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	<title>Anima Ex Machina &#187; Computability, Universality and Unsolvability</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>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>

		<guid isPermaLink="false">http://www.mathrix.org/liquid/?p=421</guid>
		<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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		<title>Physics-like computation, Wolfram&#8217;s PCE and Church&#8217;s thesis</title>
		<link>http://www.mathrix.org/liquid/archives/physics-like-computation-wolframs-principle-of-computational-and-churchs-thesis</link>
		<comments>http://www.mathrix.org/liquid/archives/physics-like-computation-wolframs-principle-of-computational-and-churchs-thesis#comments</comments>
		<pubDate>Wed, 07 Jan 2009 20:32:31 +0000</pubDate>
		<dc:creator>Hector Zenil</dc:creator>
				<category><![CDATA[Computability, Universality and Unsolvability]]></category>
		<category><![CDATA[Foundations of Computation]]></category>
		<category><![CDATA[General]]></category>
		<category><![CDATA[physics of computation]]></category>
		<category><![CDATA[Principle of Computational Equivalence]]></category>

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		<description><![CDATA[The lack of correspondence between the abstract and the physical world seems sometimes to suggest that there are profound incompatibilities between what can be thought and what actually happens in the real world. One can ask, for example, how often one faces undecidable problems. However, the question of undecidability has been considered to be better [...]]]></description>
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		<title>The Shortest Universal Turing Machine Implementation Contest</title>
		<link>http://www.mathrix.org/liquid/archives/the-shortest-universal-turing-machine-implementation-contest</link>
		<comments>http://www.mathrix.org/liquid/archives/the-shortest-universal-turing-machine-implementation-contest#comments</comments>
		<pubDate>Mon, 22 Dec 2008 23:52:23 +0000</pubDate>
		<dc:creator>Hector Zenil</dc:creator>
				<category><![CDATA[Algorithmic information theory]]></category>
		<category><![CDATA[Complexity]]></category>
		<category><![CDATA[Computability, Universality and Unsolvability]]></category>
		<category><![CDATA[Foundations of Computation]]></category>
		<category><![CDATA[New Ideas]]></category>
		<category><![CDATA[Recreation]]></category>
		<category><![CDATA[Add new tag]]></category>
		<category><![CDATA[Turing machine]]></category>

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		<description><![CDATA[The Shortest Universal Turing Machine Implementation Contest ANNOUNCEMENT 23 Dec &#8211; 2008 http://www.mathrix.org/experimentalAIT/TuringMachine.html Contest Overview In the spirit of the busy beaver competition though related to program-size complexity, we are pleased to announce the &#8220;Shortest Universal Turing Machine Implementation Contest&#8221;. The contest is open-ended and open to anyone. To enter, a competitor must submit a [...]]]></description>
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