Gregory Chaitin's Books

Meta Math!

The Quest for Omega

By: Gregory Chaitin

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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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242

Publisher

Vintage

Published Date

ISBN 10

1400077974

ISBN 13

9781400077977

Goedel's Way

Exploits into an undecidable world

By: Gregory Chaitin,Francisco A Doria,Newton C.A. da Costa

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Goedel's Way

Exploits into an undecidable world

By: Gregory Chaitin,Francisco A Doria,Newton C.A. da Costa

Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines. The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8

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162

Publisher

CRC Press

Published Date

ISBN 10

0203169573

ISBN 13

9780203169575

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

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World Scientific

Published Date

ISBN 10

9812770828

ISBN 13

9789812770820

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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242

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World Scientific

Published Date

ISBN 10

9810236956

ISBN 13

9789810236953

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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368

Publisher

World Scientific

Published Date

ISBN 10

9812708952

ISBN 13

9789812708953

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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368

Publisher

World Scientific

Published Date

ISBN 10

9814474703

ISBN 13

9789814474702

Meta Math!

The Quest for Omega

By: Gregory Chaitin

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Meta Math!

The Quest for Omega

By: Gregory Chaitin

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242

Publisher

Vintage

Published Date

ISBN 10

1400077974

ISBN 13

9781400077977

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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332

Publisher

World Scientific

Published Date

ISBN 10

9810201710

ISBN 13

9789810201715

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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176

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1852334177

ISBN 13

9781852334178

Classical Econophysics

By: Allin F. Cottrell,Paul Cockshott,Gregory John Michaelson,Ian P. Wright,Victor Yakovenko

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Classical Econophysics

By: Allin F. Cottrell,Paul Cockshott,Gregory John Michaelson,Ian P. Wright,Victor Yakovenko

This book sets out to address some basic questions drawing from classical political economy and information theory and using an econophysics methodology: What is information? Why is it valuable? What is the relationship between money and information?

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Page Count

385

Publisher

Routledge

Published Date

ISBN 10

1134020767

ISBN 13

9781134020768

Electronic Monuments

By: Gregory L. Ulmer

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Electronic Monuments

By: Gregory L. Ulmer

While corporations, governmental groups, and public relations firms debated the best way to memorialize the event of 9/11, sites of commemoration could be seen across the country and especially on the Internet. Greg Ulmer suggests that this reality points us to a new sense of monumentality, one that is collaborative in nature rather than iconic. From a do-it-yourself Mount Rushmore to an automated tribute to the devastating annual toll of traffic deaths in the United States, Electronic Monuments describes commemoration as a fundamental experience, joining individual and collective identity, and adapting both to the emerging apparatus of “electracy,” or digital literacy. Concerns about the destruction of civic life caused by the society of the spectacle are refocused on the question of how a collectivity remembers who or what it is. Ulmer proposes that the Internet makes it possible for monumentality to become a primary site of self-knowledge, one that supports a new politics, ethics, and dimension of education. The Internet thus holds the promise of bringing citizens back into the political equation as witnesses and monitors. Gregory L. Ulmer is professor of English and media studies at the University of Florida, Gainesville.

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332

Publisher

U of Minnesota Press

Published Date

ISBN 10

0816645833

ISBN 13

9780816645831

Computation and Its Limits

By: Paul Cockshott,Lewis M Mackenzie,Gregory Michaelson

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Computation and Its Limits

By: Paul Cockshott,Lewis M Mackenzie,Gregory Michaelson

Although we are entirely unaware of it, computation is central to all aspects of our existences. Every day we solve, or try to solve, a myriad of problems, from the utterly trivial to the bafflingly complex. This book explains why it is possible to do computation and what the ultimate limits of it are, as understood by modern science.

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246

Publisher

Oxford University Press

Published Date

ISBN 10

0199640327

ISBN 13

9780199640324

Systemic Choices

Nonlinear Dynamics and Practical Management

By: Gregory A. Daneke

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Systemic Choices

Nonlinear Dynamics and Practical Management

By: Gregory A. Daneke

The revolution in social scientific theory and practice known as nonlinear dynamics, chaos, or complexity, derived from recent advances in the physical, biological, and cognitive sciences, is now culminating with the widespread use of tools and concepts such as praxis, fuzzy logic, artificial intelligence, and parallel processing. By tracing a number of conceptual threads from mathematics, economics, cybernetics, and various other applied systems theoretics, this book offers a historical framework for how these ideas are transforming the social sciences. Daneke goes on to address a variety of persistent philosophical issues surrounding this paradigm shift, ranging from the nature of human rationality to free will. Finally, he describes this shift as a path for revitalizing the social sciences just when they will be most needed to address the human condition in the new millennium. Systemic Choices describes how praxis and other complex systems tools can be applied to a number of pressing policy and management problems. For example, simulations can be used to grow a number of robust hybrid industrial and/or technological strategies between cooperation and competition. Likewise, elements of international agreements could be tested for sustainability under adaptively evolving institutional designs. Other concrete applications include strategic management, total quality management, and operational analyses. This exploration of a wide range of technical tools and concepts will interest economists, political scientists, sociologists, psychologists, and those in the management disciplines such as strategy, organizational behavior, finance, and operations. Gregory A. Daneke is Professor of Technology Management, Arizona State University, and of Human and Organization Development, The Fielding Institute.

