[18] Quick calculation: Suppose we take Ajeya’s best-guess distribution and modify it by lowering the part to the right of 10^35 and raising the part to the left of 10^35, until the 10^35 mark is the 80-percentile mark instead of the 50-percentile mark. And suppose we do this raising and lowering in a “distribution-preserving way,” i.e. the shape of the curve before the 10^35 mark looks exactly the same, it’s just systematically bigger. In other words, we redistribute 30 percentage points of probability mass from above 10^35 to below, in proportion to how the below-10^35 mass is already distributed.
Well, in this case, then 60% of the redistributed mass should end up before the old 30% mark. (Because the 30% mark is 60% of the mass prior to the old median, the 10^35 mark.) And 60% of 30 percentage points is 18, so that means +18 points added before the old 30% mark. This makes it the new 48% mark. So the new 48% mark should be right where the old 30% mark is, which is (eyeballing the spreadsheet) a bit after 2040, 10 years sooner. (Ajeya’s best guess median is a bit after 2050.) This is, I think, a rather conservative estimate of how cruxy this disagreement is.
First, my answer to Question Two is 0.9, not 0.8, and that’s after trying to be humble and whatnot. Second, this procedure of redistributing probability mass in proportion to how it is already distributed produces an obviously silly outcome, where there is a sharp drop-off in probability at the 10^35 mark. Realistically, if you are convinced that the answer to Question Two is 0.8 (or whatever) then you should think the probability distribution tapers off smoothly, being already somewhat low by the time the 80th-percentile mark at 10^35 is reached.
Thus, realistically, someone who mostly agrees with Ajeya but answers Question Two with “0.8” should have somewhat shorter timelines than the median-2040-ish I calculated
[18] Quick calculation: Suppose we take Ajeya’s best-guess distribution and modify it by lowering the part to the right of 10^35 and raising the part to the left of 10^35, until the 10^35 mark is the 80-percentile mark instead of the 50-percentile mark. And suppose we do this raising and lowering in a “distribution-preserving way,” i.e. the shape of the curve before the 10^35 mark looks exactly the same, it’s just systematically bigger. In other words, we redistribute 30 percentage points of probability mass from above 10^35 to below, in proportion to how the below-10^35 mass is already distributed.
Well, in this case, then 60% of the redistributed mass should end up before the old 30% mark. (Because the 30% mark is 60% of the mass prior to the old median, the 10^35 mark.) And 60% of 30 percentage points is 18, so that means +18 points added before the old 30% mark. This makes it the new 48% mark. So the new 48% mark should be right where the old 30% mark is, which is (eyeballing the spreadsheet) a bit after 2040, 10 years sooner. (Ajeya’s best guess median is a bit after 2050.) This is, I think, a rather conservative estimate of how cruxy this disagreement is.
First, my answer to Question Two is 0.9, not 0.8, and that’s after trying to be humble and whatnot. Second, this procedure of redistributing probability mass in proportion to how it is already distributed produces an obviously silly outcome, where there is a sharp drop-off in probability at the 10^35 mark. Realistically, if you are convinced that the answer to Question Two is 0.8 (or whatever) then you should think the probability distribution tapers off smoothly, being already somewhat low by the time the 80th-percentile mark at 10^35 is reached.
Thus, realistically, someone who mostly agrees with Ajeya but answers Question Two with “0.8” should have somewhat shorter timelines than the median-2040-ish I calculated