...for our wisdom is better than the strength of men or of horses. ... nor is it right to prefer strength to excellent wisdom. For if there should be in the city [any athlete whose skill] is honoured more than strength ... the city would not on that account be any better governed.

...That day in the account of creation, or those days that are numbers according to its recurrence, are beyond the experience and knowledge of us mortal earthbound men. And if we are able to make any effort towards an understanding of those days, we ought not to rush forward with an ill considered opinion, as if no other reasonable and plausible interpretation could be offered.

[The] subjective [historical] element in geologic studies accounts for two characteristic types that can be distinguished among geologists: one considering geology as a creative art, the other regarding geology as an exact science.

[We] can easily distinguish what relates to Mathematics in any question from that which belongs to the other sciences. But as I considered the matter carefully it gradually came to light that all those matters only were referred to Mathematics in which order and measurements are investigated, and that it makes no difference whether it be in numbers, figures, stars, sounds or any other object that the question of measurement arises. I saw consequently that there must be some general science to explain that element as a whole which gives rise to problems about order and measurement, restricted as these are to no special subject matter. This, I perceived was called “Universal Mathematics,” not a far-fetched asignation, but one of long standing which has passed into current use, because in this science is contained everything on account of which the others are called parts of Mathematics.

In a 1852 letter, Nightingale records the opinion of a young surgeon:
The account he gives of nurses beats everything that even I know of. This young prophet says that they are all drunkards, without exception, Sisters and all, and that there are but two whom the surgeon can trust to give the patients their medicines.

Question: A hollow indiarubber ball full of air is suspended on one arm of a balance and weighed in air. The whole is then covered by the receiver of an air pump. Explain what will happen as the air in the receiver is exhausted.
Answer: The ball would expand and entirely fill the vessell, driving out all before it. The balance being of greater density than the rest would be the last to go, but in the end its inertia would be overcome and all would be expelled, and there would be a perfect vacuum. The ball would then burst, but you would not be aware of the fact on account of the loudness of a sound varying with the density of the place in which it is generated, and not on that in which it is heard.

Question: Account for the delicate shades of colour sometimes seen on the inside of an oyster shell. State and explain the appearance presented when a beam of light falls upon a sheet of glass on which very fine equi-distant parallel lines have been scratched very close to one another.
Answer: The delicate shades are due to putrefaction; the colours always show best when the oyster has been a bad one. Hence they are considered a defect and are called chromatic aberration.
The scratches on the glass will arrange themselves in rings round the light, as any one may see at night in a tram car.

A chemical compound once formed would persist for ever, if no alteration took place in surrounding conditions. But to the student of Life the aspect of nature is reversed. Here, incessant, and, so far as we know, spontaneous change is the rule, rest the exception—the anomaly to be accounted for. Living things have no inertia and tend to no equilibrium.

A first step in the study of civilization is to dissect it into details, and to classify these in their proper groups. Thus, in examining weapons, they are to be classed under spear, club, sling, bow and arrow, and so forth; among textile arts are to be ranged matting, netting, and several grades of making and weaving threads; myths are divided under such headings as myths of sunrise and sunset, eclipse-myths, earthquake-myths, local myths which account for the names of places by some fanciful tale, eponymic myths which account for the parentage of a tribe by turning its name into the name of an imaginary ancestor; under rites and ceremonies occur such practices as the various kinds of sacrifice to the ghosts of the dead and to other spiritual beings, the turning to the east in worship, the purification of ceremonial or moral uncleanness by means of water or fire. Such are a few miscellaneous examples from a list of hundreds … To the ethnographer, the bow and arrow is the species, the habit of flattening children’s skulls is a species, the practice of reckoning numbers by tens is a species. The geographical distribution of these things, and their transmission from region to region, have to be studied as the naturalist studies the geography of his botanical and zoological species.

A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.

A physician’s subject of study is necessarily the patient, and his first field for observation is the hospital. But if clinical observation teaches him to know the form and course of diseases, it cannot suffice to make him understand their nature; to this end he must penetrate into the body to find which of the internal parts are injured in their functions. That is why dissection of cadavers and microscopic study of diseases were soon added to clinical observation. But to-day these various methods no longer suffice; we must push investigation further and, in analyzing the elementary phenomena of organic bodies, must compare normal with abnormal states. We showed elsewhere how incapable is anatomy alone to take account of vital phenenoma, and we saw that we must add study of all physico-chemical conditions which contribute necessary elements to normal or pathological manifestations of life. This simple suggestion already makes us feel that the laboratory of a physiologist-physician must be the most complicated of all laboratories, because he has to experiment with phenomena of life which are the most complex of all natural phenomena.

A science calling itself “psychology” and professing to be a science of the human mind (not merely the sick mind), ought to form its estimate of human beings by taking into account healthy minds as well as sick ones.

