Gregory Chaitin: Difference between revisions

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|caption          = Chaitin in 2008
|caption          = Chaitin in 2008
|birth_date        = {{birth date and age |df=yes|1947|6|25}}
|birth_date        = {{birth date and age |df=yes|1947|6|25}}
|birth_place      = [[Chicago]]<ref>[http://www.umcs.maine.edu/~chaitin/60.pdf Gregory Chaitin (2007), Algorithmic information theory: "Chaitin Research Timeline"] {{webarchive |url=https://web.archive.org/web/20120323024501/http://www.umcs.maine.edu/~chaitin/60.pdf |date=23 March 2012 }}</ref>
|birth_place      = [[Chicago]]<ref>[https://arxiv.org/pdf/math/0701164 Gregory Chaitin (2007), Algorithmic information theory: "Chaitin Research Timeline"]</ref>
|death_date        =
|death_date        =
|death_place      =
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|citizenship       =
|citizenship      = [[Argentina|Argentine]]-[[United States|American]]
|nationality       = [[Argentina|Argentine]]-[[United States|American]]
|fields            = {{ubl|[[Biology]]|[[Mathematics]]|[[Computer science]]}}
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|doctoral_students = [https://www.hectorzenil.com Hector Zenil],[https://felipeabrahao.academia.edu Felipe S Abrahão]
|notable_students  =
|notable_students  =
|known_for        = {{ubl|[[Algorithmic Information Theory]]|[[Chaitin's constant]]|[[Chaitin's algorithm]]}}
|known_for        = {{ubl|[[Algorithmic Information Theory]]|[[Chaitin's constant]]|[[Chaitin's algorithm]]}}
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|website          = {{URL|https://uba.academia.edu/GregoryChaitin}}
|website          = {{URL|https://independent.academia.edu/VirginiaChaitin}}
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Gregory Chaitin is [[Jewish]].  He attended the [[Bronx High School of Science]] and the [[City College of New York]], where he (still in his teens) developed the theory that led to his independent discovery of [[Kolmogorov complexity|algorithmic complexity]].<ref>{{Citation |last1=Li |last2=Vitanyi |title=An Introduction to Kolmogorov Complexity and Its Applications |publisher=Springer |year=1997 |url=https://books.google.com/books?id=LKEmB_GQ53QC |page=92 |quote=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.... |isbn=9780387948683 }}</ref><ref>{{Citation |last=Chaitin |first=G. J. |title=On the Length of Programs for Computing Finite Binary Sequences |journal=Journal of the ACM |volume=13 |issue=4 |date=October 1966 |pages=547–569 |doi=10.1145/321356.321363|s2cid=207698337 }}</ref>
Gregory Chaitin is [[Jewish]].  He attended the [[Bronx High School of Science]] and the [[City College of New York]], where he (still in his teens) developed the theory that led to his independent discovery of [[Kolmogorov complexity|algorithmic complexity]].<ref>{{Citation |last1=Li |last2=Vitanyi |title=An Introduction to Kolmogorov Complexity and Its Applications |publisher=Springer |year=1997 |url=https://books.google.com/books?id=LKEmB_GQ53QC |page=92 |quote=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.... |isbn=9780387948683 }}</ref><ref>{{Citation |last=Chaitin |first=G. J. |title=On the Length of Programs for Computing Finite Binary Sequences |journal=Journal of the ACM |volume=13 |issue=4 |date=October 1966 |pages=547–569 |doi=10.1145/321356.321363|s2cid=207698337 }}</ref>


Chaitin has defined [[Chaitin's constant]] Ω, a [[real number]] whose digits are [[normal number|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 number|definable]], with asymptotic approximations from below (but not from above), but not [[computability theory (computation)|computable]].
In 1975 Chaitin defined [[Chaitin's constant]] Ω, a [[real number]] whose digits are [[normal number|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 number|definable]], with asymptotic approximations from below (but not from above), but not [[computability theory (computation)|computable]].


