On the ubiquity of power law behavior

The signature of power law behavior (short things are more probable than long ones in a predictable way) is often used as a benchmark (for instance, of a system poised at criticality).

In that pursuit, many remind us that we need to be mindful that all sorts of (not very remarkable). things can have that signature. One of the most colorful illustrations I've read is this one here:

Some Effects of Intermittent Silence

George A. Miller

1957

Imagine that a monkey hits the keys of a typewriter at random, subject only to these constraints: (1) he must hit the space bar with a probability of p() and all the other keys with a probability of p(L) = 1 - P() and (2) he must never hit the space bar twice.

Word length will fall off with power law behavior.