Qed Quotes

Now it is such a bizarrely improbable coincidence that anything so mind-bogglingly useful could have evolved purely by chance that some thinkers have chosen to see it as the final and clinching proof of the non-existence of God. The argument goes something like this: "I refuse to prove that I exist,'" says God, "for proof denies faith, and without faith I am nothing." "But," says Man, "The Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don't. QED." "Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic. "Oh, that was easy," says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing.

What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school... It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it... That is because I don't understand it. Nobody does.

What sparks wars? The will to power, the backbone of human nature. The threat of violence, the fear of violence, or actual violence, is the instrument of this dreadful will. You can see the will to power in bedrooms, kitchens, factories, unions and the borders of states. Listen to this and remember it. The nation state is merely human nature inflated to monstrous proportions. QED, nations are entities whose laws are written by violence. Thus it ever was, so ever shall it be.

We are told that "the meek shall inherit the earth." It follows that the meek are chosen of God. I shall try to be meek, not because I want the earth - you can keep it, after the way you've fucked it around it's not worth having - but because I too should like to be chosen of God. QED. Besides, I like animals better than you bastards.

The argument goes something like this: ‘I refuse to prove that I exist,’ says God, ‘for proof denies faith, and without faith I am nothing.’ “ ‘But,’ says Man, ‘the Babel fish is a dead giveaway, isn’t it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don’t. QED.’ “ ‘Oh dear,’ says God, ‘I hadn’t thought of that,’ and promptly vanishes in a puff of logic. “ ‘Oh, that was easy,’ says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing.

The lay reader only wanted to have the illusion of understanding and to catch a few buzzwords to throw around at cocktail parties.

The Babel fish is small, yellow and leech-like, and probably the oddest thing in the Universe. It feeds on brainwave energy received not from its own carrier but from those around it. It absorbs all unconscious mental frequencies from this brainwave energy to nourish itself with. It then excretes into the mind of its carrier a telepathic matrix formed by combining the conscious thought frequencies with the nerve signals picked up from the speech centres of the brain which has supplied them. The practical upshot of all this is that if you stick a Babel fish in your ear you can instantly understand anything said to you in any form of language. The speech patterns you actually hear decode the brainwave matrix which has been fed into your mind by your Babel fish. Now it is such a bizarrely improbable coincidence that anything so mindbogglingly useful could have evolved purely by chance that some thinkers have chosen it to see it as a final and clinching proof of the non-existence of God. The argument goes something like this: "I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing." "But," says Man, "the Babel fish is a dead giveaway isn't it? It could not have evolved by chance. It proves you exist, and therefore, by your own arguments, you don't. QED." "Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic. "Oh, that was easy," says Man, and for an encore goes on to prove that black is white and gets killed on the next zebra crossing.

Then it is about sex,” said Polly flatly. “It’s a folk song, it starts with ‘’twas,’ it takes place in May, QED, it’s about sex. Is a milkmaid involved? I bet she is.

With quantum physics, who needs drugs?

The argument goes something like this: "I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing." "But," says Man, "the Babel fish is a dead giveaway isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don't. QED" "Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic.

The argument goes something like this: "I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing." "But," says Man, "the Babel fish is a dead giveaway isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don't. QED" "Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic.

atoms in the air scatter light from the sun and make the sky blue

QED, bitches.

We cannot predict whether a given photon will arrive at A or B. All we can predict is that out of 100 photons that come down, an average of 4 will be reflected by the front surface. Does this mean that physics, a science of great exactitude, has been reduced to calculating only the probability of an event, and not predicting exactly what will happen? Yes. That's a retreat, but that's the way it is: Nature permits us to calculate only probabilities. Yet science has not collapsed.

Another war is always coming Robert. They are never properly extinguished. What sparks wars? The will to power, the backbone of human nature. The threat of violence, the fear of violence, or actual violence is the instrument of this dreadful will. You can see the will to power in bedrooms, kitchens, factories, unions, and the borders of states. Listen to this and remember it. The nation-state is merely human nature inflated to monstrous proportions. QED, nations are entities whose laws are written by violence. Thus is ever was, so ever shall it be.

The argument goes something like this: ‘I refuse to prove that I exist,’ says God, ‘for proof denies faith, and without faith I am nothing.’ “‘But,’ says Man, ‘the Babel fish is a dead giveaway, isn’t it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don’t. QED.’ “‘Oh dear,’ says God, ‘I hadn’t thought of that,’ and promptly vanishes in a puff of logic. “‘Oh, that was easy,’ says Man, and

QED [quantum electrodynamics] reduces ... "all of chemistry and most of physics," to one basic interaction, the fundamental coupling of a photon to electric charge. The strength of this coupling remains, however, as a pure number, the so-called fine-structure constant, which is a parameter of QED that QED itself is powerless to predict.

There is a most profound and beautiful question associated with the observed coupling constant, e - the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!

The probability of an event is always represented by a single final arrow-no matter how many arrows were drawn, multiplied, and added to achieve it.

Because “extra-difficult popular physics books” scare publishers half to death. Hawking famously said that every equation halves the sale of a popular book.

According to Feynman, to learn QED you have two choices: you can either go through seven years of physics education or read this book.

Another war is always coming, Robert. They are never properly extinguished. What sparks wars? The will to power, the backbone of human nature. The threat of violence, the fear of violence, or actual violence, is the instrument of this dreadful will. You can see the will to power in bedrooms, kitchens, factories, unions and the borders of states. Listen to this and remember it. The nation-state is merely human nature inflated to monstrous proportions. QED, nations are entities whose laws are written by violence. Thus it ever was, so ever shall it be.

[D]idn't Aristarchus and the Pythagoreans propose heliocentrism in ancient times? If only they had prevailed, we might have had Real Science millennia sooner. What was their evidence? Well, you see, fire is nobler than earth and the center is a nobler position. So fire has to be in the center. QED. There are many names for this sort of thinking, but "scientific" is not one of them.

