the same movie, and in this surrogate data the probability of the whole network remaining silent changes slightly, but this change is ten times larger than the standard error in the measurement. Conditional independence thus is excluded, based just on this one statistic, with a likelihood ratio of more than ten thousand (Appendix \[cond\_ind\], Fig \[silence\]). Apart from these arguments, experiments show that electrically evoked spikes in retinal ganglion cells feed back into the retinal circuitry via electrical synapses and modulate the response of other ganglion cells to visual input [@asari+meister_12]. This is a direct demonstration that retinal ganglion cells are not conditionally independent encoders of their visual input, as are the more common measurements of “noise correlations” between ganglion cells [@mastronarde_83; @brivanlou+al_98; @field+chichilnisky_07].

In interacting models that are equivalent to a collection of independent spins responding to a fluctuating field, criticality usually requires that the distribution of fluctuations be very special, e.g. with the variance tuned to a particular value. In this sense, saying that correlations result from fluctuating inputs wouldn’t really “explain” our observations. Recently, it has been suggested that sufficiently broad distributions of fluctuations might lead more generically to critical phenomenology [@schwab+al_13], but this argument requires that 