OBVIOUSLY the answer to this question is:
I would assemble a documentary crew, and make a movie about me visiting the town and city halls of every town and city in America. I would travel the minimum distance possible, and do nothing particularly interesting at any location. I would release my video into the Creative Commons, and open up a website to go with the video. There would be a google map-like toy that invites users to plot their own tour of all the towns and cities in Europe. This will be my way of testing initiates into the Better Bayesian Conspiracy. Every initiate would be challenged to think up increasingly epic ways to secretly use P=NP. When involved in the Bayesian Conspiracy events, we would be just like the rest, except we would know all the right dance steps and purposefully misstep in amusing (to one another) ways. We would be the Bayesian who always seems to be smiling at some in-joke, we would be the lummox who just can't seem to get the right answer, we would be the pushy person in a mask telling young initiates that the answer is "one sixth". Eventually, we would be all of the members, at which point some of us would splinter off and form an even more nested, more hidden, more conspiratorial conspiracy of esoteric knowledge. Hopefully they would be at least twice as interested in fun as my shadow organization. One day, in three hundred years, I will play through a copy of my traveling salesman documentary and notice that somebody had quietly inserted the kth digit of a binary number into every frame. Four picoseconds later, I will find out that it was a secret message from a child of mine that I never had, sent from the future at the border of the nearest Tegmark universe.... but that is another story that has nothing to do with 3SATs or salesmen or even polynomials.
Many experts suspect that there is no polynomial-time solution to the so-called NP-complete problems, though no-one has yet been able to rigorously prove this and there remains the possibility that a polynomial-time algorithm will one day emerge. However unlikely this is, today I would like to invite LW to play a game I played with with some colleagues called what-would-you-do-with-a-polynomial-time-solution-to-3SAT? 3SAT is, of course, one of the most famous of the NP-complete problems and a solution to 3SAT would also constitute a solution to *all* the problems in NP. This includes lots of fun planning problems (e.g. travelling salesman) as well as the problem of performing exact inference in (general) Bayesian networks. What's the most fun you could have?