|Institutions||Federal University of Rio de Janeiro
IBM Thomas J. Watson Research Center
|Known for||Chaitin-Kolmogorov complexity
|Influences||Gottfried Wilhelm Leibniz|
Gregory John Chaitin (pronounced "CHAY tin")[pronunciation?] (born 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 new incompleteness theorem in reaction to Gödel's incompleteness theorem.
Mathematics and computer science
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 but not computable.
Chaitin's early work on algorithmic information theory paralleled the earlier work of Kolmogorov.
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).
Indeed, 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, they're true by accident. They are random mathematical facts". Chaitin proposes that mathematicians must abandon any hope of proving those mathematical facts and adopt a quasi-empirical methodology.
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 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 is now a professor at the Federal University of Rio de Janeiro.
Some philosophers and logicians[who?] strongly disagree with the philosophical conclusions that Chaitin has drawn from his theorems. The logician Torkel Franzén criticized Chaitin’s interpretation of Gödel's incompleteness theorem and the alleged explanation for it that Chaitin’s work represents.
- Information, Randomness & 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)
- The Unknowable (Springer-Verlag 1999)
- Exploring Randomness (Springer-Verlag 2001)
- Conversations with a Mathematician (Springer-Verlag 2002)
- 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 preprint)
- Teoria algoritmica della complessità (G. Giappichelli Editore 2006)
- Thinking about Gödel & Turing (World Scientific 2007)
- Mathematics, Complexity and Philosophy (Editorial Midas 2011)
- Gödel's Way (CRC Press 2012)
- Proving Darwin: Making Biology Mathematical (Pantheon Books 2012)
- Gregory Chaitin (2007), Algorithmic information theory: "Chaitin Research Timeline"[dead link]
- Li; Vitanyi (1997), An Introduction to Kolmogorov Complexity and Its Applications, Springer, p. 92, "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
- Panu Raatikainen, "Exploring Randomness and The Unknowable" Notices of the American Mathematical Society Book Review October 2001.
- Franzén, Torkel (2005), Gödel's Theorem: An Incomplete Guide to its Use and Abuse, Wellesley, Massachusetts: A K Peters, Ltd., ISBN 1-56881-238-8
- Pagallo, Ugo (2005), Introduzione alla filosofia digitale. Da Leibniz a Chaitin [Introduction to Digital Philosophy: From Leibniz to Chaitin] (in Italian), G. Giappichelli Editore, ISBN 88-348-5635-X
- Calude, Cristian S., ed. (2007), Randomness and Complexity. From Leibniz to Chaitin, World Scientific, ISBN 978-981-277-082-0
- G J Chaitin Home Page
- List of publications of G J Chaitin
- Video of lecture on metabiology: "Life as evolving software"
- Video of lecture on "Leibniz, complexity and incompleteness"
- Works by or about Gregory Chaitin in libraries (WorldCat catalog)
- New Scientist article (March, 2001) on Chaitin, Omegas and Super-Omegas
- A short version of Chaitin's proof