shown in Fig \[alpha\_fig\]C. Corresponding to the variations in $S(E)$ shown in Fig \[alpha\_fig\]B, we see in Fig \[alpha\_fig\]D that there is a peak in the specific heat of the model ensemble near $\alpha=1$. As we look at larger and larger networks, this peak rises and moves toward $\alpha = 1$, which describes the real system.

Couldn’t it just be ... ?
=========================

In equilibrium thermodynamics, poising a system at a critical point involves careful adjustment of temperature, pressure, and other parameters. Finding that the retina seems to have poised itself near criticality should thus be treated with some skepticism. Here we consider some of the pitfalls that might mislead us into thinking that the system is critical when it is not; see also Appendix \[app:alt\].

Part of our analysis is based on the use of maximum entropy models, and one could worry that the inference of these models is unreliable for finite data sets [@mastromatteo+marsili_11; @marsili+al_13]. Expanding on the discussion in Ref [@tkacik+al_14a], we can show that signatures of criticality, such as the peak in specific heat, are not the result of over fitting to a limited data set. As an example, we see a clear peak in the 