It’s interesting that some people find science so easy and others find it kind of dull and difficult, especially kids. You know, some of them just eat it up. And I don’t know why it is. It’s the same perhaps, but also, for instance, lots of people love music and I never could carry a tune, and I lose a great deal of pleasure out of that. And I think people lose a lot of pleasure who find science dull. In the case of science, I think that one of the things that make it very difficult is it takes a lot of imagination. It’s very hard to imagine all the crazy things that things really are like.

Nothing’s really as it seems. We’re used to get, you know, hot and cold, all that hot and cold is the speeds that the atoms are jiggling. If they jiggle more, it corresponds to hotter, and colder is jiggling less. So if you have a cup of coffee or something sitting on a table, and the atoms are jiggling a great deal in the coffee, they bounce against the cup, and the cup then gets shaking, and the atoms in the cup shake and they bounce against the saucer, and that heats the cup and heats everything else. A hot thing spreads its heat into other things by mere contact, because the atoms that are jiggling a lot in the hot thing shake the ones that are jiggling only a little bit in the cold thing. So that the hot—“heat,” we say—goes into the cold thing. It spreads. But what’s spreading is just jiggling and irregular motions, which is easy to kind of understand.

It brings up another thing that’s kind of curious. That I say the things jiggle, and if you’re used to balls bouncing, you know they slow up and stop after a while. But we have to imagine with the atoms a perfect elasticity. They never lose any energy. Every time they bounce, they keep on bouncing all the time. They don’t lose anything. They’re perpetually moving. And that the things that happen when we say something loses energy—if a ball comes down and bounces, it shakes irregularly some of the atoms in the floor. And then, when it comes up again, it leaves some of those atoms moving, the jiggling. So as it bounces it’s passing its extra energies, its extra motions, to little patches on the floor each time it bounces, and loses a little each time until it settles down—we say, as if all the motion has stopped.

But what’s left is the floor is shaking more than it was before and the atoms in the ball are shaking more than they were before. That the organized motion of all these atoms moving the same way, falling down, and the quiet floor is now transformed into a ball sitting on the ground. But all that motion is still there in a form, or the energy of motion, in the form of the jiggling of the floor which is a little bit warmer. Unbelievable! But anybody who’s hammered a great deal on something knows that it’s true: that if you pound something and hit it a lot, you can feel the temperature difference, it heats up. It heats up simply because you’re jiggling it.

This picture of atoms is a beautiful one that you can keep looking at all kinds of things this way. You see a little drop of water, a tiny drop, and the atoms attract each other. They like to be next to each other. They want as many partners as they can get. Now, the guys that are at the surface have only partners on one side here, in the air, and the other side, so they’re trying to get in. And you can imagine this team of people, these teeming people, all moving very fast, all trying to get to have as many partners as possible. And the guys at the edge are very unhappy and nervous, and they keep pounding in, trying to get in, and that makes it a tight ball instead of flat. And that’s what, you know, surface tension, the way you even you realize when you see how sometimes a water drop sits like this on a table, then you start to imagine why it sits like that: because everybody’s trying to get into the water. And at the same time while all this is happening, there are these atoms that are leaving the surface, and the water drop is slowly disappearing.

I find myself trying to imagine all kinds of things all the time, and I get a kick out of it, just like a runner gets a kick out of sweating. I get a kick out of thinking about these things. I can’t stop. I mean, I could talk forever. If you cooled off the water, so the jiggling is less and less and it jiggles slower and slower, then the atoms get stuck in place. They like to be with their friend—there’s a force of attraction—and they get packed together. They’re not rolling over each other. They’re in a nice pattern—like oranges in a crate in a nice organized pattern—all just jiggling in place, but not having enough motion to get loose of their own place and to break the structure down. And that’s what I’m describing is a solid. It’s ice. It has a structure. If you held the atoms at one end in a certain position, all the rest are lined up in a position sticking out, and it’s solid at the end. Whereas if you heat that harder, then they begin to get loose and roll all over each other, and that’s the liquid.

And if you heat that still harder, and they bounce harder, then they simply bounce apart from each other and they’re just individual—I say atoms, there’s really little groups about it; it’s molecules—which come flying and hit. And although they have a tendency to stick, they’re moving too fast. Their hands don’t grab, so to speak, as they pass, and they fly apart again. And this is the gas we call steam.

You can get all kinds of understanding. When I was a kid with this air, which I was always interested in, I noticed that when I pumped up my tires in a bicycle—you can learn a lot by having a bicycle—they’d pump up the tires, that the pump would get hot. And that also understands, you see: as the pump handle comes down and the atoms are coming up against it and bouncing off, and it’s moving in, the ones that are coming off have a bigger speed than the ones that are coming in, so that as it comes down, and each time they collide, it speeds them up. And so they’re hotter. When you compress the gas it heats. And when you pull the piston back out, then atoms which are coming fast at the piston feel a receding or sort of a give. It gives, and it comes out with less energy. It’s like going up against something which is soft and yielding, it goes boom, boom, and it loses. And so as you pull the piston out and the atoms are hit, they lose their speed and they cool off. And gases are cool when they expand.

And the fun of it is that all these things which you see or notice in the world about it—the pump heats the gas, and the gas cools when it expands, or the steam evaporates until you cover the cover, and all these things—you can understand from these simple pictures. And that’s kind of a lot of fun to think about. I don’t want to take this stuff seriously. I think we should just have fun imagining it and not worry about. There’s no teacher going to ask you questions at the end. Otherwise it’s a horrible subject.

The atoms like each other to different degrees. Oxygen, for instance, in the air, would like to be next to carbon. And if they’re getting near each other, they snap together. If they’re not too close, though, they repel and they go apart. So they don’t know that they could snap together. It’s just as if you had a ball that was trying to climb a hill and there was a hole it could go into, like a volcano hole, a deep one. It’s rolling along. It doesn’t go down in the deep hole, because if it starts to climb the hill and then rolls away again. But if you made it go fast enough, it’ll fall into the hole.

