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Algorithmics and the Limits of Complexity

  • Daniel Parrochia (a1)
Abstract
The Argument

Dagognet's work shows that making algorithmic compressions seems to be one of the major targets of scientific progress. This effort has been so successful that until recently one might have thought everything could be algorithmically compressed. Indeed, this statement, which might be seen as a scientific translation of the Hegelian thesis in its strong form (“the real is rational and the rational is real”), admits to some objective limits in computer science. Though a lot of algorithms are successful, there exist today, and perhaps forever, logical and physical limits that cannot allow us to cherish the dream of a “theory of everything.” Moreover, a complete mastery of complexity does not seem possible — because some domains of reality are too complicated to be computable, because the human brain is too limited, because computers cannot do that much better than the human brain, and because, ultimately, there are some kinds of things it would make no sense to compress. This paper shows that Dagognet's work came to recognize what a glance at the history of algorithmics has made evident.

The Argument

Dagognet's work shows that making algorithmic compressions seems to be one of the major targets of scientific progress. This effort has been so successful that until recently one might have thought everything could be algorithmically compressed. Indeed, this statement, which might be seen as a scientific translation of the Hegelian thesis in its strong form (“the real is rational and the rational is real”), admits to some objective limits in computer science. Though a lot of algorithms are successful, there exist today, and perhaps forever, logical and physical limits that cannot allow us to cherish the dream of a “theory of everything.” Moreover, a complete mastery of complexity does not seem possible — because some domains of reality are too complicated to be computable, because the human brain is too limited, because computers cannot do that much better than the human brain, and because, ultimately, there are some kinds of things it would make no sense to compress. This paper shows that Dagognet's work came to recognize what a glance at the history of algorithmics has made evident.

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C. A. Bennett 1982. “The Thermodyamics of Computation — A Review”. International Journal of Theoretical Physics 21 (12) (December): 905–40.

A. Benvéniste , M. Métivier , and P. Priouret . 1990. Adaptative Algorithms and Stochastic Approximations. Berlin: Springer Verlag.

Barry W. Boehm , and Giuseppe Jacopini Corrado . 1966. “Flow Diagrams, Turing Machines and Languaes with only Two Formation Rules.” Communication of the the ACM 9: 366–71.

Edsger W. Dijkstra , and V. Wikes Maurice . 1968. “GOTO Statement Considered Harmful.” Communication of the ACM (Association for Computing Machinery) 11 (3) (March): 147158.

J. Edmonds 1965. “Paths, Trees, and Flowers.” Canadian Journal of Mathematics 17: 449–67.

E. Fredkin , and T. Toffoli 1982. “Conservative Logic.” International Journal of Theoretical Physics 21 (3–4) (04): 219–53.

C. A. R. Hoare 1969. “An Axiomatic Basis for Computer Programming.” Communication of the ACM 12 (10) (10, 03): 576–82.

R. Z. Khas'minskii 1966. “On Stochastic Processes Defined by Differential Equations with a Smaller Parameter.” Theory of Probability and Its Applications 11 (2): 211–28.

H. J. Kushner , H. Huang 1979. “Rates of convergence for Stochastic Approximation Type of Algorithms.” SIAM Journal Control and Opt. 17 (1): 607–17.

R. Landauer 1985. “Fundamental Physical Limitations of the Computational Process.” Annals of the New York Academy of Science 426: 161–70.

H. Robbins and S. Monro 1951. “A Stochastic Approximation Method.” Ann Math Stat. 22: 400407.

Maurice V. Wilkes 1968. “The Outer and Inner Syntax of a Programming Language.” The Computer Journal (March).

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Science in Context
  • ISSN: 0269-8897
  • EISSN: 1474-0664
  • URL: /core/journals/science-in-context
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