Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable omega 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.
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I bought this book, from a New Scientist review, for my husband who is extremely gifted in math, and not so much verbally. Reading is a chore. So when, out of all the Christmas books past, he pronounced this volume a really, really good book and read some every day - I knew it was extraordinary. Now I hope he finishes soon so I can start it!
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irreducible mathematical information, irreducible mathematical facts, uncomputable reals, algorithmic independence, formal axiomatic theory, most concise program, halting probability, smallest computer program, formal axiomatic system, kth program, nth question, irreducible information, theoretic computational complexity, sufficiently great values, algorithmic information content, algorithmic information theory, smallest program, elegant program, digital physics, formal axiomatic theories, kth digit, specific real number, possible computer programs, algorithmic randomness, independent tosses Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, New Kind of Science, Kurt Gödel, Scientific American, Meta Math, Oxford University Press, Bertrand Russell, Hermann Weyl, New Directions, Gregory Chaitin, Philosophy of Mathematics, David Hilbert, Emile Borel, Cambridge University Press, Stephen Wolfram, Princeton University Press, The Open World, Alan Turing, The Limits of Mathematics, The Unknowable, Wolfram Media, The Character of Physical Law, Buenos Aires, World Scientific, Yale University Press Browse Sample Pages:
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irreducible mathematical information, irreducible mathematical facts, uncomputable reals, algorithmic independence, formal axiomatic theory, most concise program, halting probability, smallest computer program, formal axiomatic system, kth program, nth question, irreducible information, theoretic computational complexity, sufficiently great values, algorithmic information content, algorithmic information theory, smallest program, elegant program, digital physics, formal axiomatic theories, kth digit, specific real number, possible computer programs, algorithmic randomness, independent tosses Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, New Kind of Science, Kurt Gödel, Scientific American, Meta Math, Oxford University Press, Bertrand Russell, Hermann Weyl, New Directions, Gregory Chaitin, Philosophy of Mathematics, David Hilbert, Emile Borel, Cambridge University Press, Stephen Wolfram, Princeton University Press, The Open World, Alan Turing, The Limits of Mathematics, The Unknowable, Wolfram Media, The Character of Physical Law, Buenos Aires, World Scientific, Yale University Press Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Surprise Me!
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