How Future Depends on Past and Rare Events in Systems of Life

Abstract

The dependence on history of both present and future dynamics of life is a common intuition in biology and in humanities. Historicity will be understood in terms of changes of the space of possibilities (or of "phase space") as well as by the role of diversity in life's structural stability and of rare events in history formation. We hint to a rigorous analysis of "path dependence" in terms of invariants and invariance preserving transformations, as it may be found also in physics, while departing from the physico-mathematical analyses. The idea is that the (relative or historicized) invariant traces of past organismal or ecosystemic transformations contribute to the understanding (or the "theoretical determination") of present and future states of affairs. This yields a peculiar form of unpredictability (or randomness) in biology, at the core of novelty formation: the changes of observables and pertinent parameters may depend also on past events. In particular, in relation to the properties of synchronic measurement in physics, the relevance of diachronic measurement in biology is highlighted. This analysis may a fortiori apply to cognitive and historical human dynamics, while allowing to investigate some general properties of historicity in biology. 1.2-Determination and Path Dependence, from Physics to Biology History is irrelevant in most existing physical theories. However, in sect. 2, we will briefly discuss the key role of historical analysis, in cosmology and, more pertinently, "path dependence" in Riemann's manifold (by Levi-Civita's parallel transport) as well as in cascades of singularities and critical transitions. Some informal references will be also made to how statistical physics and condensed matter physics describe path dependent phenomena. The very interesting cases of "history dependence", or, more precisely, process dependence, in physics just quoted, and further discussed below, may help in the transitions from the theories of the inert to theories in biology. In (Longo, Montévil, 2014) we insisted on the possibility of this complex conceptual transition by focusing on an extension of the notion of critical phase transition. For example, physical theories of criticality are widely used in theoretical biology, since the '80s, and the reader may refer to (Longo, Montévil, 2014) for "extended criticality" in biology and references to "criticality" in physics. Others consider statistical physics and condensed matter physics as a possible theoretical junction between physics and biology (see (Goldenfeld, Woese, 2011) for an insightful survey). Biological Theories, however, are or may need to be at least as different from existing physical ones, as Relativity and Hydrodynamics are far from Quantum Mechanics (well ... these three theories present even physico-mathematical incompatibilities). Some theories of the inert may be enlightening for biology, in particular by suitable formal extensions, such as extended criticality or a two dimensional theory of biological time, where time acts as an operat...

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