Chaitin, Gregory J.
Overview
Works:  62 works in 275 publications in 5 languages and 5,748 library holdings 

Genres:  Popular works 
Roles:  Author, Author of introduction 
Classifications:  QA267, 511.3 
Publication Timeline
.
Most widely held works by
Gregory J Chaitin
Algorithmic information theory by
Gregory J Chaitin(
Book
)
50 editions published between 1977 and 2004 in English and Undetermined and held by 701 WorldCat member libraries worldwide
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 socalled exponential diophantine equation
50 editions published between 1977 and 2004 in English and Undetermined and held by 701 WorldCat member libraries worldwide
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 socalled exponential diophantine equation
The limits of mathematics : a course on information theory and limits of formal reasoning by
Gregory J Chaitin(
Book
)
34 editions published between 1997 and 2014 in English and held by 529 WorldCat member libraries worldwide
"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."Jacket
34 editions published between 1997 and 2014 in English and held by 529 WorldCat member libraries worldwide
"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."Jacket
Proving Darwin : making biology mathematical by
Gregory J Chaitin(
Book
)
6 editions published between 2012 and 2013 in English and held by 396 WorldCat member libraries worldwide
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
6 editions published between 2012 and 2013 in English and held by 396 WorldCat member libraries worldwide
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
The unknowable by
Gregory J Chaitin(
Book
)
23 editions published between 1999 and 2001 in English and Japanese and held by 382 WorldCat member libraries worldwide
"This companion volume to Chaitin's "The Limits of Mathematics", also published by Springer, gives a historical survey of the work this century on the foundations of mathematics, in which the author was a major participant. "The Unknowable" is a readable and concrete introduction to Chaitin's ideas, and it includes a detailed explanation of the programming language used by Chaitin in both volumes. It will enable computer users to interact with the author's proofs and discover for themselves how they work. The software for "The Unknowable" can be downloaded from the author's Web site."BOOK JACKET
23 editions published between 1999 and 2001 in English and Japanese and held by 382 WorldCat member libraries worldwide
"This companion volume to Chaitin's "The Limits of Mathematics", also published by Springer, gives a historical survey of the work this century on the foundations of mathematics, in which the author was a major participant. "The Unknowable" is a readable and concrete introduction to Chaitin's ideas, and it includes a detailed explanation of the programming language used by Chaitin in both volumes. It will enable computer users to interact with the author's proofs and discover for themselves how they work. The software for "The Unknowable" can be downloaded from the author's Web site."BOOK JACKET
Exploring randomness by
Gregory J Chaitin(
Book
)
16 editions published between 2000 and 2002 in English and held by 301 WorldCat member libraries worldwide
This essential companion volume to CHAITIN's highly successful books The Unknowable and The Limits of Mathematics, also published by Springer, presents the technical core of his theory of programsize complexity, also known as algorithmic information theory. (The two previous volumes are more concerned with applications to metamathematics.) LISP is used to present the key algorithms and to enable computer users to interact with the author's 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: http://www.cs.auckland.ac.nz/CDMTCS/chaitin/ait/ "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 he's seen. Don't miss it." John Casti, Santa Fe Institute, Author of "Goedel: A Life of Logic."
16 editions published between 2000 and 2002 in English and held by 301 WorldCat member libraries worldwide
This essential companion volume to CHAITIN's highly successful books The Unknowable and The Limits of Mathematics, also published by Springer, presents the technical core of his theory of programsize complexity, also known as algorithmic information theory. (The two previous volumes are more concerned with applications to metamathematics.) LISP is used to present the key algorithms and to enable computer users to interact with the author's 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: http://www.cs.auckland.ac.nz/CDMTCS/chaitin/ait/ "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 he's seen. Don't miss it." John Casti, Santa Fe Institute, Author of "Goedel: A Life of Logic."
Gödel's way : exploits into an undecidable world by
Gregory J Chaitin(
Book
)
9 editions published between 2011 and 2012 in English and Undetermined and held by 234 WorldCat member libraries worldwide
"Kurt Gödel (19061978) was an AustrianAmerican 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 admits time machines. The Gödel incompleteness phenomenon  one cannot prove nor disprove all true mathematical sentences in the usual formal 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 CostaDoria 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 CostaDoria 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."
9 editions published between 2011 and 2012 in English and Undetermined and held by 234 WorldCat member libraries worldwide
"Kurt Gödel (19061978) was an AustrianAmerican 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 admits time machines. The Gödel incompleteness phenomenon  one cannot prove nor disprove all true mathematical sentences in the usual formal 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 CostaDoria 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 CostaDoria 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."
