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International Conference on Current Trends in Theory and Practice of Computer Science

SOFSEM 2006: SOFSEM 2006: Theory and Practice of Computer Science pp 1–13Cite as

How Can Nature Help Us Compute?

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3831))

Abstract

Ever since Alan Turing gave us a machine model of algorithmic computation, there have been questions about how widely it is applicable (some asked by Turing himself). Although the computer on our desk can be viewed in isolation as a Universal Turing Machine, there are many examples in nature of what looks like computation, but for which there is no well-understood model. In many areas, we have to come to terms with emergence not being clearly algorithmic. The positive side of this is the growth of new computational paradigms based on metaphors for natural phenomena, and the devising of very informative computer simulations got from copying nature. This talk is concerned with general questions such as:

– Can natural computation, in its various forms, provide us with genuinely new ways of computing?

– To what extent can natural processes be captured computationally?

– Is there a universal model underlying these new paradigms?

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References

  1. Braverman, M.: Hyperbolic Julia Sets are Poly-Time Computable. In: Brattka, V., Staiger, L., Weihrauch, K. (eds.) Proceedings of the 6th Workshop on Computability and Complexity in Analysis, Wittenberg, Germany, August 16–20, 2004. ENTCS, vol. 120, pp. 17–30. Elsevier, Amsterdam (2005)

    Google Scholar 

  2. Brooks, R.A.: Intelligence without Representations. Artificial Intelligence 47, 139–159 (1987)

    Article  Google Scholar 

  3. Brooks, R.A.: Intelligence without Reason. A.I. Memo No. 1293, The A.I. Laboratory. M.I.T., Cambridge (1991)

    Google Scholar 

  4. Brooks, R.A.: The Relationship between Matter and Life. Nature 409, 409–411 (2001)

    Article  Google Scholar 

  5. Chaitin, G.J.: Algorithmic Information Theory. Cambridge University Press, Cambridge (1987)

    Book  Google Scholar 

  6. Church, A.: A Note on the Entscheidungsproblem. J. Symbolic Logic 1, 40–41, 101–102 (1936)

    Google Scholar 

  7. Cooper, S.B.: Beyond Gödel’s Theorem: Turing Nonrigidity Revisited. In: Makowsky, J.A., Ravve, E.V. (eds.) Proceedings of the Annual European Summer Meeting of the Association of Symbolic Logic, Logic Colloquium  1995, Haifa, Israel, August 9–18, 1995. Lecture Notes in Logic, vol. 11, pp. 44–50. Springer, Berlin (1998)

    Google Scholar 

  8. Cooper, S.B.: Clockwork or Turing U/universe? – Remarks on Causal Determinism and Computability. In: Cooper, S.B., Truss, J.K. (eds.) Models and Computability. London Mathematical Society Lecture Note Series, vol. 259, pp. 63–116. Cambridge University Press, Cambridge (1999)

    Chapter  Google Scholar 

  9. Cooper, S.B.: The Incomputable Alan Turing. In: Turing 2004: A Celebration of His Life and Achievements, electronically published by the British Computer Society (2005)

    Google Scholar 

  10. Cooper, S.B.: Definability as Hypercomputational Effect. Applied Mathematics and Computation (to appear)

    Google Scholar 

  11. Cooper, S.B., Odifreddi, P.: Incomputability in Nature. In: Cooper, S.B., Goncharov, S.S. (eds.) Computability and Models: Perspectives East and West, pp. 137–160. Kluwer Academic/ Plenum Publishers, New York (2003)

    Google Scholar 

  12. Damasio, A.: The Feeling Of What Happens. Harcourt, Orlando (1999)

    Google Scholar 

  13. Davis, M.: The Myth of Hypercomputation. In: Teuscher, C. (ed.), pp. 195–211 (2004)

    Google Scholar 

  14. Einstein, A.: Out of My Later Years. Philosophical Library, New York (1950)

    MATH  Google Scholar 

  15. Etesi, G., Németi, I.: Non-Turing Computations via Malament-Hogarth Space-Times. Int. J. Theoretical Phys. 41, 341–370 (2002)

    Article  MATH  Google Scholar 

  16. Gandy, R.O.: The Confluence of Ideas in 1936. In: Herken, R. (ed.) The Universal Turing Machine: A Half-Century Survey, pp. 51–102. Oxford University Press, New York (1988)

    Google Scholar 

  17. Gandy, R.O., Yates, C.E.M. (eds.): Collected Works of A.M. Turing: Mathematical Logic. North-Holland, Amsterdam (2001)

    MATH  Google Scholar 

  18. Goldin, D., Wegner, P.: Computation Beyond Turing Machines: Seeking Appropriate Methods to Model Computing and Human Thought. Communications of the ACM 46, 100–102 (2003)

    Article  Google Scholar 

  19. Hadamard, J.: The Psychology of Invention in the Mathematical Field. Princeton Univ. Press, Princeton (1945)

    MATH  Google Scholar 

  20. Hertling, P.: Is the Mandelbrot Set Computable? Math. Logic Quarterly 51, 5–18 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  21. Kreisel, G.: Mathematical Logic: What Has It Done for the Philosophy of Mathematics? In: Schoenman, R. (ed.) Bertrand Russell, Philosopher of the Century, pp. 201–272. Allen and Unwin, London (1967)

