Feynman came up with his own symbols to write maths:
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 had also invented a set of symbols for the typewriter, like FORTRAN has to do, so I could type equations. I also fixed typewriters, with paper clips and rubber bands (the rubber bands didn’t break down like they do here in Los Angeles), but I wasn’t a professional repairman; I’d just fix them so they would work.
But the whole problem of discovering what was the matter, and figuring out what you have to do to fix it—that was interesting to me, like a puzzle.
When I worked, there were certain things I didn’t like, such as tipping. I thought we should be paid more, and not have to have any tips. But when I proposed that to the boss, I got nothing but laughter. She told everybody, “Richard doesn’t want his tips, hee, hee, hee; he doesn’t want his tips, ha, ha, ha.” The world is full of this kind of dumb smart-alec who doesn’t understand anything.
“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.
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.
The electron is a theory that we use; it is so useful in understanding the way nature works that we can almost call it real. I wanted to make the idea of a theory clear by analogy. In the case of the brick, my next question was going to be, “What about the inside of the brick?”—and I would then point out that no one has ever seen the inside of a brick. Every time you break the brick, you only see a surface. That the brick has an inside is a simple theory which helps us understand things better.
After that I went around to the biology table at dinner time. I had always had some interest in biology, and the guys talked about very interesting things. Some of them invited me to come to a course they were going to have in cell physiology. I knew something about biology, but this was a graduate course. “Do you think I can handle it? Will the professor let me in?” I asked. They asked the instructor, E. Newton Harvey, who had done a lot of research on light-producing bacteria. Harvey said I could join this special, advanced course provided one thing—that I would do all the work, and report on papers just like everybody else. Before the first class meeting, the guys who had invited me to take the course wanted to show me some things under the microscope. They had some plant cells in there, and you could see some little green spots called chloroplasts (they make sugar when light shines on them) circulating around. I looked at them and then looked up: “How do they circulate? What pushes them around?” I asked. Nobody knew. It turned out that it was not understood at that time. So right away I found out something, about biology: it was very easy to find a question that was very interesting, and that nobody knew the answer to. In physics you had to go a little deeper before you could find an interesting question that people didn’t know.
After the war, every summer I would go traveling by car somewhere in the United States. One year, after I was at Caltech, I thought, “This summer, instead of going to a different place, I’ll go to a different field.”
It was right after Watson and Crick’s discovery of the DNA spiral. There were some very good biologists at Caltech because Delbrück had his lab there, and Watson came to Caltech to give some lectures on the coding systems of DNA. I went to his lectures and to seminars in the biology department and got full of enthusiasm.
It was a very exciting time in biology, and Caltech was a wonderful place to be. I didn’t think I was up to doing actual research in biology, so for my summer visit to the field of biology I thought I would just hang around the biology lab and “wash dishes,” while I watched what they were doing.
I went over to the biology lab to tell them my desire, and Bob Edgar, a young post-doc who was sort of in charge there, said he wouldn’t let me do that. He said, “You’ll have to really do some research, just like a graduate student, and we’ll give you a problem to work on.” That suited me fine.
I tried with Hildegarde Lamfrom to discover whether peas could use the same ribosomes as bacteria. The question was whether the ribosomes of bacteria can manufacture the proteins of humans or other organisms. Hildegarde said, “I’ll need a lot of ribosomes from bacteria.” Meselson and I had extracted enormous quantities of ribosomes from E.coli for some other experiment. I said, “Hell, I’ll just give you the ribosomes we’ve got. We have plenty of them in my refrigerator at the lab.” It would have been a fantastic and vital discovery if I had been a good biologist.
But I wasn’t a good biologist. We had a good idea, a good experiment, the right equipment, but I screwed it up: I gave her infected ribosomes—the grossest possible error that you could make in an experiment like that. We were there at the right place, we were doing the right things, but I was doing things as an amateur—stupid and sloppy.
The other work on the phage I never wrote up—Edgar kept asking me to write it up, but I never got around to it. That’s the trouble with not being in your own field: You don’t take it seriously.
While I was at Harvard that week, Watson suggested something and we did an experiment together for a few days. It was an incomplete experiment, but I learned some new lab techniques from one of the best men in the field. But that was my big moment: I gave a seminar in the biology department at Harvard!
I always do that, get into something and see how far I can go. I learned a lot of things in biology, and I gained a lot of experience. I got better at pronouncing the words, knowing what not to include in a paper or a seminar, and detecting a weak technique in an experiment. But I love physics, and I love to go back to it.
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.
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.
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.
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?”
Then they explain how it works. The carbon tetrachloride comes in here, the uranium nitrate from here comes in here, it goes up and down, it goes up through the floor, comes up through the pipes, coming up from the second floor, bluuuuurp—going through the stack of blueprints, down-up-down-up, talking very fast, explaining the very, very complicated chemical plant.
