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	Gregory Chaitin - Wikipedia, the free encyclopedia
		Chaitin has defined Chaitin's constant Ω, a real number whose digits are equidistributed and which is sometimes informally described as an expression of the probability that a random program will halt.
		In metaphysics, Chaitin claims that algorithmic information theory is the key to solving problems in the field of biology (obtaining a formal definition of ‘life’, its origin and evolution) and neuroscience (the problem of consciousness and the study of the mind).
		Chaitin is also the originator of using graph coloring to do register allocation in compiling.
	en.wikipedia.org /wiki/Gregory_Chaitin (445 words)

	Chaitin's constant - Wikipedia, the free encyclopedia
		In the computer science subfield of algorithmic information theory a Chaitin constant or halting probability is a construction by Gregory Chaitin which describes the probability that a randomly generated program for a given model of computation or programming language will halt.
		Chaitin's constant is uncompressible (others may say irreducible, or algorithmically random).
		Omega and why math has no TOEs article based on one written by Gregory Chaitin which appeared in the August 2004 edition of Mathematics Today, on the occasion of the 50th anniversary of Alan Turing's death.
	en.wikipedia.org /wiki/Chaitin's_constant (768 words)

	New Scientist: The Omega Man
		Chaitin has shown that there are an infinite number of mathematical facts but, for the most part, they are unrelated to each other and impossible to tie together with unifying theorems.
		Chaitin's mathematical curse is not an abstract theorem or an impenetrable equation: it is simply a number.
		Chaitin had arranged his equation so that there was one particular variable, a parameter which he called N, that provided the key to finding Omega.
	www.dc.uba.ar /people/profesores/becher/ns.html (2388 words)

	Information
		Chaitin terms the latter numbers "incompressible" and it is these numbers that he takes as central to his assertion that "randomness" is endemic to arithmetic/mathematics.
		Chaitin's case for the existence of incompressible numbers derives from an exploration of the halting problem as applied to a universal Turing machine.
		Chaitin's case for the significance of incompressible numbers relates to diophantine questions and to a proof that there does not exist a general mechanical procedure for their solution.
	serendip.brynmawr.edu /local/scisoc/information/8july04.html (929 words)

	Elizabeth Chaitin, DHCE
		Chaitin completed her master's degree in social work at the University of Pittsburgh in 1988, her master's degree in medical ethics a the University of Pittsburgh in 1996 and her doctorate in health care ethics at Duquesne University in 2000.
		Chaitin is part of the teaching faculty for Internal Medicine and Family Practice Residency programs of the UPMC Shadyside and also serves as a clinical instructor for the Medical Resident of these programs.
		Dr. Chaitin is an Assistant Professor of Medicine at the University of Pittsburgh School of Medicine in the Division of General Medicine in the Section of Palliative Care and Medical Ethics.
	www.pitt.edu /~bioethic/facChaitin.htm (240 words)

	Mailgate: sci.math: Re: Raatikainen's critique of Chaitin
		Chaitin's theorem shows that there is > no way to get around it, since assuming that the axiom system is > consistent only improves the information complexity of the axiom > system by a finite amount, so you can still only know a finite number > of bits of Omega.
		But the important question (which is really what I was getting at) is for sufficiently large N, can one conceive of enough plausible axioms with an information complexity greater than N? When I wrote that, I thought not, but I don't have a proof of this.
		The only difference is that because Chaitin's results > are so much stronger and are so shocking and go against the grain of > how most mathematicians think, most mathematicians don't want to > believe them; therefore, you get reactions that fit into the 4 > categories that I mentioned when I started this thread.
	mailgate.supereva.com /sci/sci.math/msg200960.html (793 words)

	Chaitin’s Constant
		It has no pattern or structure to it whatsoever, but consists instead of an infinitely long string of 0's and 1's in which each digit is as unrelated to its predecessor as one coin toss is from the next.
		To derive it, Chaitin considered all the possible programs that a hypothetical computer known as a Turing machine could run, and then looked for the probability that a program, chosen at random from among all the possible programs, will halt.
		This is extraordinary enough in itself, but Chaitin has found that Omega infects the whole of mathematics, placing fundamental limits on what we can know.
	www.daviddarling.info /encyclopedia/C/Chaitins_constant.html (530 words)