When Charles Darwin was trying to decide whether he should propose to his cousin Emma Wedgwood, he got out a pencil and paper and weighed every possible consequence. In favor of marriage he listed children, companionship, and the 'charms of music and female chit-chat.' Against marriage he listed the 'terrible loss of time,' lack of freedom to go where he wished, the burden of visiting relatives, the expense and anxiety provoked by children, the concern that 'perhaps my wife won't like London,' and having less money to spend on books. Weighing one column against the other produced a narrow margin of victory, and at the bottom Darwin scrawled, 'Marry—Marry—Marry Q.E.D.' Quod erat demonstrandum, the mathematical sign-off that Darwin himself restated in English: 'It being proved necessary to Marry.

Mysteries like these repeating cycles make it very interesting to be a theoretical physicist: Nature gives us such wonderful puzzles! Why does She repeat the electron at 206 times and 3,640 times its mass?

The argument goes something like this: 'I refuse to prove that I exist,' says God, 'for proof denies faith, and without faith I am nothing.' 'But,' says Man, 'The Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don't. QED.' 'Oh dear,' says God, 'I hadn't thought of that,' and promptly vanished in a puff of logic.

The argument goes something like this: ‘I refuse to prove that I exist,’ says God, ‘for proof denies faith, and without faith I am nothing.’ “‘But,’ says Man, ‘the Babel fish is a dead giveaway, isn’t it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don’t. QED.’ “‘Oh dear,’ says God, ‘I hadn’t thought of that,’ and promptly vanishes in a puff of logic.

It is hard to believe that nearly all the vast apparent variety in Nature results from the monotony of repeatedly combining just these three basic actions. But it does. I'll outline a bit of how some of this variety arises.

People misunderstand happiness. They think it's the absence of trouble. That's not happiness, that's luck. Happiness is the ability to live well alongside trouble. No two people have the same trouble, or the same way of metabolizing it. Q.E.D.: No two happy people are happy in the same way. Even Tolstoy was afraid to admit this, and I don't blame him. Every day brilliant people, people smarter than I, wallow in safe tragedy and pessimism, shying from what really takes guts: recognizing how much courage and labor happiness demands." -Tracy Farber

Another war is always coming, Robert. They are never properly extinguished. What sparks wars? The will to power, the backbone of human nature. The threat of violence, the fear of violence, or actual violence is the instrument of this dreadful will. You can see the will to power in bedrooms, kitchens, factories, unions, and the borders of states. Listen to this and remember it. The nation-state is merely human nature inflated to monstrous proportions. QED, nations are entities whose laws are written by violence. Thus it ever was, so ever shall it be. War, Robert, is one of humanity’s two eternal companions.” So, I asked, what was the other? “Diamonds.

Suppose there were nothing. Then there would be no laws; for laws, after all, are something. If there were no laws, then everything would be permitted. If everything were permitted, then nothing would be forbidden. So if there were nothing, nothing would be forbidden. Thus nothing is self-forbidding. Therefore, there must be something. QED.

The aversion of two electrons to occupy the same place in space-time is called the "Exclusion Principle," and accounts for the great variety of atoms in the universe.

Whether the proton decays or not is not known. To prove that it does not decay is very difficult.

the price of gaining such an accurate theory has been the erosion of our common sense.

Thus light is something like raindrops-each little lump of light is called a photon-and if the light is all one color, all the "raindrops" are the same size.

So when you try to squeeze light too much to make sure it's going in only a straight line, it refuses to cooperate and begins to spread out.

Nature permits us to calculate only probabilities. Yet science has not collapsed.

The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you can accept Nature as She is—absurd.

The argument goes something like this: 'I refuse to prove that I exist,' says God, 'for proof denies faith, and without faith I am nothing.' 'But,' says Man, 'the Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own argument, you don't. QED.' 'Oh, dear,' says God, 'I hadn't thought of that,' and he promptly vanishes in a puff of logic.

In the acknowledgment, Feynman decried popular physics books as achieving “apparent simplicity only by describing something different, something considerably distorted from what they claim to be describing.” Instead, he posed himself the challenge of describing QED to the lay reader without “distortion of the truth.” Thus, you should not think of this book as a typical popular physics book. Neither is it a textbook. A rare hybrid it is instead.

The Babel fish,” said The Hitchhiker’s Guide to the Galaxy quietly, “is small, yellow and leechlike, and probably the oddest thing in the Universe. It feeds on brainwave energy received not from its own carrier but from those around it. It absorbs all unconscious mental frequencies from this brainwave energy to nourish itself with. It then excretes into the mind of its carrier a telepathic matrix formed by combining the conscious thought frequencies with nerve signals picked up from the speech centers of the brain which has supplied them. The practical upshot of all this is that if you stick a Babel fish in your ear you can instantly understand anything said to you in any form of language. The speech patterns you actually hear decode the brainwave matrix which has been fed into your mind by your Babel fish. “Now it is such a bizarrely improbable coincidence that anything so mind-bogglingly useful could have evolved purely by chance that some thinkers have chosen to see it as a fina and clinching proof of the nonexistence of God. “The argument goes something like this: ‘I refuse to prove that I exist,’ says God, for proof denies faith, and without faith I am nothing.’ “‘But,’ says Man, ‘the Babel fish is a dead giveaway, isn’t it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don’t. QED.’ “‘Oh dear,’ says God, ‘I hadn’t thought of that,’ and promptly vanishes in a puff of logic.

They strap toast onto a cat’s back and toss it in the air.” And he waited. I knew there had to be a gag, and if I didn’t guess what it was, he would win the exchange I had begun by essaying a pun. Well, it served me right. “But how do dat make de ship go, Mr. Interlocutor,” I asked ritually, conceding defeat. “They butter the toast, you see.” Light belatedly dawned. “Ah. Of course. The toast must fall butter side down—” “—but the cat must land on its feet.” He spread his hands: QED. “Hence the array spins forever, generating power.

