In Ian Banks "The Culture", society contained both hyper-intelligent "machines" and humans. In a way, the "machines" broght the humans along for the ride: they where "just like us", but only moreso, and the humans wheren't all that much of a burden.
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Originally posted by John Henry
If we consider only these two options as a possibility, then statistically, on an undefined timescale, option two is a certainty. This is simply because for every time we don't wipe ourselves out, we have another chance to do it, but if we wipe ourselves out even once, we don't get a chance to undo it. So as time approaches a limit in infinity, the probability of us having wiped ourselves out at some point in that time approaches 1.
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That assumes we are always able to wipe ourselves out. If we, say, causally disconnected parts of humanity from other parts, or to a lesser extent spread out enough, the limit of the product probabilities could converge to a non-zero chance of survival.
For instance, imagine a technology where you can build "bud" universes and then detatch them from ours. Humans build some, populate them, and disconnect: now, no one set of humans could wipe out all of them. Or, less dramatically, imagine we spread over a galaxy or two...
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However, I don't think these are the only two possibilities. If we manage to stay alive long enough we will all die of something far bigger than us, like being engulfed by the Sun.
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Or the heat death of the universe. =)