The complete FUN TO IMAGINE with Richard Feynman

It is interesting that some people find science simple, while others find it boring and difficult. Especially children, some children just accept things as they are. I don't know why, maybe it's the same for all subjects. For example, many people like music, but I can never keep up with the tune. I've also missed out on a lot of fun because of it. Similarly, I think those who find science boring also miss out on a lot of fun. As far as science is concerned, I think one of the reasons it is difficult is that science requires a rich imagination. It is hard to imagine all these strange objects in their original form. Nothing is as simple as it appears, like the familiar concept of hot and cold. Hot and cold depend on the speed of atomic vibration. The faster the atoms vibrate, the hotter it is, and the slower they vibrate, the colder it is. If you have a large collection of atoms, say a cup of coffee, on a table, the atoms in the cup are vibrating intensely, constantly hitting the inner walls of the cup. The cup is vibrated, and thus the atoms of the cup itself also vibrate more intensely. They collide with each other, the cup is heated, and everything around it is heated. Then, hot things transfer heat to other things simply through contact, because the atoms in hot objects vibrate more vigorously, causing the inactive atoms in cold objects to vibrate along. Thus, heat enters the cold object, and heat is transferred. But what is transferred is only vibration, a kind of random motion, which is easy to understand. This leads to another interesting point: when I say objects vibrate, you imagine little balls bouncing. You know that this bouncing gradually slows down and stops after a while. But we must imagine that atoms have perfect elasticity; they do not lose any energy. They keep colliding, always colliding, but without losing any energy. They are in perpetual motion. As for objects that do lose energy, like a ball bouncing on the floor, it randomly transfers vibrations to some atoms on the floor. When the ball bounces up, it leaves behind a group of atoms moving faster, vibrating continuously. So, as the ball bounces, it transfers its excess energy, its excess motion, to the atoms on the floor. Each time it rebounds, it loses a little heat until it stops. At this point, we say its downward motion has ended. But what is left behind is that the atoms on the floor are vibrating more vigorously than before, and the atoms in the ball are also vibrating more vigorously. Originally, all the atoms in the ball were moving in an orderly manner as they fell. And the calm floor has now become a ball resting on the floor. But all the motion still exists in the form of kinetic energy. The vibration of the atoms in the floor makes the floor a little warmer, unbelievable! But those who often hammer things know this is true. If you hit something, hit it many times, you can feel the temperature rise, it gets a little hot. The object being hit gets hot simply because you are making it vibrate. This atomic picture is extremely beautiful. You can observe all sorts of things in this way. You observe a small drop of water, a very small drop. The atoms attract each other; they like to be close together. They want to have as many companions as possible. And now the atoms on the surface of the water drop have companions on only one side. The other side is air, so they want to get in. You can imagine a crowd of people, all moving rapidly, all wanting as many companions as possible. Those at the edges are unhappy, very tense, they keep pushing, trying to get in, and this forms a tight ball, not spread out into a sheet. This is surface tension. Sometimes when you see a drop of water standing on a table like a ball, you start to wonder why it is like that. Because every atom wants to get into the water. While trying to get in, some atoms are also leaving the surface. So the water drop slowly disappears. I find myself constantly trying to imagine all these phenomena. I get pleasure from imagining, just as a runner gets pleasure from sweating. I get joy from thinking about these phenomena. I can't stop; I can go on and on. If you can cool water, then the atoms vibrate less and less, vibrating slower and slower. Then the atoms will be confined to a region. They like to be with their companions. Attraction exists, so they will huddle together. They won't squeeze each other, and they will form beautiful patterns, like oranges neatly arranged in a fruit box, each only able to wiggle in a fixed position, but without enough kinetic energy to escape its confined position and disrupt the structure. What I am describing is the solid state, i.e., ice, which has a structure. If you place atoms in a specific position, then the rest of the atoms line up, eventually forming a solid. And if you continue to heat them, then they start to lose their constraints and roll over each other. This is the liquid state. And if you heat them even more, then they will bounce more vigorously. They will collide with each other and bounce off. So they become individual. Although I say atoms, they are actually combinations of atoms, molecules. Molecules fly around and collide. Although they tend to stay together, they move too fast. In simple terms, when they meet head-on, their "hands" can't hold on, so they fly apart again. This gaseous state is what we call "steam." You will gain an understanding of various phenomena. When I was a child, I was always interested in "air." I noticed that when I pumped air into my bicycle tires (a bicycle is something you can learn a lot from), I pumped air into the tires, and the pump got hot. This is actually easy to understand. As the piston of the pump is pushed down, the atoms hit it and rebound, but the piston is moving downwards. The speed of the atoms after rebounding from hitting the piston is greater than before hitting it. So, as the piston continues to move down, the atoms increase their speed with each collision. So when you compress a gas, it gets hotter. And when you pull the piston out, fast-moving atoms hit the piston and lose some kinetic energy, so the atoms' energy decreases. It's like punching cotton; it sinks in, "bang, bang." Energy is lost. When you pull the piston out, the atoms hit it and their speed decreases, so the temperature decreases. So when a gas expands, the temperature decreases. The interesting thing is that all the phenomena you observe in this world, such as gas compressing and heating up, expanding and cooling down, or water evaporating if the cup is not covered, can be understood with a simple atomic picture. Thinking this way is very interesting. I don't want to take this thinking too seriously. I think we should imagine happily, without any worries. There won't be a teacher asking questions at the end, otherwise it would be an annoying subject. Different atoms want to be close to each other to different degrees. For example, oxygen atoms in the air want to be close to carbon atoms. If they get too close, they combine vigorously. If they are not very close, they repel each other and separate. So they don't know they can combine. It's like a ball trying to climb a hill. There's a hole in front of it, which it can go into, like a crater. A deep opening, but the ball just circles around it and doesn't fall in. Because as the ball starts to climb the slope, it rolls back. But if you make it go fast enough to pass the critical point, it will fall into the hole. So if something like wood comes into contact with oxygen, and there are carbon atoms in the wood, oxygen atoms come and hit the carbon