Category: Science

“What we call the stars are only inferences, inferences drawn from the only physical reality we have yet gotten from them—from a careful study of the unendingly complex undulations of the electric and magnetic fields reaching us on earth.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. II

“By experiments with charges and currents we find a number c2 which turns out to be the square of the velocity of propagation of electromagnetic influences. From static measurements—by measuring the forces between two unit charges and between two unit currents—we find that c=3.00×108 meters/sec. When [James Clerk] Maxwell first made this calculation with his equations, he said that bundles of electric and magnetic fields should be propagated at this speed. He also remarked on the mysterious coincidence that this was the same as the speed of light. ‘We can scarcely avoid the inference,’ said Maxwell, ‘that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.’ Maxwell had made one of the great unifications of physics. Before his time, there was light, and there was electricity and magnetism. The latter two had been unified by the experimental work of Faraday, Oersted, and Ampère. Then, all of a sudden, light was no longer ‘something else,’ but was only electricity and magnetism in this new form—little pieces of electric and magnetic fields which propagate through space on their own.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. II

“One of the basic laws of physics is that electric charge is indestructible; it is never lost or created. Electric charges can move from place to place but never appear from nowhere. We say that charge is conserved.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. II (emphases in original)

“The total amount of information which has been acquired about the physical world since the beginning of scientific progress is enormous, and it seems almost impossible that any one person could know a reasonable fraction of it. But it is actually quite possible for a physicist to retain a broad knowledge of the physical world rather than to become a specialist in some narrow area. The reasons for this are threefold: First, there are great principles which apply to all the different kinds of phenomena—such as the principles of the conservation of energy and of angular momentum. A thorough understanding of such principles gives an understanding of a great deal all at once. Second, there is the fact that many complicated phenomena, such as the behavior of solids under compression, really basically depend on electrical and quantum-mechanical forces, so that if one understands the fundamental laws of electricity and quantum mechanics, there is at least some possibility of understanding many of the phenomena that occur in complex situations. Finally, there is a most remarkable coincidence: The equations for many different physical situations have exactly the same appearance. Of course, the symbols may be different—one letter is substituted for another—but the mathematical form of the equations is the same. This means that having studied one subject, we immediately have a great deal of direct and precise knowledge about the solutions of the equations of another.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. II

“Whenever one is trying to understand a new phenomenon it is a good idea to take a somewhat oversimplified model; then, having understood the problem with that model, one is better able to proceed to tackle the more exact calculation.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. II

“Birds are dinosaurs in the same way that bats are mammals.” – Gregory S. Paul, The Princeton Field Guide to Dinosaurs

“The more clearly you picture the history of life as an unbroken series of ecosystems, and not just a line of related species, the more clearly you understand the tragedy of what we’re doing to Earth, the consequences of depleting the planet we like to claim we’ve inherited.” – Verlyn Klinkenborg, “What Were Dinosaurs For?”

“From a long view of the history of mankind—seen from, say, ten thousand years from now—there can be little doubt that the most significant event of the 19th century will be judged as Maxwell’s discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. II

“The entire universe is in a glass of wine, if we look at it closely enough.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. I

“The retina is, in fact, the brain: in the development of the embryo, a piece of the brain comes out in front, and long fibers grow back, connecting the eyes to the brain. The retina is organized in just the way the brain is organized and, as someone has beautifully put it, ‘The brain has developed a way to look out upon the world.’ The eye is a piece of brain that is touching light, so to speak, on the outside.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. I

“I’d hate to die twice. It’s so boring.” – Richard P. Feynman’s last words, as reported by Alan Lightman in “The One and Only”

“No pencil has ever yet given anything like the true effect of an iceberg. In a picture, they are huge, uncouth masses, stuck in the sea, while their chief beauty and grandeur,—their slow, stately motion; the whirling of the snow about their summits, and the fearful groaning and cracking of their parts,—the picture cannot give. This is the large iceberg; while the small and distant islands, floating on the smooth sea, in the light of a clear day, look like little floating fairy isles of sapphire.” – Richard Henry Dana, Two Years Before the Mast

“At twelve o’clock we went below, and had just got through dinner, when the cook put his head down the scuttle and told us to come on deck and see the finest sight that we had ever seen. ‘Where away, cook?’ asked the first man who was up. ‘On the larboard bow.’ And there lay, floating in the ocean, several miles off, an immense, irregular mass, its top and points covered with snow, and its center of a deep indigo color. This was an iceberg, and of the largest size, as one of our men said who had been in the Northern ocean. As far as the eye could reach, the sea in every direction was of a deep blue color, the waves running high and fresh, and sparkling in the light, and in the midst lay this immense mountain-island, its cavities and valleys thrown into deep shade, and its points and pinnacles glittering in the sun. All hands were soon on deck, looking at it, and admiring in various ways its beauty and grandeur. But no description can give any idea of the strangeness, splendor, and, really, the sublimity, of the sight. Its great size;—for it must have been from two to three miles in circumference, and several hundred feet in height;—its slow motion, as its base rose and sank in the water, and its high points nodded against the clouds; the dashing of the waves upon it, which, breaking high with foam, lined its base with a white crust; and the thundering sound of the cracking of the mass, and the breaking and tumbling down of huge pieces; together with its nearness and approach, which added a slight element of fear,—all combined to give to it the character of true sublimity. The main body of the mass was, as I have said, of an indigo color, its base crusted with frozen foam; and as it grew thin and transparent toward the edges and top, its color shaded off from a deep blue to the whiteness of snow.” – Richard Henry Dana, Two Years Before the Mast

