Hanson et al. are conditioning on the observation that the universe is 13.8 billion years old. On page 18 they write
Note that by assuming a uniform distribution over our origin rank r (i.e., that we are equally likely to be any percentile rank in the GC origin time distribution), we can convert distributions over model times τ (e.g., an F(τ ) over GC model origin times) into distributions over clock times t. This in effect uses our current date of 13.8Gyr to estimate a distribution over the model timescale constant k. If instead of the distribution F(τ ) we use the distribution F0(τ ), which considers only those GCs who do not see any aliens at their origin date, we can also apply the information that we humans do not now see aliens.
Formally (and I think spelling it out helps) with SSA with the above reference class, our likelihood ratio is the ratio of [number of observers in pre-grabby civiliations that observe Y] to [number of observers in pre-grabby civilizations] where Y is our observation that the universe is 13.8 billion years old, we are on a planet that has been habitable for ~4.5Gy and has total habitability of ~5.5Gy, we don’t observe any grabby civilizations, etc
You originally wrote “We could further condition on something like “observing that computers were invented [80] years ago” … This conditioning means we don’t have to consider that longer-lived planets will have greater populations.”
I interpreted this comment as you saying “We could restrict our SSA reference class to only include observers for whom computers were invented 80 years ago”. (Is that right?)
And then I was trying to respond to that by saying “Well if we can do that, why can’t we equally well restrict our SSA reference class to only include observers for whom the universe is 13.8 billion years old? And then “humanity is early” stops being true.”
I interpreted this comment as you saying “We could restrict our SSA reference class to only include observers for whom computers were invented 80 years ago”. (Is that right?)
What I wanted to say was: keep the reference class the same, but restrict the types of observers we are we saying we are contained in(the numerator in the SSA ratio) to be only those who (amongst other things) observe the invention of the computer 80 years ago.
And then I was trying to respond to that by saying “Well if we can do that, why can’t we equally well restrict our SSA reference class to only include observers for whom the universe is 13.8 billion years old? And then “humanity is early” stops being true.”
Yep, one can do this. We might still be atypical if we think longer-lived planets are habitable (since life has more time to appear there) but could also restrict the reference class further. Eventually we end up at minimal reference class SSA
Doesn’t sound snarky at all :-)
Hanson et al. are conditioning on the observation that the universe is 13.8 billion years old. On page 18 they write
Formally (and I think spelling it out helps) with SSA with the above reference class, our likelihood ratio is the ratio of [number of observers in pre-grabby civiliations that observe Y] to [number of observers in pre-grabby civilizations] where Y is our observation that the universe is 13.8 billion years old, we are on a planet that has been habitable for ~4.5Gy and has total habitability of ~5.5Gy, we don’t observe any grabby civilizations, etc
Oh, I think I phrased my last comment poorly.
You originally wrote “We could further condition on something like “observing that computers were invented [80] years ago” … This conditioning means we don’t have to consider that longer-lived planets will have greater populations.”
I interpreted this comment as you saying “We could restrict our SSA reference class to only include observers for whom computers were invented 80 years ago”. (Is that right?)
And then I was trying to respond to that by saying “Well if we can do that, why can’t we equally well restrict our SSA reference class to only include observers for whom the universe is 13.8 billion years old? And then “humanity is early” stops being true.”
Ah, I don’t think I was very clear either.
What I wanted to say was: keep the reference class the same, but restrict the types of observers we are we saying we are contained in(the numerator in the SSA ratio) to be only those who (amongst other things) observe the invention of the computer 80 years ago.
Yep, one can do this. We might still be atypical if we think longer-lived planets are habitable (since life has more time to appear there) but could also restrict the reference class further. Eventually we end up at minimal reference class SSA