Proofs and types
Categories, types, and structures: an introduction to category theory for the working computer scientist
Ergodic theorems for individual random sequences
Theoretical Computer Science - Special issue Kolmogorov complexity
IEEE Concurrency
On the Proofs of Some Formally Unprovable Propositions and Prototype Proofs in Type Theory
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Randomness and determinism in the interplay between the continuum and the discrete†
Mathematical Structures in Computer Science
Abstract machines of systems biology
Transactions on Computational Systems Biology III
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Incomputability in physics and biology
Mathematical Structures in Computer Science
| Hi-index | 0.00 |
This text presents a survey and a conceptual analysis of a path which goes from Programming to Physics and Biology. Schrodinger'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 Poincare's analysis of unpredictability in non-linear systems, at the core of Turing's 1952 work. The relevance of planetary ''resonance'', in Poincare'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 Schrodinger.