A student who wishes now-a-days to study geometry by dividing it sharply from analysis, without taking account of the progress which the latter has made and is making, that student no matter how great his genius, will never be a whole geometer. He will not possess those powerful instruments of research which modern analysis puts into the hands of modern geometry. He will remain ignorant of many geometrical results which are to be found, perhaps implicitly, in the writings of the analyst. And not only will he be unable to use them in his own researches, but he will probably toil to discover them himself, and, as happens very often, he will publish them as new, when really he has only rediscovered them.

A wonderful exhilaration comes from holding in the mind the deepest questions we can ask. Such questions animate all scientists. Many students of science were first attracted to the field as children by popular accounts of important unsolved problems. They have been waiting ever since to begin working on a mystery. [With co-author Arthur Zajonc]

Abstruse mathematical researches … are … often abused for having no obvious physical application. The fact is that the most useful parts of science have been investigated for the sake of truth, and not for their usefulness. A new branch of mathematics, which has sprung up in the last twenty years, was denounced by the Astronomer Royal before the University of Cambridge as doomed to be forgotten, on account of its uselessness. Now it turns out that the reason why we cannot go further in our investigations of molecular action is that we do not know enough of this branch of mathematics.

Adam is fading out. It is on account of Darwin and that crowd. I can see that he is not going to last much longer. There's a plenty of signs. He is getting belittled to a germ—a little bit of a speck that you can't see without a microscope powerful enough to raise a gnat to the size of a church. They take that speck and breed from it: first a flea; then a fly, then a bug, then cross these and get a fish, then a raft of fishes, all kinds, then cross the whole lot and get a reptile, then work up the reptiles till you've got a supply of lizards and spiders and toads and alligators and Congressmen and so on, then cross the entire lot again and get a plant of amphibiums, which are half-breeds and do business both wet and dry, such as turtles and frogs and ornithorhyncuses and so on, and cross-up again and get a mongrel bird, sired by a snake and dam'd by a bat, resulting in a pterodactyl, then they develop him, and water his stock till they've got the air filled with a million things that wear feathers, then they cross-up all the accumulated animal life to date and fetch out a mammal, and start-in diluting again till there's cows and tigers and rats and elephants and monkeys and everything you want down to the Missing Link, and out of him and a mermaid they propagate Man, and there you are! Everything ship-shape and finished-up, and nothing to do but lay low and wait and see if it was worth the time and expense.

Aging is an inevitable process. I surely wouldn't want to grow younger. The older you become, the more you know; your bank account of knowledge is much richer.

All knowledge is good. It is impossible to say any fragment of knowledge, however insignificant or remote from one’s ordinary pursuits, may not some day be turned to account.

All those things [scientific research] which you would think would recommend me to the trustees my opponent is using against me. I am shamefully abused as being an atheist, an infidel. It has been positively asserted that I seek to make proselytes to infidelity, and that in my writings I have tried to prove that geology overthrows the Mosaic account of the creation. You may judge of my feelings.”

Always preoccupied with his profound researches, the great Newton showed in the ordinary-affairs of life an absence of mind which has become proverbial. It is related that one day, wishing to find the number of seconds necessary for the boiling of an egg, he perceived, after waiting a minute, that he held the egg in his hand, and had placed his seconds watch (an instrument of great value on account of its mathematical precision) to boil!
This absence of mind reminds one of the mathematician Ampere, who one day, as he was going to his course of lectures, noticed a little pebble on the road; he picked it up, and examined with admiration the mottled veins. All at once the lecture which he ought to be attending to returned to his mind; he drew out his watch; perceiving that the hour approached, he hastily doubled his pace, carefully placed the pebble in his pocket, and threw his watch over the parapet of the Pont des Arts.

Among our sensations it is difficult not to confuse what comes from the part of objects with what comes from the part of our senses. … Supposing this, one clearly sees that it is not easy to say much about colors,… and that all one can expect in such a difficult subject is to give some general rules and to derive from them consequences that can be of some use in the arts and satisfy somewhat the natural desire we have to render account of everything that appears to us.

An attempt to study the evolution of living organisms without reference to cytology would be as futile as an account of stellar evolution which ignored spectroscopy.

Anaximenes and Anaxagoras and Democritus say that its [the earth’s] flatness is responsible for it staying still: for it does not cut the air beneath but covers it like a lid, which flat bodies evidently do: for they are hard to move even for the winds, on account of their resistance.

And let me adde, that he that throughly understands the nature of Ferments and Fermentations, shall probably be much better able than he that Ignores them, to give a fair account of divers Phænomena of severall diseases (as well Feavers and others) which will perhaps be never throughly understood, without an insight into the doctrine of Fermentation.

Aristotle’s opinion … that comets were nothing else than sublunary vapors or airy meteors … prevailed so far amongst the Greeks, that this sublimest part of astronomy lay altogether neglected; since none could think it worthwhile to observe, and to give an account of the wandering and uncertain paths of vapours floating in the Ether.

