consider a world in which P equals NP. What does this mean? All internet crypto could break, almost immediately if a valid a solution were found. What does thi

consider a world in which P equals NP. What does this mean? All internet crypto could break, almost immediately if a valid a solution were found. What does this do to society? A philosophical class on skeptisim, or a class on software security - they both lead to the same conclusion, that the outside world is a potentially terrifying place. Identities can give rise to trust in something out side of you - but it's impossible to form identities without a "one way" computational mechanism like P != NP. Our ability to say "You know me by my words; you can recognize my language, but cant speak it yourself" - that doesn't work any more if P = NP. The ability to say "yes, that's MarkPNeyer saying that" is the same as the ability to speak with my voice. Now consider a world in which P does not equal NP. - it suggests that a single expert is not as powerful as large groups; a single person acting alone is like a single turing machine. A quantum computer is sort of like society - everyone tries their own way, and if someone finds a solution that works, it is made obvious to everyone else through their success. - it provides a meaningful basis for identity. Someone can publish cryptogrpahically signed statements attesting to a believe, and we can trust that it's the same person (or group of people) operating behind that identity, becuase of the meanignful difference between verifying a truth (this is the same person who posted these keys) and finding a solution (find the private key which leads to posting these two things.) Now, of course the "world I want to live in" does't directly suggest anything one way or the other - I'm just hoping you can stop seeing "P != NP" as being defeatist - if anything, it's a wonderful result, from a philosophical perspective, because it implies a world rich, full of diversity, with meaningful notions of identity. If P = NP, the polynomial time hierarchy collapses - and there's a good chance society does as well.