Gregory Chaitin

Gregory Chaitin
Born	1947 (1947) Chicago[1]
Residence	United States
Nationality	American
Fields	Mathematics Computer science
Institutions	IBM Thomas J. Watson Research Center
Known for	Chaitin-Kolmogorov complexity Chaitin's constant Chaitin's algorithm

Gregory John Chaitin^{[pronunciation?]} (born 1947) is an Argentine-American mathematician and computer scientist.

Mathematics and computer science

Beginning in 2009 Chaitin has worked on metabiology, a field parallel to biology dealing with the random evolution of artificial software (computer programs) instead of natural software (DNA).

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. He attended the Bronx High School of Science and City College of New York, where he (still in his teens) developed the theories that led to his independent discovery of Kolmogorov complexity.^[2][3]

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.

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

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.

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. He is an emeritus researcher at IBM's Thomas J. Watson Research Center and also a visiting professor at the Computer Science Department of the University of Auckland, and on the international committee of the Valparaíso Complex Systems Institute.

Criticism

Some philosophers and logicians strongly disagree with the philosophical conclusions that Chaitin has drawn from his theorems.^[4] The logician Torkel Franzén ^[5] criticizes Chaitin’s interpretation of Gödel's incompleteness theorem and the alleged explanation for it that Chaitin’s work represents.

See also

• Digital philosophy
• Halting problem

Bibliography

• Information, Randomness & Incompleteness (World Scientific 1975) [1]
• 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 Metamaths: The Quest for Omega, Atlantic Books 2006),
• Teoria algoritmica della complessità (G. Giappichelli Editore 2006),
• Thinking about Gödel & Turing (World Scientific 2007),
• Gödel's Way (CRC Press 2012),
• Proving Darwin: Making Biology Mathematical (Pantheon Books 2012 (upcoming)).

Notes

1. ^ Gregory Chaitin (2007), Algorithmic information theory: "Chaitin Research Timeline"
2. ^ Li and Vitanyi, An Introduction to Kolmogorov Complexity and Its Applications, Springer 1997, page 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 [...]"
3. ^ Chaitin, GJ, On the Length of Programs for Computing Finite Binary Sequences, Journal of the ACM (JACM), 13:4, October 1966, 547-569.
4. ^ Panu Raatikainen "Exploring Randomness and The Unknowable" Notices of the American Mathematical Society Book Review October 2001
5. ^ Torkel Franzén Gödel's Theorem: An Incomplete Guide to its Use and Abuse. Wellesley, Massachusetts: A K Peters, Ltd., 2005. x + 172 pp. ISBN 1-56881-238-8.

References

• Ugo Pagallo, Introduzione alla filosofia digitale. Da Leibniz a Chaitin, (G. Giappichelli Editore, 2005) ISBN 88-348-5635-X
• Cristian S. Calude (ed.), Randomness and Complexity. From Leibniz to Chaitin, (World Scientific, 2007) ISBN 13 978-981-277-082-0

External links

• G J Chaitin Home Page
• List of publications of G J Chaitin
• Video of lecture on metabiology: "Life as evolving software"
• 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

Persondata
Name	Chaitin, Gregory
Alternative names
Short description	Argentinian mathematician and computer scientist
Date of birth	15 November 1947
Place of birth	Argentina
Date of death
Place of death