[EY:] I’ve come to accept that to some extent [Marcello and I] have different and complementary abilities—now and then he’ll go into a complicated blaze of derivations and I’ll look at his final result and say “That’s not right” and maybe half the time it will actually be wrong.
In other words, he’s no better than random chance, which is vastly different from “[thinking] he can do advanced math with little effort using some intuition.” By the same logic, you’d accept P=NP trivially.
I don’t understand. The base rate for Marcello being right is greater than 0.5.
Maybe EY meant that, on the occasions that Eliezer objected to the final result, he was correct to object half the time. So if Eliezer objected to just 1% of the derivations, on that 1% our confidence in the result of the black box would suddenly drop down to 50% from 99.5% or whatever.
I don’t understand. The base rate for Marcello being right is greater than 0.5.
Maybe EY meant that, on the occasions that Eliezer objected to the final result, he was correct to object half the time. So if Eliezer objected to just 1% of the derivations, on that 1% our confidence in the result of the black box would suddenly drop down to 50% from 99.5% or whatever.
Yes, but that’s not “no better than random chance.”
Sure. I was suggesting a way in which an objection which is itself only 50% correct could be useful, contra Dmytry.
Oh, right. The point remains that even a perfect Oracle isn’t an efficient source of math proofs.