Feynman Lectures Quotes

It doesn't make a difference how beautiful your guess is. It doesn't make a difference how smart you are, who made the guess, or what his name is. If it disagrees with experiment, it's wrong.

psychoanalysis is not a science: it is at best a medical process, and perhaps even more like witch-doctoring.

If we were to name the most powerful assumption of all, which leads one on and on in an attempt to understand life, it is that all things are made of atoms, and that everything that living things do can be understood in terms of the jigglings and wigglings of atoms.

It is probably better to realize that the probability concept is in a sense subjective, that it is always based on uncertain knowledge, and that its quantitative evaluation is subject to change as we obtain more information.

Mathematics is not a science from our point of view, in the sense that it is not a natural science. The test of its validity is not experiment.

THE QUESTION IS, OF COURSE, IS IT GOING TO BE POSSIBLE TO AMALGAMATE EVERYTHING, AND MERELY DISCOVER THAT THIS WORLD REPRESENTS DIFFERENT ASPECTS OF ONE THING?

Something, somewhere, somewhen, must have happened differently... PETUNIA EVANS married Michael Verres, a Professor of Biochemistry at Oxford. HARRY JAMES POTTER-EVANS-VERRES grew up in a house filled to the brim with books. He once bit a math teacher who didn't know what a logarithm was. He's read Godel, Escher, Bach and Judgment Under Uncertainty: Heuristics and Biases and volume one of The Feynman Lectures on Physics. And despite what everyone who's met him seems to fear, he doesn't want to become the next Dark Lord. He was raised better than that. He wants to discover the laws of magic and become a god. HERMIONE GRANGER is doing better than him in every class except broomstick riding. DRACO MALFOY is exactly what you would expect an eleven-year-old boy to be like if Darth Vader were his doting father. PROFESSOR QUIRRELL is living his lifelong dream of teaching Defense Against the Dark Arts, or as he prefers to call his class, Battle Magic. His students are all wondering what's going to go wrong with the Defense Professor this time. DUMBLEDORE is either insane, or playing some vastly deeper game which involved setting fire to a chicken. DEPUTY HEADMISTRESS MINERVA MCGONAGALL needs to go off somewhere private and scream for a while. Presenting: HARRY POTTER AND THE METHODS OF RATIONALITY You ain't guessin' where this one's going.

Every object is a mixture of lots of things, so we can deal with it only as a series of approximations and idealizations.

CURIOSITY DEMANDS THAT WE ASK QUESTIONS, THAT WE TRY TO PUT THINGS TOGETHER AND TRY TO UNDERSTAND THIS MULTITUDE OF ASPECTS AS PERHAPS RESULTING FROM THE ACTION OF A RELATIVELY SMALL NUMBER OF ELEMENTAL THINGS AND FORCES ACTING IN AN INFINITE VARIETY OF COMBINATIONS

Philosophers have said before that one of the fundamental requisites of science is that whenever you set up the same conditions, the same thing must happen. This is simply not true, it is not a fundamental condition of science.

I dedicate this lecture to showing what ridiculous conclusions and rare statements such a man as myself can make. I wish, therefore, to destroy any image of authority that has previously been generated.

A few years after I gave some lectures for the freshmen at Caltech (which were published as the Feynman Lectures on Physics), I received a long letter from a feminist group. I was accused of being anti-women because of two stories: the first was a discussion of the subtleties of velocity, and involved a woman driver being stopped by a cop. There's a discussion about how fast she was going, and I had her raise valid objections to the cop's definitions of velocity. The letter said I was making the women look stupid. The other story they objected to was told by the great astronomer Arthur Eddington, who had just figured out that the stars get their power from burning hydrogen in a nuclear reaction producing helium. He recounted how, on the night after his discovery, he was sitting on a bench with his girlfriend. She said, "Look how pretty the stars shine!" To which he replied, "Yes, and right now, I'm the only man in the world who knows how they shine." He was describing a kind of wonderful loneliness you have when you make a discovery. The letter claimed that I was saying a women is incapable of understanding nuclear reactions. I figured there was no point in trying to answer their accusations in detail, so I wrote a short letter back to them: "Don't bug me, Man!

In its efforts to learn as much as possible about nature, modern physics has found that certain things can never be "known" with certainty. Much of our knowledge must always remain uncertain. The most we can know is in terms of probabilities.

After the lecture, I talked to a student: “You take all those notes—what do you do with them?

This specialty of reducing deep ideas to simple, understandable terms is evident throughout The Feynman Lectures on Physics, but nowhere more so than in his treatment of quantum mechanics.

