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.

References

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).
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