Perspectives on Organisms

Biological time, Symmetries and Singularities

  • Giuseppe Longo
  • Maël Montévil

Part of the Lecture Notes in Morphogenesis book series (LECTMORPH)

Table of contents

  1. Front Matter
    Pages 1-15
  2. Giuseppe Longo, Maël Montévil
    Pages 1-22
  3. Giuseppe Longo, Maël Montévil
    Pages 23-73
  4. Giuseppe Longo, Maël Montévil
    Pages 75-97
  5. Giuseppe Longo, Maël Montévil
    Pages 99-119
  6. Giuseppe Longo, Maël Montévil
    Pages 121-136
  7. Giuseppe Longo, Maël Montévil
    Pages 137-160
  8. Giuseppe Longo, Maël Montévil
    Pages 161-185
  9. Giuseppe Longo, Maël Montévil
    Pages 187-213
  10. Giuseppe Longo, Maël Montévil
    Pages 249-258
  11. Back Matter
    Pages 259-282

About this book


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.


Allometric Laws Biological Evolution Biological Rhythms Biological Time Darwin’s Evolution Gould’s Analysis Phenotypic Complexity Symmetry in Biology Theoretical Biology

Authors and affiliations

  • Giuseppe Longo
    • 1
  • Maël Montévil
    • 2
  1. 1.Centre Interdisciplinaire Cavaillès (CIRPHLES)CNRS and Ecole Normale SupérieureParisFrance
  2. 2.Anatomy and Cell BiologyTuft UniversityBostonUSA

Bibliographic information