And so if it’s something like wood in oxygen—there’s carbon in the wood from a tree—and the oxygen comes and hits the carbon, but not hard enough, it just goes away again. The air has always coming, nothing’s happening. If you can get it faster by heating it up somehow, somewhere, somehow get it started, a few of them come fast. They go over the top, so to speak. They come close enough to the carbon and snap in. And that gives a lot of jiggly motion which might hit some other atoms, making those go faster, so they can climb up and bump against other carbon atoms, and they jiggle and they make others jiggle, and you get a terrible catastrophe which is one after the other. All these things are going faster and faster, and snapping in, and the whole thing is changing. That catastrophe is a fire.

It’s just a way of looking at it and these things are happening. They’re perpetual. Once it gets started, it keeps on going. The heat makes the other atoms capable of reaching, to make more heat, to make other atoms, and so on. So this terrible snapping is producing a lot of jiggling. And if I put with all that activity of the atoms there, and I put a cup of coffee over that massive wood that’s doing this, it’s going to get a lot of jiggling. So that’s what the heat of the fire is.

And then, of course if—you see, this is what happens we just start to think. You just go on and on. Wonder where… how did it get started? Why is it that the wood’s been sitting around all this time with the oxygen all this time? And it didn’t do this earlier or something? Where did I get this from? Well, it came from a tree. And the substance of the tree is carbon. And where did that come from? That comes from the air. It’s carbon dioxide from the air. People look at trees and they think it comes out of the ground; the plants grow out of the ground. But if you ask where the substance comes from, you find out—where do they come from—the trees come out of the air? They surely come out of the ground! No, they come out of the air.

The carbon the oxide in the air goes into the tree and it changes it, kicking out the oxygen, and pushing the oxygen away from the carbon, and leaving the carbon substance with water. Water comes out of the ground, you see. Only, how did it get in there? It came out of the air, didn’t it? It came down from the sky. So in fact, most of a tree, almost all of the tree, is out of the ground—I’m sorry, it’s out of the air. There’s a little bit from the ground, some minerals and so forth.

Now, of course I told you the oxygen—we know that oxygen and carbon stick together very tight. How is it the tree is so smart to manage to take the carbon dioxide—which is the carbon–oxygen nicely combined—and undo that so easy? Ah, life! “Life has some mysterious force!” No. The sun is shining, and it’s the sunlight that comes down and knocks this oxygen away from the carbon. So it takes sunlight to get the plant to work. And so the sun all the time is doing the work of separating the oxygen away from the carbon. The oxygen is some kind of terrible byproduct, which it spits back into the air, and leaving the carbon and water and stuff to make the substance of the tree.

Then, when we take the substance of the tree and stick it in the fireplace, and there’s all the oxygen made by these trees, and all the carbon would much prefer to be close together again. And once you let the heat to get it started, it continues and makes an awful lot of activity while it’s going back together again. And all this nice light and everything comes out, and everything is being undone. You’re going back from carbon and oxygen back to carbon dioxide. And the light and heat that’s coming out, that’s the light and heat of the sun that went in. So it’s sort of stored sun that’s coming out when you burn a log.

Next question: how is it the sun is so jiggly, so hot? I gotta stop somewhere. I’ll leave you something to imagine!

Most elastic things, like steel springs and so on, is nothing but this electrical thing pulling back. You pull the atoms a little bit apart when you bend something, and then they try to come back together again. But rubber bands work on a different principle. There are some long molecules, like chains, and other little ones that are shaking all the time that are bombarding them, these chains. And the chains are all kind of kinky and knocked about and shake. When you pull open the rubber band, the strings get straighter. But these strings are being bombarded on the side by these other atoms trying to shorten them, by kinking them. So it pulls back. It’s trying to pull back, and it’s pulling back only because of the heat. So if you heat a rubber band, it’ll pull more strongly, for instance. If you hang a weight with a rubber band and put a little match to it, it’s kind of fun to watch it rise, when it heats more.

And there’s another thing you can check that this idea is right; that it’s heat that drives a rubber band. If you pull the band out—just like when we push the piston and the gas—if you pull the band out, these tightening strings hitting those molecules makes them move faster. And so it’s warmer. And if you take the band and let it in, then the molecules hitting the strings would sort of give as the thing hits it. They give in to the soft, like. And they lose energy when they hit these retiring strings. So it cools.

And there is a little way you can do this. You’re not very sensitive. It’s a small effect. If you take a fairly wide rubber band and put it between your lips and pull it out, you’ll certainly notice it’s hotter. And if you then hold it out and let it in, you’ll notice it’s cooler. At least you’ll notice a certain difference in what happens when you expand it, when you contract it.

And I’ve always found rubber bands fascinating. To think that when they’re sitting on an old package of papers for a long time, holding those papers together, it’s done by a perpetual pounding, pounding, pounding of the atoms against these chains to hold it, trying to kink them and trying to kink them year after year—well, rubber bands don’t last that long, but anyhow, for a long time trying to hold this whole thing together.

The world is a dynamic mess of jiggling things, if you look at it right. And if you’re magnified, you can hardly see anything anymore because everything’s jiggling and they’re all in patterns and they’re all lots of little balls. It’s lucky that we have such a large-scale of view of everything that we can see them as things without having to worry about all these little atoms all the time.

15:08

Feynman

What do you mean, “what’s the feeling between the two magnets?”

15:16

Feynman

Listen to my question: what is the meaning when you say that there’s a feeling? Of course you feel it. Now, what do you want to know?

15:29

Feynman

The magnets repel each other.

15:42

Feynman

Of course it’s a reasonable question. It’s an excellent question. Okay? But the problem that you’re asking—you see, when you ask why something happens, how does a person answer why something happens? For example: Aunt Minnie is in the hospital. Why? Because she went out and she slipped on the ice and broke her hip. That satisfies people. It satisfies, but it wouldn’t satisfy someone who came from another planet and knew nothing about things. At first you should understand why, when you break your hip, do you go to the hospital? How do you get to the hospital when the hip was broken? Well, because her husband, seeing that the hip was broken, called the hospital up and sent somebody to get her. All that is understood by people.