	Pantheon \| Catalog \| Meta Math! by Gregory Chaitin
		Now their successor, Gregory Chaitin, digs even deeper into the foundations of mathematics, demonstrating that mathematics is riddled with randomness, enigmas, and paradoxes.
		Chaitin’s revolutionary discovery, the Omega number, is an exquisitely complex representation of unknowability in mathematics.
		Gregory Chaitin works at the IBM Thomas J. Watson Research Center in Westchester County, New York, and is a visiting professor in the Computer Science Department of the University of Auckland, New Zealand.
	www.randomhouse.com /pantheon/catalog/display.pperl?isbn=9780375423130 (287 words)

	American Scientist Online - Two Philosophies of Mathematical Weirdness (Site not responding. Last check: 2007-10-12)
		One of Chaitin's revelations is that the innocent-looking continuum implied by the white space in every illustration in a calculus book is made up almost entirely of numbers that are unspeakable, meaning that even God wouldn't be able to identify any of them because the task would never end.
		Chaitin has no patience with "straights," such as that rigid fellow Isaac Newton, whose reputation Chaitin is determined to ruin once and for all.
		Chaitin is the most optimistic bearer of bad news in the history of science.
	www.americanscientist.org /template/BookReviewTypeDetail/assetid/50737;jsessionid=aaafvmmX44waeQ (2424 words)

	MathTrek: The Limits of Mathematics
		Conversely, Chaitin also showed that it is impossible for a program to prove that a number more complex than the program is random.
		Chaitin's work indicates that there is an infinite number of mathematical statements that one can make about, say, arithmetic that can't be reduced to the axioms of arithmetic.
		In Chaitin's view, that's practically the same as saying that the structure of arithmetic is random.
	blog.sciencenews.org /2006/03/the_limits_of_mathematics.html (2051 words)

	Limits, Uncertainty, and Randomness
		Chaitin's work focuses on the problems of mathematical "truth" as a convenient fiction.
		There are infinitely many possible mathematical facts, but, according to Chaitin, the underlying relationships among them are impossible to establish.
		Even worse, Chaitin's results demonstrate that not only is there no structure to the foundation of mathematics, the foundation is in fact random.
	www.mathematica-journal.com /issue/v8i3/edpick/html/Links/index_lnk_4.html (279 words)

	Julia Chaitin, Ph.D. (Site not responding. Last check: 2007-10-12)
		Julia Chaitin received her Ph.D. in Social Psychology (in the Department of Behavioral Sciences) from Ben Gurion University of the Negev in Beer Sheva, Israel.
		Chaitin specializes in qualitative research, basing her work on narrative research, storytelling, and inter-group facilitation.
		In 2001-2002, Dr. Chaitin held the Lentz Post-Doctoral Fellowship in Peace and Conflict Resolution Research at the University of Missouri, St. Louis.
	shss.nova.edu /faculty/chaitin (290 words)

	Read This: Conversations with a Mathematician
		Chaitin's own critique of Penrose's use of Gödel's theorem provides a good example of the difficulty.
		Probably the most controversial claim Chaitin makes is that, because of the prevalence of incompleteness, mathematics should adopt a more experimental methodology, closer to that used in the other sciences.
		Chaitin suggested some lecture transcripts and an interview on his web site, saying that they were "more understandable" than his books.
	www.maa.org /reviews/convchaitin.html (905 words)

	PrintThisPage (Site not responding. Last check: 2007-10-12)
		Chaitin, Randomness and Gödel's theorem, Mondes en Développement, n.
		Chaitin, The Unknowable, Springer-Verlag, 1999; reprint; MR 2000h:68071.
		Calude, Chaitin Omega numbers, Solovay machines, and incompleteness, CDMTCS report 114.
	www.mathsoft.com /printThisPage.aspx?1165 (186 words)