atoms, but the temperature is not high enough, so the oxygen atoms run away. Air always comes and goes, and nothing happens. If you heat the oxygen atoms in some way to make them faster, to accelerate a few atoms at first, meaning to make them pass the critical point, they get close enough to the carbon atoms, and then they combine vigorously. This will produce more vigorous vibrations, possibly hitting other atoms, making them move faster, so they can pass the critical point and hit other carbon atoms. Their continuous vibration causes other atoms to vibrate together, and a terrible disaster occurs. One atom after another vibrates faster and faster, combining vigorously, and everything changes. This "disaster" is fire. This is one way to describe "fire." This collision is always happening, never stopping. Once it starts, it continues. The heat produced allows other atoms to have the ability to collide, producing more heat, causing more atoms to behave the same way. So this vigorous combination triggers a lot of vibration. If I put those less energetic atoms over there, for example, if I put a cup of cold coffee next to a pile of burning wood, the atoms in the coffee will vibrate vigorously, which is the heat of the fire. Of course, there will be... See, this is what happens when you start thinking, you can't stop at all. You just want to know how it started. Why did the wood stay with the oxygen for so long without "fire" appearing before? Where did this heat come from? Actually, it comes from the tree. The substance of the tree is carbon, and where did that carbon come from? It comes from carbon dioxide in the air. People look at trees and think trees grow from the ground. Plants grow from the ground. But if you ask where the substance of the tree comes from, think carefully about where it comes from. Trees come from the air? Of course, trees do come from the air. Carbon dioxide in the air enters the trees, changes, kicks out oxygen atoms, forming oxygen and releasing it, leaving carbon atoms. Carbon and water form the substance of the tree. Water comes from the ground, and carbon atoms enter the trees from the air, right? It comes from the sky. Therefore, almost all trees come from the ground. Sorry, I misspoke, they come from the air. There are indeed a small amount of minerals from underground, etc. Of course, I told you oxygen atoms... Oxygen atoms and carbon atoms combine very tightly. So how does the tree cleverly absorb carbon dioxide? At this point, carbon atoms and oxygen atoms are tightly bound, yet the tree can easily break it down? Ah! Life, is it some mysterious power of life? Wrong, it is the shining of the sun, sunlight shines in and separates the oxygen atoms and carbon atoms. Therefore, sunlight is needed for plants to grow. So the role of the sun is to continuously separate oxygen atoms and carbon atoms. Oxygen, as a kind of bad byproduct, is released into the air, leaving carbon atoms and water, which form the substance of the tree. Then we put the substance of the tree in the fireplace. The oxygen produced by the tree wants to combine with the carbon in the tree again. Once you heat it to trigger their combination, the whole process will continue. During their vigorous combination, intense thermal motion is produced, resulting in beautiful light and other things. It's as if nothing happened, you turned oxygen and carbon back into carbon dioxide. But light and heat are produced, which are actually the light and heat of the sun radiating in. So when you light a fire, it's like releasing the sun stored in the wood. The next question is, why is the sun so active and so hot? I'll stop here and leave you with a question to imagine. Most elastic things, like steel bars or springs, are due to forces related to electricity pulling them back. When you bend something, you are pulling the atoms slightly farther apart, so these atoms try to come back together. But rubber bands work differently. There are some long chain-like molecules, and some small molecules that are constantly vibrating and hitting these chain molecules. And the chain molecules are all twisted and funny shapes. When you straighten the rubber band, the chain molecules straighten out. But these chain molecules are constantly being hit from the sides by other atoms trying to twist them and make them contract. So the rubber band tries to contract. It contracts solely due to heat. So if you heat the rubber band, it will contract more. For example, if you hang a heavy object with a rubber band and then bring a lit match close to the rubber band, it's quite interesting to watch the heavy object rise as the rubber band is heated. Another thing can prove this point is correct, proving that it is indeed heat that drives the contraction of the rubber band. When you stretch a rubber band, it's like compressing the piston and the gas inside. If you stretch the rubber band, the straightened chain molecules hit other molecules, making them move faster, so the temperature rises. And when you contract the rubber band, the molecules lose some energy when they hit the chain molecules, like hitting something soft. When they hit the contracting molecular chains, they lose energy. So the temperature decreases. There is a small way to verify this. You don't need to be very sensitive; it's a small test. If you take a wide rubber band and place it between your lips, and quickly pull it outwards, you will definitely feel the temperature rise. If you compress it in the middle, you will feel the temperature decrease. At least you can feel the difference between stretching and compressing it. I have always found it interesting to think about how rubber bands work. When a rubber band is used to tie a bundle of documents for a long time, the force holding the documents together is achieved by the continuous impact of atoms. These atoms are always trying to twist the chain molecules, twisting them continuously, so the rubber band can hold the documents. Year after year, of course, the shelf life of a rubber band is not that long. In short, for a long time, it can hold a whole bundle of documents. If you look at it correctly, it is a dynamic chaotic world of vibrating objects. If you magnify everything, you can hardly see anything clearly, because all objects are vibrating in their own way, with little vibrating balls everywhere. Fortunately, we can all see things from a macroscopic perspective and see them as "objects" without being bothered by these tiny atoms all the time. If you have two magnets, and you bring them close together, you can feel them repelling each other. Turn one of them around, and they will attract each other. So, what is the "feeling" between these two magnets? What do you mean by "what is the feeling between two magnets"? There is indeed something, right? When you bring the same poles of two magnets close together, you can feel a repulsive force. Listen carefully to my question. What do you mean by "there is a feeling"? Of course you can feel it, what do you want to know? I want to know what is happening between these two magnets. Magnets repel each other. So what does that mean? Why is that? How do they do it? I want to say that I think this is a very reasonable question. Of course it is reasonable, it is an excellent question. But the way you phrase your question needs refinement. You are asking why this happens. How should one answer questions like "Why does this happen?" For example, Aunt Minnie is in the hospital, why? Because she fell. She went out and fell on the ice, injuring her thigh. Such an answer is sufficient. But to aliens who know nothing about Earth, this answer