Abstract
When we look at biology and ecology, it is surprising to note the role chance plays – often in a subtle alliance with some extremely solid determinisms – in many vital phenomena. The oft-suspected presence of chaotic or intermittent systems, sometimes equated with chance, is also a surprise. Certainly, a no doubt naive viewpoint would lead us to suppose that we need to banish chance and all that is erratic and chaotic if we want things to function properly, the way we try to do in technological systems.
Le hasard a longtemps été nié par l’Église, qui y voyait une insulte aux plans de Dieu. Puis il a été nié par les savants pour qui l’Univers était une mécanique bien huilée. Á la limite, il y avait des lois que nous ne connaissons pas encore.1
Robert Solé
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Notes
- 1.
“The Church long denied the existence of chance, which it took to be an insult to God’s plan.Then its existence was denied by scholars for whom the Universe was a well-oiled machine. At the very worst, there were laws that we did not yet know.” (Translation: AD) Le Monde Littéraire, December 7, 2007, concerning the book Qu’est-ce le hasard? by Denis Lejeune, Éditions Max Milo, 2007.
- 2.
However, sensitivity to initial conditions, which is characteristic of chaotic systems, nevertheless enables us to make short-term previsions and even the least costly changes to the dynamics of such a system. Indeed, as we will see later (cf. Fig. 2.7), at the start two neighbouring trajectories do not immediately diverge. Thus, if we have a good model, it is possible to foresee the state of the chaotic system after a not-too-long interval. This is what meteorologists attempt to do. In the case of technological systems with chaotic behaviours, we can also calculate the impetus needed to arrive, after a while, close to a value chosen beforehand and, thus, to control such a system during short intervals of time. It is easy to imagine the controlling algorithm.
- 3.
It was later shown that these models were the average models for stochastic processes known as Galton-Watson’s branching processes (Galton and Watson, 1874; Lebreton, 1981). We also highlighted the relationships with Aristid Lindenmayer’s formal language theory used to represent shapes and especially morphogenetic processes (Pavé, 1979). A didactic account can be found in Pavé (1994) and in (Thellier, 2004).
- 4.
All too often we still forget that spatial distribution, or, more generally, the shapes that we see – whether they are those of organisms or landscapes or the distribution of vegetation over the continents or even the continents themselves – are the result of temporal processes (Schmidt-Lainé and Pavé, 2002). These shapes change over time at variable speeds. Bergson said: “Toute forme a son origine dans le mouvement qui la trace. La forme n'est que le mouvement enregistré.” This phrase, cited in the article by Yves Souchon et al. (2002), concerns the shape of a river “All shapes originate in movement. The shape itself is just a record of that movement” (Translation: AD). Depending, however, on the scale of observation, the organisational level considered and the nature of the processes, these changes might be overlooked; for example, if we look at continental vegetation over a scale that varies from decades to a millennium, we might overlook continental drift. This is no longer true if we are working in paleoecology over a scale of millions of years.
- 5.
“Les incertitudes sur les deux variables “conjuguées” p et q [comme la vitesse et la quantité de mouvement] ne sont pas indépendantes. On ne peut pas poursuivre la détermination de l’une d’elles avec une précision croissante sans rendre par la même de plus en plus grande l’erreur portant sur l’autre. À la limite, une précision absolue dans la localisation de la particule correspondrait donc à une quantité de mouvement complètement indéterminée, et réciproquement. Il est donc impossible de définir ici, d’une façon qui ait un sens théorique, “l’état initial” du mouvement d’une particule d’une façon qui permette la prévision selon le schéma déterministe de la mécanique classique. ”
- 6.
Sir Ronald Fisher, no doubt one of the most renowned statisticians of the twentieth century, carried out a large part of his studies starting from such examples. He was also a population geneticist and one of the first authors of the synthetic theory of evolution (cf. 2.5). He spent much of his career working at the Rothamsted Experimental Station in Great Britain.
- 7.
- 8.
For a presentation of genetic algorithms, we can refer, for example, to the sites: http://www2.toulouse.inra.fr/centre/esr/CV/bontemps/WP/AlgoGene.html or http://www.rennard.org/alife/french/gavintr.html. The second site also presents information on cellular automatons, artificial life, etc. All are good examples of “bio-inspired” information technology.
- 9.
Today, based on arguments coming principally from the molecular analysis of parts of genomes, three reigns are proposed: Archaens, Bacteria and eukaryotes. Classification methods lead to a tree with a single root, which may correspond to a hypothetical ancestor named LUCA (Last Universal Common Ancestor).
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Pavé, A. (2010). Questioning Chance. In: On the Origins and Dynamics of Biodiversity: the Role of Chance. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6244-7_1
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