	Meta Math! : The Quest for Omega (Peter N. Nevraumont Books) (Site not responding. Last check: 2007-10-12)
		Chaitin shows that no mathematics, even at his level, will suffice to compute what Omega is. And once again is illustrated the lesson from Gýdel: there are strict limitations to what can be known by means of even the purest of mathematics.
		Chaitin repeatedly emphasizes with delight that mathematicians cannot take a machine-like approach to their work.
		Chaitin, in contrast, gives the impression that his quest for Ω is the summit in the line of mathematical thought since the Pythagorean school.
	mountainstatestech.com /bookstore/item_00375423133P.html (1971 words)

	G J Chaitin Home Page
		Chaitin achieves this remarkable feat by allowing us inside his thoughts and obsessions---the mind of a mathematician on the trail of a unique discovery.
		Without ever straying too far from the familiar concepts of number and algorithm, he manages to give a glimpse of the strange lawlessness that lies beneath the apparent elegance and perfection of mathematics.
		Chaitin's papers up to 1992 are collected in his three World Scientific books.
	www.cs.umaine.edu /~chaitin (784 words)

	Amazon.co.uk: Conversations with a Mathematician: Math, Art, Science and the Limits of Reason: Books (Site not responding. Last check: 2007-10-12)
		This book collects his most wide-ranging and non-technical lecture transcripts and interviews, and it will be of interest to anyone concerned with the philosophy of mathematics, with the similarities and differences between physics and mathematics, or with the creative process and mathematics as an art.
		G. Chaitin is at the IBM Thomas J. Watson Research Center in New York.
		This book collects his most wide-ranging and non-technical lectures and interviews, and it will be of interest to anyone concerned with the philosophy of mathematics, with the similarities and differences between physics and mathematics, or with the creative process and mathematics as an art.
	www.amazon.co.uk /exec/obidos/ASIN/1852335491 (586 words)

	Gregory Chaitin: "Randomness is the at jimlog 2.0 (Site not responding. Last check: 2007-10-12)
		Gregory Chaitin: "Randomness is the at jimlog 2.0
		Gregory Chaitin: "Randomness is the true foundation of mathematics."
		Gregory Chaitin: "Randomness is the - TrackBack (0)
	www.jimgilliam.com /archives/000285.php (25 words)

	Studley’s Chaitin Promoted To Assistant Director
		Chaitin is based in the firm’s San Francisco office.
		In addition to focusing on educational institutions, Chaitin has specific expertise in the technology industry and has completed transactions on behalf of Rapt, Inc., a software applications provider, and Flagship Studios, an entertainment software firm.
		Chaitin graduated from the University of Kansas with a Bachelor of Arts.
	www.emediawire.com /releases/2005/3/prweb218978.htm (365 words)

	Information Theory and Creationism: Algorithmic Information Theory (Chaitin, Solomonoff & Kolmogorov)
		Kolmogorov, Chaitin, and Solomonoff independently came up with the idea of representing the complexity of a string based on its compressibility by representing it as a program.
		Chaitin extended the work of Turing by defining the halting probability.
		Chaitin showed that Ω is not only irrational and transcendental, but is an uncomputable real number.
	www.talkorigins.org /faqs/information/algorithmic.html (3567 words)

	Amazon.com: Meta Math!: The Quest for Omega (Peter N. Nevraumont Books): Books: Gregory Chaitin (Site not responding. Last check: 2007-10-12)
		Note the exclamation point: Chaitin is on fire about math and is unable to restrain his enthusiasm.
		Chaitin explains these two achievements here, in prose that is difficult for general readers to follow, but the spirit he brings to his subject will be apparent to all.
		Chaitin's freewheeling expressions of mathematical creativity will be this work's lasting impression.
	www.amazon.com /exec/obidos/tg/detail/-/0375423133?v=glance (3748 words)

	SS > NF reviews > Gregory J. Chaitin
		Here are three Gregory Chaitin lectures on his algorithmic complexity theory and the halting probability Omega.
		The lectures are "Randomness in arithmetic and the decline and fall of reductionism in pure mathematics", "Elegant LISP programs", "An invitation to algorithmic information theory".
		Chaitin produced his first theoretical results in the 1970s.
	www-users.cs.york.ac.uk /~susan/bib/nf/c/chaitin.htm (553 words)

