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	<title>Anima Ex Machina &#187; Foundations of Computation</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>An alternative method (to compression) for approximating the algorithmic complexity of strings</title>
		<link>http://www.mathrix.org/liquid/archives/shortstringscomplexity</link>
		<comments>http://www.mathrix.org/liquid/archives/shortstringscomplexity#comments</comments>
		<pubDate>Wed, 20 Jul 2011 20:49:53 +0000</pubDate>
		<dc:creator>Hector Zenil</dc:creator>
				<category><![CDATA[Algorithmic information theory]]></category>
		<category><![CDATA[Foundations of Computation]]></category>
		<category><![CDATA[New Ideas]]></category>

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		<description><![CDATA[The method introduced in my doctoral dissertation was featured in the French version of Scientific American Pour La Science in its July 2011 issue No. 405 under the title Le défi des faibles complexités. Jean-Paul Delahaye points out that: Comme les très petites durées ou longueurs, les faibles complexités sont délicates à évaluer. Paradoxalement, les [...]]]></description>
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		<title>&#8220;The World is Either Algorithmic or Mostly Random&#8221; awarded a 3rd Place Prize in this year&#8217;s FQXi contest</title>
		<link>http://www.mathrix.org/liquid/archives/fqxi</link>
		<comments>http://www.mathrix.org/liquid/archives/fqxi#comments</comments>
		<pubDate>Fri, 10 Jun 2011 14:33:00 +0000</pubDate>
		<dc:creator>Hector Zenil</dc:creator>
				<category><![CDATA[Algorithmic information theory]]></category>
		<category><![CDATA[Complexity]]></category>
		<category><![CDATA[Foundations of Computation]]></category>
		<category><![CDATA[Foundations of Physics]]></category>
		<category><![CDATA[General]]></category>
		<category><![CDATA[New Ideas]]></category>

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		<description><![CDATA[Based on the combined ratings of the contest community and the panel of expert reviewers appointed by the FXQi, which included the members of the institute, I was awarded a 3rd Place Prize for my work The World is Either Algorithmic or Mostly Random in this year’s FQXi contest on the topic Is Reality Digital [...]]]></description>
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		<slash:comments>2</slash:comments>
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		<title>Compression-based Investigation of Cellular Automata, A Phase Transition Coefficient and a Conjecture Related to Universal Computation</title>
		<link>http://www.mathrix.org/liquid/archives/compression-based-investigation-of-the-dynamical-properties-of-cellular-automata-phase-transition-classification-and-a-universality-conjecture</link>
		<comments>http://www.mathrix.org/liquid/archives/compression-based-investigation-of-the-dynamical-properties-of-cellular-automata-phase-transition-classification-and-a-universality-conjecture#comments</comments>
		<pubDate>Sun, 22 Aug 2010 02:18:32 +0000</pubDate>
		<dc:creator>Hector Zenil</dc:creator>
				<category><![CDATA[Algorithmic information theory]]></category>
		<category><![CDATA[Computability, Universality and Unsolvability]]></category>
		<category><![CDATA[Computer Science]]></category>
		<category><![CDATA[Foundations of Computation]]></category>
		<category><![CDATA[New Ideas]]></category>

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		<description><![CDATA[In a recent paper, forthcoming in the Journal of Complex Systems, vol. 19, I present a method for studying the qualitative behavior of cellular automata and other abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm. I show that the compression-based approach classifies cellular automata (CA) into clusters according to their heuristic behavior, with these clusters showing a correspondence with Wolfram's main classes of systemic behavior. I also present a Gray code-based numbering scheme for initial conditions optimal for this kind of investigations, and a compression based method for estimating a characteristic exponent in the form of a phase transition coefficient measuring the resiliency or sensitivity of a system to its initial conditions. I also conjecture that universal systems have large transition coefficients.]]></description>
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		<title>Comments on Turing&#8217;s very first Universal machine approaching Turing&#8217;s 100th. birthday anniversary</title>
		<link>http://www.mathrix.org/liquid/archives/turings-very-first-universal-machine</link>
		<comments>http://www.mathrix.org/liquid/archives/turings-very-first-universal-machine#comments</comments>
		<pubDate>Tue, 18 May 2010 00:56:45 +0000</pubDate>
		<dc:creator>Hector Zenil</dc:creator>
				<category><![CDATA[Computability, Universality and Unsolvability]]></category>
		<category><![CDATA[Computer Science]]></category>
		<category><![CDATA[Foundations of Computation]]></category>
		<category><![CDATA[Minds and Machines]]></category>

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		<description><![CDATA[The idea that a machine could perform the tasks of any other machine is the description of a Universal (Turing) machine. Its invention is considered by many to have been one of the major landmarks giving rise to the field of computer science. &#8216;Universal&#8217; means that one can &#8216;program&#8217; a general-purpose machine to perform the [...]]]></description>
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