How I'm rushing through this! How much each sentence in this brief story contains. "The stars are made of the same atoms as the earth." I usually pick one small topic like this to give a lecture on. Poets say science takes away from the beauty of the stars—mere globs of gas atoms. Nothing is "mere." I too can see the stars on a desert night, and feel them. But do I see less or more ? The vastness of the heavens stretches my imagina-tion—stuck on this carousel my little eye can catch one-million-year-old light. A vast pattern—of which I am a part—perhaps my stuff was belched from some forgotten star, as one is belching there. Or see them with the greater eye of Palomar, rushing all apart from some common starting point when they were perhaps all together. What is the pattern, or the meaning, or the why ? It does not do harm to the mystery to know a little about it. For far more marvelous is the truth than any artists of the past imagined! Why do the poets of the present not speak of it ? What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?

We could, of course, use any notation we want; do not laugh at notations; invent them, they are powerful. In fact,mathematics is, to a large extent, invention of better notations.

If you want to win this argument with Dad, look in chapter two of the first book of the Feynman Lectures on Physics. There's a quote there about how philosophers say a great deal about what science absolutely requires, and it is all wrong, because the only rule in science is that the final arbiter is observation - that you just have to look at the world and report what you see. Um... off the top of my head I can't think of where to find something about how it's an ideal of science to settle things by experiment instead of arguments -

The attempts to try to represent the electric field as the motion of some kind of gear wheels, or in terms of lines, or of stresses in some kind of material have used up more effort of physicists than it would have taken simply to get the right answers about electrodynamics. It is interesting that the correct equations for the behavior of light were worked out by MacCullagh in 1839. But people said to him: 'Yes, but there is no real material whose mechanical properties could possibly satisfy those equations, and since light is an oscillation that must vibrate in something, we cannot believe this abstract equation business'.

What is this "zero mass"? The masses given here are the masses of the particles at rest. The fact that a particle has zero mass means, in a way, that it cannot be at rest. A photon is never at rest, it is always moving at 186,000 miles a second.

there is a physical problem that is common to many fields, that is very old, and that has not been solved. It is not the problem of finding new fundamental particles, but something left over from a long time ago—over a hundred years. Nobody in physics has really been able to analyze it mathematically satisfactorily in spite of its importance to the sister sciences. It is the analysis of circulating or turbulent fluids.

No phenomenon directly involving a frequency has yet been detected above approximately 10^12 cycles per second. We only deduce the higher frequencies from the energy of the particles, by a rule which assumes that the particle-wave idea of quantum mechanics is valid.

There was an interesting early relationship between physics and biology in which biology helped physics in the discovery of the conservation of energy, which was first demonstrated by Mayer in connection with the amount of heat taken in and given out by a living creature.

We might like to turn the idea around and think that the true explanation of the near symmetry of nature is this: that God made the laws only nearly symmetrical so that we should not be jealous of His perfection!

[Paul Olum] was president of the University of Oregon when he heard of [Richard] Feynman’s death. He realized that the young genius he had met at Princeton had become a part of him, impossible to extricate. “My wife died three years ago, also of cancer,” he said. ... I think about her a lot. I have to admit I have Dick’s books and other things of Dick’s. I have all of the Feynman lectures and other stuff. And there are things that have pictures of Dick on them. The article in Science about the Challenger episode. And also some of the recent books. I get a terrible feeling every time I look at them. How could someone like Dick Feynman be dead? This great and wonderful mind. This extraordinary feeling for things and ability is in the ground and there’s nothing there anymore. It’s an awful feeling. And I feel it—— A lot of people have died and I know about it. My parents are both dead and I had a younger brother who is dead. But I have this feeling about just two people. About my wife and about Dick. I suppose, although this wasn’t quite like childhood, it was graduate students together, and I do have more—— I don’t know, romantic, or something, feelings about Dick, and I have trouble realizing that he’s dead. He was such an extraordinarily special person in the universe. Gleick, James (2011-02-22). Genius: The Life and Science of Richard Feynman (p. 145). Open Road Media. Kindle Edition.

Electrons, when they were first discovered, behaved exactly like particles or bullets, very simply. Further research showed, from electron diffraction experiments for example, that they behaved like waves. As time went on there was a growing confusion about how these things really behaved ---- waves or particles, particles or waves? Everything looked like both. This growing confusion was resolved in 1925 or 1926 with the advent of the correct equations for quantum mechanics. Now we know how the electrons and light behave. But what can I call it? If I say they behave like particles I give the wrong impression; also if I say they behave like waves. They behave in their own inimitable way, which technically could be called a quantum mechanical way. They behave in a way that is like nothing that you have seen before. Your experience with things that you have seen before is incomplete. The behavior of things on a very tiny scale is simply different. An atom does not behave like a weight hanging on a spring and oscillating. Nor does it behave like a miniature representation of the solar system with little planets going around in orbits. Nor does it appear to be somewhat like a cloud or fog of some sort surrounding the nucleus. It behaves like nothing you have seen before. There is one simplication at least. Electrons behave in this respect in exactly the same way as photons; they are both screwy, but in exactly in the same way…. The difficulty really is psychological and exists in the perpetual torment that results from your saying to yourself, "But how can it be like that?" which is a reflection of uncontrolled but utterly vain desire to see it in terms of something familiar. I will not describe it in terms of an analogy with something familiar; I will simply describe it. There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe there ever was such a time. There might have been a time when only one man did, because he was the only guy who caught on, before he wrote his paper. But after people read the paper a lot of people understood the theory of relativity in some way or other, certainly more than twelve. On the other hand, I think I can safely say that nobody understands quantum mechanics. So do not take the lecture too seriously, feeling that you really have to understand in terms of some model what I am going to describe, but just relax and enjoy it. I am going to tell you what nature behaves like. If you will simply admit that maybe she does behave like this, you will find her a delightful, entrancing thing. Do not keep saying to yourself, if you can possible avoid it, "But how can it be like that?" because you will get 'down the drain', into a blind alley from which nobody has escaped. Nobody knows how it can be like that.

