It is not NP != P that is proposed as a physical law. It is the impossibility of building computers that quickly solve NP-complete problems. It is really more like a heuristic to quickly shoot down some physical theories. The 2nd law is a bad metaphor. The impossibility of faster-than-light communication is a better one. If your proposed physical theory makes faster-than-light communication possible, that makes the theory look suspicious. Analogously, if your proposed physical theory makes solving SAT feasible with a polynomial amount of resources, that should make the theory look suspicious, says Aaronson.
EDIT: As an important example, the possibility of general time travel could make you solve SAT easily. It is a nice exercise to figure out how. Harry Potter tried it in Methods of Rationality, and Aaronson has a whole lecture about it.
I totally agree. I guess you could imagine Maxwell’s demon as an example where untangling a supposed violation of the 2nd law led to new understanding.
It is not NP != P that is proposed as a physical law. It is the impossibility of building computers that quickly solve NP-complete problems. It is really more like a heuristic to quickly shoot down some physical theories. The 2nd law is a bad metaphor. The impossibility of faster-than-light communication is a better one. If your proposed physical theory makes faster-than-light communication possible, that makes the theory look suspicious. Analogously, if your proposed physical theory makes solving SAT feasible with a polynomial amount of resources, that should make the theory look suspicious, says Aaronson.
EDIT: As an important example, the possibility of general time travel could make you solve SAT easily. It is a nice exercise to figure out how. Harry Potter tried it in Methods of Rationality, and Aaronson has a whole lecture about it.
I totally agree. I guess you could imagine Maxwell’s demon as an example where untangling a supposed violation of the 2nd law led to new understanding.