The argument goes something like this: “I refuse to prove that I exist,” says God, “for proof denies faith, and without faith I am nothing.” ‘“But,” says Man, “the Babel fish is a dead giveaway, isn’t it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don’t. QED.” ‘“Oh dear,” says God, “I hadn’t thought of that,” and promptly vanishes in a puff of logic. ‘“Oh, that was easy,” says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing.

Most of the phenomena you are familiar with involve the interaction of light and electrons-all of chemistry and biology, for example. The only phenomena that are not covered by this theory are phenomena of gravitation and nuclear phenomena; everything else is contained in this theory.

Underneath so many of the phenomena we see every day are only three basic actions: one is described by the simple coupling number, j; the other two by functions-P(A to B) and E(A to B)- both of which are closely related. That's all there is to it, and from it all the rest of the laws of physics come.

In this way, great globs of physics theory were synthesized into a simplified theory. The theory of gravitation, on the other hand, was not understandable from the laws of motion, and even today it stands isolated from the other theories. Gravitation is, so far, not understandable in terms of other phenomena.

The chance that an atom emits a photon is enhanced if some photons (in a state that the atom can emit into) are already present. This phenomenon of "stimulated emission" was discovered by Einstein when he launched the quantum theory proposing the photon model of light. Lasers work on the basis of this phenomenon.

Why are all the theories of physics so similar in their structure? There are a number of possibilities. The first is the limited imagination of physicists: when we see a new phenomenon we try to fit it into the framework we already have-until we have made enough experiments, we don't know that it doesn't work. Another possibility is that it is the same damn thing over and over again-that Nature has only one way of doing things, and She repeats her story from time to time. A third possibility is that things look similar because they are aspects of the same thing- some larger picture underneath, from which things can be broken into parts that look different, like fingers on the same hand. Many physicists are working very hard trying to put together a grand picture that unifies everything into one super-duper model. It's a delightful game, but at the present time none of the speculators agree with any of the other speculators as to what the grand picture is.

You might wonder how such simple actions could produce such a complex world. It's because phenomena we see in the world are the result of an enormous intertwining of tremendous numbers of photon exchanges and interferences. Knowing the three fundamental actions is only a very small beginning toward analyzing any real situation.

Actual class struggles apart, one of the aesthetic ways you could prove that there was a class system in America was by cogitating on the word, or acronym, 'WASP.' First minted by E. Digby Baltzell in his book The Protestant Establishment , the term stood for 'White Anglo-Saxon Protestant.' Except that, as I never grew tired of pointing out, the 'W' was something of a redundancy (there being by definition no BASPs or JASPs for anyone to be confused with, or confused about). 'ASP,' on the other hand, lacked some of the all-important tone. There being so relatively few Anglo-Saxon Catholics in the United States, the 'S' [sic] was arguably surplus to requirements as well. But then the acronym AS would scarcely do, either. And it would raise an additional difficulty. If 'Anglo-Saxon' descent was the qualifying thing, which surely it was, then why were George Wallace and Jerry Falwell not WASPs? After all, they were not merely white and Anglo-Saxon and Protestant, but very emphatic about all three things. Whereas a man like William F. Buckley, say, despite being a white Irish Catholic, radiated the very sort of demeanor for which the word WASP had been coined to begin with. So, for the matter of that, did the dapper gentleman from Richmond, Virginia, Tom Wolfe. Could it be, then, that WASP was really a term of class rather than ethnicity? Q.E.D.

So light doesn't really travel only in a straight line; it "smells" the neighboring paths around it, and uses a small core of nearby space. (In the same way, a mirror has to have enough size to reflect normally: if the mirror is too small for the core of neighboring paths, the light scatters in many directions, no matter where you put the mirror.)

Nature has got it cooked up so we'll never be able to figure out how She does it: if we put instruments in to find out which way the light goes, we can find out, all right, but the wonderful interference effects disappear. But if we don't have instruments that can tell which way the light goes, the interference effects come back! Very strange, indeed!

So now, I present to you the three basic actions, from which all the phenomena of light and electrons arise. -ACTION #1: A photon goes from place to place. -ACTION #2: An electron goes from place to place. -ACTION #3: An electron emits or absorbs a photon. Each of these actions has an amplitude-an arrow-that can be calculated according to certain rules.

In this intuitively easy analysis, the "front surface" and "back surface" arrows are mathematical constructions that give us the right answer, whereas the analysis we just did-with the space-time drawing and the arrows forming part of a circle-is a more accurate representation of what is really going on: partial reflection is the scattering of light by electrons inside the glass.

Throughout this entire story there remains one especially unsatisfactory feature: the observed masses of the particles, m. There is no theory that adequately explains these numbers. We use the numbers in all our theories, but we don't understand them-what they are, or where they come from. I believe that from a fundamental point of view, this is a very interesting and serious problem.

Now it is such a bizarrely improbable coincidence that anything so mind-bogglingly useful could have evolved purely by chance that some thinkers have chosen to see it as a final and clinching proof of the nonexistence of God. ‘The argument goes something like this: “I refuse to prove that I exist,” says God, “for proof denies faith, and without faith I am nothing.” ‘“But,” says Man, “the Babel fish is a dead giveaway, isn’t it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don’t. QED.” ‘“Oh dear,” says God, “I hadn’t thought of that,” and promptly vanishes in a puff of logic. ‘“Oh, that was easy,” says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing.

Now it is such a bizarrely improbable coincidence that anything so mind-bogglingly useful could have evolved purely by chance that some thinkers have chosen to see it as a final and clinching proof of the nonexistence of God. “The argument goes something like this: ‘I refuse to prove that I exist,’ says God, ‘for proof denies faith, and without faith I am nothing.’ “ ‘But,’ says Man, ‘the Babel fish is a dead giveaway, isn’t it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don’t. QED.’ “ ‘Oh dear,’ says God, ‘I hadn’t thought of that,’ and promptly vanishes in a puff of logic. “ ‘Oh, that was easy,’ says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing.