If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or atomic fact, or whatever you wish to call it) that all things are made of atoms...(italics in original).

Even a very small effect sometimes requires profound changes in our ideas

We do not yet know all the basic laws: there is an expanding frontier of ignorance

Only with quantitative observations can one arrive at quantitative relationships, which are the heart of physics.

A physical understanding is a completely unmathematical, imprecise, and inexact thing, but absolutely necessary for a physicist.

Murray Gell-Mann countered in the following weeks by giving a beautiful set of six lectures concerning the linguistic relations of all the languages of the world.

We call the sum of the weights times the heights gravitational potential energy—the energy which an object has because of its relationship in space, rela- tive to the earth.

The general name of energy which has to do with location relative to some- thing else is called potential energy.

Although it is interesting and worth while to study the physical laws simply because they help us to understand and to use nature, one ought to stop every once in a while and think, “What do they really mean?” The meaning of any statement is a subject that has interested and troubled philosophers from time immemorial, and the meaning of physical laws is even more interesting, because it is generally believed that these laws represent some kind of real knowledge. The meaning of knowledge is a deep problem in philosophy, and it is always important to ask, “What does it mean?

All things, even ourselves, are made of fine-grained, enormously strongly interacting plus and minus parts, all neatly balanced out. Once in a while, by accident, we may rub off a few minuses or a few plusses (usually it is easier to rub off minuses), and in those circumstances we find the force of electricity unbalanced, and we can then see the effects of these electrical attractions.

Another most interesting change in the ideas and philosophy of science brought about by quantum mechanics is this: it is not possible to predict exactly what will happen in any circumstance. For example, it is possible to arrange an atom which is ready to emit light, and we can measure when it has emitted light by picking up a photon particle, which we shall describe shortly. We cannot, however, predict when it is going to emit the light or, with several atoms, which one is going to. You may say that this is because there are some internal "wheels" which we have not looked at closely enough. No, there are no internal wheels; nature, as we understand it today, behaves in such a way that it is fundamentally impossible to make a precise prediction of exactly what will happen in a given experiment.

To summarize: every reversible machine, no matter how it operates, which drops one pound one foot and lifts a three-pound weight always lifts it the same distance, X. This is clearly a universal law of great utility.

Is no one inspired by our present picture of the universe? This value of science remains unsung by singers, you are reduced to hearing not a song or poem, but an evening lecture about it. This is not yet a scientific age.

The theoretical physicist Richard Feynman was such a lauded lecturer in large part because, like Hui Tzu, he was skilled in finding the right analogies to illustrate his explanations of extremely abstract-and extremely difficult-concepts. He once compared a drop of water magnified 2,000 times to "a kind of teeming...like a crowd at a football game as seen from a very great distance." That description has all the precision of good physics and good poetry.

More was discovered about the electrical force. The natural interpretation of electrical interaction is that two objects simply attract each other: plus against minus. However, this was discovered to be an inadequate idea to represent it. A more adequate representation of the situation is to say that the existence of the positive charge, in some sense, distorts, or creates a "condition" in space, so that when we put the negative charge in, it feels a force. This potentiality for produc- ing a force is called an electric field.

How can we tell whether the rules which we "guess" at are really right if we cannot analyze the game very well? There are, roughly speaking, three ways. First, there may be situations where nature has arranged, or we arrange nature, to be simple and to have so few parts that we can predict exactly what will happen, and thus we can check how our rules work. (In one corner of the board there may be only a few chess pieces at work, and that we can figure out exactly.) A second good way to check rules is in terms of less specific rules derived from them. For example, the rule on the move of a bishop on a chessboard is that it moves only on the diagonal. One can deduce, no matter how many moves may be made, that a certain bishop will always be on a red square. So, without being able to follow the details, we can always check our idea about the bishop's motion by finding out whether it is always on a red square. Of course it will be, for a long time, until all of a sudden we find that it is on a black square (what happened of course, is that in the meantime it was captured, another pawn crossed for queening, and it turned into a bishop on a black square). That is the way it is in physics. For a long time we will have a rule that works excellently in an over-all way, even when we cannot follow the details, and then some time we may discover a new rule. From the point of view of basic physics, the most interesting phenomena are of course in the new places, the places where the rules do not work—not the places where they do work! That is the way in which we discover new rules. The third way to tell whether our ideas are right is relatively crude but prob-ably the most powerful of them all. That is, by rough approximation. While we may not be able to tell why Alekhine moves this particular piece, perhaps we can roughly understand that he is gathering his pieces around the king to protect it, more or less, since that is the sensible thing to do in the circumstances. In the same way, we can often understand nature, more or less, without being able to see what every little piece is doing, in terms of our understanding of the game.