Now, when you explain a why, you have to be in some framework that you allow something to be true. Otherwise you’re perpetually asking why. Why did the husband call up the hospital? Because husband is interested in his wife’s welfare. Not always. Some husbands aren’t interested in their wife’s welfare when they’re drunk and they’re angry. And so you begin to get a very interesting understanding of the world and all its complications. In order to, if you try to follow anything up, you go deeper and deeper in various directions.

For example, you could go: why did she slip on the ice? Well, ice is slippery. Everybody knows that, no problem. But you ask: why is ice slippery? That’s kind of curious. Ice is extremely slippery. It’s very interesting. You say: how does it work? You could either say I’m satisfied that you’ve answered me—ice is slippery, that explains it—or you could go on and say: why is ice slippery? And then you’re involved with something, because there aren’t many things as slippery as ice. It’s very hard to get greasy stuff, but that’s sort of wet and slimy. But a solid that’s so slippery?

Because it is (in the case of ice) that when you stand on it, they say, momentarily the pressure melts the ice a little bit, so you’ve got a sort of instantaneous water surface on which you’re slipping. Why on ice and not on other things? Because water expands when it freezes, so the pressure tries to undo the expansion and melts it. It’s capable of melting it. But other substances contract when they’re freezing and when you’re pushing, they’re just as satisfied to be solid.

Why does water expand when it freezes and other substances don’t expand when they freeze? Alright? Am I answering your question? But I’m telling you how difficult a why question is. You have to know what it is that you’re permitted to understand and allow to be understood and known, and what it is you’re not. You’ll notice in this example that the more I ask why, it gets interesting after all. That’s my idea that the deeper the thing is, the more interesting. And we could even go further and say: why did she fall down when she slipped? That has to do with gravity. It involves in all the planets and everything else. Never mind. It goes on and on.

Now, when you ask, for example, why two magnets repel, there are many different levels. It depends on whether you’re a student of physics or an ordinary person that doesn’t know anything or not. If you’re somebody who doesn’t know anything at all about it, all I can say is that there’s a magnetic force that makes them repel when you’re feeling that force. And you say: but that’s very strange, because I don’t feel a kind of force like that in other circumstances. When you turn them the other way they attract. There’s a very analogous force, electrical force, which is the same kind of a question. And you say that’s also very weird.

But you’re not at all disturbed by the fact that when you put your hand on a chair, it pushes you back. But we found out by looking at it that that’s the same force, as a matter of fact—the electrical force, not magnetic, exactly, in that case. But it’s the same electrical repulsions that are involved in keeping your finger away from the chair. Because it’s electrical forces in minor and microscopic details. There’s other forces involved, but it’s connected to electrical forces.

It turns out that the magnetic and the electric force with which I wish to explain these things, this repulsion in the first place, is what ultimately is the deeper thing that we can start with, to explain many other things that looked like everybody would just accept them. You know, you can’t put your hand through the chair. That’s taken for granted. But that you can’t put your hand through the chair, when looked at more closely why, it involves these same repulsive forces that appear in magnets.

The situation you then have to explain is: why in magnets it goes over a bigger distance than in ordinary? And there it has to do with the fact that in iron all the electrons are spinning in the same direction. They all get lined up, and they magnify the effect of the force until it’s large enough at a distance that you can feel it. But it’s a force which is present all the time, and very common, and is a basic force—almost; I mean, I can go a little further back if I were more technical—but in the early level, I have to tell you that’s going to be one of the things you’ll just have to take as an element in the world, the existence of magnetic repulsion or electrical. Electrical attraction, magnetic attraction.

I can’t explain that attraction in terms of anything else that’s familiar to you. For example, if we say the magnets attract like as if they were connected by rubber bands, I would be cheating you, because they’re not connected by rubber bands. I shouldn’t be in trouble. You’ll soon asked me about the nature of the bands. And secondly, if you were curious enough, you’d ask me why rubber bands tend to pull back together again, and I would end up explaining that in terms of electrical forces, which are the very things that I’m trying to use the rubber bands to explain. So I have cheated very badly, you see.

So I’m not going to be able to give you an answer to why magnets attract each other, except to tell you that they do, and to tell you that that’s one of the elements in the world of different kinds of forces. There are electrical forces, magnetic forces, gravitational forces, and others. And those are some of the parts. If you were a student I could go further. I could tell you that the magnetic forces are related to the electrical forces very intimately, that our relationship between the gravity forces and electrical forces remains unknown, and so on. But I really can’t do a good job, any job, of explaining magnetic force in terms of something else that you’re more familiar with, because I don’t understand it in terms of anything else that you’re more familiar with.

This stuff of fantasizing and looking at the world, imagining things—which really isn’t fantasizing, because you’re only trying to imagine the way it really is—comes in handy sometimes. The other day I was at the dentist and he’s getting ready with his electric drill to make holes, and I thought I’d better figure something fast or else it’s going to hurt. And then I thought about this little motor going around, and what was it that made it turn? And what was going on? And what’s going on is: there’s a dam some distance away here, and water going over the dam turns a great big wheel. Alright? And this wheel is connected with long thin pieces of copper, which split up into other pieces of copper and split up and spread all over the city. And then they’re connected back through another little gadget that makes wheels turn. All the wheels of the city are turning because this thing turns. If this thing stops, all the wheels stop. It starts again, they all start again.

And I think that’s kind of a marvelous thing of nature. It’s kind of—it’s extremely curious. That phenomenon I like to think about a lot, because all it is is copper and iron. See, sometimes we think it’s a man-made generator. It’s very complicated. The phenomenon is a result of some special something that we made. But it’s nature doing it, and it’s just iron and copper. And if you took a big long loop of copper and had iron at each end and moved a piece of iron here, the other iron moves at the other piece. And if you get it down to nothing, you know, just moving a piece of iron in a loop of copper and seeing another piece of iron move, you realize what a fantastic mystery nature is.

You don’t even need the iron. You could, if you at least get this pump primed and started, by jiggling copper strands around fast enough, knotting them and unknotting them and so forth, you can get other copper strands to move at the other end of a long connection. And what is it? It’s only copper and motion. And we’re so used to circumstances in which these electrical phenomena are all canceled out. Everything’s sort of neutral. We’re pushing and pulling. It’s really very dull. But nature has these wonderful things, magnetic forces and electrical. If you comb your hair with your comb and you get some strange conditions. So you put it in front of a piece of paper and it lifts up the paper, or the paper jiggles at a distance, far away.

