THINKING ABOUT GÖDEL AND TURING: Essays on Complexity, 1970-2007

by Gregory Chaitin

Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable Ω number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as Gödel and Turing.This book contains 23 non-technical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of program-size complexity or algorithmic information content in order to shed further light on the fundamental work of Gödel and Turing on the limits of mathematical methods, both in logic and in computation. Chaitin argues here that his information-theoretic approach to metamathematics suggests a quasi-empirical view of mathematics that emphasizes the similarities rather than the differences between mathematics and physics. He also develops his own brand of digital philosophy, which views the entire universe as a giant computation, and speculates that perhaps everything is discrete software, everything is 0's and 1's.Chaitin's fundamental mathematical work will be of interest to philosophers concerned with the limits of knowledge and to physicists interested in the nature of complexity.

Genres: Mathematics, Science, Theory, Philosophy, Logic, Programming, Computers

368 pages, Hardcover

First published August 6, 2007

About the author

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 in this book was carried out at the Federal University of Rio de Janeiro in Brazil, where Chaitin is now a professor. An Argentine-American, he is an honorary professor at the University of Buenos Aires and has an honorary doctorate from the National University of Cordoba, the oldest university in Argentina.

Reviews

[Nick Black · Rating 5 out of 5]

OMG this looks fantastic! How'd I miss it? And why on earth is the hardcover $118 despite being in-print? That's quite a chunk of change for some essays and an "illustrated edition" -- what the hell kind of illustration does one provide for theorems of algorithmic information complexity, for that matter? I'm going to try and find out, and then pick up either this or the paperback version...(update Sun May 24 16:45:34 EDT 2009 acquired new from Amazon, as some dickless motherfucker picked up the $20 used copy i had my eye on. Went for the cheaper paperback edition thanks to john.bova's insight.)

[DJ]

might be a good accompaniment to a course on Godel's theorem with Len Adleman

[Samuel · Rating 5 out of 5]

A wonderful collection of essays that distills Chaitins results and view on things.