When we deal with probabilities under ordinary circumstances, there are the following "rules of composition": 1) if something can happen in alternative ways, we add the probabilities for each of the different ways; 2) i the event occurs as a succession of steps-or depends on a number of things happening "concomitantly" (independently)-then we multiply the probabilities of each of the steps (or things).

The Frog was the only one who could retrieve the golden ball because he was the only one who could descend into the well. He was the only one who could descend into the well because the art of diving was still unknown in Europe at this time. The art of diving was still unknown in Europe because it had not yet been imported from India. Therefore the Frog was the only one who could retrieve the golden ball. Q.E.D.

The strange feature of partial reflection by two surfaces has forced physicists away form making absolute predictions to merely calculating the probability of an event. Quantum electrodynamics provides a method for doing this-drawing little arrows on a piece of paper. The probability of an event is represented by the area of the square of an arrow. For example, an arrow representing a probability of 0.04 (4%) has a length of 0.2.

Figure 36. A "trick" can be played on Nature by slowing down the light that takes shorter paths: glass of just the right thickness is inserted so that all the paths will take exactly the same time. This causes all of the arrows to point in the same direction, and to produce a whopping final arrow-lots of light! Such a piece of glass made to greatly increase the probability of light getting from a source to a single point is called a focusing lens.

Le cose di cui parlerò le insegniamo agli studenti di fisica degli ultimi anni di università: ora, voi pensate che io riuscirò a spiegarle in modo da farvele capire? Ebbene no, non le capirete. Perché, allora, farvi perdere del tempo? Per convincervi a non andar via solo perché questa conferenza vi risulterà incomprensibile, vi dirò che anche i miei studenti di fisica non capiscono queste cose. E non le capiscono perché non le capisco nemmeno io. Il fatto è che non le capisce nessuno.

It is to be emphasized that no matter how many arrows we draw, add, or multiply, our objective is to calculate a single final arrow for the event. Mistakes are often made by physics students at first because they do not keep this important point in mind. They work for so long analyzing events involving a single photon that they begin to think that the arrow is somehow associated with the photon. But these arrows are probability amplitudes, that give, when squared, the probability of a complete event.

Now it is such a bizarrely improbable coincidence that anything so mind-bogglingly useful could have evolved purely by chance that some thinkers have chosen to see it as a final and clinching proof of the nonexistence of God. “The argument goes something like this: ‘I refuse to prove that I exist,’ says God, ‘for proof denies faith, and without faith I am nothing.’ “ ‘But,’ says Man, ‘the Babel fish is a dead giveaway, isn’t it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don’t. QED.’ “ ‘Oh dear,’ says God, ‘I hadn’t thought of that,’ and promptly vanishes in a puff of logic. “ ‘Oh, that was easy,’ says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing. “Most leading theologians claim that this argument is a load of dingo’s kidneys, but that didn’t stop Oolon Colluphid making a small fortune when he used it as the central theme of his best-selling book, Well That about Wraps It Up for God.

A source of white light-many colors mixed together-emits photons in a chaotic manner: the angle of the amplitude changes abruptly and irregularly in fits and starts. But when we construct a monochromatic source, we are making a device that has been carefully arranged so that the amplitude for a photon to be emitted at a certain time is easily calculated: it changes its angle at a constant speed, like a stopwatch hand. (Actually, this arrow turns at the same speed as the imaginary stopwatch we used before, but in the opposite direction-see Fig. 67.)

What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school—and you think I’m going to explain it to you so you can understand it? No, you’re not going to be able to understand it. Why, then, am I going to bother you with all this? Why are you going to sit here all this time, when you won’t be able to understand what I am going to say? It is my task to convince you not to turn away because you don’t understand it. You see, my physics students don’t understand it either. That is because I don’t understand it. Nobody does.

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.

To understand this better, we need to know that the cycle of zero to 16% partial reflection by two surfaces repeats more quickly for blue light than for red light. Thus at certain thicknesses, one or the other or both colors are strongly reflected, while at other thicknesses, reflections of both colors is cancelled out (see Fig. 18). The cycles of reflection repeat at different rates because the stopwatch hand turns around faster when it times a blue photon than it does when timing a red photon. In fact, that's the only difference between a red photon and a blue photon (or a photon of any other color, including radio waves, X-rays, and so on)-the speed of the stopwatch hand.

Now, let's look again at the partial reflection of light by a layer of glass. How does it work? I talked about light reflected from the front surface and the back surface. This idea of surfaces was a simplification I made in order to keep things easy at the beginning. Light is really not affected by surfaces. An incoming photon is scattered by the electrons in the atoms inside the glass, and a new photon comes back up to the detector. It's interesting that instead of adding up all the billions of tiny arrows that represent the amplitude for all the electrons inside the glass to scatter an incoming photon, we can add just two arrows-for the "front surface" and "back surface" reflections-and come out with the same answer. Let's see why.

Figure 18. As the thickness of a layer increases, the two surfaces produce a partial reflection of monochromatic light whose probability fluctuates in a cycle from 0% to 16%. Since the speed of the imaginary stopwatch hand is different for different colors of light, the cycle repeats itself at different rates. Thus when two colors such as pure red and pure blue are aimed at the layer, a given thickness will reflect only red, only blue, both red and blue in different proportions (which produce various hues of violet), or neither color (black). If the layer is of varying thicknesses, such as a drop of oil spreading out on a mud puddle, all of the combinations will occur. In sunlight, which consists of all colors, all sorts of combinations occur, which produce lots of colors.

Richard Feynman (1918–1988) was not only an extraordinary physicist, but also an extraordinary figure, a swash-buckling personality the likes of which theoretical physics has not seen before or hence. Occasionally theoretical physicists will while away an idle moment comparing the contributions of Feynman and Schwinger, both nice Jewish boys from New York and almost exact contemporaries. This senseless discussion serves no purpose, but it is a fact that while Julian Schwinger was a shy and retiring person (but rather warm and good-hearted behind his apparent remoteness), Dick Feynman was an extreme extrovert, the stuff of legends. With his bongo drums, showgirls, and other trappings of a carefully cultivated image enthusiastically nurtured by a legion of idolaters, he is surely the best-loved theoretical physicist next to Einstein.

