A Propositional Lattice for the Logic of Temporal Predictions

  • H. Atmanspacher
Conference paper
Part of the Research Reports in Physics book series (RESREPORTS)

Abstract

The concept of chaos, apart from its significance with respect to the modelling of specific complex systems and the prediction of their behavior, bears important implications for our general understanding of nature and the natural sciences. One of the central quantities characterizing chaotic systems is the dynamical entropy K. It can be interpreted as a temporal rate of internal information production of a system due to the specific dynamical laws governing its evolution. These laws can be formalized in different ways, using different types of operators acting on a phase space distribution function. Two respective operator formalisms refer to the Liouville operator L and to an information (or entropy) operator M. Both are incommensurable in the sense of a non-vanishing commutator given by K (Sec.2).

Keywords

Entropy Soliton Posite Tempo Exter 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    I. Prigogine, Non - Equilibrium Statistical Mechanics ( Interscience, New York, 1962 ).MATHGoogle Scholar
  2. 2.
    I. Prigogine, From Being to Becoming, 2nd ed. (Freeman= San Francisco, 1980 ).Google Scholar
  3. 3.
    R. Shaw, Z. Naturforsch. 36a, 80 (1981).MATHADSMathSciNetGoogle Scholar
  4. 4.
    J.D. Farmer, Z. Naturforsch. 37a, 1304 (1982).ADSMathSciNetGoogle Scholar
  5. 5.
    H. Atmanspacher and H. Scheingraber, Found. Phys. 17, 939 (1987).CrossRefADSMathSciNetGoogle Scholar
  6. 6.
    A.M. Fraser, Ph.D. Thesis, University of Texas at Austin 1988.Google Scholar
  7. 7.
    H. Atmanspacher, in Parallelism, Learning, Evolution,eds. J. Becker, F. Mündemann, and I.Eisele (Springer, Berlin, 1991) in press.Google Scholar
  8. 8.
    P. Grassberger and I. Procaccia, Phys. Rev. Lett. 50, 346 (1983).CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    H. Atmanspacher and H. Scheingraber, Phys. Rev. A 34, 253 (1986).ADSGoogle Scholar
  10. 10.
    S. Goldstein, Israel J. Math. 38, 241 (1981).CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    A.N. Kolmogorov, Dokl. Akad. Nauk. SSSR 119, 861 (1958).MATHMathSciNetGoogle Scholar
  12. 12.
    Y. Sinai, Dokl. Akad. Nauk. SSSR 124, 768 (1959).Google Scholar
  13. 13.
    J.B. Pesin, Russ. Math. Survey 32, 455 (1977).Google Scholar
  14. 14.
    C.F. v. Weizsäcker, Aufbau der Physik (Hanser, München, 1985) Sec.5.Google Scholar
  15. 15.
    H. Atmanspacher, Found. Phys. 19, 553 (1989).CrossRefADSGoogle Scholar
  16. 16.
    B. Misra, Proc. Ntl. Acad. Sci. USA 75, 1627 (1978).CrossRefADSGoogle Scholar
  17. 17.
    B. Misra, I. Prigogine, and M. Courbage, Physica 98A, 1 (1979).Google Scholar
  18. 18.
    Y. Elskens and I. Prigogine, Proc. Ntl. Acad. Sci. USA 83, 5756 (1986).CrossRefMATHADSMathSciNetGoogle Scholar
  19. 19.
    N.G. Krylov, Works on the Foundations of Statistical Physics (Princeton University Press, Princeton, 1979 ).Google Scholar
  20. 20.
    J.M. Jauch, Foundations of Quantum Mechanics (Addison Wesley, Reading, 1968).MATHGoogle Scholar
  21. 21.
    G. Birkhoff and J. von Neumann, Ann. Math. 37, 823 (1936).CrossRefGoogle Scholar
  22. 22.
    R. Balian, Y. Alhassid, and H. Reinhardt, Phys. Rep. 131, 1 (1986).CrossRefADSMathSciNetGoogle Scholar
  23. 23.
    Y. Elkana, in Sciences and Cultures. Sociology of the Sciences, Vol.5, E. Mendelsohn and Y. Elkana, eds. ( Reidel, Dordrecht, 1981 ) pp. 1–76.Google Scholar
  24. 24.
    H. Putnam, Reason, Truth, and History (Cambridge University Press, Cambridge, 1981 ).Google Scholar
  25. 25.
    J. Margolis, Pragmatism Without Foundations ( Blackwell, Oxford, 1986 ).Google Scholar
  26. 26.
    P. Feyerabend, Against Method (New Left Books, 1975 ).Google Scholar
  27. 27.
    T. Kuhn, The Structure of Scientific Revolutions (Univ. Chicago Press, Chicago, 1962 ).Google Scholar
  28. 28.
    H. Atmanspacher, F.R. Krueger, and H. Scheingraber, in Parallelism, Learning, Evolution,eds. J. Becker, F. Mündemann, and I. Eisele (Springer, Berlin, 1991) in press.Google Scholar
  29. 29.
    H. Atmanspacher, in Information Dynamics,eds. H. Atmanspacher and H. Scheingraber (Plenum Press, New York, 1991) in press. For a concrete empirical consequence concerning cosmological redshifts we refer to H. Atmanspacher and H. Scheingraber, “An internal observer’s view of moving objects in a closed universe”, preprint 1991.Google Scholar
  30. 30.
    G. Birkhoff, Lattice Theory, 3rd ed. (AMS Coll. Publ., Vol. 25, Providence, 1979 ).Google Scholar
  31. 31.
    M. Jammer, The Philosophy of Quantum Mechanics ( Wiley & Sons, New York, 1974 ).Google Scholar
  32. 32.
    H. Primas, Chemistry, Quantum Mechanics, and Reductionism (Springer, Berlin, 1983 ).CrossRefGoogle Scholar
  33. 33.
    D. Finkelstein, in The Universal Turing Machine - A Half Century Survey, ed. R. Herken ( Oxford University Press, Oxford, 1988 ).Google Scholar
  34. 34.
    J.A. Wheeler, in Some Strangeness in the Proportion, ed. H. Woolf ( Addison Wesley, Reading, 1980 ).Google Scholar
  35. 35.
    See P.A.M. Dirac, Proc. Roy. Soc. (London) A180, 1 (1942).CrossRefGoogle Scholar
  36. 36.
    D. Finkelstein and J. Hallidy, “An algebraic language for quantum space-time topology”, preprint 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • H. Atmanspacher
    • 1
  1. 1.Max Planck Institut für Extraterrestrische PhysikGarchingGermany

Personalised recommendations