What I thought was: I’ll shake this electron. It will make some nearby electron shake, and the effect back from the nearby electron would be the origin of the force of radiation reaction. So I did some calculations and took them to Wheeler.
Wheeler, right away said, “Well, that isn’t right because it varies inversely as the square of the distance of the other electrons, whereas it should not depend on any of these variables at all. It’ll also depend inversely upon the mass of the other electron; it’ll be proportional to the charge on the other electron.”
What bothered me was, I thought he must have done the calculation. I only realized later that a man like Wheeler could immediately see all that stuff when you give him the problem. I had to calculate, but he could see.
Then he said, “And it’ll be delayed—the wave returns late—so all you’ve described is reflected light.”
“Oh! Of course,” I said.
“But wait,” he said. “Let’s suppose it returns by advanced waves—reactions backward in time—so it comes back at the right time. We saw the effect varied inversely as the square of the distance, but suppose there are a lot of electrons, all over space: the number is proportional to the square of the distance. So maybe we can make it all compensate.”
We found out we could do that. It came out very nicely, and fit very well. It was a classical theory that could be right, even though it differed from Maxwell’s standard, or Lorentz’s standard theory. It didn’t have any trouble with the infinity of self-action, and it was ingenious. It had actions and delays, forwards and backwards in time—we called it “half-advanced and half-retarded potentials.”
Wheeler and I thought the next problem was to turn to the quantum theory of electrodynamics, which had difficulties (I thought) with the self-action of the electron. We figured if we could get rid of the difficulty first in classical physics, and then make a quantum theory out of that, we could straighten out the quantum theory as well.
Now that we had got the classical theory right, Wheeler said, “Feynman, you’re a young fella—you should give a seminar on this. You need experience in giving talks. Meanwhile, I’ll work out the quantum theory part and give a seminar on that later.”
So it was to be my first technical talk, and Wheeler made arrangements with Eugene Wigner to put it on the regular seminar schedule.
A day or two before the talk I saw Wigner in the hail. “Feynman,” he said, “I think that work you’re doing with Wheeler is very interesting, so I’ve invited Russell to the seminar.” Henry Norris Russell, the famous, great astronomer of the day, was coming to the lecture!
Wigner went on. “I think Professor von Neumann would also he interested.” Johnny von Neumann was the greatest mathematician around. “And Professor Pauli is visiting from Switzerland, it so happens, so I’ve invited Professor Pauli to come”—Pauli was a very famous physicist—and by this time, I’m turning yellow. Finally, Wigner said, “Professor Einstein only rarely comes to our weekly seminars, but your work is so interesting that I’ve invited him specially, so he’s coming, too.”
By this time I must have turned green, because Wigner said, “No, no! Don’t worry! I’ll just warn you, though: If Professor Russell falls asleep—and he will undoubtedly fall asleep—it doesn’t mean that the seminar is bad; he falls asleep in all the seminars. On the other hand, if Professor Pauli is nodding all the time, and seems to be in agreement as the seminar goes along, pay no attention. Professor Pauli has palsy.”
I went back to Wheeler and named all the big, famous people who were coming to the talk he got me to give, and told him I was uneasy about it.
“It’s all right,” he said. “Don’t worry. I’ll answer all the questions.”
So I prepared the talk, and when the day came, I went in and did something that young men who have had no experience in giving talks often do—I put too many equations up on the blackboard. You see, a young fella doesn’t know how to say, “Of course, that varies inversely, and this goes this way … because everybody listening already knows; they can see it. But he doesn’t know. He can only make it come out by actually doing the algebra—and therefore the reams of equations.
As I was writing these equations all over the blackboard ahead of time, Einstein came in and said pleasantly, “Hello, I’m coming to your seminar. But first, where is the tea?”
I told him, and continued writing the equations.
Then the time came to give the talk, and here are these monster minds in front of me, waiting! My first technical talk—and I have this audience! I mean they would put me through the wringer! I remember very clearly seeing my hands shaking as they were pulling out my notes from a brown envelope.
But then a miracle occurred, as it has occurred again and again in my life, and it’s very lucky for me: the moment I start to think about the physics, and have to concentrate on what I’m explaining, nothing else occupies my mind—I’m completely immune to being nervous. So after I started to go, I just didn’t know who was in the room. I was only explaining this idea, that’s all.
But then the end of the seminar came, and it was time for questions. First off, Pauli, who was sitting next to Einstein, gets up and says, “I do not sink dis teory can be right, because of dis, and dis, and dis,” and he turns to Einstein and says, “Don’t you agree, Professor Einstein?”
Einstein says, “Nooooooooooooo,” a nice, German sounding “No, “—very polite. “I find only that it would be very difficult to make a corresponding theory for gravitational interaction.” He meant for the general theory of relativity, which was his baby. He continued: “Since we have at this time not a great deal of experimental evidence, I am not absolutely sure of the correct gravitational theory.” Einstein appreciated that things might he different from what his theory stated; he was very tolerant of other ideas.
I wish I had remembered what Pauli said, because I discovered years later that the theory was not satisfactory when it came to making the quantum theory. It’s possible that that great man noticed the difficulty immediately and explained it to me in the question, but I was so relieved at not having to answer the questions that I didn’t really listen to them carefully. I do remember walking up the steps of Palmer Library with Pauli, who said to me, “What is Wheeler going to say about the quantum theory when he gives his talk?”
I said, “I don’t know. He hasn’t told me. He’s working it out himself.”
“Oh?” he said. “The man works and doesn’t tell his assistant what he’s doing ‘on the quantum theory?” He came closer to me and said in a low, secretive voice, “Wheeler will never give that seminar.”
And it’s true. Wheeler didn’t give the seminar. He thought it would he easy to work out the quantum part; he thought he had it, almost. But he didn’t. And by the time the seminar came around, he realized he didn’t know how to do it, and therefore didn’t have anything to say.
I never solved it, either—a quantum theory of half-advanced, half-retarded potentials—and I worked on it for years.
Mixing Paints
A Different Box of Tools
Mindreaders
The Amateur Scientist
Part 3. Feynman, the Bomb, and the Military
Fizzled Fuses
Wheeler, right away said, “Well, that isn’t right because it varies inversely as the square of the distance of the other electrons, whereas it should not depend on any of these variables at all. It’ll also depend inversely upon the mass of the other electron; it’ll be proportional to the charge on the other electron.”
What bothered me was, I thought he must have done the calculation. I only realized later that a man like Wheeler could immediately see all that stuff when you give him the problem. I had to calculate, but he could see.
Then he said, “And it’ll be delayed—the wave returns late—so all you’ve described is reflected light.”
“Oh! Of course,” I said.
“But wait,” he said. “Let’s suppose it returns by advanced waves—reactions backward in time—so it comes back at the right time. We saw the effect varied inversely as the square of the distance, but suppose there are a lot of electrons, all over space: the number is proportional to the square of the distance. So maybe we can make it all compensate.”
We found out we could do that. It came out very nicely, and fit very well. It was a classical theory that could be right, even though it differed from Maxwell’s standard, or Lorentz’s standard theory. It didn’t have any trouble with the infinity of self-action, and it was ingenious. It had actions and delays, forwards and backwards in time—we called it “half-advanced and half-retarded potentials.”
Wheeler and I thought the next problem was to turn to the quantum theory of electrodynamics, which had difficulties (I thought) with the self-action of the electron. We figured if we could get rid of the difficulty first in classical physics, and then make a quantum theory out of that, we could straighten out the quantum theory as well.
Now that we had got the classical theory right, Wheeler said, “Feynman, you’re a young fella—you should give a seminar on this. You need experience in giving talks. Meanwhile, I’ll work out the quantum theory part and give a seminar on that later.”
So it was to be my first technical talk, and Wheeler made arrangements with Eugene Wigner to put it on the regular seminar schedule.
A day or two before the talk I saw Wigner in the hail. “Feynman,” he said, “I think that work you’re doing with Wheeler is very interesting, so I’ve invited Russell to the seminar.” Henry Norris Russell, the famous, great astronomer of the day, was coming to the lecture!