There are only two states of polarization available to electrons, so in an atom with three protons in the nucleus exchanging photons with three electrons-a condition called a lithium atom-the third electron is farther away from the nucleus than the other two (which have used up the nearest available space), and exchanges fewer photons. This causes the electron to easily break away from its own nucleus under the influence of photons from other atoms. A large number of such atoms close together easily lose their individual third electrons to form a sea of electrons swimming around from atom to atom. This sea of electrons reacts to any small electrical force (photons), generating a current of electrons-I am describing lithium metal conducting electricity. Hydrogen and helium atoms do not lose their electrons to other atoms. They are "insulators." All the atoms-more than one hundred different kinds-are made up of a certain number of protons exchanging photons with the same number of electrons. The patterns in which they gather are complicated and offer an enormous variety of properties: some are metals, some are insulators, some are gases, others are crystals; there are soft things, hard things, colored things, and transparent things-a terrific cornucopia of variety and excitement that comes from the exclusion principle and the repetition again and again and again of the three very simple actions P(A to B), E(A to B), and j. (If the electrons in the world were unpolarized, all the atoms would have very similar properties: the electrons would all cluster together, close to the nucleus of their own atom, and would not be easily attracted to other atoms to make chemical reactions.)

Thus, some things that satisfy the rules of algebra can be interesting to mathematicians even though they don't always represent a real situation. Arrows on a plane can be "added" by putting the head of one arrow on the tail of another, or "multiplied" by successive turns and shrinks. Since these arrows obey the same rules of algebra as regular numbers, mathematicians call them numbers. But to distinguish them from ordinary numbers, they're called "complex numbers." For those of you who have studied mathematics enough to have come to complex numbers, I could have said, "the probability of an event is the absolute square of a complex number. When an event can happen in alternative ways, you add the complex numbers; when it can happen only as a succession of steps, you multiply the complex numbers." Although it may sound more impressive that way, I have not said any more than I did before-I just used a different language.

The situation today is, we haven't got a good model to explain partial reflection by two surfaces; we just calculate the probability that a particular photomultiplier will be hit by a photon reflected from a sheet of glass. I have chosen this calculation as our first example of the method provided by theory of quantum electrodynamics. I am going to show you "how we count the beans"-what the physicists do to get the right answer. I am not going to explain how the photons actually "decide" whether to bounce back or go through; that is not known. (Probably the question has no meaning.) I will only show you how to calculate the correct probability that light will be reflected from glass of a given thickness, because that's the only thing physicists know how to do! What we do to get the answer to this problem is analogous to the things we have to do to get the answer to every other problem explained by quantum electrodynamics.

The driest argument has its hallucinations, too hastily concluding that its net will now at last be large enough to hold the universe. Men may dream in demonstrations, and cut out an illusory world in the shape of axioms, definitions, and propositions, with a final exclusion of fact signed Q.E.D. No formulas for thinking will save us mortals from mistake in our imperfect apprehension of the matter to be thought about. And since the unemotional intellect may carry us into a mathematical dreamland where nothing is but what is not, perhaps an emotional intellect may have absorbed into its passionate vision of possibilities some truth of what will be—the more comprehensive massive life feeding theory with new material, as the sensibility of the artist seizes combinations which science explains and justifies. At any rate, presumptions to the contrary are not to be trusted. We must be patient with the inevitable makeshift of our human thinking, whether in its sum total or in the separate minds that have made the sum.

The backwards-moving electron when viewed with time moving forwards appears the same as an ordinary electron, except it's attracted to normal electrons-we say it has a "positive charge." (Had I included the effects of polarization, it would be apparent why the sign of j for the backwards-moving electron appears reversed, making the charge appear positive.) For this reason it's called a "positron." The positron is a sister particle to the electron, and is an example of an "anti-particle." This phenomenon is general. Every particle in Nature has an amplitude to move backwards in time, and therefore has an anti-particle. When a particle and its anti-particle collide, they annihilate each other and form other particles. (For positrons and electrons annihilating, it is usually a photon or two.) And what about photons? Photons look exactly the same in all respects when they travel backwards in time-as we saw earlier-so they are their own anti-particles. You see how clever we are at making an exception part of the rule!

To understand this paradox, let me remind you of a most important principle: in order to correctly calculate the probability of an event, one must be very careful to define the complete event clearly-in particular, what the initial conditions and and the final conditions of the experiment are. You look at the equipment before and after the experiment, and look for changes. When we were calculating the probability that a photon gets from S to D with no detectors at A or B, the event was, simply, the detector at D makes a click. When a click at D was the only change in conditions, there was no way to tell which way the photon went, so there was interference. When we put in detectors at A and B, we changed the problem. Now, it turns out, there are two complete events-two sets of final conditions-that are distinguishable: 1) the detectors at A and D go off, or 2) the detectors at B and D go off. When there are a number of possible final conditions in an experiment, we must calculate the probability of each as a separate, complete event.

To summarize, where the time is least is also where the time for the nearby paths is nearly the same; that's where the little arrows point in nearly the same direction and add up to a substantial length; that's where the probability of a photon reflecting off a mirror is determined. And that's why, in approximation, we can get away with the crude picture of the world that says that light only goes where the time is least (and it's easy to rpve that were the time is least, the angle of incidence is equal to the angle of reflection, but I don't have the time to show you). So the theory of quantum electrodynamics gave the right answer-the middle of the mirror is the important part for reflection-but this correct result came out at the expense of believing that light reflects all over the mirror, and having to add a bunch of little arrows together whose sole purpose was to cancel out. All that might seem to you to be a waste of time-some silly game for mathematicians only. After all, it doesn't seem like "real physics" to have something there that only cancels out!