is far from enough. First, you understand "Why do you go to the hospital if you hurt your thigh?" "Since you hurt your thigh, how did you get to the hospital?" That's because her husband saw her fall and injure her thigh and called the hospital to pick her up. All of this is widely understood. Now, if you are asked to explain "why," you must accept some things as true within a certain framework, otherwise you will keep asking why. Why did the husband call the hospital? Because the husband cares about his wife's health, and he doesn't always care. Some husbands don't care about their wives' health when they are drunk or angry. So you begin to vividly understand the world and its complexity. In order to... If you want to continue to understand this matter, you can delve deeper from different angles. For example, you can ask "Why did she slip on the ice?" Because everyone knows ice is slippery, it goes without saying. But you insist on asking "Why is ice so slippery?" This is a bit strange. Ice is very slippery, an interesting phenomenon. You ask "What is the principle behind it being so slippery?" Either you say, "Saying that ice is slippery is enough, it already explains why she fell." Or you continue to ask, "Why is ice so slippery?" This involves some principles. Because not many things are as slippery as ice. It's hard to find slippery things, and these are wet and sticky. But why is it so slippery as a solid? Because of the object "ice." When you stand on ice, the pressure immediately causes the ice to melt slightly. So you get instantaneous moisture, causing you to slide on the ice. Why does this happen on ice but not when standing on other objects? Because ice expands... When water freezes, its volume expands. So the pressure compresses the volume of the ice, causing it to melt. Pressure can melt ice. But when other objects cool down, it's the opposite. When you compress them, they become firmer. So why does water expand when it freezes, while other objects do not expand when they cool down? Do you understand? I am not answering your question, but telling you how difficult these "why" questions are. You must know what you take for granted, what you can understand and grasp, and what you haven't grasped. Through this example, you can see that the more "why" questions I ask, the more interesting the question becomes. My point is, the deeper things are, the more interesting they are. You can even continue to ask "Why did she fall when she slipped?" This is because of gravity. This involves various planets and other objects. Don't dwell on it, the question can continue. Now when you ask "Why do two magnets repel each other?" The answer has different levels, depending on whether you are a physics student or an ordinary person who knows nothing. If you know nothing about physics, I can only tell you that magnetic force makes magnets repel each other. This is the force you feel, but you will find it strange because you don't feel such a force in other situations. When you turn a magnet around, they attract each other. There is a very similar force, the electric field force. The electric field force has the same question, and you will find it strange. But you are not bothered at all when you press your hand on a chair, and the chair pushes back at you. But we have found that this is actually the same force. It is the electric field force. The force that separates your fingers from the chair is also the same electric field force. (Because all matter is composed of...) From a microscopic perspective, it is the electric field force. There are other forces involved, but they are all related to the electric field force. It turns out that I want to use magnetic force and electric field force to explain the phenomenon, i.e., the initial repulsive phenomenon. These two forces are fundamentally deeper, and we must start with them. We explain many other phenomena based on them, and these phenomena seem... Everyone has already accepted these phenomena. You know that your hand cannot pass through a chair, and this is taken for granted. But when your hand cannot pass through the chair, you lean in and ask "Why?" The reason is the same as the repulsive force that appears between magnets. So it becomes an explanation for the following question: "Why can the repulsive phenomenon of magnets occur at a greater distance?" This is related to all the electrons in the magnet rotating in the same direction. They are all neatly aligned, enhancing the effect of the force, making the magnetic force strong enough for you to perceive. But this force has always existed, it is very common, it is a fundamental force, or almost so. If I could be more professional, I could go into more detail, but at a basic level, I can only tell you that you must accept the existence of magnetic repulsion or electromagnetic attraction as a fundamental element of this world. I cannot explain this phenomenon with anything you are familiar with. For example, if I say that magnets attract each other like being connected by a rubber band, I am deceiving you. Because they are not connected by a rubber band, I should not create trouble for myself. You will immediately ask me about the nature of a rubber band. Then, if you are curious, you will ask me, "Why does a rubber band tend to pull back together?" Then I will eventually explain the problem of the rubber band with the electric field force, and I was trying to explain electromagnetic force with the rubber band just now. You can see that I am seriously cheating. Therefore, I cannot answer "Why do magnets attract each other?" I can only tell you that they do, and tell you that it is one of the fundamental forces in the world. Fundamental forces include electric field force, magnetic force, gravity, and a few others. These forces are fundamental components. If you are a student, I can tell you in more detail that electric field force and magnetic force are very closely related, and the relationship between gravity and electric field force is not yet clear. And so on. But I really can't explain it well, not even based on things you are more familiar with, because I don't understand magnetic force based on anything you are more familiar with. Looking at the world through imagination, these imagined things are not really fantasies, because you are just trying to imagine what it is like in reality, and sometimes it is useful. One day I went to the dentist, and he was about to drill a hole in my tooth with an electric drill. I thought I'd better think of something else quickly, or it would hurt a lot. So I thought about this small motor that was running. What makes it run? What happens in this process? The process is as follows: not far from here, there is a dam. The water flowing through the dam makes a huge wheel turn, you know. This wheel is connected to thin copper wires. These copper wires are divided into other copper wires, and then into more, until they cover the entire city. Then these wires are connected back to another small device, making the wheel turn. All the wheels in the city are turning because this big wheel is turning. If it stops, all the wheels will stop. If it starts turning again, all the wheels will turn. I think this is the magic of nature, this phenomenon is very strange. I like to think about this phenomenon because it only involves copper and iron. See, sometimes we think man-made generators are very complex, and this phenomenon is the result of something special we created. But this is produced by nature, with only iron and copper. If you take a large and long copper ring, place iron blocks at both ends, and then move the iron