And that, in fact, turns out, that that is the thing that’s deeper inside of everything than the things we’re used to. We’re used to forces that only act directly, right? You push with your finger, it only acts directly. But then you have to imagine what it is that’s pushing with the finger. Here’s this little thing, it’s made out of little balls and atoms. And it’s got another bunch of atoms that I’m pushing. And there’s a little space between those atoms. And this pushing is going through that space. And the only thing that happens with the comb and the paper is that circumstances have arisen which make it possible to see that these forces go through a bigger distance than just the short distance between the atoms.

What it is, is that you have charges, like electrons, that are both the same. They repel each other with a force. They’re little tiny particles; they’re a piece of the atom. And they repel each other with a force which is enormous. Its inverse is the square of the distance, just like gravity is inverse as a square of the distance. But gravity is attractive, and this is repulsive. And for two electrons the gravity is so weak compared to the electricity, the electricity is so much more enormous than the gravity. I can’t express it because I don’t know the name of the number. It’s one with 38 or 40 zeros after the one. Bigger is electricity. It’s so enormous that if I were all electrons—well, the number’s too big.

So if there’s also, however, for electrical things, other kind of charge, positive charges—example: protons are positive; they’re inside the nucleus of the atom—and they attract electrons. Opposite charges attract and like charges repel. So you have to imagine enormous forces where likes are trying to get away from likes and unlikes are trying to get near the opposite. What would happen if you had a lot of them? All the likes would collect with unlikes. They attract each other. And they’d get an intimate mixture of pluses and minuses all on top of each other, very close together. You wouldn’t have a lot of pluses anywhere because they repel each other. They’ll all be compensated by minuses very close. And you get these little knots of plus and minus.

The reason that the knots don’t get smaller and smaller is because they are particles, and they have quantum mechanical effects that we won’t discuss, that makes it that you can’t get any smaller than a certain size. And so you get these little lumps which are balls. They’re the atoms. The atoms have positive and negative charge, and they’re neutralized. They cancel their charges as nearly as they can. And because this force is so big, it ends up nowhere with very little left. Because it’s so big it cancels out. There’s always so exactly the same pluses and minuses in any normal material.

When you comb your hair, it rubs just a little bit extra. Just a few extra minuses, say, here, and somewhere else a few extra pluses. But the forces are so big there’s just the extra ones which make a force that we can see that seems to be at a long range. And that we find mysterious. And that we need an explanation for. And we try to find an explanation for it in terms of ideas like the forces that are inside of rubber bands or steel bars or twisted things. We like to have some kind of puller at a distance, because we’re used to it that we don’t get any push until we’re touching. But the fact is that the reason we don’t get any push until we’re touching is it’s the same force as you see in a long distance, only it’s come down to short because the pluses and minuses have cancelled out so well that you don’t feel anything until it gets very, very close. When it gets close enough, of course, it makes a difference which is plus and which is minus and where they are in every [???].

So it’s kind of fun to imagine this intimate mixture of highly attractive opposites which is so strong that they cancel out the effects. And it’s only sometimes, when you have an excess of one kind or another, that you get this mysterious electrical force. And how can I explain a mysterious electrical force in any other way? Why should I try to explain it in terms of something like jelly or other things which are made, and I understand the other way around in terms of strong long-distance forces which have all cancelled out? So it’s the electrical forces, in fact—and the magnetic forces, in fact—that we have to accept as the base reality in which we’re going to explain all the other things.

So again it turns out it’s hard to understand, and you have to do a lot of imagining, that the real world has as its base a force which acts at a long distance; that we haven’t got much experience with that force—we have peculiar phenomena here and there, but ordinarily we don’t have much experience with that force—is simply because that’s what requires explanation. That’s what requires imagination. The long-distance force we have no other picture for.

And in the example of the generator, what happens is that the electrons which are part of an atom, they’re pushed by the motion of the copper wires. And it’s wonderful to think that you push a few here, and they get too close together, so they push the others, because they repel at a long distance. It’s not just like water which repels at a short distance, but it’s a wonderful fluid which repels at a long distance, and the effects therefore can go very quickly through the wire. If there’s a little concentration it goes zing through the wire all over the city at once. And you can use that stuff to make signals. You can push a few electrons here and there by talking in a telephone at the other end of the line. A long line of copper across the city, the electrons respond because of these very rapid interactions over these long distances to what you’re saying in this room.

And to discover experimentally the existence of these long forces and these rapid-motion actions and so forth was a tremendous thing for human beings. I think that the discovery of electricity and magnetism, and the electromagnetic effects which were finally worked out—the full equations for everything, was worked out by Maxwell in 1873—it’s probably the most fundamental transformation of… the most remarkable thing in history, the biggest change in history.

I went to a scientific school; MIT. And in fraternity, when you first joined, they try to keep you from being—if you think you’re smart—from feeling that you’re too smart by giving you what looked like simple questions to try to figure out what actually happens. It’s like training for imagination, you know. It’s kind of fun. And I thought I’d tell you some of them that I remember. I learned them. Of course, once you learn them, the next time somebody comes along with this wonderful puzzle, you look at them kind of quietly, you wait two or three seconds or five seconds to show that you were thinking, and then you come up with this answer to astonish your friends. But the fact was, of course, that you were trained by your fraternity brothers as to how to answer these things early on.

One of the questions we got was the problem about the mirror. It’s an old problem. You look at a mirror—and let’s say you part your hair on the right side—and you look in the mirror and the image has got its hair parted on the left side. So the image is left to right mixed up. It’s not top and bottom mixed up, because the top of the head of the image is up there at the top, and the bottom or the feet are at the bottom. And the question is: how does a mirror know to get the left and right mixed up and not the up and down?

You get a better idea of the problem if you think of lying down and looking at the mirror. Well, your hair is still on the left side. And now the left and right was the up and down. Whereas the up and down, which look okay, was the right and left before. And the mirror somehow figured out what you’re going to do when you’re looking at it. So to describe in a sort of symmetrical way what a mirror does, that it doesn’t look lopsided. And it takes left and mixes it up with right, and it doesn’t do the same with up and down.

