Incomputability in physics and biology

Mathematical Structures in Computer Science

Volumn 22, Issue 5, 2012, Pages 880-900

  Longo, Giuseppe ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRETE DATA; FINE-GRAINED ANALYSIS; HILBERT; PHYSICAL MEASUREMENT; POINCARE; THEORETICAL FRAMEWORK; UNDECIDABILITY;

RANDOM PROCESSES;

BIOLOGY;

EID: 84866065604     PISSN: 09601295     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0960129511000569     Document Type: Article

References (59)

1. Asperti, A. and Longo, G. (1991) Categories, Types and Structures, M.I.T. Press. (Out of print, but available from http://www.di.ens.fr/users/longo.
2. Bachelard, G. (1940) La Philosophie du non? Essai d'une philosophie du nouvel esprit scientifique, PUF, Paris.
3. Bailly, F. and Longo, G. (2007) Randomness and determinism in the interplay between the Continuum and the Discrete. Mathematical Structures in Computer Science 17 (2) 289-307.
4. Bailly, F. and Longo, G. (2011) Mathematics and Natural Sciences. The physical singularity of Life, Imperial College Press. (The original book was in French: Hermann, Paris, 2006; the Introduction and Longo's papers are available from http://www.di.ens.fr/users/longo.)
5. Bailly, F. and Longo, G. (2008) Extended Critical Situation. Journal of Biological Systems 16 (2) 309-336.
6. Bailly, F. and Longo, G. (2009) Biological Organization and Anti-Entropy. Journal of Biological Systems 17 (1) 63-96.
7. Bell, J. (1998) A Primer in Infinitesimal Analysis, Cambridge University Press.
8. Boi, L. (1995) Le probl̀eme math'ematique de l'espace, Springer-Verlag.
9. Braverman, M. and Yampolski, M. (2006) Non-computable Julia sets. Journal of the American Mathematical Society 19 551-578. (Pubitemid 44035237)
10. Buiatti, M. and Longo, G. (2012) Randomness and Multi-level Interactions in Biology. (In preparation, preliminary version available from http://www.di.ens.fr/users/longo.
11. Calude, C. (2002) Information and randomness, Springer-Verlag.
12. Cencini, M. (2010) Chaos From Simple models to complex systems, World Scientific.
13. Cooper, B. S. and Odifreddi, P. (2003) Incomputability in Nature. In: Cooper, B. S. and Goncharov, S. S. (eds.) Computability and Models - Perspectives East and West, Kluwer Academic/Plenum 137-160.
14. Costa J., Lo B. and Mycka J. (2009) A foundation for real recursive function theory. Annals of Pure and Applied Logic 160 (3) 255-288.
15. da Costa, N. and Doria, F. (1991) Undecidability and incompleteness in classical mechanics. International Journal of Theoretical Physics 30 1041-1073.
16. Einstein, A., Podolsky, B. and Rosen, N. (1935) Can Quantum-Mechanical Description of Physical Reality be Considered Complete? Physical Review 41 777-780.
17. Frege, G. (1884) Die Grundlagen der Arithmetik. (English translation
18. Austin, J. L. (1980) The Foundations of Arithmetic, Basil Blackwell Limited.
19. Fox Keller, E. (2000) The Century of the Gene, Harvard University Press.
20. Gacs, P., Hoyrup, M. and Rojas, C. (2011) Randomness on Computable Probability Spaces - A Dynamical Point of View. In: Albers, S. and Marion, J.-Y. (eds.) Preface: Special Issue on Theoretical Aspects of Computer Science (STACS). Theory of Computing Systems 48 (3) 465-485.
21. Goldfarb, W. (1988) Poincar'e Against the Logicists. In: Aspray, W. and Kitcher, P. (eds.) Essays in the History and Philosophy of Mathematics, Minnesota Studies in the Philosophy of Science, Volume XI 61-81.
22. Gould, S. J. (1989) Wonderful Life, Harvard University Press.
23. Gould, S. J. (1998) Full House, Harmony Books.
24. Hilbert, D. (1899) Grundlagen der Geometrie. (English translation: Unger, L. and Bernays, P. (1971) Foundations of Geometry, Open Court.
25. Kaern, M., Elston, T. C., Blake, W. J. and Collins, J. J. (2005) Stocasticity in gene expression: From theories to phenotypes. Nature Review Genetics 6 451-464. (Pubitemid 40733890)
26. Krivine, J., Milner, R. and Troina, A. (2008) Stochastic Bigraphs. Proceedings of MFPS XXIV: Mathematical Fondations of Programming Semantics. Electronic Notes in Theoretical Computer Science 218 73-96.
27. Kuhn, T. S. (1961) The Function of Measurement in Modern Physical Science. Isis 52 161-193.
28. Kuhn, T. S. (1962) The Structure of Scientific Revolutions, University of Chicago Press.