Chaitin is also the originator of using [[graph coloring]] to do [[register allocation]] in [[compiling]], a process known as [[Chaitin's algorithm]].<ref>G.J. Chaitin, ''Register Allocation and Spilling via Graph Coloring'', [https://patents.google.com/patent/US4571678 US Patent 4,571,678] (1986) [cited from [http://ssw.jku.at/Teaching/PhDTheses/Hoflehner/index.html ''Register Allocation on the Intel® Itanium® Architecture''], p.155]</ref>
Chaitin is also the originator of using [[graph coloring]] to do [[register allocation]] in [[compiling]], a process known as [[Chaitin's algorithm]].<ref>G.J. Chaitin, ''Register Allocation and Spilling via Graph Coloring'', [https://patents.google.com/patent/US4571678 US Patent 4,571,678] (1986) [cited from [http://ssw.jku.at/Teaching/PhDTheses/Hoflehner/index.html ''Register Allocation on the Intel® Itanium® Architecture''], p.155]</ref>


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 theory|information-theoretic]] formalizations of the theory of [[evolution]], and is a member of the Institute for Advanced Studies at [[Mohammed VI Polytechnic University]].
He was formerly a researcher at IBM's Thomas J. Watson Research Center in New York, where he wrote more than 10 books that have been translated into about 15 languages.  
 
Afterwards Chaitin became interested in questions of [[metabiology]] and [[information theory|information-theoretic]] formalizations of the theory of [[evolution]], and he was one of the founding members of the Institute for Advanced Studies at [[Mohammed VI Polytechnic University]] in Morocco.


==Other scholarly contributions==
==Other scholarly contributions==
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).
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 physics|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".<ref>{{cite arXiv|eprint = math/0303352|last1 = Chaitin|first1 = G. J.|title = From Philosophy to Program Size|year = 2003}}</ref> Chaitin proposes that mathematicians must abandon any hope of proving those mathematical facts and adopt a [[quasi-empirical]] methodology.
In recent writings, he defends a position known as [[digital physics|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".<ref>{{cite arXiv|eprint = math/0303352|last1 = Chaitin|first1 = G. J.|title = From Philosophy to Program Size|year = 2003 }}</ref> Chaitin proposes that mathematicians must abandon any hope of proving those mathematical facts and adopt a [[quasi-empirical]] methodology.


==Honors==
==Honors==
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 (Wolfram Research)|Leibniz Medal]]<ref>Zenil, Hector "Leibniz medallion comes to life after 300 years"
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 (Wolfram Research)|Leibniz Medal]]<ref>Zenil, Hector "Leibniz medallion comes to life after 300 years"
[http://www.mathrix.org/liquid/archives/the-history-of-the-chaitin-leibniz-medallion ''Anima Ex Machina'', The Blog of Hector Zenil], 3 November 2007.</ref> 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]].
[http://www.mathrix.org/liquid/archives/the-history-of-the-chaitin-leibniz-medallion ''Anima Ex Machina'', The Blog of Hector Zenil], 3 November 2007.</ref> by [[Wolfram Research]]; the medal was designed by [[Stephen Wolfram]] and [https://www.hectorzenil.com Hector Zenil], using [[Chaitin's constant | Chaitin’s number]] calculated by [[Cristian Calude]]. 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]].