And after a lot of fiddling, gradually, I could work out the answers to that one. If you wave this hand, then the hand on the mirror that waves is right opposite it. The hand on the east is the hand on the east, and the hand on the west is the hand on the west, and the head that’s up is up, and that feet that are down and down. Everything’s really alright. But what’s wrong is: if this is north, your nose is to the north of the back of your head. But in the image, the nose is to the south of the back of the head. So what happens, really, in the image is: neither the right nor left mix up with the top and bottom, but the front and back have been reversed. You see? That which is the nose on the thing is on the wrong side of the head, if you want it. Alright?

Now ordinarily, when we think of the image, we think of it as another person. And we think of the normal way that a person would get into that condition over there. It’s a psychological thing. We don’t think of the idea that the person has been squashed and pushed backwards/forwards with his nose and his head, because that’s not what ordinarily happens to people. A person gets to look like he looks in the mirror by walking around and facing you. And because people, when they walk around, don’t turn their head for their feet, we leave that part alone, but they get their right and left hands swung about, you see, when they turn around. And so we say that it’s left and right interchanged. But really, the symmetrical way is along the axis of the mirror that things get interchanged. Well, that’s kind of an easy one.

A harder one (and very entertaining) was: what keeps a train on the track? And of course the answer is, as everyone thinks: the flanges on the wheels. You know, the wheels have some kind of flange on them. But that’s not the answer. Because flanges are just safety devices. If the flanges rub against the tracks you hear a terrible squealing. They’re just in case the real mechanism doesn’t work.

There’s another problem with trains that’s connected to it. Now, people all know this about their automobile: that when you go around a corner, the outside wheels have to go further than the inside wheels. And if the wheels were connected on a solid shaft, you couldn’t do that. You can’t turn the outside wheels further than the inside wheels. And so the shaft is broken in the middle with a gear system which is called a differential. Did you ever see the differential on a railroad train? No. You look at those wheels under a freight car, and there are the two wheels, and there’s a solid steel rod going from one wheel to the other. There’s nothing. One turns the same as the other. So now, how does it go around the corner, a curve, when the outside wheel has to go further than the inside wheel?

And the answer is that the wheels are flanged like this. I mean, not flanged—they’re cones, this way. That is, they’re a little fatter closer to the train, and a little thinner further out. If you look closely, you’ll see they’ve got this beveled edge. And it’s all very simple. When they go around a curve, they slide out on the track a bit so that this wheel travels on a fatter part, a bigger diameter, and this on a smaller diameter. So when they both turn one turn, this swings further than the other. And that’s what keeps it on the track also the same way.

Suppose a train is running along on this thing, on the track, and the track’s here and here, and the two wheels are exactly balanced and it’s nice and even. Suppose accidentally it gets a bump or something and slides out this way. Then this wheel is on a bigger circumference than this one, but they’re on a solid shaft. So when it turns once around, it carries this wheel forward relative to the other, and steers the train back on the track. Of course, if it gets too far off on the other side, it goes back and forth and it stays on the track because the wheels are tapered. And the flange is a safety. Well, we had a lot of stuff like that that we had to learn to do. We’d get straightened out before we could become full-fledged members of the fraternity.

If I’m sitting next to a swimming pool and somebody dives in—and she’s not too pretty, so I can think of something else—I think of the waves and things that have formed in the water. And when there’s lots of people who have dived in the pool, there’s a very great choppiness of all these waves all over the water. And to think that it’s possible maybe that in those waves is a clue as to what’s happening in the pool, that some sort of insect or something with sufficient cleverness could sit in the corner of the pool and just be disturbed by the waves, and by the nature of the irregularities and bumping of the waves have figured out who jumped in, where and when, and what’s happening all over the pool.

And that’s what we’re doing when we’re looking at something. The light that comes out is waves just like in the swimming pool, except in three dimensions instead of the two dimensions of the pool, as they’re going in all directions. And we have an eighth of an inch black hole into which these things go, which is particularly sensitive to the parts of the waves that are coming in a particular direction. It’s not particularly sensitive when they’re coming in at the wrong angle—which we say is from the corner of our eye. And if we want to get more information in the corner of our eye, we swivel this ball about so that the hole moves from place to place

Then it’s quite wonderful that we can figure out so easy—that’s really because the light waves are easier than the waves in the water, a little bit more complicated; it would have been harder for the bug than for us, but it’s the same idea—to figure out what the thing is that we’re looking at at a distance. And this is kind of incredible because when I’m looking at you, someone standing to my left could see somebody who’s standing at my right. That is the light could be going right across this way. The waves are going this way. The waves are going this way. The waves are going this way. It’s just a complete network.

Now it’s easy to think of them as arrows passing each other, but that’s not the way it is because all it is is something shaking. It’s called the electric field, but we don’t have to bother with what it is. It’s just like the water height is going up and down. So there’s some quantities shaking about here. And in a combination of motions, and so elaborate and complicated, that that result is to produce an influence which makes me see you. At the same time, completely undisturbed by the fact that there are influences that represent the other guys seeing him on this side.

So that there’s this tremendous mess of waves all over in space, which is the light bouncing around the room and going from one thing to the other. Because, of course, most of the room doesn’t have eighth-inch black holes. It’s not interested in that light. But the light’s there anyway. I mean, it bounces off this and it bounces off that, and all this is going on. And yet we can sort it out with this instrument.

But beside all that, you see that those waves that I was talking about in the water—maybe they’re so big some of them, and then you can have slower swashes, which are longer and shorter—perhaps our animal who’s making his study is only using waves between this length and that length. So it turns out that the eye is only using waves between this length and that length, except those two lengths are hundred thousandths of an inch. And what about the slowest swashes? The waves that go more slowly, that have a longer distance from crest to trough? Those represent heat. We feel those, but our eye doesn’t see them focused very well. We don’t, in fact, at all. The shorter waves are blue, the longer waves are red. But when it gets longer than that, we call it infrared. All this is in there at the same time. That’s the heat.

