A Behavioural Foundation for Natural Computing and a Programmability Test

Part of the Studies in Applied Philosophy, Epistemology and Rational Ethics book series (SAPERE, volume 7)

Abstract

What does it mean to claim that a physical or natural system computes? One answer, endorsed here, is that computing is about programming a system to behave in different ways. This paper offers an account of what it means for a physical system to compute based on this notion. It proposes a behavioural characterisation of computing in terms of a measure of programmability, which reflects a system’s ability to react to external stimuli. The proposed measure of programmability is useful for classifying computers in terms of the apparent algorithmic complexity of their evolution in time. I make some specific proposals in this connection and discuss this approach in the context of other behavioural approaches, notably Turing’s test of machine intelligence. I also anticipate possible objections and consider the applicability of these proposals to the task of relating abstract computation to nature-like computation.

Keywords

Turing test computing nature-like computation dynamic behaviour algorithmic information theory computationalism 

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References

  1. 1.
    Ausländer, S., Ausländer, D., Müller, M., Wieland, M., Fussenegger, M.: Programmable single-cell mammalian biocomputers. Nature (2012)Google Scholar
  2. 2.
    Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for your Mathematical Plays. AK Peters Ltd. (2001)Google Scholar
  3. 3.
    Blanco, J.: Interdisciplinary Workshop with Javier Blanco: Ontological, Epistemological and Methodological Aspects of Computer Science. University of Stuttgart, Germany (July 7, 2011)Google Scholar
  4. 4.
    Chaitin, G.J.: On the length of programs for computing finite binary sequences: Statistical considerations. Journal of the ACM 16(1), 145–159 (1969)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Chalmers, D.J.: Does a Rock Implement Every Finite-State Automaton? Synthese 108, 310–333 (1996)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Cook, M.: Universality in Elementary Cellular Automata. Complex Systems 15, 1–40 (2004)MathSciNetMATHGoogle Scholar
  7. 7.
    Conrad, M.: The Price of Programmability. In: Herken, R. (ed.) The Universal Turing Machine, A Half-Century Survey. Springer (1994)Google Scholar
  8. 8.
    Berlekamp, E., Conway, K., Guy, R.: Winning Ways for your Mathematical Plays, vol. 2. Academic Press (1982)Google Scholar
  9. 9.
    Cronin, L., Krasnogor, N., Davis, B.G., Alexander, C., Robertson, N., Steinke, J.H.G., Schroeder, S.L.M., Khlobystov, A.N., Cooper, G., Gardner, P.M., Siepmann, P., Whitaker, B.J., Marsh, D.: The imitation game—a computational chemical approach to recognizing life. Nature Biotechnology 24(10) (2006)Google Scholar
  10. 10.
    Davis, M.: Universality is Ubiquitous, Invited Lecture. In: History and Philosophy of Computing (HAPOC 2011), Ghent, November 8 (2011)Google Scholar
  11. 11.
    Dennett, D.C.: Brainstorms: Philosophical Essays on Mind and Psychology. MIT Press (1981)Google Scholar
  12. 12.
    Delahaye, J.-P., Zenil, H.: Numerical Evaluation of the Complexity of Short Strings: A Glance Into the Innermost Structure of Algorithmic Randomness. Applied Math. and Comp. 219, 63–77 (2012)CrossRefGoogle Scholar
  13. 13.
    Dresner, E.: Measurement-theoretic representation and computation-theoretic realisation. The Journal of Philosophy cvii(6) (2010)Google Scholar
  14. 14.
    Fodor, J.: The Language of Thought. Harvard University Press (1975)Google Scholar
  15. 15.
    Fredkin: Finite Nature. In: Proceedings of the XXVIIth Rencotre de Moriond (1992)Google Scholar
  16. 16.
    Harnad, S.: The Symbol Grounding Problem. Physica D 42, 335–346 (1990)CrossRefGoogle Scholar
  17. 17.
    Hodgkin, A., Huxley, A.: A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology 117, 500–544 (1952)Google Scholar