Einstein put forward the famous hypothesis that accelerations give an imitation of gravitation, that the forces of acceleration (the pseudo forces) cannot be distinguished from those of gravity; it is not possible to tell how much of a given force is gravity and how much is pseudo force.

The atoms are 1 or 2 X 10-8 cm in radius. Now 10-8 cm is called an angstrom (just as another name), so we say they are 1 or 2 angstroms (Å) in radius. Another way to remember their size is this: if an apple is magnified to the size of the earth, then the atoms in the apple are approximately the size of the original apple.

Everything is fields, and a particle is just a smaller version of a field. There is a harmonic relationship involved. Disturbing ideas like those of Einstein in 1905 and Feynman Pocono Conference in 1948. Here we go; 1) The universe is ringing like a bell. Neil Turok's Public Lecture: The Astonishing Simplicity of Everything. 2) The stuff of the universe is waves or fields. 3) Scale is relative, not fixed because all of these waves are ratios of one another. 4) The geometry is fractal. This could be physical or computational. 5) If the geometry is computational then, there is no point in speaking about the relationship of the pixels on the display.

Galileo expressed the result of his observations in this way: if the location of the ball is marked at 1, 2, 3, 4,... units of time from the instant of Its release, those marks are distant from the starting point in propor- tion to the numbers 1, 4, 9, 16, ... Today we would say the distance is propor- tional to the square of the time

Newton proved to himself (and perhaps we shall be able to prove it soon) that the very fact that equal areas are swept out in equal tines is a precise sign post of the proposition that all deviations are precisely radial-that the law of areas is a direct consequence of the idea that all of the forces are directed exactly toward the sun.

The best teaching can be done only when there is a direct individual relationship between a student and a good teacher—a situation in which the student discusses the ideas, thinks about the things, and talks about the things. It’s impossible to learn very much by simply sitting in a lecture, or even by simply doing problems that are assigned.

In learning any subject of a technical nature where mathematics plays a role, one is confronted with the task of understanding and storing away in the memory a huge body of facts and ideas, held together by certain relationships which can be “proved” or “shown” to exist between them. It is easy to confuse the proof itself with the relationship which it establishes. Clearly, the important thing to learn and to remember is the relationship, not the proof. In any particular circumstance we can either say “it can be shown that” such and such is true, or we can show it. In almost all cases, the particular proof that is used is concocted, first of all, in such form that it can be written quickly and easily on the chalkboard or on paper, and so that it will be as smooth-looking as possible. Consequently, the proof may look deceptively simple, when in fact, the author might have worked for hours trying different ways of calculating the same thing until he has found the neatest way, so as to be able to show that it can be shown in the shortest amount of time! The thing to be remembered, when seeing a proof, is not the proof itself, but rather that it can be shown that such and such is true. Of course, if the proof involves some mathematical procedures or “tricks” that one has not seen before, attention should be given not to the trick exactly, but to the mathematical idea involved.

Thus Kepler's three laws are: I. Each planet moves around the sun in an ellipse, with the sun at one focus. II. The radius vector from the sun to the planet sweeps out equal areas in equal intervals of time. III. The squares of the periods of any two planets are proportional to the cubes of the semimajor axes of their respective orbits : T - a'3/2

So we see that a substance’s properties must be limited in a certain way; one cannot make up anything he wants, or he would be able to invent a substance which he could use to produce more than the maximum allowable work when he carried it around a reversible cycle. This principle, this limitation, is the only real rule that comes out of the thermodynamics.

You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won't believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!

As an example of something , let us consider the time it takes light to go across a proton, 10 to the negative 24 second. If we compare this time with the age of the universe , 2 times 10 to the tenth power years, the answer is 10 to the negative 42nd power. It has about the same number of zeros going off it, so it has been proposed that the gravitational constant is related to the age of the universe.

The question is, of course, is it going to be possible to amalgamate everything, and merely discover that this world represents different aspects of one thing? Nobody knows. All we know is that as we go along, we find that we can amalga- mate pieces, and then we find some pieces that do not fit, and we keep trying to put the jigsaw puzzle together. Whether there are a finite number of pieces, and whether there is even a border to the puzzle, is of course unknown. It will never be known until we finish the picture, if ever. What we wish to do here is to see to what extent this amalgamation process has gone on, and what the situation is at present, in understanding basic phenomena in terms of the smallest set of principles. To express it in a simple manner, what are things made of and how few elements are there ?

