Determinism, chaos, self-organization and entropy

Abstract

We discuss two changes of paradigms that occurred in science along the XX th century: the end of the mechanist determinism, and the end of the apparent incompatibility between biology, where emergence of order is law, and physics, postulating a progressive loss of order in natural systems. We recognize today that three mechanisms play a major role in the building of order: the nonlinear nature of most evolution laws, along with distance to equilibrium, and with the new paradigm, that emerged in the last forty years, as we recognize that networks present collective order properties not found in the individual nodes. We also address the result presented by Blumenfeld (L.A. Blumenfeld, Problems of Biological Physics, Springer, Berlin, 1981) showing that entropy decreases resulting from building one of the most complex biological structures, the human being, are small and may be trivially compensated for compliance with thermodynamics. Life is made at the expense of very low thermodynamic cost, so thermodynamics does not pose major restrictions to the emergence of life. Besides, entropy does not capture our idea of order in biological systems. The above questions show that science is not free of conflicts and backlashes, often resulting from excessive extrapolations.Key words: chaos, dynamical systems, entropy, evolution of Science, pattern formation, theoretical biology. E-mail: jose.pontes@uerj.br 1-IntRoDUCtIonAmong the advances and changes brought by science throughout the XX th century, two are, in our point of view, of particular importance and addressed in this work: on one hand, the end of the mechanist determinism, originated from the extrapolation of the achievements of the Newtonian mechanics at the XVII th and XVIII th centuries, and on the other, the end of the apparent incompatibility between biology, where the emergence of ordered structures is a law, and physics, postulating, since the XIX th century a progressive loss of order in natural systems, quantified by an irreversible increase of entropy.We discuss how the diffusion of the determinism principles occurred in the Western civilization, how the extrapolation of these principles beyond the limits of the movement of bodies progressively took place, some conflicts and consequences of that extrapolation, and the new vision we currently have of evolution. We recognize today that the future can be changed and we understand that the onset of both order, with unpredictable features, namely, the onset of the fully new and of the aperiodic

Prevalence of Fibonacci numbers in orbital period ratios in solar planetary and satellite systems and in exoplanetary systems

“…Tsiganis et al, 2005;Batygin et al, 2015;and Tamayo et al, 2017 for the Trappist-1 system) or by tidal transfer from the primary (Peale, 1976). Self-organization processes are found in astrophysics (Aschwanden, 2017; and in many other fields (Aschwanden, 2018;Marov and Kolesnichenko, 2013;Haken, 2006;Feltz et al, 2006;Mishra et al, 1994;Gor'kavyi and Fridman,1991;Krinsky, 1984;Kernbach, 2008;Pontes, 2016). The second aspect is linked to the preferential grouping of period ratios close to irreducible fractions of the type where p and q are small positive integers.…”