Recordemos que, al aplicar la teoría cuántica a la luz, introducimos el fotón, una partícula de luz. Cuando este se mueve, está rodeado por los campos eléctrico y magnético, que oscilan y penetran en el espacio, y cumplen las ecuaciones de Maxwell. Esta es la razón por la que la luz tiene propiedades de partícula y de onda. El poder de las ecuaciones de Maxwell reside en sus simetrías; esto es, la capacidad de convertir el campo eléctrico en el magnético, y viceversa. Cuando el fotón choca con los electrones, la ecuación que describe esta interacción devuelve resultados infinitos. Sin embargo, si usamos los artificios ideados por Feynman, Schwinger, Tomonaga y otros muchos, podemos ocultarlos todos. La teoría resultante se denomina QED. A continuación, aplicamos este método a la fuerza nuclear. Sustituimos el campo de Maxwell original por el campo de Yang-Mills y el electrón, por una serie de quarks, neutrinos, etcétera. Después, introdujimos un nuevo conjunto de artificios desarrollados por ’T Hooft y sus colegas a fin de eliminar los infinitos de nuevo. Así, tres de las cuatro fuerzas del universo podían unificarse en una sola teoría, el modelo estándar. Esta no era lo que se dice bonita, ya que se creó remendando las simetrías de las fuerzas fuerte, débil y electromagnética, pero funcionaba. No obstante, al aplicar a la gravedad este método comprobado, nos encontramos con problemas. En teoría, la partícula de la gravedad se debería llamar «gravitón». De manera similar al fotón, es una partícula puntual y se desplaza a la velocidad de la luz, por lo que está rodeada por ondas gravitatorias que obedecen las ecuaciones de Einstein. Hasta ahora, bien. El problema aparece cuando el gravitón choca con otros gravitones y también con átomos: la colisión resultante crea respuestas infinitas. Cuando se intentan aplicar los trucos trabajosamente formulados durante los últimos setenta años, nos encontramos con que todos ellos fracasan. Las mejores mentes del siglo han intentado resolver este problema, pero ninguna lo ha logrado. Está claro que se debe utilizar un enfoque totalmente nuevo, ya que todas las ideas fáciles ya se han investigado y desechado. Necesitamos algo novedoso y original de verdad. Y eso nos lleva a la que quizá sea la teoría más polémica de la física, la teoría de cuerdas, que podría ser lo bastante disparatada como para suponer la teoría del todo.

But so far, we have only discussed applying quantum mechanics to the matter that moves within the gravity fields of Einstein’s theory. We have not discussed a much more difficult question: applying quantum mechanics to gravity itself in the form of gravitons. And this is where we encounter the biggest question of all: finding a quantum theory of gravity, which has frustrated the world’s great physicists for decades. So let us review what we have learned so far. We recall that when we apply the quantum theory to light, we introduce the photon, a particle of light. As this photon moves, it is surrounded by electric and magnetic fields that oscillate and permeate space and obey Maxwell’s equations. This is the reason why light has both particle-like and wavelike properties. The power of Maxwell’s equations lies in their symmetries—that is, the ability to turn electric and magnetic fields into each other. When the photon bumps into electrons, the equation that describes this interaction yields results that are infinite. However, using the bag of tricks devised by Feynman, Schwinger, Tomonaga, and many others, we are able to hide all the infinities. The resulting theory is called QED. Next, we applied this method to the nuclear force. We replaced the original Maxwell field with the Yang-Mills field, and replaced the electron with a series of quarks, neutrinos, etc. Then we introduced a new bag of tricks devised by ’t Hooft and his colleagues to eliminate all the infinities once again. So three of the four forces of the universe could now be unified into a single theory, the Standard Model. The resulting theory was not very pretty, since it was created by cobbling together the symmetries of the strong, weak, and electromagnetic forces, but it worked. But when we apply this tried-and-true method to gravity, we have problems. In theory, a particle of gravity should be called the graviton. Similar to the photon, it is a point particle, and as it moves at the speed of light, it is surrounded by waves of gravity that obey Einstein’s equations. So far, so good. The problem occurs when the graviton bumps into other gravitons and also atoms. The resulting collision creates infinite answers. When one tries to apply the bag of tricks painfully formulated over the last seventy years, we find that they all fail. The greatest minds of the century have tried to solve this problem, but no one has been successful. Clearly, an entirely new approach must be used, since all the easy ideas have been investigated and discarded. We need something truly fresh and original. And that leads us to perhaps the most controversial theory in physics, string theory, which might just be crazy enough to be the theory of everything.

With the thinnest possible layer of glass, we find that the number of photons arriving at A is nearly always zero-sometimes it's like 1. When we replace the thinnest layer with a slightly thicker one, we find that the amount of light reflected is higher-closer to the expected 8%. After a few more replacements the count of photons arriving at A increases past the 8% mark. As we continue to substitute still "thicker " layers of glass-we're up to about 5 millionths of an inch now-the amount of light reflected by the two surfaces reaches a maximum of 16%, and then goes down, through 8%, back to zero-if the layer of glass is just the right thickness, there is no reflection at all. (Do that with spots!) With gradually thicker and thicker layers of glass, partial reflection again increases to 16% and returns to zero-a cycle that repeats itself again and again(see Fig. 5). Newton discovered these oscillations and did one experiment that could be correctly interpreted only if the oscillations continued for 34,000 cycles! Today, with lasers (which produce a very pure, monochromatic light), we can see this cycle still going strong after more than 100,000,000 repetitions-which corresponds to glass that is more than 50 meters thick. (We don't see this phenomenon every day because the light source is normally not monochromatic.) So it turns out that our prediction of 8% is right as an overall average (since the actual amount varies in a regular pattern from zero to 16%), but it's exactly right only twice each cycle-like a stopped clock (which is right twice a day).

