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
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.
When I was a junior or senior I used to eat at a certain restaurant in Boston. I went there by myself, often on successive evenings. People got to know me, and I had the same waitress all the time.
I noticed that they were always in a hurry, rushing around, so one day, just for fun, I left my tip, which was usually ten cents (normal for those days), in two nickels, under two glasses: I filled each glass to the very top, dropped a nickel in, and with a card over it, turned it over so it was upside down on the table. Then I slipped out the card (no water leaks out because no air can come in—the rim is too close to the table for that).
I put the tip under two glasses because I knew they were always in a hurry. If the tip was a dime in one glass, the waitress, in her haste to get the table ready for the next customer, would pick up the glass, the water would spill out, and that would be the end of it. But after she does that with the first glass, what the hell is she going to do with the second one? She can’t just have the nerve to lift it up now!
On the way out I said to my waitress, “Be careful, Sue. There’s something funny about the glasses you gave me—they’re filled in on the top, and there’s a hole on the bottom!”
The next day I came back, and I had a new waitress. My regular waitress wouldn’t have anything to do with me. “Sue’s very angry at you,” my new waitress said. “After she picked up the first glass and water went all over the place, she called the boss out. They studied it a little bit, but they couldn’t spend all day figuring out what to do, so they finally picked up the other one, and water went out
I laughed.
She said, “It’s not funny! How would
“I’d get a soup plate and then slide the glass very carefully over to the edge of the table, and let the water run into the soup plate—it doesn’t have to run onto the floor. Then I’d take the nickel out.”
“Oh, that’s a goood idea,” she said.
That evening I left my tip under a coffee cup, which I left upside down on the table.
The next night I came and I had the same new waitress.
“What’s the idea of leaving the cup upside down last time?”
“Well, I thought that even though you were in a hurry, you’d have to go back into the kitchen and get a soup plate; then you’d have to
“I
My masterpiece of mischief happened at the fraternity. One morning I woke up very early, about five o’clock, and couldn’t go back to sleep, so I went downstairs from the sleeping rooms and discovered some signs hanging on strings which said things like “DOOR! DOOR! WHO STOLE THE DOOR?” I saw that someone had taken a door off its hinges, and in its place they hung a sign that said, “PLEASE CLOSE THE DOOR!”—the sign that used to be on the door that was missing.
I immediately figured out what the idea was. In that room a guy named Pete Bernays and a couple of other guys liked to work very hard, and always wanted it quiet. If you wandered into their room looking for something, or to ask them how they did problem such and such, when you would leave you would always hear these guys scream, “Please close the door!”
Somebody had gotten tired of this, no doubt, and had taken the door off. Now this room, it so happened, had two doors, the way it was built, so I got an idea: I took the other door off its hinges, carried it downstairs, and hid it in the basement behind the oil tank. Then I quietly went back upstairs and went to bed.
Later in the morning I made believe I woke up and came downstairs a little late. The other guys were milling around, and Pete and his friends were all upset: The doors to their room were missing, and they had to study, blah, blah, blah, blah. I was coming down the stairs and they said, “Feynman! Did you take the doors?”
“Oh, yeah!” I said. “I took the door. You can see the scratches on my knuckles here, that I got when my hands scraped against the wall as I was carrying it down into the basement.”
They weren’t satisfied with my answer; in fact, they didn’t believe me.
The guys who took the first door had left so many clues—the handwriting on the signs, for instance—that they were soon found out. My idea was that when it was found out who stole the first door, everybody would think they also stole the other door. It worked perfectly: The guys who took the first door were pummeled and tortured and worked on by everybody, until finally, with much pain and difficulty, they convinced their tormentors that they had only taken one door, unbelievable as it might be.
I listened to all this, and I was happy.
The other door stayed missing for a whole week, and it became more and more important to the guys who were trying to study in that room that the other door be found.
Finally, in order to solve the problem, the president of the fraternity says at the dinner table, “We have to solve this problem of the other door. I haven’t been able to solve the problem myself, so I would like suggestions from the rest of you as to how to straighten this out, because Pete and the others are trying to study.”
Somebody makes a suggestion, then someone else.
After a little while, I get up and make a suggestion. “All right,” I say in a sarcastic voice, “whoever you are who stole the door, we know you’re wonderful. You’re so
The next guy makes his suggestion: “I have another idea,” he says. “I think that you, as president, should ask each man on his word of honor towards the fraternity to say whether he took the door or not.”
The president says, “That’s a