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Topic: Algorithmic information theory

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	Theory - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-07)
		For a given body of theory to be considered part of established knowledge, it is usually necessary for the theory to characterize a critical experiment, that is, an experimental result which cannot be predicted by any established theory.
		Unfortunately, the usage of the term is muddled by cases such as string theory and "theories of everything," each probably better characterized at present as a bundle of competing hypotheses for a protoscience.
		In the humanities, theory is often used as an abbreviation for critical theory or literary theory, referring to continental philosophy's aesthetics or its attempts to understand the structure of society and to conceptualize alternatives.
	www.bexley.us /project/wikipedia/index.php/Theory (1461 words)

	Complexity & Information Theory
		The central idea of algorithmic information theory is to quantify the information content of an object or bit string in terms of its shortest description.
		We define the algorithmic information content I(x) of an object (or bit string) x as the length of the shortest self delimiting program(s) for a Universal Turing Machine U which generates a description of that object for a given level of precision.
		The string's algorithmic information content, or aglorithmic complexity, is bounded from above by the length of the binary sequence specifying 'forty', together with the code which tells the computer to print a digit a certain number of times.
	www.mulhauser.net /research/tutorials/complexity/complexity.html (1531 words)

	Algorithmic information theory - Open Encyclopedia (Site not responding. Last check: 2007-11-07)
		Algorithmic information theory is a field of study which attempts to capture the concept of complexity by using tools from theoretical computer science.
		The chief idea is to define the complexity (or Kolmogorov complexity) of a string as the length of the shortest program which outputs that string.
		The first surprising result is that K(s) cannot be computed: there is no general algorithm which takes a string s as input and produces the number K(s) as output.
	open-encyclopedia.com /Algorithmic_information_theory (928 words)

	Nick Szabo -- Introduction to Algorithmic Information Theory
		Information is used to describe the cultural structures of science, legal and market institutions, art, music, knowledge, and beliefs.
		Information is also used in describing the structures and processes of biological phenomena, and phenomena of the physical world.
		Algorithmic information theory is a far-reaching synthesis of computer science and information theory.
	szabo.best.vwh.net /kolmogorov.html (1710 words)

	Learn more about Algorithmic information theory in the online encyclopedia. (Site not responding. Last check: 2007-11-07)
		The first surprising result is that I(s) cannot be computed: there is no general algorithm which takes a string s as input and produces the number I(s) as output.
		It has the desirable properties of statistical invariance (the inference transforms with a re-parameterisation, such as from polar co-ordinates to Cartesian co-ordinates), statistical consistency (even for very hard problems, MML will converge to any underlying model) and efficiency (the MML model will converge to any true underlying model about as quickly as is possible).
		C.S. Wallace and D.L. Dowe showed a formal connection between MML and algorithmic information theory (or Kolmogorov complexity) in 1999.
	www.onlineencyclopedia.org /a/al/algorithmic_information_theory.html (994 words)

	Kolmogorov complexity - Wikipedia, the free encyclopedia
		In computer science, Kolmogorov complexity, (also known as descriptive complexity, Kolmogorov-Chaitin complexity, or algorithmic entropy) of an object such as a piece of text is a measure of how much information is needed to specify the object.
		Algorithmic information theory is the area of computer science that studies Kolmogorov complexity and other complexity measures on strings (or other data structures).
		It has the desirable properties of statistical invariance (the inference transforms with a re-parametrisation, such as from polar coordinates to Cartesian coordinates), statistical consistency (even for very hard problems, MML will converge to any underlying model) and efficiency (the MML model will converge to any true underlying model about as quickly as is possible).
	en.wikipedia.org /wiki/Algorithmic_information_theory (1723 words)

	(Svozil K.) Quantum Information Theory (Site not responding. Last check: 2007-11-07)
		Abstract: The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation.
		The fundamental atoms processed by quantum computation are the quantum bits which are dealt with in quantum information theory.
		The theory of quantum computation will be based upon a model of universal quantum computer whose elementary unit is a two-port interferometer capable of arbitrary U(2) transformations.
	www.jucs.org /jucs_2_5/quantum_information_theory (126 words)

