Cambiamenti di simmetrie ed aleatorio: dalla fisica alla biologia

Giuseppe Longo (Centre Cavaillès, CNRS - Ecole Normale Supérieure, Paris)
22/11/2013 - 11:00
Dipartimento di Matematica e Fisica: aula seminari 311, edificio C, Largo San Leonardo Murialdo 1, 00146 Roma.

Symmetries play a major role both in the origin and the foundations of Geometry and of physics. Their relevance extended up to the modern interactions between mathematics and physics, in particular since the work by E. Noether and H. Weyl in the first half of last century. We will briefly hint to their impact and then introduce our ongoing theoretical analysis in biology. In this discipline, symmetries play a radically different role. In particular, the dynamics of biological organisms, in their various levels of organization, are not “just” processes, but permanent (extended, in our terminology) critical transitions and, thus, symmetry changes. Within the limits of a relative structural stability (or interval of viability), variability is at the core of these transitions. If time allows, we discuss the novel notion of ”enablement” and restrict causal analyses to differential cases (a difference that causes a difference). Mutations or other causal differences will allow us to stress that ”non conservation principles” are at the core of evolution, in contrast to physical (equilibrium or stationary) dynamics, largely based on conservation principles as symmetries.


Francis Bailly, Giuseppe Longo. Mathematics and Natural Sciences. The physical singularity of life phenomena. Imperial College, 2011.

G. Longo, M. Montévil, Perspectives on Organisms: Biological Time, Symmetries and Singularities, Springer, 2013 (in print).
Downloadable from :

Buiatti M. , Longo G. Randomness and Multi-level Interactions in Biology. In Theory of Biosciences, vol. 132, n. 3:139-158, 2013.

Giuseppe Longo, Maël Montévil. Randomness Increases Order in Biological Evolution. Invited paper, conference on ''Computations, Physics and Beyond'', Auckland, New Zealand, February 21-24, 2012; LNCS volume (Dinneen et al. eds), Springer, 2012 (revised for the S. J. Gould Conference, Venice, 2012).

Longo G., Palamidessi C., Paul T.. Some bridging results and challenges in classical, quantum and computational randomness. In "Randomness through Computation", H. Zenil (ed), pp. 73–92, World Sci., 2010.