Thinking about Gödel and Turing : essays on complexity, 19702007 by
Gregory J Chaitin(
Book
)
19 editions published between 2007 and 2008 in English and held by 195 WorldCat member libraries worldwide
Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable 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 Godel and Turing. This book contains 23 nontechnical 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 programsize complexity or algorithmic information content in order to shed further light on the fundamental work of Godel and Turing on the limits of mathematical methods, both in logic and in computation. Chaitin argues here that his informationtheoretic approach to metamathematics suggests a quasiempirical 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
19 editions published between 2007 and 2008 in English and held by 195 WorldCat member libraries worldwide
Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable 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 Godel and Turing. This book contains 23 nontechnical 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 programsize complexity or algorithmic information content in order to shed further light on the fundamental work of Godel and Turing on the limits of mathematical methods, both in logic and in computation. Chaitin argues here that his informationtheoretic approach to metamathematics suggests a quasiempirical 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
Informationtheoretic incompleteness by
Gregory J Chaitin(
Book
)
10 editions published between 1992 and 1998 in English and Undetermined and held by 141 WorldCat member libraries worldwide
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 informationtheoretic incompleteness theorems. The nontechnical part includes the lecture given by Chaitin in Gšdel's classroom at the University o
10 editions published between 1992 and 1998 in English and Undetermined and held by 141 WorldCat member libraries worldwide
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 informationtheoretic incompleteness theorems. The nontechnical part includes the lecture given by Chaitin in Gšdel's classroom at the University o
Randomness and complexity : from Leibniz to Chaitin by
Cristian Calude(
Book
)
10 editions published in 2007 in English and held by 104 WorldCat member libraries worldwide
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
10 editions published in 2007 in English and held by 104 WorldCat member libraries worldwide
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
Meta math! : the quest for omega by
Gregory J Chaitin(
Book
)
11 editions published between 2005 and 2008 in English and Undetermined and held by 101 WorldCat member libraries worldwide
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. From the Trade Paperback edition
11 editions published between 2005 and 2008 in English and Undetermined and held by 101 WorldCat member libraries worldwide
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. From the Trade Paperback edition
Hasard et complexité en mathématiques by
Gregory J Chaitin(
Book
)
2 editions published in 2009 in French and held by 75 WorldCat member libraries worldwide
2 editions published in 2009 in French and held by 75 WorldCat member libraries worldwide
Logica matematica : strutture rappresentazioni deduzioni by
Vincenzo Manca(
Book
)
2 editions published in 2001 in Italian and held by 18 WorldCat member libraries worldwide
2 editions published in 2001 in Italian and held by 18 WorldCat member libraries worldwide
The limits of mathematics by
Gregory J Chaitin(
Book
)
8 editions published between 1994 and 2001 in English and Japanese and held by 17 WorldCat member libraries worldwide
Abstract: "This condensed version of RC 20190 will be the main handout for a course on algorithmic information theory to be given 2229 May 1996 at the Rovaniemi Institute of Technology, Rovaniemi, Finland (see announcement at http://www.rotol.fi)."
8 editions published between 1994 and 2001 in English and Japanese and held by 17 WorldCat member libraries worldwide
Abstract: "This condensed version of RC 20190 will be the main handout for a course on algorithmic information theory to be given 2229 May 1996 at the Rovaniemi Institute of Technology, Rovaniemi, Finland (see announcement at http://www.rotol.fi)."
Alla ricerca di omega by
Gregory J Chaitin(
Book
)
2 editions published in 2007 in Italian and held by 12 WorldCat member libraries worldwide
2 editions published in 2007 in Italian and held by 12 WorldCat member libraries worldwide
Information and randomness : an algorithmic perspective by
Cristian Calude(
Book
)
6 editions published between 1994 and 2002 in English and held by 12 WorldCat member libraries worldwide
The book presents in a mathematical clear way the fundamentals of algorithmic information theory and a few selected applications. This 2nd edition presents new and important results obtained in recent years: the characterization of computable enumerable random reals, the construction of an Omega Number for which ZFC cannot determine any digits, and the first successful attempt to compute the exact values of 64 bits of a specific Omega Number. Finally, the book contains a discussion of some interesting philosophical questions related to randomness and mathematical knowledge. "Professor Calude has produced a firstrate exposition of uptodate work in information and randomness." D.S. Bridges, Canterbury University, coauthor, with Errett Bishop, of Constructive Analysis; "The second edition of this classic work is highly recommended to anyone interested in algorithmic information and randomness." G.J. Chaitin, IBM Research Division, New York, author of Conversations with a Mathematician; "This book is a must for a comprehensive introduction to algorithmic information theory and for anyone interested in its applications in the natural sciences." K. Svozil, Technical University of Vienna, author of Randomness & Undecidability in Physics