block at this end, the iron block at the other end will also move. If you trace it back to its source, it is the iron block at the end of the copper ring that is moved, and the iron block at the other end moves along. You realize how mysterious nature's secrets are. You don't even need iron blocks. If you want to start the pump, you can rotate the copper wire at a very fast speed, making it constantly knot and untie, etc. Then, through a long connection, you can make other copper wires move at the other end. And what does this involve? Only copper wires, and the movement of copper wires. We are accustomed to these electrical phenomena being canceled out. Everything is neutral: there is pushing and pulling, all very rigid. Nature, however, has these wonderful phenomena. When you comb your hair, magnetic forces and electric field forces are involved. Strange things will happen on your comb. If you place the comb in front of a piece of paper, it can attract the paper, and the paper will jump from a distance. And this is actually deeper than the everyday phenomena we are familiar with. We are familiar with direct forces, right? You push with your finger, and the force acts directly on the chair. But you have to imagine what is pushing this finger. This finger is made of very small atoms. There is another group of atoms on the chair pushing the finger. There are small gaps between these two groups of atoms, and this pushing force passes through this gap. The only difference between what happens between the comb and the paper is that there is a reason for this situation that allows us to see these forces acting at a greater distance, not just at short distances between atoms. The reason is that the electric charges carried by electrons are the same. There is a force of repulsion between them. Electrons are a very small part of atoms, but their repulsive force is very large. This force is inversely proportional to the square of the distance, just like gravity is inversely proportional to the square of the distance. But gravity is attractive, and this is repulsive. For two electrons, gravity is much weaker than the electric field force. The electric field force is much stronger than gravity. I can't express it because I don't know the name of this ratio. It's probably "1" followed by 38 or 40 "0"s. The electric field force is stronger. The electric field force is so strong that if I were made of it... this number is too enormous. However, there are other types of charges in charged matter, positive charges. For example, protons are positively charged, located in the nucleus of atoms and attract electrons. Opposite charges attract, and like charges repel. So you have to imagine a vast number of forces. Like charges try to move away from each other, and opposite charges try to move closer. What happens if you have a large amount of charge? You get all like charges gathering near opposite charges because they attract each other. So you get a mixture of positive and negative charges closely intertwined, positive and negative charges very close together. There won't be many positive charges anywhere, because they repel each other. They are all filled with negative charges. You get these small clusters full of positive and negative charges. The reason these clusters don't gradually shrink is because they are particles, and there are quantum mechanical effects. I won't go into detail, but this makes them not smaller than a certain size. So you get these small balls, which are atoms. Atoms are composed of positive and negative charges, and are electrically neutral. They cancel each other out as much as possible. Because this force is so large, it eventually disappears, and perhaps a small force appears. Because the forces are so large and cancel each other out, in ordinary matter there are always the same number of positive and negative charges. When you comb your hair, the friction of combing reduces some, say it reduces some negative charges, then other places have a small amount of positive charge. But the electric field force is very large, even such a small amount of charge can produce a force visible to the naked eye, which seems to act at a great distance. We find this mysterious and need an explanation. We try to explain it with some concepts, such as the forces inside twisted objects like rubber bands and steel bars. We want to find a pulling force that can act at a distance, because we are used to any pushing force only occurring on contact. But in fact, the pushing force we produce on contact is the same force as the long-range force you see, it just acts at a short distance. Because positive and negative charges happen to cancel each other out, you can only feel this force when they are very close. When they are close enough, it affects which is positively charged, which is negatively charged, changes in position, etc., causing them to repel each other. So the fun is in imagining this uniform mixture of opposite charges with extremely strong attraction. Because this force is so strong, it cancels out this effect. Only in some cases, when one type of charge is in excess, does this mysterious electric field force appear. How else can I explain the mysterious electric field force? Why do I explain it with things like gels, which are made of electric field force? And I understand it the other way around: strong long-range forces are canceled out. So we must accept that electric field force and magnetic force are actually fundamental facts, and use them as a basis to explain all other things. So again, it is difficult to understand, and you need to have a rich imagination. The real world is based on a force that acts at a distance, and we don't understand that force very well. We occasionally discover strange phenomena, but generally we don't understand that force very well. It is this force that needs to be explained, it needs to be imagined, because we have no other physical picture of long-range forces. In the example of the generator, what happens is that electrons, as part of atoms, are pushed by the movement of the copper wire. Think about it carefully, if you push some electrons here, they get very close to each other, then they will push other electrons, because they repel at a distance. So it's not like water repelling at close range, but like a wonderful liquid that can repel at a distance. Therefore, the repulsive effect can be transmitted quickly through the wire from a central point, and then instantly spread throughout the city through the wire. You can use it to send signals. When you make a phone call, you are pushing some electrons to various places. Through copper wires spanning the city, the electrons at the other end react to what you say in this room. This is due to this fast interaction at a distance. They discovered through experiments that these long-range forces exist, and this rapid motion, etc. It is a great contribution to humanity. I think the discovery of electricity and magnetism, and electromagnetic effects, the complete equations derived by Maxwell in 1873, may be the most fundamental transformation, the most outstanding discovery in history, the biggest change in history. I went to MIT, a research institution, for college. When I first joined a fraternity, they would give you seemingly simple questions to try to figure out what was actually happening, so that you wouldn't feel too smart. It's like an imagination exercise, quite interesting. I'll tell you about some questions I remember. I learned a few, and once you learn them, the next time someone gives you these clever puzzles, you just look at them quietly for three