Key ideas: Published in 1985. "That one person could have so many wonderfully crazy things happen to him in one life is sometimes hard to believe. That one person could invent so much innocent mischief in one life is surely an inspiration!" (Ralph Leighton)
The main reason people hired me was the Depression. They didn’t have any money to fix their radios, and they’d hear about this kid who would do it for less. So I’d climb on roofs to fix antennas, and all kinds of stuff. I got a series of lessons of ever-increasing difficulty. Ultimately I got some job like converting a DC set into an AC set, and it was very hard to keep the hum from going through the system, and I didn’t build it quite right. I shouldn’t have bitten that one off, but I didn’t know.
One job was really sensational. I was working at the time for a printer, and a man who knew that printer knew I was trying to get jobs fixing radios, so he sent a fellow around to the print shop to pick me up. The guy is obviously poor—his car is a complete wreck—and we go to his house which is in a cheap part of town....
And all the time, on the way to his house, he’s saying things like, “Do you know anything about radios? How do you know about radios—you’re just a little boy!”
He’s putting me down the whole way, and I’m thinking, “So what’s the matter with him? So it makes a little noise.”...
I start walking back and forth, thinking, and I realize that one way it can happen is that the tubes are heating up in the wrong order...
So the guy says, “What are you doing? You come to fix the radio, but you’re only walking back and forth!”
I say, “I’m thinking!"...
So I changed the tubes around, stepped to the front of the radio, turned the thing on, and it’s as quiet as a lamb: it waits until it heats up, and then plays perfectly—no noise.
When a person has been negative to you, and then you do something like that, they’re usually a hundred percent the other way, kind of to compensate. He got me other jobs, and kept telling everybody what a tremendous genius I was, saying, “He fixes radios by thinking!” The whole idea of thinking, to fix a radio—a little boy stops and thinks, and figures out how to do it—he never thought that was possible.
Another thing I did in high school was to invent problems and theorems. I mean, if I were doing any mathematical thing at all, I would find some practical example for which it would be useful. I invented a set of right-triangle problems. But instead of giving the lengths of two of the sides to find the third, I gave the difference of the two sides.
A typical example was: There’s a flagpole, and there’s a rope that comes down from the top. When you hold the rope straight down, it’s three feet longer than the pole, and when you pull the rope out tight, it’s five feet from the base of the pole. How high is the pole?
I developed some equations for solving problems like that, and as a result I noticed some connection—perhaps it was sin2+cos2=1—that reminded me of trigonometry.
Now, a few years earlier, perhaps when I was eleven or twelve, I had read a book on trigonometry that I had checked out from the library, but the book was by now long gone. I remembered only that trigonometry had something to do with relations between sines and cosines. So I began to work out all the relations by drawing triangles, and each one I proved by myself. I also calculated the sine, cosine, and tangent of every five degrees, starting with the sine of five degrees as given, by addition and half-angle formulas that I had worked out.
While I was doing all this trigonometry, I didn’t like the symbols for sine, cosine, tangent, and so on. To me, “sin f” looked like s times i times n times f! So I invented another symbol, like a square root sign, that was a sigma with a long arm sticking out of it, and I put the f underneath. For the tangent it was a tau with the top of the tau extended, and for the cosine I made a kind of gamma, but it looked a little bit like the square root sign....
I didn’t like f(x)—that looked to me like f times x. I also didn’t like dy/dx—you have a tendency to cancel the d’s—so I made a different sign, something like an & sign. For logarithms it was a big L extended to the right, with the thing you take the log of inside, and so on.
I thought my symbols were just as good, if not better, than the regular symbols—it doesn’t make any difference what symbols you use—but I discovered later that it does make a difference. Once when I was explaining something to another kid in high school, without thinking I started to make these symbols, and he said, “What the hell are those?” I realized then that if I’m going to talk to anybody else, I’ll have to use the standard symbols, so I eventually gave up my own symbols.
I often listened to my roommates [at MIT]—they were both seniors—studying for their theoretical physics course. One day they were working pretty hard on something that seemed pretty clear to me, so I said, “Why don’t you use the Baronallai’s equation?”
“What’s that!” they exclaimed. “What are you talking about!”
I explained to them what I meant and how it worked in this case, and it solved the problem. It turned out it was Bernoulli’s equation that I meant, but I had read all this stuff in the encyclopedia without talking to anybody about it, so I didn’t know how to pronounce anything.