I’m completely dazed. Worse, I don’t know what the symbols on the blueprint mean! There is some kind of a thing that at first I think is a window. It’s a square with a little cross in the middle, all over the damn place. I think it’s a window, but no, it can’t be a window, because it isn’t always at the edge. I want to ask them what it is.
You must have been in a situation like this when you didn’t ask them right away. Right away it would have been OK. But now they’ve been talking a little bit too long. You hesitated too long. If you ask them now they’ll say, “What are you wasting my time all this time for?” What am I going to do?
I get an idea. Maybe it’s a valve. I take my finger and I put it down on one of the mysterious little crosses in the middle of one of the blueprints on page three, and I say, “What happens if this valve gets stuck?”—figuring they’re going to say, “That’s not a valve, sir, that’s a window.”
So one looks at the other and says, “Well, if that valve gets stuck—” and he goes up and down on the blueprint, up and down, the other guy goes up and down, back and forth, back and forth, and they both look at each other. They turn around to me and they open their mouths like astonished fish and say, “You’re absolutely right, sir.”
So they rolled up the blueprints and away they went and we walked out. And Mr. Zumwalt, who had been following me all the way through, said, “You’re a genius. I got the idea you were a genius when you went through the plant once and you could tell them about evaporator C-21 in building 90–207 the next morning,” he says, “but what you have just done is so fantastic I want to know how, how do you do that?” I told him you try to find out whether it’s a valve or not.
Von Neumann gave me an interesting idea: that you don’t have to be responsible for the world that you’re in. So I have developed a very powerful sense of social irresponsibility as a result of Von Neumann’s advice. It’s made me a very happy man ever since. But it was Von Neumann who put the seed in that grew into my active irresponsibility!
I don’t believe I can really do without teaching. The reason is, I have to have something so that when I don’t have any ideas and I’m not getting anywhere I can say to myself, “At least I’m living; at least I’m doing something; I’m making some contribution”—it’s just psychological.
So I got this new attitude. I’m going to play with physics, whenever I want to, without worrying about any importance whatsoever.
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. I went on to work out equations of wobbles. Then I thought about how electron orbits start to move in relativity. Then there’s the Dirac Equation in electrodynamics. And then quantum electrodynamics. And before I knew it (it was a very short time) I was “playing”—working, really—with the same old problem that I loved so much, that I had stopped working on when I went to Los Alamos: my thesis-type problems; all those old-fashioned, wonderful things. 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.
Now that I have been at Caltech since 1951, I’ve been very happy here. It’s exactly the thing for a one-sided guy like me. There are all these people who are close to the top, who are very interested in what they are doing, and who I can talk to. So I’ve been very comfortable.
That was tremendously exciting, and very important—it was a fundamental discovery. And I realized, as I finally got to my office, that this is where I’ve got to be. Where people from all different fields of science would tell me stuff, and it was all exciting. It was exactly what I wanted, really.
When you’re young, you have all these things to worry about—should you go there, what about your mother. And you worry, and try to decide, but then something else comes up. It’s much easier to just plain decide.
Never mind—nothing is going to change your mind. I did that once when I was a student at MIT. I got sick and tired of having to decide what kind of dessert I was going to have at the restaurant, so I decided it would always be chocolate ice cream, and never worried about it again—I had the solution to that problem.
About a month later I was at a meeting, and Leona Marshall came over and said, “It’s funny you didn’t accept our offer at Chicago. We were so disappointed, and we couldn’t understand how you could turn down such a terrific offer.” “It was easy,” I said, “because I never let them tell me what the offer was.”
A week later I got a letter from her. I opened it, and the first sentence said, “The salary they were offering was—, a tremendous amount of money, three or four times what I was making. Staggering! Her letter continued, “I told you the salary before you could read any further. Maybe now you want to reconsider, because they’ve told me the position is still open, and we’d very much like to have you.”
So I wrote them back a letter that said, “After reading the salary, I’ve decided that I must refuse. The reason I have to refuse a salary like that is I would be able to do what I’ve always wanted to do—get a wonderful mistress, put her up in an apartment, buy her nice things. . . . With the salary you have offered, I could actually do that, and I know what would happen to me. I’d worry about her, what she’s doing; I’d get into arguments when I come home, and so on. All this bother would make me uncomfortable and unhappy. I wouldn’t be able to do physics well, and it would be a big mess! What I’ve always wanted to do would be bad for me, so I’ve decided that I can’t accept your offer.”
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.”
That was for me: 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 that I’m kind of slow and I don’t understand the problem, because I ask a lot of these “dumb” questions: “Is a cathode plus or minus? Is an an-ion this way, or that way?”
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 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, physical 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!”
During the conference I was staying with my sister in Syracuse. I brought the paper home and said to her, “I can’t understand these things that Lee and Yang are saying. It’s all so complicated.” “No,” she said, “what you mean is not that you can’t understand it, but that you didn’t invent it. You didn’t figure it out your own way, from hearing the clue. What you should do is imagine you’re a student again, and take this paper upstairs, read every line of it, and check the equations. Then you’ll understand it very easily.”
