Advertisement

Real Numbers, Chaos, and the Principle of a Bounded Density of Information

  • Gilles Dowek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7913)

Abstract

Two definitions of the notion of a chaotic transformation are compared: sensitivity to initial conditions and sensitivity to perturbations. Only the later is compatible with the idea that information has a finite density.

Keywords

Rational Number Decimal Digit Bounded Density Newtonian Theory Macroscopic State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arrighi, P., Dowek, G.: The principle of a finite density of information. In: Zenil, H. (ed.) Irreducibility and Computational Equivalence: Wolfram Science 10 Years After the Publication of A New Kind of Science (2012)Google Scholar
  2. 2.
    Bekenstein, J.D.: Universal upper bound to entropy-to-energy ratio for bounded systems. Phys. Rev. D 23, 287–298 (1981)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Berthoz, A., Simplexité, L., Jacob, O. (2009)Google Scholar
  4. 4.
    Dowek, G.: La notion de nombre réel : une solution simplexe? (to appear)Google Scholar
  5. 5.
    Gandy, R.: Church’s thesis and principles for mechanisms. In: The Kleene Symposium. North-Holland (1980)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Gilles Dowek
    • 1
  1. 1.INRIAParis Cedex 13France

Personalised recommendations