Another month, another rationality quotes thread. The rules are:
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The example I'm thinking about is a non-random graph on the square grid where west/east neighbors are connected and north/south neighbors aren't. Its density is asymptotically right at the critical threshold and could be pushed over by adding additional west/east non-neighbor edges. The connected components are neither finite nor giant.
If all EW edges exist, you're really in a 1d situation.
Models at criticality are interesting, but are they relevant to epidemiology? They are relevant to creating a magnet because we can control the temperature and we succeed or fail while passing through the phase transition, so detail may matter. But for epidemiology, we know which direction we want to push the parameter and we just want to push it as hard as possible.