Pit vipers that you got down here in the desert, they have a little thing that they can see the longer waves, and pick out mice—which are radiating their heat, their longer waves, by their body heat—by looking at them with this eye, which is the pit of the pit viper. But we can’t. We aren’t able to do that. And then these waves get longer and longer, all through the same space. All these things are going on at the same time. So that, in this space, there’s not only my vision of you, but information from Moscow Radio that’s being broadcast at the present moment, and the seeing of somebody from Peru. All the radio waves are just the same kind of waves, only longer waves. And there’s the radar from the airplane, which is looking at the ground to figure out where it is, which is coming through this room at the same time. Plus the X-rays, cosmic rays, and all these other things, which are the same kind of waves, exactly the same waves, but shorter, faster, or longer, slower. It’s exactly the same thing.

So this big field—this area of irregular motions of this electric field, this vibration—contains this tremendous information. And it’s all really there. That’s what gets you. If you don’t believe it, then you pick a piece of wire and connect it to a box. And in the wire the electrons will be pushed back and forth by this electric field, sloshing just at the right speed for a certain kind of long ways. And you turn some knobs on the box to get the sloshing just right, and you hear Radio Moscow. But you know that it was there. How else did it get there? It was there all the time. It was only when you turn on the radio that you notice it. But that all these things are going through the room at the same time—which everybody knows—but you’ve got to stop and think about it to really get the pleasure about the complexity, the inconceivable nature of nature.

When we were talking about the atoms, one of the trouble that people have with the atoms is that they’re so tiny and it’s so hard to imagine the scale; that the size of the atoms are in size, compared to an apple, it’s the same scale as an apple is to the size of the Earth. And that’s a kind of a hard thing to take. And you have to go through all these things all the time. And people find these numbers inconceivable. And I do, too.

And the only thing you do is you just change your scale. I mean, you’re just thinking of small balls, but you don’t try to think of exactly how small they are too often, or you get kind of a bit nutty, alright? But in astronomy, you have the same thing in reverse, because the distances to these stars are so enormous. We know that light goes so fast that it takes a few seconds to go to the moon and back, or it goes around the Earth seven and a half times in a second. And it goes for a year, two years, three years before it gets to the nearest other star that there is to us.

But all our stars are in—the stars that are nearby—in a great galaxy, a big mass of stars, which is called a galaxy, a group. But this galaxy is—what is it? Something 100,000 light years. 100,000 years. And then there’s another patch of stars. It takes a million years for the light to get here, going at this enormous rate. And you just go crazy trying to make too real that distance. You have to do everything in proportion. It’s easy to say the galaxies are little patches of stars, and they’re ten times as far apart as they are big. So that’s an easy picture. Everyone gets it. But you just go to a different scale. That’s easy. Once in a while, you try to come back to Earth scale to discuss the galaxies. But it’s kind of hard.

The number of stars that we see at night is only about 5,000. But the number of stars in our galaxy, the telescopes have shown when you improve the instrument—oh, we look at a galaxy, we look at the stars, all the light that we see, the little tiny and influence, spreads from the star over this enormous distance of three light years for the nearest star. On, on, on, this light from the star is spreading. The wave fronts are getting wider and wider, weaker and weaker, weaker and weaker, out into all of space. And finally, the tiny fraction of it comes in one square, way to the other inch, tiny little black hole, and does something to me. So I know it’s there.

Well, I’d like to know a little bit more about it. I’d rather gather a little more of this tiny fraction of this front of light. And so I make a big telescope, which is a kind of funnel, that the light that comes over this big area (200 inches across) is very carefully organized. So it’s all concentrated back, so it can go through a pupil. Actually, it’s better to photograph it, or nowadays to use photo cells. They’re better instruments. But anyway, the idea of the telescope is to focus the light from a bigger area to a smaller area, so that we see things that are weaker, less light. And in that way, we find there’s a very large number of stars in the galaxy. There’s so many that, if you tried to name them one a second, naming all the stars in our galaxy—I don’t mean all the stars in the universe, just this galaxy here—it takes 3,000 years. And yet, that’s not a very big number. Because if those stars were to drop one dollar bill on the Earth during a year, each star dropping one dollar bill, they might take care of the deficit which is suggested for the budget of the United States. So you see what kind of numbers we have to deal with.

At any rate, I think that the numbers are a problem in astronomy; the sizes and numbers. And the best thing to do is to relax and enjoy the tininess of us and the enormity of the rest of the universe. Of course, if you’re feeling depressed by that, you can always look out at the other way and think of how big you are compared to the atoms and the parts of atoms, and then you’re an enormous universe to those atoms. So you can sort of stand in the middle and enjoy everything both ways.

But the great part of astronomy is the imagination that’s been necessary to guess what kinds of structures, what kinds of things, can be happening to produce the light and the effects of the light and the stars that we do see. And I could take an example, a historical example. See, at many times in science, by using imagination, you’ve imagined something which could be according to all the known knowledge of the laws, and you don’t know whether it is yet or not. And that’s very interesting. There’s a creative imagination, you like to call it—not just imagining things that are relatively easy, but something different.

And to take an example of a star, as we understand it: an ordinary star like the sun is a great big ball of gas of hydrogen that’s burning up the hydrogen and so forth, and it’s an enormous mass of gas. And it’s held together by gravity. You don’t have to always understand gravity as curved space. It’s good enough for this purpose—the force is inversely square the distance: when things are closer together, the force is stronger. And it pulls everything together. By the way, that’s why the world is round, because the globe of Earth is pulled together as much as possible, and if it had a great mountain and a regularity of a bump, so it would be pulled in by gravity and it all gets smooth. Rocks aren’t strong enough to hold a bump much bigger than a few miles, and Mount Everest is our biggest bump. But on the moon, where the gravity is less, the bumps are higher, the mountains are bigger on the moon.