==Bibliography==
==Bibliography==
*''Algorithmic Information Theory'' ([[Cambridge University Press]] 1987) ([https://web.archive.org/web/20111215170328/http://www.cs.auckland.ac.nz/~chaitin/cup.pdf online])
*''Information, Randomness & Incompleteness'' ([[World Scientific]] 1987) ([https://books.google.com/books?id=dDbE2lNiHjkC&dq=Chaitin+G.J.+%281975%29+Randomness+and+Mathematical+Proof.&pg=PA3 online])
*''Information, Randomness & Incompleteness'' ([[World Scientific]] 1987) ([https://books.google.com/books?id=dDbE2lNiHjkC&dq=Chaitin+G.J.+%281975%29+Randomness+and+Mathematical+Proof.&pg=PA3 online])
*''Algorithmic Information Theory'' ([[Cambridge University Press]] 1987) ([https://web.archive.org/web/20111215170328/http://www.cs.auckland.ac.nz/~chaitin/cup.pdf online])
*''Information-theoretic Incompleteness'' ([[World Scientific]] 1992) ([https://web.archive.org/web/20100514220011/http://www.cs.auckland.ac.nz/~chaitin/ps3.pdf online])
*''Information-theoretic Incompleteness'' ([[World Scientific]] 1992) ([https://web.archive.org/web/20100514220011/http://www.cs.auckland.ac.nz/~chaitin/ps3.pdf online])
*''The Limits of Mathematics'' ([[Springer-Verlag]] 1998) ([https://www.academia.edu/99397030/The_Limits_of_Mathematics_A_Course_on_Information_Theory_and_the_Limits_of_Formal_Reasoning_Springer_Verlag_1998_ online] {{Webarchive|url=https://web.archive.org/web/20230425213929/https://www.academia.edu/99397030/The_Limits_of_Mathematics_A_Course_on_Information_Theory_and_the_Limits_of_Formal_Reasoning_Springer_Verlag_1998_ |date=25 April 2023 }})
*''The Limits of Mathematics'' ([[Springer-Verlag]] 1998) ([https://www.academia.edu/99397030/The_Limits_of_Mathematics_A_Course_on_Information_Theory_and_the_Limits_of_Formal_Reasoning_Springer_Verlag_1998_ online] {{Webarchive|url=https://web.archive.org/web/20230425213929/https://www.academia.edu/99397030/The_Limits_of_Mathematics_A_Course_on_Information_Theory_and_the_Limits_of_Formal_Reasoning_Springer_Verlag_1998_ |date=25 April 2023 }})
*''The Unknowable'' ([[Springer-Verlag]] 1999) ([https://www.academia.edu/92235376/LISP_A_Formalism_for_Expressing_Mathematical_Algorithms_Springer_Verlag_1999_ online])
*''The Unknowable'' ([[Springer-Verlag]] 1999) ([https://www.academia.edu/92235376/LISP_A_Formalism_for_Expressing_Mathematical_Algorithms_Springer_Verlag_1999_ online])
*''Exploring Randomness'' ([[Springer-Verlag]] 2001) ([https://www.academia.edu/43381055/The_number_of_n_bit_strings_with_maximum_complexity_is_random_Springer_Verlag_2001_ online])
*''Exploring Randomness'' ([[Springer-Verlag]] 2001)
*''Conversations with a Mathematician'' ([[Springer-Verlag]] 2002) ([https://www.academia.edu/100602330/The_Creative_Life_Conversations_with_a_Mathematician_Springer_Verlag_2002_ online])
*''Conversations with a Mathematician'' ([[Springer-Verlag]] 2002) ([https://www.academia.edu/100602330/The_Creative_Life_Conversations_with_a_Mathematician_Springer_Verlag_2002_ online])
*''From Philosophy to Program Size'' ([http://ioc.ee/ Tallinn Cybernetics Institute] 2003)
*''From Philosophy to Program Size'' ([http://ioc.ee/ Tallinn Cybernetics Institute] 2003) ({{arXiv|math/0303352}})
*''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}})
*''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 complessità'' ([http://www.giappichelli.it/ G. Giappichelli Editore] 2006)
*''Thinking about Gödel & Turing'' ([[World Scientific]] 2007) ([https://www.academia.edu/100314710/Thinking_about_Gödel_and_Turing_Essays_on_Complexity_1970_2007_World_Scientific_2007_ online] {{Webarchive|url=https://web.archive.org/web/20230429215701/https://www.academia.edu/100314710/Thinking_about_G%C3%B6del_and_Turing_Essays_on_Complexity_1970_2007_World_Scientific_2007_ |date=29 April 2023 }})
*''Thinking about Gödel & Turing'' ([[World Scientific]] 2007) ([https://www.academia.edu/100314710/Thinking_about_Gödel_and_Turing_Essays_on_Complexity_1970_2007_World_Scientific_2007_ online] {{Webarchive|url=https://web.archive.org/web/20230429215701/https://www.academia.edu/100314710/Thinking_about_G%C3%B6del_and_Turing_Essays_on_Complexity_1970_2007_World_Scientific_2007_ |date=29 April 2023 }})
*''Mathematics, Complexity and Philosophy'' ([https://web.archive.org/web/20120425234032/http://www.editorialmidas.es/ Editorial Midas] 2011)
*''Gödel's Way'' ([[CRC Press]] 2012)
*''Proving Darwin: Making Biology Mathematical'' ([[Pantheon Books]] 2012) ([https://www.academia.edu/43376660/A_mathematical_theory_of_evolution_and_biological_creativity_CDMTCS_2011_ online])
*''Proving Darwin: Making Biology Mathematical'' ([[Pantheon Books]] 2012) ([https://www.academia.edu/43376660/A_mathematical_theory_of_evolution_and_biological_creativity_CDMTCS_2011_ online])
*''Philosophical Mathematics: Infinity, Incompleteness, Irreducibility'' ([[Academia.edu]] 2024)  ([https://www.academia.edu/122592748/PHILOSOPHICAL_COMPUTATIONS_Reflections_on_the_fiftieth_anniversary_of_the_halting_probability_2024_ online])
*''The Perfect Language'' (Jerusalem theology talk 2015)  ([https://inference-review.com/article/the-perfect-language online] [https://www.worldscientific.com/doi/abs/10.1142/9781786343161_0002 online])
*''A Life in Mathematics'' (autobiographical essay 2021)  ([https://researchspace.auckland.ac.nz/server/api/core/bitstreams/ffe3578c-8311-4dd1-b5e4-3ff26354f363/content online])
*''Infinity, Incompleteness, Irreducibility'' (course notes 2024)  ([https://www.academia.edu/144579067/Part_I_Course_Notes_Infinity_Incompleteness_Irreducibility online])


