Thank you for this excellent and detailed post, I expect to use it in the future as a go-to reference for explaining this point. You might be interested in an old paper where Nick Bostrom and I went through some of this reasoning (with similar conclusions but much less explanation) in the course of discussing the implications of anthropic theories for the possible difficulty of evolving intelligence.
I am not so sure about the specific numerical estimates you give, as opposed to the ballpark being within a few orders of magnitude for SIA and ADT+total views (plus auxiliary assumptions), i.e. the vicinity of “(roughly the largest value that doesn’t make the Fermi observation too unlikely, as shown in the next two sections”. But that’s compatible with much or most of our expected on the total view coming from scenarios where we don’t overlap with aliens much.
″ However, varying the planet formation rate at particular times in the history of the Universe can make a large difference.”
We also update our uncertainty about this sort of temporal structure to some extent from our observation of late existence. Ideally we would want to let as much as possible vary so that we don’t asymmetrically immunize some parameters against update.
“For this reason I will ignore scenarios where life is extraordinarily unlikely to colonise the Universe, by making fs loguniform between 10−4 and 1.”
This seems overall too pessimistic to me as a pre-anthropic prior for colonization (~10% credence).
I am not so sure about the specific numerical estimates you give, as opposed to the ballpark being within a few orders of magnitude for SIA and ADT+total views (plus auxiliary assumptions)
I definitely agree about some numbers. Maybe I should have been more explicit about this in the post, but I have low credence in the exact distribution of f (as well as fl, fi, and fs): it depends far too much on the absolute rate of planet formation and the speed at which civilisations travel.
However, I’m much more willing to believe that the average fraction of space that would be occupied by alien civilisations in our absence is somewhere between 30 % and 95 %, or so. A lot of the arbitrary assumptions that affects f cancels out when running the simulation, and the remaining parameters affects the result surprisingly little. My main (known) uncertainties are
Whether it’s safe to assume that intergalactic colonisation is possible. From the perspective of total consequentialism, this is largely a pragmatic question about where we can have the most impact (which is affected by a lot of messy empirical questions).
How much the results would change if we allowed for a late increase in life more sudden than the one in Appendix C (either because of a sudden shift in planet formation or because of something like gamma ray bursts). Anthropics should affect our credence in this, as you point out, and the anthropic update would be quite large in favor. However, the prior probability of a very sudden increase seems small. That prior is very hard to quantify, and I think my simulation would be less reliable in the more extreme cases, so this possibility is quite hard to analyse.
Do you agree, or do you have other reasons to doubt the 30%-95% number?
This seems overall too pessimistic to me as a pre-anthropic prior for colonization
I agree that the mean is too pessimistic. The distribution is too optimistic about the impossibility of lower numbers, though, which is what matters after the anthropic update. I mostly just wanted a distribution that illustrated the idea about the late filter without having it ruin the rest of the analysis.f has almost exactly the same distribution after updating, anyway, as long as fs assigns negligible probability to numbers below 10−10.
Thank you for this excellent and detailed post, I expect to use it in the future as a go-to reference for explaining this point. You might be interested in an old paper where Nick Bostrom and I went through some of this reasoning (with similar conclusions but much less explanation) in the course of discussing the implications of anthropic theories for the possible difficulty of evolving intelligence.
I am not so sure about the specific numerical estimates you give, as opposed to the ballpark being within a few orders of magnitude for SIA and ADT+total views (plus auxiliary assumptions), i.e. the vicinity of “(roughly the largest value that doesn’t make the Fermi observation too unlikely, as shown in the next two sections”. But that’s compatible with much or most of our expected on the total view coming from scenarios where we don’t overlap with aliens much.
″ However, varying the planet formation rate at particular times in the history of the Universe can make a large difference.”
We also update our uncertainty about this sort of temporal structure to some extent from our observation of late existence. Ideally we would want to let as much as possible vary so that we don’t asymmetrically immunize some parameters against update.
“For this reason I will ignore scenarios where life is extraordinarily unlikely to colonise the Universe, by making fs loguniform between 10−4 and 1.”
This seems overall too pessimistic to me as a pre-anthropic prior for colonization (~10% credence).
I definitely agree about some numbers. Maybe I should have been more explicit about this in the post, but I have low credence in the exact distribution of f (as well as fl, fi, and fs): it depends far too much on the absolute rate of planet formation and the speed at which civilisations travel.
However, I’m much more willing to believe that the average fraction of space that would be occupied by alien civilisations in our absence is somewhere between 30 % and 95 %, or so. A lot of the arbitrary assumptions that affects f cancels out when running the simulation, and the remaining parameters affects the result surprisingly little. My main (known) uncertainties are
Whether it’s safe to assume that intergalactic colonisation is possible. From the perspective of total consequentialism, this is largely a pragmatic question about where we can have the most impact (which is affected by a lot of messy empirical questions).
How much the results would change if we allowed for a late increase in life more sudden than the one in Appendix C (either because of a sudden shift in planet formation or because of something like gamma ray bursts). Anthropics should affect our credence in this, as you point out, and the anthropic update would be quite large in favor. However, the prior probability of a very sudden increase seems small. That prior is very hard to quantify, and I think my simulation would be less reliable in the more extreme cases, so this possibility is quite hard to analyse.
Do you agree, or do you have other reasons to doubt the 30%-95% number?
I agree that the mean is too pessimistic. The distribution is too optimistic about the impossibility of lower numbers, though, which is what matters after the anthropic update. I mostly just wanted a distribution that illustrated the idea about the late filter without having it ruin the rest of the analysis.f has almost exactly the same distribution after updating, anyway, as long as fs assigns negligible probability to numbers below 10−10.