Argentine-American mathematician
Gregory John Chaitin
(
CHY
-tin
; 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
Godel's incompleteness theorem
.
[2]
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
. Along with the works of e.g.
Solomonoff
,
Kolmogorov
,
Martin-Lof
, 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
[
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]
Gregory Chaitin is
Jewish
and 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
algorithmic complexity
.
[5]
[6]
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
, 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. 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-theoretic
formalizations of the theory of
evolution
, and is a member of the Institute for Advanced Studies at
Mohammed VI Polytechnic University
.
Other scholarly contributions
[
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]
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
[
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]
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
. In 2009 he was given the degree of doctor of philosophy
honoris causa
by the
National University of Cordoba
. He was formerly a researcher at
IBM
's
Thomas J. Watson Research Center
and a professor at the
Federal University of Rio de Janeiro
.
Criticism
[
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]
Some philosophers and logicians disagree with the philosophical conclusions that Chaitin has drawn from his theorems related to what Chaitin thinks is a kind of fundamental arithmetic randomness.
[10]
The logician
Torkel Franzen
criticized Chaitin's interpretation of
Godel's incompleteness theorem
and the alleged explanation for it that Chaitin's work represents.
[11]
Bibliography
[
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]
References
[
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]
- ^
Gregory Chaitin (2007), Algorithmic information theory: "Chaitin Research Timeline"
Archived
23 March 2012 at the
Wayback Machine
- ^
Review of Meta Math!: The Quest for Omega, By Gregory Chaitin
SIAM News, Volume 39, Number 1, January/February 2006
- ^
Calude, C.S. (2002).
Information and Randomness: An Algorithmic Perspective
. Texts in Theoretical Computer Science. An EATCS Series. Springer-Verlag.
- ^
R. Downey, and D. Hirschfeldt (2010),
Algorithmic Randomness and Complexity
, Springer-Verlag.
- ^
Li; Vitanyi (1997),
An Introduction to Kolmogorov Complexity and Its Applications
, Springer, p. 92,
ISBN
9780387948683
,
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
,
S2CID
207698337
- ^
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]
- ^
Chaitin, G. J. (2003). "From Philosophy to Program Size".
arXiv
:
math/0303352
.
- ^
Zenil, Hector "Leibniz medallion comes to life after 300 years"
Anima Ex Machina
, The Blog of Hector Zenil
, 3 November 2007.
- ^
Panu Raatikainen, "Exploring Randomness and The Unknowable"
Notices
of the American Mathematical Society
Book Review October 2001.
- ^
Franzen, Torkel
(2005),
Godel's Theorem: An Incomplete Guide to its Use and Abuse
, Wellesley, Massachusetts:
A K Peters, Ltd.
,
ISBN
978-1-56881-238-0
Further reading
[
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]
- 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
978-88-348-5635-2
, archived from
the original
on 22 July 2011
, retrieved
16 April
2008
- Calude, Cristian S., ed. (2007),
Randomness and Complexity. From Leibniz to Chaitin
, World Scientific,
ISBN
978-981-277-082-0
- Wuppuluri, Shyam; Doria, Francisco A., eds. (2020),
Unravelling Complexity: The Life and Work of Gregory Chaitin
, World Scientific,
doi
:
10.1142/11270
,
ISBN
978-981-12-0006-9
,
S2CID
198790362
External links
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