But my roommates were very excited, and from then on they discussed their physics problems with me—I wasn’t so lucky with many of them—and the next year, when I took the course, I advanced rapidly. That was a very good way to get educated, working on the senior problems and learning how to pronounce things.
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.
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 clever! We can’t figure out who you are, so you must be some sort of super-genius. You don’t have to tell us who you are; all we want to know is where the door is. So if you will leave a note somewhere, telling us where the door is, we will honor you and admit forever that you are a super-marvel, that you are so smart that you could take the other door without our being able to figure out who you are. But for God’s sake, just leave the note somewhere, and we will be forever grateful to you for it.”
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 very good idea. On the fraternity word of honor!” So he goes around the table, and asks each guy, one by one: “Jack, did you take the door?”
“No, sir, I did not take the door.”
“Tim: Did you take the door?”
“No, sir! I did not take the door!”
“Maurice. Did you take the door?”
“No, I did not take the door, sir.”
“Feynman, did you take the door?”
“Yeah, I took the door.”
“Cut it out, Feynman; this is serious! Sam! Did you take the door …”—it went all the way around. Everyone was shocked. There must be some real rat in the fraternity who didn’t respect the fraternity word of honor!
That night I left a note with a little picture of the oil tank and the door next to it, and the next day they found the door and put it back.
Sometime later I finally admitted to taking the other door, and I was accused by everybody of lying. They couldn’t remember what I had said. All they could remember was their conclusion after the president of the fraternity had gone around the table and asked everybody, that nobody admitted taking the door. The idea they remembered, but not the words.
People often think I’m a faker, but I’m usually honest, in a certain way—in such a way that often nobody believes me!
When I was a student at MIT I was interested only in science; I was no good at anything else. But at MIT there was a rule: You have to take some humanities courses to get more “culture.” Besides the English classes required were two electives, so I looked through the list, and right away I found astronomy—as a humanities course! So that year I escaped with astronomy. Then next year I looked further down the list, past French literature and courses like that, and found philosophy. It was the closest thing to science I could find.
When I was an undergraduate at MIT I loved it. I thought it was a great place, and I wanted to go to graduate school there too, of course. But when I went to Professor Slater and told him of my intentions, he said, “We won’t let you in here.”
I said, “What?”
Slater said, “Why do you think you should go to graduate school at MIT?”
“Because MIT is the best school for science in the country.”
“You think that?”
“Yeah.”
“That’s why you should go to some other school. You should find out how the rest of the world is.”
So I decided to go to Princeton.
MIT had built a new cyclotron while I was a student there, and it was just beautiful! The cyclotron itself was in one room, with the controls in another room. It was beautifully engineered. The wires ran from the control room to the cyclotron underneath in conduits, and there was a whole console of buttons and meters. It was what I would call a gold-plated cyclotron.
Now I had read a lot of papers on cyclotron experiments, and there weren’t many from MIT. Maybe they were just starting. But there were lots of results from places like Cornell, and Berkeley, and above all, Princeton. Therefore what I really wanted to see, what I was looking forward to, was the PRINCETON CYCLOTRON. That must be something!
So first thing on Monday, I go into the physics building and ask, “Where is the cyclotron—which building?”
“It’s downstairs, in the basement—at the end of the hall.”
In the basement? It was an old building. There was no room in the basement for a cyclotron. I walked down to the end of the hall, went through the door, and in ten seconds I learned why Princeton was right for me—the best place for me to go to school. In this room there were wires strung all over the place! Switches were hanging from the wires, cooling water was dripping from the valves, the room was full of stuff, all out in the open. Tables piled with tools were everywhere; it was the most godawful mess you ever saw. The whole cyclotron was there in one room, and it was complete, absolute chaos!
It reminded me of my lab at home. Nothing at MIT had ever reminded me of my lab at home. I suddenly realized why Princeton was getting results. They were working with the instrument. They built the instrument; they knew where everything was, they knew how everything worked, there was no engineer involved, except maybe he was working there too. It was much smaller than the cyclotron at MIT, and “gold-plated”?—it was the exact opposite. When they wanted to fix a vacuum, they’d drip glyptal on it, so there were drops of glyptal on the floor. It was wonderful!
Because they worked with it. They didn’t have to sit in another room and push buttons! (Incidentally, they had a fire in that room, because of all the chaotic mess that they had—too many wires—and it destroyed the cyclotron. But I’d better not tell about that!)
