The Doomsday Argument

The "Doomsday Argument" is both a puzzle and a philosophical debate.

It was originally posed by the physicist Brandon Carter and has subsequently generated considerable debate among philosophers. Here it is in a nutshell:

Suppose you had a special power of reincarnation. When you died, your memory was erased and you were randomly reborn as any human in the past, present, or future.

Is it more likely that you will be in the first third of humans to ever be born, or the last two-thirds?

It seems obvious the latter is the safer bet, by about 2 to 1.

Okay, now take out the fantasy element. Let's say you, today, having never been reincarnated had to take that bet. You don't have any information that the reincarnated you didn't have. Would you still bet that you were in the last two-thirds of people to be born?

If not, why not?

If yes, consider this: About 60 billion people have been born up to this point in history. Assume that the Earth's population will shortly stabilize at 20 billion people (we're just over 6 billion now), with an average life expectancy of 75 years (we're just under 60 now).

If you're in the last two-thirds of people to ever be born, mankind will be extinct in under 500 years.

Changing the assumptions about population growth rates, death rates, etc. can, of course, change the expected probabilities. But what doesn't seem to change is the remarkably high probability that most humans who will ever have lived will have already been born by the next turn of the millenium.

If you've been following the logic here, you're probably scratching your head. Something seems wrong, but what?

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