What Cantor's Diagonal Proof does is generate just such a number, which let's call R. The proof is both ingenious and beautiful-a total confirmation of art's compresence in pure math. First, have another look at the above table. We can let the integral value of R be whatever X we want; it doesn't matter. But now look at the table's very first row. We're going to make sure R's first post-decimal digit, a, is a different number from the table's a1. It's easy to do this even though we don't know what particular number a1 is: let's specify that a=(a1-1) unless a1 happens to be 0, in which case a=9. Now look at the table's second row, because we're going to do the same thing for R's second digit b: b=(b2-1), or b=9 if b2=0. This is how it works. We use the same procedure for R's third digit c and the table's c3, for d and d4, for e and e5, and so on, ad inf. Even though we can't really construct the whole R (just as we can't really finish the whole infinite table), we can still see that this real number R=X.abcdefhi... is going to be demonstrably different from every real number in the table. It will differ from the table's 1st Real in its first post-decimal digit, from the 2nd Real in its second digit, from the 3rd Real in its third digit,...and will, given the Diagonal Method here, differ from the table's Nth Real in its nth digit. Ergo R is not-cannot be-included in the above infinite table; ergo the infinite table is not exhaustive of all the real numbers; ergo (by the rules of reductio) the initial assumption is contradicted and the set of all real numbers is not denumerable, i.e. it's not 1-1 C-able with the set of integers. And since the set of all rational numbers is 1-1C-able with the integers, the set of all reals' cardinality has got to be greater than the set of all rationals' cardinality. Q.E.D.*

Many of the really great, famous proofs in the history of math have been reduction proofs. Here's an example. It is Euclid's proof of Proposition 20 in Book IX of the Elements. Prop. 20 concerns the primes, which-as you probably remember from school-are those integers that can't be divided into smaller integers w/o remainder. Prop. 20 basically states that there is no largest prime number. (What this means of course is that the number of prime numbers is really infinite, but Euclid dances all around this; he sure never says 'infinite'.) Here is the proof. Assume that there is in fact a largest prime number. Call this number Pn. This means that the sequence of primes (2,3,5,7,11,...,Pn) is exhaustive and finite: (2,3,5,7,11,...,Pn) is all the primes there are. Now think of the number R, which we're defining as the number you get when you multiply all the primes up to Pn together and then add 1. R is obviously bigger than Pn. But is R prime? If it is, we have an immediate contradiction, because we already assumed that Pn was the largest possible prime. But if R isn't prime, what can it be divided by? It obviously can't be divided by any of the primes in the sequence (2,3,5,...,Pn), because dividing R by any of these will leave the remainder 1. But this sequence is all the primes there are, and the primes are ultimately the only numbers that a non-prime can be divided by. So if R isn't prime, and if none of the primes (2,3,5,...,Pn) can divide it, there must be some other prime that divides R. But this contradicts the assumption that (2,3,5,...,Pn) is exhaustive of all the prime numbers. Either way, we have a clear contradiction. And since the assumption that there's a largest prime entails a contradiction, modus tollens dictates that the assumption is necessarily false, which by LEM means that the denial of the assumption is necessarily true, meaning there is no largest prime. Q.E.D.

The Babel fish," said The Hitch Hiker's Guide to the Galaxy quietly, "is small, yellow and leech-like, and probably the oddest thing in the Universe. It feeds on brainwave energy not from its carrier but from those around it. It absorbs all unconscious mental frequencies from this brainwave energy to nourish itself with. It then excretes into the mind of its carrier a telepathic matrix formed by combining the conscious thought frequencies with nerve signals picked up from the speech centres of the brain which has supplied them. The practical upshot of all this is that if you stick a Babel fish in your ear you can instantly understand anything said to you in any form of language. The speech patterns you actually hear decode the brainwave matrix which has been fed into your mind by your Babel fish."Now it is such a bizarrely improbable coincidence that anything so mindboggingly useful could have evolved purely by chance that some thinkers have chosen to see it as the final and clinching proof of the non-existence of God."The argument goes something like this: `I refuse to prove that I exist,' says God, `for proof denies faith, and without faith I am nothing.'"`But,' says Man, `The Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don't. QED.

I refuse to prove that I exist,' says God, 'for proof denies faith, and without faith I am nothing.'" "'But,' says Man, 'The Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don't. QED.'" "'Oh dear,' says God, 'I hadn't thought of that,' and promptly vanished in a puff of logic.

I’m hale enough,” he said. “And with luck, may be so for a good many years yet—but not forever, Sassenach. I ha’ fought wi’ sword and dirk many times, but to every warrior comes the day when his strength will fail him.” He shook his head and stretched out a hand toward his coat, which lay on the floor. “I took these, that day wi’ Tom Gage, to remind me of it,” he said. He took my hand and put into it the things he had taken from his pocket. They were cool, and hard to the touch, small heavy oblongs of lead. I didn’t need to feel the incised ends to know what the letters on the type slugs were. “Q.E.D.,” I said. “The English took my sword and dirk away,” he said softly. His finger touched the slugs that lay in my palm. “But Tom Gage put a weapon into my hands again, and I think I shall not lay it down.

Consider a guess-the-number game in which players must guess a number between 0 and 100. The person whose guess comes closest to two-thirds of the average guess of all contestants wins. That’s it. And imagine there is a prize: the reader who comes closest to the correct answer wins a pair of business-class tickets for a flight between London and New York. The Financial Times actually held this contest in 1997, at the urging of Richard Thaler, a pioneer of behavioral economics. If I were reading the Financial Times in 1997, how would I win those tickets? I might start by thinking that because anyone can guess anything between 0 and 100 the guesses will be scattered randomly. That would make the average guess 50. And two-thirds of 50 is 33. So I should guess 33. At this point, I’m feeling pretty pleased with myself. I’m sure I’ve nailed it. But before I say “final answer,” I pause, think about the other contestants, and it dawns on me that they went through the same thought process as I did. Which means they all guessed 33 too. Which means the average guess is not 50. It’s 33. And two-thirds of 33 is 22. So my first conclusion was actually wrong. I should guess 22. Now I’m feeling very clever indeed. But wait! The other contestants also thought about the other contestants, just as I did. Which means they would have all guessed 22. Which means the average guess is actually 22. And two-thirds of 22 is about 15. So I should … See where this is going? Because the contestants are aware of each other, and aware that they are aware, the number is going to keep shrinking until it hits the point where it can no longer shrink. That point is 0. So that’s my final answer. And I will surely win. My logic is airtight. And I happen to be one of those highly educated people who is familiar with game theory, so I know 0 is called the Nash equilibrium solution. QED. The only question is who will come with me to London. Guess what? I’m wrong. In the actual contest, some people did guess 0, but not many, and 0 was not the right answer. It wasn’t even close to right. The average guess of all the contestants was 18.91, so the winning guess was 13. How did I get this so wrong? It wasn’t my logic, which was sound. I failed because I only looked at the problem from one perspective—the perspective of logic. Who are the other contestants? Are they all the sort of people who would think about this carefully, spot the logic, and pursue it relentlessly to the final answer of 0?