	Algorithmic information theory (from information theory) -- Encyclopædia Britannica
		in mathematics and mechanics, theory that studies systems behaving unpredictably and randomly despite their seeming simplicity and fact that forces involved are supposedly governed by well-understood physical laws; applications of theory are diverse, including study of turbulent flow of fluids, irregularities in heartbeat, traffic jams, population dynamics, chemical...
		The theory's evolution in the 19th century was preceded by more than two centuries of observations of small life forms under the microscope.
		class of quantum field theory used to describe subatomic particles and their associated relativistic quantum fields; all measurable physical properties remain unchanged when certain mathematical symmetry operations are performed on the quantum fields; believed that the final unification of the four fundamental interactions—gravitational, electromagnetic, strong, and...
	www.britannica.com /eb/article-214957?tocId=214957 (917 words)

	A New Version of Algorithmic Information Theory
		Algorithmic information theory may be viewed as the result of adding the idea of program-size complexity to recursive function theory.
		The main application of algorithmic information theory is its information-theoretic incompleteness theorems.
		This theory is concerned with the size of programs, but up to now these have never been programs that one could actually program out and run on interesting examples.
	www.umcs.maine.edu /~chaitin/nv.html (3613 words)

	Goedel's Theorem and Information
		Algorithmic information theory focuses on individual objects rather than on the ensembles and probability distributions considered in Claude Shannon and Norbert Wiener's information theory.
		To Turing's theorem in recursive function theory that the halting problem is unsolvable, there corresponds in algorithmic information theory the theorem that the base-two expansion of Ω is algorithmically random.
		Information theory suggests that the Gödel phenomenon is natural and widespread, not pathological and unusual.
	www.cs.umaine.edu /~chaitin/georgia.html (5536 words)

	Information Theory and Creationism: Algorithmic Information Theory (Chaitin, Solomonoff & Kolmogorov)
		An algorithm producing the digits of π is an example of a non-halting algorithm π is an irrational and transcendental number; it cannot be expressed as a polynomial with rational coefficients and therefore has an infinite number of digits).
		Algorithmically random has a different definition and is a different concept, even though very long algorithmically random strings have symbol distributions with statistical properties.
		It must be stressed that, despite a similarity in notation and form to Classical Information Theory, Algorithmic Information Theory deals with individual strings, while Classical Information Theory deals with the statistical behavior of information sources.
	www.talkorigins.org /faqs/information/algorithmic.html (3567 words)

	Quantum algorithmic information theory
		The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation.
		In particular, the fundamental atom of information, the bit, must be represented by whatever physical theories are available and must be experimentally producible and manipulable by whatever physical operations are available.
		As has been pointed out before, in quantum information theory a qbit may be in a coherent superposition of the two classical states t and f.
	tph.tuwien.ac.at /~svozil/publ/qait.htm (8229 words)

	Algorithmic Information Theory - Chaitin (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		Abstract: This paper reviews algorithmic information theory, which is an attempt to apply information-theoretic and probabilistic ideas to recursive function theory.
		Typical concerns in this approach are, for example, the number of bits of information required to specify an algorithm, or the probability that a program whose bits are chosen by coin flipping produces a given output.
		During the past few years the definitions of algorithmic information theory have been reformulated.
	citeseer.ist.psu.edu /chaitin77algorithmic.html (944 words)

	Information Theory and Creationism: Algorithmic Information Theory (Chaitin, Solomonoff & Kolmogorov)
		Given a universal Turing machine (UTM) U, the algorithmic information content, also called algorithmic complexity or Kolmogorov complexity H(X) of string X is defined as the length of the shortest program p on U producing string X.
		It may be shown that if a string is algorithmically random, it is also algorithmically random read backwards.
		It must be stressed that, despite a similarity in notation and form to Classical Information Theory, Algorithmic Information Theory deals with individual objects, while Classical Information Theory deals with the statistical behavior of information sources.
	home.mira.net /~reynella/debate/algorith.htm (1194 words)

	Omniseek: /Computing /Artificial Life /Science: Math: Information Theory /
		A controversial paper by Max Tegmark suggesting that the algorithmic information content of the universe as a whole is close to zero.
		Information Revisited: Introduction to the Proceedings FIS 94
		An agenda of quantum algorithmic information theory, ordered `top-down' by Karl Svozil : the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation.
	www.omniseek.com /srch/{2307} (357 words)

	information theory -- Encyclopædia Britannica
		Most closely associated with the work of the American electrical engineer Claude Elwood Shannon in the mid-20th century, information theory is chiefly of interest to communication engineers, though some of the concepts have been adopted…
		More results on "information theory" when you join.
		Although control theory has deep connections with classical areas of mathematics, such as the calculus of variations and the theory of differential equations, it did not become a field in its own right until the late 1950s and early 1960s.
	www.britannica.com /eb/article-9106012 (883 words)