== References ==
== References ==
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==Further reading==
==Further reading==
* {{Citation |first=Ugo |last=Pagallo |title=Introduzione alla filosofia digitale. Da Leibniz a Chaitin |language=Italian |trans-title=Introduction to Digital Philosophy: From Leibniz to Chaitin |url=http://www.giappichelli.it/home/88-348-5635-X,3485635.asp1 |publisher=G. Giappichelli Editore |year=2005 |isbn=978-88-348-5635-2 |ref=none |access-date=16 April 2008 |archive-url=https://web.archive.org/web/20110722034613/http://www.giappichelli.it/home/88-348-5635-X,3485635.asp1 |archive-date=22 July 2011 }}
* {{Citation |first=Ugo |last=Pagallo |title=Introduzione alla filosofia digitale. Da Leibniz a Chaitin |language=Italian |trans-title=Introduction to Digital Philosophy: From Leibniz to Chaitin |url=http://www.giappichelli.it/home/88-348-5635-X,3485635.asp1 |publisher=G. Giappichelli Editore |year=2005 |isbn=978-88-348-5635-2 |ref=none |access-date=16 April 2008 |archive-url=https://web.archive.org/web/20110722034613/http://www.giappichelli.it/home/88-348-5635-X,3485635.asp1 |archive-date=22 July 2011 }}
* {{Citation |editor-first=Cristian S. |editor-last=Calude |title=Randomness and Complexity. From Leibniz to Chaitin |publisher=World Scientific |year=2007 |isbn=978-981-277-082-0 |ref=none}}
* {{Citation |editor-first=Cristian S. |editor-last=Calude |title=Randomness and Complexity. From Leibniz to Chaitin |publisher=World Scientific |year=2007 |isbn=978-981-277-082-0 |doi=10.1142/6577 |ref=none}}
* {{Citation |editor-first=Shyam |editor-last=Wuppuluri |editor2-first=Francisco A. |editor2-last=Doria|title=Unravelling Complexity: The Life and Work of Gregory Chaitin |publisher=World Scientific |year=2020 |isbn=978-981-12-0006-9 |doi=10.1142/11270 |s2cid=198790362 }}
* {{Citation |editor-first=Shyam |editor-last=Wuppuluri |editor2-first=Francisco A. |editor2-last=Doria|title=Unravelling Complexity: The Life and Work of Gregory Chaitin |publisher=World Scientific |year=2020 |isbn=978-981-12-0006-9 |doi=10.1142/11270 |s2cid=198790362 }}
* {{Citation |first=Dan |last=Gusfield |title=Proven Impossible: Elementary Proofs of Profound Impossibility from Arrow, Bell, Chaitin, Gödel, Turing and More |publisher=Cambridge University Press |year=2024 |isbn=978-1-009-34950-5 |doi=10.1017/9781009349451}}


