= \sum_{{\rm i}=1}^N \sigma_{\rm i}$ counts the number of neurons that spike simultaneously, and $Z$ is set to insure normalization. All of the parameters $\{h_{\rm i},\, J_{\rm ij},\, V(K)\}$ are determined by the measured averages $\{\langle \sigma_{\rm i}\rangle,\, \langle \sigma_{\rm i}\sigma_{\rm j}\rangle,\, P(K)\}$.

This model accurately predicts the correlations among triplets of neurons (Fig 7 in [@tkacik+al_14a]), and the probability of spiking in individual neurons depends on the pattern of activity in the rest of the population as the model predicts (Fig 9 in [@tkacik+al_14a]). One can even predict the time dependent response of single cells from the behavior of the population, without reference to the visual stimulus (Fig 15 in [@tkacik+al_14a]). Most important for our present discussion, we have checked that the distribution of the energy $E (\{\sigma_{\rm i}\})$ across the patterns of activity that occur in the data agrees with the distribution predicted by the model, deep into the tail of patterns that occur only once in the two hour long experiment (Fig 8 in [@tkacik+al_14a]). This distribution is very closely related to the plot of entropy vs energy that we would like to construct, and so the agreement with experiment gives us confidence.

The direct counting of 