I learned a lot of different things from different schools. MIT is a very good place; I’m not trying to put it down. I was just in love with it. It has developed for itself a spirit, so that every member of the whole place thinks that it’s the most wonderful place in the world—it’s the center, somehow, of scientific and technological development in the United States, if not the world. It’s like a New Yorker’s view of New York: they forget the rest of the country. And while you don’t get a good sense of proportion there, you do get an excellent sense of being with it and in it, and having motivation and desire to keep on—that you’re specially chosen, and lucky to be there.
So MIT was good, but Slater was right to warn me to go to another school for my graduate work. And I often advise my students the same way. Learn what the rest of the world is like. The variety is worthwhile.
Paul Olum and I shared a bathroom. We got to be good friends, and he tried to teach me mathematics. He got me up to homotopy groups, and at that point I gave up. But the things below that I understood fairly well.
One thing I never did learn was contour integration. I had learned to do integrals by various methods shown in a book that my high school physics teacher Mr. Bader had given me.
One day he told me to stay after class. “Feynman,” he said, “you talk too much and you make too much noise. I know why. You’re bored. So I’m going to give you a book. You go up there in the back, in the corner, and study this book, and when you know everything that’s in this book, you can talk again.”
So every physics class, I paid no attention to what was going on with Pascal’s Law, or whatever they were doing. I was up in the back with this book: Advanced Calculus, by Woods. Bader knew I had studied Calculus for the Practical Man a little bit, so he gave me the real works—it was for a junior or senior course in college. It had Fourier series, Bessel functions, determinants, elliptic functions—all kinds of wonderful stuff that I didn’t know anything about.
That book also showed how to differentiate parameters under the integral sign—it’s a certain operation. It turns out that’s not taught very much in the universities; they don’t emphasize it. But I caught on how to use that method, and I used that one damn tool again and again. So because I was self-taught using that book, I had peculiar methods of doing integrals.
The result was, when guys at MIT or Princeton had trouble doing a certain integral, it was because they couldn’t do it with the standard methods they had learned in school. If it was contour integration, they would have found it; if it was a simple series expansion, they would have found it. Then I come along and try differentiating under the integral sign, and often it worked. So I got a great reputation for doing integrals, only because my box of tools was different from everybody else’s, and they had tried all their tools on it before giving the problem to me.
They decided to do something utterly illegal and censor the mail of people inside the United States—which they have no right to do. So it had to be set up very delicately as a voluntary thing.
We would all volunteer not to seal the envelopes of the letters we sent out, and it would be all right for them to open letters coming in to us; that was voluntarily accepted by us. We would leave our letters open; and they would seal them if they were OK. If they weren’t OK in their opinion, they would send the letter back to us with a note that there was a violation of such and such a paragraph of our “understanding.” < So, very delicately amongst all these liberal-minded scientific guys, we finally got the censorship set up, with many rules. We were allowed to comment on the character of the administration if we wanted to, so we could write our senator and tell him we didn’t like the way things were run, and things like that. They said they would notify us if there were any difficulties.
There were other things. Like the hole in the fence, I was always trying to point these things out in a non-direct manner. And one of the things I wanted to point out was this—that at the very beginning we had terribly important secrets; we’d worked out lots of stuff about bombs and uranium and how it worked, and so on; and all this stuff was in documents that were in wooden filing cabinets that had little, ordinary common padlocks on them.
Of course, there were various things made by the shop, like a rod that would go down and then a padlock to hold it, but it was always just a padlock. Furthermore, you could get the stuff out without even opening the padlock. You just tilt the cabinet over backwards. The bottom drawer has a little rod that’s supposed to hold the papers together, and there’s a long wide hole in the wood underneath. You can pull the papers out from below.
So I used to pick the locks all the time and point out that it was very easy to do. And every time we had a meeting of everybody together, I would get up and say that we have important secrets and we shouldn’t keep them in such things; we need better locks.
One day Teller got up at the meeting, and he said to me, “I don’t keep my most important secrets in my filing cabinet; I keep them in my desk drawer. Isn’t that better?”
I said, “I don’t know. I haven’t seen your desk drawer.” He was sitting near the front of the meeting, and I’m sitting further back. So the meeting continues, and I sneak out and go down to see his desk drawer.
