What troubles me, is that it seems there's no working hypothesis (as you put it) in P != NP. P != NP has become instead an unspoken behavioral axiom. Meaning, it's not a true axiom, but influences the behavior for future search. It has been reduced to "I believe in P != NP, because no one could yet prove P = NP" and this could have spelled to some "Trying to prove P = NP is a research dead end". It's no surprise that the pool (pdf file) linked to at the Wikipedia article reveals much of the work has been done on trying to prove P != NP. There's already something seriously wrong.
So all this is in fact my stab at those researchers whose lack of evidence on P = NP have them behaving like P != NP is the solution, halting or moving research or even already advocating the solution on faith, which makes me doubt their value as scientists. It's more distressing when you think the huge revolution and scientific advance it could be if someone proved P = NP. The prize is too great to be ignored. Whereas the future seems bleak if P != NP.
But P = NP can indeed be a wild goose chase, while P != NP seems a lot harder to prove (or even plain impossible). So it may be many years, hundreds of years, thousands before we reach a solution, if we ever do. A t-shirt is a funny and I certainly am not having a go at it, or you for putting P != NP on it. But I felt I had to comment.
When I move to "dogmatic belief", I steer away from Science. In that brave old world of belief and faith, the rules are played differently. In here, I proved P != NP through my belief in the form of a canon of faith. This canon serves both to prove the solution and to validate it. I equaled the solution and its validation.Quote:
Mario, while I still don't entirely understand why even the dogmatic belief that P != NP would suggest that P == NP,
Back on the scientific world, this makes no sense. But in the reality I emerged myself in, I actually unknowingly made a strong case for P = NP and didn't prove P != NP. It's not possible to prove P != NP in this reality of faith I got myself into. Every effort will put me closer to P = NP.
I struggling with words at this point. I don't know what else I can say. I'm not proposing the belief finds its echo in scientific reality. I'm saying that in the pseudo-reality imposed by faith, trying to prove P != NP will in fact have you unwillingly prove P = NP. In that pseudo-reality. Not in the scientific reality.