Wigner went on. “I think Professor von Neumann would also he interested.” Johnny von Neumann was the greatest mathematician around. “And Professor Pauli is visiting from Switzerland, it so happens, so I’ve invited Professor Pauli to come”—Pauli was a very famous physicist—and by this time, I’m turning yellow. Finally, Wigner said, “Professor Einstein only rarely comes to our weekly seminars, but your work is so interesting that I’ve invited him specially, so he’s coming, too.”
By this time I must have turned green, because Wigner said, “No, no! Don’t worry! I’ll just warn you, though: If Professor Russell falls asleep—and he will undoubtedly fall asleep—it doesn’t mean that the seminar is bad; he falls asleep in all the seminars. On the other hand, if Professor Pauli is nodding all the time, and seems to be in agreement as the seminar goes along, pay no attention. Professor Pauli has palsy.”
I went back to Wheeler and named all the big, famous people who were coming to the talk he got me to give, and told him I was uneasy about it.
“It’s all right,” he said. “Don’t worry. I’ll answer all the questions.”
So I prepared the talk, and when the day came, I went in and did something that young men who have had no experience in giving talks often do—I put too many equations up on the blackboard. You see, a young fella doesn’t know how to say, “Of course, that varies inversely, and this goes this way … because everybody listening already knows; they can see it. But he doesn’t know. He can only make it come out by actually doing the algebra—and therefore the reams of equations.
As I was writing these equations all over the blackboard ahead of time, Einstein came in and said pleasantly, “Hello, I’m coming to your seminar. But first, where is the tea?”
I told him, and continued writing the equations.
Then the time came to give the talk, and here are these monster minds in front of me, waiting! My first technical talk—and I have this audience! I mean they would put me through the wringer! I remember very clearly seeing my hands shaking as they were pulling out my notes from a brown envelope.
But then a miracle occurred, as it has occurred again and again in my life, and it’s very lucky for me: the moment I start to think about the physics, and have to concentrate on what I’m explaining, nothing else occupies my mind—I’m completely immune to being nervous. So after I started to go, I just didn’t know who was in the room. I was only explaining this idea, that’s all.
But then the end of the seminar came, and it was time for questions. First off, Pauli, who was sitting next to Einstein, gets up and says, “I do not sink dis teory can be right, because of dis, and dis, and dis,” and he turns to Einstein and says, “Don’t you agree, Professor Einstein?”
Einstein says, “Nooooooooooooo,” a nice, German sounding “No, “—very polite. “I find only that it would be very difficult to make a corresponding theory for gravitational interaction.” He meant for the general theory of relativity, which was his baby. He continued: “Since we have at this time not a great deal of experimental evidence, I am not absolutely sure of the correct gravitational theory.” Einstein appreciated that things might he different from what his theory stated; he was very tolerant of other ideas.
I wish I had remembered what Pauli said, because I discovered years later that the theory was not satisfactory when it came to making the quantum theory. It’s possible that that great man noticed the difficulty immediately and explained it to me in the question, but I was so relieved at not having to answer the questions that I didn’t really listen to them carefully. I do remember walking up the steps of Palmer Library with Pauli, who said to me, “What is Wheeler going to say about the quantum theory when he gives his talk?”
I said, “I don’t know. He hasn’t told me. He’s working it out himself.”
“Oh?” he said. “The man works and doesn’t tell his assistant what he’s doing ‘on the quantum theory?” He came closer to me and said in a low, secretive voice, “Wheeler will never give that seminar.”
And it’s true. Wheeler didn’t give the seminar. He thought it would he easy to work out the quantum part; he thought he had it, almost. But he didn’t. And by the time the seminar came around, he realized he didn’t know how to do it, and therefore didn’t have anything to say.
I never solved it, either—a quantum theory of half-advanced, half-retarded potentials—and I worked on it for years.
Mixing Paints
The reason why I say I’m “uncultured” or “anti-intellectual” probably goes all the way back to the time when I was in high school. I was always worried about being a sissy; I didn’t want to be too delicate. To me, no real man ever paid any attention to poetry and such things. How poetry ever got written—that never struck me! So I developed a negative attitude toward the guy who studies French literature, or studies too much music or poetry—all those “fancy” things. I admired better the steel-worker, the welder, or the machine shop man. I always thought the guy who worked in the machine shop and could make things, now he was a real guy! That was my attitude. To be a practical man was, to me, always somehow a positive virtue, and to be “cultured” or “intellectual” was not. The first was right, of course, but the second was crazy.
I still had this feeling when I was doing my graduate study at Princeton, as you’ll see. I used to eat often in a nice little restaurant called Papa’s Place. One day while I was eating there, a painter in his painting clothes came down from an upstairs room he’d been painting, and sat near me. Somehow we struck up a conversation and he started talking about how you’ve got to learn a lot to be in the painting business. “For example,” he said, “in this restaurant, what colors would you use to paint the walls, if you had the job to do?”
I said I didn’t know, and he said, “You have a dark band up to such-and-such a height, because, you see, people who sit at the tables rub their elbows against the walls, so you don’t want a nice, white wall there. It gets dirty too easily. But above that, you do want it white to give a feeling of cleanliness to the restaurant.”
The guy seemed to know what he was doing, and I was sitting there, hanging on his words, when he said, “And you also have to know about colors—how to get different colors when you mix the paint. For example, what colors would you mix to get yellow?”
I didn’t know how to get yellow by mixing paints. If it’s light, you mix green and red, but I knew he was talking paints. So I said, “I don’t know how you get yellow without using yellow.”
“Well,” he said, “if you mix red and white, you’ll get yellow.”
“Are you sure you don’t mean pink?”
“No,” he said, “you’ll get yellow”—and I believed that he got yellow, because he was a professional painter, and I always admired guys like that. But I still wondered how he did it.
I got an idea. “It must be some kind of chemical change. Were you using some special kind of pigments that make a chemical change?”
“No,” he said, “any old pigments will work. You go down to the five-and-ten and get some paint—just a regular can of red paint and a regular can of white paint—and I’ll mix ‘em, and I’ll show how you get yellow.”
At this juncture I was thinking, “Something is crazy. I know enough about paints to know you won’t get yellow, but he must know that you do get yellow, and therefore something interesting happens. I’ve got to see what it is!”
So I said, “OK, I’ll get the paints.”
The painter went back upstairs to finish his painting job, and the restaurant owner came over and said to me, “What’s the idea of arguing with that man? The man is a painter; he’s been a painter all his life, and he says he gets yellow. So why argue with him?”
I felt embarrassed. I didn’t know what to say. Finally I said, “All my life, I’ve been studying light. And I think that with red and white you can’t get yellow—you can only get pink.”
So I went to the five-and-ten and got the paint, and brought it back to the restaurant. The painter came down from upstairs, and the restaurant owner was there too. I put the cans of paint on an old chair, and the painter began to mix the paint. He put a little more red, he put a little more white—it still looked pink to me—and he mixed some more. Then he mumbled something like, “I used to have a little tube of yellow here to sharpen it up a bit—then this’ll be yellow.”
“Oh!” I said. “Of course! You add yellow, and you can get yellow, but you couldn’t do it without the yellow.”
The painter went back upstairs to paint.
The restaurant owner said, “That guy has his nerve, arguing with a guy who’s studied light all his life!”
But that shows you how much I trusted these “real guys.” The painter had told me so much stuff that was reasonable that I was ready to give a certain chance that there was an odd phenomenon I didn’t know. I was expecting pink, but my set of thoughts were, “The only way to get yellow will be something new and interesting, and I’ve got to see this.”
I’ve very often made mistakes in my physics by thinking the theory isn’t as good as it really is, thinking that there are lots of complications that are going to spoil it—an attitude that anything can happen, in spite of what you’re pretty sure should happen.
I still had this feeling when I was doing my graduate study at Princeton, as you’ll see. I used to eat often in a nice little restaurant called Papa’s Place. One day while I was eating there, a painter in his painting clothes came down from an upstairs room he’d been painting, and sat near me. Somehow we struck up a conversation and he started talking about how you’ve got to learn a lot to be in the painting business. “For example,” he said, “in this restaurant, what colors would you use to paint the walls, if you had the job to do?”