I don’t even have to pick the lock on the desk drawer. It turns out that if you put your hand in the back, underneath, you can pull out the paper like those toilet paper dispensers. You pull out one, it pulls another, it pulls another … I emptied the whole damn drawer, put everything away to one side, and went back upstairs.
The meeting was just ending, and everybody was coming out, and I joined the crew and ran to catch up with Teller, and I said, “Oh, by the way let me see your desk drawer.”
“Certainly,” he said, and he showed me the desk.
I looked at it and said, “That looks pretty good to me. Let’s see what you have in there.”
“I’ll be very glad to show it to you,” he said, putting in the key and opening the drawer. “If,” he said, “you hadn’t already seen it yourself.”
The trouble with playing a trick on a highly intelligent man like Mr. Teller is that the time it takes him to figure out from the moment that he sees there is something wrong till he understands exactly what happened is too damn small to give you any pleasure!
Within a week I was in the cafeteria and some guy, fooling around, throws a plate in the air. As the plate went up in the air I saw it wobble, and I noticed the red medallion of Cornell on the plate going around. It was pretty obvious to me that the medallion went around faster than the wobbling.
I had nothing to do, so I start to figure out the motion of the rotating plate. I discover that when the angle is very slight, the medallion rotates twice as fast as the wobble rate—two to one. It came out of a complicated equation! Then I thought, “Is there some way I can see in a more fundamental way, by looking at the forces or the dynamics, why it’s two to one?”
I don’t remember how I did it, but I ultimately worked out what the motion of the mass particles is, and how all the accelerations balance to make it come out two to one.
I still remember going to Hans Bethe and saying, “Hey, Hans! I noticed something interesting. Here the plate goes around so, and the reason it’s two to one is …” and I showed him the accelerations.
He says, “Feynman, that’s pretty interesting, but what’s the importance of it? Why are you doing it?”
“Hah!” I say. “There’s no importance whatsoever. I’m just doing it for the fun of it.” His reaction didn’t discourage me; I had made up my mind I was going to enjoy physics and do whatever I liked...
It was effortless. It was easy to play with these things. It was like uncorking a bottle: Everything flowed out effortlessly. I almost tried to resist it! There was no importance to what I was doing, but ultimately there was. The diagrams and the whole business that I got the Nobel Prize for came from that piddling around with the wobbling plate.
In regard to education in Brazil, I had a very interesting experience. I was teaching a group of students who would ultimately become teachers, since at that time there were not many opportunities in Brazil for a highly trained person in science. These students had already had many courses, and this was to be their most advanced course in electricity and magnetism—Maxwell’s equations, and so on.
The university was located in various office buildings throughout the city, and the course I taught met in a building which overlooked the bay.
I discovered a very strange phenomenon: I could ask a question, which the students would answer immediately. But the next time I would ask the question—the same subject, and the same question, as far as I could tell—they couldn’t answer it at all!
For instance, one time I was talking about polarized light, and I gave them all some strips of polaroid.
Polaroid passes only light whose electric vector is in a certain direction, so I explained how you could tell which way the light is polarized from whether the polaroid is dark or light.
We first took two strips of polaroid and rotated them until they let the most light through. From doing that we could tell that the two strips were now admitting light polarized in the same direction—what passed through one piece of polaroid could also pass through the other. But then I asked them how one could tell the absolute direction of polarization, for a single piece of polaroid.
They hadn’t any idea.
I knew this took a certain amount of ingenuity, so I gave them a hint: “Look at the light reflected from the bay outside.”
Nobody said anything.
Then I said, “Have you ever heard of Brewster’s Angle?”
“Yes, sir! Brewster’s Angle is the angle at which light reflected from a medium with an index of refraction is completely polarized.”
“And which way is the light polarized when it’s reflected?”
“The light is polarized perpendicular to the plane of reflection, sir.” Even now, I have to think about it; they knew it cold! They even knew the tangent of the angle equals the index!
I said, “Well?”
Still nothing. They had just told me that light reflected from a medium with an index, such as the bay outside, was polarized; they had even told me which way it was polarized.
I said, “Look at the bay outside, through the polaroid. Now turn the polaroid.”
“Ooh, it’s polarized!” they said.
After a lot of investigation, I finally figured out that the students had memorized everything, but they didn’t know what anything meant.
When they heard “light that is reflected from a medium with an index,” they didn’t know that it meant a material such as water. They didn’t know that the “direction of the light” is the direction in which you see something when you’re looking at it, and so on. Everything was entirely memorized, yet nothing had been translated into meaningful words.
