Topic Archive: Turing
Schroedinger’s and Turing’s analyses of life phenomena have a twofold aspects. They both follow, first, a “coding paradigm”, of embryogenesis or of human computations and deductions respectively, and then move towards a more “dynamicist” approach. Schroedinger, in the second part of his 1944 book, hints to biological organization as negentropy – a variant of Gibbs dynamical analysis of energy – that we revitalized as anti-entropy, see references. Turing, after stressing that “the nervous system is surely not a Discrete State machine” (1950), invents the mathematics for an action/reaction/diffusion process, a “continuous system” (1952), where chemical matter (an hardware with no software) organizes itself along morphogenesis.
We will hint to the paths for thought opened by Turing’s dynamics as continuous deformations at the core of Turing’s pioneering paper of 1952, where symmetry breakings are a key component of the bio-chemical processes.
Schrödinger, E. What Is Life?, Cambridge University Press, 1944.
Alan M. Turing, “On Computable Numbers with an Application to the Entscheidungsproblem”, Proc. London Math. Soc. 42, 230-265, 1936.
Alan M. Turing, “The Chemical Basis of Morphogenesis”, Philo. Trans. Royal Soc., B237, 37-72, 1952.
Francis Bailly, Giuseppe Longo. Mathematics and Natural Sciences : the Physical Singularity of Life, Imperial College Press, London, 2011.
Giuseppe Longo, Maël Montévil, Perspectives on Organisms: Biological Time, Symmetries and Singularities, Springer, 2013.
Papers in http://www.di.ens.fr/users/longo:
Giuseppe Longo, “From exact sciences to life phenomena: following Schrödinger and Turing on Programs, Life and Causality”. Information and Computation, 207, 5: 543-670, 2009.
Francis Bailly, Giuseppe Longo. Biological Organization and Anti-Entropy. In J. Biological Systems, Vol. 17, No. 1, pp. 63-96, 2009.
Giuseppe Longo. Incomputability in Physics and Biology. Invited Lecture, Proceedings of Computability in Europe, Azores, Pt, June 30 – July 4, LNCS 6158, Springer, 2010.
Longo G., P. A. Miquel, C. Sonnenschein, A. Soto. Is Information a proper observable for biological organization? Progress in Biophysics and Molecular Biology, Vol. 109, Issue 3, pp. 108-114, August 2012.
A group of brilliant innovators spanning three centuries were concerned with the nature of human reason. This endeavor led to the all-purpose digital computer. Except for Turing, none of them had any idea that his work might have such a tremendous application to our modern world. Leibniz saw far, but not that far. Boole could hardly have imagined that his algebra of logic would be used to design complex electronic circuits. Frege would have been amazed to find equivalents of his logical rules incorporated into computer programs for carrying out deductions. Cantor certainly never anticipated the ramifications of his diagonal method. Hilbert’s program to secure the foundations of mathematics was pointed in a very different direction. And Goedel, living his life of the mind, hardly thought of application to mechanical devices (M. Davis). However, Turing’s great vision has now been realized.