Chaitin, Gregory J.Overview
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Most widely held works about
Gregory J Chaitin
Most widely held works by
Gregory J Chaitin
Randomness and complexity from Leibniz to Chaitin
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10 editions published in 2007 in English and held by 905 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
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18 editions published between 2005 and 2013 in English and held by 786 WorldCat member libraries worldwide Explores the enigmas, paradoxes, and random qualities that exist within the field of mathematics and discusses the author's groundbreaking discovery of the Omega number, a complex representation of unknowability
Algorithmic information theory
by Gregory J Chaitin
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35 editions published between 1987 and 2004 in English and Undetermined and held by 681 WorldCat member libraries worldwide
Thinking about Gödel and Turing essays on complexity 19702007
by Gregory J Chaitin
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10 editions published between 2007 and 2008 in English and held by 544 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
The limits of mathematics : a course on information theory and limits of formal reasoning
by Gregory J Chaitin
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35 editions published between 1993 and 2003 in English and Undetermined and held by 517 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
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9 editions published between 2012 and 2013 in English and held by 395 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
Information, randomness & incompleteness : papers on algorithmic information theory
by Gregory J Chaitin
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22 editions published between 1987 and 1990 in English and Spanish and held by 381 WorldCat member libraries worldwide 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 Gödel's incompleteness theorem, using an informationtheoretic 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 unpredictabilit
The unknowable
by Gregory J Chaitin
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15 editions published between 1999 and 2000 in English and held by 355 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
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11 editions published between 2000 and 2002 in English and held by 289 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
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10 editions published between 2011 and 2012 in English and held by 266 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. "
Informationtheoretic incompleteness
by Gregory J Chaitin
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7 editions published between 1992 and 1998 in English and Undetermined and held by 148 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
Meta maths : the quest for Omega
by Gregory J Chaitin
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8 editions published between 2005 and 2007 in English and held by 95 WorldCat member libraries worldwide
Hasard et complexité en mathématiques
by Gregory J Chaitin
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2 editions published in 2009 in French and held by 72 WorldCat member libraries worldwide
Conversations with a mathematician : math, art, science, and the limits of reason : a collection of his most wideranging and nontechnical lectures and interviews
by Gregory J Chaitin
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6 editions published between 2001 and 2003 in English and held by 48 WorldCat member libraries worldwide
Logica matematica : strutture rappresentazioni deduzioni
by Vincenzo Manca
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2 editions published in 2001 in Italian and held by 12 WorldCat member libraries worldwide
Conversations with a Mathematician Math, Art, Science and the Limits of Reason
by Gregory J Chaitin
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4 editions published between 2001 and 2002 in English and held by 11 WorldCat member libraries worldwide G.J. Chaitin is at the IBM Thomas J. Watson Research Center in New York. He has shown that God plays dice not only in quantum mechanics, but even in the foundations of mathematics, where Chaitin discovered mathematical facts that are true for no reason, that are true by accident. This book collects his most wideranging and nontechnical lectures and interviews, and it will be of interest to anyone concerned with the philosophy of mathematics, with the similarities and differences between physics and mathematics, or with the creative process and mathematics as an art. "Chaitin has put a scratch on the rock of eternity." Jacob T. Schwartz, Courant Institute, New York University, USA "(Chaitin is) one of the great ideas men of mathematics and computer science." Marcus Chown, author of The Magic Furnace, in NEW SCIENTIST "Finding the right formalization is a large component of the art of doing great mathematics." John Casti, author of Mathematical Mountaintops, on Godel, Turing and Chaitin in NATURE "What mathematicians over the centuries  from the ancients, through Pascal, Fermat, Bernoulli, and de Moivre, to Kolmogorov and Chaitin  have discovered, is that it ÄrandomnessÜ is a profoundly rich concept." Jerrold W. Grossman in the MATHEMATICAL INTELLIGENCER
Information and randomness : an algorithmic perspective
by Cristian Calude
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6 editions published between 1994 and 2002 in English and held by 8 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
Alla ricerca di omega
by Gregory J Chaitin
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2 editions published in 2007 in Italian and held by 6 WorldCat member libraries worldwide
Numeri, caso e sequenze
by Roberto Magari
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1 edition published in 1988 in Italian and held by 5 WorldCat member libraries worldwide
Speculations on biology, information and complexity
by Gregory J Chaitin
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1 edition published in 2006 in English and held by 4 WorldCat member libraries worldwide more
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Associated Subjects
BiologyMathematical models BiologyPhilosophy Biomathematics Chaitin, Gregory J Coding theory Combinatorial analysis Computational complexity Computer algorithms Computer programmingPhilosophy Computer science Computer scienceMathematics Computer software Distribution (Probability theory) Electronic data processing 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, Symbolic and mathematical Machine theory Mathematics MathematicsPhilosophy Metamathematics 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
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
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