A 2-dimensional Geometry for Biological Time

TL;DR

This paper introduces a 2-dimensional geometric framework for modeling biological time, capturing rhythms and phenomena that traditional linear models cannot, with potential applications in understanding biological differences and pathologies.

Contribution

It proposes a novel 2D manifold model for biological time, incorporating autonomous rhythms and an extra dimension for cognitive representation, advancing beyond traditional physical time models.

Findings

Visual representation of biological rhythms like heartbeat.

Application hints for interspecific differences and pathologies.

Mathematical formalization of biological rhythms in 2D space.

Abstract

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.