I can feel some inferential distance here that isn’t successfully being bridged. It’s far from clear to me that the default assumption here should be that no NP-hard problems need to be solved and that the burden of proof is on those who claim otherwise.
I guess to me the notion of “solve an NP-hard problem” (for large N and hard cases, i.e., the problem really is NP hard) seems extremely exotic—all known intelligence, all known protein folding, and all known physical phenomena must be proceeding without it—so I feel a bit at a loss to relate to the question. It’s like bringing up PSPACE completeness—I feel a sense of ‘where did that come from?’ and find it hard to think of what to say, except for “Nothing that’s happened so far could’ve been PSPACE complete.”
Agreed if you mean “Nothing that’s happened so far could’ve been [computationally hard] to predict given the initial conditions.”
But the reverse problem—finding initial conditions that produce a desired output—could be very hard. Nature doesn’t care about this, but an AI plausibly might.
I’m not sure how protein folding fits into this picture, to be honest. (Are people just trying to figure out what happens to a given protein in physics, or trying to find a protein that will make something good happen?) But more generally, the statement “P=NP” is more or less equivalent to “The reverse problem I mention above is always easy.” Things become very different if this is true.
I can feel some inferential distance here that isn’t successfully being bridged. It’s far from clear to me that the default assumption here should be that no NP-hard problems need to be solved and that the burden of proof is on those who claim otherwise.
I guess to me the notion of “solve an NP-hard problem” (for large N and hard cases, i.e., the problem really is NP hard) seems extremely exotic—all known intelligence, all known protein folding, and all known physical phenomena must be proceeding without it—so I feel a bit at a loss to relate to the question. It’s like bringing up PSPACE completeness—I feel a sense of ‘where did that come from?’ and find it hard to think of what to say, except for “Nothing that’s happened so far could’ve been PSPACE complete.”
Agreed if you mean “Nothing that’s happened so far could’ve been [computationally hard] to predict given the initial conditions.”
But the reverse problem—finding initial conditions that produce a desired output—could be very hard. Nature doesn’t care about this, but an AI plausibly might.
I’m not sure how protein folding fits into this picture, to be honest. (Are people just trying to figure out what happens to a given protein in physics, or trying to find a protein that will make something good happen?) But more generally, the statement “P=NP” is more or less equivalent to “The reverse problem I mention above is always easy.” Things become very different if this is true.