to five seconds, pretending to be thinking seriously, and then you give the answer, surprising your friends. But in reality, you've already heard the question in your fraternity and already know the answer. One we encountered was about mirrors. This is an old question. You look in the mirror, suppose you comb your hair to the right. You see the image in the mirror, its hair is on the left. Therefore, the mirror image is swapped left and right, not up and down. Because in the mirror image, the head is still up and the feet are still down. The question is, how does the mirror know to swap left and right without swapping up and down? When you lie down and look in the mirror, you will understand this question more deeply. Your hair is still on the left, right? And now your left and right directions have become up and down directions. However, the up and down direction that looks normal is actually the previous left and right direction. When you look in the mirror, the mirror somehow knows what you are doing. So, describing the mirror's action symmetrically is that the mirror does not favor one side; it always swaps left and right, but not up and down. After playing with you for a while, we gradually say we can find the answer. If you wave one hand, then the hand directly facing you in the mirror image waves. If it's the hand pointing west, then the hand in the mirror image also points west; if it's east, the hand in the mirror image also points east. The head still points up, and the feet are still down. Everything seems fine. The problem is, if this is north, then your nose is north of the back of your head. But in the mirror image, your nose is south of the back of your head. So what actually changes is not the up and down or left and right in the mirror image, but the front and back are flipped. The nose in the mirror image is in the opposite direction relative to the head, do you understand? Usually, when we think about this mirror image, we treat it as another person. We usually think that he will adapt to the situation in the mirror image. This is a psychological problem. We don't think he is flattened, and his head and nose are swapped front and back. Because normally this doesn't happen to people. We would think of a person as tall as you, walking around to your opposite side. And a person walking by wouldn't turn their head and feet upside down. So we ignore this part. But when they turn around, they turn their left and right hands. So we say left and right are swapped. But in reality, it is symmetrical along the axis of the mirror, with a front-to-back flip. This is a simple problem. A difficult problem is: "What keeps a train on the tracks?" Of course, everyone will think the answer is: the flanges on the wheels. That is, there are some rims on the wheels. But this is not the correct answer, because the flanges are just safety devices. If the flanges rub against the rails, you will hear a sharp, piercing sound. The function of the flanges is just to prevent the real mechanism from failing. There is another related problem with trains. Nowadays, people know that when a car turns, the outer wheel travels a greater distance than the inner wheel. If the wheels are connected to a solid axle, you cannot turn, because you cannot make the outer wheel travel more than the inner wheel. So a gear system, a differential, is added in the middle of the drive shaft. Have you seen a differential on a train? No. Look at the wheels of those freight cars. There are wheels on both sides. A solid steel rod connects one wheel to the other. Nothing in the middle, both wheels turn the same way. So how does the train turn? Making the outer wheel travel a greater distance than the inner wheel. The answer is that the edge of the train wheel is shaped like this. Not the flanges, but the wheel itself is conical. That is, the wheel is thicker near the train and thinner towards the outside. If you look closely, you will see that they have a beveled edge. The principle is very simple. When the train turns, the wheels tilt slightly along the track. Therefore, the outer wheel rotates with a larger radius, and the inner wheel rotates with a smaller radius. So when both wheels rotate at the same time, the outer wheel travels farther than the inner wheel. This is also how the train stays on the rails. Assume the train is running on the tracks. The rails are on both sides, and the two wheels are balanced, not deviating. Suddenly, the train hits something accidentally, and the car deviates outwards a bit. At this point, the outer wheel's circumference is larger than the inner wheel's. Since they are connected by a solid axle, as the wheels continue to rotate, the outer wheel moves forward relative to the inner wheel. So it pulls the train back onto the track. Of course, if this causes the train to deviate to the other side, it will oscillate back and forth until it returns to the track. The reason is that the wheels are conical, and the flanges serve as protection. At that time, we had to learn a lot of knowledge like this. Only by solving these problems could we become full members of the fraternity. Suppose I am sitting by the pool, and a lady jumps into the water. She is not very beautiful, so I can think of other things. I thought about the waves formed in the water and other things. When many people jump into the pool, the water surface is full of rolling waves. I thought maybe under these waves, there are clues to what is happening in the pool. If some insects are smart enough, they can sit in the corner of the pool and feel the disturbance of the water waves. Insects, through the irregularity and bumpiness of the water waves, can know who jumped into the pool, and what happened somewhere in the pool. This is the same as what we do when we look at an object. Light has been proven to be a wave, just like the water waves in the pool, except that water waves are two-dimensional, and light waves are three-dimensional and can propagate in all directions. And we have a "black hole" (pupil) with a diameter of 3 millimeters, through which various lights can enter, but we can only perceive light of certain wavelengths from certain directions. If light comes from the wrong direction, we are not particularly sensitive. We say light comes from the corner of the eye. And if we want to get more information from the corner of the eye, we turn our eyeballs around. Then we will be surprised to find that it is very simple. This is because light waves are indeed simpler, and water waves are slightly more complex. Light waves are more difficult for insects, but the principle is the same. It is all about being able to see something clearly at a greater distance. Nature is truly magical, because when I look at you, the person on my left can see the person on my right. That is to say, light can propagate in this direction, light waves go in this direction, and there is light going that way, and also going this way, it is a complete network. So it is easy to see them as arrows penetrating each other, but this is not the case, because all of these are oscillating, called electromagnetic fields. But we don't need to care what it is; it's like the rising and falling of water. So there is a quantity that is oscillating. The result of this combination of fine and complex movements is that I can see you. Similarly, it allows someone to see the person on the other side without being affected at all. So there are a large number of light waves in space. Light reflects in space, from one thing to another. Of course, most of space does not have a 3-millimeter "black hole" that is not interested in light. But