“The difficulties of science are to a large extent the difficulties of notations, the units, and all the other artificialities which are invented by man, not by nature.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. I

“It will turn out . . . that many simple things can be deduced mathematically more rapidly than they can be really understood in a fundamental or simple sense. This is a strange characteristic, and . . . there are circumstances in which mathematics will produce results which no one has really been able to understand in any direct fashion.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. I (emphasis in original)

“Suppose that the true laws of motion of atoms were given by some strange equation which does not have the property that when we go to a larger scale we reproduce the same law, but instead has the property that if we go to a larger scale, we can approximate it by a certain expression such that, if we extend that expression up and up, it keeps reproducing itself on a larger and larger scale. That is possible, and in fact that is the way it works. Newton’s laws are the ‘tail end’ of the atomic laws, extrapolated to a very large size. The actual laws of motion of particles on a fine scale are very peculiar, but if we take large numbers of them and compound them, they approximate, but only approximate, Newton’s laws. Newton’s laws then permit us to go on to a higher and higher scale, and it still seems to be the same law. In fact, it becomes more and more accurate as the scale gets larger and larger. This self-reproducing factor of Newton’s laws is thus really not a fundamental feature of nature, but is an important historical feature. We would never discover the fundamental laws of the atomic particles at first observation because the first observations are much too crude. In fact, it turns out that the fundamental atomic laws, which we call quantum mechanics, are quite different from Newton’s laws, and are difficult to understand because all our direct experiences are with large-scale objects and the small-scale atoms behave like nothing we see on a large scale. So we cannot say, ‘An atom is just like a planet going around the sun,’ or anything like that. It is like nothing we are familiar with because there is nothing like it. As we apply quantum mechanics to larger and larger things, the laws about the behavior of many atoms together do not reproduce themselves, but produce new laws, which are Newton’s laws, which then continue to reproduce themselves from, say, micro-microgram size, which still is billions and billions of atoms, on up to the size of the earth, and above.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. I (emphases in original)

“Space of itself, and time of itself will sink into mere shadows, and only a kind of union between them shall survive.” – Hermann Minkowski (quoted by Richard P. Feynman, The Feynman Lectures on Physics, Vol. I)

“Do not laugh at notations; invent them, they are powerful. In fact, mathematics is, to a large extent, invention of better notations.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. I

“What we mean by ‘right now’ is a mysterious thing which we cannot define and we cannot affect, but it can affect us later, or we could have affected it if we had done something far enough in the past. When we look at the star Alpha Centauri, we see it as it was four years ago; we might wonder what it is like ‘now.’ ‘Now’ means at the same time from our special coordinate system. We can only see Alpha Centauri by the light that has come from our past, up to four years ago, but we do not know what it is doing ‘now’; it will take four years before what it is doing ‘now’ can affect us. Alpha Centauri ‘now’ is an idea or concept of our mind; it is not something that is really definable physically at the moment, because we have to wait to observe it; we cannot even define it right ‘now.’ Furthermore, the ‘now’ depends on the coordinate system. If, for example, Alpha Centauri were moving, an observer there would not agree with us because he would put his axes at an angle, and his ‘now’ would be a different time.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. I (emphasis in original)

“Poincaré made the following statement of the principle of relativity: ‘According to the principle of relativity, the laws of physical phenomena must be the same for a fixed observer as for an observer who has a uniform motion of translation relative to him, so that we have not, nor can we possibly have, any means of discerning whether or not we are carried along in such a motion.’ When this idea descended upon the world, it caused a great stir among philosophers, particularly the ‘cocktail-party philosophers,’ who say, ‘Oh, it is very simple: Einstein’s theory says all is relative!’ In fact, a surprisingly large number of philosophers, not only those found at cocktail parties (but rather than embarrass them, we shall just call them ‘cocktail-party philosophers’), will say, ‘That all is relative is a consequence of Einstein, and it has profound influences on our ideas.’ In addition, they say ‘It has been demonstrated in physics that phenomena depend upon your frame of reference.’ We hear that a great deal, but it is difficult to find out what it means. Probably the frames of reference that were originally referred to were the coordinate systems which we use in the analysis of the theory of relativity. So the fact that ‘things depend upon your frame of reference’ is supposed to have had a profound effect on modern thought. One might well wonder why, because, after all, that things depend upon one’s point of view is so simple an idea that it certainly cannot have been necessary to go to all the trouble of the physical relativity theory in order to discover it. That what one sees depends upon his frame of reference is certainly known to anybody who walks around, because he sees an approaching pedestrian first from the front and then from the back; there is nothing deeper in most of the philosophy which is said to have come from the theory of relativity than the remark that ‘A person looks different from the front than from the back.’ The old story about the elephant that several blind men describe in different ways is another example, perhaps, of the theory of relativity from the philosopher’s point of view. But certainly there must be deeper things in the theory of relativity than just this simple remark that ‘A person looks different from the front than from the back.’ Of course relativity is deeper than this, because we can make definite predictions with it. It certainly would be rather remarkable if we could predict the behavior of nature from such a simple observation alone.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. I (emphasis in original)

