Punctuated Equilibrium and Belarus

Impossible to stop water boiling by removing a couple of molecules

(Владимир Цеслер, Арт-Сядзіба)

A power law is characterized by the fact that what happens at one scale is exactly the same as what happens at another scale. It’s just twice, or half, as much. Things like earthquakes or forest fires follow a power law, or might follow an approximate power law, because the consequence is scale-free: what happens at a certain size is the same as what’s happening at another, just different, scale.

The idea of scale-free is a very powerful thing in science, and particularly in physics, because that is the distribution that occurs when a system tends to be near some kind of phase transition, the so called transition between system behaviors. 

When you talk about earthquakes or forest fires having distributions of sizes and of events that are characteristic of phase transitions it’s not because they are literally undergoing a transition from one phase to another. They are perpetually stuck between them, agglomerating and dissipating, coalescing and fragmenting