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	Gregory Chaitin
		Chaitin is an expert on topics of mathematical logic and researches uncertainty.
		Chaitin's Big Omega is a real number between 0 and 1, which represents the probability that a Turing program picked at random will halt.
		Chaitin's number, although maximally uncomputable, is not the hardest to deal with of its class.
	clublet.com /c/c/why?GregoryChaitin (627 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)

	Barnes & Noble.com - Books: Meta Math!, by Gregory Chaitin, Paperback, Reprinted Edition
		Gregory Chaitin, one of the foremost mathematicians, disagrees.
		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.
	search.barnesandnoble.com /booksearch/isbnInquiry.asp?isbn=1400077974 (445 words)

	Chaitin's constant
		Chaitin's constant, Ω (capital omega), also called the halting probability, is a construction by Gregory Chaitin.
		It is important to realize that Chaitin's constant is not a constant in the usual sense: it is not a fixed, canonically defined number such as π or e since its definition depends on the arbitrary choice of computation model and program encoding.
		If you fix, in addition to the computation model and encoding mentioned above, a specific consistent axiomatic system for the natural numbers, say Peano's axioms, then there exists a constant N such that no digit of Ω after the N-th can be proven to be one or zero within that system.
	www.ebroadcast.com.au /lookup/encyclopedia/ch/Chaitin's_constant.html (459 words)

	Gregory Chaitin
		Gregory Chaitin, American contemporary mathematician and computer scientist who, beginning in the late 1960s, has made important contributions to algorithmic information theory, in particular a new incompleteness theorem similar in spirit to Gödel's incompleteness theorem.
		Chaitin has defined Chaitin's constant Ω, a real number whose digits are randomly distributed and which expresses the probability that a random program will halt.
		Chaitin's work on algorithmic information theory paralleled the work of Kolmogorov in many respects.
	www.ebroadcast.com.au /lookup/encyclopedia/gr/Gregory_Chaitin.html (141 words)

	YouTube - Broadcast Yourself.
		Gregory Chaitin Lecture Carnegie-Mellon University 2000 Pt 1
		Gregory Chaitin Lecture Carnegie-Mellon University 2000 Pt 2
		Gregory Chaitin Lecture Carnegie-Mellon University 2000 Pt 3
	www.youtube.com /view_play_list?p=86ECDEDE3FA8D8D1 (714 words)

	Chaitin’s Constant
		Discovered by Gregory Chaitin, Omega is definable but not computable.
		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.
	www.daviddarling.info /encyclopedia/C/Chaitins_constant.html (527 words)

	'Meta Math!' seeks to identify things that can't be known (Site not responding. Last check: 2007-09-17)
		Chaitin would argue that the world we live in is a very complicated and unpredictable place.
		Chaitin describes a creative process where he works on a problem late into the night and then wakes up the next morning full of new ideas.
		Chaitin believes that we need new ideas about how human society should be organized in the face of what we now know (and don't know) about the way the world works.
	www.decaturdaily.com /decaturdaily/books/051023/book3.shtml (867 words)

	Amazon.ca: Meta Math!: the Quest for Omega: Books: Gregory Chaitin (Site not responding. Last check: 2007-09-17)
		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.
		His asides often directly speak to students who might want to become professional mathematicians, stoking their fire, for example, with the vulnerability of even ancient theorems to new analysis (he sketches two ways, in addition to Euclid's, to prove the infinity of prime numbers).
	www.amazon.ca /Meta-Math-Quest-Gregory-Chaitin/dp/0375423133 (341 words)

	YouTube - Broadcast Yourself.
		Gregory Chaitin Lecture Lisbon University 2004 Pt 1
		Gregory Chaitin Lecture Lisbon University 2004 Pt 2
		Gregory Chaitin Lecture Lisbon University 2004 Pt 3
	www.youtube.com /view_play_list?p=151048A96FB6BE9F (322 words)

	Amazon.de: The Unknowable. (Springer Series in Discrete Mathematics and Theoretical Comp): English Books: Gregory J. ... (Site not responding. Last check: 2007-09-17)
		This essential companion volume to Chaitin's highly successful "The Limits of Mathematics", also published by Springer, gives a brilliant historical survey of the work of this century on the foundations of mathematics, in which the author was a major participant.
		The Unknowable is a very readable and concrete introduction to Chaitin's ideas, and it includes a detailed explanation of the programming language used by Chaitin in both volumes.
		Firstly I agree that Chaitin is not a modest man. I don't think that really matters, because he has made a major contribution to my understanding of this whole area which previously I had found almost impenetrable.
	www.amazon.de /Unknowable-Gregory-J-Chaitin/dp/9814021725 (923 words)

	Meta Math!: The Quest for Omega (Peter N. Nevraumont Books) - Nutricraze
		Certainly Chaitin's unique approach to tackling the notion of incompleteness cuts to the core of the matter, and is free from the beautiful self-referential chains that bind the reader from a clear understanding of Godel's first and second incompleteness theorems.
		Even so, Chaitin's opinions of science, his iconic worship of Leibniz (and consequent condemnation of Newton), his accusative implication that Godel's contributions to deductive logic are overblown and confusing, make this book difficult to read.
		Chaitin shows that no mathematics, even at his level, will suffice to compute what Omega is. And once again is illustrated the lesson from GÃ½del: there are strict limitations to what can be known by means of even the purest of mathematics.
	www.petcraze.com /book.php?ItemID=0375423133 (1652 words)

	American Scientist Online - Two Philosophies of Mathematical Weirdness (Site not responding. Last check: 2007-09-17)
		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 (2424 words)

