Expression Quotes (88 quotes)
Une même expression, dont les géomètres avaient considéré les propriétés abstraites, … représente'aussi le mouvement de la lumière dans l’atmosphère, quelle détermine les lois de la diffusion de la chaleur dans la matière solide, et quelle entre dans toutes les questions principales de la théorie des probabilités.
The same expression whose abstract properties geometers had considered … represents as well the motion of light in the atmosphere, as it determines the laws of diffusion of heat in solid matter, and enters into all the chief problems of the theory of probability.
The same expression whose abstract properties geometers had considered … represents as well the motion of light in the atmosphere, as it determines the laws of diffusion of heat in solid matter, and enters into all the chief problems of the theory of probability.
A biologist, if he wishes to know how many toes a cat has, does not "frame the hypothesis that the number of feline digital extremities is 4, or 5, or 6," he simply looks at a cat and counts. A social scientist prefers the more long-winded expression every time, because it gives an entirely spurious impression of scientificness to what he is doing.
A good theoretical physicist today might find it useful to have a wide range of physical viewpoints and mathematical expressions of the same theory (for example, of quantum electrodynamics) available to him. This may be asking too much of one man. Then new students should as a class have this. If every individual student follows the same current fashion in expressing and thinking about electrodynamics or field theory, then the variety of hypotheses being generated to understand strong interactions, say, is limited. Perhaps rightly so, for possibly the chance is high that the truth lies in the fashionable direction. But, on the off-chance that it is in another direction—a direction obvious from an unfashionable view of field theory—who will find it?
A historical fact is rather like the flamingo that Alice in Wonderland tried to use as a croquet mallet. As soon as she got its neck nicely straightened out and was ready to hit the ball, it would turn and look at her with a puzzled expression, and any biographer knows that what is called a “fact” has a way of doing the same.
Above, far above the prejudices and passions of men soar the laws of nature. Eternal and immutable, they are the expression of the creative power they represent what is, what must be, what otherwise could not be. Man can come to understand the: he is incapable of changing them.
Again, it [the Analytical Engine] might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine. Supposing for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.
Art has a double face, of expression and illusion, just like science has a double face: the reality of error and the phantom of truth.
Art is an expression of the world order and is, therefore, orderly, organic, subject to mathematical law, and susceptible to mathematical analysis.
As physicists have arranged an extensive series of effects under the general term of Heat, so they have named another series Light, and a third they have called Electricity. We find ... that all these principles are capable of being produced through the medium of living bodies, for nearly all animals have the power of evolving heat; many insects, moreover, can voluntarily emit light; and the property of producing electricity is well evinced in the terrible shock of the electric eel, as well as in that of some other creatures. We are indeed in the habit of talking of the Electric fluid, or the Galvanic fluid, but this in reality is nothing but a licence of expression suitable to our finite and material notions.
Ask a scientist what he conceives the scientific method to be, and he will adopt an expression that is at once solemn and shifty eyed: solemn because he feels he ought to declare an opinion; shifty eyed because he is wondering how to conceal the fact that he has no opinion to declare. If taunted he would probably mumble something about “Induction” and “Establishing the Laws of Nature”, but if anyone working in a laboratory professed to be trying to establish the Laws of Nature by induction, we should think he was overdue for leave.
At their best, at their most creative, science and engineering are attributes of liberty—noble expressions of man’s God-given right to investigate and explore the universe without fear of social or political or religious reprisals.
Chemistry has the same quickening and suggestive influence upon the algebraist as a visit to the Royal Academy, or the old masters may be supposed to have on a Browning or a Tennyson. Indeed it seems to me that an exact homology exists between painting and poetry on the one hand and modern chemistry and modern algebra on the other. In poetry and algebra we have the pure idea elaborated and expressed through the vehicle of language, in painting and chemistry the idea enveloped in matter, depending in part on manual processes and the resources of art for its due manifestation.
