DNA, differential methods and the Böhm-out technique (written in 2008)

Giuseppe Longo, Pierre-E. Tendero. The differential method and the causal incompleteness of Programming Theory in Molecular Biology. In Foundations of Science, n. 12, pp. 337-366, 2007 (DNA-incompl.pdf) (A version for Logicians and computer scientists: Dna_Differential_Methods_and_Bohm-out.pdf; version préliminaire et plus étendue dans "Evolution des concepts fondateurs de la biologie du XXIe siècle", (Miquel ed.) DeBoeck, Paris, 2008 (alphaMdT-ADN.pdf); una traduzione in italiano e' apparsa a cura di e per Naturalmente).The "DNA is a program" metaphor is still widely used in Molecular Biology. There are good historical reasons for the use of such a metaphor or theoretical model. Yet we argue that both the metaphor and the model are essentially inadequate also from the point of view of Physics and Computer Science. Relevant work has already been done, in Biology, criticizing the programming paradigm. We will refer to empirical evidence and theoretical writings in Biology, although our arguments will be mostly based on a comparison with the use of differential methods (in Molecular Biology: a mutation or alike is observed or induced and its phenotypic consequences are observed) as applied in Computer Science and in Physics, where this fundamental tool for empirical investigation originated and acquired a well-justified status. In particular, as we will argue, the programming paradigm is not theoretically sound as a causal (as in Physics) or deductive (as in Programming) framework for relating the genome to the phenotype, in contrast to the physicalist and computational grounds that this paradigm claims to propose