“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.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. I (emphasis in original)

“The glory of mathematics is that we do not have to say what we are talking about. The glory is that the laws, the arguments, and the logic are independent of what ‘it’ is. If we have any other set of objects that obey the same system of axioms as Euclid’s geometry, then if we make new definitions and follow them out with correct logic, all the consequences will be correct, and it makes no difference what the subject was. In nature, however, when we draw a line or establish a line by using a light beam and a theodolite, as we do in surveying, are we measuring a line in the sense of Euclid? No, we are making an approximation; the cross hair has some width, but a geometrical line has no width, and so, whether Euclidean geometry can be used for surveying or not is a physical question, not a mathematical question. However, from an experimental standpoint, not a mathematical standpoint, we need to know whether the laws of Euclid apply to the kind of geometry that we use in measuring land; so we make a hypothesis that it does, and it works pretty well; but it is not precise, because our surveying lines are not really geometrical lines. Whether or not those lines of Euclid, which are really abstract, apply to the lines of experience is a question for experience; it is not a question that can be answered by sheer reason.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. I (emphasis in original)

“In order to understand physical laws you must understand that they are all some kind of approximation. Any simple idea is approximate; as an illustration, consider an object, … what is an object? Philosophers are always saying, ‘Well, just take a chair for example.’ The moment they say that, you know that they do not know what they are talking about any more. What is a chair? Well, a chair is a certain thing over there … certain?, how certain? The atoms are evaporating from it from time to time—not many atoms, but a few—dirt falls on it and gets dissolved in the paint; so to define a chair precisely, to say exactly which atoms are chair, and which atoms are air, or which atoms are dirt, or which atoms are paint that belongs to the chair is impossible. So the mass of a chair can be defined only approximately. In the same way, to define the mass of a single object is impossible, because there are not any single, left-alone objects in the world—every object is a mixture of a lot of things, so we can deal with it only as a series of approximations and idealizations.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. I (emphases in original)

“We cannot define anything precisely! If we attempt to, we get into that paralysis of thought that comes to philosophers, who sit opposite each other, one saying to the other, ‘You don’t know what you are talking about!’ The second one says, ‘What do you mean by know? What do you mean by talking? What do you mean by you?,’ and so on. In order to be able to talk constructively, we just have to agree that we are talking about roughly the same thing.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. I (emphases in original)

“Our most precise description of nature must be in terms of probabilities. There are some people who do not like this way of describing nature.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. I (emphases in original)

“The true logic of this world is in the calculus of probabilities.” – James Clerk Maxwell (quoted by Richard P. Feynman in The Feynman Lectures on Physics, Vol. I )

“What is time? It would be nice if we could find a good definition of time. Webster defines ‘a time’ as ‘a period,’ and the latter as ‘a time,’ which doesn’t seem to be very useful. Perhaps we should say: ‘Time is what happens when nothing else happens.’ Which also doesn’t get us very far. Maybe it is just as well if we face the fact that time is one of the things we probably cannot define (in the dictionary sense), and just say that it is what we already know it to be: it is how long we wait!” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. I (emphasis in original)

“An object has energy from its sheer existence.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. I (emphasis in original)

“A poet once said, ‘The whole universe is in a glass of wine.’ We will probably never know in what sense he meant that, for poets do not write to be understood. But it is true that if we look at a glass of wine closely enough we see the entire universe.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. I

“The things with which we concern ourselves in science appear in myriad forms, and with a multitude of attributes. For example, if we stand on the shore and look at the sea, we see the water, the waves breaking, the foam, the sloshing motion of the water, the sound, the air, the winds and the clouds, the sun and the blue sky, and light; there is sand and there are rocks of various hardness and permanence, color and texture. There are animals and seaweed, hunger and disease, and the observer on the beach; there may be even happiness and thought. Any other spot in nature has a similar variety of things and influences. It is always as complicated as that, no matter where it is. 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.” – Richard P. Feynman, The Feynman Lectures on Physics, Vol. 1