Each of us has read somewhere that in New Guinea pidgin the word for 'piano' is (I use English spelling) 'this fellow you hit teeth belonging to him he squeal all same pig'. I am inclined to doubt whether this expression is authentic; it looks just like the kind of thing a visitor to the Islands would facetiously invent. But I accept 'cut grass belong head belong me' for 'haircut' as genuine... Such phrases seem very funny to us, and make us feel very superior to the ignorant foreigners who use long winded expressions for simple matters. And then it is our turn to name quite a simple thing, a small uncomplicated molecule consisting of nothing more than a measly 11 carbons, seven hydrogens, one nitrogen and six oxygens. We sharpen our pencils, consult our rule books and at last come up with 3-[(1, 3- dihydro-1, 3-dioxo-2H-isoindol-2-yl) oxy]-3-oxopropanoic acid. A name like that could drive any self-respecting Papuan to piano-playing.
Economists use the expression “opportunity costs” for losses incurred through certain choices made over others, including ignorance and inaction. For systematics, or more precisely the neglect of systematics and the biological research dependent upon it, the costs are very high.
Energy is the measure of that which passes from one atom to another in the course of their transformations. A unifying power, then, but also, because the atom appears to become enriched or exhausted in the course of the exchange, the expression of structure.
Every appearance in nature corresponds to some state of the mind, and that state of the mind can only be described by presenting that natural appearance as its picture. An enraged man is a lion, a cunning man is a fox, a firm man is a rock, a learned man is a torch. A lamb is innocence; a snake is subtle spite; flowers express to us the delicate affections. Light and darkness are our familiar expressions for knowledge and ignorance ; and heat for love. Visible distance behind and before us, is respectively our image of memory and hope.
Every physical fact, every expression of nature, every feature of the earth, the work of any and all of those agents which make the face of the world what it is, and as we see it, is interesting and instructive. Until we get hold of a group of physical facts, we do not know what practical bearings they may have, though right-minded men know that they contain many precious jewels, which science, or the expert hand of philosophy will not fail top bring out, polished, and bright, and beautifully adapted to man's purposes.
Evolution in the biosphere is therefore a necessarily irreversible process defining a direction in time; a direction which is the same as that enjoined by the law of increasing entropy, that is to say, the second law of thermodynamics. This is far more than a mere comparison: the second law is founded upon considerations identical to those which establish the irreversibility of evolution. Indeed, it is legitimate to view the irreversibility of evolution as an expression of the second law in the biosphere.
Experiments may be of two kinds: experiments of simple fact, and experiments of quantity. ...[In the latter] the conditions will ... vary, not in quality, but quantity, and the effect will also vary in quantity, so that the result of quantitative induction is also to arrive at some mathematical expression involving the quantity of each condition, and expressing the quantity of the result. In other words, we wish to know what function the effect is of its conditions. We shall find that it is one thing to obtain the numerical results, and quite another thing to detect the law obeyed by those results, the latter being an operation of an inverse and tentative character.
First, [Newton’s Law of Universal Gravitation] is mathematical in its expression…. Second, it is not exact; Einstein had to modify it…. There is always an edge of mystery, always a place where we have some fiddling around to do yet…. But the most impressive fact is that gravity is simple…. It is simple, and therefore it is beautiful…. Finally, comes the universality of the gravitational law and the fact that it extends over such enormous distances…
For the sake of persons of ... different types, scientific truth should be presented in different forms, and should be regarded as equally scientific, whether it appears in the robust form and the vivid coloring of a physical illustration, or in the tenuity and paleness of a symbolic expression.
He should avail himself of their resources in such ways as to advance the expression of the spirit in the life of mankind. He should use them so as to afford to every human being the greatest possible opportunity for developing and expressing his distinctively human capacity as an instrument of the spirit, as a centre of sensitive and intelligent awareness of the objective universe, as a centre of love of all lovely things, and of creative action for the spirit.
Heredity is the general expression of the periodicity of organic life. All generations belong to a continuous succession of waves, in which every single one resembles its predecessors and its followers.
