of the experiment; a small segment of the data is shown in Fig \[fig1\]B. Importantly, our experiments monitored a substantial fraction of the RGCs in the area of the retina from which we record, capturing the behavior of an almost complete local population responsible for encoding a small patch of the visual world. The experiment collected a total of $\sim 2\times 10^6$ spikes, and time was discretized in bins of duration $\Delta\tau = 20\,{\rm ms}$; for each neuron ${\rm i}$, $\sigma_{\rm i}=1$ in a bin denotes that the neuron emitted at least one spike, and $\sigma_{\rm i}=0$ that it was silent.

Counting states
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Conceptually, estimating the function $n(E)$ and hence the entropy vs energy is easy: we count how often each state occurs, thus estimating its probability, and then count how many states have (log) probabilities in a given range. In Fig \[fig1\]C and D we show the first steps in this process. We identify the unique patterns of activity—combinations of spiking and silence across all 160 neurons—that occur in the experiment, and then count how many times each of these patterns occurs.

Even without trying to compute $S(E)$, the results of Fig \[fig1\]D are surprising. With $N$ neurons 