From exact sciences to life phenomena: Following Schrödinger and Turing on Programs, Life and Causality, Information and Computation
This text presents a survey and a conceptual analysis of a path which goes from Programming to Physics and Biology. Schrödinger’s early reflections on coding and the genome will be a starting point: by his (and Turing’s) remarks, a link is explicitly made between the notion of program and the analysis of causality and determination in Physics. In particular, Turing’s work in Computing and in Morphogenesis (his 1952 paper on continuous dynamics) will be seen as part of a scientific path which goes from Laplace’s understanding of deterministic predictability to the developments of Poincaré’s analysis of unpredictability in non-linear systems, at the core of Turing’s 1952 work. The relevance of planetary “resonance”, in Poincaré’s Three Body Theorem, and its analogies and differences with logical circularities will then be discussed. On these grounds, some recent technical results will be mentioned relating algorithmic randomness, a strong form of logical undecidability, and physical (deterministic) unpredictability. This will be a way to approach the issue of resonances and circularities in System Biology, where these notions have a deeply different nature, in spite of some confusion which is often made. Finally, three aspects of the author’s (and his collaborators’) recent work in System Biology will be surveyed. They concern an approach to biological structural stability, as “extended criticality”, the structure of time and of biological rhythms and the role of a proper biological observable, “organization”. This is described in terms of “anti-entropy”, a new notion inspired by a remark by Schrödinger.