Hitherto the principle of causality was universally accepted as an indispensable postulate of scientific research, but now we are told by some physicists that it must be thrown overboard. The fact that such an extraordinary opinion should be expressed in responsible scientific quarters is widely taken to be significant of the all-round unreliability of human knowledge. This indeed is a very serious situation.
I can understand your aversion to the use of the term ‘religion’ to describe an emotional and psychological attitude which shows itself most clearly in Spinoza ... I have not found a better expression than ‘religious’ for the trust in the rational nature of reality that is, at least to a certain extent, accessible to human reason.
I do not believe that a moral philosophy can ever be founded on a scientific basis. … The valuation of life and all its nobler expressions can only come out of the soul’s yearning toward its own destiny. Every attempt to reduce ethics to scientific formulas must fail. Of that I am perfectly convinced.
I do not claim that intelligence, however defined, has no genetic basis–I regard it as trivially true, uninteresting, and unimportant that it does. The expression of any trait represents a complex interaction of heredity and environment ... a specific claim purporting to demonstrate a mean genetic deficiency in the intelligence of American blacks rests upon no new facts whatever and can cite no valid data in its support. It is just as likely that blacks have a genetic advantage over whites. And, either way, it doesn’t matter a damn. An individual can’t be judged by his group mean.
I feel very strongly indeed that a Cambridge education for our scientists should include some contact with the humanistic side. The gift of expression is important to them as scientists; the best research is wasted when it is extremely difficult to discover what it is all about ... It is even more important when scientists are called upon to play their part in the world of affairs, as is happening to an increasing extent.
I have found no better expression than ‘religious’ for confidence in the rational nature of reality, insofar as it is accessible to human reason. Whenever this feeling is absent, science degenerates into uninspired empiricism.
I shall devote only a few lines to the expression of my belief in the importance of science ... it is by this daily striving after knowledge that man has raised himself to the unique position he occupies on earth, and that his power and well-being have continually increased.
I should study Nature’s laws in all their crossings and unions; I should follow magnetic streams to their source and follow the shores of our magnetic oceans. I should go among the rays of the aurora, and follow them to their beginnings, and study their dealings and communications with other powers and expressions of matter.
I suppose that I tend to be optimistic about the future of physics. And nothing makes me more optimistic than the discovery of broken symmetries. In the seventh book of the Republic, Plato describes prisoners who are chained in a cave and can see only shadows that things outside cast on the cave wall. When released from the cave at first their eyes hurt, and for a while they think that the shadows they saw in the cave are more real than the objects they now see. But eventually their vision clears, and they can understand how beautiful the real world is. We are in such a cave, imprisoned by the limitations on the sorts of experiments we can do. In particular, we can study matter only at relatively low temperatures, where symmetries are likely to be spontaneously broken, so that nature does not appear very simple or unified. We have not been able to get out of this cave, but by looking long and hard at the shadows on the cave wall, we can at least make out the shapes of symmetries, which though broken, are exact principles governing all phenomena, expressions of the beauty of the world outside.
If A denotes one of the two constant traits, for example, the dominating one, a the recessive, and the Aa the hybrid form in which both are united, then the expression:
A + 2Aa + a
gives the series for the progeny of plants hybrid in a pair of differing traits.
A + 2Aa + a
gives the series for the progeny of plants hybrid in a pair of differing traits.
If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.
If the hand be held between the discharge-tube and the screen, the darker shadow of the bones is seen within the slightly dark shadow-image of the hand itself... For brevity's sake I shall use the expression 'rays'; and to distinguish them from others of this name I shall call them 'X-rays'.
In order that the relations between science and the age may be what they ought to be, the world at large must be made to feel that science is, in the fullest sense, a ministry of good to all, not the private possession and luxury of a few, that it is the best expression of human intelligence and not the abracadabra of a school, that it is a guiding light and not a dazzling fog.
In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.
In the expressions we adopt to prescribe physical phenomena we necessarily hover between two extremes. We either have to choose a word which implies more than we can prove, or we have to use vague and general terms which hide the essential point, instead of bringing it out. The history of electrical theories furnishes a good example.
In the social production of their life, men enter into definite relations that are indispensable and independent of their will; these relations of production correspond to a definite stage of development of their material forces of production. The sum total of these relations of production constitutes the economic structure of society - the real foundation, on which rises a legal and political superstructure and to which correspond definite forms of social consciousness. The mode of production of material life determines the social, political and intellectual life process in general. It is not the consciousness of men that determines their being, but, on the contrary, their social being that determines their consciousness. At a certain stage of their development, the material productive forces in society come in conflict with the existing relations of production, or - what is but a legal expression for the same thing - with the property relations within which they have been at work before. From forms of development of the productive forces these relations turn into fetters. Then begins an epoch of social revolution. With the change of the economic foundation the entire immense superstructure is more or less rapidly transformed. In considering such transformations a distinction should always be made between the material transformation of the economic conditions of production, which can be determined with the precision of natural science, and the legal, political, religious, aesthetic or philosophic - in short, ideological forms in which men become conscious of this conflict and fight it out. Just as our opinion of an individual is not based on what he thinks of himself, so we can not judge of such a period of transformation by its own consciousness; on the contrary, this consciousness must be explained rather from the contradictions of material life, from the existing conflict between the social productive forces and the relations of production. No social order ever disappears before all the productive forces for which there is room in it have been developed; and new, higher relations of production never appear before the material conditions of their existence have matured in the womb of the old society itself. Therefore, mankind always sets itself only such tasks as it can solve; since, looking at the matter more closely, we will always find that the task itself arises only when the material conditions necessary for its solution already exist or are at least in the process of formation. In broad outlines we can designate the Asiatic, the ancient, the feudal, and the modern bourgeois modes of production as so many progressive epochs in the economic formation of society. The bourgeois relations of production are the last antagonistic form of the social process of production - antagonistic not in the sense of individual antagonism, but of one arising from the social conditions of life of the individuals; at the same time the productive forces developing in the womb of bourgeois society create the material conditions for the solution of that antagonism. This social formation constitutes, therefore, the closing chapter of the prehistoric stage of human society.
In the summer of 1937, … I told Banach about an expression Johnny [von Neumann] had once used in conversation with me in Princeton before stating some non-Jewish mathematician’s result, “Die Goim haben den folgendenSatzbewiesen” (The goys have proved the following theorem). Banach, who was pure goy, thought it was one of the funniest sayings he had ever heard. He was enchanted by its implication that if the goys could do it, Johnny and I ought to be able to do it better. Johnny did not invent this joke, but he liked it and we started using it.
Is not Cuvier the great poet of our era? Byron has given admirable expression to certain moral conflicts, but our immortal naturalist has reconstructed past worlds from a few bleached bones; has rebuilt cities, like Cadmus, with monsters’ teeth; has animated forests with all the secrets of zoology gleaned from a piece of coal; has discovered a giant population from the footprints of a mammoth.
It is a good thing for a physician to have prematurely grey hair and itching piles. The first makes him appear to know more than he does, and the second gives him an expression of concern which the patient interprets as being on his behalf.
It is not always the truth that tells us where to look for new knowledge. We don’t search for the penny under the lamp post where the light is. We know we are more likely to find it out there in the darkness. My favorite way of expressing this notion to graduate students who are trying to do very hard experiments is to remind them that “God loves the noise as much as he does the signal.”
It is the constant aim of the mathematician to reduce all his expressions to their lowest terms, to retrench every superfluous word and phrase, and to condense the Maximum of meaning into the Minimum of language.
