<<feynman-examples>>
The below quotes from Richard Feynman in “Surely You’re Joking, Mr. Feynman!” I knew Richard Feynman well, from the age of 9, and spent as much time with him as I could. He had a peculiar way of thinking, and I very consciously copied his method. The gist of it is to always look at examples, then tweak them. Turn them upside down, inside out, left-to-right, and keep pushing till they go wrong, then force yourself to understand why. This practice forces the brain to recognize all kinds of wrongness quickly and to stay out of mind traps.
So you should do with \belex. Study the examples, then push on them until they break. Make sure you understand and can back out. Of course, this is a variation of the methodology of Test-Driven Development, very important for programmer productivity (productivity).
That was the first time I was in Japan. I was eager to go back, and said I would go to any university they wanted me to. So the Japanese arranged a whole series of places to visit for a few days at a time.
At all these places everybody working in physics would tell me what they were doing and I’d discuss it with them. They would tell me the general problem they were working on, and would begin to write a bunch of equations.
“Wait a minute,” I would say. “Is there a particular example of this general problem?”
“Why yes; of course.”
“Good. Give me one example.” I can’t understand anything in general unless I’m carrying along in my mind a specific example and watching it go. Some people think in the beginning I’m kind of slow and I don’t understand the problem, because I ask a lot of these “dumb” questions.
But later, when the guy’s in the middle of a bunch of equations, he’ll say something and I’ll say “Wait a minute! There’s an error! That can’t be right!”
The guy looks at his equations, and sure enough, after a while he finds the mistake and wonders, “How the hell did this guy, who hardly understood anything at the beginning, find that mistake in the mess of all these equations?”
He thinks I’m following the steps mathematically, but that’s not what I’m doing. I have the specific example of what he’s trying to analyze, and I know from instinct and experience the properties of the thing. So when the equation says it should behave so-and-so, and I know that’s the wrong way around, I jump up and say “Wait! There’s a mistake!”