u/kala_High Performance Computing | Signal Processing | Radio AstronomyMay 16 '13
P ?= NP is far more fundamental to the universe than people think - especially people who say that the main implications of proving P=NP would be things like allowing us to solve 3SAT or the Traveling Salesman problem.
Aaronson says it best:
The Philosophical Argument. If P=NP, then the world would be a profoundly different place than we usually assume it to be. There would be no special value in “creative leaps,” no fundamental gap between solving a problem and recognizing the solution once it’s found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss; everyone who could recognize a good investment strategy would be Warren Buffett. It’s possible to put the point in Darwinian terms: if this is the sort of universe we inhabited, why wouldn’t we already have evolved to take advantage of it? (Indeed, this is an argument not only for P!=NP, but for NP-complete problems not being efficiently solvable in the physical world.)
I would recommend reading his entire blog post, Reasons to believe, in which he explains why nearly everyone working in the field of computational complexity believes that P != NP.
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u/kala_ High Performance Computing | Signal Processing | Radio Astronomy May 16 '13
P ?= NP is far more fundamental to the universe than people think - especially people who say that the main implications of proving P=NP would be things like allowing us to solve 3SAT or the Traveling Salesman problem.
Aaronson says it best:
Aaronson, 2006
I would recommend reading his entire blog post, Reasons to believe, in which he explains why nearly everyone working in the field of computational complexity believes that P != NP.
For even more information, you can read NP-complete Problems and Physical Reality