Skip to main content
SpringerLink
Log in
Book cover

Conference on Computability in Europe

CiE 2012: How the World Computes pp 450–461Cite as

What is Turing’s Comparison between Mechanism and Writing Worth?

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7318))

Abstract

In one of the many and fundamental side-remarks made by Turing in his 1950 paper (The Imitation Game paper), an analogy is made between Mechanism and Writing. Turing is aware that his Machine is a writing/re-writing mechanism, but he doesn’t go deeper into the comparison. Striding along the history of writing, we shall hint here at the nature and the role of alphabetic writing in the invention of Turing’s (and today’s) notion of computability. We shall stress that computing is a matter of alphabetic sequence checking and replacement, far away from the physical world, yet related to it once the role of physical measurement is taken into account. Turing Morphogenesis paper, 1952, provides the guidelines for the modern analysis of “continuous dynamics” at the core Turing’s late and innovative approach to bio-physical processes.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Asperti, A., Longo, G.: Categories, Types and Structures; Category Theory for the working computer scientist. M.I.T. Press (1991)

    Google Scholar 

  2. Bailly G, Longo G.: Mathematics and Natural Sciences: the Physical Singularity of Life. Imperial Coll. Press, London (2011)

    Google Scholar 

  3. Barendregt, H.: The Lambda Calculus: its syntax and semantics. North Holland, Amsterdam (1984)

    MATH  Google Scholar 

  4. Braverman, M., Yampolski, M.: Non-computable Julia sets. Journ. Amer. Math. Soc. 19, 551–578 (2006)

    Article  MATH  Google Scholar 

  5. Bezem, M., Klop, J.W., Roel de Vrijer, R.: Term Rewriting Systems. Cambridge Univ. Press, Cambridge (2003)

    MATH  Google Scholar 

  6. Church, A.: A set of postulates for the foundation of Logic. Annals of Math. 33(2), 346–366, 34, 37–54 (1932-1933)

    Article  MathSciNet  Google Scholar 

  7. Church, A.: A formalisation of the simple theory of types. JSL 5, 56–58 (1940)

    Article  MathSciNet  MATH  Google Scholar 

  8. Curry, H.B., Feys, E.: Combinatory Logic, vol. I. North-Holland, Amsterdam (1968)

    MATH  Google Scholar 

  9. Curry, H.B., Hindley, J.R., Seldin, J.: Combinatory Logic, vol. II. North-Holland, Amsterdam (1972)

    MATH  Google Scholar 

  10. Herrenschmidt, C.: Les trois écritures; langue, nombre, code. Gallimard, Paris (2007)

    Google Scholar 

  11. Hindley, R.: Basic Simple Type Theory. Cambridge University Press, Cambridge (1997)

    Book  MATH  Google Scholar 

  12. Hindley, R., Longo, G.: Lambda-calculus models and extensionality. Zeit. für Mathemathische Logik und Grundlagen der Mathematik 26(2), 289–310 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kleene, S.C.: Lambda definability and recursiveness. Duke Math. J. 2, 340–353 (1936)

    Article  MathSciNet  Google Scholar 

  14. Lambek, J., Scott, P.J.: Introduction to higher order Categorial Logic. Cambridge Univ. Press, Cambridge (1986)

    Google Scholar 

  15. Lassègue’s page (downloadable articles), http://www.lassegue.net

  16. Laskar, J.: Large scale chaos in the Solar System. Astron. Astrophysics 287, L9–L12 (1994)

    Google Scholar 

  17. Longo’s page (downloadable articles), http://www.di.ens.fr/users/longo

  18. Longo, G.: Set-theoretical models of lambda-calculus: Theories, expansions, isomorphisms. Annals of Pure and Applied Logic 24, 153–188 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  19. Longo, G., Moggi, E.: A category-theoretic characterization of functional completeness. Theoretical Computer Science 70(2), 193–211 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  20. Longo, G.: Critique of Computational Reason in the Natural Sciences. In: Gelenbe, E., et al. (eds.) Fundamental Concepts in Computer Science. Imperial College Press, London (2008)

    Google Scholar 

  21. Longo G.: Incomputability in Physics and Biology. To appear in MSCS (2012) (see Longo’s web page); Preliminary version: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds.): CiE 2010. LNCS, vol. 6158. Springer, Heidelberg (2010)

    Google Scholar 

  22. Yu, P.S.: Shadowing in dynamical systems. Springer (1999)

    Google Scholar 

  23. Pour-El, M.B., Richards, J.I.: Computability in analysis and physics. Perspectives in Mathematical Logic. Springer, Berlin (1989)

    MATH  Google Scholar 

  24. Schmandt-Besserat, D.: How Writing Came About. University of Texas Press, Austin (1992)

    Google Scholar 

  25. Schmandt-Besserat, D.: From Tokens to Writing: the Pursuit of Abstraction. Bull. Georg. Natl. Acad. Sci. 175(3), 162–167 (2007)

    Google Scholar 

  26. Scott, D.: Continuous lattices. In: Lawvere (ed.) Toposes, Algebraic Geometry and Logic. SLNM, vol. 274, pp. 97–136. Springer, Berlin (1972)

    Chapter  Google Scholar 

  27. Scott, D.: Data types as lattices. SIAM Journal of Computing 5, 522–587 (1976)

    Article  MATH  Google Scholar 

  28. Turing, A.M.: Computing Machinery and Intelligence. Mind LIX, 433–460 (1950)

    Google Scholar 

  29. Turing, A.M.: The Chemical Basis of Morphogenesis. Philo. Trans. Royal Soc. B 237, 37–72 (1952)

    Article  Google Scholar 

  30. Weihrauch, K.: Computable analysis. Springer, Berlin (2000)

    Book  MATH  Google Scholar 

  31. Weihrauch, K., Zhong, N.: Is wave equation computable or computers can beat the Turing Machine? Proc. London Math. Soc. 85(3), 312–332 (2002)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre de Recherche en Épistémologie Appliquée (CREA), École Polytechnique, 32, boulevard Victor, 75015, Paris, France

    Jean Lassègue

  2. Centre International de Recherches en Philosophie, Lettres, Savoirs (CIRPHLES), Département de philosophie, École Normale Supérieure, 45 rue dUlm, 75005, Paris, France

    Giuseppe Longo

Authors
  1. Jean Lassègue
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giuseppe Longo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

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

    S. Barry Cooper

  2. Computer Laboratory, University of Cambridge, Willialm Gates Building, J.J. Thomson Avenue, CB3 0FD, Cambridge, UK

    Anuj Dawar

  3. Institute for Logic, Language and Computation, University of Amsterdam, 1090 GE, Amsterdam, The Netherlands

    Benedikt Löwe

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lassègue, J., Longo, G. (2012). What is Turing’s Comparison between Mechanism and Writing Worth?. In: Cooper, S.B., Dawar, A., Löwe, B. (eds) How the World Computes. CiE 2012. Lecture Notes in Computer Science, vol 7318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30870-3_46

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-30870-3_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30869-7

  • Online ISBN: 978-3-642-30870-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation