I wrote a letter to her and proposed. Somebody who’s wise could have told me that was dangerous: When you’re away and you’ve got nothing but paper, and you’re feeling lonely, you remember all the good things and you can’t remember the reasons you had the arguments. And it didn’t work out. The arguments started again right away, and the marriage lasted for only two years.

There was a man at the U.S. Embassy who knew I liked samba music. I think I told him that when I had been in Brazil the first time, I had heard a samba band practicing in the street, and I wanted to learn more about Brazilian music.

He said a small group, called a regional, practiced at his apartment every week, and I could come over and listen to them play.

There were three or four people—one was the janitor from the apartment house-and they played rather quiet music up in his apartment; they had no other place to play. One guy had a tambourine that they called a pandeiro, and another guy had a small guitar. I kept hearing the beat of a drum somewhere, but there was no drum! Finally I figured out that it was the tambourine, which the guy was playing in a complicated way, twisting his wrist and hitting the skin with his thumb. I found that interesting, and learned how to play the pandeiro, more or less.

Then the season for Carnaval began to come around. That’s the season when new music is presented. They don’t put out new music and records all the time; they put them all out during Carnaval time, and it’s very exciting.

It turned out that the janitor was the composer for a small samba “school”—not a school in the sense of education, but in the sense of fish—from Copacabana Beach, called Farзantes deCopacabana, which means “Fakers from Copacabana,” which was just right for me, and he invited me to be in it.

Now this samba school was a thing where guys from the favelas—the poor sections of the city—would come down, and meet behind a construction lot where some apartment houses were being built, and practice the new music for the Carnaval.

I chose to play a thing called a “frigideira,” which is a toy frying pan made of metal, about six inches in diameter, with a little metal stick to beat it with. It’s an accompanying instrument which makes a tinkly, rapid noise that goes with the main samba music and rhythm and fills it out. So I tried to play this thing and everything was going all right. We were practicing, the music was roaring along and we were going like sixty, when all of a sudden the head of the batteria section, a great big black man, yelled out, “STOP! Hold it, hold it—wait a minute!” And everybody stopped. “Something’s wrong with the frigideiras!” he boomed out. “0 Americano, outra vez! ” (“The American again!”)

So I felt uncomfortable. I practiced all the time. I’d walk along the beach holding two sticks that I had picked up, getting the twisty motion of the wrists, practicing, practicing, practicing. I kept working on it, but I always felt inferior, that I was some kind of trouble, and wasn’t really up to it.

Well, it was getting closer to Carnaval time, and one evening there was a conversation between the leader of the band and another guy, and then the leader started coming around, picking people out: “You!” he said to a trumpeter. “You!” he said to a singer. “You!”—and he pointed to me. I figured we were finished. He said, “Go out in front!”

We went out to the front of the construction site—the five or six of us—and there was an old Cadillac convertible, with its top down. “Get in!” the leader said.

There wasn’t enough room for us all, so some of us had to sit up on the back. I said to the guy next to me, “What’s he doing—is he putting us out?”

“Nao sй, nгo sй.” (“I don’t know.”)

We drove off way up high on a road which ended near the edge of a cliff overlooking the sea. The car stopped and the leader said, “Get out!”—and they walked us right up to the edge of the cliff!

And sure enough, he said, “Now line up! You first, you next, you next! Start playing! Now march!”

We would have marched off the edge of the cliff—except for a steep trail that went down. So our little group goes down the trail—the trumpet, the singer, the guitar, the pandeiro, and the frigideira—to an outdoor party in the woods. We weren’t picked out because the leader wanted to get rid of us; he was sending us to this private party that wanted some samba music! And afterwards he collected money to pay for some costumes for our band.

After that I felt a little better, because I realized that when he picked the frigideira player, he picked me!

Another thing happened to increase my confidence. Some time later, a guy came from another samba school, in Leblon, a beach further on. He wanted to join our school.

The boss said, “Where’re you from?”

“Leblon.”

“What do you play?”

“Frigideira.”

“OK. Let me hear you play the frigideira.”

So this guy picked up his frigideira and his metal stick and … “brrra -dup -dup; chick -a -chick.” Gee whiz! It was wonderful!

The boss said to him, “You go over there and stand next to O Americano, and you’ll learn how to play the frigideira!”

My theory is that it’s like a person who speaks French who comes to America. At first they’re making all kinds of mistakes, and you can hardly understand them. Then they keep on practicing until they speak rather well, and you find there’s a delightful twist to their way of speaking—their accent is rather nice, and you love to listen to it. So I must have had some sort of accent playing the frigideira, because I couldn’t compete with those guys who had been playing it all their lives; it must have been some kind of dumb accent. But whatever it was, I became a rather successful frigideira player.

One day, shortly before Carnaval time, the leader of the samba school said, “OK, we’re going to practice marching in the street.”

We all went out from the construction site to the street, and it was full of traffic. The streets of Copacabana were always a big mess. Believe it or not, there was a trolley line in which the trolley cars went one way, and the automobiles went the other way. Here it was rush hour in Copacabana, and we were going to march down the middle of Avenida Atlantica.

I said to myself, “Jesus! The boss didn’t get a license, he didn’t OK it with the police, he didn’t do anything. He’s decided we’re just going to go out.”

So we started to go out into the street, and everybody, all around, was excited. Some volunteers from a group of bystanders took a rope and formed a big square around our band, so the pedestrians wouldn’t walk through our lines. People started to lean out of the windows. Everybody wanted to hear the new samba music. It was very exciting!

As soon as we started to march, I saw a policeman, way down at the other end of the road. He looked, saw what was happening, and started diverting traffic! Everything was informal. Nobody made any arrangements, but it worked fine. The people were holding the ropes around us, the policeman was diverting the traffic, the pedestrians were crowded and the traffic was jammed, but we were going along great! We walked down the street, around the corners, and all over the damn Copacabana, at random!

Finally we ended up in a little square in front of the apartment where the boss’s mother lived. We stood there in this place, playing, and the guy’s mother, and aunt, and so on, came down. They had aprons on; they had been working in the kitchen, and you could see their excitement—they were almost crying. It was really nice to do that human stuff. And all the people leaning out of the windows—that was terrific! And I remembered the time I had been in Brazil before, and had seen one of these samba bands—how I loved the music and nearly went crazy over it—and now I was in it!

By the way, when we were marching around the streets of Copacabana that day, I saw in a group on the sidewalk two young ladies from the embassy. Next week I got a note from the embassy saying, “It’s a great thing you are doing, yak, yak, yak …” as if my purpose was to improve relations between the United States and Brazil! So it was a “great” thing I was doing.

Well, in order to go to these rehearsals, I didn’t want to go dressed in my regular clothes that I wore to the university. The people in the band were very poor, and had only old, tattered clothes. So I put on an old undershirt, some old pants, and so forth, so I wouldn’t look too peculiar. But then I couldn’t walk out of my luxury hotel on Avenida Atlantica in Copacabana Beach through the lobby. So I always took the elevator down to the bottom and went out through the basement.

A short time before Carnaval, there was going to be a special competition between the samba schools of the beaches—Copacabana, Ipanema, and Leblon; there were three or four schools, and we were one. We were going to march in costume down Avenida Atlantica. I felt a little uncomfortable about marching in one of those fancy Carnaval costumes, since I wasn’t a Brazilian. But we were supposed to be dressed as Greeks, so I figured I’m as good a Greek as they are.

On the day of the competition, I was eating at the hotel restaurant, and the head waiter, who had often seen me tapping on the table when there was samba music playing, came over to me and said, “Mr. Feynman, this evening there’s going to be something you will love! It’s tipicoBrasileiro—typical Brazilian: There’s going to be a march of the samba schools right in front of the hotel! And the music is so good—you must hear it.”

I said, “Well, I’m kind of busy tonight. I don’t know if I can make it.”

“Oh! But you’d love it so much! You must not miss it! It’s tipicoBrasileiro!”

He was very insistent, and as I kept telling him I didn’t think I’d be there to see it, he became disappointed.

That evening I put on my old clothes and went down through the basement, as usual. We put on the costumes at the construction lot and began marching down Avenida Atlantica, a hundred Brazilian Greeks in paper costumes, and I was in the back, playing away on the frigideira.

Big crowds were along both sides of the Avenida; everybody was leaning out of the windows, and we were coming up to the Miramar Hotel, where I was staying. People were standing on the tables and chairs, and there were crowds and crowds of people. We were playing along, going like sixty, as our band started to pass in front of the hotel. Suddenly I saw one of the waiters shoot up in the air, pointing with his arm, and through all this noise I can hear him scream, “0 PROFESSOR!” So the head waiter found out why I wasn’t able to be there that evening to see the competition—I was in it!

The next day I saw a lady I knew from meeting her on the beach all the time, who had an apartment overlooking the Avenida. She had some friends over to watch the parade of the samba schools, and when we went by, one of her friends exclaimed, “Listen to that guy play the frigideira—heisgood!” I had succeeded. I got a kick out of succeeding at something I wasn’t supposed to be able to do.

