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Meta Math!: The Quest for Omega Paperback – November 14, 2006
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Copyright © American Library Association. All rights reserved --This text refers to an out of print or unavailable edition of this title.
“Math’s dark secret is out. . . . Chaitin explains why omega, a number he discovered thirty years ago, has him convinced that math is based on randomness.”
“Captivating. . . . With extraordinary skill and a gentle humor, Chaitin shares his profound insights.”
–Paul Davies, author of How to Build a Time Machine
“A clearly written and witty look at a difficult subject. . . . Chaitin explains with infectious enthusiasm how mathematics doesn't equal certainty.” –Science News
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Top Customer Reviews
However, he is a better philosopher than he is usually given credit for. His views on the foundations and meaning of mathematics are very original. By avoiding, on the one hand, the formalistic view that mathematical statements are meaningless, and, on the other hand, the conventional view that the current mathematical foundations (for the specialist, I am referring to the ZFC axioms for set theory augmented by large cardinal axioms) are adequate, he is able to show that mathematics is ultimately an empirical science.
The overwhelming inexhaustibility of mathematics is clearer in Chaitin's formulation than in Godel's -- the sense that everything we know about math is an infinitesimal fraction of what there is to know about it. The other major theme which Chaitin clarifies is that mathematics is not logically prior to physics, which Godel also knew, but which is now much more sharply established. And his approach provides a very intuitive way, for those familiar with computer programming, to understand the work of Godel and Turing that avoids the usual self-referential fussing.
That doesn't mean this is a good book. It is badly written, unnecessarily self-congratulatory, and at an uneven technical level.Read more ›
I guess I should blame myself. My first response to the editorial comment naming the author as the intellectual heir to Gödel and Turing was, "Gregory who?" Shelah, Solovay, Martin: these are names I know, but who is Gregory Chaitin? I should have gone with my gut. In retrospect, it is telling that all the jacket quotes are from freewheeling authors of popularizations, not from respected philosophers, logicians, or scientists.
The entire book is written in an embarrassingly gushing, adolescent style full of boldface and exclamation points. I know that the author was trying to write an enthusiastic, accessible book of philosophical and methodological advocacy, but this doesn't excuse shoddy editorial craftsmanship.
Don't take my word for it. Let the author speak for himself. From page 7, "Gödel's 1931 work on incompleteness, Turing's 1936 work on uncomputability, and my own work on the role of information, randomness and complexity have shown increasingly emphatically that the role that Hilbert envisioned for formalism in mathematics is best served by computer programming languages[.]"
Imagine if a working composer wrote, "Bach's preludes and fugues, Beethoven's symphonies, and my own string quartets have shown increasingly emphatically...Read more ›
Most Recent Customer Reviews
This book is great.
Other reviewers might bash it because they are coming from the perspective of a mathematician or because Chaitin writes about his OWN accomplishments... Read more
With academic background in Physics and Math, I love this sort of books that take you on a journey into mathematical subjects in detail. Read morePublished 6 months ago by Justin Time
Of course you are aware that an 1-liter bottle filled with 0.5 liter of a liquid can be represented as a half-filled or as a half-empty bottle. Read morePublished on August 15, 2013 by ScienceThinker
Guy is full of ego but NOT full of crap as some reviews have said. At the prices this has dropped to, it's well worth a scan, even if just for the breathtaking feeling of how... Read morePublished on May 27, 2013 by Let's Compare Options Preptorial
Chaitin takes you on an energetic, idiosyncratic Grand Tour of the major metamathematical milestones associated with luminaries like Hilbert, Gödel and Turing. Read morePublished on December 21, 2012 by Gerald L. Hull
Meta Math! describes for the general reader Chaitin's main results in the mathematical theory of computation complexity and his philosophical ruminations about the nature of... Read morePublished on December 16, 2012 by Stephen Schwartz
I was given this book to read during the holiday. How disappointing. I figured something was up when the start of the book is a lot of quotes - even whole pages - of the works of... Read morePublished on July 7, 2012 by theRangel
Paraphrasing elegant program definition: No smaller book in the same language has the same output, I'd to say that this book is almost Elegant!. Read morePublished on February 13, 2012 by hernan_eche
I landed on this book after reading about Omega in Cover and Thomas text on information theory. I have to agree with them that Chaitin's Omega is a "magical, mystical number". Read morePublished on October 23, 2010 by Fazul