So if I asked, “What is Brewster’s Angle?” I’m going into the computer with the right keywords. But if I say, “Look at the water,” nothing happens—they don’t have anything under “Look at the water”!
Later I attended a lecture at the engineering school. The lecture went like this, translated into English: “Two bodies … are considered equivalent … if equal torques … will produce … equal acceleration. Two bodies, are considered equivalent, if equal torques, will produce equal acceleration.” The students were all sitting there taking dictation, and when the professor repeated the sentence, they checked it to make sure they wrote it down all right. Then they wrote down the next sentence, and on and on. I was the only one who knew the professor was talking about objects with the same moment of inertia, and it was hard to figure out.
I didn’t see how they were going to learn anything from that. Here he was talking about moments of inertia, but there was no discussion about how hard it is to push a door open when you put heavy weights on the outside, compared to when you put them near the hinge—nothing!
After the lecture, I talked to a student: “You take all those notes—what do you do with them?”
“Oh, we study them,” he says. “We’ll have an exam.”
“What will the exam be like?”
“Very easy. I can tell you now one of the questions.” He looks at his notebook and says, “ ‘When are two bodies equivalent?’ And the answer is, ‘Two bodies are considered equivalent if equal torques will produce equal acceleration.’ So, you see, they could pass the examinations, and “learn” all this stuff, and not know anything at all, except what they had memorized.
Then I went to an entrance exam for students coming into the engineering school. It was an oral exam, and I was allowed to listen to it. One of the students was absolutely super: He answered everything nifty! The examiners asked him what diamagnetism was, and he answered it perfectly. Then they asked, “When light comes at an angle through a sheet of material with a certain thickness, and a certain index N, what happens to the light?”
“It comes out parallel to itself, sir—displaced.”
“And how much is it displaced?”
“I don’t know, sir, but I can figure it out.” So he figured it out.
He was very good. But I had, by this time, my suspicions.
After the exam I went up to this bright young man, and explained to him that I was from the United States, and that I wanted to ask him some questions that would not affect the result of his examination in any way. The first question I ask is,“Can you give me some example of a diamagnetic substance?”
“No.”
Then I asked, “If this book was made of glass, and I was looking at something on the table through it, what would happen to the image if I tilted the glass?”
“It would be deflected, sir, by twice the angle that you’ve turned the book.”
I said, “You haven’t got it mixed up with a mirror, have you?”
“No, sir!”
He had just told me in the examination that the light would be displaced, parallel to itself, and therefore the image would move over to one side, but would not be turned by any angle. He had even figured out how much it would be displaced, but he didn’t realize that a piece of glass is a material with an index, and that his calculation had applied to my question.
At the end of the academic year, the students asked me to give a talk about my experiences of teaching in Brazil. At the talk there would be not only students, but professors and government officials, so I made them promise that I could say whatever I wanted. They said, “Sure. Of course. It’s a free country.”
So I came in, carrying the elementary physics textbook that they used in the first year of college. They thought this book was especially good because it had different kinds of typeface—bold black for the most important things to remember, lighter for less important things, and so on.
Right away somebody said, “You’re not going to say anything bad about the textbook, are you? The man who wrote it is here, and everybody thinks it’s a good textbook.”
“You promised I could say whatever I wanted.”...
Then I say, “The main purpose of my talk is to demonstrate to you that no science is being taught in Brazil!”
I can see them stir, thinking, “What? No science? This is absolutely crazy! We have all these classes.”
So I tell them that one of the first things to strike me when I came to Brazil was to see elementary school kids in bookstores, buying physics books. There are so many kids learning physics in Brazil, beginning much earlier than kids do in the United States, that it’s amazing you don’t find many physicists in Brazil—why is that? So many kids are working so hard, and nothing comes of it.
Then I gave the analogy of a Greek scholar who loves the Greek language, who knows that in his own country there aren’t many children studying Greek. But he comes to another country, where he is delighted to find everybody studying Greek—even the smaller kids in the elementary schools.
He goes to the examination of a student who is coming to get his degree in Greek, and asks him, “What were Socrates’ ideas on the relationship between Truth and Beauty?”—and the student can’t answer. Then he asks the student, What did Socrates say to Plato in the Third Symposium?” the student lights up and goes, “Brrrrrrrrr-up ”—he tells you everything, word for word, that Socrates said, in beautiful Greek.
