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Gregory Chaitin

January 01, 1970

Gregory John Chaitin (/ˈtʃaɪtɪn/ CHY-tin; born 25 June 1947) is an Argentine-American mathematician and computer scientist. Beginning in the late 1960s, Chaitin made contributions to algorithmic information theory and metamathematics, in particular a computer-theoretic result equivalent to Gödel's incompleteness theorem.[2] He is considered to be one of the founders of what is today known as algorithmic (Solomonoff–Kolmogorov–Chaitin, Kolmogorov or program-size) complexity together with Andrei Kolmogorov and Ray Solomonoff. Along with the works of e.g. Solomonoff, Kolmogorov, Martin-Löf, and Leonid Levin, algorithmic information theory became a foundational part of theoretical computer science, information theory, and mathematical logic.[3][4] It is a common subject in several computer science curricula. Besides computer scientists, Chaitin's work draws attention of many philosophers and mathematicians to fundamental problems in mathematical creativity and digital philosophy.

Gregory Chaitin
Chaitin in 2008
Born (1947-06-25) 25 June 1947 (age 76)
Chicago[1]
NationalityArgentine-American
Known for
Scientific career
Fields
Institutions
Websiteuba.academia.edu/GregoryChaitin

Mathematics and computer science edit

Gregory Chaitin is Jewish and he attended the Bronx High School of Science and City College of New York, where he (still in his teens) developed the theory that led to his independent discovery of algorithmic complexity.[5][6]

Chaitin has defined Chaitin's constant Ω, a real number whose digits are equidistributed and which is sometimes informally described as an expression of the probability that a random program will halt. Ω has the mathematical property that it is definable, with asymptotic approximations from below (but not from above), but not computable.

Chaitin is also the originator of using graph coloring to do register allocation in compiling, a process known as Chaitin's algorithm.[7]

He was formerly a researcher at IBM's Thomas J. Watson Research Center in New York. He has written more than 10 books that have been translated to about 15 languages. He is today interested in questions of metabiology and information-theoretic formalizations of the theory of evolution, and is a member of the Institute for Advanced Studies at Mohammed VI Polytechnic University.

Other scholarly contributions edit

Chaitin also writes about philosophy, especially metaphysics and philosophy of mathematics (particularly about epistemological matters in mathematics). In metaphysics, Chaitin claims that algorithmic information theory is the key to solving problems in the field of biology (obtaining a formal definition of 'life', its origin and evolution) and neuroscience (the problem of consciousness and the study of the mind).

In recent writings, he defends a position known as digital philosophy. In the epistemology of mathematics, he claims that his findings in mathematical logic and algorithmic information theory show there are "mathematical facts that are true for no reason, that are true by accident".[8] Chaitin proposes that mathematicians must abandon any hope of proving those mathematical facts and adopt a quasi-empirical methodology.

Honors edit

In 1995 he was given the degree of doctor of science honoris causa by the University of Maine. In 2002 he was given the title of honorary professor by the University of Buenos Aires in Argentina, where his parents were born and where Chaitin spent part of his youth. In 2007 he was given a Leibniz Medal[9] by Wolfram Research. In 2009 he was given the degree of doctor of philosophy honoris causa by the National University of Córdoba. He was formerly a researcher at IBM's Thomas J. Watson Research Center and a professor at the Federal University of Rio de Janeiro.

Criticism edit

Some philosophers and logicians disagree with the philosophical conclusions that Chaitin has drawn from his theorems related to what Chaitin thinks is a kind of fundamental arithmetic randomness.[10] The logician Torkel Franzén criticized Chaitin's interpretation of Gödel's incompleteness theorem and the alleged explanation for it that Chaitin's work represents.[11]

Bibliography edit

References edit

  1. ^ Gregory Chaitin (2007), Algorithmic information theory: "Chaitin Research Timeline" 23 March 2012 at the Wayback Machine
  2. ^ Review of Meta Math!: The Quest for Omega, By Gregory Chaitin SIAM News, Volume 39, Number 1, January/February 2006
  3. ^ Calude, C.S. (2002). Information and Randomness: An Algorithmic Perspective. Texts in Theoretical Computer Science. An EATCS Series. Springer-Verlag.
  4. ^ R. Downey, and D. Hirschfeldt (2010), Algorithmic Randomness and Complexity, Springer-Verlag.
  5. ^ Li; Vitanyi (1997), An Introduction to Kolmogorov Complexity and Its Applications, Springer, p. 92, ISBN 9780387948683, G.J.Chaitin had finished the Bronx High School of Science, and was an 18-year-old undergraduate student at City College of the City University of New York, when he submitted two papers.... In his [second] paper, Chaitin puts forward the notion of Kolmogorov complexity....
  6. ^ Chaitin, G. J. (October 1966), "On the Length of Programs for Computing Finite Binary Sequences", Journal of the ACM, 13 (4): 547–569, doi:10.1145/321356.321363, S2CID 207698337
  7. ^ G.J. Chaitin, Register Allocation and Spilling via Graph Coloring, US Patent 4,571,678 (1986) [cited from Register Allocation on the Intel® Itanium® Architecture, p.155]
  8. ^ Chaitin, G. J. (2003). "From Philosophy to Program Size". arXiv:math/0303352.
  9. ^ Zenil, Hector "Leibniz medallion comes to life after 300 years" Anima Ex Machina, The Blog of Hector Zenil, 3 November 2007.
  10. ^ Panu Raatikainen, "Exploring Randomness and The Unknowable" Notices of the American Mathematical Society Book Review October 2001.
  11. ^ Franzén, Torkel (2005), Gödel's Theorem: An Incomplete Guide to its Use and Abuse, Wellesley, Massachusetts: A K Peters, Ltd., ISBN 978-1-56881-238-0

