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Meta Math!: The Quest for Omega (Peter N. Nevraumont Books)

3.57  ·  Rating Details ·  231 Ratings  ·  31 Reviews

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

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Hardcover, 240 pages
Published October 4th 2005 by Pantheon (first published 2005)
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Fortunr
Jan 29, 2017 Fortunr rated it really liked it  ·  review of another edition
“Omega”, a deceptively simple concept, but pregnant with deep implications in many realms of human inquiry: in layman terms, this is a real number expressing the “halting probability” that a randomly constructed program will halt after a finite number of processing steps.
At first glance, this seems just a technical tidbit with limited applicability, and of interest only to computer sciences practitioners. In reality the extraordinary features of such number, in conjunction with the important fin
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Colin
Jan 31, 2009 Colin rated it did not like it
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
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David Rim
Jun 15, 2007 David Rim rated it liked it  ·  review of another edition
Recommends it for: noone in particular
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
Maurizio Codogno
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
Jack
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
Charles
The point of this book is to define and state the significance of a real number called omega (Ω). It is related to the halting probability and is defined on page 129 in the following way:

Given the set of all possible computer programs you select one at random (p) and run it on a specific computer. Each time the computer requests the next bit of the program, you flip a fair coin to generate it. The computer then must decide by itself when to stop reading the program. You sum for each program that
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Alex Lee
Understandably Chaitin's enthusiasm comes at us in full force from the very beginning. It's a distraction, but it's also an integral part of how he considers his subject.

Chaitin tries to make a careful argument many times about his subject, but it's difficult because he wastes no words in constructing the bits of reasoning he lays out for us. He nearly takes an interdisciplinary approach in order to approach the same structure from more than one point of view -- and I find it to be successful. I
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Luca Mauri
Dec 26, 2013 Luca Mauri rated it did not like it  ·  review of another edition
Shelves: finished, on, 2008, 10, feb
Questo libro commette due tra i peggiori errori possibili nella divulgazione: non spiega niente e l'autore inserisce continuamente note personali che non sono collegate alla sua supposta scoperta. Il libro dovrebbe condurre il lettore alla scopera di Omega, peccato che prima di introdurre il concetto il libro sia gi�� bello e finito, nel mezzo ci sono una serie di concetti che spaziano dalla matematica alla logica all'informatica alla biologia che sono debolmente legati.
L'autore fa diverse dimos
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Abhaga
Sep 05, 2015 Abhaga rated it it was ok  ·  review of another edition
Reading this book is like hearing to an overexcited person who just cannot get enough of himself. Very self indulgent, Chaitin will recount random facts from his life that have no connection to topic at hand. He will remind you every few paragraphs how beautiful his results are and how much he is proud of them. He will go on tangents which should have no place in a small expository book like this. And he is not good at explaining things. To him, "that is all there is to it".

But having said that,
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Ben
Jun 17, 2008 Ben rated it liked it  ·  review of another edition
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
Roberta
I skimmed through main part of this book, skipping over much of the math and exclamation points. The math was frequently beyond my limited math education, but I did understand enough to appreciate his enthusiasm for elegance, beauty, and awe of the limitations of knowledge, seen in the concept of unsolvability.

The text of the first part of the book was often tedious, but I was enthralled with the appendices. They described the fascinating philosophy of mathematics, enthusiasms my husband had oft
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Alecsphys
I have to admit that this book is really written in an ugly way from a stylistic point of view. Often it seems that the author is speaking and not writing. To much informal. The content is really interesting, but it could be written in a more clean and concise form. What the author calls demonstrations are not really that but simple explanations. The typographical choices are not so good for me too. Some visions of the math and science in general are not fitting mine, others yes. The good point ...more
Chris
Jun 08, 2008 Chris rated it really liked it  ·  review of another edition
Recommended to Chris by: Aaron Thomas
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
John
Jun 22, 2011 John rated it liked it  ·  review of another edition
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.
Rui
May 28, 2016 Rui rated it really liked it  ·  review of another edition
Shelves: math
Short book about the number capital omega. The result is interesting, the book could be 1/5 as long.

Omega is the probability that a random program halts. No more than a finite number of bits of omega can be calculated by a formal system. And so most bits of omega are unprovable theorems. Omega is as close to random as math gets.
Jeffrey
Feb 09, 2009 Jeffrey rated it it was amazing  ·  review of another edition
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.
Jef
May 23, 2008 Jef rated it it was amazing
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.
Sean Brooks
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.
Jsmith
Jun 13, 2008 Jsmith rated it it was amazing  ·  review of another edition
Shelves: math
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.
Roger B
Jul 19, 2014 Roger B rated it liked it
Shelves: math
Written at a (frustratingly) high level, interesting ideas that touch on a number of math areas (Diophantine equations, information complexity, irreducibility, randomness, computer programming) as well as philosophical ones as well.
Gabe Steinman Dalpiaz
Very interesting and passionate. Could use a bit more fleshing out though, and it really wouldn't hurt if Chaitin made a bit more of an effort to baby readers through the more mathematical parts. His excitement is contagious though
Max
Mar 03, 2008 Max rated it really liked it
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.
Worakarn Isaratham
interesting content, awful writing.
Mike
Aug 23, 2014 Mike rated it it was amazing  ·  review of another edition
Fascinating book giving novel insight to the measurement of complexity.
Jonathan
Aug 30, 2013 Jonathan rated it it was ok  ·  review of another edition
Mr chaitin book show that he is thinks a lot of himself. He is not in the same conversation that contains Gödel or Hilbert. Not even close
Mike
Sep 18, 2008 Mike rated it really liked it  ·  review of another edition
I learned some very remarkable new things about the real number system, from this book.
Laura
Jul 29, 2009 Laura marked it as to-read  ·  review of another edition
I'm approaching this with a great deal of skepticism.
Nathan Letwory
Jan 09, 2009 Nathan Letwory rated it it was amazing  ·  review of another edition
Shelves: learning, english
Interesting book on maths
Sean
Mar 26, 2009 Sean marked it as to-read
NULL
Tim
Jan 26, 2014 Tim rated it really liked it  ·  review of another edition
Great ideas dealt with at a high level. Sometimes a little more depth would be appropriate.
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Gregory Chaitin is widely known for his work on metamathematics and for his discovery of the celebrated Omega number, which proved the fundamental unknowability of math. He is the author of many books on mathematics, including Meta Math! The Quest for Omega. Proving Darwin is his first book on biology. Chaitin was for many years at the IBM Watson Research Center in New York. The research described ...more
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