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This paper proposes a systemic perspective for some aspects of both phylogenesis and ontogenesis, in the light of the notion of " biological organization " as negative entropy, following some hints by Schrödinger. To this purpose, we introduce two extra principles to the thermodynamic ones, which are (mathematically) compatible with the traditional… (More)

Deuxième point : la méthode. Les concepts de temps et d'espace pris en compte par nos mathématiques ont été conçus à partir d'un enracinement dans des problèmes propres aux sciences physiques. Il n'est pas étonnant qu'il faille les réviser : l'approche méthodologique des auteurs consiste en une révision critique à la fois historique et généalogique des… (More)

- Francis Bailly, Giuseppe Longo
- Mathematical Structures in Computer Science
- 2007

This paper is a conceptual analysis of the role of the mathematical continuum vs. the discrete in the understanding of randomness, as a notion with a physical meaning or origin. The presentation is " informal " , as we will not write formulas; yet, we will refer to non-obvious technical results from various scientific domains. And we will propose a… (More)

- Francis Bailly, Giuseppe Longo, Mael Montevil
- Progress in biophysics and molecular biology
- 2011

This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of life, such as rhythms, both physical (circadian, seasonal...) and properly biological (heart beating, respiration,… (More)

1. Introduction The foundational analysis of mathematics has been strictly linked to, and often originated, philosophies of knowledge. Since Plato and Aristotle, to Saint Augustin and Descartes, Leibniz, Kant, Husserl and Wittgenstein, analyses of human knowledge have been largely endebted to insights into mathematics, its proof methods and its conceptual… (More)

- Giuseppe Longo, F. Bailly
- 2007

The notions of " construction principles " is proposed as a complementary notion w.r. to the familiar " proof principles " of Proof Theory. The aim is to develop a parallel analysis of these principles in Mathematics and Physics : common construction principles, in spite of different proof principles, justify the effectiveness of Mathematics in Physics. The… (More)

1. Introduction The foundational analysis of mathematics has been strictly linked to, and often originated, philosophies of knowledge. Since Plato and Aristotle, to Saint Augustin and Descartes, Leibniz, Kant, Husserl and Wittgenstein, analyses of human knowledge have been largely endebted to insights into mathematics, its proof methods and its conceptual… (More)

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