A Philosophical Argument for P != NP

David Levin sent me a link to a great blog post that talked about the question of whether P == NP.  From the post:

More often than I can remember, I've been asked some form of the following question: "If you computer scientists can't prove P=NP or P!=NP, then why aren't we justified in believing whichever one we want? And why is the 'consensus' that P!=NP anything more than a shared prejudice -- something you repeat to each other so your work won't seem irrelevant?"

The author then goes to offer 10 arguments for why it's overwhelmingly likely that P != NP.

I found the Philosophy Argument (#9) to be truly beautiful:

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.)

It's beautiful for many reasons.  First, the analogy itself is beautiful.  Second, it's self-referential -- after reading it, I was struck by its elegance and surprised that I had never seen it in that way.  But, of course, that's the point -- it's very hard to formulate such an analogy, but it is comparatively easy to appreciate it.

Very nice indeed.