If it can be controlled in thermonuclear reactions, it turns out that the energy that can be obtained from 10 quarts of water per second is equal to all of the electrical power generated in the United States. With 150 gallons of running water a minute, you have enough fuel to supply all the energy which is used in the United States today! Therefore it is up to the physicist to figure out how to liberate us from the need for having energy. It can be done.

What about the inside of the earth? A great deal is known about the speed of earthquake waves through the earth and the density of distribution of the earth. However, physicists have been unable to get a good theory as to how dense a substance should be at the pressures that would be expected at the center of the earth. In other words, we cannot figure out the properties of matter very well in these circumstances. We do much less well with the earth than we do with the conditions of matter in the stars. The mathematics involved seems a little too difficult, so far, but perhaps it will not be too long before someone realizes that it is an important problem, and really work it out. The other aspect, of course, is that even if we did know the density, we cannot figure out the circulating currents. Nor can we really work out the properties of rocks at high pressure. We cannot tell how fast the rocks should "give"; that must all be worked out by experiment.

If we burn the carbon with very little oxygen in a very rapid reaction (for example, in an automobile engine, where the explosion is so fast that there is not time for it to make carbon dioxide) a considerable amount of carbon monoxide is formed. In many such rearrangements, a very large amount of energy is released, forming explosions, flames, etc., depending on the reactions. Chemists have studied these arrangements of the atoms, and found that every substance is some type of arrange- ment of atoms.

By extending our techniques—and if necessary our definitions—still further we can infer the time duration of still faster physical events. We can speak of the period of a nuclear vibration. We can speak of the lifetime of the newly discovered strange resonances (particles) mentioned in Chapter 2. Their complete life occupies a time span of only 10-24 second, approximately the time it would take light (which moves at the fastest known speed) to cross the nucleus of hydrogen (the smallest known object).

What else can you do with the law of gravitation? If we look at the moons of Jupiter we can understand everything about the way they move around that planet. Incidentally, there was once a certain difficulty with the moons of Jupiter that is worth remarking on. These satellites were studied very carefully by Rømer, who noticed that the moons sometimes seemed to be ahead of schedule, and sometimes behind. (One can find their schedules by waiting a very long time and finding out how long it takes on the average for the moons to go around.) Now they were ahead when Jupiter was particularly close to the earth and they were behind when Jupiter was farther from the earth. This would have been a very difficult thing to explain according to the law of gravitation—it would have been, in fact, the death of this wonderful theory if there were no other explanation. If a law does not work even in one place where it ought to, it is just wrong. But the reason for this discrepancy was very simple and beautiful: it takes a little while to see the moons of Jupiter because of the time it takes light to travel from Jupiter to the earth. When Jupiter is closer to the earth the time is a little less, and when it is farther from the earth, the time is more. This is why moons appear to be, on the average, a little ahead or a little behind, depending on whether they are closer to or farther from the earth. This phenomenon showed that light does not travel instantaneously, and furnished the first estimate of the speed of light. This was done in 1676.

Now the jiggling motion is what we represent as heat: when we increase the temperature, we increase the motion. If we heat the water, the jiggling increases and the volume between the atoms increases, and if the heating continues there comes a time when the pull between the molecules is not enough to hold them together and they do fly apart and become separated from one another. Of course, this is how we manufacture steam out of water—by increasing the temperature; the particles fly apart because of the increased motion.

So the chemical properties of a substance depend only on a number, the number of electrons. (The whole list of elements of the chemists really could have been called 1, 2, 3, 4, 5, etc. Instead of saying "carbon," we could say "element six," meaning six electrons, but of course, when the elements were first discovered, it was not known that they could be numbered that way, and secondly, it would make everything look rather complicated. It is better to have names and symbols for these things, rather than to call everything by number.)

The gravitational attraction relative to the electrical repulsion between two electrons is 1 divided by 4.17 times ten to the 42nd power! As an example of something , let us consider the time it takes light to go across a proton, 10 to the negative 24 second. If we compare this time with the age of the universe , 2 times 10 to the tenth power years, the answer is 10 to the negative 42nd power. It has about the same number of zeros going off it, so it has been proposed that the gravitational constant is related to the age of the universe.

Professor Weyl,* the mathematician, gave an excellent definition of symmetry, which is that a thing is symmetrical if there is something that you can do to it so that after you have finished doing it it looks the same as it did before. That is the sense in which we say that the laws of physics are symmetrical; that there are things we can do to the physical laws, or to our way of representing the physical laws, which make no difference, and leave everything unchanged in its effects. It is this aspect of physical laws that is going to concern us in this lecture.

One of the most interesting technical problems may or may not be called psychology. The central problem of the mind, if you will, or the nervous system, is this: when an animal learns something, it can do something different than it could before, and its brain cell must have changed too, if it is made out of atoms. In what way is it different ? We do not know where to look, or what to look for, when something is memorized. We do not know what it means, or what change there is in the nervous system, when a fact is learned. This is a very impor- tant problem which has not been solved at all.

