Information Theoretic Incompleteness

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Information Theoretic Incompleteness

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Author : Gregory J. Chaitin
language : en
Publisher: World Scientific
Release Date : 1992

Information Theoretic Incompleteness written by Gregory J. Chaitin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Computers categories.

In this mathematical autobiography, Gregory Chaitin presents a technical survey of his work and a nontechnical discussion of its significance. The volume is an essential companion to the earlier collection of Chaitin's papers Information, Randomness and Incompleteness, also published by World Scientific.The technical survey contains many new results, including a detailed discussion of LISP program size and new versions of Chaitin's most fundamental information-theoretic incompleteness theorems. The nontechnical part includes the lecture given by Chaitin in G?del's classroom at the University of Vienna, a transcript of a BBC TV interview, and articles from New Scientist, La Recherche, and the Mathematical Intelligencer.

Information Randomness Incompleteness

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Author : Gregory J. Chaitin
language : en
Publisher: World Scientific
Release Date : 1987

Information Randomness Incompleteness written by Gregory J. Chaitin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Computers categories.

The papers gathered in this book were published over a period of more than twenty years in widely scattered journals. They led to the discovery of randomness in arithmetic which was presented in the recently published monograph on ?Algorithmic Information Theory? by the author. There the strongest possible version of G”del's incompleteness theorem, using an information-theoretic approach based on the size of computer programs, was discussed. The present book is intended as a companion volume to the monograph and it will serve as a stimulus for work on complexity, randomness and unpredictability, in physics and biology as well as in metamathematics.

Algorithmic Information Theory

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Author : Gregory. J. Chaitin
language : en
Publisher: Cambridge University Press
Release Date : 2004-12-02

Algorithmic Information Theory written by Gregory. J. Chaitin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-02 with Computers categories.

Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gödel's incompleteness theorem, using an information theoretic approach based on the size of computer programs. One half of the book is concerned with studying the halting probability of a universal computer if its program is chosen by tossing a coin. The other half is concerned with encoding the halting probability as an algebraic equation in integers, a so-called exponential diophantine equation.

Information Theoretic Incompleteness

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Author : G. J. Chaitin
language : en
Publisher:
Release Date : 1992

Information Theoretic Incompleteness written by G. J. Chaitin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.

Information Randomness Incompleteness

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Author : Gregory J. Chaitin
language : en
Publisher: World Scientific
Release Date : 1990-01-01

Information Randomness Incompleteness written by Gregory J. Chaitin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.

This book contains in easily accessible form all the main ideas of the creator and principal architect of algorithmic information theory. This expanded second edition has added thirteen abstracts, a 1988 Scientific American Article, a transcript of a EUROPALIA 89 lecture, an essay on biology, and an extensive bibliography. Its new larger format makes it easier to read. Chaitin's ideas are a fundamental extension of those of G”del and Turning and have exploded some basic assumptions of mathematics and thrown new light on the scientific method, epistemology, probability theory, and of course computer science and information theory.

Thinking About G Del And Turing

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Author : Gregory J. Chaitin
language : en
Publisher: World Scientific
Release Date : 2007

Thinking About G Del And Turing written by Gregory J. Chaitin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable ê 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 G”del 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 G”del 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.

Thinking About G Del And Turing

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Author :
language : en
Publisher:
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Thinking About G Del And Turing written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

The Limits Of Mathematics

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Author : Gregory J. Chaitin
language : en
Publisher: Springer
Release Date : 1998

The Limits Of Mathematics written by Gregory J. Chaitin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Computers categories.

This book presents the final version of Chaitin's course on the limits of mathematical reasoning. This course uses algorithmic information theory to show that mathematics has serious limitations, and features a new more didactic approach to algorithmic information theory using LISP and Mathematica software. The thesis of the book is that the incompleteness phenomenon discovered by Godel is much more widespread and serious than hitherto suspected.

Randomness And Complexity From Leibniz To Chaitin

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Author :
language : en
Publisher:
Release Date :

Randomness And Complexity From Leibniz To Chaitin written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Randomness And Complexity

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Author : Cristian Calude
language : en
Publisher: World Scientific
Release Date : 2007

Randomness And Complexity written by Cristian Calude and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Science categories.

The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin's 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays.