Gregory J Chaitin's Books

Thinking about Gdel and Turing

Essays on Complexity, 1970-2007

By: Gregory J. Chaitin

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Thinking about Gdel and Turing

Essays on Complexity, 1970-2007

By: Gregory J. Chaitin

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 Gdel 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 Gdel 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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Page Count

368

Publisher

World Scientific

Published Date

ISBN 10

9812708952

ISBN 13

9789812708953

Randomness and Complexity

From Leibniz to Chaitin

By: Cristian Calude,Gregory J. Chaitin

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Randomness and Complexity

From Leibniz to Chaitin

By: Cristian Calude,Gregory J. Chaitin

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.

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466

Publisher

World Scientific

Published Date

ISBN 10

9812770828

ISBN 13

9789812770820

Information, Randomness & Incompleteness

Papers on Algorithmic Information Theory

By: Gregory J. Chaitin

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Information, Randomness & Incompleteness

Papers on Algorithmic Information Theory

By: Gregory J. Chaitin

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 Gdel 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.

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Page Count

332

Publisher

World Scientific

Published Date

ISBN 10

9810201710

ISBN 13

9789810201715

The Unknowable

By: Gregory J. Chaitin

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The Unknowable

By: Gregory J. Chaitin

This essential companion to Chaitins highly successful The Limits of Mathematics, gives a brilliant historical survey of important work on the foundations of mathematics. The Unknowable is a very readable introduction to Chaitins ideas, and includes software (on the authors website) that will enable users to interact with the authors proofs. "Chaitins new book, The Unknowable, is a welcome addition to his oeuvre. In it he manages to bring his amazingly seminal insights to the attention of a much larger audience His work has deserved such treatment for a long time." JOHN ALLEN PAULOS, AUTHOR OF ONCE UPON A NUMBER

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Page Count

148

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9814021725

ISBN 13

9789814021722

Thinking About Godel And Turing: Essays On Complexity, 1970–2007

By: Gregory J Chaitin

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Thinking About Godel And Turing: Essays On Complexity, 1970–2007

By: Gregory J 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.

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Page Count

368

Publisher

World Scientific

Published Date

ISBN 10

9814474703

ISBN 13

9789814474702

Information-Theoretic Incompleteness

By: Gregory J. Chaitin

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Information-Theoretic Incompleteness

By: Gregory J. Chaitin

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.

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Page Count

242

Publisher

World Scientific

Published Date

ISBN 10

9810236956

ISBN 13

9789810236953

Exploring RANDOMNESS

By: Gregory J. Chaitin

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Exploring RANDOMNESS

By: Gregory J. Chaitin

This essential companion to Chaitin's successful books The Unknowable and The Limits of Mathematics, presents the technical core of his theory of program-size complexity. The two previous volumes are more concerned with applications to meta-mathematics. LISP is used to present the key algorithms and to enable computer users to interact with the authors proofs and discover for themselves how they work. The LISP code for this book is available at the author's Web site together with a Java applet LISP interpreter. "No one has looked deeper and farther into the abyss of randomness and its role in mathematics than Greg Chaitin. This book tells you everything hes seen. Don miss it." John Casti, Santa Fe Institute, Author of Goedel: A Life of Logic.

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Page Count

164

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1447103076

ISBN 13

9781447103073

Meta Math!

The Quest for Omega

By: Gregory Chaitin

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Meta Math!

The Quest for Omega

By: Gregory Chaitin

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 universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.

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Page Count

242

Publisher

Vintage

Published Date

ISBN 10

1400077974

ISBN 13

9781400077977

Conversations with a Mathematician

Math, Art, Science and the Limits of Reason

By: Gregory J. Chaitin

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Conversations with a Mathematician

Math, Art, Science and the Limits of Reason

By: Gregory J. Chaitin

The author, G. J. Chaitin, shows that God plays dice not only in quantum mechanics but also in the foundations of mathematics. According to Chaitin there exist mathematical facts that are true for no reason. This fascinating and provocative text contains a collection of his most wide-ranging and non-technical lectures and interviews. It will be of interest to anyone concerned with the philosophy of mathematics, the similarities and differences between physics and mathematics, and mathematics as art.

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Page Count

162

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1447101855

ISBN 13

9781447101857

Meta Maths

The Quest for Omega

By: Gregory J. Chaitin

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Meta Maths

The Quest for Omega

By: Gregory J. Chaitin

Meta Maths is the story of Chaitin's revolutionary discovery: [OMEGA] is otherwise known as the Omega number. The Omega number is Chaitin's representation of the profound enigma at the heart of maths, which sheds light on the very nature of life itself. Chaitin demonstrates that mathematics is as much art as logic and as much science as pure reasoning. His book is a thrilling journey to the frontiers of mathematics and a celebration of its sheer beauty.

