No, it wouldn’t change anything in the paper because we’re not such a civilization and so our arrival time wouldn’t be sampled from the arrival time of descendant civilizations.
What would change it is if there is actually a chance that we’re a descendant civilization ourselves; that is, we’re currently in an area of space which has already been colonized by a grabby alien civilization. In this case it’s indeed true that every result in the paper would radically change.
I look around me and make two observations: (1) I observe that I am not a member of a “descendent civilization” (i.e., I am on a planet in which intelligent life arose endogenously, as opposed to being colonized by a grabby civilization from elsewhere, at least for all appearances, and let’s assume this is definitely the case for the sake of argument), (2) I observe that my civilization arose when the universe was 13.8 billion years old.
According to the Grabby Aliens paper,
When I make observation #2, I’m supposed to feel surprised, and thus make updates towards theories-about-the-universe in which this observation would have been less surprising.
When I make observation #1, I guess I’m supposed to shrug and say “whatever, descendent civilizations are not in my reference class, who cares about them.”
If that’s right, why the difference? 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, 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?
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.
No, it wouldn’t change anything in the paper because we’re not such a civilization and so our arrival time wouldn’t be sampled from the arrival time of descendant civilizations.
What would change it is if there is actually a chance that we’re a descendant civilization ourselves; that is, we’re currently in an area of space which has already been colonized by a grabby alien civilization. In this case it’s indeed true that every result in the paper would radically change.
I look around me and make two observations: (1) I observe that I am not a member of a “descendent civilization” (i.e., I am on a planet in which intelligent life arose endogenously, as opposed to being colonized by a grabby civilization from elsewhere, at least for all appearances, and let’s assume this is definitely the case for the sake of argument), (2) I observe that my civilization arose when the universe was 13.8 billion years old.
According to the Grabby Aliens paper,
When I make observation #2, I’m supposed to feel surprised, and thus make updates towards theories-about-the-universe in which this observation would have been less surprising.
When I make observation #1, I guess I’m supposed to shrug and say “whatever, descendent civilizations are not in my reference class, who cares about them.”
If that’s right, why the difference? 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, 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?
(Sorry if I’m misunderstanding.)
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.