  18. 18.
    Kolmogorov, A.N.: Three approaches to the quantitative definition of information. Problems of Information and Transmission 1(1), 1–7 (1965)MathSciNetGoogle Scholar
  19. 19.
    Langton, C.G.: Studying artificial life with cellular automata. Physica D: Nonlinear Phenomena 22(1-3), 120–149 (1986)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Lloyd, S.: Computational capacity of the Universe. Physical Review Letters 88, 237901 (2002)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Li, M., Vitányi, P.: An Introduction to Kolmogorov Complexity and Its Applications, 3rd edn. Springer (2008)Google Scholar
  22. 22.
    McCullock, W., Pitts, W.: A Logical Calculus of Ideas Immanent in Nervous Activity. Bulletin of Mathematical Biophysics 5(4), 115–133 (1943)CrossRefGoogle Scholar
  23. 23.
    Minsky, M.: Computation: Finite and Infinite Machines. Prentice Hall (1967)Google Scholar
  24. 24.
    Parsons, W.T.: Patterns in the Noise: Physics as the Ultimate Environmental Science. FQXi’s, Essay Contest, Questioning the Foundations (2012)Google Scholar
  25. 25.
    Penrose, R.: The Emperor’s New Mind. Oxford University Press (1989)Google Scholar
  26. 26.
    Perlis, A.J.: Epigrams on Programming. SIGPLAN Notices 17(9), 7–13 (1982)CrossRefGoogle Scholar
  27. 27.
    Piccinini, G.: Computers. Pacic Philosophical Quarterly 89, 32–73 (2008)CrossRefGoogle Scholar
  28. 28.
    Putnam, H.: Representation and Reality. MIT Press, Cambridge (1988)Google Scholar
  29. 29.
    Margolus, N.: Physics-like Models of Computation. Physica 10D, 81–95 (1984)MathSciNetGoogle Scholar
  30. 30.
    Scott, D.S.: Outline of a mathematical theory of computation. Technical Monograph PRG-2. Oxford University Computing Laboratory, England (November 1970); Theoretical Computer Science 412, 183–190 (2011)Google Scholar
  31. 31.
    Searle, J.R.: The Rediscovery of the Mind. MIT Press (1992)Google Scholar
  32. 32.
    Searle, J.R.: Is the Brain a Digital Computer. In: Philosophy in a New Century, pp. 86–106. Cambridge University Press (2008)Google Scholar
  33. 33.
    Sutner, K.: Computational Processes, Observers and Turing IncompletenessGoogle Scholar
  34. 34.
    Turner, R.: Specification. Minds and Machines 21(2), 135–152 (2011)CrossRefGoogle Scholar
  35. 35.
    Thomson, A.: Machine man and other writings. Cambridge University Press (1996)Google Scholar
  36. 36.
    Turing, A.M.: Systems of logic based on ordinals. Proc. London Math. Soc. 45 (1939)Google Scholar
  37. 37.
    Turing, A.M.: Computing Machinery and Intelligence. Mind 59, 433–460 (1950)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Wolfram, S.: A New Kind of Science. Wolfram Media (2002)Google Scholar
  39. 39.
    Woods, D., Neary, T.: The complexity of small universal Turing machines: a survey. Theor. Comput. Sci. 410(4-5), 443–450 (2009)MathSciNetMATHCrossRefGoogle Scholar
  40. 40.
    Zenil, H.: Compression-based investigation of the behaviour of cellular automata and other systems. Complex Systems 19(2) (2010)Google Scholar
  41. 41.
    Zenil, H., Soler-Toscano, F., Joosten, J.J.: Empirical Encounters With Computational Irreducibility and Unpredictability. Minds and Machines 222(3), 149–165 (2012)CrossRefGoogle Scholar
  42. 42.
    Zenil, H.: On the Dynamic Qualitative Behaviour of Universal Computation. Complex Systems 20(3) (2012)Google Scholar
  43. 43.
    Zenil, H.: What is Nature-like Computation? A Behavioural Approach and a Notion of Programmability. Philosophy & Technology (2013), doi:10.1007/s13347-012-0095-2 Google Scholar
  44. 44.
    Zenil, H.: Programmability for Natural Computation and the Game of Life as a Case Study. J. of Experimental & Theoretical Artificial Intelligence (forthcoming)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institut d’Histoire et de Philosophie des Sciences et des TechniquesParis 1 Sorbonne-Panthéon/ENS Ulm/CNRSParisFrance

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