Giuseppe Longo

The first part of this paper highlights some key aspects of the differences in the use of mathematical tools in physics and in biology. Scientific knowledge is viewed as a network of interactions, some than as a hierarchically organized structure where mathematics would display the essence of phenomena. The concept of "unity" in the biological phenomenon is then discussed. In the second part, a foundational issue in mathematics is revisited, following recent perspective in the physiology of action. The relevance of the historical formation of mathematical concepts is stressed in several parts

We propose a reflection on the construction of scientific knowledge and in so doing an image of this knowledge. This will allow us to develop a comparative analysis of some of the main principles underpinning the constitution of the different sciences. We will highlight the role of critical thought in science, or even “negative results,” which pose limits and hence open new trajectories. In particular, we will address a misleading point of view, based on some informal concepts taken from computer science, which dominates the biological imaginary. An “ethics of knowledge” will follow, as a critical and open perspective, capable of taking on the well-intentioned responsibility of proposing universal, though not absolute, principles of knowledge.

La cognition humaine paraît étroitement liée à la structure de l'espace et du temps relativement auxquels le corps, le geste, l'intelligibilité semblent devoir se déterminer. Pourtant, ce qui, après les approches physico-mathématiques de Galilée et de Newton, fut caractérisé par Kant comme formes de l'intuition sensible, n'a cessé au cours des siècles qui suivirent de se trouver remis en cause dans leur saisie première par les développements théoriques. En mathématiques d'abord, avec les géométries non-euclidiennes, en physique ensuite, où relativité générale puis théories quantiques et critiques ont dû remanier profondément l'objectivité de ces concepts pour en faire des catégories, certes toujours aussi essentielles, mais de plus en plus contre-intuitives, et maintenant en biologie où la temporalité, notamment, et la causalité se révèlent largement différentes de celles de la physique. C'est ce que nous tentons de présenter et de discuter dans ce texte en vue d'en dégager la pertinence pour la cognition elle-même.

This authored monograph introduces a genuinely theoretical approach to biology. Starting point is the investigation of empirical biological scaling including their variability, which is found in the literature, e.g. allometric relationships, fractals, etc. The book then analyzes two different aspects of biological time: first, a supplementary temporal dimension to accommodate proper biological rhythms; secondly, the concepts of protension and retention as a means of local organization of time in living organisms. Moreover, the book investigates the role of symmetry in biology, in view of its ubiquitous importance in physics. In relation with the notion of extended critical transitions, the book proposes that organisms and their evolution can be characterized by continued symmetry changes, which accounts for the irreducibility of their historicity and variability. The authors also introduce the concept of anti-entropy as a measure for the potential of variability, being equally understood as alterations in symmetry. By this, the book provides a mathematical account of Gould's analysis of phenotypic complexity with respect to biological evolution. The target audience primarily comprises researchers interested in new theoretical approaches to biology, from physical, biological or philosophical backgrounds, but the book may also be beneficial for graduate students who want to enter this field.

Dans la mythologie grecque, Prométhée - le 'prévoyant' - déroba le feu aux dieux et le transmit aux hommes. Zeus, courroucé par ce transfert technologique, condamna Prométhée à un châtiment itéré à l'identique, à l'infini, algorithmique. Le problème que pose l'ancien mythe est celui des limites de la connaissance. En termes modernes, jusqu'à quel point pouvons-nous transformer la nature sans une connaissance des conséquences de nos actions sur elle? Cette question nous pousse à analyser les limites des sciences : à une techno-science devenue toujours plus invasive, la science répond en se donnant à elle-même des limites"--Page 4 of cover.

The rich blend of theories and experiences that made the history of physics possible still now enlightens the scientific method. We stress the need to learn from this method the force of making its principles explicit, while developing a rich diversity of theories, which are often incompatible. Unity is preserved by common founding principles and their mathematical form, such as the understanding of conservation properties (energy, momentum etc.) in terms of symmetries. When moving from the inert to the living state of matter, new challenges are posed, beginning with biological “heterogenesis”, as “genesis of and from diversity” in a changing space of pertinent observables and parameters: the Darwinian ecosystem. The question that is posed is how we may consistently embed the theories of the inert into biology. By naturalization we mean an analysis of physics as part of the sciences of nature, not as the science governing them all. In particular, the founding symmetry principles of physical theories, often used to “naturalize” (but, actually, to “physicalize”) other sciences, will instead be framed in more general dynamics which deal with fundamental changes of symmetries, as they apply, in our views, in all historical sciences, beginning with biology. This paper will accordingly explore the notion of (non-)conservative extension of theories in a precise mathematical sense. We stress a perspectival epistemology that promotes a dialogue of theories, in search for bridges or even unity, inspired by the method of “unification” at the core of major theoretical inventions in physics. Our main motivation is the need to go beyond the strong dualistic separation of space (or of the more general “phase space”) as a pre-given container of the dynamics of matter, that biased physics from Aristotle to Newton and, in a technically different way, even Einstein.

Zalamea’s book is as original as it is belated. It is indeed surprising, if we give it a moment’s thought, just how greatly behind schedule philosophical reflection on contemporary mathematics lags, especially considering the momentous changes that took place in the second half of the twentieth century. Zalamea compares this situation with that of the philosophy of physics: he mentions D’Espagnat’s work on quantum mechanics, but we could add several others who, in the last few decades, have elaborated an extremely timely philosophy of contemporary physics (see for example Bitbol 2000; Bitbol et al. 2009). As was the case in biology, philosophy – since Kant’s crucial observations in the Critique of Judgment, at least – has often “run ahead” of life sciences, exploring and opening up a space for reflections that are not derived from or integrated with its contemporary scientific practice. Some of these reflections are still very much auspicious today. And indeed, some philosophers today are saying something truly new about biology...

The ongoing MOOC revolution is bound to change the academic world on an unprecedented scale. It is in fact very likely that in the coming decades universities all over the world will shrink in size and number, while professors will assume more and more the role of specialized tutors looking after lectures delivered by a small number of world known academic “superstars”. In what follows we shall analyze some aspect of the phenomenon, focusing on the reasons why, like it or not, the academic world cannot avoid a radical rethinking of its role and goals.