light is always there, constantly reflecting. Reflection continues, and we can distinguish it with this "instrument (eyes)." But setting that aside, in the water waves discussed earlier, perhaps some water waves are too large, producing long or short waves. And animals have only learned to utilize certain lengths of waves. Similarly, the human eye can only recognize light of certain wavelength ranges, and these wavelengths are all around a few hundred nanometers. What about slower waves? The slower the wave, the farther the distance from crest to trough. They represent heat, which we can feel but cannot see with the naked eye, because we cannot see them at all. Blue light has a shorter wavelength, red light has a longer wavelength. When the wavelength is longer, it is infrared. All light appears at the same time, which is heat. Desert vipers have an organ that can "see" longer wavelength electromagnetic waves to search for mice, because mice radiate long waves due to their body temperature. That is, they see mice by monitoring body temperature. This thermosensitive organ is the viper's pit organ. But we humans cannot do this. These wavelengths get longer and longer, all propagating in the same space, and propagating at the same time. So in this space, not only can I see you, but Moscow radio is broadcasting at this time, and someone in Peru will "see" it. All radio waves are the same type of wave, just longer waves. There is also radar on airplanes, observing the ground to determine their position, and also entering space. There are also X-rays, cosmic rays, and all other types of waves. They are all exactly the same waves, just shorter, faster, longer, or slower. It is all the same substance. So the irregular motion in this large electromagnetic field, this vibration, contains a lot of information. This is real, and this is what attracts you. If you don't believe it, then take a wire and connect it to a box, and the electrons in the wire will be pushed and pulled by the electric field, oscillating at an appropriate speed to produce some long waves. Then, by appropriately turning the knob on the box, you can hear the broadcast from Moscow. Then you will know the existence of electromagnetic waves, otherwise where would the broadcast sound come from? Radio waves have always been there; you only notice them when you turn on the radio. All these electromagnetic waves are constantly propagating in space at the same time, which everyone knows. But you have to stop and think to truly enjoy it, to appreciate the charm of nature's complex and irresistible nature. When we talk about atoms, one problem we encounter is that atoms are too small, and it is difficult to imagine their scale. The size of an atom compared to an apple is like the size of an apple compared to the Earth. This kind of thinking is difficult; you have to constantly keep the proportions of these things in mind. People find these numbers unbelievable, and so do I. And all you have to do is change your scale. You just have to think of atoms as small balls, without constantly thinking about how small they are. Otherwise, you're a bit strange, right? But in astronomy, it's the opposite. Because we are too far from these stars. You know that light travels very fast, it takes only a few seconds to travel to the moon and back from Earth, or light can circle the Earth seven and a half times in one second. But it takes years, three or four years, for light to reach the nearest star to our solar system. But all the stars around us are in one galaxy, the Milky Way, a large cluster of stars. And the diameter of the Milky Way is about hundreds of thousands of light-years, perhaps one hundred thousand light-years. Then there is another cluster of stars. It takes a million years for light from there to reach Earth at such a high speed. If you try to think of this distance too realistically, you will go crazy. You have to scale everything down proportionally, that's easier. Let's say galaxies are small clusters of stars, and the distance between galaxies is ten times their size. Just describe it simply like this, you are just using a different scale, so it's easier to think. Occasionally, you try to discuss galaxies on Earth's scale, and it becomes a bit difficult. The stars we can see at night are only about five thousand. But when you upgrade your equipment and use a telescope, the number of stars in the Milky Way shown is... Oh, right! We look at a galaxy, those stars, all the faint light we see is spread out from the stars over such a long distance. The nearest stars are three light-years apart. It keeps spreading, spreading, starlight continues to spread, the wavefront becomes wider and wider, and the light becomes weaker and weaker, gradually weakening in space. Finally, a very small amount of light enters this 3-millimeter "black hole" (pupil). It stimulates me slightly, so I know that star is there. To get more information, I want to collect more of the wavefront of this small amount of starlight. So I build a large telescope, somewhat like a funnel. Starlight shines on this area with a diagonal length of 200 inches, and after fine processing, the light is converged at the back, and then it can pass through the pupil. In fact, photography is better. Now they use photoelectric components, which are better devices. But in any case, a telescope converges light from a larger area to a smaller area. So we can see dimmer objects. Through telescopes, we find that the number of stars in the Milky Way is a very large number. So many that if you count one per second, and want to count all the stars in the Milky Way, not all the stars in the universe, just this one galaxy, it would take three thousand years to finish counting! And this is not even a very large number. Because if all these stars threw one dollar to Earth this year, each star throwing one dollar, this money might fill the US government's budget deficit. From this, you know what kind of astronomical numbers we are dealing with! In short, I think numbers are the difficulty of astronomy, size and quantity. The best way is to relax, enjoy your own insignificance, and appreciate the vastness of the universe. Of course, if you feel frustrated by this, you can think of it from another perspective. Think about how big you are compared to an atom. Then, compared to an atom, you are a huge universe. So you are in the middle, able to appreciate things at both ends of the scale. But an important part of astronomy is imagination; you need to guess what kind of structure it is, what might have happened to produce the light of the stars that we can see. Let me give an example, a historical example. In the history of science, many times, by using imagination, based on existing knowledge and laws, people imagined what things might be like. And you don't know if it is indeed like that. This is very interesting, you can call it creative imagination. Not just imagining relatively simple things, but unusual things. Taking stars like the sun as an example, a normal star like the sun is just a big balloon full of hydrogen. It uses hydrogen and other substances as fuel, a huge mass of gas. It is held together by gravity. You don't always need to understand gravity as curved spacetime; knowing that the magnitude of gravity is inversely proportional to the square of the distance is enough. The closer objects are, the stronger the gravity. Gravity pulls all matter together. By the way, this is why the Earth is round: because the Earth is pulled together as much as possible. If it had uneven places like high mountains, it would be pulled by gravity, and eventually