	A New Kind of Science: The NKS Forum - Chaitin e-book online
		Abstract - 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.
		This book is an opportunity to get inside the head of a creative mathematician and see what makes him tick, and opens a window for its readers onto a glittering world of high-altitude thought that few intellectual mountain climbers can ever glimpse.
	forum.wolframscience.com /showthread.php?s=&threadid=457 (353 words)

	Mediated » Meta Math! - Gregory Chaitin (2005)
		Chaitin is working in the same area, but with computers and programs, and so some of the key questions are about whether one can prove that a particular program is the ‘most elegant’ or shortest expression possible.
		Chaitin notes that Wolfram has a different point of view; that the universe contains seemingly random, pseudo-random, complexity that is the result of fairly simple rules (cellular automata).
		In the end, my understanding is that Chaitin recommends that Mathematics take a more experimental approach, since there are limits to what the formal approaches can discover.
	www.perival.com /blog/?p=119 (414 words)

	Chaitin MY STORY, MY LIFE, MY IDENTITY
		A word-for-word transcription is made of the interview, and it is from this text that the researcher searches to connect the experiences that the autobiographer has shared and the meanings that he or she gives to them.
		Chaitin, J. The relevance and meaning of the Holocaust for children and grandchildren of survivors: The case of paradoxical relevance.
		Chaitin, J., and Bar-On, D. The family during the Holocaust: Memories of parent child relationships.
	www.ualberta.ca /~iiqm/backissues/3_4/html/chaitin.html (6107 words)

	New Scientist Archive - Opinion - Heart of darkness
		AT THE heart of pure mathematics, maintains Gregory Chaitin, is total unadulterated randomness.
		They range from the "mathematical equivalent of finger warm-ups for pianists" to substantial programming projects, from questions Chaitin can formulate precisely, but not answer, to questions he cannot even formulate.
		Chaitin challenges readers to follow his lead and forge their own path into the fl hole of randomness, the "darkness at the edge of mathematics".
	www.newscientist.com /article/mg16922745.000.html (252 words)

	Kolmogorov Complexity II
		Consider for example a string S that is Chaitin random and is of Kolmogorov complexity k.
		Suppose we have a predicate Random, such that Random(S) means that S is Chaitin random (of maximal Kolmogorov complexity for its length, incompressible, etc.).
		Chaitin has described a problem in elementary number theory that is equivalent to knowing Chaitin-Omega.
	www.oswego.edu /~delancey/309_DIR/LLT_LECTURES/14_kolmogorov_2_out.html (1219 words)

	Chaitin
		G.J. Chaitin's 2 March 2000 Carnegie Mellon University School of Computer Science Distinguished Lecture.
		The lecture was videotaped; this is an edited transcript.
		Chaitin is at the IBM T. Watson Research Center in New York.
	www.cs.unm.edu /~sto/files/chaitin.html (8305 words)

	INFORMATION-THEORETIC INCOMPLETENESS
		In this mathematical autobiography, Gregory Chaitin presents a technical survey of his work and a nontechnical discussion of its significance.
		The volume is an essential companion to the earlier collection of Chaitin's papers Information, Randomness and Incompleteness, also published by World Scientific.
		The nontechnical part includes the lecture given by Chaitin in Gödel's classroom at the University of Vienna, a transcript of a BBC TV interview, and articles from New Scientist, La Recherche, and the Mathematical Intelligencer.
	www.worldscibooks.com /compsci/1861.html (201 words)

	(C. Calude, C. Grozea) Kraft-Chaitin Inequality Revisited (Site not responding. Last check: 2007-10-12)
		This extension, known as Kraft-Chaitin Theorem, was obtained by Chaitin in his seminal paper [4] (see also, [3, 2]).
		The aim of this note is to offer a simpler proof of Kraft-Chaitin Theorem based on a new construction of the prefix-free code.
		The Finite, the Unbounded and the Infinite, Proceedings of the Summer School "Chaitin Complexity and Applications", Mangalia, Romania, 27 June - 6 July, 1995.
	www.jucs.org /jucs_2_5/kraft_chaitin_inequality_revisited (141 words)

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