It is very desirable to have a word to express the Availability for work of the heat in a given magazine; a term for that possession, the waste of which is called Dissipation. Unfortunately the excellent word Entropy, which Clausius has introduced in this connexion, is applied by him to the negative of the idea we most naturally wish to express. It would only confuse the student if we were to endeavour to invent another term for our purpose. But the necessity for some such term will be obvious from the beautiful examples which follow. And we take the liberty of using the term Entropy in this altered sense ... The entropy of the universe tends continually to zero.
Laws alone can not secure freedom of expression; in order that every man present his views without penalty there must be spirit of tolerance in the entire population.
Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.
Museums are, in a way, the cathedrals of the modern world, places where sacred issues are expressed and where people come to reflect on them. A museum is also a kind of bridge between the academy and the public.
One of the principal obstacles to the rapid diffusion of a new idea lies in the difficulty of finding suitable expression to convey its essential point to other minds. Words may have to be strained into a new sense, and scientific controversies constantly resolve themselves into differences about the meaning of words. On the other hand, a happy nomenclature has sometimes been more powerful than rigorous logic in allowing a new train of thought to be quickly and generally accepted.
Our confused wish finds expression in the confused question as to the nature of force and electricity. But the answer which we want is not really an answer to this question. It is not by finding out more and fresh relations and connections that it can be answered; but by removing the contradictions existing between those already known, and thus perhaps by reducing their number. When these painful contradictions are removed, the question as to the nature of force will not have been answered; but our minds, no longer vexed, will cease to ask illegitimate questions.
Over the past fifty years or so, scientists have allowed the conventions of expression available to them to become entirely too confining. too confining. The insistence on bland impersonality and the widespread indifference to anything like the display of a unique human author in scientific exposition, have transformed the reading of most scientific papers into an act of tedious drudgery.
Perhaps we see equations as simple because they are easily expressed in terms of mathematical notation already invented at an earlier stage of development of the science, and thus what appears to us as elegance of description really reflects the interconnectedness of Nature's laws at different levels.
Religion and science ... constitute deep-rooted and ancient efforts to find richer experience and deeper meaning than are found in the ordinary biological and social satisfactions. As pointed out by Whitehead, religion and science have similar origins and are evolving toward similar goals. Both started from crude observations and fanciful concepts, meaningful only within a narrow range of conditions for the people who formulated them of their limited tribal experience. But progressively, continuously, and almost simultaneously, religious and scientific concepts are ridding themselves of their coarse and local components, reaching higher and higher levels of abstraction and purity. Both the myths of religion and the laws of science, it is now becoming apparent, are not so much descriptions of facts as symbolic expressions of cosmic truths.
Science is not the enemy of humanity but one of the deepest expressions of the human desire to realize that vision of infinite knowledge. Science shows us that the visible world is neither matter nor spirit; the visible world is the invisible organization of energy.
Sir Hiram Maxim is a genuine and typical example of the man of science, romantic, excitable, full of real but somewhat obvious poetry, a little hazy in logic and philosophy, but full of hearty enthusiasm and an honorable simplicity. He is, as he expresses it, “an old and trained engineer,” and is like all of the old and trained engineers I have happened to come across, a man who indemnifies himself for the superhuman or inhuman concentration required for physical science by a vague and dangerous romanticism about everything else.
The artist does not illustrate science; … [but] he frequently responds to the same interests that a scientist does, and expresses by a visual synthesis what the scientist converts into analytical formulae or experimental demonstrations.
The beauty and genius of a work of art may be reconceived, though its first material expression be destroyed; a vanished harmony may yet again inspire the composer, but when the last individual of a race of living things breathes no more, another heaven and another earth must pass before such a one can be again.
The expression Similia similibus is a Latin phrase and means that an imaginary disease can best be cured by an imaginary remedy.
The exterior appearance of human life is but the material embodiment, the substantial expression, of thought—the hieroglyphic writing of the soul.
The fascination of any search after truth lies not in the attainment, which at best is found to be very relative, but in the pursuit, where all the powers of the mind and character are brought into play and are absorbed by the task. One feels oneself in contact with something that is infinite and one finds joy that is beyond expression in sounding the abyss of science and the secrets of the infinite mind.
