determine the thermodynamic behavior [@castellana+bialek_13]. Hints of criticality also are observable in vastly simpler models, which capture the distribution of summed activity in the network but ignore the identity of individual neurons [@simplest].

Discussion
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The traditional formulation of the neural coding problem makes an analogy to a dictionary, asking for the “meaning” of each neural response in terms of events in the outside world [@spikes]. But before we can build a dictionary, we need to know the lexicon, and for large populations of neurons this already is a difficult problem: what is the set of responses that the network actually uses? With 160 neurons, the number of possible responses is larger than the number of words in the vocabulary of a well educated English speaker, and is more comparable to the number of possible short phrases or sentences. In passing from letters to words to sentences, we encounter many features of language that leave an imprint on the probability distribution: the joint distribution of letters in words embodies spelling rules [@stephens+bialek_10], while the joint distribution of words in sentences encodes aspects of grammar [@pereira_00] and semantic categories [@pereira+al_93]. By analogy, the joint distribution of activity among neurons should reveal 