that can either spike or remain silent, there are $2^N$ possible states. We know that not all these states can be visited equally often, since spikes are less common than silences, but even taking account of this bias, and trying to capture the correlations among neurons, our best estimate of the entropy for the patterns of activity we observe is $S\sim 0.15\,{\rm bits}/{\rm neuron}$ (see below). With $N=160$ cells, this is a total entropy of $S = 24\,{\rm bits}$, which means that the patterns of activity are spread over $2^S \sim 1.67\times 10^7$ possibilities. This is one hundred times larger than the number of samples that we collect during our experiment. Indeed, most of the states that we see in the full population occur only once. But roughly one thousand states occur with sufficient frequency that we can make a reasonable estimate of their probability just by counting across the $\sim 2\,{\rm hrs}$ of the experiment. Thus, the probability distribution $P({\mathbf \sigma})$ is extremely inhomogeneous.

To probe more deeply into the long tail of low probability events, we can construct models of the distribution of states. As described in detail elsewhere [@tkacik+al_14a], we have done this using the maximum entropy 