z-H-4.html#%_toc_start">textbook</a>, <a href="http://groups.csail.mit.edu/mac/users/gjs/6946/linux-install.htm">scmutils</a>, <a href="http://groups.csail.mit.edu/mac/users/gjs/6946/">course</a>
<li />Physics department: <a href="http://mit.edu/physics/undergrad/majors/seniorthesis.html">thesis page</a>, <a href="http://mit.edu/physics/undergrad/ug_thesis_policy.pdf">policy.pdf</a>
</ul>
<h2>Schedule</h2>
My course schedule etc can be found at <a href="http://bnewbold.net/cal/">
bnewbold.net/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 />Ides of March (15th)
<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 />March 23-27
<td />Spring break week
<tr /><td />May 8
<td />Final due to department (non-doctoral degree)
</table>
<h2><a href="journal/">Journal Entries</a></h2>
<h2><a href="references.html">References, Reading List</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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