Vlad Tarko — Ergodicity for Dummies (via Lars Syll)

... you obtain two different results: one statistical analysis over the entire ensemble of people at a certain moment in time, and one statistical analysis for one person over a certain period of time. The first one may not be representative for a longer period of time, while the second one may not be representative for all the people. The idea is that an ensemble is ergodic if the two types of statistics give the same result. Many ensembles, like the human populations, are not ergodic.

Lars P. Syll
Ergodicity for Dummies
Vlad Tarko in Statistics & Econometrics, Theory of Science & Methodology

See also On Bayesianism, uncertainty and consistency in “large worlds”