Théorie mathématique des catégories en biologie et notion d’équivalence naturelle chez Robert Rosen

Revue d'Histoire des Sciences 66 (1):167-197 (2013)

Authors
Franck Varenne
University Of Rouen
Abstract
The aim of this paper is to describe and analyze the epistemological justification of a proposal initially made by the bio-mathematician Robert Rosen in 1958. In this theoretical proposal, Rosen suggests using the mathematical concept of « category » and the correlative concept of « natural equivalence » in mathematical modeling applied to living beings. Our questions are the following: according to Rosen, to what extent does the mathematical notion of category give access to more « natural » formalisms in the modeling of living beings? Is the so-called « naturalness » of some kinds of equivalences (which the mathematical notion of category makes it possible to generalize and to put at the forefront) analogous to the naturalness of living systems? Rosen appears to answer « yes » and to ground this transfer of the concept of « natural equivalence » in biology on such an analogy. But this hypothesis, although fertile, remains debatable. Finally, this paper makes a brief account of the later evolution of Rosen’s arguments about this topic. In particular, it sheds light on the new role played by the notion of « category » in his more recent objections against computational models that since the 1990’s are pervading almost every domain of biology.
Keywords category  theoretical biology  Robert Rosen  Nicholas Rashevsky  computational models  mathematical theory of categories
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DOI 10.3917/rhs.661.0167
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General Theory of Natural Equivalences.Saunders MacLane & Samuel Eilenberg - 1945 - Transactions of the American Mathematical Society:231-294.

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