	AIT05 mainpage (Site not responding. Last check: 2007-11-07)
		Welcome to the Algorithmic Information Theory Conference in Vaasa 16th-18th May 2005
		Algorithmic Information Theory is an international meeting bringing together mathematicians, computer theorists, logicians, mathematical physicists and scientists in related fields to assess the impact of recent development in the foundations of mathematics, computability, computation and computer-
		supported mathematical theory exploration, and to stimulate further research in these and related fields.
	www.uwasa.fi /ait05 (62 words)

	Open Directory - Science: Math: Applications: Information Theory (Site not responding. Last check: 2007-11-07)
		Information Theory - Site promotes activities in the areas of information and communications theory in Australia.
		Information Theory - A basic introduction and history of information theory from Bell Labs.
		Introduction To Algorithmic Information Theory - An introduction to the synthesis of computation and information theory by Nick Szabo.
	dmoz.org /Science/Math/Applications/Information_Theory (320 words)

	Chaitin, Algorithmic Information Theory (Site not responding. Last check: 2007-11-07)
		Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gödel's incompleteness theorem, using an information theoretic approach based on the size of computer programs.
		This is the first book on this subject and will be of interest to computer scientists, mathematicians, physicists and philosophers interested in the nature of randomness and in the limitations of the axiomatic method.
		His exciting discoveries and speculations invade such areas as logic, induction, simplicity, the philosophy of mathematics and science, randomness, proof theory, chaos, information theory, computer complexity, diophantine analysis, and even the origin and evolution of life.
	www.umcs.maine.edu /~chaitin/cup.html (346 words)

	INFORMATION, RANDOMNESS AND INCOMPLETENESS (Site not responding. Last check: 2007-11-07)
		This book contains in easily accessible form all the main ideas of the creator and principal architect of algorithmic information theory.
		Chaitin's ideas are a fundamental extension of those of Gödel and Turning and have exploded some basic assumptions of mathematics and thrown new light on the scientific method, epistemology, probability theory, and of course computer science and information theory.
		"One will find [Information, Randomness and Incompleteness] all kinds of articles which are popularizations or epistemological reflections and presentations which permit one to rapidly obtain a precise idea of the subject and of some of its applications (in particular in the biological domain).
	www.worldscibooks.com /compsci/1048.htm (274 words)

	G J Chaitin Home Page
		Gregory Chaitin has devoted his life to the attempt to understand what mathematics can and cannot achieve, and is a member of the digital philosophy/digital physics movement.
		Its members believe that the world is built out of digital information, out of 0 and 1 bits, and they view the universe as a giant information-processing machine, a giant digital computer.
		Algorithmic Information Theory, Cambridge University Press, 1987 [hardcover], 2004 [paperback].
	www.cs.auckland.ac.nz /CDMTCS/chaitin (487 words)

	Algorithmic Information Theory - van Lambalgen (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		Abstract: We present a critical discussion of the claim (most forcefully propounded by Chaitin) that algorithmic information theory sheds new light on G6del's first incompleteness theorem.
		Algorithmic information theory, J. Symbolic Logic 54 (1989), 1389--1400.
		1 IEEE Transactions on lnformqtion Theory (context) - The, for et al.
	citeseer.ist.psu.edu /vanlambalgen89algorithmic.html (471 words)

	Information Theory and Creationism
		Werner Gitt, author of "In the Beginning was Information", arguing that information in living systems must have been created by Jesus Christ.
		It is easy to make false, scientific-sounding claims when discussing complex ideas such as Information Theory.
		The complete mathematical background for Classical and Algorithmic Information Theory is not provided here; it is quite detailed and on-line references are provided for those who want to read more.
	www.talkorigins.org /faqs/information/infotheory.html (358 words)

	Recommended Cryptography Books: Prerequisites for Algorithmic Information Theory (Site not responding. Last check: 2007-11-07)
		The only reason this doesn't get a "thumbs up" is because it is a less mature explanation of his current work on Algorithmic Information Theory (AIT).
		But 14 years later, he brought us three (most likely "thumbs up") books on AIT, entitled "The Unknowable", "The Limits of Mathematics", and "Exploring Randomness" respectively.
		AIT is a blending of information theory and complexity theory, which is perhaps the most promising new way to theoretically formalize patterns and structures.
	www.youdzone.com /cryptobooks_0521343062_prereqs.html (109 words)

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