==External links==
==External links==
{{wikiquote}}
{{wikiquote}}
*[https://ufrj.academia.edu/GregoryChaitin G J Chaitin Home Page from academia.edu]
 
*[https://rocky.github.io/gjchaitin.pdf Greg Chaitin, Computer Programmer]
*[https://researchspace.auckland.ac.nz/server/api/core/bitstreams/ffe3578c-8311-4dd1-b5e4-3ff26354f363/content G J Chaitin Autobiography]
*[https://independent.academia.edu/VirginiaChaitin G J Chaitin Home Page from academia.edu]
*[http://cs.umaine.edu/~chaitin/ G J Chaitin Home Page from UMaine.edu in the Internet Archive] {{Webarchive|url=https://web.archive.org/web/20131029184916/http://cs.umaine.edu/~chaitin/ |date=29 October 2013 }}
*[http://cs.umaine.edu/~chaitin/ G J Chaitin Home Page from UMaine.edu in the Internet Archive] {{Webarchive|url=https://web.archive.org/web/20131029184916/http://cs.umaine.edu/~chaitin/ |date=29 October 2013 }}
*[https://ufrj.academia.edu/GregoryChaitin List of publications of G J Chaitin]
*{{YouTube|RlYS_GiAnK8|Video of lecture on metabiology: "Life as evolving software"}} (a single mutating software organism)
*{{YouTube|RlYS_GiAnK8|Video of lecture on metabiology: "Life as evolving software"}}
*{{YouTube|W0YjaOmAjF8|Video of lecture on metabiology 2.0: "Von Neumann on biology and life as evolving software”}} (a gas of software organisms and mutagens)
*[http://videolectures.net/ephdcs08_chaitin_lcai/ Video of lecture on "Leibniz, complexity and incompleteness"]
*[http://videolectures.net/ephdcs08_chaitin_lcai/ Video of lecture on "Leibniz, complexity and incompleteness"]
*[https://web.archive.org/web/20060510171405/http://www.dc.uba.ar/people/profesores/becher/ns.html New Scientist article (March, 2001) on Chaitin, Omegas and Super-Omegas]
*[https://web.archive.org/web/20060510171405/http://www.dc.uba.ar/people/profesores/becher/ns.html New Scientist article (March, 2001) on Chaitin, Omegas and Super-Omegas]

Latest revision as of 18:45, 31 December 2025

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Gregory John Chaitin (Template:IPAc-en Script error: No such module "Respell".; 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.[1] 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.[2] 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.

Mathematics and computer science

Gregory Chaitin is Jewish. He attended the Bronx High School of Science and the 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]

In 1975 Chaitin 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, where he wrote more than 10 books that have been translated into about 15 languages.

Afterwards Chaitin became interested in questions of metabiology and information-theoretic formalizations of the theory of evolution, and he was one of the founding members of the Institute for Advanced Studies at Mohammed VI Polytechnic University in Morocco.

Other scholarly contributions

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

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; the medal was designed by Stephen Wolfram and Hector Zenil, using Chaitin’s number calculated by Cristian Calude. 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.

Bibliography

References

<templatestyles src="Reflist/styles.css" />

  1. ↑ Review of Meta Math!: The Quest for Omega, By Gregory Chaitin SIAM News, Volume 39, Number 1, January/February 2006
  2. ↑ Panu Raatikainen, "Exploring Randomness and The Unknowable" Notices of the American Mathematical Society Book Review October 2001.
  3. ↑ Script error: No such module "citation/CS1".
  4. ↑ R. Downey, and D. Hirschfeldt (2010), Algorithmic Randomness and Complexity, Springer-Verlag.
  5. ↑ Script error: No such module "citation/CS1".
  6. ↑ Script error: No such module "citation/CS1".
  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. ↑ Script error: No such module "citation/CS1".
  9. ↑ Zenil, Hector "Leibniz medallion comes to life after 300 years" Anima Ex Machina, The Blog of Hector Zenil, 3 November 2007.

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Further reading

  • Script error: No such module "citation/CS1".
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External links

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