Saturday, November 15, 2008
P != NP
I had an odd dream last night. I dreamt that I was giving a presentation at a conference, showing a proof that P doesn't equal NP. It seemed I had this closed box, which every year I would bring to the conference, and if someone could successfully complete my challenge, I would show them the contents of the box. It seems that inside that box was a secret set of numbers that helped me to come with all sorts of answers. This year, the answer I came with was that NP didn't equal P. To prove this I had a set of five objects. Each object was a set of tubes that were different, but precise diameters. These tubes were chosen with the help of the numbers in my box. The tubes were handcrafted, and on each object was drawn some sort of histogram. The histogram of each object conformed to certain properties, thus somehow proving that P != NP. The proof was simple to show, but hard to come up with. The proof it seemed (as I realized after I woke), was in the spirit of NP, easily verifiable, but not easily come by.