Once upon a time I taught a boy to ride a bicycle. Johnny was seventeen years old, about two years my junior, and had never learned to balance his weight above two rotating cobwebs. He was extremely bright and later in life was to run his own computer company. But he was not what you might call a "jock!"
To this scientific brain I explained the physics of the bicycle: camber angles, trail, centrifugal forces, negative feedback loops, and in particular how a bicycle is in fact never on balance, but is always in a cycle of fall and recovery. I explained how when you want to turn to the right you have first to be falling to the right, and to accomplish that you have to turn the front wheel imperceptively to the left. Never mind that most people have absolutely no idea that that is what they are doing, Johnny needed to know. And understand he did.
But did he learn to ride a bicycle that day? Get ready for it. The answer is yes. He rode away. But did he "intellectualise" his way down the street, monitoring hundreds of physical processes? Of course not. For Johnny the incomprehensible was tantamount to the impossible. My explanation had only made the impossible possible.
It was an early lesson for me as a teacher: Occasionally, some people need to understand theory in order to be able to set their intuition free.