One of the most impressive discoveries was the origin of the energy of the stars, that makes them continue to burn. One of the men who discovered this was out with his girl friend the night after he realized that nuclear reactions must be going on in the stars in order to make them shine. She said "Look at how pretty the stars shine!" He said "Yes, and right now I am the only man in the world who knows why they shine." She merely laughed at him. She was not impressed with being out with the only man who, at that moment, knew why stars shine. Well, it is sad to be alone, but that is the way it is in this world.

Throughout these lectures I have delighted in showing you that the price of gaining such an accurate theory has been the erosion of our common sense. We must accept some very bizarre behavior: the amplification and suppression of probabilities, light reflecting from all parts of a mirror, light travelling in paths other than a straight line, photons going faster or slower than the conventional speed of light, electrons going backwards in time, photons suddenly disintegrating into a positron-electron pair, and so on. That we must do, in order to appreciate what Nature is really doing underneath nearly all the phenomena we see in the world.

If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or the atomic fact, or whatever you wish to call it) that all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied.

Something, somewhere, somewhen, must have happened differently… PETUNIA EVANS married Michael Verres, a Professor of Biochemistry at Oxford. HARRY JAMES POTTER-EVANS-VERRES grew up in a house filled to the brim with books. He once bit a math teacher who didn’t know what a logarithm was. He’s read Godel, Escher, Bach and Judgment Under Uncertainty: Heuristics and Biases and volume one of The Feynman Lectures on Physics. And despite what everyone who’s met him seems to fear, he doesn’t want to become the next Dark Lord. He was raised better than that. He wants to discover the laws of magic and become a god. HERMIONE GRANGER is doing better than him in every class except broomstick riding. DRACO MALFOY is exactly what you would expect an eleven-year-old boy to be like if Darth Vader were his doting father. PROFESSOR QUIRRELL is living his lifelong dream of teaching Defense Against the Dark Arts, or as he prefers to call his class, Battle Magic. His students are all wondering what’s going to go wrong with the Defense Professor this time. DUMBLEDORE is either insane, or playing some vastly deeper game which involved setting fire to a chicken. DEPUTY HEADMISTRESS MINERVA MCGONAGALL needs to go off somewhere private and scream for a while. Presenting: HARRY POTTER AND THE METHODS OF RATIONALITY You ain’t guessin’ where this one’s going.

Universal gravitation What else can we understand when we understand gravity? Everyone knows the earth is round. Why is the earth round? That is easy ; it is due to gravitation. The earth can be understood to be round merely because everything attracts everything else and so it has attracted itself together as far as it can! If we go even further, the earth is not exactly a sphere because it is rotating and this brings in centrifugal effects which tend to oppose gravity near the equator. It turns out that the earth should be elliptical, and we even get the right shape forthe ellipse. We can thus deduce that the sun, the moon, and the earth should be (nearly) spheres just from the law of gravitation.

Assuming, however, that there is some kind of memory thing, the brain is such an enormous mass of interconnect ing wires and nerves that it probably cannot be analyzed in a straightforward manner. There is an analog of this to computing machines and computing ele- ments, in that they also have a lot of lines, and they have some kind of element, analogous, perhaps, to the synapse, or connection of one nerve to another. This is a very interesting subject which we have not the time to discuss further—the relationship between thinking and computing machines. It must be appreciated, of course, that this subject will tell us very little about the real complexities of ordinary human behavior. All human beings are so different. It will be a long time before we get there.

A description of nature is what we are concerned with here. From this point of view, then, a gas, and indeed all matter, is a myriad of moving particles. Thus many of the things we saw while standing at the seashore can immediately be connected. First the pressure: this comes from the collisions of the atoms with the walls or whatever; the drift of the atoms, if they are all moving in one direc- tion on the average, is wind; the random internal motions are the heat. There are waves of excess density, where too many particles have collected, and so as they Tush off they push up piles of particles farther out, and so on. This wave of excess density is sound. It is a tremendous achievement to be able to understand so much. Some of these things were described in the previous chapter.

If we had an atom and wished to see the nucleus, we would have to magnify it until the whole atom was the size of a large room, and then the nucleus would be a bare speck which you could just about make out with the eye, but very nearly all the weight of the atom is in that infinitesimal nucleus. What keeps the electrons from simply falling in? This principle: If they were in the nucleus, we would know their position precisely, and the uncertainty principle would then require that they have a very large (but uncertain) momentum, i.e., a very large kinetic energy. With this energy they would break away from the nucleus. They make a compromise: they leave them- selves a little room for this uncertainty and then jiggle with a certain amount of minimum motion in accordance with this rule.

