Introduction of the Aristotle's final causation in CAST concept and method of incursion and hyperincursion

  • Daniel M. Dubois
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1030)

Abstract

This paper will analyse the concept and method of incursion and hyperincursion firstly applied to the Fractal Machine, an hyperincursive cellular automata with sequential computations where time plays a central role. This computation is incursive, for inclusive recursion, in the sense that an automaton is computed at the future time t+1 in function of its neighbour automata at the present and/or past time steps but also at the future time t+1. The hyperincursion is an incursion when several values can be generated at each time step. The incursive systems may be transformed to recursive ones. But the incursive inputs, defined at the future time step, cannot always be transformed to recursive inputs. This is possible by self-reference. A self-reference Fractal Machine gives rise to A non deterministic hyperincursive field rises in a self-reference Fractal Machine. This can be related to the Final Cause of Aristotle. Simulations will show the generation of fractal patterns from incursive equations with interference effects like holography. The incursion is also a tool to control systems. The Pearl-Verhulst chaotic map will be considered. Incursive stabilisation of the numerical instabilities of discrete linear and non-linear oscillators based on Lotka-Volterra equation systems will be simulated. Finally the incursive discrete diffusion equation is considered.

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References

  1. 1.
    D. M. Dubois: Total Incursive Control of Linear, Non-linear and Chaotic systems. in G. Lasker (ed.): Advances in Computer Cybernetics. Int. Inst. for Advanced Studies in Syst. Res. and Cybernetics, vol. II, 167–171 (1995)Google Scholar
  2. 2.
    D. M. Dubois: ContrÔle-commande incursif d'un système chaotique. Bull. de l'A.I.LG, nℴ6–7, 11–12 (1994)Google Scholar
  3. 3.
    D. M. Dubois: Hyperincursivity: inclusive recursivity without time arrow. Proceedings of the 13th International Congress on Cybernetics, Namur, 152–156 (1992)Google Scholar
  4. 4.
    D. M. Dubois: The fractal machine: the wholeness of the memory chaos. Proceedings of the 13th International Congress on Cybernetics, Namur, 147–151 (1992)Google Scholar
  5. 5.
    D. M. Dubois: The Fractal Machine. Presses Universitaires de Liège 1992Google Scholar
  6. 6.
    D. M. Dubois: The hyperincursive fractal machine as a quantum holographic brain. Communication & Cognition-Artificial Intelligence 9-4, 335–372 (1992)Google Scholar
  7. 7.
    D. M. Dubois (editor): Designing new Intelligent Machines (COMETT European Symposium, Liège April 1992). Communication & Cognition-Artificial Intelligence, 9–4 (1992), sequel 10-1-2 (1993)Google Scholar
  8. 8.
    D. M. Dubois: Mathematical fundamentals of the fractal theory of artificial intelligence. Invited paper in New Mathematical tools in artificial intelligence. Communication & Cognition — Artificial Intelligence, 8-1, 5–48 (1991)Google Scholar
  9. 9.
    D. M. Dubois: Fractal Algorithms for holographic Memory of inversible neural Networks. Invited paper in Issues in Connectionism: part II. Communication & Cognition Artificial Intelligence, 8-2, 137–189 (1991)Google Scholar
  10. 10.
    D. M. Dubois: Self-Organisation of fractal objects in XOR rule-based multilayer Networks. In EC2 (ed.): Neural Networks & their Applications, Neuro-NÎmes 90, Proceedings of the third International Workshop, 555–557 (1990)Google Scholar
  11. 11.
    D. M. Dubois: Le Labyrinthe de L'intelligence: de l'intelligence naturelle à l'intelligence fractale. Academia (Louvain-la-Neuve) 1990, 321 p., 2ème édition, InterEditions (Paris)/Academia 1990, 331 p, 2ème tirage, 1991Google Scholar
  12. 12.
    D. M. Dubois: Un modèle fractal des systèmes intelligents. In AFCET France (ed.): Actes du 1er Congrès Européen de Systémique, Tome II, 665–674, 1989Google Scholar
  13. 13.
    D. M. Dubois, G. Resconi: Hyperincursivity: a new mathematical theory. Presses Universitaires de Liège 1992Google Scholar
  14. 14.
    D. M. Dubois, G. Resconi: Advanced Research in Incursion Theory applied to Ecology, Physics and Engineering. COMETT European Lecture Notes in Incursion. Edited by A.I.Lg., Association des Ingénieurs de l'Université de Liège, D/1995/3603/01, 1995Google Scholar
  15. 15.
    D. M. Dubois, G. Resconi: Hyperincursive Fractal Machine beyond the Turing Machine. In Lasker (ed.): Advances in Cognitive Engineering and Knowledge-based Systems. Int. Inst. for Adv. Studies in Syst. Res. and Cybernetics, 212–216 (1994)Google Scholar
  16. 16.
    D. M. Dubois, G. Resconi: Introduction to hyperincursion with applications to computer science, quantum mechanics and fractal processes. Communication & Cognition — Artificial Intelligence, vol. 10, Nℴ1–2, 109–148 (1993)Google Scholar
  17. 17.
    D. M. Dubois, G. Resconi: Holistic Control by Incursion of Feedback Systems, Fractal Chaos and Numerical Instabilities. In R. Trappl (ed.): Cybernetics and Systems'94. World Scientific, 71–78 (1994)Google Scholar
  18. 18.
    A. J. Lotka: Elements of Physical Biology. William and Wilkins, Baltimore 1925Google Scholar
  19. 19.
    B. Mandelbrot: The Fractal Geometry of Nature. Freeman, San Francisco 1983Google Scholar
  20. 20.
    R. M. May: Simple mathematical models with very complicated dynamics. Nature 261, 459–467 (1976)Google Scholar
  21. 21.
    R. Pearl: Studies in human biology. William and Wilkins, Baltimore 1924Google Scholar
  22. 22.
    R. Rosen: Causal Structures in Brains and Machines, Int. J. Gen. Syst. 12, 107–126 (1986)Google Scholar
  23. 23.
    A. Rosenblueth, N. Wiener, J. Bigelow: Behavior, purpose and teleology. Philosophy of Science, 10, 18–24 (1943)Google Scholar
  24. 24.
    F. Scheid: Theory and Problems of Numerical Analysis. McGraw-Hill Inc. 1986Google Scholar
  25. 25.
    F. Varela: Autonomie et connaissance. Seuil 1989Google Scholar
  26. 26.
    P. F. Verhulst: Nuov. Mem. Acad. Royale, Bruxelles, 18, 1, 1845 & 20, 1, 1847Google Scholar
  27. 27.
    V. Volterra: LeÇon sur la théorie mathématique de la lutte pour la vie Gauthier-Villars 1931Google Scholar
  28. 28.
    E. von Glasersfeld: Teleology and the Concepts of Causation. In: G. Van de Vijver (ed.): Sel-organizing and Complex Systems. Philosophica 1990, 46, pp. 17–43Google Scholar
  29. 29.
    S. Wolfram (ed.): Theory and Application of Cellular Automata. World Scientific, Singapore/Teanek, N. Y. 1986Google Scholar
  30. 30.
    K. Zuse: The Computing Universe. International Journal of Theoretical Physics 21, 6/7, 589–600 (1982)Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Daniel M. Dubois
    • 1
  1. 1.Institut de MathématiqueUniversité de LiègeLiègeBelgium

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