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	<title>Anima Ex Machina &#187; Foundations of Math</title>
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	<description>The blog of Hector Zenil</description>
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		<title>Turing&#8217;s Deep Field: Visualizing the Computational Universe</title>
		<link>http://www.mathrix.org/liquid/archives/visualizing-the-computational-universe-or-turings-deep-field</link>
		<comments>http://www.mathrix.org/liquid/archives/visualizing-the-computational-universe-or-turings-deep-field#comments</comments>
		<pubDate>Thu, 05 Jan 2012 06:41:14 +0000</pubDate>
		<dc:creator>Hector Zenil</dc:creator>
				<category><![CDATA[Complexity]]></category>
		<category><![CDATA[Computability, Universality and Unsolvability]]></category>
		<category><![CDATA[Computer Science]]></category>
		<category><![CDATA[Foundations of Computation]]></category>
		<category><![CDATA[Foundations of Math]]></category>
		<category><![CDATA[Mathematical Logic]]></category>
		<category><![CDATA[automatic theorem proving]]></category>
		<category><![CDATA[busy beaver]]></category>
		<category><![CDATA[computer runtimes]]></category>
		<category><![CDATA[halting problem]]></category>
		<category><![CDATA[halting times]]></category>
		<category><![CDATA[length of proofs]]></category>
		<category><![CDATA[Turing machines]]></category>

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		<description><![CDATA[I generated this image in the course of an investigation of the distribution of runtimes of programs in relation to the lengths of mathematical proofs, the results of which are being published in my paper bearing the title &#8220;Computer Runtimes and the Length of Proofs with an Algorithmic Probabilistic Application to Optimal Waiting Times in [...]]]></description>
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		<title>Collections of axioms and information on theories dependency</title>
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		<pubDate>Sat, 03 Mar 2007 14:26:54 +0000</pubDate>
		<dc:creator>Hector Zenil</dc:creator>
				<category><![CDATA[Foundations of Math]]></category>
		<category><![CDATA[Mathematical Logic]]></category>

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		<description><![CDATA[List of Axioms from Computer Science Department, University of Miami Documentation, Computer Science Department, University of Miami List of axioms collected from Wikipedia. MBase: A Mathematical Knowledge Base. A collection of definitions, theorems and proofs. The Mathematical Atlas. Methamath. Proof symbolic visualizations, University of Texas.]]></description>
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		<title>&#8220;The ways of paradox&#8221;: Quine on Berry&#8217;s paradox.</title>
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		<pubDate>Sat, 03 Mar 2007 13:54:56 +0000</pubDate>
		<dc:creator>Hector Zenil</dc:creator>
				<category><![CDATA[Foundations of Math]]></category>
		<category><![CDATA[paradoxes]]></category>
		<category><![CDATA[Quine]]></category>

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		<description><![CDATA[&#8220;Ten has a one-syllable name. Seventy-seven has a five-syllable name. The seventh power of seven hundred seventy-seven has a name that, if we were to work it out, might run to 100 syllables or so; but this number can also be specified more briefly in other terms. I have just specified it in 15 syllables. [...]]]></description>
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		<title>Book on self-reference (comprising papers by various contributors)</title>
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		<pubDate>Sat, 03 Mar 2007 13:50:19 +0000</pubDate>
		<dc:creator>Hector Zenil</dc:creator>
				<category><![CDATA[Foundations of Math]]></category>
		<category><![CDATA[selfreference]]></category>

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		<description><![CDATA[Table of contents and introduction: http://www.imm.dtu.dk/~tb/genintro.pdf]]></description>
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		<title>On single and shortest axioms for Boolean logic</title>
		<link>http://www.mathrix.org/liquid/archives/on-single-and-shortest-axioms</link>
		<comments>http://www.mathrix.org/liquid/archives/on-single-and-shortest-axioms#comments</comments>
		<pubDate>Sat, 03 Mar 2007 13:42:39 +0000</pubDate>
		<dc:creator>Hector Zenil</dc:creator>
				<category><![CDATA[Foundations of Math]]></category>
		<category><![CDATA[Mathematical Logic]]></category>
		<category><![CDATA[axioms]]></category>
		<category><![CDATA[Boolean logic]]></category>
		<category><![CDATA[simple programs]]></category>

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		<description><![CDATA[Both the philosopher Charles Sanders Peirce in 1880 and the American logician H. M. Sheffer in 1913 realized that the truth-functions of elementary logic could all be defined from a single operation. The Sheffer stroke, also known as the Nand operation, is a logical operator with the following meaning: p Nand q is true if [...]]]></description>
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