# Gregory Chaitin

Gregory Chaitin | |
---|---|

Born |
Chicago ^{[1]} | November 15, 1947

Residence | United States |

Nationality | American |

Fields |
Biology Mathematics Computer science |

Institutions |
Federal University of Rio de Janeiro IBM Thomas J. Watson Research Center |

Known for |
Chaitin-Kolmogorov complexity Chaitin's constant Chaitin's algorithm |

Influences | Gottfried Wilhelm Leibniz |

**Gregory John Chaitin** (/ˈtʃaɪtᵻn/ * CHY-tən*; born 15 November 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. He is considered to be one of the founders of what is today known as Kolmogorov (or Kolmogorov-Chaitin) complexity together with Andrei Kolmogorov and Ray Solomonoff. Today, algorithmic information theory is a common subject in any computer science curriculum.

## Mathematics and computer science

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 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 followed after the work of Solomonoff, Kolmogorov, and Martin-Löf.

Chaitin is also the originator of using graph coloring to do register allocation in compiling, a process known as Chaitin's algorithm.^{[4]}

He was formerly a researcher at IBM's Thomas J. Watson Research Center in New York and remains an emeritus researcher. He has written more than 10 book titles 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.

## 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, they're true by accident. They are random mathematical facts".^{[5]} 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^{[6]} 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.

## Criticism

Some philosophers and logicians strongly disagree with the philosophical conclusions that Chaitin has drawn from his theorems.^{[7]}
The logician Torkel Franzén^{[8]} criticized Chaitin’s interpretation of Gödel's incompleteness theorem and the alleged explanation for it that Chaitin’s work represents.

## See also

## Bibliography

*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)

## Notes

- ↑ Gregory Chaitin (2007), Algorithmic information theory: "Chaitin Research Timeline" Archived 23 March 2012 at the Wayback Machine.
- ↑ 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 - ↑ 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] - ↑ "Professor Gregory John Chaitin". IT History Society. Retrieved 2016-07-12.
- ↑ Zenil, Hector "Leibniz medallion comes to life after 300 years"
*Anima Ex Machina*, The Blog of Hector Zenil, November 3rd, 2007. - ↑ 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

## References

- 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

## External links

- G J Chaitin Home Page
- 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"
- 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