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242

Published Date

ISBN 10

1843545241

ISBN 13

9781843545248

The LIMITS of MATHEMATICS

A Course on Information Theory and the Limits of Formal Reasoning

By: Gregory J. Chaitin

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The LIMITS of MATHEMATICS

A Course on Information Theory and the Limits of Formal Reasoning

By: Gregory J. Chaitin

As a teenager, Greg created independently of Kolmogorov and Solomonoff, what we call today algorithmic information theory, a sub ject of which he is the main architect. His 1965 paper on gedanken experiments on automata, which he wrote when he was in high school, is still of interest today. He was also heavily involved in IBM, where he has worked for almost thirty years, on the development of RISC technology. Greg's results are widely quoted. My favorite portrait of Greg can be found in John Horgan's-a writer for Scientific American-1996 book The End 01 Science. Greg has gotten many honors. He was a guest of distinguished people like Prigogine, the King and Queen of Belgium, and the Crown Prince of Japan. Just to be brief, allow me to paraphrase Bette Davis in All About Eve. She said, "Fasten your seat belts, it's going to be a bumpy talk!" Ladies and Gentlemen, Greg Chaitin! [Laughter & Applause] CRISTIAN CALUDE introducing GREGORY CHAITIN at the DMTCS'96 meeting at the University of Auckland.

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Page Count

150

Publisher

Springer

Published Date

ISBN 10

1447111214

ISBN 13

9781447111214

Exploring RANDOMNESS

By: Gregory J. Chaitin

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Exploring RANDOMNESS

By: Gregory J. Chaitin

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164

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Springer Science & Business Media

Published Date

ISBN 10

1447103076

ISBN 13

9781447103073

Conversations with a Mathematician

Math, Art, Science and the Limits of Reason

By: Gregory J. Chaitin

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Conversations with a Mathematician

Math, Art, Science and the Limits of Reason

By: Gregory J. Chaitin

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162

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1447101855

ISBN 13

9781447101857

Randomness and Complexity

From Leibniz to Chaitin

By: Cristian S. Calude,Gregory J. Chaitin

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Randomness and Complexity

From Leibniz to Chaitin

By: Cristian S. Calude,Gregory J. Chaitin

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. Sample Chapter(s). Chapter 1: On Random and Hard-to-Describe Numbers (902 KB). Contents: On Random and Hard-to-Describe Numbers (C H Bennett); The Implications of a Cosmological Information Bound for Complexity, Quantum Information and the Nature of Physical Law (P C W Davies); What is a Computation? (M Davis); A Berry-Type Paradox (G Lolli); The Secret Number. An Exposition of Chaitin''s Theory (G Rozenberg & A Salomaa); Omega and the Time Evolution of the n-Body Problem (K Svozil); God''s Number: Where Can We Find the Secret of the Universe? In a Single Number! (M Chown); Omega Numbers (J-P Delahaye); Some Modern Perspectives on the Quest for Ultimate Knowledge (S Wolfram); An Enquiry Concerning Human (and Computer!) [Mathematical] Understanding (D Zeilberger); and other papers. Readership: Computer scientists and philosophers, both in academia and industry.

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Page Count

466

Publisher

World Scientific

Published Date

ISBN 10

9812770836

ISBN 13

9789812770837

Meta Maths

The Quest for Omega

By: Gregory J. Chaitin

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Meta Maths

The Quest for Omega

By: Gregory J. Chaitin

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242

Published Date

ISBN 10

1843545241

ISBN 13

9781843545248

Information, Randomness & Incompleteness

Papers on Algorithmic Information Theory

By: Gregory J. Chaitin

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Information, Randomness & Incompleteness

Papers on Algorithmic Information Theory

By: Gregory J. Chaitin

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Page Count

332

Publisher

World Scientific

Published Date

ISBN 10

9810201710

ISBN 13

9789810201715

Algorithmic Information Theory

By: Gregory. J. Chaitin

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Algorithmic Information Theory

By: Gregory. J. Chaitin

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.

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Page Count

192

Publisher

Cambridge University Press

Published Date

ISBN 10

0521616042

ISBN 13

9780521616041

Proving Darwin

Making Biology Mathematical

By: Gregory J. Chaitin

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Proving Darwin

Making Biology Mathematical

By: Gregory J. Chaitin

Explains how evolution works on a mathematical level, arguing that mathematical theory is an essential part of evolution while highlighting mathematical principles in the biological world.

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Page Count

146

Publisher

Pantheon

Published Date

ISBN 10

0375423141

ISBN 13

9780375423147

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