But what Socrates was talking about in the Third Symposium was the relationship between Truth and Beauty!
What this Greek scholar discovers is, the students in another country learn Greek by first learning to pronounce the letters, then the words, and then sentences and paragraphs. They can recite, word for word, what Socrates said, without realizing that those Greek words actually mean something. To the student they are all artificial sounds. Nobody has ever translated them into words the students can understand.
I said, “That’s how it looks to me, when I see you teaching the kids ‘science’ here in Brazil.” (Big blast, right?)
Then I held up the elementary physics textbook they were using. “There are no experimental results mentioned anywhere in this book, except in one place where there is a ball, rolling down an inclined plane, in which it says how far the ball got after one second, two seconds, three seconds, and so on. The numbers have ‘errors’ in them—that is, if you look at them, you think you’re looking at experimental results, because the numbers are a little above, or a little below, the theoretical values.
The book even talks about having to correct the experimental errors—very fine. The trouble is, when you calculate the value of the acceleration constant from these values, you get the right answer. But a ball rolling down an inclined plane, if it is actually done, has an inertia to get it to turn, and will, if you do the experiment, produce five-sevenths of the right answer, because of the extra energy needed to go into the rotation of the ball. Therefore this single example of experimental ‘results’ is obtained from a fake experiment. Nobody had rolled such a ball, or they would never have gotten those results!
“I have discovered something else,” I continued. “By flipping the pages at random, and putting my finger in and reading the sentences on that page, I can show you what’s the matter—how it’s not science, but memorizing, in every circumstance. Therefore I am brave enough to flip through the pages now, in front of this audience, to put my finger in, to read, and to show you.”
So I did it. Brrrrrrrup—I stuck my finger in, and I started to read: “Triboluminescence. Triboluminescence is the light emitted when crystals are crushed …”
I said, “And there, have you got science? No! You have only told what a word means in terms of other words. You haven’t told anything about nature—what crystals produce light when you crush them, why they produce light. Did you see any student go home and try it? He can’t.
“But if, instead, you were to write, ‘When you take a lump of sugar and crush it with a pair of pliers in the dark, you can see a bluish flash. Some other crystals do that too. Nobody knows why. The phenomenon is called “triboluminescence.”‘ Then someone will go home and try it. Then there’s an experience of nature.” I used that example to show them, but it didn’t make any difference where I would have put my finger in the book; it was like that everywhere.
Finally, I said that I couldn’t see how anyone could he educated by this self-propagating system in which people pass exams, and teach others to pass exams, but nobody knows anything. “However,” I said, “I must be wrong. There were two students in my class who did very well, and one of the physicists I know was educated entirely in Brazil. Thus, it must be possible for some people to work their way through the system, had as it is.”...
Then something happened which was totally unexpected for me. One of the students got up and said, “I’m one of the two students whom Mr. Feynman referred to at the end of his talk. I was not educated in Brazil; I was educated in Germany, and I’ve just come to Brazil this year.”
The other student who had done well in class had a similar thing to say. And the professor I had mentioned got up and said, “I was educated here in Brazil during the war, when, fortunately, all of the professors had left the university, so I learned everything by reading alone. Therefore I was not really educated under the Brazilian system.”
I didn’t expect that. I knew the system was bad, but 100 percent—it was terrible!
I never looked at the original data; I only read those reports, like a dope. Had I been a good physicist, when I thought of the original idea back at the Rochester Conference I would have immediately looked up “how strong do we know it’s T?”—that would have been the sensible thing to do. I would have recognized right away that I had already noticed it wasn’t satisfactorily proved.
Since then I never pay any attention to anything by “experts.” I calculate everything myself. When people said the quark theory was pretty good, I got two Ph. D.s, Finn Ravndal and Mark Kislinger, to go through the whole works with me, just so I could check that the thing was really giving results that fit fairly well, and that it was a significantly good theory. I’ll never make that mistake again, reading the experts’ opinions. Of course, you only live one life, and you make all your mistakes, and learn what not to do, and that’s the end of you.
I went back to my dormitory room and I wrote out carefully, as best I could, what I thought the subject of “the ethics of equality in education” might be, and I gave some examples of the kinds of problems I thought we might be talking about,
For instance, in education, you increase differences. If someone’s good at something, you try to develop his ability, which results in differences, or inequalities. So if education increases inequality, is this ethical? Then, after giving some more examples, I went on to say that while “the fragmentation of knowledge” is a difficulty because the complexity of the world makes it hard to learn things, in light of my definition of the realm of the subject, I couldn’t see how the fragmentation of knowledge had anything to do with anything approximating what the ethics of equality in education might more or less be.
