  This paper proposes an abstract mathematical frame for describing some
features of biological time. The key point is that usual physical (linear)
representation of time is insufficient, in our view, for the understanding key
phenomena of life, such as rhythms, both physical (circadian, seasonal ...) and
properly biological (heart beating, respiration, metabolic ...). In particular,
the role of biological rhythms do not seem to have any counterpart in
mathematical formalization of physical clocks, which are based on frequencies
along the usual (possibly thermodynamical, thus oriented) time. We then suggest
a functional representation of biological time by a 2-dimensional manifold as a
mathematical frame for accommodating autonomous biological rhythms. The
"visual" representation of rhythms so obtained, in particular heart beatings,
will provide, by a few examples, hints towards possible applications of our
approach to the understanding of interspecific differences or intraspecific
pathologies. The 3-dimensional embedding space, needed for purely mathematical
reasons, allows to introduce a suitable extra-dimension for "representation
time", with a cognitive significance.