I said I didn’t know, and he said, “You have a dark band up to such-and-such a height, because, you see, people who sit at the tables rub their elbows against the walls, so you don’t want a nice, white wall there. It gets dirty too easily. But above that, you do want it white to give a feeling of cleanliness to the restaurant.”
The guy seemed to know what he was doing, and I was sitting there, hanging on his words, when he said, “And you also have to know about colors—how to get different colors when you mix the paint. For example, what colors would you mix to get yellow?”
I didn’t know how to get yellow by mixing paints. If it’s light, you mix green and red, but I knew he was talking paints. So I said, “I don’t know how you get yellow without using yellow.”
“Well,” he said, “if you mix red and white, you’ll get yellow.”
“Are you sure you don’t mean pink?”
“No,” he said, “you’ll get yellow”—and I believed that he got yellow, because he was a professional painter, and I always admired guys like that. But I still wondered how he did it.
I got an idea. “It must be some kind of chemical change. Were you using some special kind of pigments that make a chemical change?”
“No,” he said, “any old pigments will work. You go down to the five-and-ten and get some paint—just a regular can of red paint and a regular can of white paint—and I’ll mix ‘em, and I’ll show how you get yellow.”
At this juncture I was thinking, “Something is crazy. I know enough about paints to know you won’t get yellow, but he must know that you do get yellow, and therefore something interesting happens. I’ve got to see what it is!”
So I said, “OK, I’ll get the paints.”
The painter went back upstairs to finish his painting job, and the restaurant owner came over and said to me, “What’s the idea of arguing with that man? The man is a painter; he’s been a painter all his life, and he says he gets yellow. So why argue with him?”
I felt embarrassed. I didn’t know what to say. Finally I said, “All my life, I’ve been studying light. And I think that with red and white you can’t get yellow—you can only get pink.”
So I went to the five-and-ten and got the paint, and brought it back to the restaurant. The painter came down from upstairs, and the restaurant owner was there too. I put the cans of paint on an old chair, and the painter began to mix the paint. He put a little more red, he put a little more white—it still looked pink to me—and he mixed some more. Then he mumbled something like, “I used to have a little tube of yellow here to sharpen it up a bit—then this’ll be yellow.”
“Oh!” I said. “Of course! You add yellow, and you can get yellow, but you couldn’t do it without the yellow.”
The painter went back upstairs to paint.
The restaurant owner said, “That guy has his nerve, arguing with a guy who’s studied light all his life!”
But that shows you how much I trusted these “real guys.” The painter had told me so much stuff that was reasonable that I was ready to give a certain chance that there was an odd phenomenon I didn’t know. I was expecting pink, but my set of thoughts were, “The only way to get yellow will be something new and interesting, and I’ve got to see this.”
I’ve very often made mistakes in my physics by thinking the theory isn’t as good as it really is, thinking that there are lots of complications that are going to spoil it—an attitude that anything can happen, in spite of what you’re pretty sure should happen.
A Different Box of Tools
At the Princeton graduate school, the physics department and the math department shared a common lounge, and every day at four o’clock we would have tea. It was a way of relaxing in the afternoon, in addition to imitating an English college. People would sit around playing Go, or discussing theorems. In those days topology was the big thing.
I still remember a guy sitting on the couch, thinking very hard, and another guy standing in front of him, saying, “And therefore such-and-such is true.”
“Why is that?” the guy on the couch asks.
“It’s trivial! It’s trivial!” the standing guy says, and he rapidly reels off a series of logical steps: “First you assume thus-and-so, then we have Kerchoff’s this-and-that; then there’s Waffenstoffer’s Theorem, and we substitute this and construct that. Now you put the vector which goes around here and then thus-and-so …” The guy on the couch is struggling to understand all this stuff, which goes on at high speed for about fifteen minutes!
Finally the standing guy comes out the other end, and the guy on the couch says, “Yeah, yeah. It’s trivial.”
We physicists were laughing, trying to figure them out. We decided that “trivial” means “proved.” So we joked with the mathematicians: “We have a new theorem—that mathematicians can prove only trivial theorems, because every theorem that’s proved is trivial.”
The mathematicians didn’t like that theorem, and I teased them about it. I said there are never any surprises—that the mathematicians only prove things that are obvious.
Topology was not at all obvious to the mathematicians. There were all kinds of weird possibilities that were “counterintuitive.” Then I got an idea. I challenged them: “I bet there isn’t a single theorem that you can tell me—what the assumptions are and what the theorem is in terms I can understand—where I can’t tell you right away whether it’s true or false.”
It often went like this: They would explain to me, “You’ve got an orange, OK? Now you cut the orange into a finite number of pieces, put it back together, and it’s as big as the sun. True or false?”
“No holes?”
“No holes.”
“Impossible! There ain’t no such a thing.”
“Ha! We got him! Everybody gather around! It’s So-and-so’s theorem of immeasurable measure!”
Just when they think they’ve got me, I remind them, “But you said an orange! You can’t cut the orange peel any thinner than the atoms.”
“But we have the condition of continuity: We can keep on cutting!”
“No, you said an orange, so I assumed that you meant a real orange.”
So I always won. If I guessed it right, great. If I guessed it wrong, there was always something I could find in their simplification that they left out.
Actually, there was a certain amount of genuine quality to my guesses. I had a scheme, which I still use today when somebody is explaining something that I’m trying to understand: I keep making up examples. For instance, the mathematicians would come in with a terrific theorem, and they’re all excited. As they’re telling me the conditions of the theorem, I construct something which fits all the conditions. You know, you have a set (one ball)—disjoint (two halls). Then the balls turn colors, grow hairs, or whatever, in my head as they put more conditions on. Finally they state the theorem, which is some dumb thing about the ball which isn’t true for my hairy green ball thing, so I say, “False!”
If it’s true, they get all excited, and I let them go on for a while. Then I point out my counterexample.
“Oh. We forgot to tell you that it’s Class 2 Hausdorff homomorphic.”
“Well, then,” I say, “It’s trivial! It’s trivial!” By that time I know which way it goes, even though I don’t know what Hausdorff homomorphic means.
I guessed right most of the time because although the mathematicians thought their topology theorems were counterintuitive, they weren’t really as difficult as they looked. You can get used to the funny properties of this ultra-fine cutting business and do a pretty good job of guessing how it will come out.
Although I gave the mathematicians a lot of trouble, they were always very kind to me. They were a happy hunch of boys who were developing things, and they were terrifically excited about it. They would discuss their “trivial” theorems, and always try to explain something to you if you asked a simple question.
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.
I still remember a guy sitting on the couch, thinking very hard, and another guy standing in front of him, saying, “And therefore such-and-such is true.”
“Why is that?” the guy on the couch asks.
“It’s trivial! It’s trivial!” the standing guy says, and he rapidly reels off a series of logical steps: “First you assume thus-and-so, then we have Kerchoff’s this-and-that; then there’s Waffenstoffer’s Theorem, and we substitute this and construct that. Now you put the vector which goes around here and then thus-and-so …” The guy on the couch is struggling to understand all this stuff, which goes on at high speed for about fifteen minutes!
Finally the standing guy comes out the other end, and the guy on the couch says, “Yeah, yeah. It’s trivial.”
We physicists were laughing, trying to figure them out. We decided that “trivial” means “proved.” So we joked with the mathematicians: “We have a new theorem—that mathematicians can prove only trivial theorems, because every theorem that’s proved is trivial.”
The mathematicians didn’t like that theorem, and I teased them about it. I said there are never any surprises—that the mathematicians only prove things that are obvious.
Topology was not at all obvious to the mathematicians. There were all kinds of weird possibilities that were “counterintuitive.” Then I got an idea. I challenged them: “I bet there isn’t a single theorem that you can tell me—what the assumptions are and what the theorem is in terms I can understand—where I can’t tell you right away whether it’s true or false.”
