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Giuseppe Longo
École Normale Supérieure
  1. Marriages of Mathematics and Physics: A Challenge for Biology.Arezoo Islami & Giuseppe Longo - 2017 - Progress in Biophysics and Molecular Biology 131:179-192.
    The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical (...)
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  2.  91
    From Physics to Biology by Extending Criticality and Symmetry Breakings.Giuseppe Longo & Maël Montévil - 2011 - Progress in Biophysics and Molecular Biology 106:340 - 347.
    Symmetries play a major role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century. Herein, we briefly review their role by recalling how symmetry changes allow to conceptually move from classical to relativistic and quantum physics. We then introduce our ongoing theoretical analysis in biology and show that symmetries play a radically different role in this discipline, when compared to those in current physics. By this comparison, we stress that (...)
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  3.  89
    A 2-Dimensional Geometry for Biological Time.Francis Bailly, Giuseppe Longo & Maël Montévil - 2011 - Progress in Biophysics and Molecular Biology 106:474 - 484.
    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, metabolic …). In particular, the role of biological rhythms do not seem to have any counterpart in mathematical formalization of physical clocks, which are based on frequencies along the usual (...)
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  4.  58
    The Inert Vs. The Living State of Matter: Extended Criticality, Time Geometry, Anti-Entropy - An Overview.Giuseppe Longo & Maël Montévil - 2012 - Frontiers in Physiology 3:39.
    The physical singularity of life phenomena is analyzed by means of comparison with the driving concepts of theories of the inert. We outline conceptual analogies, transferals of methodologies and theoretical instruments between physics and biology, in addition to indicating significant differences and sometimes logical dualities. In order to make biological phenomenalities intelligible, we introduce theoretical extensions to certain physical theories. In this synthetic paper, we summarize and propose a unified conceptual framework for the main conclusions drawn from work spanning a (...)
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  5.  64
    Protention and Retention in Biological Systems.Giuseppe Longo & Maël Montévil - 2011 - Theory in Biosciences 130:107-117.
    This article proposes an abstract mathematical frame for describing some features of cognitive and biological time. We focus here on the so called “extended present” as a result of protentional and retentional activities (memory and anticipation). Memory, as retention, is treated in some physical theories (relaxation phenomena, which will inspire our approach), while protention (or anticipation) seems outside the scope of physics. We then suggest a simple functional representation of biological protention. This allows us to introduce the abstract notion of (...)
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  6.  36
    Randomness Increases Order in Biological Evolution.Giuseppe Longo & Maël Montévil - 2012 - In M. Dinneen, B. Khoussainov & A. Nies (eds.), Computation, Physics and Beyond. Berlin Heidelberg: pp. 289-308.
    n this text, we revisit part of the analysis of anti-entropy in Bailly and Longo (2009} and develop further theoretical reflections. In particular, we analyze how randomness, an essential component of biological variability, is associated to the growth of biological organization, both in ontogenesis and in evolution. This approach, in particular, focuses on the role of global entropy production and provides a tool for a mathematical understanding of some fundamental observations by Gould on the increasing phenotypic complexity along evolution. Lastly, (...)
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