everything would become smooth. The strength of rocks can only support protrusions of a few thousand meters. So Mount Everest is the highest mountain. But on the moon, where gravity is weaker, protrusions are higher, and mountains on the moon are larger. Returning to the topic of stars, in short, stars are condensed by gravity. It has a nuclear fuel that we haven't mentioned, which makes hydrogen burn and produce energy, making it run. After a while, it consumes a lot of fuel. People start to think about what will happen next. It is possible that the gas will just hover under gravity, quietly hovering. But another possibility is to think like this: If I compress these things more, gravity will be stronger, pulling them together. Actually, if you push a little, the pressure increases. When you push gas together, more atoms collide with each other, so the pressure rises, but gravity also increases. The result is that pressure wins, and the star expands again. If you compress a star like this, it will oscillate. Indeed, some stars are constantly oscillating and wobbling. But the fact is, if you continue to analyze, you compress it to an unbelievable density, for example, compressing the entire mass of the sun to the size of the Earth, or even smaller. Then all the nuclear matter, all the atomic nuclei are tightly packed together, and the space occupied by electrons is completely squeezed out. When a star is compressed to that extent, gravity is very strong, enough to overcome pressure again. Even though the pressure is already very high, gravity is even greater than very high. This mass will remain stable, but its size will be different. Only neutrons are left, nuclear matter, just a pile of nuclear matter. This possibility was proposed by Oppenheimer and Volkov, and is called a neutron star. People waited for many years to see if such neutron stars existed, until recently strange pulsars were discovered, emitting flashing radio waves and flashes. These radio waves flash at a rate of, say, 30 times per second, or ten times per second, or once per second. At first, this was incredible. We are accustomed to stars being huge and rotating slowly. How can a star rotate thirty times per second? In fact, these are very small neutron stars, and they rotate very fast. For reasons unknown, they are emitting a beam of radio waves, like airport searchlights, constantly rotating, beep beep beep. So we receive flashes, beep beep beep... very fast. Imagine a star with a mass equivalent to the sun, somehow rotating thirty times per second, very fast. Another very large number, hard to imagine such an imaginary object, right? The overall idea is that this star is very dense, and a spoonful of it would be very heavy. If you put such a heavy spoonful of matter on the surface of the Earth, it would go straight through to the center. Ideas like this require a lot of imagination. Performing mathematical calculations and analyzing them helps ensure you don't make mistakes. It turns out that such stars are possible, and later they were indeed found. This example well illustrates how useful imagination is. You can use imagination, make guesses in advance, and make progress. Furthermore, it is difficult to imagine what might exist in the universe to explain observed phenomena. As far as astronomy is concerned, we see a lot of phenomena, but we don't have enough imagination to understand what is producing these phenomena. Quasars are sources of very powerful light and radio waves, coming from distant places. We can observe them because they are too bright. Their exact origin has only recently been gradually understood. Let's mention another crazy concept created by imagination: black holes. Black holes are the result of pushing Einstein's logic of gravity to the extreme. Calculations in extreme situations. Suppose you have a pile of matter, a very large amount. The gravity produced is so strong that even light is attracted back when it escapes. Nothing is faster than light, nothing can escape, and you cannot see a black hole. How are black holes formed? If you initially have a large amount of matter, it will condense. Reaching a state where even light cannot escape. So there will be an object that continuously attracts other objects. Something goes in, but nothing comes out. This is called a black hole. You might say, since black holes absorb everything, how do they produce the energy we see? Is it an explanation for quasars? In fact, it is very likely. Because objects don't fall directly, but gradually fall in while rotating. As objects fall in irregularly, they move rapidly and fall into this vortex. This process generates a lot of energy and friction, leading to different effects. Electromagnetic effects may cause matter streams to be ejected from quasars and radio galaxies. And the specific way we haven't truly understood. We don't have a concrete picture to imagine why there are radio jets in galaxies, emitting radio waves? Some galaxies emit huge jets, with large clouds of matter on both sides, emitting radio waves. So there must be some source of emission. It's like being excited and ejecting this matter with immense energy. Some speculate that this might be a "form" of black hole. And this "form" is a challenge to imagination. No one has given a convincing answer to this question yet. You ask me, can ordinary people, by studying hard, imagine various things like I do? Of course they can! I was also an ordinary person who studied hard. There are no miraculous people in the world. It's just that they happen to be interested in these things, and they have learned all this knowledge. It's all about people. There is no special talent or magical ability to understand quantum mechanics and imagine electromagnetic fields. It requires continuous training, reading, learning, and research. So if you find an ordinary person, as long as he is willing to invest a lot of time, study hard, think, and calculate, then he becomes a scientist. When I am truly doing my own thing, thinking about the profound and difficult work that I care about, I don't think I can describe it well. First of all, it's like asking a centipede which leg goes first and which leg goes second. The thinking process is very fast, and I can't be completely sure what flashes through my mind. But I know it involves a mixture of equations, solving these equations, and also the picture of the physical processes described by these equations. But they are not as clearly distinguished as I say, it's a tricky thing. It's hard to describe this thinking, and I don't know what the benefit of describing it is. One thing touched me, and I was very curious about it. I suspect that the thinking process in everyone's brain might be very different, the actual mental images or semi-images of imagination. When we discuss high-level and complex issues together, we think we are communicating smoothly, we are communicating. But what we are actually doing is running a large translation mechanism in our brains, translating the completely different language of the other person into our own images. I found this because at a very basic level, my interest... I don't want to reveal too many details. In fact, I am doing some experiments to figure out our time resolution. So what I have to do is try to count to one minute. In fact, I might count to 48 and say a minute has passed. So I will self-correct, and 48 is one minute. I feel like I'm counting seconds, but it's accurate enough. It turns out that if you repeat it continuously, you can be very precise. When you count to 48, 47, or 49, you are very close to one minute. And I am trying to figure