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Perplexed comments on The Absolute Self-Selection Assumption - Less Wrong
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Comments (38)
So you're going with "randomly generated". Which is fine, but it needs to be spelled out.
You need to be very careful pulling intuitions about randomness from the finite case and applying it to the infinite case. In particular, it is no longer true that just because something happened, it has a positive probability. Any given real number has probability zero of being picked from the uniform distribution on [0,1) yet one certainly will be picked. And we can pick an infinite number of times and never encounter a duplicate.
I'm not attacking this assumption in order to attack your final conclusion, I'm just attacking this assumption.
Not in a finite amount of time.
What do you mean?
Drawing from a continuous distribution happens fairly often, so your comment confuses me. Or maybe you'd say that those aren't "really infinite" and are confined to a certain number of bits, but quantum mechanics would be an exception to that.
As Cyan pointed out, when you choose a number confined to a certain number of bits, you are actually choosing from among the rationals.
I don't understand your reference to QM. I wasn't objecting to the randomness aspect. I was simply pointing out that to actually receive that randomly chosen real, you will (almost certainly) need to receive an infinite number of bits, and assuming finite channel capacity, that will take an infinite amount of time. So that event you mentioned, the one with an infinitesimal probability (zero probability for all practical purposes) is not going to actually happen (i.e. finish happening).
It was a minor quibble, which I now regret making.