Because problems such as the following, taken from Daniel Dennett’s Darwin’s Dangerous Idea (p. 134), just do my head in:
There is a famous story about the mathematician and physicist (and coinventor of the computer) John von Neumann, who was legendary for his lightning capacity to do prodigious calculations in his head. (Like most famous stories, this one has many versions, of which I choose the one that best makes the point I am pursuing.) One day a colleague approached him with a puzzle that had two paths to solution, a laborious, complicated calculation and an elegant, Aha!-type solution. This colleague had a theory: in such a case, mathematicians work out the laborious solution while the (lazier, but smarter) physicists pause and find the quick and easy solution. Which solution would von Neumann find? You know the sort of puzzle: Two trains, 100 miles apart, are approaching each other on the same track, one going 30 miles per hour, the other going 20 miles per hour. A bird flying 120 miles per hour starts at train A (when they are 100 miles apart), flies to train B, turns around and flies back to the approaching train A, and so forth, until the trains collide. How far has the bird flown when the collision occurs? “[Read the solution below the fold],” Von Neumann answered almost instantly. “Darn,” replied his colleague, “I predicted you’d do it the hard way.” “Ay!” von Neumann cried in embarrassment, smiting his forehead. “There’s an easy way!” (Hint: how long till the trains collide?)
The solution is two hundred and forty miles. And why it is so is an absolute bloody mystery!
P.S. Figuring out the time it took for the trains to collide was simple enough, or so I believed when I tackled the problem during my spare time at work. Factoring in the bird was another matter entirely.