I took her advice, and checked through the whole thing, and found it to be very obvious and simple. I had been afraid to read it, thinking it was too difficult.
I went on and checked some other things, which fit, and new things fit, and I was very excited. It was the first time, and the only time, in my career that I knew a law of nature that nobody else knew. (Of course it wasn’t true, but finding out later that at least Murray Gell-Mann—and also Sudarshan and Marshak—had worked out the same theory didn’t spoil my fun.)
I went to Professor Bacher and told him about our success, and he said, “Yes, you come out and say that the neutron-proton coupling is V instead of T. Everybody used to think it was T. Where is the fundamental experiment that says it’s T? Why don’t you look at the early experiments and find out what was wrong with them?”
I went out and found the original article on the experiment that said the neutron-proton coupling is T, and I was shocked by something. I remembered reading that article once before (back in the days when I read every article in the Physical Review—it was small enough).
And I remembered, when I saw this article again, looking at that curve and thinking, “That doesn’t prove anything!” You see, it depended on one or two points at the very edge of the range of the data, and there’s a principle that a point on the edge of the range of the data—the last point—isn’t very good, because if it was, they’d have another point further along.
And I had realized that the whole idea that neutron-proton coupling is T was based on the last point, which wasn’t very good, and therefore it’s not proved. I remember noticing that! And when I became interested in beta decay, directly, I read all these reports by the “beta-decay experts,” which said it’s T. 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.
I wanted very much to learn to draw, for a reason that I kept to myself: I wanted to convey an emotion I have about the beauty of the world. It’s difficult to describe because it’s an emotion. It’s analogous to the feeling one has in religion that has to do with a god that controls everything in the whole universe: there’s a generality aspect that you feel when you think about how things that appear so different and behave so differently are all run “behind the scenes” by the same organization, the same physical laws. It’s an appreciation of the mathematical beauty of nature, of how she works inside; a realization that the phenomena we see result from the complexity of the inner workings between atoms; a feeling of how dramatic and wonderful it is. It’s a feeling of awe—of scientific awe—which I felt could be communicated through a drawing to someone who had also had this emotion. It could remind him, for a moment, of this feeling about the glories of the universe.
I noticed that the teacher didn’t tell people much (the only thing he told me was my picture was too small on the page). Instead, he tried to inspire us to experiment with new approaches. I thought of how we teach physics: We have so many techniques—so many mathematical methods—that we never stop telling the students how to do things. On the other hand, the drawing teacher is afraid to tell you anything. If your lines are very heavy, the teacher can’t say, “Your lines are too heavy,” because some artist has figured out a way of making great pictures using heavy lines. The teacher doesn’t want to push you in some particular direction.
So the drawing teacher has this problem of communicating how to draw by osmosis and not by instruction, while the physics teacher has the problem of always teaching techniques, rather than the spirit, of how to go about solving physical problems.
They were always telling me to “loosen up,” to become more relaxed about drawing. I figured that made no more sense than telling someone who’s just learning to drive to “loosen up” at the wheel. It isn’t going to work. Only after you know how to do it carefully can you begin to loosen up. So I resisted this perennial loosen-up stuff.
What I got out of that story was something still very new to me: I understood at last what art is really for, at least in certain respects. It gives somebody, individually, pleasure. You can make something that somebody likes so much that they’re depressed, or they’re happy, on account of that damn thing you made!
In science, it’s sort of general and large: You don’t know the individuals who have appreciated it directly. I understood that to sell a drawing is not to make money, but to be sure that it’s in the home of someone who really wants it; someone who would feel bad if they didn’t have it. This was interesting. So I decided to sell my drawings. However, I didn’t want people to buy my drawings because the professor of physics isn’t supposed to be able to draw, isn’t that wonderful, so I made up a false name. My friend Dudley Wright suggested “Au Fait,” which means “It is done” in French. I spelled it O-f-e-y, which turned out to be a name the blacks used for “whitey.” But after all, I was whitey, so it was all right.
My “agent” looked at it and wanted to take it around. “You can’t sell that,” I said, “it’s on newsprint.” “Oh, never mind,” she said. A few weeks later she came back with this picture in a beautiful wooden frame with a red band and a gold edge. It’s a funny thing which must make artists, generally, unhappy—how much improved a drawing gets when you put a frame around it.
My agent told me that a particular lady got all excited about the drawing and they took it to a picture framer. He told them that there were special techniques for mounting drawings on newsprint: Impregnate it with plastic, do this, do that. So this lady goes to all that trouble over this drawing I had made, and then has my agent bring it back to me. “I think the artist would like to see how lovely it is, framed,” she said. I certainly did. There was another example of the direct pleasure somebody got out of one of my pictures. So it was a real kick selling the drawings.
I used to give philosophical talks about science—how science satisfies curiosity, how it gives you a new world view, how it gives man the ability to do things, how it gives him power— 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. They didn’t understand technology; they didn’t understand their time.
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