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	<title>Mathematics and physics</title>
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		<title>Mathematics and physics</title>
		<link>http://borcherds.wordpress.com</link>
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		<title>Large cardinals and knot theory</title>
		<link>http://borcherds.wordpress.com/2008/01/26/large-cardinals-and-knot-theory/</link>
		<comments>http://borcherds.wordpress.com/2008/01/26/large-cardinals-and-knot-theory/#comments</comments>
		<pubDate>Sat, 26 Jan 2008 07:01:48 +0000</pubDate>
		<dc:creator>richard borcherds</dc:creator>
				<category><![CDATA[mathematics]]></category>
		<category><![CDATA[knot theory]]></category>
		<category><![CDATA[large cardinals]]></category>

		<guid isPermaLink="false">http://borcherds.wordpress.com/?p=15</guid>
		<description><![CDATA[I just came across the paper by P. Dehornoy: From large cardinals to braids via distributive algebra.  J. Knot Theory Ramifications  4  (1995),  no. 1, 33-79, 	which rather amazingly describes an application
of large cardinals in set theory to knot theory. The connection goes via left distributive algebras:
these are sets with a [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=borcherds.wordpress.com&blog=1058029&post=15&subd=borcherds&ref=&feed=1" />]]></description>
		<wfw:commentRss>http://borcherds.wordpress.com/2008/01/26/large-cardinals-and-knot-theory/feed/</wfw:commentRss>
		<slash:comments>10</slash:comments>
	
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		<title>Probability paradox</title>
		<link>http://borcherds.wordpress.com/2007/12/27/probability-paradox/</link>
		<comments>http://borcherds.wordpress.com/2007/12/27/probability-paradox/#comments</comments>
		<pubDate>Thu, 27 Dec 2007 04:52:31 +0000</pubDate>
		<dc:creator>richard borcherds</dc:creator>
				<category><![CDATA[mathematics]]></category>
		<category><![CDATA[Gaussian measure]]></category>
		<category><![CDATA[probability]]></category>

		<guid isPermaLink="false">http://borcherds.wordpress.com/2007/12/27/probability-paradox/</guid>
		<description><![CDATA[A result that amazed me when I first heard of it is that Gaussian measure on infinite dimensional Hilbert spaces does not exist. 
At first sight it seems obvious that it exists: on any finite dimensional quotient one can define a Gaussian probability measure, and these are all &#8220;compatible&#8221;. So their &#8220;inverse limit&#8221; should give [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=borcherds.wordpress.com&blog=1058029&post=14&subd=borcherds&ref=&feed=1" />]]></description>
		<wfw:commentRss>http://borcherds.wordpress.com/2007/12/27/probability-paradox/feed/</wfw:commentRss>
		<slash:comments>12</slash:comments>
	
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		<title>Uselessness of set theory?</title>
		<link>http://borcherds.wordpress.com/2007/12/25/uselessness-of-set-theory/</link>
		<comments>http://borcherds.wordpress.com/2007/12/25/uselessness-of-set-theory/#comments</comments>
		<pubDate>Tue, 25 Dec 2007 06:38:20 +0000</pubDate>
		<dc:creator>richard borcherds</dc:creator>
				<category><![CDATA[mathematics]]></category>
		<category><![CDATA[logic]]></category>
		<category><![CDATA[set theory]]></category>

		<guid isPermaLink="false">http://borcherds.wordpress.com/2007/12/25/uselessness-of-set-theory/</guid>
		<description><![CDATA[Mathematics is supposedly based on set theory. But if one looks closely, it is amazing (to me) just how little set theory is really used. Almost all &#8220;ordinary&#8221; mathematics seems to use no sets larger than the continuum. In other words most of mathematics can be carried out in second order arithmetic: roughly speaking this [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=borcherds.wordpress.com&blog=1058029&post=13&subd=borcherds&ref=&feed=1" />]]></description>
		<wfw:commentRss>http://borcherds.wordpress.com/2007/12/25/uselessness-of-set-theory/feed/</wfw:commentRss>
		<slash:comments>39</slash:comments>
	
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		<title>TeXmacs</title>
		<link>http://borcherds.wordpress.com/2007/06/15/texmacs/</link>
		<comments>http://borcherds.wordpress.com/2007/06/15/texmacs/#comments</comments>
		<pubDate>Fri, 15 Jun 2007 03:49:28 +0000</pubDate>
		<dc:creator>richard borcherds</dc:creator>
				<category><![CDATA[mathematics]]></category>

