I guess I wasn’t necessarily thinking of them as exact duplicates. If there are 10^100 ways the 21st century can go, and for some reason each of the resulting civilizations wants to know how all the other civilizations came out when the dust settled, each civilization ends up having a lot of other civilizations to think about. In this scenario, an effect on the far future still seems to me to be “only” a million times as big as the same effect on the 21st century, only now the stuff isomorphic to the 21st century is spread out across many different far future civilizations instead of one.
Maybe 1⁄1,000,000 is still a lot, but I’m not sure how to deal with uncertainty here. If I just take the expectation of the fraction of the universe isomorphic to the 21st century, I might end up with some number like 1⁄10,000,000 (because I’m 10% sure of the 1⁄1,000,000 claim) and still conclude the relative importance of the far future is huge but hugely below infinity.
I guess I wasn’t necessarily thinking of them as exact duplicates. If there are 10^100 ways the 21st century can go, and for some reason each of the resulting civilizations wants to know how all the other civilizations came out when the dust settled, each civilization ends up having a lot of other civilizations to think about. In this scenario, an effect on the far future still seems to me to be “only” a million times as big as the same effect on the 21st century, only now the stuff isomorphic to the 21st century is spread out across many different far future civilizations instead of one.
Maybe 1⁄1,000,000 is still a lot, but I’m not sure how to deal with uncertainty here. If I just take the expectation of the fraction of the universe isomorphic to the 21st century, I might end up with some number like 1⁄10,000,000 (because I’m 10% sure of the 1⁄1,000,000 claim) and still conclude the relative importance of the far future is huge but hugely below infinity.