It often went like this: They would explain to me, “You’ve got an orange, OK? Now you cut the orange into a finite number of pieces, put it back together, and it’s as big as the sun. True or false?”
“No holes?”
“No holes.”
“Impossible! There ain’t no such a thing.”
“Ha! We got him! Everybody gather around! It’s So-and-so’s theorem of immeasurable measure!”
Just when they think they’ve got me, I remind them, “But you said an orange! You can’t cut the orange peel any thinner than the atoms.”
“But we have the condition of continuity: We can keep on cutting!”
“No, you said an orange, so I assumed that you meant a real orange.”
So I always won. If I guessed it right, great. If I guessed it wrong, there was always something I could find in their simplification that they left out.
Actually, there was a certain amount of genuine quality to my guesses. I had a scheme, which I still use today when somebody is explaining something that I’m trying to understand: I keep making up examples. For instance, the mathematicians would come in with a terrific theorem, and they’re all excited. As they’re telling me the conditions of the theorem, I construct something which fits all the conditions. You know, you have a set (one ball)—disjoint (two halls). Then the balls turn colors, grow hairs, or whatever, in my head as they put more conditions on. Finally they state the theorem, which is some dumb thing about the ball which isn’t true for my hairy green ball thing, so I say, “False!”
If it’s true, they get all excited, and I let them go on for a while. Then I point out my counterexample.
“Oh. We forgot to tell you that it’s Class 2 Hausdorff homomorphic.”
“Well, then,” I say, “It’s trivial! It’s trivial!” By that time I know which way it goes, even though I don’t know what Hausdorff homomorphic means.
I guessed right most of the time because although the mathematicians thought their topology theorems were counterintuitive, they weren’t really as difficult as they looked. You can get used to the funny properties of this ultra-fine cutting business and do a pretty good job of guessing how it will come out.
Although I gave the mathematicians a lot of trouble, they were always very kind to me. They were a happy hunch of boys who were developing things, and they were terrifically excited about it. They would discuss their “trivial” theorems, and always try to explain something to you if you asked a simple question.
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.
Mindreaders
My father was always interested in magic and carnival tricks, and wanting to see how they worked. One of the things he knew about was mindreaders. When he was a little boy growing up in a small town called Patchogue, in the middle of Long Island, it was announced on advertisements posted all over that a mindreader was coming next Wednesday. The posters said that some respected citizens—the mayor, a judge, a banker—should take a five-dollar bill and hide it somewhere, and when the mindreader came to town, he would find it.
When he came, the people gathered around to watch him do his work. He takes the hands of the banker and the judge, who had hidden the five-dollar bill, and starts to walk down the street. He gets to an intersection, turns the corner, walks down another street, then another, to the correct house. He goes with them, always holding their hands, into the house, up to the second floor, into the right room, walks up to a bureau, lets go of their hands, opens the correct drawer, and there’s the five-dollar bill. Very dramatic!
In those days it was difficult to get a good education, so the mindreader was hired as a tutor for my father. Well, my father, after one of his lessons, asked the mindreader how he was able to find the money without anyone telling him where it was.
The mindreader explained that you hold onto their hands, loosely and as you move, you jiggle a little bit. You come to an intersection, where you can go forward, to the left, or to the right. You jiggle a little bit to the left, and if it’s incorrect, you feel a certain amount of resistance, because they don’t expect you to move that way. But when you move in the right direction, because they think you might he able to do it, they give way more easily and there’s no resistance. So you must always be jiggling a little bit, testing out which seems to be the easiest way.
My father told me the story and said he thought it would still take a lot of practice. He never tried it himself.
Later, when I was doing graduate work at Princeton, I decided to try it on a fellow named Bill Woodward. I suddenly announced that I was a mindreader, and could read his mind. I told him to go into the “laboratory”—a big room with rows of tables covered with equipment of various kinds, with electric circuits, tools, and junk all over the place—pick out a certain object, somewhere, and come out. I explained, “Now I’ll read your mind and take you right up to the object.”
He went into the lab, noted a particular object, and came out. I took his hand and started jiggling. We went down this aisle, then that one, right to the object. We tried it three times. One time I got the object right on—and it was in the middle of a whole bunch of stuff. Another time I went to the right place but missed the object by a few inches—wrong object. The third time, something went wrong. But it worked better than I thought. It was very easy.
Some time after that, when I was about twenty-six or so, my father and I went to Atlantic City where they had various carnival things going on outdoors. While my father was doing some business, I went to see a mindreader. He was seated on the stage with his back to the audience, dressed in robes and wearing a great big turban. He had an assistant, a little guy who was running around through the audience, saying things like, “Oh, Great Master, what is the color of this pocketbook?”
“Blue!” says the master.
“And oh, Illustrious Sir, what is the name of this woman?”
“Marie!”
Some guy gets up: “What’s my name?”
“Henry.”
I get up and say, “What’s my name?”
He doesn’t answer. The other guy was obviously a confederate, but I couldn’t figure out how the mindreader did the other tricks, like telling the color of the pocketbook. Did he wear earphones underneath the turban?
When I met up with my father, I told him about it. He said, “They have a code worked out, but I don’t know what it is. Let’s go back and find out.”
We went back to the place, and my father said to me, “Here’s fifty cents. Go get your fortune read in the booth back there, and I’ll see you in half an hour.”
I knew what he was doing. He was going to tell the man a story, and it would go smoother if his son wasn’t there going, “Ooh, ooh!” all the time. He had to get me out of the way.
When he came back he told me the whole code: “Blue is ‘Oh, Great Master,’ Green is ‘Oh, Most Knowledgeable One,’” and so forth. He explained, “I went up to him, afterwards, and told him I used to do a show in Patchogue, and we had a code, but it couldn’t do many numbers, and the range of colors was shorter. I asked him, ‘How do you carry so much information?’”
The mindreader was so proud of his code that he sat down and explained the whole works to my father. My father was a salesman. He could set up a situation like that. I can’t do stuff like that.
When he came, the people gathered around to watch him do his work. He takes the hands of the banker and the judge, who had hidden the five-dollar bill, and starts to walk down the street. He gets to an intersection, turns the corner, walks down another street, then another, to the correct house. He goes with them, always holding their hands, into the house, up to the second floor, into the right room, walks up to a bureau, lets go of their hands, opens the correct drawer, and there’s the five-dollar bill. Very dramatic!
In those days it was difficult to get a good education, so the mindreader was hired as a tutor for my father. Well, my father, after one of his lessons, asked the mindreader how he was able to find the money without anyone telling him where it was.
The mindreader explained that you hold onto their hands, loosely and as you move, you jiggle a little bit. You come to an intersection, where you can go forward, to the left, or to the right. You jiggle a little bit to the left, and if it’s incorrect, you feel a certain amount of resistance, because they don’t expect you to move that way. But when you move in the right direction, because they think you might he able to do it, they give way more easily and there’s no resistance. So you must always be jiggling a little bit, testing out which seems to be the easiest way.
My father told me the story and said he thought it would still take a lot of practice. He never tried it himself.
Later, when I was doing graduate work at Princeton, I decided to try it on a fellow named Bill Woodward. I suddenly announced that I was a mindreader, and could read his mind. I told him to go into the “laboratory”—a big room with rows of tables covered with equipment of various kinds, with electric circuits, tools, and junk all over the place—pick out a certain object, somewhere, and come out. I explained, “Now I’ll read your mind and take you right up to the object.”
He went into the lab, noted a particular object, and came out. I took his hand and started jiggling. We went down this aisle, then that one, right to the object. We tried it three times. One time I got the object right on—and it was in the middle of a whole bunch of stuff. Another time I went to the right place but missed the object by a few inches—wrong object. The third time, something went wrong. But it worked better than I thought. It was very easy.
Some time after that, when I was about twenty-six or so, my father and I went to Atlantic City where they had various carnival things going on outdoors. While my father was doing some business, I went to see a mindreader. He was seated on the stage with his back to the audience, dressed in robes and wearing a great big turban. He had an assistant, a little guy who was running around through the audience, saying things like, “Oh, Great Master, what is the color of this pocketbook?”