The next day I brought my paper into the meeting, and the guy said, “Yes, Mr. Feynman has brought up some very interesting questions we ought to discuss, and we’ll put them aside for some possible future discussion.”
They completely missed the point. I was trying to define the problem, and then show how “the fragmentation of knowledge” didn’t have anything to do with it. And the reason that nobody got anywhere in that conference was that they hadn’t clearly defined the subject of “the ethics of equality in education,” and therefore no one knew exactly what they were supposed to talk about.
There was a sociologist who had written a paper for us all to read—something he had written ahead of time. I started to read the damn thing, and my eyes were coming out: I couldn’t make head nor tail of it! ... until finally I said to myself, “I’m gonna stop, and read one sentence slowly, so I can figure out what the hell it means.”
So I stopped—at random—and read the next sentence very carefully. I can’t remember it precisely, but it was very close to this:
“The individual member of the social community often receives his information via visual, symbolic channels.”
I went back and forth over it, and translated. You know what it means? “People read.”
There was a special dinner at some point, and the head of the theology place, a very nice, very Jewish man, gave a speech.... He talked about the big differences in the welfare of various countries, which cause jealousy, which leads to conflict, and now that we have atomic weapons, any war and we’re doomed, so therefore the right way out is to strive for peace by making sure there are no great differences from place to place, and since we have so much in the United States, we should give up nearly everything to the other countries until we’re all even.
Everybody was listening to this, and we were all full of sacrificial feeling, and all thinking we ought to do this. But I came back to my senses on the way home.
I started to say that the idea of distributing everything evenly is based on a theory that there’s only X amount of stuff in the world, that somehow we took it away from the poorer countries in the first place, and therefore we should give it back to them.
But this theory doesn’t take into account the real reason for the differences between countries—that is, the development of new techniques for growing food, the development of machinery to grow food and to do other things, and the fact that all this machinery requires the concentration of capital.
It isn’t the stuff, but the power to make the stuff, that is important. But I realize now that these people were not in science; they didn’t understand it....
When it came time to evaluate the conference at the end, the others told how much they got out of it, how successful it was, and so on. When they asked me, I said, “This conference was worse than a Rorschach test: There’s a meaningless inkblot, and the others ask you what you think you see, but when you tell them, they start arguing with you!
I understood what they were trying to do. Many people thought we were behind the Russians after Sputnik, and some mathematicians were asked to give advice on how to teach math by using some of the rather interesting modern concepts of mathematics. The purpose was to enhance mathematics for the children who found it dull.
I’ll give you an example: They would talk about different bases of numbers—five, six, and so on—to show the possibilities. That would be interesting for a kid who could understand base ten—something to entertain his mind. But what they had turned it into, in these books, was that every child had to learn another base! And then the usual horror would come: “Translate these numbers, which are written in base seven, to base five.”
Translating from one base to another is an utterly useless thing. If you can do it, maybe it’s entertaining; if you can’t do it, forget it. There’s no point to it.
Finally I come to a book that says, “Mathematics is used in science in many ways. We will give you an example from astronomy, which is the science of stars.” I turn the page, and it says, “Red stars have a temperature of four thousand degrees, yellow stars have a temperature of five thousand degrees …”—so far, so good. It continues: “Green stars have a temperature of seven thousand degrees, blue stars have a temperature of ten thousand degrees, and violet stars have a temperature of … (some big number).” There are no green or violet stars, but the figures for the others are roughly correct. It’s vaguely right—but already, trouble! That’s the way everything was: Everything was written by somebody who didn’t know what the hell he was talking about, so it was a little bit wrong, always! And how we are going to teach well by using books written by people who don’t quite understand what they’re talking about,
I cannot understand. I don’t know why, but the books are lousy; UNIVERSALLY LOUSY!...
Then comes the list of problems. It says, “John and his father go out to look at the stars. John sees two blue stars and a red star. His father sees a green star, a violet star, and two yellow stars. What is the total temperature of the stars seen by John and his father?”—and I would explode in horror.