Suppose we had some kind of device with particles moving with a certain definite symmetry, and suppose their movements were bilaterally symmetrical (fig. 20). Then, following the laws of physics, with all the movements and collisions, you could expect, and rightly, that if you look at the same picture later on it will still be bilaterally symmetrical. So there is a kind of conservation, the conservation of the symmetry character. This should be in the table, but it is not like a number that you measure, and we will discuss it in much more detail in the next lecture. The reason this is not very interesting in classical physics is because the times when there are such nicely symmetrical initial conditions are very rare, and it is therefore a not very important or practical conservation law. But

For example, the force of electricity between two charged objects looks just like the law of gravitation: the force of electricity is a constant, with a minus sign, times the product of the charges, and varies inversely as the square of the distance. It is in the opposite direction-likes repel. But is it still not very remarkable that the two laws involve the same function of distance? Perhaps gravitation and electricity are much more closely related than we think. Many attempts have been made to unify them; the so called unified-field theory is only a very elegant attempt to combine electricity and gravitation; but, in comparing gravitation and electricity , the most interesting thing is the relative strengths of the forces. Any theory that contains them both must also deduce how strong the gravity is.

In order to verify the conservation of energy, we must be careful that we have not put any in or taken any out. Second, the energy has a large number of different forms, and there is a formula for each one. These are: gravitational energy, kinetic energy, heat energy, elastic energy, electrical energy, chemical energy, radiant energy, nuclear energy, mass energy. If we total up the formulas for each of these contributions, it will not change except for energy going in and out. It is important to realize that in physics today, we have no knowledge of what energy is. We do not have a picture that energy comes in little blobs of a definite amount. It is not that way. However, there are formulas for calculating some numerical quantity, and when we add it all together it gives "28"'—always the same number. It is an abstract thing in that it does not tell us the mechanism or the reasons for the various formulas.

One very important feature of pseudo forces is that they are always proportional to the masses; the same is true of gravity. The possibility exists, therefore, that gravity is a pseudo force. Is it not possible that perhaps gravitation is due simply to the fact that we do not have the right coordinate system? After all, we can always get a force proportional to the mass if we imagine that a body is accelerating. For instance, a man shut up in a box that is standing still on the earth finds himself held to the floor of the box with a certain force that is proportional to his mass. But if there were no earth at all and the box were standing still, the man inside would float in space. On the other hand, if there were no earth at all and something were pulling the box along with an acceleration g, then the man in the box analyzing physics would find a pseudo force which would pull him to the floor, just as gravity does.

It is the nuclear "burning" of hydrogen which supplies the energy of the sun; the hydrogen is converted into helium. Furthermore, ultimately, the manufacture of various chemical elements proceeds in the centers of the stars, from hydrogen. The stuff of which we are made, was "cooked" once, in a star, and spit out. How do we know? Because there is a clue. The proportion of the different isotopes— how much C12 , how much C13 , etc., is something which is never changed by chemical reactions, because the chemical reactions are so much the same for the two. The proportions are purely the result of nuclear reactions. By looking at the proportions of the isotopes in the cold, dead ember which we are, we can discover what the furnace was like in which the stuff of which we are made was formed. That furnace was like the stars, and so it is very likely that our elements were "made" in the stars and spit out in the explosions which we call novae and super- novae. Astronomy is so close to physics that we shall study many astronomical things as we go along.

Why are the equations from different phenomena so similar? We might say: "It is the underlying unity of nature." But what does that mean? What could such a statement mean? It could mean simply that the equations are similar for different phenomena; but then, of course, we have given no explanation. The underlying unity might mean that everything is made out of the same stuff, and therefore obeys the same equations. That sounds like a good explanation, but let us think. The electrostatic potential, the diffusion of neutrons, heat flow - are we really dealing with the same stuff? Can we really imagine that the electrostatic potential is physically identical to the temperature, or to the density of particles? Certainly is not exactly the same as the thermal energy of particles. The displacement of a membrane is certainly not like a temperature. Why, then, is there an underlying unity? [...] Is it possible that this is the clue? That the thing which is common to all the phenomena is the space, the framework into which the physics is put? - Lecture notes on physics,Vol. 3, p. 1, 1964

The differ- ence between solids and liquids is, then, that in a solid the atoms are arranged in some kind of an array, called a crystalline array, and they do not have a random position at long distances; the position of the atoms on one side of the crystal is determined by that of other atoms millions of atoms away on the other side of the crystal. Figure 1-4 is an invented arrangement for ice, and although it con- tains many of the correct features of ice, it is not the true arrangement. One of the correct features is that there is a part of the symmetry that is hexagonal. You can see that if we turn the picture around an axis by 120°, the picture returns to itself. So there is a symmetry in the ice which accounts for the six-sided appearance of snowflakes. Another thing we can see from Fig. 1-4 is why ice shrinks when it melts. The particular crystal pattern of ice shown here has many "holes" in it, as does the true ice structure. When the organization breaks down, these holes can be occupied by molecules. Most simple substances, with the exception of water and type metal, expand upon melting, because the atoms are closely packed in the solid crystal and upon melting need more room to jiggle around, but an open structure collapses, as in the case of water.

