# Schroedinger and Turing on the Logic of Life: from the “coding” to the “genesis” of forms.

## Giuseppe Longo

### CNRS & Ecole Normale Supérieure, Paris

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.

References

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.

The main research area Giuseppe Longo has been interested in concerns syntactic and semantic properties of the “logical base” of functional languages: Combinatory Logic, Lambda-calculus and their extensions. However, he always investigated these topics in its broadest setting which relates them to Recursion Theory, Proof Theory and Category Theory. He also worked at the applications of functional approaches to Object-Oriented programming, Philosophy of Mathematics and Cognitive Sciences.