If that’s right, what’s the basis for saying that “descendent civilizations” are not in my reference class and I shouldn’t consider them in my anthropic update...
This is an assumption made by the paper: it assumes that the prior on us being a descendant civilization is low. If your point is that rejecting this leads to the central conclusions of the paper falling apart, that’s a correct assessment.
...but “civilizations that start when the universe is 1 trillion years old” are in my reference class and I should consider them in my anthropic update?
Think of it as you having a prior over the time at which a grabby alien civilization will arrive on Earth for the first time from a different point of origin. Conditional on any such time T, our likelihood of having arrived when we have is
tn∫T0xndx∼tnTn+1
with support T≥t. You can now use this likelihood for a Bayesian update over your prior for T.
Just to illustrate this, suppose you start with a scale-invariant improper prior p(T)∼1/T - scale invariance is desirable when we’re completely agnostic about the timescales involved. Bayesian update with n hard steps takes us to a posterior ∼1/Tn+2 supported on T≥t, and computing the expected value of T gives
∫∞tdT/Tn+1∫∞tdT/Tn+2=(n+1)tn=t+tn
In other words, with the roughly n=10 hard steps that Hanson takes in his paper and t≈1.36×1010 years, grabby aliens should arrive on Earth within roughly 1.36 billion years in expectation.
Hanson does something in the same spirit but different: he matches the median (he can do it for any percentile, but the central result is the one coming from the median) of the distribution of our arrival time directly with T minus how long the grabby aliens would have to travel to get here. This seems reasonable but there’s no formal justification for it as far as I can see. The Bayesian approach, however, doesn’t raise any problems of anthropic reference classes and gives more or less the same answer.
This is an assumption made by the paper: it assumes that the prior on us being a descendant civilization is low. If your point is that rejecting this leads to the central conclusions of the paper falling apart, that’s a correct assessment.
Think of it as you having a prior over the time at which a grabby alien civilization will arrive on Earth for the first time from a different point of origin. Conditional on any such time T, our likelihood of having arrived when we have is
tn∫T0xndx∼tnTn+1
with support T≥t. You can now use this likelihood for a Bayesian update over your prior for T.
Just to illustrate this, suppose you start with a scale-invariant improper prior p(T)∼1/T - scale invariance is desirable when we’re completely agnostic about the timescales involved. Bayesian update with n hard steps takes us to a posterior ∼1/Tn+2 supported on T≥t, and computing the expected value of T gives
∫∞tdT/Tn+1∫∞tdT/Tn+2=(n+1)tn=t+tn
In other words, with the roughly n=10 hard steps that Hanson takes in his paper and t≈1.36×1010 years, grabby aliens should arrive on Earth within roughly 1.36 billion years in expectation.
Hanson does something in the same spirit but different: he matches the median (he can do it for any percentile, but the central result is the one coming from the median) of the distribution of our arrival time directly with T minus how long the grabby aliens would have to travel to get here. This seems reasonable but there’s no formal justification for it as far as I can see. The Bayesian approach, however, doesn’t raise any problems of anthropic reference classes and gives more or less the same answer.