Further reading edit

  • Pagallo, Ugo (2005), [Introduction to Digital Philosophy: From Leibniz to Chaitin] (in Italian), G. Giappichelli Editore, ISBN 978-88-348-5635-2, archived from the original on 22 July 2011, retrieved 16 April 2008
  • Calude, Cristian S., ed. (2007), Randomness and Complexity. From Leibniz to Chaitin, World Scientific, ISBN 978-981-277-082-0
  • Wuppuluri, Shyam; Doria, Francisco A., eds. (2020), Unravelling Complexity: The Life and Work of Gregory Chaitin, World Scientific, doi:10.1142/11270, ISBN 978-981-12-0006-9, S2CID 198790362

External links edit

 
Wikiquote has quotations related to Gregory Chaitin.
  • G J Chaitin Home Page from academia.edu
  • G J Chaitin Home Page from UMaine.edu in the Internet Archive 29 October 2013 at the Wayback Machine
  • List of publications of G J Chaitin
  • Video of lecture on metabiology: "Life as evolving software" on YouTube
  • Video of lecture on "Leibniz, complexity and incompleteness"
  • A short version of Chaitin's proof
  • Gregory Chaitin extended film interview and transcripts for the 'Why Are We Here?' documentary series
  • Chaitin Lisp on github

January 01, 1970
gregory, chaitin, gregory, john, chaitin, born, june, 1947, argentine, american, mathematician, computer, scientist, beginning, late, 1960s, chaitin, made, contributions, algorithmic, information, theory, metamathematics, particular, computer, theoretic, resul. Gregory John Chaitin ˈ tʃ aɪ t ɪ n CHY tin born 25 June 1947 is an Argentine American mathematician and computer scientist Beginning in the late 1960s Chaitin made contributions to algorithmic information theory and metamathematics in particular a computer theoretic result equivalent to Godel s incompleteness theorem 2 He is considered to be one of the founders of what is today known as algorithmic Solomonoff Kolmogorov Chaitin Kolmogorov or program size complexity together with Andrei Kolmogorov and Ray Solomonoff Along with the works of e g Solomonoff Kolmogorov Martin Lof and Leonid Levin algorithmic information theory became a foundational part of theoretical computer science information theory and mathematical logic 3 4 It is a common subject in several computer science curricula Besides computer scientists Chaitin s work draws attention of many philosophers and mathematicians to fundamental problems in mathematical creativity and digital philosophy Gregory ChaitinChaitin in 2008Born 1947 06 25 25 June 1947 age 76 Chicago 1 NationalityArgentine AmericanKnown forAlgorithmic Information TheoryChaitin s constantChaitin s algorithmScientific careerFieldsBiologyMathematicsComputer scienceInstitutionsMohammed VI Polytechnic University Federal University of Rio de Janeiro University of Buenos Aires IBM T J Watson Research CenterWebsiteuba wbr academia wbr edu wbr GregoryChaitin Contents 1 Mathematics and computer science 2 Other scholarly contributions 3 Honors 4 Criticism 5 Bibliography 6 References 7 Further reading 8 External linksMathematics and computer science editGregory Chaitin is Jewish and he attended the Bronx High School of Science and City College of New York where he still in his teens developed the theory that led to his independent discovery of algorithmic complexity 5 6 Chaitin has defined Chaitin s constant W a real number whose digits are equidistributed and which is sometimes informally described as an expression of the probability that a random program will halt W has the mathematical property that it is definable with asymptotic approximations from below but not from above but not computable Chaitin is also the originator of using graph coloring to do register allocation in compiling a process known as Chaitin s algorithm 7 He was formerly a researcher at IBM s Thomas J Watson Research Center in New York He has written more than 10 books that have been translated to about 15 languages He is today interested in questions of metabiology and information theoretic formalizations of the theory of evolution and is a member of the Institute for Advanced Studies at Mohammed VI Polytechnic University Other scholarly contributions editChaitin also writes about philosophy especially metaphysics and philosophy of mathematics particularly about epistemological matters in mathematics In metaphysics Chaitin claims that algorithmic information theory is the key to solving problems in the field of biology obtaining a formal definition of life its origin and evolution and neuroscience the problem of consciousness and the study of the mind In recent writings he defends a position known as digital philosophy In the epistemology of mathematics he claims that his findings in mathematical logic and algorithmic information theory show there are mathematical facts that are true for no reason that are true by accident 8 Chaitin proposes that mathematicians must abandon any hope of proving those mathematical facts and adopt a quasi empirical methodology Honors editIn 1995 he was given the degree of doctor of science honoris causa by the University of Maine In 2002 he was given the title of honorary