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PopularScience
Susan Stepney
plus.maths.org
Mathematical Association of America
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Gregory Chaitin

Meta Math!:The Quest for Omega

Gregory Chaitin has done significant work on how computability is limited by complexity. In Meta Math!:The Quest for Omega he gives an account of some of his work aimed at the non-specialist reader. The book starts with his early fascination with Gödel's incompleteness theorem as well as his interest in computing, and in particular the LISP programming language. He explains how several of the philosophical ideas which seem to have arisen with the advent of the computer age, such as the universe being built out of information, were in fact thought of by Leibniz several centuries before.

Chaitin then moves on to consider the real numbers, and in particular the idea of a random real - since the real numbers form an uncountable set, most of them will not have any compact description. In the final number he gets on to the particular random real Ω. and shows what powerful results can be obtained from the idea that a given system has a certain complexity, and this limits the complexity of what can be generated from that system.

The book might seem hard to follow sometimes, but I think it's worth sticking at it, as any problems aren't so much due to technicalities as to the number of new concepts which Chaitin introduces. Indeed his enthusiasm for his work is obvious, and if you read this books then, who knows, maybe you'll pick up some of that enthusiasm too.

Amazon.com info
Paperback 240 pages  
ISBN: 1400077974
Salesrank: 1135386
Weight:0.79 lbs
Published: 2006 Vintage
Amazon price $11.76
Marketplace:New from $7.95:Used from $2.99
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Amazon.co.uk info
Paperback 220 pages  
ISBN: 1400077974
Salesrank: 1267645
Weight:0.79 lbs
Published: 2006 Unknown 4
Amazon price £12.73
Marketplace:New from £6.45:Used from £2.13
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Amazon.ca info
Paperback 240 pages  
ISBN: 1400077974
Salesrank: 842094
Weight:0.79 lbs
Published: 2006 Vintage
Amazon price CDN$ 18.76
Marketplace:New from CDN$ 10.86:Used from CDN$ 0.01
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Product Description
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.

Chaitin’s revolutionary discovery, the Omega number, is an exquisitely complex representation of unknowability in mathematics. His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.