“Blue!” says the master.
“And oh, Illustrious Sir, what is the name of this woman?”
“Marie!”
Some guy gets up: “What’s my name?”
“Henry.”
I get up and say, “What’s my name?”
He doesn’t answer. The other guy was obviously a confederate, but I couldn’t figure out how the mindreader did the other tricks, like telling the color of the pocketbook. Did he wear earphones underneath the turban?
When I met up with my father, I told him about it. He said, “They have a code worked out, but I don’t know what it is. Let’s go back and find out.”
We went back to the place, and my father said to me, “Here’s fifty cents. Go get your fortune read in the booth back there, and I’ll see you in half an hour.”
I knew what he was doing. He was going to tell the man a story, and it would go smoother if his son wasn’t there going, “Ooh, ooh!” all the time. He had to get me out of the way.
When he came back he told me the whole code: “Blue is ‘Oh, Great Master,’ Green is ‘Oh, Most Knowledgeable One,’” and so forth. He explained, “I went up to him, afterwards, and told him I used to do a show in Patchogue, and we had a code, but it couldn’t do many numbers, and the range of colors was shorter. I asked him, ‘How do you carry so much information?’”
The mindreader was so proud of his code that he sat down and explained the whole works to my father. My father was a salesman. He could set up a situation like that. I can’t do stuff like that.
The Amateur Scientist
When I was a kid I had a “lab.” It wasn’t a laboratory in the sense that I would measure, or do important experiments.
Instead, I would play: I’d make a motor, I’d make a gadget that would go off when something passed a photocell. I’d play around with selenium; I was piddling around all the time. I did calculate a little bit for the lamp bank, a series of switches and bulbs I used as resistors to control voltages. But all that was for application. I never did any laboratory kind of experiments.
I also had a microscope and loved to watch things under the microscope.It took patience: I would get something under the microscope and I would watch it interminably. I saw many interesting things, like everybody sees—a diatom slowly making its way across the slide, and so on.
One day I was watching a paramecium and I saw something that was not described in the books I got in school—in college, even. These books always simplify things so the world will be more like they want it to be: When they’re talking about the behavior of animals, they always start out with, “The paramecium is extremely simple; it has a simple behavior. It turns as its slipper shape moves through the water until it hits something, at which time it recoils, turns through an angle, and then starts out again.”
It isn’t really right. First of all, as everybody knows, the paramecia, from time to time, conjugate with each other—they meet and exchange nuclei. How do they decide when it’s time to do that? (Never mind; that’s not my observation.)
I watched these paramecia hit something, recoil, turn through an angle, and go again. The idea that it’s mechanical, like a computer program—it doesn’t look that way. They go different distances, they recoil different distances, they turn through angles that are different in various cases; they don’t always turn to the right; they’re very irregular. It looks random, because you don’t know what they’re hitting; you don’t know all the chemicals they’re smelling, or what.
One of the things I wanted to watch was what happens to the paramecium when the water that it’s in dries up. It was claimed that the paramecium can dry up into a sort of hardened seed. I had a drop of water on the slide under my microscope, and in the drop of water was a paramecium and some “grass”—at the scale of the paramecium, it looked like a network of jackstraws. As the drop of water evaporated, over a time of fifteen or twenty minutes, the paramecium got into a tighter and tighter situation: there was more and more of this back-and-forth until it could hardly move. It was stuck between these “sticks,” almost jammed.
Then I saw something I had never seen or heard of: the paramecium lost its shape. It could flex itself, like an amoeba. It began to push itself against one of the sticks, and began dividing into two prongs until the division was about halfway up the paramecium, at which time it decided that wasn’t a very good idea, and backed away.
So my impression of these animals is that their behavior is much too simplified in the books. It is not so utterly mechanical or one-dimensional as they say. They should describe the behavior of these simple animals correctly. Until we see how many dimensions of behavior even a one-celled animal has, we won’t be able to fully understand the behavior of more complicated animals.
I also enjoyed watching hugs. I had an insect book when I was about thirteen. It said that dragonflies are not harmful; they don’t sting. In our neighborhood it was well known that “darning needles,” as we called them, were very dangerous when they’d sting. So if we were outside somewhere playing baseball, or something, and one of these things would fly around, everybody would run for cover, waving their arms, yelling, “A darning needle! A darning needle!”
So one day I was on the beach, and I’d just read this book that said dragonflies don’t sting. A darning needle came along, and everybody was screaming and running around, and I just sat there. “Don’t worry!” I said. “Darning needles don’t sting!”
The thing landed on my foot. Everybody was yelling and it was a big mess, because this darning needle was sitting on my foot, And there I was, this scientific wonder, saying it wasn’t going to sting me.
You’re sure this is a story that’s going to come out that it stings me—but it didn’t. The book was right. But I did sweat a bit.
I also had a little hand microscope. It was a toy microscope, and I pulled the magnification piece out of it, and would hold it in my hand like a magnifying glass, even though it was a microscope of forty or fifty power. With care you could hold the focus. So I could go around and look at things right out in the street.
So when I was in graduate school at Princeton, I once took it out of my pocket to look at some ants that were crawling around on some ivy. I had to exclaim out loud, I was so excited. What I saw was an ant and an aphid, which ants take care of—they carry them from plant to plant if the plant they’re on is dying. In return the ants get partially digested aphid juice, called “honeydew.” I knew that; my father had told me about it, but I had never seen it.
So here was this aphid and sure enough, an ant came along, and patted it with its feet—all around the aphid, pat, pat, pat, pat, pat. This was terribly exciting! Then the juice came out of the back of the aphid. And because it was magnified, it looked like a big, beautiful, glistening ball, like a balloon, because of the surface tension. Because the microscope wasn’t very good, the drop was colored a little bit from chromatic aberration in the lens—it was a gorgeous thing!
The ant took this ball in its two front feet, lifted it off the aphid, and held it. The world is so different at that scale that you can pick up water and hold it! The ants probably have a fatty or greasy material on their legs that doesn’t break the surface tension of the water when they hold it up. Then the ant broke the surface of the drop with its mouth, and the surface tension collapsed the drop right into his gut. It was very interesting to see this whole thing happen!
In my room at Princeton I had a bay window with a U-shaped windowsill. One day some ants came out on the windowsill and wandered around a little bit. I got curious as to how they found things. I wondered, how do they know where to go? Can they tell each other where food is, like bees can? Do they have any sense of geometry?
This is all amateurish; everybody knows the answer, but I didn’t know the answer, so the first thing I did was to stretch some string across the U of the bay window and hang a piece of folded cardboard with sugar on it from the string. The idea of this was to isolate the sugar from the ants, so they wouldn’t find it accidentally. I wanted to have everything under control.
Next I made a lot of little strips of paper and put a fold in them, so I could pick up ants and ferry them from one place to another. I put the folded strips of paper in two places:
Some were by the sugar (hanging from the string), and the others were near the ants in a particular location. I sat there all afternoon, reading and watching, until an ant happened to walk onto one of my little paper ferries. Then I took him over to the sugar. After a few ants had been ferried over to the sugar, one of them accidentally walked onto one of the ferries nearby, and I carried him back.
I wanted to see how long it would take the other ants to get the message to go to the “ferry terminal.” It started slowly but rapidly increased until I was going mad ferrying the ants back and forth.
But suddenly, when everything was going strong, I began to deliver the ants from the sugar to a different spot. The question now was, does the ant learn to go back to where it just came from, or does it go where it went the time before?
After a while there were practically no ants going to the first place (which would take them to the sugar), whereas there were many ants at the second place, milling around, trying to find the sugar. So I figured out so far that they went where they just came from.
In another experiment, I laid out a lot of glass microscope slides, and got the ants to walk on them, back and forth, to some sugar I put on the windowsill. Then, by replacing an old slide with a new one, or by rearranging the slides, I could demonstrate that the ants had no sense of geometry: they couldn’t figure out where something was. If they went to the sugar one way and there was a shorter way back, they would never figure out the short way.
