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gjm comments on Avoiding doomsday: a "proof" of the self-indication assumption - Less Wrong
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What bugs me about the doomsday argument is this: it's a stopped clock. In other words, it always gives the same answer regardless of who applies it.
Consider a bacterial colony that starts with a single individual, is going to live for N doublings, and then will die out completely. Each generation, applying the doomsday argument, will conclude that it has a better than 50% chance of being the final generation, because, at any given time, slightly more than half of all colony bacteria that have ever existed currently exist. The doomsday argument tells the bacteria absolutely nothing about the value of N.
The fact that every generation gets the same answer doesn't (of itself) imply that it tells the bacteria nothing. Suppose you have 65536 people and flip a coin 16 [EDITED: for some reason I wrote 65536 there originally] times to decide which of them will get a prize. They can all, equally, do the arithmetic to work out that they have only a 1/65536 chance of winning. Even the one of them who actually wins. The fact that one of them will in fact win despite thinking herself very unlikely to win is not a problem with this.
Similarly, all our bacteria will think themselves likely to be living near the end of their colony's lifetime. And most of them will be right. What's the problem?
I think you mean 16 times.
Er, yes. I did change my mind a couple of times about what (2^n,n) pair to use, but I wasn't ever planning to have 2^65536 people so I'm not quite sure how my brain broke. Thanks for the correction.