6 editions published between 1994 and 2002 in English and held by 12 WorldCat member libraries worldwide
The book presents in a mathematical clear way the fundamentals of algorithmic information theory and a few selected applications. This 2nd edition presents new and important results obtained in recent years: the characterization of computable enumerable random reals, the construction of an Omega Number for which ZFC cannot determine any digits, and the first successful attempt to compute the exact values of 64 bits of a specific Omega Number. Finally, the book contains a discussion of some interesting philosophical questions related to randomness and mathematical knowledge. "Professor Calude has produced a firstrate exposition of uptodate work in information and randomness." D.S. Bridges, Canterbury University, coauthor, with Errett Bishop, of Constructive Analysis; "The second edition of this classic work is highly recommended to anyone interested in algorithmic information and randomness." G.J. Chaitin, IBM Research Division, New York, author of Conversations with a Mathematician; "This book is a must for a comprehensive introduction to algorithmic information theory and for anyone interested in its applications in the natural sciences." K. Svozil, Technical University of Vienna, author of Randomness & Undecidability in Physics
Teoria algoritmica della complessità by
Gregory J Chaitin(
Book
)
1 edition published in 2006 in Italian and held by 9 WorldCat member libraries worldwide
1 edition published in 2006 in Italian and held by 9 WorldCat member libraries worldwide
Logic by
Wilfrid Hodges(
Book
)
1 edition published in 1991 in Italian and held by 8 WorldCat member libraries worldwide
If a man supports Arsenal one day and Spurs the next then he is fickle but not necessarily illogical. From this starting point, and assuming no previous knowledge of logic, Wilfrid Hodges takes the reader through the whole gamut of logical expressions in a simple and lively way. Readers who are more mathematically adventurous will find optional sections introducing rather more challenging material
1 edition published in 1991 in Italian and held by 8 WorldCat member libraries worldwide
If a man supports Arsenal one day and Spurs the next then he is fickle but not necessarily illogical. From this starting point, and assuming no previous knowledge of logic, Wilfrid Hodges takes the reader through the whole gamut of logical expressions in a simple and lively way. Readers who are more mathematically adventurous will find optional sections introducing rather more challenging material
Numeri, caso e sequenze by
Roberto Magari(
Book
)
1 edition published in 1988 in Italian and held by 8 WorldCat member libraries worldwide
1 edition published in 1988 in Italian and held by 8 WorldCat member libraries worldwide
Demostrando a Darwin : la biología en clave matemática by
Gregory J Chaitin(
Book
)
1 edition published in 2013 in Spanish and held by 8 WorldCat member libraries worldwide
1 edition published in 2013 in Spanish and held by 8 WorldCat member libraries worldwide
Cambridge Tracts in Theoretical Computer Science, 1 by
Gregory J Chaitin(
)
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
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Related Identities
 Calude, Cristian 1952 Author Editor
 Doria, Francisco Antônio
 Costa, Newton C. A. da
 Mansuy, Roger
 Forget, Hugo
 Cambridge University Press Publisher
 Centre for Discrete Mathematics & Theoretical Computer Science
 Manca, Vincenzo Author
 Salomaa, Arto Author of introduction
 黒川, 利明 1948
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Associated Subjects
Algorithms BiologyMathematical models BiologyPhilosophy Biomathematics Coding theory Combinatorial analysis Computational complexity Computer programming Computer programmingPhilosophy Computer science Computer scienceMathematics Computer software Distribution (Probability theory) Evolution (Biology)Mathematical models Evolution (Biology)Mathematics Evolution (Biology)Philosophy EvolutionMathematical models EvolutionMathematics EvolutionPhilosophy Gödel's theorem Incompleteness theorems Information theory Information theory in mathematics Kolmogorov complexity LISP (Computer program language) Logic Logic, Symbolic and mathematical Machine theory MathematicsPhilosophy Metamathematics Philosophy Reasoning Statistics Stochastic processes Turing machines
Alternative Names
Chaitin, G. J.
Chaitin, G. J. 1947
Chaitin, G. J. (Gregory J.)
Chaitin , Gregory
Chaitin, Gregory 1947
Chaitin, Gregory J.
Chaitin, Gregory John
Chaitin, Gregory John 1947
Gregory Chaitin Amerikaans wiskundige
Gregory Chaitin amerikansk datavetare och matematiker
Gregory Chaitin amerikansk informatikar og matematikar
Gregory Chaitin amerikansk informatiker og matematiker
Gregory Chaitin matematico e informatico argentino naturalizzato statunitense
Gregory Chaitin mathématicien américain
Gregory Chaitin USamerikanischer Mathematiker
Хайтин, Грегори
グレゴリー・チャイティン
チャイティン, G. J
チャイティン, グレゴリー
チャイティン, グレゴリー・J
格里戈里·蔡廷
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