Introduction

During the Cerisy week that we organized in 2016, on the theme of Sciences de la vie, sciences de l'information (Gaudin et al. 2018; Life Sciences, Information Sciences), many questions were raised about the role of chance in the development and evolution of living beings. With the aim of further investigating this very specific question, that is, the role of chance in life, we once again invited eminent specialists in life, evolution, physics, probability and philosophy to Cerisy, during the week of August 29 to September 5, 2019.

This book is a collation of the main contributions presented on this occasion. In the first part, "Randomness in all of its Aspects", we will try to identify the concept in its various avatars. This part begins with a presentation by Cristian S. Calude and Giuseppe Longo who distinguish, from a scientific and philosophical point of view, the three generally recognized types of chance: "Common, Biological and Quantum Randomness". We can define common chance as either: the meeting of two independent chains of causality; or, as an event for which we ignore the causality or for a law which we know is very sensitive to small disturbances, disturbances which as Calude and Longo discuss, may in fact exist below the sensitivity threshold of our measuring instruments. This sensitivity to small initial disturbances leads to chaos in the mathematical sense of the term, and was illustrated at Cerisy by the screening of Etienne Ghys's videos, as commented on by Grégory Miermont. For his part, Gilles Pagès presents the point of view of the probabilist, who does not acknowledge chance, only probabilities. He also reminds us of the importance of the Monte-Carlo method, which consists of the creation of randomness through computer simulations, and shows us that the process by which mathematician-computer scientists "draw random numbers" is not so simple. Pagès goes on to echo Paul Lévy's declaration: "Nature ignores chance". In a very enlightening talk on the historical and etymological origins of words, Clarisse Herrenschmidt checks this statement by reminding us that many languages have made an allocation for the concept of chance and have found words to express it.

Niels Bohr's interpretation of quantum physics has continued to engage, even scientists, by introducing what seems to be an intrinsic probability. This helped to inspire an article by François Vannucci on wave-particle duality: quantum randomness but statistical determinism. Einstein never really accepted indeterminacy and we see that the challenge to "Bohrian" indeterminism continues; this was illustrated by a disturbing presentation by Stéphane Douady. This indeterminacy extends to astrophysics and the theory of multiple universes, as we will discover from the inspired pen of Michel Cassé.

Does chance govern our decisions? Mathias Pessiglione explains how and why the brain does not maximize an expected utility. Nonetheless, reflecting on this further, he explains the mechanism of random decision-making in the brain, thereby posing the question of free will. Chance as divine intervention, as has often been suggested, could be another name for the hand of God when he does not want to reveal himself. This naturally leads to philosophical and poetic reflections before moving on to the second part of this account, devoted to biology and evolution. We will therefore focus on the meaning of life as captured by the poetic intelligence of Georges Amar, on a meandering path from Hölderlin to William of Ockham and Spinoza, passing many poets, including Rimbaud, Baudelaire and many others. "Le hasard et le divin" (Chance and the Divine) is the apt title chosen by Bertrand Vergely to share with us his thoughts on randomness, necessity and inner life, culminating in a passage on chance and Grace. This first part will end with a semantic exploration of the words "chance" and "creation", as guided by Ivan Magrin-Chagnolleau who defines himself as an "artist-researcher". Beyond semantics, he invites us to reflect on the links between randomness and artistic creation. Randomness is the only source of creation in genetics, as per Jacques Monod's vision. However, forms may require subjectivity to exist in order for them to work. This brings us to the tipping point, or kairos, alluded to by Bertrand Vergely, a moment in which the artist and the researcher has but a split second in which to grab it by the horns.

In the second part, "Randomness, Biology and Evolution", we begin with the topical subject of epigenetics, through a brilliant chapter by David Sitbon and Jonathan B. Weitzmann. The latter very clearly defines the pathways of randomness in sexual reproduction, in terms of the pairing of alleles and mutations. They also explain the role of chromatin in gene expression, and how the environment is involved in this epigenetic process. In a well-documented article, Bernard Dujon explains how genes are exchanged between neighboring species, or more distantly, during a horizontal transfer. This process is well known in prokaryotes, in particular through the introduction of foreign DNA using retroviruses (a process used in gene therapy). In contrast, the extent of this phenomenon in multicellular eukaryotes is only just beginning to be understood. The acquisition of genes by horizontal transmission justifies the title: "Quand l'acquis devient héréditaire" (When Acquisition becomes Hereditary). The link between the environment and randomness becomes obvious when one considers that this horizontal acquisition results from encounters, of a random nature, within a given biotope (i.e. the role of environment).

From reproduction to evolution, it is but a step to join Philippe Grandcolas as he tries to show that evolution does not happen completely at random. Evolutionary pressure and the environment constrain evolution. Philippe Grandcolas discusses the significance of adaptive pressure and specific inheritance. By analyzing the notions of convergence and parallelism, as well as the presentation of some evolutionary experiments, Philippe Grandcolas qualifies Gould's examination on the eventual "replay" of evolution.

With Amaury Lambert, we remain in the field of evolution and focus, more precisely, on the transition from genotype to phenotype in terms of the constraints of Waddington's1 epigenetic landscape. After distinguishing between the different types of randomness in evolution, Lambert models how the phenotype can resist genetic hazards, thereby providing a precise meaning for the notion of "canalization" as introduced by Waddington. From this standpoint, it becomes normal to wonder whether the emergence of life is the result of random chance. Asking himself this question, Antonio Lazcano gives us a remarkably well-sourced contribution on the history of scientific ideas pertaining to the origins of life, which leads to the conclusion, already glimpsed by Mayr2, that biology cannot be reduced to physics and chemistry since "Nothing in biology makes sense, except in the light of evolution"3. Therefore, we can qualify biology as a "historical science". Like history, evolution has its constraints and its own contingency, and therefore, very probably, random chance played a part in the emergence of life. Establishing this, however, brings about the question, is evolution naturally accompanied by an increase in complexity and an increase in biodiversity?

This question is asked by Jean-Paul Delahaye. To try and give a precise meaning to this question, Jean-Paul Delahaye reminds us of the notions of Kolmogorov computational complexity and Benett structural complexity4. Like the Universe, which tends to become increasingly complex in the sense of Benett, Jean-Paul Delahaye hypothesizes that evolution is likewise a process that tends toward complexification, one that sometimes backtracks on itself with the result of it being erased. The growing complexity of living things is reflected upon in terms of biodiversity. There seems to be a certain human attraction to complexity, in particular by living organisms, a tropism that opens the door for a discussion on the ethics of organized complexity and it is along this line of questioning that Jean-Paul Delahaye, by way of recommendation, brings about his conclusion.

The purpose of this introduction is to give a brief overview on the richness of this work. From mathematics to the humanities, by way of biology, there are many questions and concepts linked to randomness to uncover. The contributions gathered here have the advantage of presenting the latest scientific results in a synthesized form, and with an abundant bibliography, that will serve both researchers and doctoral students. Yes, randomness is a part of life, evolution and reproduction, but always under certain constraints; importantly, according to the vision of quantum physics, individual randomness does not deter statistical determinism. This is a vast subject for multidisciplinary reflection that speaks to the irreducible individuation of man in a Universe that is increasingly explained and statistically deterministic.

Acknowledgments

This week could not have happened without the understanding of the many working colleagues and their laboratories, who carried some of the cost. We would like to thank EDF Île-de-France for the support given to the association of friends of Cerisy-Pontigny, which made it...