professor by the University of Buenos Aires in Argentina where his parents were born and where Chaitin spent part of his youth In 2007 he was given a Leibniz Medal 9 by Wolfram Research In 2009 he was given the degree of doctor of philosophy honoris causa by the National University of Cordoba He was formerly a researcher at IBM s Thomas J Watson Research Center and a professor at the Federal University of Rio de Janeiro Criticism editThis article s criticism or controversy section may compromise the article s neutrality Please help rewrite or integrate negative information to other sections through discussion on the talk page July 2016 Some philosophers and logicians disagree with the philosophical conclusions that Chaitin has drawn from his theorems related to what Chaitin thinks is a kind of fundamental arithmetic randomness 10 The logician Torkel Franzen criticized Chaitin s interpretation of Godel s incompleteness theorem and the alleged explanation for it that Chaitin s work represents 11 Bibliography editInformation Randomness amp Incompleteness World Scientific 1987 online Algorithmic Information Theory Cambridge University Press 1987 online Information theoretic Incompleteness World Scientific 1992 online The Limits of Mathematics Springer Verlag 1998 online The Unknowable Springer Verlag 1999 online Exploring Randomness Springer Verlag 2001 online Conversations with a Mathematician Springer Verlag 2002 online From Philosophy to Program Size Tallinn Cybernetics Institute 2003 Meta Math The Quest for Omega Pantheon Books 2005 reprinted in UK as Meta Maths The Quest for Omega Atlantic Books 2006 arXiv math 0404335 Teoria algoritmica della complessita G Giappichelli Editore 2006 Thinking about Godel amp Turing World Scientific 2007 online Mathematics Complexity and Philosophy Editorial Midas 2011 Godel s Way CRC Press 2012 Proving Darwin Making Biology Mathematical Pantheon Books 2012 online Building the World from Information amp Computation Academia edu 2023 online Philosophical Mathematics Infinity Incompleteness Irreducibility Academia edu 2023 online References edit Gregory Chaitin 2007 Algorithmic information theory Chaitin Research Timeline Archived 23 March 2012 at the Wayback Machine Review of Meta Math The Quest for Omega By Gregory Chaitin SIAM News Volume 39 Number 1 January February 2006 Calude C S 2002 Information and Randomness An Algorithmic Perspective Texts in Theoretical Computer Science An EATCS Series Springer Verlag R Downey and D Hirschfeldt 2010 Algorithmic Randomness and Complexity Springer Verlag Li Vitanyi 1997 An Introduction to Kolmogorov Complexity and Its Applications Springer p 92 ISBN 9780387948683 G J Chaitin had finished the Bronx High School of Science and was an 18 year old undergraduate student at City College of the City University of New York when he submitted two papers In his second paper Chaitin puts forward the notion of Kolmogorov complexity Chaitin G J October 1966 On the Length of Programs for Computing Finite Binary Sequences Journal of the ACM 13 4 547 569 doi 10 1145 321356 321363 S2CID 207698337 G J Chaitin Register Allocation and Spilling via Graph Coloring US Patent 4 571 678 1986 cited from Register Allocation on the Intel Itanium Architecture p 155 Chaitin G J 2003 From Philosophy to Program Size arXiv math 0303352 Zenil Hector Leibniz medallion comes to life after 300 years Anima Ex Machina The Blog of Hector Zenil 3 November 2007 Panu Raatikainen Exploring Randomness and The Unknowable Notices of the American Mathematical Society Book Review October 2001 Franzen Torkel 2005 Godel s Theorem An Incomplete Guide to its Use and Abuse Wellesley Massachusetts A K Peters Ltd ISBN 978 1 56881 238 0Further reading editPagallo Ugo 2005 Introduzione alla filosofia digitale Da Leibniz a Chaitin Introduction to Digital Philosophy From Leibniz to Chaitin in Italian G Giappichelli Editore ISBN 978 88 348 5635 2 archived from the original on 22 July 2011 retrieved 16 April 2008 Calude Cristian S ed 2007 Randomness and Complexity From Leibniz to Chaitin World Scientific ISBN 978 981 277 082 0 Wuppuluri Shyam Doria Francisco A eds 2020 Unravelling Complexity The Life and Work of Gregory Chaitin World Scientific doi 10 1142 11270 ISBN 978 981 12 0006 9 S2CID 198790362External links edit nbsp Wikiquote has quotations related to Gregory Chaitin G J Chaitin Home Page from academia edu G J Chaitin Home Page from UMaine edu in the Internet Archive Archived 29 October 2013 at the Wayback Machine List of publications of G J Chaitin Video of lecture on metabiology Life as evolving software on YouTube Video of lecture on Leibniz complexity and incompleteness New Scientist article March 2001 on Chaitin Omegas and Super Omegas A short version of Chaitin s proof Gregory Chaitin extended film interview and transcripts for the Why Are We Here documentary series Chaitin Lisp on github Retrieved from https en wikipedia org w index php title Gregory Chaitin amp oldid 1182949387, wikipedia, wiki, book, books, library,

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