Gregory Chaitin

{{short description|Argentine-American mathematician}} {{Use dmy dates|date=September 2020}} {{Infobox scientist | name = Gregory Chaitin | image = Gregory Chaitin hiking.jpg | caption = Chaitin in 2008 | birth_date = {{birth date and age |df=yes|1947|6|25}} | birth_place = Chicago<ref>[https://arxiv.org/pdf/math/0701164 Gregory Chaitin (2007), Algorithmic information theory: "Chaitin Research Timeline"]</ref> | death_date = | death_place = | fields = {{ubl|Biology|Mathematics|Computer science}} | workplaces = {{Plainlist| * Mohammed VI Polytechnic University * Federal University of Rio de Janeiro * University of Buenos Aires * IBM T.J. Watson Research Center }} | alma_mater =  | doctoral_advisor =  | academic_advisors =  | doctoral_students = | notable_students = | known_for = {{ubl|Algorithmic information theory|Chaitin's constant|Chaitin's algorithm}} | influences = | influenced = | awards = | website = | religion = | signature =  | footnotes = }}

'''Gregory John Chaitin''' ({{IPAc-en|ˈ|tʃ|aɪ|t|ɪ|n}} {{respell|CHY|tin}}; born 25 June 1947)  is an Argentine-American mathematician and computer scientist. His work was foundational to the development of algorithmic information theory, and has been influential on metamathematics.<ref>{{cite book|title=Information and Randomness: An Algorithmic Perspective|last=Calude|first=C.S.|publisher=Springer-Verlag|year=2002|series=Texts in Theoretical Computer Science. An EATCS Series}}</ref><ref>R. Downey, and D. Hirschfeldt (2010), ''Algorithmic Randomness and Complexity'', Springer-Verlag.</ref> He independently discovered what is today known as algorithmic (Kolmogorov or Solomonoff–Kolmogorov–Chaitin) complexity simultaneously with Andrei Kolmogorov and Ray Solomonoff.<ref>Panu Raatikainen, "Exploring Randomness and The Unknowable" [https://www.ams.org/notices/200109/rev-panu.pdf ''Notices'' of the American Mathematical Society] Book Review October 2001.</ref>

==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.<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>

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.<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, 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".<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== 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<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; 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== *''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-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 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) *''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) ({{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}}) *''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 }}) *''Proving Darwin: Making Biology Mathematical'' (Pantheon Books 2012) ([https://www.academia.edu/43376660/A_mathematical_theory_of_evolution_and_biological_creativity_CDMTCS_2011_ 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 == {{Reflist}}

==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 |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 |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== {{wikiquote}}

*[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 }} *{{YouTube|RlYS_GiAnK8|Video of lecture on metabiology: "Life as evolving software"}} (a single mutating software organism) *{{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"] *[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] *[http://www.flownet.com/gat/chaitin.html A short version of Chaitin's proof] *[https://www.whyarewehere.tv/people/gregory-chaitin/ Gregory Chaitin extended film interview and transcripts for the 'Why Are We Here?' documentary series] *[https://github.com/mew-cx/chaitin_lisp Chaitin Lisp on github]

{{DEFAULTSORT:Chaitin, Gregory}} Category:1947 births Category:Living people Category:The Bronx High School of Science alumni Category:City College of New York alumni Category:Argentine mathematicians Category:Argentine computer scientists Category:20th-century American mathematicians Category:21st-century American mathematicians Category:American information theorists Category:IBM employees Category:Philosophers of mathematics Category:Epistemologists Category:Metaphysics writers Category:American logicians Category:21st-century American philosophers Category:Argentine information theorists Category:Mathematicians from New York (state)