From Turing’s Work to Current Challenges for the Mathematical Understanding of Living Beings

Turing sharply distinguishes the imitation from the modeling of a phenomenon. The latter aims to grasp the causal structure of the phenomenon studied. However, in biology, there is no well-established theoretical framework for modeling practices. We start from the link between the living and thermodynamics, especially the second principle. This discussion will lead us to the theoretical and epistemological challenges in the mathematical understanding of living beings. In particular, the historicity of living phenomena is a difficulty rarely taken into account in this field. We believe that the historicity of living phenomena requires a complete reversal of the epistemology of physics in order to understand living organisms with theoretical and conceptual accuracy. This challenge is relevant both for theoretical practices and for interpreting protocols and experimental results.