Foundations of Science

, Volume 16, Issue 4, pp 331–333 | Cite as

Symmetries and Symmetry-Breakings: The Fabric of Physical Interactions and the Flow of Time

  • Giuseppe Longo


This short note develops some ideas along the lines of the stimulating paper by Heylighen (Found Sci 15 4(3):345–356, 2010a). It summarizes a theme in several writings with Francis Bailly, downloadable from this author’s web page. The “geometrization” of time and causality is the common ground of the analysis hinted here and in Heylighen’s paper. Heylighen adds a logical notion, consistency, in order to understand a possible origin of the selective process that may have originated this organization of natural phenomena. We will join our perspectives by hinting to some gnoseological complexes, common to mathematics and physics, which may shed light on the issues raised by Heylighen.


Symmetries Order Time arrow Groups Semi-groups Logical consistency 


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  1. Bailly, F., & Longo, G. (2006). Mathématiques et sciences de la nature. La singularité physique du vivant, Paris: Hermann (ongoing translation in English. Imperial College Press/World Sci., 2011. see
  2. Heylighen, F. (2010a). The self-organization of time and causality: Steps towards understanding the ultimate origin. Foundations of Science, 15, 4(3), 345–356. doi: 10.1007/s10699-010-9171-1. arXiv:0912.5508v2.
  3. Heylighen, F. (2010b). Symmetry, potentiality and reversibility. Foundations of Science. doi: 10.1007/s10699-010-9211-x. arXiv:0912.5508v2.
  4. Longo, G., Montévil, M. (2011). From physics to biology by extending criticality and symmetry breakings. Progress in Biophysics and Molecular Biology (to appear).Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Dépt. d’InformatiqueCNRS, ENS et CREAParisFrance

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