Anyway, to get back to the star: it’s all held together by gravity. And it’s got a nuclear fuel, which we’ve haven’t been talking about, that’s burning up the hydrogen and generating energy, which keeps things going. And after a while it would use the fuel up. People began to think about what would happen then. And it would be possible to just be gas sort of hanging around held together by gravity, but quiet. But another possibility was to think: if I push the stuff together closer, the gravity is stronger. Would it hold together? Well, if you push a little bit together, the pressure increases. When you push the gas together, there are more atoms and they pound harder, so the pressure’s higher. But the gravity is stronger. And it turns out the pressure wins. So it would just come out again. If you’re pushing a star in like that, it oscillates. And there are some stars that are oscillating and vibrating and so on.

But it turns out if you keep on analyzing, and you push it together very far to the incredible concentration of the whole mass of the sun is down to the size of the Earth or smaller, then it turns all the nuclear matter, all the nuclei of the atoms are all stuck next to each other tight. The spaces where the electrons are. And it’s all squashed out, and it comes out that when you get to that far, the gravity is stronger now, has overpowered the pressure again. Even though the pressure’s got to be enormous, the gravity’s got to be even more enormous. And the thing will stay steady at a different size and be nothing but a neutron’s nuclear matter. Solid nuclear matter.

And this possibility was worked out by Oppenheimer and Volkov, and it’s called a neutron star. And people waited to see if there were any such neutron stars for years, until recently they found these strange pulsars which emit flashes of radio waves—and later they found light—which can go thirty times a second, for instance, the fastest ones, or maybe teb times a second, or one a second. And at first that’s very mysterious. You’re used to stars being big and slow, and how can anything in a star move in a thirtieth of a second?

Well, these things are very small neutron stars, and they’re spinning very fast. And for reasons not yet understood, they were emitting a beam of radio waves, like a searchlight in an airport or something, those things that go around, so we get these flashes—tick-tick-tick-tick-tick—that fast. To imagine a star the mass of the sun doing something, turning so fast as thirty times a second—another one of these big number, hard to conceive, imaginary things, okay? And the whole idea that there could be a star of such enormous density that a teaspoon would weigh so much of the matter that, if you put it down on the Earth’s surface, it’s so heavy it’ll just plow right through to the center of the Earth, and things like that. It took a lot of imagination, it comes out of the mathematics and the analysis and all this that helped you to make sure you’re not making a mistake.

And it turns out that such a star was possible, and it turned out later, in fact, they do exist. And that’s a good example of how imagination is a useful thing, and produces a guessing ahead of time, and how we make advances by using it—besides just the very difficult thing of imagining all the things that might be up there to explain the things we see. In the case of astronomy we have a large number of things that we see that we have not yet quite clearly got the imagination to see what it is that’s producing them.

Quasars are very powerful sources of light and radio waves from very great distances. We can see them because they’re so bright. And the exact cause of their source has only gradually been recently understood in terms of another nutty concept of imagination: the black hole—which is something that comes from following the logic of the gravity theory of Einstein to its ultimate; working out the consequences and crazy circumstances.

Suppose you had an amount of matter so great that the gravity forces so much that even light trying to get out falls back. Nothing can go faster than light and nothing could escape. You couldn’t see it. How would you get there? If you had a lot of matter to start with, it could fall together and get into this condition that no longer could the light come out. And so you would have this thing which would continue to attract things to it. Things would go in and nothing would come out. That’s called a black hole. You say: well, how can a black hole, which is absorbing everything, make all this energy that we see? Is that an explanation of the quasar?

Actually, it may well be. Because if the things are falling in, don’t go plonk in, but go around, falling in by swirling, then as they fall in irregularly and so forth, and in the fast motions that it produces, they go down this whirlpool, they generate a lot of energy and friction and so forth of different kinds of effects, magnetic and electric effects, that could make the jets of matter that come out of the quasar and the radio galaxies in ways that are not really understood. We don’t have a real picture of why there are jets of radio waves, matter emitting radio waves—in galaxies; they’re all in galaxies—which great jets have come out of, big clouds of matter on each side, which are emitting radio waves. So there’s some kind of a source in there that sort of gets wound up on them and shoots these jets of material out with tremendous energy. And it’s guessed that maybe that’s a black hole somehow or other. And the somehow or other is the challenge of imagination which has not yet been answered by anybody with any great confidence.

You ask me if an ordinary person, by studying hard, would get to be able to imagine these things like I imagine—of course. I was an ordinary person who studied hard. There’s no miracle people. It just happens they got interested in this thing and they learned all this stuff. They’re just people. There’s no talent, a special miracle ability, to understand quantum mechanics, or a miracle ability to imagine electromagnetic fields that comes without practice and reading and learning and study. So if you say you take an ordinary person who’s willing to devote a great deal of time and study and work and thinking and mathematics and time, then he’s become a scientist.

When I’m actually doing my own things and I’m working in the high, deep, and esoteric stuff that I worry about, I don’t think I can describe very well what it’s like. First of all, it’s like asking a centipede: which leg comes after which? It happens quickly, and I’m not exactly sure what flashes and stuff go in the head. But I know it’s a crazy mixture of partial equations, partial solving the equation, then having some sort of picture of what’s happening that the equation is saying is happening. But they’re not that well separated as the words I’m using. And it’s a kind of a nutty thing. It’s very hard to describe, and I don’t know that it does any good to describe it.

And that is something that struck me that’s very curious. I suspect that what goes on in every man’s head might be very, very different—the actual imagery or semi-imagery which comes—and that when we’re talking to each other at these high and complicated levels, and we think we’re speaking very well and we’re communicating, but what we’re really doing is having some kind of big translation scheme going on for translating what this fellow says into our images, which are very different.

I found that out because, at the very lowest level—I won’t go into the details—but I got interested in, well, I was doing some experiments, and I was trying to figure out something about our time sense. And so what I would do is" I would try to count to a minute. Actually, say, I’d count to 48 and it would be one minute. So I’d calibrate myself and I would count minute and 48. I think I was counting seconds, but it’s close now. And then it turns out if you repeat that, you can do very accurately. When you get the 48 or 47 or 49, not far off, you’re very close to a minute. And I would try to find out what affected that time sense, and whether I could do anything at the same time as I was counting.

