Thread by @DellAnnaLuca

THE HIDDEN SIDE OF NON-ERGODICITY

Most examples of non-ergodicity are activities in which the outcome of a person completing them many times is lower than the outcome of many people completing it once. For example, Russian Roulette.

But there are cases in which its higher.

1/9

2/ First, if you don’t know about ergodicity, I suggest reading this thread:

https://twitter.com/dellannaluca/status/1339621378765537282

3/ One classic example of non-ergodicity is Russian Roulette. The expected outcome of 600 people playing it once is 100 dead and 500 winners, whereas the outcome of a single person playing it 100 times is 1 dead and no winner.

4/ However, there are activities with an opposite effect. The outcome of 100 people cooking one tart for the first time is 100 terrible tarts, whereas the outcome of one person cooking 100 tarts is a 5 terrible tarts (at the beginning) and 95 great tarts (once learning kicks in).

5/ Why? And why does it matter?

6/ One interpretation of the field of ergodicity is that it concerns itself with the study of the “phantom consequences” of actions, that do not matter if the action is performed once but affect the *next* time it is performed.

https://twitter.com/dellannaluca/status/1339621397358915589?s=21

7/ For example, if a skier breaks his leg in a race, the consequences are “only” pain and losing the race. But in the context of a championship there’s an additional consequence: losing all future races (because he cannot participate). This is the phantom consequence.

8/ Similarly, if I cook a tart and it’s the only time in my life I will ever cook one, the fact that I learned how to make better tarts is irrelevant. A “phantom consequence”.

But if cooking more tarts is a possibility, then the learning becomes a real and valuable consequence.

9/ Hence, in all cases in which repeated actions are a possibility, it’s important to consider “phantom consequences” that are impossible to observe by studying a single action in a vacuum.

10/ Also, for completeness:

https://twitter.com/dellannaluca/status/1339560980267888641

11/ By the way, a new review of my book "Ergodicity: Definition, Examples, And Implications, As Simple As Possible" (copies on gum.co/ergodicity)