Meta Math!: The Quest for Omega

by Gregory Chaitin

Book Overview

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... This description may be from another edition of this product.

• Format: Hardcover
• Language: English
• ISBN: 0375423133
• ISBN13: 9780375423130
• Release Date: October 2005
• Publisher: Pantheon Books
• Length: 220 Pages
• Weight: 0.05 lbs.
• Dimensions: 0.9" x 6.4" x 9.5"

Customer Reviews

A great pleasure; a great book

This is one of my favorite math/science books, ever. It's right up in the company of George Gamow's One, Two, Three... Infinity; Erwin Schrodinger's What is Life; and Richard Feynman's Lectures on Physics. Chaitin's work conveys that great rarity, a powerful new idea, presented in a form that rewards reading over and over until it gradually sinks in. Thank you, Greg.

An outstanding book

An outstanding book in meta mathematics, taking us from beginnings of meta mathematics with Hilbert and Godel through to the randomness embodied in omega, the halting probability. The trail moves through Leibniz, Godel's incompleteness, Turing's halting and incompleteness, to Algorithmic Information Theory which proves the key to finding Omega, the number whose bits show irreducible randomness in mathematics. The writer assumes no major existing knowledge, but leads you quickly into high ground. Some discussions also touch on philosophy and the history of ideas. His enthusiasm is infectious; a great read.

Math IS sexy...(ladies take note)

I found a book of this style to be refreshing. What struck me the most, and what I liked the most about the book, was the enthusiasm in Chaitin's tone and delivery--it was contagious. As someone who's slogged through a math graduate program, I have all too often been subject to dreadfully dry math texts where the author seems to delight in wringing every last drop of intuition (and emotion) out of an explaination, to leave a long string of theorems with very short proofs (Chaitin addresses this phenomenon early in his book). His writing produces a math related book that can serve to motivate(!)--what an idea. He also rolls back the curtain a little bit on the intuitive process and openly discusses how mathematical ideas are born and evolve into common acceptance. Chaitin is not afraid to try something new here and, for my part, succeeds. To keep things simple, Chaitin keeps explainations quite tame. This didn't bother me until a hundred or so pages into the book, he unveils the book's punchline--the number omega--without much of a hint as to why it must be between 0 and 1 (that is, a probability in the strict sense). A little footnote there about Kraft's inequality would have been nice. Yes, there's an ego behind these ideas, and yes, the author is self-promoting (as he mentions early in the book, it's likely not enough to just HAVE an idea, it has to be PUSHED into the awareness of ones peers and, perhaps, the general public)--I just didn't find those aspects that distracting (history has a way of giving merit where it's due). In all, the book might be nice for someone who likes (or wants to return to) a sense of PLAY in math. It is NOT a book for the mathematical ascetic.

A Mathematician Describes His Love Affair

Why do mathematicians do the things they do? Those of us who use math mostly to figure out the tip at a restaurant or balance the checkbook are far removed from the professors who are doing research and experiments (words that have not always been connected to pure mathematics) or who are doing just the basic proofs that mathematicians are famous for. G. H. Hardy wrote the classic text to explain his passion for his work, _A Mathematician's Apology_, in 1940. Now comes _Meta Math! The Quest for Omega_ (Pantheon Books) by Gregory Chaitin. It covers some ground that will be familiar to readers of the superb _Gödel, Escher, Bach_ by Douglas Hofstadter, and indeed, Chaitin shows his own proofs for some of Gödel's and Alan Turing's work. He goes on to describe his efforts in pursuing the weird number Omega, a number so long and complicated it is "just across the border between what we can deal with and things that transcend our abilities as mathematicians." Readers who pick up this book should be warned that if Omega is across a border of understanding that challenges mathematicians like Chaitin, it is too complicated for a book of 200 pages to make plain to the uninitiated. Chaitin has, however, given an explanation of his work on Omega that will give ordinary readers some idea of the nature of the questions involved; as he says about good questions, "You can't answer them in five minutes and it would be no good if you could." Even better, he has shown just why he keeps probing at these esoteric frontiers of knowledge. The discussion on the big ideas here goes back to ancient Greece, and you could trace it back longer if there were more of a written record. The ideas may be big ones, and forever unresolvable, but Chaitin is undaunted in the pursuit of trying to clear up a further corner or two. Omega itself is a defined as a probability; one can write a computer program to generate pi, but no program can generate Omega to any known degree of accuracy. It is thus a number that can be defined and discussed, but cannot be truly known. Chaitin shows that no mathematics, even at his level, will suffice to compute what Omega is. And once again is illustrated the lesson from Gödel: there are strict limitations to what can be known by means of even the purest of mathematics. But this is no reason to despair (and Chaitin comes off far from pessimistic). Math is still a useful guide, and so often models the outside world with utility. That even the purest mathematics is subject to the same sort of unknowns that all the sciences have to put up with is quite agreeable to Chaitin. In fact, he is obviously delighted by his endeavor to clear up his little corners of knowledge, even though the effort might only mean that more questions have to be answered. He clearly relishes this sort of role rather than the one that David Hilbert proposed for mathematicians at the turn of the last century. Hilbert exhorted mathematicians to work out a formal

Best Book About Math I've Read

MetaMath is the best book about math that I have read. I say that because of the author's uniquely refreshing attitude about how real math is really done. I wish that I had had this book to read when I was pursuing a degree in Math some years back. It would have given me permission to be creative, use my imagination, be more bold and adventurous in playing with matematical concepts and getting down to their vital roots. My math classes gave me none of that, and left me with the feeling that the study of mathematics was nothing more than the study of polished and perfected theorems stripped out of their historical context. The specific topic of MetaMath is the Incompleteness Theorem. I have also read several books on that (Goedel's contribution specifically.) But MetaMath helped me really really understand what the Incompleteness Theorem is all about, and why it is important. Now it seems so clear. A set of closed axioms can never suffice to explain something that is intrinsically open ended and infinite. New axioms must always be added as our knowledge of the mathematical frontiers expand. I thoroughly enjoyed this book. Kudos to the author for his very healthy and encouraging attitude to all explorers of scientific and mathematical truth. I cannot imagine that anyone but the most stodgy stuffed shirt would not find benefit and enjoyment from reading this mind expanding work.