gjm comments on timeless quantum immortality - Less Wrong Discussion
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This also explains why you find yourself in a world that has already perfected immortality technology.
... Oh, wait.
[EDITED to add: I see that you sort-of addressed this "... would require a more complicated Universe". But I don't understand that at all. How would it require a more complicated universe?]
It's a flawed argument but if for some reason there was a high complexity penalty to being born in an older Universe then it could be more likely to be born in a younger Universe where immortality technology has not quite been invented yet.