My wife would talk about the volcano downstairs. That’s only an example: it was perpetually like that. Perpetual absurdity! There’s no purpose whatsoever in adding the temperature of two stars. Nobody ever does that except, maybe, to then take the average temperature of the stars, but not to find out the total temperature of all the stars! It was awful! All it was was a game to get you to add, and they didn’t understand what they were talking about. It was like reading sentences with a few typographical errors, and then suddenly a whole sentence is written backwards. The mathematics was like that. Just hopeless!...
What finally clinched it, and made me ultimately resign, was that the following year we were going to discuss science books. I thought maybe the science would be different, so I looked at a few of them.
The same thing happened: something would look good at first and then turn out to be horrifying. For example, there was a book that started out with four pictures: first there was a wind-up toy; then there was an automobile; then there was a boy riding a bicycle; then there was something else. And underneath each picture it said, “What makes it go?”
I thought, “I know what it is: They’re going to talk about mechanics, how the springs work inside the toy; about chemistry, how the engine of the automobile works; and biology, about how the muscles work.”
It was the kind of thing my father would have talked about: “What makes it go? Everything goes because the sun is shining.” And then we would have fun discussing it:
“No, the toy goes because the spring is wound up,” I would say.
“How did the spring get wound up?” he would ask.
“I wound it up.”
“And how did you get moving?”
“From eating.”
“And food grows only because the sun is shining. So it’s because the sun is shining that all these things are moving.” That would get the concept across that motion is simply the transformation of the sun’s power.
I turned the page. The answer was, for the wind-up toy, “Energy makes it go.” And for the boy on the bicycle, “Energy makes it go.” For everything, “Energy makes it go.”
Now that doesn’t mean anything. Suppose it’s “Wakalixes.” That’s the general principle: “Wakalixes makes it go.” There’s no knowledge coming in. The child doesn’t learn anything; it’s just a word!
What they should have done is to look at the wind-up toy, see that there are springs inside, learn about springs, learn about wheels, and never mind “energy.” Later on, when the children know something about how the toy actually works, they can discuss the more general principles of energy.
It’s also not even true that “energy makes it go,” because if it stops, you could say, “energy makes it stop” just as well, What they’re talking about is concentrated energy being transformed into more dilute forms, which is a very subtle aspect of energy. Energy is neither increased nor decreased in these examples; it’s just changed from one form to another. And when the things stop, the energy is changed into heat, into general chaos.
During the Middle Ages there were all kinds of crazy ideas, such as that a piece of rhinoceros horn would increase potency. Then a method was discovered for separating the ideas—which was to try one to see if it worked, and if it didn’t work, to eliminate it. This method became organized, of course, into science. And it developed very well, so that we are now in the scientific age. It is such a scientific age, in fact, that we have difficulty in understanding how witch doctors could ever have existed, when nothing that they proposed ever really worked—or very little of it did...
I think the educational and psychological studies I mentioned are examples of what I would like to call cargo cult science. In the South Seas there is a cargo cult of people.
During the war they saw airplanes land with lots of good materials, and they want the same thing to happen now. So they’ve arranged to make things like runways, to put fires along the sides of the runways, to make a wooden hut for a man to sit in, with two wooden pieces on his head like headphones and bars of bamboo sticking out like antennas—he’s the controller—and they wait for the airplanes to land. They’re doing everything right. The form is perfect. It looks exactly the way it looked before. But it doesn’t work. No airplanes land. So I call these things cargo cult science, because they follow all the apparent precepts and forms of scientific investigation, but they’re missing something essential, because the planes don’t land.
Now it behooves me, of course, to tell you what they’re missing. But it would be just about as difficult to explain to the South Sea Islanders how they have to arrange things so that they get some wealth in their system. It is not something simple like telling them how to improve the shapes of the earphones. But there is one feature I notice that is generally missing in cargo cult science.
That is the idea that we all hope you have learned in studying science in school—we never explicitly say what this is, but just hope that you catch on by all the examples of scientific investigation. It is interesting, therefore, to bring it out now and speak of it explicitly. It’s a kind of scientific integrity, a principle of scientific thought that corresponds to a kind of utter honesty—a kind of leaning over backwards. For example, if you’re doing an experiment, you should report everything that you think might make it invalid—not only what you think is right about it: other causes that could possibly explain your results; and things you thought of that you’ve eliminated by some other experiment, and how they worked—to make sure the other fellow can tell they have been eliminated...
In summary, the idea is to try to give all of the information to help others to judge the value of your contribution; not just the information that leads to judgment in one particular direction or another.