The great object of human thought is the discovery of truth or, in other words, to arrive at conceptions and expressions of things which shall agree with the nature of things.
The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. Out of it grew, in the mind of classical antiquity, the idea of pure science. Geometry became one of the most powerful expressions of that sovereignty of the intellect that inspired the thought of those times. At a later epoch, when the intellectual despotism of the Church, which had been maintained through the Middle Ages, had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science “more geometrico.”
The laws expressing the relations between energy and matter are, however, not solely of importance in pure science. They necessarily come first in order ... in the whole record of human experience, and they control, in the last resort, the rise or fall of political systems, the freedom or bondage of nations, the movements of commerce and industry, the origin of wealth and poverty, and the general physical welfare of the race.
The meaning of life is contained in every single expression of life. It is present in the infinity of forms and phenomena that exist in all of creation.
The method of scientific investigation is nothing but the expression of the necessary mode of working of the human mind. It is simply the mode at which all phenomena are reasoned about, rendered precise and exact.
The more an idea is developed, the more concise becomes its expression: the more a tree is pruned, the better is the fruit.
The most abstract statements or propositions in science are to be regarded as bundles of hypothetical maxims packed into a portable shape and size. Every scientific fact is a short-hand expression for a vast number of practical directions: if you want so-and-so, do so-and-so.
The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression, more exact, compact, and ready than ordinary language. The great body of physical science, a great deal of the essential facts of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of the great complex world-wide States that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write.
The quantum hypothesis will eventually find its exact expression in certain equations which will be a more exact formulation of the law of causality.
The self is the class (not the collection) of the experiences (or autopsychological states). The self does not belong to the expression of the basic experience, but is constructed only on a very high level.
The typewriting machine, when played with expression, is no more annoying than the piano when played by a sister or near relation.
There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that... or: There is capitalism in so far as... The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills. [p.222]
There is no art so difficult as the art of observation: it requires a skillful, sober spirit and a well-trained experience, which can only be acquired by practice; for he is not an observer who only sees the thing before him with his eyes, but he who sees of what parts the thing consists, and in what connexion the parts stand to the whole. One person overlooks half from inattention; another relates more than he sees while he confounds it with that which he figures to himself; another sees the parts of the whole, but he throws things together that ought to be separated. ... When the observer has ascertained the foundation of a phenomenon, and he is able to associate its conditions, he then proves while he endeavours to produce the phenomena at his will, the correctness of his observations by experiment. To make a series of experiments is often to decompose an opinion into its individual parts, and to prove it by a sensible phenomenon. The naturalist makes experiments in order to exhibit a phenomenon in all its different parts. When he is able to show of a series of phenomena, that they are all operations of the same cause, he arrives at a simple expression of their significance, which, in this case, is called a Law of Nature. We speak of a simple property as a Law of Nature when it serves for the explanation of one or more natural phenomena.
There is nothing which Nature so clearly reveals, and upon which science so strongly insists, as the universal reign of law, absolute, universal, invariable law... Not one jot or tittle of the laws of Nature are unfulfilled. I do not believe it is possible to state this fact too strongly... Everything happens according to law, and, since law is the expression of Divine will, everything happens according to Divine will, i.e. is in some sense ordained, decreed.
There was once an Editor of the Chemical Society, given to dogmatic expressions of opinion, who once duly said firmly that 'isomer' was wrong usage and 'isomeride' was correct, because the ending 'er' always meant a 'do-er'. 'As in water?' snapped Sidgwick.
