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shminux comments on Anthropics doesn't explain why the Cold War stayed Cold - Less Wrong
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Wikipedia mentions one case of anthropics (if you use the term loosely) making (or could have made) an honest testable prediction:
which in actuality was an argument from the measured abundance of carbon in the spectral lines, and the prediction that carbon was required as a nuclear reaction catalyst to make the Sun shine at such a low mass and temperature. The "we exist, therefore..." part was apparently added later, when Hoyle became a fan of anthropics. Still, if you want to steelman anthropics, that would be one way.
I have a better example:
The universe is largely composed of empty space. If you pick a random point in the universe, it would most likely be in the middle of nowhere, with not a single star visible. The probability of a given point not just being in a galaxy, not just being in a star system, not just being at a planet, but actually being at the thing surface of this planet is miniscule. And yet, here we are.
But of course we're here. There's nothing in space to ask the question.
Except for Boltzmann Brains.