Comment by tsimionescu
2 days ago
> As a human, I know that six to the power of one million is impossible.
This is plain wrong. If you roll a million dice, anything that comes up has the exact same probability. We think all 6 is special because it holds some meaning to us, but it is exactly as likely as any other result. So any result has a probability of 6^1M to happen. And yet, one of those 6^1M configurations will happen with probability 1.
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I'm not saying that we'll see the all six combination if we actually threw a million dice. I'm saying that if we throw a million dice, we'll see some combination, and that should be just as amazing as the all six combination, because, whatever it is, it was monumentally unlucky to happen.
My only point is that there is no way to say "events with probability < X are impossible in real life", for X > 0. For any probability value, it's trivial to construct an experiment that will be guaranteed to have an outcome whose probability is that low.
This argument I think hints at something i regard as mysterious regarding probability as applied to the real world (as opposed to the platonic, pure math concept)
My own view is that there something deep about probability akin to the measurement problem. My view is that probability is not an objective fixed thing, but that it is something relative to the observer of experiments.
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