When we put an electron in an electric field, we say it is "pulled." We then have two rules: (a) charges make a field, and (b) charges in fields have forces on them and move. The reason for this will be- come clear when we discuss the following phenomena: If we were to charge a body, say a comb, electrically, and then place a charged piece of paper at a distance and move the comb back and forth, the paper will respond by always pointing to the comb. If we shake it faster, it will be discovered that the paper is a little behind, there is a delay in the action. (At the first stage, when we move the comb rather slowly, we find a complication which is magnetism. Magnetic influences have to do with charges in relative motion, so magnetic forces and electric forces can really be attributed to one field, as two different aspects of exactly the same thing. A changing electric field cannot exist without magnetism.) If we move the charged paper farther out, the delay is greater. Then an interesting thing is observed. Although the forces between two charged objects should go inversely as the square of the distance, it is found, when we shake a charge, that the influence extends very much farther out than we would guess at first sight. That is, the effect falls off more slowly than the inverse square.

else can you do with the law of gravitation? If we look at the moons of Jupiter we can understand everything about the way they move around that planet. Incidentally, there was once a certain difficulty with the moons of Jupiter that is worth remarking on. These satellites were studied very carefully by Rømer, who noticed that the moons sometimes seemed to be ahead of schedule, and sometimes behind. (One can find their schedules by waiting a very long time and finding out how long it takes on the average for the moons to go around.) Now they were ahead when Jupiter was particularly close to the earth and they were behind when Jupiter was farther from the earth. This would have been a very difficult thing to explain according to the law of gravitation—it would have been, in fact, the death of this wonderful theory if there were no other explanation. If a law does not work even in one place where it ought to, it is just wrong. But the reason for this discrepancy was very simple and beautiful: it takes a little while to see the moons of Jupiter because of the time it takes light to travel from Jupiter to the earth. When Jupiter is closer to the earth the time is a little less, and when it is farther from the earth, the time is more. This is why moons appear to be, on the average, a little ahead or a little behind, depending on whether they are closer to or farther from the earth. This phenomenon showed that light does not travel instantaneously, and furnished the first estimate of the speed of light. This was done in 1676.

Look, if you’re going to insist that I’ve taught you something, I guess I should give you a final exam.” “Really?” “One question.” “Sure.” “Go look at an electron microscope photograph of an atom, okay? Don’t just glance at it. It is very important that you examine it very closely. Think about what it means.” “Okay.” “And then answer this question. Does it make your heart flutter?” “Does it make my heart flutter?” “Yes or no. It’s a yes or no question. No equations allowed.” “All right, I’ll let you know.” “Don’t be dense. I don’t need to know. You need to know. This exam is self-graded. And it’s not the answer that counts, it’s what you do with the information.” We locked eyes. His younger face flashed in my mind. The energetic, smiling bongo drum player I had seen pictured in the front of his book, The Feynman Lectures on Physics. A question popped from my lips.

A number of collections and adaptations of his lectures have been published, including The Feynman Lectures on Physics, QED (Penguin, 1990), The Character of Physical Law (Penguin, 1992), Six Easy Pieces (Penguin, 1998), The Meaning of It All (Penguin, 1999), Six Not-So-Easy Pieces (Penguin, 1999), The Feynman Lectures on Gravitation (Penguin, 1999), The Feynman Lectures on Computation (Penguin, 1999) and The Pleasure of Finding Things Out (Penguin, 2001). His memoirs, Surely You’re Joking, Mr Feynman, were published in 1985.

Richard Feynman very famously does this in “Six Easy Pieces,” one of his early physics lectures. He basically explains mathematics in three pages. He starts from the number line—counting—and then he goes all the way up to precalculus. He just builds it up through an unbroken chain of logic. He doesn’t rely on any definitions.

In a famous series of lectures on the character of physical law delivered at Cornell University in 1964, the great physicist Richard Feynman put it this way: I think it is safe to say that no one understands quantum mechanics. Do not keep saying to yourself, if you can possibly avoid it, “But how can it be like that?” because you will go “down the drain” into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that. This chimes, as we have seen, with J. B. S. Haldane’s famous assertion that “the Universe is not only queerer than we suppose but queerer than we can suppose.

In private, with pencil on scratch paper, he labored over aphorisms that he later delivered in spontaneous-seeming lectures: Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry.

Knowledge was rarer then. A secondhand magazine was an occasion. For a Far Rockaway teenager merely to find a mathematics textbook took will and enterprise. Each radio program, each telephone call, each lecture in a local synagogue, each movie at the new Gem theater on Mott Avenue carried the weight of something special. Each book Richard possessed burned itself into his memory. When a primer on mathematical methods baffled him, he worked through it formula by formula, filling a notebook with self-imposed exercises. He and his friends traded mathematical tidbits like baseball cards. If a boy named Morrie Jacobs told him that the cosine of 20 degrees multiplied by the cosine of 40 degrees multiplied by the cosine of 80 degrees equaled exactly one-eighth, he would remember that curiosity for the rest of his life,