It was also pretty clear from rearranging the glass slides that the ants left some sort of trail. So then came a lot of easy experiments to find out how long it takes a trail to dry up, whether it can be easily wiped off, and so on. I also found out the trail wasn’t directional. If I’d pick up an ant on a piece of paper, turn him around and around, and then put him back onto the trail, he wouldn’t know that he was going the wrong way until he met another ant. (Later, in Brazil, I noticed some leaf-cutting ants and tried the same experiment on them. They could tell, within a few steps, whether they were going toward the food or away from it—presumably from the trail, which might be a series of smells in a pattern: A, B, space, A, B, space, and so on.)
I tried at one point to make the ants go around in a circle, but I didn’t have enough patience to set it up. I could see no reason, other than lack of patience, why it couldn’t be done.
One thing that made experimenting difficult was that breathing on the ants made them scurry. It must be an instinctive thing against some animal that eats them or disturbs them. I don’t know if it was the warmth, the moisture, or the smell of my breath that bothered them, but I always had to hold my breath and kind of look to one side so as not to confuse the experiment while I was ferrying the ants.
One question that I wondered about was why the ant trails look so straight and nice. The ants look as if they know what they’re doing, as if they have a good sense of geometry. Yet the experiments that I did to try to demonstrate their sense of geometry didn’t work.
Many years later, when I was at Caltech and lived in a little house on Alameda Street, some ants came out around the bathtub. I thought, “This is a great opportunity.” I put some sugar on the other end of the bathtub, and sat there the whole afternoon until an ant finally found the sugar. It’s only a question of patience.
The moment the ant found the sugar, I picked up a colored pencil that I had ready (I had previously done experiments indicating that the ants don’t give a damn about pencil marks—they walk right over them—so I knew I wasn’t disturbing anything), and behind where the ant went I drew a line so I could tell where his trail was. The ant wandered a little bit wrong to get back to the hole, so the line was quite wiggly unlike a typical ant trail.
When the next ant to find the sugar began to go back, I marked his trail with another color. (By the way he followed the first ant’s return trail back, rather than his own incoming trail. My theory is that when an ant has found some food, he leaves a much stronger trail than when he’s just wandering around.)
This second ant was in a great hurry and followed, pretty much, the original trail. But because he was going so fast he would go straight out, as if he were coasting, when the trail was wiggly. Often, as the ant was “coasting,” he would find the trail again. Already it was apparent that the second ant’s return was slightly straighter. With successive ants the same “improvement” of the trail by hurriedly and carelessly “following” it occurred.
I followed eight or ten ants with my pencil until their trails became a neat line right along the bathtub. It’s something like sketching: You draw a lousy line at first; then you go over it a few times and it makes a nice line after a while.
I remember that when I was a kid my father would tell me how wonderful ants are, and how they cooperate. I would watch very carefully three or four ants carrying a little piece of chocolate back to their nest. At first glance it looks like efficient, marvelous, brilliant cooperation. But if you look at it carefully you’ll see that it’s nothing of the kind: They’re all behaving as if the chocolate is held up by something else. They pull at it one way or the other way. An ant may crawl over it while it’s being pulled at by the others. It wobbles, it wiggles, the directions are all confused. The chocolate doesn’t move in a nice way toward the nest.
The Brazilian leaf-cutting ants, which are otherwise so marvelous, have a very interesting stupidity associated with them that I’m surprised hasn’t evolved out. It takes considerable work for the ant to cut the circular arc in order to get a piece of leaf. When the cutting is done, there’s a fifty-fifty chance that the ant will pull on the wrong side, letting the piece he just cut fall to the ground. Half the time, the ant will yank and pull and yank and pull on the wrong part of the leaf, until it gives up and starts to cut another piece. There is no attempt to pick up a piece that it, or any other ant, has already cut. So it’s quite obvious, if you watch very carefully that it’s not a brilliant business of cutting leaves and carrying them away; they go to a leaf, cut an arc, and pick the wrong side half the time while the right piece falls down.
In Princeton the ants found my larder, where I had jelly and bread and stuff, which was quite a distance from the window. A long line of ants marched along the floor across the living room. It was during the time I was doing these experiments on the ants, so I thought to myself, “What can I do to stop them from coming to my larder without killing any ants? No poison; you gotta be humane to the ants!”
What I did was this: In preparation, I put a bit of sugar about six or eight inches from their entry point into the room, that they didn’t know about. Then I made those ferry things again, and whenever an ant returning with food walked onto my little ferry I’d carry him over and put him on the sugar. Any ant coming toward the larder that walked onto a ferry I also carried over to the sugar. Eventually the ants found their way from the sugar to their hole, so this new trail was being doubly reinforced, while the old trail was being used less and less. I knew that after half an hour or so the old trail would dry up, and in an hour they were out of my larder. I didn’t wash the floor; I didn’t do anything but ferry ants.
Instead, I would play: I’d make a motor, I’d make a gadget that would go off when something passed a photocell. I’d play around with selenium; I was piddling around all the time. I did calculate a little bit for the lamp bank, a series of switches and bulbs I used as resistors to control voltages. But all that was for application. I never did any laboratory kind of experiments.
I also had a microscope and loved to watch things under the microscope.It took patience: I would get something under the microscope and I would watch it interminably. I saw many interesting things, like everybody sees—a diatom slowly making its way across the slide, and so on.
One day I was watching a paramecium and I saw something that was not described in the books I got in school—in college, even. These books always simplify things so the world will be more like they want it to be: When they’re talking about the behavior of animals, they always start out with, “The paramecium is extremely simple; it has a simple behavior. It turns as its slipper shape moves through the water until it hits something, at which time it recoils, turns through an angle, and then starts out again.”
It isn’t really right. First of all, as everybody knows, the paramecia, from time to time, conjugate with each other—they meet and exchange nuclei. How do they decide when it’s time to do that? (Never mind; that’s not my observation.)
I watched these paramecia hit something, recoil, turn through an angle, and go again. The idea that it’s mechanical, like a computer program—it doesn’t look that way. They go different distances, they recoil different distances, they turn through angles that are different in various cases; they don’t always turn to the right; they’re very irregular. It looks random, because you don’t know what they’re hitting; you don’t know all the chemicals they’re smelling, or what.
One of the things I wanted to watch was what happens to the paramecium when the water that it’s in dries up. It was claimed that the paramecium can dry up into a sort of hardened seed. I had a drop of water on the slide under my microscope, and in the drop of water was a paramecium and some “grass”—at the scale of the paramecium, it looked like a network of jackstraws. As the drop of water evaporated, over a time of fifteen or twenty minutes, the paramecium got into a tighter and tighter situation: there was more and more of this back-and-forth until it could hardly move. It was stuck between these “sticks,” almost jammed.
Then I saw something I had never seen or heard of: the paramecium lost its shape. It could flex itself, like an amoeba. It began to push itself against one of the sticks, and began dividing into two prongs until the division was about halfway up the paramecium, at which time it decided that wasn’t a very good idea, and backed away.
So my impression of these animals is that their behavior is much too simplified in the books. It is not so utterly mechanical or one-dimensional as they say. They should describe the behavior of these simple animals correctly. Until we see how many dimensions of behavior even a one-celled animal has, we won’t be able to fully understand the behavior of more complicated animals.
I also enjoyed watching hugs. I had an insect book when I was about thirteen. It said that dragonflies are not harmful; they don’t sting. In our neighborhood it was well known that “darning needles,” as we called them, were very dangerous when they’d sting. So if we were outside somewhere playing baseball, or something, and one of these things would fly around, everybody would run for cover, waving their arms, yelling, “A darning needle! A darning needle!”
So one day I was on the beach, and I’d just read this book that said dragonflies don’t sting. A darning needle came along, and everybody was screaming and running around, and I just sat there. “Don’t worry!” I said. “Darning needles don’t sting!”
The thing landed on my foot. Everybody was yelling and it was a big mess, because this darning needle was sitting on my foot, And there I was, this scientific wonder, saying it wasn’t going to sting me.
