The renormalization group teaches us that we can describe macroscopic phenomena with models that are simpler and more universal than the underlying microscopic mechanisms.  Can we construct similar paths to simplification in biological systems?  After summarizing some of the obvious reasons for pessimism, I will describe efforts that my colleagues and I have made to systematically coarse-grain the patterns of activity that are observed, experimentally, in a real network of neurons (the mouse hippocampus).  We find that distributions of coarse-grained variables approach a fixed, non-Gaussian form as the coarse-graining scale is increased, and along this trajectory we see scaling of both static and dynamic quantities.  Scaling is precise across two decades, and exponents are reproducible, sometimes to the second decimal place.    All of this suggests that the dynamics of these networks are described by a non-trivial fixed point.

This is joint work with CD Brody, JL Gauthier, L Meshulam, and DW Tank.