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In this paper, following the technical approach to biological time, rhythms and retention/protention in Longo and Montévil (Perspectives on organisms: Biological time, symmetries and singularities. Springer, Berlin, 2014), we develop a philosophical frame for the proposed dimensions and mathematical structure of biological time, as a working example of "theory building". We first introduce what "theory building" means to our perspective, in order to make explicit our theoretical tools and discuss the general epistemological issue. Then, through a conceptual articulation between physics and biology, we introduce protention (anticipation) and retention (memory), as proper biological observables. This theoretical articulation, which we consider at the core of moving from physical to biological theorizing, allows us to use some of the properties of these observables as principles around which it is possible to outline a proper geometrical schema for biological time. We then philosophically motivate the analysis of "time" as an operator that acts in biological dynamics in a constitutive way. In other words, space and time become specials concepts of order, actively involved in the theoretical organization of biology, in contrast to existing theories in physics where they appear as parameters. In this approach, we first consider the usual dimension of an irreversible physical time. We then add to it a dimension specific to the internal rhythms of organisms. We motivate this dimensional extension by the relative autonomy of biological rhythms with respect to physical time. This second dimension of time is "compactified" in a simple but rigorous mathematical sense. In short, as soon as there are life phenomena, their rhythms scan biological time. We will consider such a statement as a starting point for an original notion of biological inertia.

DOI: 10.1007/978-3-319-72787-5_12

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