	Gregory Chaitin - Wikipedia, la enciclopedia libre
		Gregory J. Chaitin (nacido en Nueva York en 1947) es un matemático y científico de la computación argentino-estadounidense.
		Chaitin también escribe sobre filosofía, especialmente acerca de metafísica y filosofía de la matemática (particularmente sobre asuntos epistemológicos en la matemática).
		Chaitin propone que los matemáticos deberían abandonar toda esperanza de probarlos y adoptar una metodología cuasi-empírica.
	es.wikipedia.org /wiki/Gregory_Chaitin (532 words)

	Ivars Peterson's 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 suggests 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, so there's no way to prove whether the statements are true or false by using arithmetic.
		In Chaitin's view, that's practically the same as saying that the structure of arithmetic is random.
	www.maa.org /mathland/mathtrek_2_23_98.html (1307 words)

	Vintage Catalog \| Meta Math! by Gregory Chaitin
		Gregory Chaitin, one of the world’s foremost mathematicians, leads us on a spellbinding journey, illuminating the process by which he arrived at his groundbreaking theory.
		In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery.
		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 /vintage/catalog/display.pperl?isbn=9781400077977 (231 words)

	Read This: Meta Math! The Quest for Omega
		Also, Chaitin says, "If something important is true, there are many reasons that it is true." And although I remember reading in The Interpretation of Dreams that most dreams have many interpretations (and my dreaming experience seems to verify this), I'm not sure that every fact has many reasons.
		As a writer, I might suggest that Chaitin incorporate this section into the rest of the book, and I might also say that that might not be necessary; Chaitin's commendable humility, along with his reminders of the hierarchy of giants standing on one anothers' shoulders, has already come through big-time.
		As mentioned above, Chaitin believes that mathematics, or a lot of it, needs to be done experimentally (since so much of it is random, and not dependant on any theorems or theory), and in that way at least, math should be approached as physics.
	www.maa.org /reviews/metamath.html (2928 words)

	Mathematics Controversy over the foundations of mathematics - Chaitlin
		Gregory Chaitin, author of "The Limits of Mathematics," and the principal architect of algorithmic information theory, says that we will never have a Theory of Everything, because of a number called W, Omega, that is infinitely long and impossible to compute.
		Chaitin's book uses algorithmic information theory to show that mathematics has serious limitations, and features a new more didactic approach to algorithmic information theory using LISP and Mathematica software.
		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.vtweb.com /gosai/science/mathematics-controversy.html (8536 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)

	Meta Math! by Gregory Chaitin
		Chaitin at times assumes the typical reader is nearly as smart as he is).
		The few I read were informed discussions about the philosophical basis of mathematics and its practice.
		Except for Chaitin's which read as him trying to make himself sound like the cleverest, most important person in foundational mathematics.
	www.physicsforums.com /showthread.php?t=112029 (388 words)

	Math Trek: The Limits of Mathematics, Science News Online, March 4, 2006
		To sort through the relationship between random sequences and the types of numbers that mathematicians and scientists use in their work, Chaitin defined the "complexity" of a number as the length of the shortest computer program (or set of instructions) that would spew out the number.
		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.
		Additional information about Gregory Chaitin and his writings is available at http://www.umcs.maine.edu/~chaitin/.
	www.sciencenews.org /articles/20060304/mathtrek.asp (1504 words)

	Popular Science - Greg Chaitin
		Gregory J. Chaitin is at the IBM Thomas J. Watson Research Center in New York and is the discoverer of the remarkable Omega number.
		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.
	www.popularscience.co.uk /biographies/chaitin.htm (193 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)

	Descartes Update: Chaitin
		that in the 1960's, an American mathematician named Gregory Chaitin would begin working on a proof that the very structure of arithmetic is random.
		Now, Chaitin doesn't at all "give up" on math: he counsels instead against the (futile) search for certain foundations, and advises more work in experimental arithmetic.
		But we didn't talk then about Chaitin's work--and learning about it for this first time this morning, I realized that the opposition (I heard us) set up in our series was another of those false binaries I've talked about elsewhere: the relationships between numbers no more form a formal axiomatic system than does...
	serendip.brynmawr.edu /~adalke/descartes/chaitin.html (707 words)

	Omega and why maths has no TOEs
		Gregory Chaitin has been fascinated by this theorem ever since he was a child, and now, in time for the centenary of Gödel's birth in 2006, he has published his own book, called Meta Math!
		Gregory Chaitin is at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York, and is an honorary professor at the University of Buenos Aires and a visiting professor at the University of Auckland.
		The author of nine books, he is also a member of the International Academy of the Philosophy of Science, as well as the Honorary President of the Scientific Committee of the Institute of Complex Systems in Valparaiso, Chile.
	www.plus.maths.org.uk /issue37/features/omega/index.html (3317 words)

	Math Digest (Site not responding. Last check: 2007-09-17)
		In his book The Unknowable, Gregory Chaitin describes how he was inspired by the work of the Kurt Goedel and Alan Turing to become a mathematician.
		Today Chaitin is one of the pioneers of algorithmic complexity theory, a branch of mathematics that attempts to measure how difficult it is to solve problems by computer.
		According to the review, Chaitin finds "randomness at the heart of arithmetic, and therefore of mathematics as a whole." Chown writes, "The Unknowable is Chaitin's enthusiastic and extremely readable exposition of all these ideas."
	e-math.ams.org /mathmedia/mathdigest/200003-chaitin.html (113 words)

	High Quality Science Video Online - www.101science.com
		Gregory Chaitin Lecture Mälardalen University 2005 Pt 1
		Gregory Chaitin Lecture Mälardalen University 2005 Pt 2
		Gregory Chaitin Lecture Mälardalen University 2005 Pt 3
	www.101science.com /Video.htm (698 words)

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