out what affects time resolution. Can I do other things while counting? I find I can do many things, but some things I cannot. For example, what I find difficult is... I was in college, and I had to do laundry, and I had to take out the socks. I had to make a list of "how many pairs of socks," about 6 to 8 pairs. I couldn't count the socks because the counting system was already occupied, and I couldn't count the socks again. But I found that I could arrange the socks regularly, and then I could recognize the number. With practice, I learned a method. I can count the number of lines of text on a newspaper, grouping the lines to look at them. 3, 3, 3, 1, this is a group of ten lines, continue 3, 3, 3, 1. Without reading out the number, just grouping them visually. So I kept practicing, and I could count how many lines there were on the newspaper. At the same time, I was also counting seconds in my mind. So I can perform this wonderful little trick: "48, exactly one minute, and there are 67 lines on the newspaper," you see? This is quite wonderful. I found that I could read many things. No, sorry... Yes, I could read while counting and get a general understanding of the article. But I couldn't speak, I couldn't say anything. Because I was talking to myself, silently reciting "1, 2, 3" in my mind, or reciting it in my mind. Then I went downstairs for breakfast and saw John Tukey, who was a mathematician at Princeton at the time. We had many discussions, and I told him about these experiments and what I could do. He said, "This is unreasonable!" He said, "I don't understand why speaking would be difficult, and I absolutely cannot believe you can read." I also didn't believe it, so we had him count. He probably counted to 52 for 60 seconds, I don't remember the exact number. Then he said, "Okay, what do you want me to say? Mary had a little lamb, I can say anything, blah blah blah. 52! Exactly one minute." He could actually do it, and I couldn't at all. He wanted me to read, because he absolutely didn't believe I could read. So we compared notes and found that when he was counting in his mind, he could see magnetic strips in his mind, with numbers constantly changing on them, "click, click, click." The numbers printed on the magnetic strips would change, and he could see them. So he was actually using the visual system, not the auditory system. He could say anything he wanted, but if you asked him to read, he couldn't look at the timer in his mind. But for me, it was the other way around. So I found that, at least for very simple operations like counting, everyone thinks they are doing the same thing, but in reality, their brains operate very differently. So I was shocked. If this is true at the most basic level, then when we learn mathematics, Bessel functions, exponentials, electric fields, all this knowledge, the way we store this information, and the way we think about this knowledge, if we understand each other's thoughts, we will find that they are truly completely different. In fact, sometimes it is difficult for others to understand facts that seem obvious to you, or vice versa. This may be because it is difficult to convert what you say into their own unique framework. Now I am speaking like a psychologist, and you should know that I know nothing about this! Assume that the behavior of small objects is very different from the behavior of large objects that you are familiar with. Because when animals evolved, when brains evolved, brains are accustomed to processing... brains are designed for normal situations. But if the underlying operating mechanism of fundamental particles is determined by some other rules and characteristics, their behavior is completely different from any large-scale object. Then there will be difficulties in understanding and imagining reality. And this difficulty, we must face. The behavior of small-scale objects is so strange! It is so different! It has an incredible difference from the behavior of any large-scale object. You might say, "Electrons behave like waves," no, not entirely. "Electrons behave like particles," no, not entirely. "Electrons are like a cloud around the nucleus," no, not entirely. If you want to get a clear and distinct image of an atom, so that you can know its exact behavior precisely, there is an accurate image, in other words, a true and accurate image of reality. I don't know how to do it, because this image must be in mathematical form: we have a mathematical expression, a strange mathematical expression, and I don't understand how it works. But we can write down a mathematical expression to calculate what this thing will do without having to visualize it. It's a bit like a computer; you input specific numbers into it. You have a formula to calculate the time it takes for a car to reach different destinations. It has an algorithm that can calculate the time it takes for a car to reach different destinations. You cannot imagine what the car looks like; it is just doing calculations. We know how to calculate, but we cannot depict this car. This is not 100%, because for some approximate situations, some approximate images are feasible. Electrons are like a cloud around the nucleus, and when you squeeze it, it repels you. This image is helpful for understanding the stiffness of some materials. Electrons are like waves, behaving in this way and that way, which is helpful for understanding some other phenomena. So when you study certain aspects of atomic behavior, for example, when I talk about temperature and so on, atoms are like little balls. This is enough; it gives a good picture of temperature. But if you ask more specific questions, you raise some questions like, "When you cool helium, even to absolute zero, it shouldn't have any motion, so how can it become a perfect fluid, flowing without resistance and not solidifying?" And if you want to get a complete picture of the atom, I can't do it. But I can use my equations to explain why helium moves like this, and the results of the equations are exactly as we observe helium's behavior. So we know our theory is correct, but we don't have an image that matches the theory. This may be because we haven't captured the correct image, or it may be because there is no correct image that people can use to depict with familiar things. Let's assume it's the latter possibility: there is no correct image that can be depicted with familiar objects. Then is it possible to develop a sense of familiarity with unfamiliar things by learning, by understanding the properties of atoms and learning quantum mechanics, by practicing solving equations until they become second nature? Like knowing that two balls colliding will shatter, this kind of second nature. You won't say, "When two balls get close to each other, they turn blue." You know what will happen. So the question is, can you understand these situations better than we do today? As generations pass, can they invent teaching methods that enable future generations to see things in a clever way, and be well-trained, so that they don't have our troubles when describing atoms? There is still a school of thought that does not believe that the behavior of atoms is so different from the behavior of large objects. I think this is a deep-seated prejudice, a prejudice of only being accustomed to the behavior of large objects. They are always looking, waiting for the day when we discover that at the bottom of quantum mechanics, there are ordinary little balls colliding, or particles moving, etc. I think they will eventually fail. I think nature's imagination is stronger than human imagination; she will never let us relax!