Surely You're Joking, Mr. Feynman! (11 page)

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 coining 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 hunch of stuff. Another time I went to the right place hut 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.