Suppose we treat ourselves as a random sample of intelligent life, and make two observations: first, we’re on a planet that will last for X billion years, and second that we emerged after Y billion years. And we’re trying to figure out Z, the expected time that life would take to emerge (if planet longevity weren’t an issue).
This paper reasons from these facts to conclude that the Z >> Y, and that (as a testable prediction) we’ll eventually find that planets which are much longer-lived than the Earth are probably much less habitable for other reasons, because otherwise we would almost certainly have emerged there.
But it seems like this reasoning could go exactly the other way. In particular, why shouldn’t we instead reason: “We have some prior over how habitable long-lived planets are. According to this prior, it would be quite improbable if Z >> Y, because then we would have almost definitely found ourselves on a long-lived planet.
So what I’m wondering is, what licenses us to ignore this when doing the original bayesian calculation of Z?
We’re not licensed to ignore it, and in fact such an update should be done. Ignoring that update represents an implicit assumption that our prior over “how habitable are long-lived planets?” is so weak that the update wouldn’t have a big effect on our posterior. In other words, if the beliefs “long-lived planets are habitable” and “Z is much bigger than Y” are contradictory, we should decrease our confidence in both; but if we’re much more confident in the latter than the former, we mostly decrease the probability mass we place on the former.
Of course, maybe this could flip around if we get overwhelmingly strong evidence that long-lived planets are habitable. And that’s the Popperian point of making the prediction: if it’s wrong, the theory making the prediction (ie “Z is much bigger than Y”) is (to some extent) falsified.
Thinking out loud:
Suppose we treat ourselves as a random sample of intelligent life, and make two observations: first, we’re on a planet that will last for X billion years, and second that we emerged after Y billion years. And we’re trying to figure out Z, the expected time that life would take to emerge (if planet longevity weren’t an issue).
This paper reasons from these facts to conclude that the Z >> Y, and that (as a testable prediction) we’ll eventually find that planets which are much longer-lived than the Earth are probably much less habitable for other reasons, because otherwise we would almost certainly have emerged there.
But it seems like this reasoning could go exactly the other way. In particular, why shouldn’t we instead reason: “We have some prior over how habitable long-lived planets are. According to this prior, it would be quite improbable if Z >> Y, because then we would have almost definitely found ourselves on a long-lived planet.
So what I’m wondering is, what licenses us to ignore this when doing the original bayesian calculation of Z?
We’re not licensed to ignore it, and in fact such an update should be done. Ignoring that update represents an implicit assumption that our prior over “how habitable are long-lived planets?” is so weak that the update wouldn’t have a big effect on our posterior. In other words, if the beliefs “long-lived planets are habitable” and “Z is much bigger than Y” are contradictory, we should decrease our confidence in both; but if we’re much more confident in the latter than the former, we mostly decrease the probability mass we place on the former.
Of course, maybe this could flip around if we get overwhelmingly strong evidence that long-lived planets are habitable. And that’s the Popperian point of making the prediction: if it’s wrong, the theory making the prediction (ie “Z is much bigger than Y”) is (to some extent) falsified.