And I found that I could do many things. I could—there were some things that not. For example, I had great difficulty—I was in the university—I had to get my laundry ready, and I was putting the socks out, and I had to make a list how many socks. You know, something like six or eight socks. And I couldn’t count them, because the counting machine was being used and I couldn’t count them—until I found that I could put them in a pattern and recognize the number. And so I learned a way after practicing by which I could go down a lines of type and newspapers and see them in groups 3 3 3 1: that’s a group of 10. 3 3 3 1—without saying the numbers, just seeing the groupings. I could therefore count the lines of type (I practiced) in the newspaper at the same time I was counting internally the seconds. And so I could do this fantastic trick of saying 48—that’s one minute—and there are 67 lines of type, you see. It was quite wonderful.

And I discovered many things I could read while I was—no, I… excuse me, yes. Yes, I could read perfectly alright while I was counting, and get an idea of what it was about. But I couldn’t speak. I couldn’t say anything, because of course I was sort of—when I counted I sort of spoke to myself inside. I would say, “One, two, three,” sort of in the head. Well, I went down to the breakfast, and there was John Tukey, who was a mathematician down at Princeton at the same time. And we had many discussions. And I was telling him about these experiments and what I could do. And he says, “That’s absurd.” He says, “I don’t see why you would have any difficulty talking whatsoever, and I can’t possibly believe that you could read.” So I couldn’t believe all this. But we calibrated him. It was 52 for him to get to 60 seconds—or whatever; I don’t remember the numbers now. And then he’d say, “Alright. What do you want me to say? Mary had a little lamb. I can speak about anything. Blah, blah, blah, blah, blah. 52. It’s a minute.” He was right. And I couldn’t possibly do that. And he wanted me to read because he couldn’t believe it.

And then we compared notes, and it turned out that when he thought of counting, what he did inside his head is: when he counted, he saw a tape with numbers that went clink, clink, clink. The tape would change with the numbers printed on it, and he could see. Well, since it’s sort of an optical system that he’s using and not voice, he could speak as much as he wanted. But if he had to read, then he couldn’t look at his clock. Whereas for me it was the other way. And that’s where I discovered—at least in this very simple operation of counting—the great difference in what goes on in a head when people think they’re doing the same thing.

And so it struck me, therefore: if that’s already true at the most elementary level—that when we learn the mathematics and the functions and the exponentials and the electric fields and all these things—that the imageries and method by which we’re storing it all, and the way we think about it, could be really (if we could get into each other’s heads) entirely different. And in fact why somebody sometimes has a great deal of difficulty understanding a point which you see as obvious, and vice versa, it may be because it’s a little hard to translate what you just said into his particular framework and so on. Now I’m talking like a psychologist—and you know I know nothing about this!

Suppose that little things behaved very differently than anything that was big. Anything that you’re familiar with. Because, you see, as the animal evolves and so on, and his brain evolves, it gets used to handling—and the brain is designed for—ordinary circumstances. But if the gut particles and the deep inner workings were by some other rules and some other character—they behaved differently, they were very different—than anything on a large scale, then there would be some kind of difficulty in understanding and imagining reality. And that difficulty we are in.

The behavior of things on a small scale is so fantastic, it’s so wonderfully different, so marvelously different than anything that behaves on a large scale. You say, “Electrons act like waves.” No they don’t, exactly. “They act like particles.” No they don’t, exactly. “They act like a kind of a fog around the nucleus.” No they don’t, exactly. And if you would like to get a clear, sharp picture of an atom so that you can tell exactly how it’s going to behave correctly—and have a good image, in other words; a really good image of reality—I don’t know how to do it. Because that image has to be mathematical. We have a mathematical expression. It’s strange. Mathematics. I don’t understand how it is, but we can write mathematical expressions and calculate what the thing is going to do, without actually being able to picture it. It would be something like a computer that you put certain numbers in, and you have the formula for at what time the car will arrive at different destinations, and the thing does the arithmetic to figure out at what time the car arrives at the different destinations—but cannot picture the car. It’s just doing the arithmetic. So we know how to do the arithmetic, but we cannot picture the car.

No. It’s not a hundred percent, because for certain approximate situations, a certain kind of approximate picture works—that it’s simply a fog around the nucleus, that when you squeeze it it repels you: it’s very good for understanding the stiffness of material. That it’s a wave which does this and that is very good for some other phenomenon, alright? So when you’re working with certain particular aspects of the behavior of atoms—for instance, when I was talking about temperature and so forth—that they’re just little balls is good enough, and it gives a very nice picture of temperature. But if you ask more specific questions and you get down to questions like: how is it that when you cool helium down even to absolute zero, where there’s not supposed to be any motion, it’s a perfect fluid that hasn’t any viscosity, has no resistance, flows perfectly, and isn’t freezing?

Well if you want to get a picture of atoms that has all of that in it, I can’t do it, you see. But I can explain why the helium behaves as it does by taking my equations and showing that consequences of them is that the helium will behave as it is observed to behave. So we know we have the theory, right? But we haven’t got the pictures that will go with the theory. And is that because we’re limited and haven’t caught on to the right pictures? Or is that because there aren’t any right pictures for people who have to make pictures out of things that are familiar to them?

Well, let’s suppose it’s the last one: that there’s no right pictures in terms of things that are familiar to them. Is it possible, then, to develop a familiarity with those things that are not familiar on hand by study, by learning about the properties of atoms and quantum mechanics, by practicing with the equations, until it becomes a kind of second nature? Just like a second nature to know that if two balls came towards each other, they’d smash into bits. You don’t say the two balls, when they come toward each other, turn blue. You know what they do.

So the question is whether you could get to know what things do better than we do today. You know, as the generations develop, will they invent ways of teaching so that the new people will learn tricky ways of looking at things, and be so well trained that they won’t have our troubles with the atom; picturing. There’s still a school of thought that cannot believe that the atomic behavior is so different than large-scale behavior. I think that’s a deep prejudice. It’s a prejudice from being so used to large-scale behavior. And they’re always seeking to find, to waiting, for the day that we discover that underneath the quantum mechanics there’s some mundane ordinary balls hitting, or particles moving, and so on. I think they’re going to be defeated. I think nature’s imagination is so much greater than man’s; she’s never going to let us relax.