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Nornagest comments on Harry Potter and the Methods of Rationality discussion thread, part 16, chapter 85 - Less Wrong Discussion
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Genetic evidence can't show where your ancestors lived, but it can gesture furtively in one direction while mouthing "look over there". Even in hunter-gatherer populations, there's enough mobility that it shouldn't take anywhere near 22,000 years for African genes to make their way to Australia (or to wherever the proto-Australians were living at the time).
There's a big difference between a few people making their way over and genes achieving fixation.
I approve of your stealth xkcd reference.