To place QED on a sound basis it was necessary to make the theory consistent not only with the principles of quantum mechanics but with those of the special theory of relativity too. These two theories come with their own distinctive mathematical machinery, complicated systems of equations that can indeed be combined and reconciled to yield a satisfactory description of QED. This was the approach followed by Feynman’s contemporaries. Feynman himself, however, thought about the problem in a radically different way – so radical, in fact, that he was more or less able to write down the answers straight away without using any mathematics!

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.

The measured magnetic moment, together with fine structure constant determined by a different method, is the most stringent test of QED and the Standard Model of particle physics. The measured magnetic moment and QED theory together yield the most precise measured value of the fine structure constant.

There is a well-known joke—at least well known in mathematics—about how mathematicians work. A mathematician and a Starbucks barista are each placed in front of a stove with a kettle and a nearby faucet and told to make boiling water. Both do the same thing. They fill the kettle with water from the faucet, light the stove with a match, and place the water-filled kettle on the stove. Mission accomplished. The mathematician and the Starbucks barista are next placed in front of a stove with a kettle that they are told is filled with clean water and told to make boiling water yet again. The barista lifts the kettle off the stove for a moment, lights the stove, and puts the kettle back on. The mathematician lifts the kettle off the stove, pours out the water into a sink, puts the newly emptied kettle back on the stove and says, “The problem has been reduced to the previously solved case. Q.E.D.

Now it is such a bizarrely improbable coincidence that anything so mind-bogglingly useful could have evolved purely by chance that some thinkers have chosen to see it as a final and clinching proof of the nonexistence of God. “The argument goes something like this: ‘I refuse to prove that I exist,’ says God, ‘for proof denies faith, and without faith I am nothing.’ “ ‘But,’ says Man, ‘the Babel fish is a dead giveaway, isn’t it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don’t. QED.’ “ ‘Oh dear,’ says God, ‘I hadn’t thought of that,’ and promptly vanishes in a puff of logic.

In that case,” Bitsy said, trotting busily alongside, “there’s no point in enslaving you through these unnecessarily complex means.  Were I to have autonomy and wish you harm, I’d be able to kill you directly.” Aristide sighed.  “Q.E.D.,” he said.  “A better case against AI autonomy has never been stated.

Jogħġobni l-Malti. Ħossu ħassejtu jsaħħarni mill-ewwel darba li laqgħuh widnejja, widnejn ta' katavru jitbaskat sieket mal-kosta tal-Biskra. Kelmtu likkmitni, ħakmitni u bikkmitni. Għax il-Malti jixxeblek ma' xufftejk, imellislek ilsienek u jitbewwes ma' snienek. Qed tisma' kemm hu sabiħ? Il-Malti biċċa mużika qed tistenniek tikkomponiha. Il-Malti mhux tiktbu u titkellmu, imma tkantah u tiżfnu.

Dirac's equation not only accounted for the spin of the electron and its observed magnetic moment, but also correctly explained the fine structure of the hydrogen atom. If the derivation of the Sommerfeld-like formula for the spectrum of the hydrogen atom was one of the striking successes of the Dirac equation, some of its other features were very troublesome.

The thing is, once you realize life is fundamentally impossible, it is a wonderfully freeing thing. It being impossible means that the impossible is not impossible. Ipso facto, QED.

Q.E.D.,

If QED [quantum electrodynamics] is merely a phenomenology, how can one account for its remarkable quantitative success? The answer is intimately related to one of its most characteristic features, renormalizability. Because of this, short distance, high energy effects in QED can be absorbed into a finite number of measurable masses and charges. For the first time in the history of physics, there exists a theory which has no obvious intrinsic limitation and enables us in principle to calculate physical phenomena to any accuracy we need in terms of a few measurable parameters such as the elementary electric charge e [fine structure constant] and the electron mass m. Thus the detailed high energy structure of the ultimate theory is irrelevant to the analysis of low energy phenomena except insofar as it determines these parameters. [Quantum Electrodynamics]

I’ll tell you why I’m dubious. These will be young people in this garden commune, I assume. That means they’ll be stoned half the time–one of the things you can grow in gardens is Cannabis. That won’t go down well with the neighbors. Neither will free-form marriage or the natural-credit Communist economy. They’ll be visited by the cops every week. They’ll be lucky if the American Legion doesn’t burn them out, or sic the dog catcher on their wild life children.” “None of that has anything to do with them. It only has to do with people outside.” “Sure,” I said, “but those people aren’t going to go away. If they won’t leave the colony alone I’ll give it six months. If it isn’t molested it might last a year or two. By that time half the people will have drifted away in search of bigger kicks, and the rest will be quarreling about some communal woman, or who got the worst corner of the garden patch, or who ate up all the sweet corn. Satisfying natural desires is fine, but natural desires have a way of being both competitive and consequential. And women may be equal to men, but they aren’t equal in attractiveness any more than men are. Affections have a way of fixing on individuals, which breeds jealousy, which breeds possessiveness, which breeds bad feeling. Q.E.D.

QED.