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Meta Math!: The Quest for Omega
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 univer...more
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 univer...more
Paperback, 240 pages
Published
November 14th 2006
by Vintage
(first published 2005)
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Gregory Chaitin si definisce un matematico quasi-empirista, filosofeggiante sulle orme di Leibnitz. Non credetegli troppo, se non per la parte filosofica. In questo libro più che di matematica si parla di metamatematica, e l'unica parte che può essere vista come empirista è data dal fatto che le dimostrazioni sono generalmente evitate, e Chaitin preferisce fare dei bei riquadroni manco avesse da fare dei lucidi. Il sottotitolo del libro, "Alla ricerca di Omega", è dovuto al fatto che il culmine...more
If your math education petered out as mine did in the early going of calculus, there is quite a lot here that will either be very heavy going or will go right past you. Fortunately those parts aren't completely essential to appreciating the work. Chaitin is mostly trying to give the layman some understanding of the deepest insights we have into complexity and uncertainty, two notions that sort of meet at the concept of computability. Personally I'm at peace with the idea that I will never truly...more
Amazingly bad. Certainly the worst book on any technical subject I've ever read - try to imagine the book a Jack Russel Terrier would write about its favorite tennis ball. Enthusiasm for a technical subject is important, using ten exclamation points a page (at times every sentence in a paragraph!) is Reader Abuse. The flow of every page is broken up and littered with distractingly bolded sentences, unnecessary subheadings, and redundant information boxes.
Chaitin takes every opportunity to remind...more
Chaitin takes every opportunity to remind...more
Chaitin has a way of making his conclusions sound less than earthshaking. As far as I can see, the main point of this book is that we can't expect to get something truly complex out of something simple. I think I got a lot out of this book though, because Chaitin also points out a number of less obvious implications for math, computer science, and physics. Its hard to tell just how well presented the specifics are, because I don't have a background in computer science. This combined with a highl...more
Beautiful exposition of Algorithmic Information Theory and why Goedel's world-shaking result of 1931 is not an anomaly but ever so much more of a rule. Hilbert's program to capture everything in a Formal Axiomatic System was dashed but human creativity was unleashed. An anthem to a kind of joie de vivre.
I'm not sure how I feel about the Quest for Omega. On the one hand its interesting in the sense that so many mathematical fields are coming together under the auspices of information / computational theory. On the other, this is weirdly unbalanced. There are really difficult concepts that are totally glossed over, and really simple concepts that are delved into. Im not being pretentious, but diophantine equations are pretty much passed by really quickly and then theres a whole chapter on Turings...more
Interesting subject about omega, which is the search for how much a binary system can 'know', compute, and but although Chaitin is very smart I don't agree with some of his optimism with what math can do, so me and him don't see eye to eye on his attempts to find omega.
I had been reading and learning about Godel's Incompleteness theorem when a friend recommended this book to me. Also a book about incompleteness, this text focuses on the field of computer science-and on the computer itself as a philosophical/mathematical device-instead of discussing Godel's arduous proof. The most interesting idea I gathered from this book is this: mathematics may be more human invention than universal law. I would highly recommend it, especially as it is short and Chaitin's en...more
interesting content, awful writing.
Chaitin makes a good effort to explain his mathematics here but books like this never quite succeed. If you really want to grok Omega you have to study his professional publications and that's rough sledding. I liked his observation that if a theorem is true there will be many proofs and if it isn't there will be none! "Diversity" hasn't conquered mathematics - yet.
Probably one of the most fascinating math books I've ever read. I'm not sure I fully understood every part of it, but it was heartening that Chaitin wasn't afraid to include equations liberally in the text. A really interesting topic for those who enjoy the work of Georg Cantor.
One of the best pieces I have ever read on Godel's Incompleteness Theorem and what it means to computability. Algorithmic complexity CAN NOT be determined formally. This should be required reading for all computer engineering majors.
Despite his obnoxious prose, Chaitin has so damn many fascinating ideas that you can't help being drawn in. I think this book would have appeal to non-geeky math types, but I've been wrong about that before.
I learned some very remarkable new things about the real number system, from this book.
Dec 12, 2011
Laura
marked it as to-read
I'm approaching this with a great deal of skepticism.
Interesting book on maths
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Jun 28, 2011 09:50am