I don’t understand this. Your last comment suggests that there may be several key events (some of which may be in the past), but I read your top-level comment as assuming that there is only one, which precludes all future key events (i.e. something like lock-in or extinction). I would have interpreted your initial post as follows:
Suppose we observe 20 past centuries during which no key event happens. By Laplace’s Law of Succession, we now think that the odds are 1⁄22 in each century. So you could say that the odds that a key event “would have occurred” over the course of 20 centuries is 1 - (1-1/22)^20 = 60.6%. However, we just said that we observed no key event, and that’s what our “hazard rate” is based on, so it is moot to ask what could have been. The probability is 0.
This seems off, and I think the problem is equating “no key event” with “not hingy”, which is too simple because one can potentially also influence key events in the distant future. (Or perhaps there aren’t even any key events, or there are other ways to have a lasting impact.)
I don’t understand this. Your last comment suggests that there may be several key events (some of which may be in the past), but I read your top-level comment as assuming that there is only one, which precludes all future key events (i.e. something like lock-in or extinction). I would have interpreted your initial post as follows:
Suppose we observe 20 past centuries during which no key event happens. By Laplace’s Law of Succession, we now think that the odds are 1⁄22 in each century. So you could say that the odds that a key event “would have occurred” over the course of 20 centuries is 1 - (1-1/22)^20 = 60.6%. However, we just said that we observed no key event, and that’s what our “hazard rate” is based on, so it is moot to ask what could have been. The probability is 0.
This seems off, and I think the problem is equating “no key event” with “not hingy”, which is too simple because one can potentially also influence key events in the distant future. (Or perhaps there aren’t even any key events, or there are other ways to have a lasting impact.)