You’re sure this is a story that’s going to come out that it stings me—but it didn’t. The book was right. But I did sweat a bit.
I also had a little hand microscope. It was a toy microscope, and I pulled the magnification piece out of it, and would hold it in my hand like a magnifying glass, even though it was a microscope of forty or fifty power. With care you could hold the focus. So I could go around and look at things right out in the street.
So when I was in graduate school at Princeton, I once took it out of my pocket to look at some ants that were crawling around on some ivy. I had to exclaim out loud, I was so excited. What I saw was an ant and an aphid, which ants take care of—they carry them from plant to plant if the plant they’re on is dying. In return the ants get partially digested aphid juice, called “honeydew.” I knew that; my father had told me about it, but I had never seen it.
So here was this aphid and sure enough, an ant came along, and patted it with its feet—all around the aphid, pat, pat, pat, pat, pat. This was terribly exciting! Then the juice came out of the back of the aphid. And because it was magnified, it looked like a big, beautiful, glistening ball, like a balloon, because of the surface tension. Because the microscope wasn’t very good, the drop was colored a little bit from chromatic aberration in the lens—it was a gorgeous thing!
The ant took this ball in its two front feet, lifted it off the aphid, and held it. The world is so different at that scale that you can pick up water and hold it! The ants probably have a fatty or greasy material on their legs that doesn’t break the surface tension of the water when they hold it up. Then the ant broke the surface of the drop with its mouth, and the surface tension collapsed the drop right into his gut. It was very interesting to see this whole thing happen!
In my room at Princeton I had a bay window with a U-shaped windowsill. One day some ants came out on the windowsill and wandered around a little bit. I got curious as to how they found things. I wondered, how do they know where to go? Can they tell each other where food is, like bees can? Do they have any sense of geometry?
This is all amateurish; everybody knows the answer, but I didn’t know the answer, so the first thing I did was to stretch some string across the U of the bay window and hang a piece of folded cardboard with sugar on it from the string. The idea of this was to isolate the sugar from the ants, so they wouldn’t find it accidentally. I wanted to have everything under control.
Next I made a lot of little strips of paper and put a fold in them, so I could pick up ants and ferry them from one place to another. I put the folded strips of paper in two places:
Some were by the sugar (hanging from the string), and the others were near the ants in a particular location. I sat there all afternoon, reading and watching, until an ant happened to walk onto one of my little paper ferries. Then I took him over to the sugar. After a few ants had been ferried over to the sugar, one of them accidentally walked onto one of the ferries nearby, and I carried him back.
I wanted to see how long it would take the other ants to get the message to go to the “ferry terminal.” It started slowly but rapidly increased until I was going mad ferrying the ants back and forth.
But suddenly, when everything was going strong, I began to deliver the ants from the sugar to a different spot. The question now was, does the ant learn to go back to where it just came from, or does it go where it went the time before?
After a while there were practically no ants going to the first place (which would take them to the sugar), whereas there were many ants at the second place, milling around, trying to find the sugar. So I figured out so far that they went where they just came from.
In another experiment, I laid out a lot of glass microscope slides, and got the ants to walk on them, back and forth, to some sugar I put on the windowsill. Then, by replacing an old slide with a new one, or by rearranging the slides, I could demonstrate that the ants had no sense of geometry: they couldn’t figure out where something was. If they went to the sugar one way and there was a shorter way back, they would never figure out the short way.
It was also pretty clear from rearranging the glass slides that the ants left some sort of trail. So then came a lot of easy experiments to find out how long it takes a trail to dry up, whether it can be easily wiped off, and so on. I also found out the trail wasn’t directional. If I’d pick up an ant on a piece of paper, turn him around and around, and then put him back onto the trail, he wouldn’t know that he was going the wrong way until he met another ant. (Later, in Brazil, I noticed some leaf-cutting ants and tried the same experiment on them. They could tell, within a few steps, whether they were going toward the food or away from it—presumably from the trail, which might be a series of smells in a pattern: A, B, space, A, B, space, and so on.)
I tried at one point to make the ants go around in a circle, but I didn’t have enough patience to set it up. I could see no reason, other than lack of patience, why it couldn’t be done.
One thing that made experimenting difficult was that breathing on the ants made them scurry. It must be an instinctive thing against some animal that eats them or disturbs them. I don’t know if it was the warmth, the moisture, or the smell of my breath that bothered them, but I always had to hold my breath and kind of look to one side so as not to confuse the experiment while I was ferrying the ants.
One question that I wondered about was why the ant trails look so straight and nice. The ants look as if they know what they’re doing, as if they have a good sense of geometry. Yet the experiments that I did to try to demonstrate their sense of geometry didn’t work.
Many years later, when I was at Caltech and lived in a little house on Alameda Street, some ants came out around the bathtub. I thought, “This is a great opportunity.” I put some sugar on the other end of the bathtub, and sat there the whole afternoon until an ant finally found the sugar. It’s only a question of patience.
The moment the ant found the sugar, I picked up a colored pencil that I had ready (I had previously done experiments indicating that the ants don’t give a damn about pencil marks—they walk right over them—so I knew I wasn’t disturbing anything), and behind where the ant went I drew a line so I could tell where his trail was. The ant wandered a little bit wrong to get back to the hole, so the line was quite wiggly unlike a typical ant trail.
When the next ant to find the sugar began to go back, I marked his trail with another color. (By the way he followed the first ant’s return trail back, rather than his own incoming trail. My theory is that when an ant has found some food, he leaves a much stronger trail than when he’s just wandering around.)
This second ant was in a great hurry and followed, pretty much, the original trail. But because he was going so fast he would go straight out, as if he were coasting, when the trail was wiggly. Often, as the ant was “coasting,” he would find the trail again. Already it was apparent that the second ant’s return was slightly straighter. With successive ants the same “improvement” of the trail by hurriedly and carelessly “following” it occurred.
I followed eight or ten ants with my pencil until their trails became a neat line right along the bathtub. It’s something like sketching: You draw a lousy line at first; then you go over it a few times and it makes a nice line after a while.
I remember that when I was a kid my father would tell me how wonderful ants are, and how they cooperate. I would watch very carefully three or four ants carrying a little piece of chocolate back to their nest. At first glance it looks like efficient, marvelous, brilliant cooperation. But if you look at it carefully you’ll see that it’s nothing of the kind: They’re all behaving as if the chocolate is held up by something else. They pull at it one way or the other way. An ant may crawl over it while it’s being pulled at by the others. It wobbles, it wiggles, the directions are all confused. The chocolate doesn’t move in a nice way toward the nest.
The Brazilian leaf-cutting ants, which are otherwise so marvelous, have a very interesting stupidity associated with them that I’m surprised hasn’t evolved out. It takes considerable work for the ant to cut the circular arc in order to get a piece of leaf. When the cutting is done, there’s a fifty-fifty chance that the ant will pull on the wrong side, letting the piece he just cut fall to the ground. Half the time, the ant will yank and pull and yank and pull on the wrong part of the leaf, until it gives up and starts to cut another piece. There is no attempt to pick up a piece that it, or any other ant, has already cut. So it’s quite obvious, if you watch very carefully that it’s not a brilliant business of cutting leaves and carrying them away; they go to a leaf, cut an arc, and pick the wrong side half the time while the right piece falls down.
In Princeton the ants found my larder, where I had jelly and bread and stuff, which was quite a distance from the window. A long line of ants marched along the floor across the living room. It was during the time I was doing these experiments on the ants, so I thought to myself, “What can I do to stop them from coming to my larder without killing any ants? No poison; you gotta be humane to the ants!”
What I did was this: In preparation, I put a bit of sugar about six or eight inches from their entry point into the room, that they didn’t know about. Then I made those ferry things again, and whenever an ant returning with food walked onto my little ferry I’d carry him over and put him on the sugar. Any ant coming toward the larder that walked onto a ferry I also carried over to the sugar. Eventually the ants found their way from the sugar to their hole, so this new trail was being doubly reinforced, while the old trail was being used less and less. I knew that after half an hour or so the old trail would dry up, and in an hour they were out of my larder. I didn’t wash the floor; I didn’t do anything but ferry ants.