There was yet another disadvantage attaching to the whole of Newton’s physical inquiries, ... the want of an appropriate notation for expressing the conditions of a dynamical problem, and the general principles by which its solution must be obtained. By the labours of LaGrange, the motions of a disturbed planet are reduced with all their complication and variety to a purely mathematical question. It then ceases to be a physical problem; the disturbed and disturbing planet are alike vanished: the ideas of time and force are at an end; the very elements of the orbit have disappeared, or only exist as arbitrary characters in a mathematical formula
This theme of mutually invisible life at widely differing scales bears an important implication for the ‘culture wars’ that supposedly now envelop our universities and our intellectual discourse in general ... One side of this false dichotomy features the postmodern relativists who argue that all culturally bound modes of perception must be equally valid, and that no factual truth therefore exists. The other side includes the benighted, old-fashioned realists who insist that flies truly have two wings, and that Shakespeare really did mean what he thought he was saying. The principle of scaling provides a resolution for the false parts of this silly dichotomy. Facts are facts and cannot be denied by any rational being. (Often, facts are also not at all easy to determine or specify–but this question raises different issues for another time.) Facts, however, may also be highly scale dependent–and the perceptions of one world may have no validity or expression in the domain of another. The one-page map of Maine cannot recognize the separate boulders of Acadia, but both provide equally valid representations of a factual coastline.
Though to the layman, the world revealed by the chemist may seem more commonplace, it is not so to him. Each new insight into how the atoms in their interactions express themselves in structure and transformations, not only of inanimate matter, but particularly also of living matter, provides a thrill.
To me, science is an expression of the human spirit, which reaches every sphere of human culture. It gives an aim and meaning to existence as well as a knowledge, understanding, love, and admiration for the world. It gives a deeper meaning to morality and another dimension to esthetics.
To sum up all, let it be known that science and religion are two identical words. The learned do not suspect this, no more do the religious. These two words express the two sides of the same fact, which is the infinite. Religion—Science, this is the future of the human mind.
Very little of Roman literature will find its way into the kingdom of heaven, when the events of this world will have lost their importance. The languages of heaven will be Chinese, Greek, French, German, Italian, and English, and the blessed Saints will dwell with delight on these golden expressions of eternal life. They will be wearied with the moral fervour of Hebrew literature in its battle with a vanished evil, and with Roman authors who have mistaken the Forum for the footstool of the living God.
We must take the abiding spiritual values which inhere in the deep experiences of religion in all ages and give them new expression in terms of the framework which our new knowledge gives us. Science forces religion to deal with new ideas in the theoretical realm and new forces in the practical realm.
When a thinker improves in expression, it is as if he thought better than before.
When physicists speak of “beauty” in their theories, they really mean that their theory possesses at least two essential features: 1. A unifying symmetry 2. The ability to explain vast amounts of experimental data with the most economical mathematical expressions.
[Describing a freshman seminar titled “How the Tabby Cat Got Her Stripes or The Silence of the Genes”:] The big idea we start with is: “How is the genome interpreted, and how are stable decisions that affect gene expression inherited from one cell to the next? This is one of the most competitive areas of molecular biology at the moment, and the students are reading papers that in some instances were published this past year. As a consequence, one of the most common answers I have to give to their questions is, “We just don't know.”
[In 1909,] Paris was the center of the aviation world. Aeronautics was neither an industry nor even a science; both were yet to come. It was an “art” and I might say a “passion”. Indeed, at that time it was a miracle. It meant the realization of legends and dreams that had existed for thousands of years and had been pronounced again and again as impossible by scientific authorities. Therefore, even the brief and unsteady flights of that period were deeply impressive. Many times I observed expressions of joy and tears in the eyes of witnesses who for the first time watched a flying machine carrying a man in the air.
[In the Royal Society, there] has been, a constant Resolution, to reject all the amplifications, digressions, and swellings of style: to return back to the primitive purity, and shortness, when men deliver'd so many things, almost in an equal number of words. They have exacted from all their members, a close, naked, natural way of speaking; positive expressions; clear senses; a native easiness: bringing all things as near the Mathematical plainness, as they can: and preferring the language of Artizans, Countrymen, and Merchants, before that, of Wits, or Scholars.
[T]he idea of protoplasm, which was really a name for our ignorance, [is] only a little less misleading than the expression “Vital force”.