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brian_jaress comments on Avoiding doomsday: a "proof" of the self-indication assumption - Less Wrong
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But that's the important part. It's called the "Doomsday Argument" for a reason: it concludes that doomsday is imminent.
Of course the last 2/3 is still going to be 2/3 of the total. So is the first 2/3.
Imminent doomsday is the only non-trivial conclusion, and it relies on the assumption that exponential growth will continue right up to a doomsday.