Part 3. Feynman, the Bomb, and the Military
Fizzled Fuses
When the war began in Europe but had not yet been declared in the United States, there was a lot of talk about getting ready and being patriotic. The newspapers had big articles on businessmen volunteering to go to Plattsburg, New York, to do military training, and so on.
I began to think I ought to make some kind of contribution, too. After I finished up at MIT, a friend of mine from the fraternity, Maurice Meyer, who was in the Army Signal Corps, took me to see a colonel at the Signal Corps offices in New York.
“I’d like to aid my country sir, and since I’m technically minded, maybe there’s a way I could help.”
“Well, you’d better just go up to Plattsburg to boot camp and go through basic training. Then we’ll be able to use you,” the colonel said.
“But isn’t there some way to use my talent more directly?”
“No; this is the way the army is organized. Go through the regular way.”
I went outside and sat in the park to think about it. I thought and thought: Maybe the best way to make a contribution is to go along with their way. But fortunately I thought a little more, and said, “To hell with it! I’ll wait awhile. Maybe something will happen where they can use me more effectively”
I went to Princeton to do graduate work, and in the spring I went once again to the Bell Labs in New York to apply for a summer job. I loved to tour the Bell Labs. Bill Shockley the guy who invented transistors, would show me around. I remember somebody’s room where they had marked a window: The George Washington Bridge was being built, and these guys in the lab were watching its progress. They had plotted the original curve when the main cable was first put up, and they could measure the small differences as the bridge was being suspended from it, as the curve turned into a parabola. It was just the kind of thing I would like to be able to think of doing. I admired those guys; I was always hoping I could work with them one day.
Some guys from the lab took me out to this seafood restaurant for lunch, and they were all pleased that they were going to have oysters. I lived by the ocean and I couldn’t look at this stuff; I couldn’t eat fish, let alone oysters.
I thought to myself, “I’ve gotta be brave. I’ve gotta eat an oyster.”
I took an oyster, and it was absolutely terrible. But I said to myself, “That doesn’t really prove you’re a man. You didn’t know how terrible it was gonna be. It was easy enough when it was uncertain.”
The others kept talking about how good the oysters were, so I had another oyster, and that was really harder than the first one.
This time, which must have been my fourth or fifth time touring the Bell Labs, they accepted me. I was very happy. In those days it was hard to find a job where you could be with other scientists.
But then there was a big excitement at Princeton. General Trichel from the army came around and spoke to us: “We’ve got to have physicists! Physicists are very important to us in the army! We need three physicists!”
You have to understand that, in those days, people hardly knew what a physicist was. Einstein was known as a mathematician, for instance—so it was rare that anybody needed physicists. I thought, “This is my opportunity to make a contribution,” and I volunteered to work for the army.
I asked the Bell Labs if they would let me work for the army that summer, and they said they had war work, too, if that was what I wanted. But I was caught up in a patriotic fever and lost a good opportunity. It would have been much smarter to work in the Bell Labs. But one gets a little silly during those times.
I went to the Frankfort Arsenal, in Philadelphia, and worked on a dinosaur: a mechanical computer for directing artillery. When airplanes flew by the gunners would watch them in a telescope, and this mechanical computer, with gears and cams and so forth, would try to predict where the plane was going to he. It was a most beautifully designed and built machine, and one of the important ideas in it was non-circular gears—gears that weren’t circular, but would mesh anyway. Because of the changing radii of the gears, one shaft would turn as a function of the other. However, this machine was at the end of the line. Very soon afterwards, electronic computers came in.
After saying all this stuff about how physicists were so important to the army the first thing they had me doing was checking gear drawings to see if the numbers were right. This went on for quite a while. Then, gradually the guy in charge of the department began to see I was useful for other things, and as the summer went on, he would spend more time discussing things with me.
One mechanical engineer at Frankfort was always trying to design things and could never get everything right. One time he designed a box full of gears, one of which was a big, eight-inch-diameter gear wheel that had six spokes. The fella says excitedly “Well, boss, how is it? How is it?”
“Just fine!” the boss replies. “All you have to do is specify a shaft passer on each of the spokes, so the gear wheel can turn!” The guy had designed a shaft that went right between the spokes!
I began to think I ought to make some kind of contribution, too. After I finished up at MIT, a friend of mine from the fraternity, Maurice Meyer, who was in the Army Signal Corps, took me to see a colonel at the Signal Corps offices in New York.
“I’d like to aid my country sir, and since I’m technically minded, maybe there’s a way I could help.”
“Well, you’d better just go up to Plattsburg to boot camp and go through basic training. Then we’ll be able to use you,” the colonel said.
“But isn’t there some way to use my talent more directly?”
“No; this is the way the army is organized. Go through the regular way.”
I went outside and sat in the park to think about it. I thought and thought: Maybe the best way to make a contribution is to go along with their way. But fortunately I thought a little more, and said, “To hell with it! I’ll wait awhile. Maybe something will happen where they can use me more effectively”
I went to Princeton to do graduate work, and in the spring I went once again to the Bell Labs in New York to apply for a summer job. I loved to tour the Bell Labs. Bill Shockley the guy who invented transistors, would show me around. I remember somebody’s room where they had marked a window: The George Washington Bridge was being built, and these guys in the lab were watching its progress. They had plotted the original curve when the main cable was first put up, and they could measure the small differences as the bridge was being suspended from it, as the curve turned into a parabola. It was just the kind of thing I would like to be able to think of doing. I admired those guys; I was always hoping I could work with them one day.
Some guys from the lab took me out to this seafood restaurant for lunch, and they were all pleased that they were going to have oysters. I lived by the ocean and I couldn’t look at this stuff; I couldn’t eat fish, let alone oysters.
I thought to myself, “I’ve gotta be brave. I’ve gotta eat an oyster.”
I took an oyster, and it was absolutely terrible. But I said to myself, “That doesn’t really prove you’re a man. You didn’t know how terrible it was gonna be. It was easy enough when it was uncertain.”
The others kept talking about how good the oysters were, so I had another oyster, and that was really harder than the first one.
This time, which must have been my fourth or fifth time touring the Bell Labs, they accepted me. I was very happy. In those days it was hard to find a job where you could be with other scientists.
But then there was a big excitement at Princeton. General Trichel from the army came around and spoke to us: “We’ve got to have physicists! Physicists are very important to us in the army! We need three physicists!”
You have to understand that, in those days, people hardly knew what a physicist was. Einstein was known as a mathematician, for instance—so it was rare that anybody needed physicists. I thought, “This is my opportunity to make a contribution,” and I volunteered to work for the army.
I asked the Bell Labs if they would let me work for the army that summer, and they said they had war work, too, if that was what I wanted. But I was caught up in a patriotic fever and lost a good opportunity. It would have been much smarter to work in the Bell Labs. But one gets a little silly during those times.
I went to the Frankfort Arsenal, in Philadelphia, and worked on a dinosaur: a mechanical computer for directing artillery. When airplanes flew by the gunners would watch them in a telescope, and this mechanical computer, with gears and cams and so forth, would try to predict where the plane was going to he. It was a most beautifully designed and built machine, and one of the important ideas in it was non-circular gears—gears that weren’t circular, but would mesh anyway. Because of the changing radii of the gears, one shaft would turn as a function of the other. However, this machine was at the end of the line. Very soon afterwards, electronic computers came in.
After saying all this stuff about how physicists were so important to the army the first thing they had me doing was checking gear drawings to see if the numbers were right. This went on for quite a while. Then, gradually the guy in charge of the department began to see I was useful for other things, and as the summer went on, he would spend more time discussing things with me.
One mechanical engineer at Frankfort was always trying to design things and could never get everything right. One time he designed a box full of gears, one of which was a big, eight-inch-diameter gear wheel that had six spokes. The fella says excitedly “Well, boss, how is it? How is it?”
“Just fine!” the boss replies. “All you have to do is specify a shaft passer on each of the spokes, so the gear wheel can turn!” The guy had designed a shaft that went right between the spokes!