Main Question or Discussion Point
I took the following excerpt from "Surely You're Joking, Mr. Feynman!"
I'd just like to know if this kind of 'fragile knowledge' as Feynman puts it, is preventable? Or can only certain gifted minds do this sort of thing? I don't consider myself able to do this kind of thing at ALL, so is it too late for me to gain these skills as I go into physics next fall?I often liked to play tricks on people when I was at MIT. One time, in
mechanical drawing class, some joker picked up a French curve (a piece of
plastic for drawing smooth curves -- a curly, funny-looking thing) and said,
"I wonder if the curves on this thing have some special formula?"
I thought for a moment and said, "Sure they do. The curves are very
special curves. Lemme show ya," and I picked up my French curve and began to
turn it slowly. "The French curve is made so that at the lowest point on
each curve, no matter how you turn it, the tangent is horizontal."
All the guys in the class were holding their French curve up at
different angles, holding their pencil up to it at the lowest point and
laying it along, and discovering that, sure enough, the tangent is
horizontal. They were all excited by this "discovery" -- even though they
had already gone through a certain amount of calculus and had already
"learned" that the derivative (tangent) of the minimum (lowest point) of any
curve is zero (horizontal). They didn't put two and two together. They
didn't even know what they "knew."
I don't know what's the matter with people: they don't learn by
understanding; they learn by some other way -- by rote, or something. Their
knowledge is so fragile!
I did the same kind of trick four years later at Princeton when I was
talking with an experienced character, an assistant of Einstein, who was
surely working with gravity all the time. I gave him a problem: You blast
off in a rocket which has a clock on board, and there's a clock on the
ground. The idea is that you have to be back when the clock on the ground
says one hour has passed. Now you want it so that when you come back, your
clock is as far ahead as possible. According to Einstein, if you go very
high, your clock will go faster, because the higher something is in a
gravitational field, the faster its clock goes. But if you try to go too
high, since you've only got an hour, you have to go so fast to get there
that the speed slows your clock down. So you can't go too high. The question
is, exactly what program of speed and height should you make so that you get
the maximum time on your clock?
This assistant of Einstein worked on it for quite a bit before he
realized that the answer is the real motion of matter. If you shoot
something up in a normal way, so that the time it takes the shell to go up
and come down is an hour, that's the correct motion. It's the fundamental
principle of Einstein's gravity -- that is, what's called the "proper time"
is at a maximum for the actual curve. But when I put it to him, about a
rocket with a clock, he didn't recognize it. It was just like the guys in
mechanical drawing class, but this time it wasn't dumb freshmen. So this
kind of fragility is, in fact, fairly common, even with more learned people.