Wednesday, November 17, 2004

Outline for a Revolution

What the Knight's Tour Problem Doesn't Teach Policy Wonks

This essay is long and boring.  I almost did not have the patience to write it.

One of my favorite ways to teach complex subjects is to use analogies.  Start out by talking about a simple subject, then compare it to the more complex topic.  The Knight Tour problem is good for this.  The problem is this: take an empty chessboard, place it on the table in front of you, situated such that there is a white square in the right-hand corner closest to you.  Put a knight on that white square.  Do not put any other pieces on the board.  Using the traditional way of moving a knight, is it possible to move the knight such that it lands on each square on the board once and only once, and ends up on the corner diagonal to the starting point?

There are three ways to solve this problem.  You could try out each possible sequence of moves.  That is a bad idea, because you will not live long enough to try them all.  You could program a computer to run through all the possibilities for you.  That is feasible, at least, but still, it will take a while.  The first two methods are called "brute force" methods, because they require a lot of effort, but are guaranteed to solve the problem.  The third way, which is the way most people do it, it to try to find some kind of short cut.

In case you have not figured it out yet, I will reveal the answer here.  After that, I set out on a zig-zag tour of my own, trying to see if math or science can teach us how to have a better government.  Read the rest at The Rest of the Story.