Abstract
In this text we will discuss different forms of randomness in Natural Sciences and present some recent results relating them. In finite processes, randomness differs in various theoretical context, or, to put it otherwise, there is no unifying notion of finite time randomness. In particular, we will introduce, classical (dynamical), quantum and algorithmic randomness. In physics, differing probabilities, as a measure of randomness, evidentiate the differences between the various notions. Yet, asymptotically, one is universal: Martin-Löf randomness provides a clearly defined and robust notion of randomness for infinite sequences of numbers. And this is based on recursion theory, that is the theory of effective computability. As a recurring issue, the question will be raised of what randomenss means in biology, phylogenesis in particular. Finally, hints will be given towards a thesis, relating finite time randomness and time irreversibility in physical processes.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Causality, A.J.: Symmetries and Quantum Mechanics. Foundations of Physics Letters 15(5), 415–438 (2002)
Adler, R.L.: Topological entropy and equivalence of dynamical systems. American Mathematical Society (1979)
Alligood, K., Sauer, T., Yorke, J.: Chaos: an introduction to Dynamical Systems. Springer, New York (2000)
Aceto, L., Longo, G., Victor, B. (eds.): The difference between Sequential and Concurrent Computations, vol. (4-5). Cambridge University Press, Cambridge (2003)
Aspect, A., Grangier, P., Roger, G.: Experimental Realization of the Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell’s Inequalities. Phys. Rev. Let. 49, 91 (1982)
Bailly, F., Longo, G.: Mathématiques et sciences de la nature. La singularité physique du vivant. Hermann, Paris (English introduction, downloadable; ongoing translation) (2006)
Bailly, F., Longo, G.: Randomness and Determination in the interplay between the Continuum and the Discrete. Mathematical Structures in Computer Science 17(2) (2007)
Bailly, F., Longo, G.: Biological Organization and Anti-Entropy. Journal of Biological Systems (to appear, 2008)
Brett, D., Pospisil, H., Valcárcel, J., Reich, L., Bork, P.: Alternative splicing and genome complexity. Nature Genetics 30 (2001)
Calude, C.: Information and Randomness: An Algorithmic Perspective. Springer, New York (1994)
Calude, C., Stay, M.: From Heisemberg to Gödel via Chaitin. International J. Theor. Phys 44(7) (2005)
Connes, A.: A. Non-commutative Geometry. Academic Press, London (1994)
Cornfeld, I., Fomin, S., Sinai, Y.G.: Ergodic Theory. Springer, New York (1982)
Dahan Delmedico, A., Chabert, J.-L., Chemla, K.: Chaos et déterminisme, Seuil (1992)
Devaney, R.L.: An introduction to Chaotic Dynamical Systems. Addison-Wesley, Reading (1989)
Feynman, R.: Lectures in Physics. Addison-Wesley, Reading (1966)
van Frassen, B.: Lois et symetries, Vrin, Paris (1994)
Fox Keller, E.: The Century of the Gene, Gallimard (2000)
Galatolo, S., Hoyrup, M., Rojas, C.: Effective symbolic dynamics, random points, statistical behavior, complexity and entropy (submitted, 2008)
Galatolo, S., Hoyrup, M., Rojas, C.: A Constructive Borel-Cantelli lemma. Constructing orbits with required statistical properties (submitted, 2008)
Gandy, R.: Church’s Thesis and the principles for Mechanisms. In: Barwise, et al. (eds.) The Kleene Symposium. North Holland, Amsterdam (1980)
Gould, S.J.: Wonderful Life, WW. Norton (1989)
Lecointre, G., Le Guyader, H.: Classification phylogénétique du vivant, Paris, Belin (2001)
Lighthill, J.: The recent recognized failure of predictability in Newtonian dynamics. Proc. R. Soc. Lond. A 407, 35–50 (1986)
Herrenschmidt, C.: Les trois écritures, Gallimard (2007)
Laskar, J.: Large scale chaos in the Solar System. Astron. Astrophysics 287, L9–L12 (1994)
Longo, G.: Laplace, Turing and the ‘imitation game’ impossible geometry: randomness, determinism and programs in Turing’s test. In: Epstein, R., Roberts, G., Beber, G. (eds.) The Turing Test Sourcebook. Kluwer, Dordrecht (2007)
Longo, G.: Critique of Computational Reason in the Natural Sciences. In: Gelenbe, E., Kahane, J.-P. (eds.) Fundamental Concepts in Computer Science. Imperial College Press/World Scientific (2008)
Longo, G., Paul, T.: The Mathematics of Computing between Logic and Physics. In: Cooper, Sorbi (eds.) Computability in Context: Computation and Logic in the Real World. Imperial College Press/World Scientific (2008)
Longo, G., Tendero, P.-E.: The differential method and the causal incompleteness of Programming Theory in Molecular Biology. Foundations of Science (12), 337–366 (2007); preliminary version in French in Evolution des concepts fondateurs de la biologie du XXIe siècle, DeBoeck, Paris (2007)
Martin-Loef, P.: The definition of random sequences. Information and Control 9, 602–619 (1966)
Monod, J.: Le Hasard et la Nécessité, PUF (1973)
Paul, T.: Échelles de temps pour l’évolution quantique à petite constante de Planck. Séminaire X-EDP, École Polytechnique, Palaiseau (2008)
Paul, T.: Semiclassical analysis and sensitivity to initial conditions. Information and Computation (to appear, 2008a)
Pour-El, M.B., Richards, J.I.: Computability in analysis and physics. Perspectives in mathematical logic. Springer, Berlin (1989)
Rojas, C.: Computability and Information in models of Randomness and Chaos. Math. Struct. in Computer Science 18, 291–307 (2008)
Turing, A.M.: Computing Machines and Intelligence. Mind LIX(236), 433–460 (1950)
Turing, A.M.: The Chemical Basis of Morphogenesis. Philo. Trans. Royal Soc. B237, 37–72 (1952)
V’yugin, V.V.: Ergodic Theorems for Individual Random Sequences. Theoretical Computer Science 207, 343–361 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Longo, G. (2009). Randomness and Determination, from Physics and Computing towards Biology. In: Nielsen, M., Kučera, A., Miltersen, P.B., Palamidessi, C., Tůma, P., Valencia, F. (eds) SOFSEM 2009: Theory and Practice of Computer Science. SOFSEM 2009. Lecture Notes in Computer Science, vol 5404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95891-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-95891-8_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-95890-1
Online ISBN: 978-3-540-95891-8
eBook Packages: Computer ScienceComputer Science (R0)