Correct—we can’t predict that we are exactly in the middle of human observational history, only roughly in the middle. This is why the prediction from the random observation model is ~200 years, with the ~ representing a range of variation around the central estimate.
Giving formal confidence intervals (like Gott does) seems a bit of a stretch in my view, since the bounds of these then become acutely sensitive to the prior distribution. Under the “vague” prior over total person-years of observations, and with a 90% confidence interval, we could predict between 100 billion and 40 trillion of person-years to come.
No I’m not disputing taking the mean to be the middle of the probability distribution, that’s elementary. I mean because the population numbers are on such different scales if we are at the end or the beginning, the mean of the total distribution may be far in the future. I don’t actually know if this is true or not because I don’t understand what the probability distribution looks like.
If we looked at just two cases instead of one, it might help things. The two cases are: we are in the last 95% or we are in the first 5%. In the 5% case, we estimate another 2 trillion people are coming. in the 95% case, we estimate another 5 billion. To calculate expected value of future people, we have to know the relative likelyhoods of cases like these. If we consider anthropic issues in a naive way (just assume all observations are equally likely) I don’t know what the distribution looks like. Maybe someone else can help. I do know that we shouldn’t just considr anthropic bias naively, we should also consider what we currently observe about the world. We are not transhuman and we are not prehistoric peasants, so that is some evidence. My intuition tells me that once you consider what you actually see as evidence, it screens off all the anthropic stuff and expected populations and such.
Correct—we can’t predict that we are exactly in the middle of human observational history, only roughly in the middle. This is why the prediction from the random observation model is ~200 years, with the ~ representing a range of variation around the central estimate.
Giving formal confidence intervals (like Gott does) seems a bit of a stretch in my view, since the bounds of these then become acutely sensitive to the prior distribution. Under the “vague” prior over total person-years of observations, and with a 90% confidence interval, we could predict between 100 billion and 40 trillion of person-years to come.
No I’m not disputing taking the mean to be the middle of the probability distribution, that’s elementary. I mean because the population numbers are on such different scales if we are at the end or the beginning, the mean of the total distribution may be far in the future. I don’t actually know if this is true or not because I don’t understand what the probability distribution looks like.
If we looked at just two cases instead of one, it might help things. The two cases are: we are in the last 95% or we are in the first 5%. In the 5% case, we estimate another 2 trillion people are coming. in the 95% case, we estimate another 5 billion. To calculate expected value of future people, we have to know the relative likelyhoods of cases like these. If we consider anthropic issues in a naive way (just assume all observations are equally likely) I don’t know what the distribution looks like. Maybe someone else can help. I do know that we shouldn’t just considr anthropic bias naively, we should also consider what we currently observe about the world. We are not transhuman and we are not prehistoric peasants, so that is some evidence. My intuition tells me that once you consider what you actually see as evidence, it screens off all the anthropic stuff and expected populations and such.