Your fame lands you on the lucrative lecture circuit taking you all over the world. One of your stops is in a very large city where you have many lectures, book signing events etc. Since you are a visitor you get back and forth by taxi cab. In this city, all the taxi drivers charge according to a two-fold formula. The fare increases as you move closer to the center of the city and increases with speed.
Speed is particularly important since increased speeds result in traffic tickets, accidents etc.
For this reason the fare increases as the square of the speed. The taxi drivers are also very considerate of your time. You specify to the driver not only your destination, but when you want to arrive. The driver never fails to arrive at exactly the time you specify. As you are driving along, you happen to have a map of the city and notice that the driver seems to be following a rather curious path.