How many lawyers, mathematicians, and engineers does it take to change a light switch? Apparently, it's a lot. NBT and I were trying to do something simple: change the off-white switches to white one, to go with our new paint job in the front hallway. Turns out we bought two-way switches instead of three-way switches, which we realized after we wired them up. And when we bought the right switches, we had to figure out which wire went where. You'd think it would be easy, but we couldn't find the right combo through trial and error, with me running down to the basement and shutting the breaker off between each iteration.
Our friend 517 had the occasion to have dinner with two certified genius mathematicians -- an American Academy of Sciences distinguished professor and a PhD student in some kind of advanced algebra. Oh, this is a very simple problem, they told him. I've written a paper about three way switches, one of the mathematicians volunteered. But it turns out there are something like thirty-six squared possible combinations, if you don't know whether the power source goes to the light, to the upstairs switch, or to the downstairs switch, and you don't know which is the common wire. That made me feel a little better about our failure to figure it out. Finally the mathematicians acknowledged that it wasn't such a simple problem after all, although they did insist that there was no need to turn the breaker off when fiddling with the wires. ("It's only dangerous if you touch the ground wires together.") 517 finally obtained a continuity tester, and we found a wiring diagram on the web that was a pretty helpful map. I ran up and down the basement stairs turning the breaker off each time, and now we have light.