		<guid isPermaLink="false">http://borcherds.wordpress.com/2007/06/15/texmacs/</guid>
		<description><![CDATA[I recently discovered the TeXmacs editor, a sort of WYSIWYG editor similar to emacs
for TeX (or more precisely Latex ). It&#8217;s freely available from 	http://texmacs.org/ and should run on any computer with TeX. It makes writing stuff in TeX a lot easier (no more tracking down missing $ or } signs for example). Strongly recommended. [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=borcherds.wordpress.com&blog=1058029&post=12&subd=borcherds&ref=&feed=1" />]]></description>
		<wfw:commentRss>http://borcherds.wordpress.com/2007/06/15/texmacs/feed/</wfw:commentRss>
		<slash:comments>18</slash:comments>
	
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		<title>My dad has more money than yours.</title>
		<link>http://borcherds.wordpress.com/2007/05/26/my-dad-has-more-money-than-yours/</link>
		<comments>http://borcherds.wordpress.com/2007/05/26/my-dad-has-more-money-than-yours/#comments</comments>
		<pubDate>Sat, 26 May 2007 14:17:11 +0000</pubDate>
		<dc:creator>richard borcherds</dc:creator>
				<category><![CDATA[mathematics]]></category>

		<guid isPermaLink="false">http://borcherds.wordpress.com/2007/05/26/my-dad-has-more-money-than-yours/</guid>
		<description><![CDATA[In this well known children&#8217;s game, both player name an integer, and the winner is the one who names the largest integer, or better still the one who utterly humiliates his opponent by naming a vastly larger integer. Integers must be named in a constructive way, say by writing down an explicit Turing machine which [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=borcherds.wordpress.com&blog=1058029&post=7&subd=borcherds&ref=&feed=1" />]]></description>
		<wfw:commentRss>http://borcherds.wordpress.com/2007/05/26/my-dad-has-more-money-than-yours/feed/</wfw:commentRss>
		<slash:comments>10</slash:comments>
	
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		<title>Toroidal black holes?</title>
		<link>http://borcherds.wordpress.com/2007/05/22/toroidal-black-holes/</link>
		<comments>http://borcherds.wordpress.com/2007/05/22/toroidal-black-holes/#comments</comments>
		<pubDate>Tue, 22 May 2007 18:37:44 +0000</pubDate>
		<dc:creator>richard borcherds</dc:creator>
				<category><![CDATA[physics]]></category>

		<guid isPermaLink="false">http://borcherds.wordpress.com/2007/05/22/toroidal-black-holes/</guid>
		<description><![CDATA[A well known theorem about black holes (due to Hawking?) states that their boundary must be a sphere, rather than a higher genus surface. For genus greater than 1 the proof seems fine, but the proof for genus 1 (a torus) seems incomplete :it rules them out physically as being unstable, but this seems to [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=borcherds.wordpress.com&blog=1058029&post=5&subd=borcherds&ref=&feed=1" />]]></description>
		<wfw:commentRss>http://borcherds.wordpress.com/2007/05/22/toroidal-black-holes/feed/</wfw:commentRss>
		<slash:comments>24</slash:comments>
	
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		<item>
		<title>Planck units (uselessness of).</title>
		<link>http://borcherds.wordpress.com/2007/05/16/planck-units-uselessness-of/</link>
		<comments>http://borcherds.wordpress.com/2007/05/16/planck-units-uselessness-of/#comments</comments>
		<pubDate>Wed, 16 May 2007 02:28:03 +0000</pubDate>
		<dc:creator>richard borcherds</dc:creator>
				<category><![CDATA[physics]]></category>

		<guid isPermaLink="false">http://borcherds.wordpress.com/2007/05/16/planck-units-uselessness-of/</guid>
		<description><![CDATA[Planck units are determined by setting the speed of light c, Planck&#8217;s constant h, and the gravitational constant all equal to 1.  The speed of light and Planck&#8217;s constant (give or take a factor of two pi) seem fundamental, but it is not clear why the gravitational constant G should be 1.
A minor problem [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=borcherds.wordpress.com&blog=1058029&post=3&subd=borcherds&ref=&feed=1" />]]></description>
		<wfw:commentRss>http://borcherds.wordpress.com/2007/05/16/planck-units-uselessness-of/feed/</wfw:commentRss>
		<slash:comments>30</slash:comments>
	
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