When the time came for Carnaval, not very many people from our school showed up. There were some special costumes that were made just for the occasion, but not enough people. Maybe they had the attitude that we couldn’t win against the really big samba schools from the city; I don’t know. I thought we were working day after day, practicing and marching for the Carnaval, but when Carnaval came, a lot of the band didn’t show up, and we didn’t compete very well. Even as we were marching around in the street, some of the band wandered off. Funny result! I never did understand it very well, but maybe the main excitement and fun was tryjng to win the contest of the beaches, where most people felt their level was. And we did win, by the way.

During that ten-month stay in Brazil I got interested in the energy levels of the lighter nuclei. I worked out all the theory for it in my hotel room, but I wanted to check how the data from the experiments looked. This was new stuff that was being worked out up at the Kellogg Laboratory by the experts at Caltech, so I made contact with them—the timing was all arranged—by ham radio. I found an amateur radio operator in Brazil, and about once a week I’d go over to his house. He’d make contact with the ham radio operator in Pasadena, and then, because there was something slightly illegal about it, he’d give me some call letters and would say, “Now I’ll turn you over to WKWX, who’s sitting next to me and would like to talk to you.”

So I’d say, “This is WKWX. Could you please tell me the spacing between the certain levels in boron we talked about last week,” and so on. I would use the data from the experiments to adjust my constants and check whether I was on the right track.

The first guy went on vacation, but he gave me another amateur radio operator to go to. This second guy was blind and operated his station. They were both very nice, and the contact I had with Caltech by ham radio was very effective and useful to me.

As for the physics itself, I worked out quite a good deal, and it was sensible. It was worked out and verified by other people later. I decided, though, that I had so many parameters that I had to adjust—too much “phenomenological adjustment of constants” to make everything fit—that I couldn’t be sure it was very useful. I wanted a rather deeper understanding of the nuclei, and I was never quite convinced it was very significant, so I never did anything with it.

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.

I taught a course at the engineering school on mathematical methods in physics, in which I tried to show how to solve problems by trial and error. It’s something that people don’t usually learn, so I began with some simple examples of arithmetic to illustrate the method. I was surprised that only about eight out of the eighty or so students turned in the first assignment. So I gave a strong lecture about having to actually try it, not just sit back and watch me do it.

After the lecture some students came up to me in a little delegation, and told me that I didn’t understand the backgrounds that they have, that they can study without doing the problems, that they have already learned arithmetic, and that this stuff was beneath them.

So I kept going with the class, and no matter how complicated or obviously advanced the work was becoming, they were never handing a damn thing in. Of course I realized what it was: They couldn’t do it!

One other thing I could never get them to do was to ask questions. Finally, a student explained it to me: “If I ask you a question during the lecture, afterwards everybody will be telling me, ‘What are you wasting our time for in the class? We’re trying to learn something. And you’re stopping him by asking a question’.”

It was a kind of one-upmanship, where nobody knows what’s going on, and they’d put the other one down as if they did know. They all fake that they know, and if one student admits for a moment that something is confusing by asking a question, the others take a high-handed attitude, acting as if it’s not confusing at all, telling him that he’s wasting their time.

I explained how useful it was to work together, to discuss the questions, to talk it over, but they wouldn’t do that either, because they would be losing face if they had to ask someone else. It was pitiful! All the work they did, intelligent people, but they got themselves into this funny state of mind, this strange kind of self-propagating “education” which is meaningless, utterly meaningless!

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.”

The lecture hall was full. I started out by defining science as an understanding of the behavior of nature. Then I asked, “What is a good reason for teaching science? Of course, no country can consider itself civilized unless … yak, yak, yak.” They were all sitting there nodding, because I know that’s the way they think.

Then I say, “That, of course, is absurd, because why should we feel we have to keep up with another country? We have to do it for a good reason, a sensible reason; not just because other countries do.” Then I talked about the utility of science, and its contribution to the improvement of the human condition, and all that—I really teased them a little bit.

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.”

Well, after I gave the talk, the head of the science education department got up and said, “Mr. Feynman has told us some things that are very hard for us to hear, but it appears to be that he really loves science, and is sincere in his criticism. Therefore, I think we should listen to him. I came here knowing we have some sickness in our system of education; what I have learned is that we have a cancer!”—and he sat down.

That gave other people the freedom to speak out, and there was a big excitement. Everybody was getting up and making suggestions. The students got some committee together to mimeograph the lectures in advance, and they got other committees organized to do this and that.

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!

Since I had gone to Brazil under a program sponsored by the United States Government, I was asked by the State Department to write a report about my experiences in Brazil, so I wrote out the essentials of the speech I had just given.