29. Kupiec, J.-J. (2009) On the lack of specificity of proteins and its consequences for a theory of biological organzation. Progress in Biophysics and Molecular Biology 102 (1) 45-52.
30. Laskar, J. (1994) Large scale chaos in the Solar System. Astronomy and Astrophysics 287 L9-L12.
31. Longo, G. (2002) Reflections on Concrete Incompleteness: Invited Lecture. In: Callaghan, P., Luo, Z., McKinna, J. and Pollack, R. (eds.) Types for Proofs and Programs. Springer-Verlag
32. Lecture Notes in Computer Science 2277 160-180. (Revised version in Philosophia Mathematica (2011) 19 (3) 255-280.
33. Longo, G. (2008) Critique of Computational Reason in the Natural Sciences. In: Gelenbe, E. and Kahane, J.-P. (eds.) Fundamental Concepts in Computer Science, Imperial College Press.
34. Longo, G. (2009) From exact sciences to life phenomena: Following Schroedinger and Turing on Programs, Life and Causality. Information and Computation 207 (5) 543-670.
35. Longo, G. (2010a) Incomputability in Physics. In: Ferreira, F., L̈owe, B.,Mayordomo, E. andMendes Gomes, L. (eds.) Programs, Proofs, Processes: Proceedings 6th Conference on Computability in Europe, CiE 2010. Springer-Verlag Lecture Notes in Computer Science 6158 276-285.
36. Longo, G. (2010b) Interfaces of Incompleteness. (Available in Italian or French from http: //www.di.ens.fr/users/longo.
37. Longo, G. and Mont'evil, M. (2011) From Physics to Biology by Extending Criticality and Symmetry Breakings. Progress in Biophysics and Molecular Biology 106 (2) 340-347.
38. Longo, G and Tendero, P.-E. (2007) The differential method and the causal incompleteness of Programming Theory in Molecular Biology. Foundations of Science 12 337-366.
39. Maynard Smith, J. (1989) Evolutionary Genetics, Oxford University Press.
40. Monod, J. (1973) Le Hasard et la Ńecessit́e, É ditions du Seuil.
41. Moore, C. (1990) Unpredictability and undecidability in dynamical systems. Physical Review Letters 64 (20) 2354-2357.
42. Mossio, M., Longo, G. and Stewart, J. (2009) Computability of closure to efficient causation. Journal of Theoretical Biology 257 (3) 489-498
43. Petersen, K. (1983) Ergodic Theory, Cambridge University Press.
44. Pilyugin, S.Y. (1999) Shadowing in dynamical systems. Springer-Verlag Lecture Notes in Mathematics 1706.
45. Poincaŕ e, H. (1903) Review of Hilbert's Foundations of geometry. Bulletin of the American Mathematical Society 10 (1) 1-23.
46. Poincaŕ e, H. (1906) Les math'ematiques et la logique. Revue de M'etaphys. et de morale 14.
47. Pour-El, M. B. and Richards, J. I. (1989) Computability in analysis and physics. Perspectives in Mathematical Logic 1, Springer-Verlag.
48. Raj, A. and van Oudenaarden, A. (2008) Nature, nurture, or chance: Stochastic gene expression and its consequences. Cell 135 216-226.
49. Riemann, B. (1854) Ü ber die Hypothesen, welche der Geometrie zu Grunde liegen. (English translation: Clifford, W. K. (1873) On the hypothesis which lie at the basis of Geometry. Nature 8 (183) 14-17 (184) 36-37.
50. Rosen, R. (1991) Life itself: a comprehensive enquiry into the nature, origin and fabrication of life, Columbia University Press.
51. Sonnenschein, C. and Soto A. (1999) The Society of Cells: Cancer and Control of Cell Proliferation, Elsevier.
52. Svozil, K.(1993) Randomness and undecidability in Physics, World Scientific.
53. Turing, A.M. (1950) Computing Machines and Intelligence. Mind LIX (236) 433-460.
54. Turing, A.M. (1952) The Chemical Basis of Morphogenesis. Philosophical Transactions of the Royal Society B237 37-72.
55. Young, L. J., Nilsen, R.,Waymire, K. G.,MacGregor, G.R. and Insel, T, R. (1999) Increased affiliative response to vasopressin in mice expressing the V1a receptor from a monogamous vole Nature 400 766-768. (Pubitemid 29399537)
56. Weihrauch, K. and Zhong, L. (2002) Is wave propagation computable or can wave computers beat the Turing machine? Proceedings of the London Mathematical Society 85.
57. Weyl, H. (1918) Das Kontinuum, Veit, Leipzig.
58. Weyl, H. (1927) Philosophie der Mathematik und Naturwissenschaft. (English translation: Helmer, O. (1949) Philosophy of Mathematics and of Natural Sciences, Princeton University Press.
59. Weyl, H. (1985) Axiomatic Versus Constructive Procedures in Mathematics (edited by Tonietti, T.). The Mathematical Intelligencer 7 (4).