If P != NP and the universe has no source of exponential computing power, then there are evidential updates too difficult for even a superintelligence to compute—even though the probabilities would be quite well-defined, if we could afford to calculate them.
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Trying to catch a flying ball, you’re probably better off with your brain’s built-in mechanisms, then [than?] using deliberative verbal reasoning to invent or manipulate probabilities.
There’s more than just P != NP that defeats trying to catch a flying ball by predicting where it will land and going there. Or, for that matter, trying to go there by computing a series of muscular actions and then doing them. You can’t sense where the ball is or what your body is doing accurately enough to plan, then execute actions with the precision required. A probability cloud perfectly calculated from all the available information isn’t good enough, if it’s bigger than your hand.
This is how to catch a ball: move so as to keep its apparent direction (both azimuth and elevation) constant.
But this doesn’t mean you’re going beyond probability theory or above probability theory.
It doesn’t mean you’re doing probability theory either, even when you reliably win. The rule “move so as to keep the apparent direction constant” says nothing about probabilities. If anyone wants to try at a probability-theoretic account of its effectiveness, I would be interested, but sceptical in advance.
If P != NP and the universe has no source of exponential computing power, then there are evidential updates too difficult for even a superintelligence to compute—even though the probabilities would be quite well-defined, if we could afford to calculate them.
...
Trying to catch a flying ball, you’re probably better off with your brain’s built-in mechanisms, then [than?] using deliberative verbal reasoning to invent or manipulate probabilities.
There’s more than just P != NP that defeats trying to catch a flying ball by predicting where it will land and going there. Or, for that matter, trying to go there by computing a series of muscular actions and then doing them. You can’t sense where the ball is or what your body is doing accurately enough to plan, then execute actions with the precision required. A probability cloud perfectly calculated from all the available information isn’t good enough, if it’s bigger than your hand.
This is how to catch a ball: move so as to keep its apparent direction (both azimuth and elevation) constant.
But this doesn’t mean you’re going beyond probability theory or above probability theory.
It doesn’t mean you’re doing probability theory either, even when you reliably win. The rule “move so as to keep the apparent direction constant” says nothing about probabilities. If anyone wants to try at a probability-theoretic account of its effectiveness, I would be interested, but sceptical in advance.