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198

Publisher

University of Michigan Press

Published Date

ISBN 10

0472023454

ISBN 13

9780472023455

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 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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148

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9814021725

ISBN 13

9789814021722

KONSULT

Theopraxesis

By: Gregory L. Ulmer

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KONSULT

Theopraxesis

By: Gregory L. Ulmer

A motto guiding Gregory L. Ulmer's career is from the poet Basho: not to follow in the footsteps of the masters, but to seek what they sought. The responsibility of humanities disciplines today is to do for the digital apparatus (social machine) what the classical Greeks did for alphabetic writing. Ulmer frames online learning as a mode of invention (heuretics), beginning with the invention of konsult itself. Konsult: Theopraxesis describes the invention of a genre of learning that is to digital media what Plato's dialogue was to alphabetic writing. The Greeks invented the practices of writing (rhetoric and logic) native to the new institution of school (the Academy), fostering a new behavior of selfhood (Socrates). Ulmer adopts this historical precedent as a relay, an inventory for what must be invented again today: a genre of learning, an educational institution, identity behavior. The insight of electracy is that each apparatus augments and institutionalizes one of the primary faculties of human intelligence: theoria in literacy; praxis in orality; poiesis in electracy. Needed today are not practices of writing, but "theopraxesis" of media. The analytical information economy of literacy required separation and isolation (siloing) of institutionalized intelligence. The multimodality of electracy enables syncretism of faculties into holistic performance: thinking-doing-making; knowledge-purpose-affect. The interface metaphor of Plato's dialogue was an oral conversation during which the illiterate interlocutor is introduced to dialectical reason as Idea. The interface metaphor of konsult is scientific consulting during which anelectrate students encounter plasmatic desire as simulacrum. This new learning is organized around an updating of Justice native to electracy.

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278

Publisher

Parlor Press LLC

Published Date

ISBN 10

1643170708

ISBN 13

9781643170701

Avatar Emergency

By: Gregory L. Ulmer

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Avatar Emergency

By: Gregory L. Ulmer

A new experience of identity is emerging within the digital apparatus under the rubric of “avatar.” This study develops “concept avatar” as an opportunity to invent a practice of citizenship native to the Internet that simulates the functionality of measure dramatized in the traditions of “descent” (“avatar”) or “incarnation,” including the original usage in the Bhagavad Gita, and the Western evolution of the virtue of prudence from the Ancient daimon, through genius and character, to the contemporary sinthome.

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317

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Parlor Press LLC

Published Date

ISBN 10

1602353425

ISBN 13

9781602353428

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

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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162

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1447101855

ISBN 13

9781447101857

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

Proving Darwin

Making Biology Mathematical

By: Gregory Chaitin

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Proving Darwin

Making Biology Mathematical

By: Gregory Chaitin

Groundbreaking mathematician Gregory Chaitin gives us the first book to posit that we can prove how Darwin’s theory of evolution works on a mathematical level. For years it has been received wisdom among most scientists that, just as Darwin claimed, all of the Earth’s life-forms evolved by blind chance. But does Darwin’s theory function on a purely mathematical level? Has there been enough time for evolution to produce the remarkable biological diversity we see around us? It’s a question no one has yet answered—in fact, no one has attempted to answer it until now. In this illuminating and provocative book, Gregory Chaitin elucidates the mathematical scheme he’s developed that can explain life itself, and examines the works of mathematical pioneers John von Neumann and Alan Turing through the lens of biology. Fascinating and thought-provoking, Proving Darwin makes clear how biology may have found its greatest ally in mathematics.

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146

Publisher

Vintage

Published Date

ISBN 10

1400077982

ISBN 13

9781400077984

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

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

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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

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150

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Springer

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ISBN 10

1852336684

ISBN 13

9781852336684

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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332

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World Scientific

Published Date

ISBN 10

9810201710

ISBN 13

9789810201715

Goedel's Way

Exploits into an undecidable world

By: Gregory Chaitin,Francisco A Doria,Newton C.A. da Costa

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Goedel's Way

Exploits into an undecidable world

By: Gregory Chaitin,Francisco A Doria,Newton C.A. da Costa

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Page Count

160

Publisher

CRC Press

Published Date

ISBN 10

1136587640

ISBN 13

9781136587641

Goedel's Way

Exploits Into an Undecidable World

By: Gregory Chaitin

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Goedel's Way

Exploits Into an Undecidable World

By: Gregory Chaitin

Kurt G�del (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein�s general relativity, as he proved that Einstein�s theory allows for time machines. The G�del incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin�s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the G�del incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life.This accessible book gives a new, detailed and elementary explanation of the G�del incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book�s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http: //www.youtube.com/watch'v=REy9noY5Sg8

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Page Count

138

Publisher

CRC Press

Published Date

ISBN 10

1138442062

ISBN 13

9781138442061

Book's by Gregory Chaitin

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