I'm confused. My takeaway was that dice rolls and coin tosses are ergodic because flipping one coin 20 times or flipping 20 coins is meaningfully equivalent. Whereas following an individual person for 1000 days is different from following 1000 people for 1 day.
Is that not the right heuristic?
Also -- why is it called ergodicity? I keep thinking it has something to do with work or thermodynamics, but I'm missing it...
In a sense. Ergodic hypothesis is basically that the phase space is explored "equally" (in a precise sense), over time. Ergodic random processes are pretty much independent of their initial state. So at a hand-wavy level its a very similar idea.
Is that not the right heuristic?
Also -- why is it called ergodicity? I keep thinking it has something to do with work or thermodynamics, but I'm missing it...