Here’s the essence of non-ergodicity: the “typical” result (technically the mode, but practically the median is acceptable) is very different from the “mean” re

Here’s the essence of non-ergodicity: the “typical” result (technically the mode, but practically the median is acceptable) is very different from the “mean” result. The language of “time” -vs- “ensemble” averages is simply about whether to include only the “typical” possibilities or to also include corner cases which have extremely low probability but extremely high payoffs. The technical point is that unless you get to play the game (“sample the process”) absurdly many times (comparable to the total number of possibilities), you will never access the corner cases, and so the averaging over the “typical” results corresponds better to reality. The “mixing” idea means that if you run the process “long enough” then there won’t be any corner cases — the extreme possibilities will thoroughly mix with the typical possibilities, so both kinds of averaging will lead to the same (correct) answer. If you grok this, everything else is technical detail and window dressing.