    Google Scholar 

  22. Kreisel, G.: Church’s Thesis: a Kind of Reducibility Axiom for Constructive Mathematics. In: Kino, A., Myhill, J., Vesley, R.E. (eds.) Intuitionism and Proof Theory: Proceedings of the Summer Conference at Buffalo N.Y. 1968, pp. 121–150. North-Holland, Amsterdam (1970)

    Chapter  Google Scholar 

  23. de Laplace, P.S.: Essai philosophique sur les probabilités (1819), English trans. by Truscott, F.W., Emory, F.L., Dover, New York (1951)

    Google Scholar 

  24. McCulloch, W., Pitts, W.: A Logical Calculus of the Ideas Immanent in Nervous Activity. Bull. Math. Biophys. 5, 115–133

    Google Scholar 

  25. Milner, R.: Elements of Interaction: Turing Award Lecture. Communications of the ACM 36, 78–89 (1993)

    Article  Google Scholar 

  26. Odifreddi, P.: Classical Recursion Theory. North-Holland, Amsterdam (1989)

    MATH  Google Scholar 

  27. Odifreddi, P.: The Mathematical Century: The 30 Greatest Problems of the Last 100 Years (trans. A. Sangalli). Princeton University Press, Princeton (2004)

    Google Scholar 

  28. Penrose, R.: Shadows of the Mind: A Search for the Missing Science of Consciousness. Oxford University Press, Oxford (1994)

    Google Scholar 

  29. Pinker, S.: How the Mind Works. W.W. Norton, New York (1997)

    Google Scholar 

  30. Rettinger, R.: A Fast Algorithm for Julia Sets of Hyperbolic Rational Functions. In: Brattka, V., Staiger, L., Weihrauch, K. (eds.) Proceedings of the 6th Workshop on Computability and Complexity in Analysis, Wittenberg, Germany, August 16–20, 2004. ENTCS, vol. 120, pp. 145–157. Elsevier, Amsterdam (2005)

    Google Scholar 

  31. Rettinger, R., Weihrauch, K.: The Computational Complexity of Some Julia Sets. In: Goemans, M.X. (ed.) Proceedings of the 35th Annual ACM Symposium on Theory of Computing, San Diego, California, USA, June 9–11, 2003, pp. 177–185. ACM Press, New York (2003)

    Google Scholar 

  32. Shaw, R.: Strange Attractors, Chaotic Behaviour, and Information Flow. Z. Naturforsch. 36A, 80–112 (1981)

    Google Scholar 

  33. Shaw, R.: The Dripping Faucet as a Model Chaotic System. The Science Frontier Express Series. Aerial Press, Santa Cruz (1984)

    Google Scholar 

  34. Smolensky, P.: On the Proper Treatment of Connectionism. Behavioral and Brain Sciences 11, 1–74 (1988)

    Article  Google Scholar 

  35. Teuscher, C. (ed.): Alan Turing: Life and Legacy of a Great Thinker. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  36. Turing, A.M.: On Computable Numbers, with an Application to the Entscheidungsproblem. Proc. London Math. Soc. 42(2), 230–265 (1936–7); Reprinted in Turing, A.M.: Collected Works: Mathematical Logic 18–53

    Google Scholar 

  37. Turing, A.M.: Systems of Logic Based on Ordinals. Proc. London Math. Soc. 45(2), 161–228 (1939); Reprinted in Turing, A.M.: Collected Works: Mathematical Logic 81–148

    Article  MATH  Google Scholar 

  38. Turing, A.M.: Intelligent Machinery. National Physical Laboratory Report (1948). In: Meltzer, B., Michie, D. (eds.) Machine Intelligence 5, pp. 3–23. Edinburgh University Press, Edinburgh (1969); Reprinted in Turing, A.M.: Collected Works: Mechanical Intelligence. In: Ince, D.C. (ed.) North-Holland, Amsterdam (1992)

    Google Scholar 

  39. van Leeuwen, J., Wiedermann, J.: The Turing Machine Paradigm in Contemporary Computing. In: Enquist, B., Schmidt, W. (eds.) Mathematics Unlimited — 2001 and Beyond. LNCS, Springer, Heidelberg (2000)

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK

    S. Barry Cooper

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  1. S. Barry Cooper
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Editors and Affiliations

  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, 182 07, Prague 8, Czech Republic

    Jiří Wiedermann  & Július Štuller  & 

  2. Department of Information and Computer Sciences, University of Utrecht, P.O. Box 80.089, 3508, Utrecht, TB, The Netherlands

    Gerard Tel

  3. Faculty of Mathematics and Physics, Charles University, Prague

    Jaroslav Pokorný

  4. Institute of Informatics and Software Engineering Faculty of Informatics and Information technologies, Slovak University of Technology, Ilkovičova 3, 842 16, Bratislava

    Mária Bieliková

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© 2006 Springer-Verlag Berlin Heidelberg

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Cooper, S.B. (2006). How Can Nature Help Us Compute?. In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds) SOFSEM 2006: Theory and Practice of Computer Science. SOFSEM 2006. Lecture Notes in Computer Science, vol 3831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11611257_1

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  • DOI: https://doi.org/10.1007/11611257_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31198-0

  • Online ISBN: 978-3-540-32217-7

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