As soon … as it was observed that the stars retained their relative places, that the times of their rising and setting varied with the seasons, that sun, moon, and planets moved among them in a plane, … then a new order of things began.… Science had begun, and the first triumph of it was the power of foretelling the future; eclipses were perceived to recur in cycles of nineteen years, and philosophers were able to say when an eclipse was to be looked for. The periods of the planets were determined. Theories were invented to account for their eccentricities; and, false as those theories might be, the position of the planets could be calculated with moderate certainty by them.

As there is no study which may be so advantageously entered upon with a less stock of preparatory knowledge than mathematics, so there is none in which a greater number of uneducated men have raised themselves, by their own exertions, to distinction and eminence. … Many of the intellectual defects which, in such cases, are commonly placed to the account of mathematical studies, ought to be ascribed to the want of a liberal education in early youth.

As to the position of the earth, then, this is the view which some advance, and the views advanced concerning its rest or motion are similar. For here too there is no general agreement. All who deny that the earth lies at the centre think that it revolves about the centre, and not the earth only but, as we said before, the counter-earth as well. Some of them even consider it possible that there are several bodies so moving, which are invisible to us owing to the interposition of the earth. This, they say, accounts for the fact that eclipses of the moon are more frequent than eclipses of the sun; for in addition to the earth each of these moving bodies can obstruct it.

Available energy is energy which we can direct into any desired channel. Dissipated energy is energy which we cannot lay hold of and direct at pleasure, such as the energy of the confused agitation of molecules which we call heat. Now, confusion, like the correlative term order, is not a property of material things in themselves, but only in relation to the mind which perceives them. A memorandum-book does not, provided it is neatly written, appear confused to an illiterate person, or to the owner who understands it thoroughly, but to any other person able to read it appears to be inextricably confused. Similarly the notion of dissipated energy could not occur to a being who could not turn any of the energies of nature to his own account, or to one who could trace the motion of every molecule and seize it at the right moment. It is only to a being in the intermediate stage, who can lay hold of some forms of energy while others elude his grasp, that energy appears to be passing inevitably from the available to the dissipated state.

Bearing in mind that it is from the vitality of the atmospheric particles that all the mischief arises, it appears that all that is requisite is to dress the wound with some material capable of killing these septic germs, provided that any substance can be found reliable for this purpose, yet not too potent as a caustic. In the course of the year 1864 I was much struck with an account of the remarkable effects produced by carbolic acid upon the sewage of the town of Carlisle, the admixture of a very small proportion not only preventing all odour from the lands irrigated with the refuse material, but, as it was stated, destroying the entozoa which usually infest cattle fed upon such pastures.

Between this body [the earth] and the heavens there are suspended, in this aerial spirit, seven stars, separated by determinate spaces, which, on account of their motion, we call wandering.

But the greatest error of all the rest is the mistaking or misplacing of the last or farthest end of knowledge: for men have entered into a desire of learning and knowledge, sometimes upon a natural curiosity and inquisitive appetite; sometimes to entertain their minds with variety and delight; sometimes for ornament and reputation; and sometimes to enable them to victory of wit and contradiction; and most times for lucre and profession; and seldom sincerely to give a true account of their gift of reason, to the benefit and use of men...

But when science, passing beyond its own limits, assumes to take the place of theology, and sets up its own conception of the order of Nature as a sufficient account of its cause, it is invading a province of thought to which it has no claim, and not unreasonably provokes the hostility of its best friends.

By their very nature chemical controls are self-defeating, for they have been devised and applied without taking into account the complex biological systems against which they have been blindly hurled.

Characteristically skeptical of the idea that living things would faithfully follow mathematical formulas, [Robert Harper] seized upon factors in corn which seemed to blend in the hybrid—rather than be represented by plus or minus signs, and put several seasons into throwing doubt upon the concept of immutable hypothetical units of inheritance concocted to account for selected results.

Dear Sir Walter ... Your account of his seizure grieved us all much. Coleridge had a dangerous attack a few weeks ago; Davy is gone. Surely these are men of power, not to be replaced should they disappear, as one alas has done.

Dick Drew took a bunch of misfits—people who wouldn’t fly in formation—and he put together a lab that created technologies that account for 20 percent of 3M's sales in 2000.

Did it ever occur to you that there’s no limit to how complicated things can get, on account of one thing always leading to another?

Dr. Wallace, in his Darwinism, declares that he can find no ground for the existence of pure scientists, especially mathematicians, on the hypothesis of natural selection. If we put aside the fact that great power in theoretical science is correlated with other developments of increasing brain-activity, we may, I think, still account for the existence of pure scientists as Dr. Wallace would himself account for that of worker-bees. Their function may not fit them individually to survive in the struggle for existence, but they are a source of strength and efficiency to the society which produces them.

ELECTRICITY, n. The power that causes all natural phenomena not known to be caused by something else. It is the same thing as lightning, and its famous attempt to strike Dr. Franklin is one of the most picturesque incidents in that great and good man's career. The memory of Dr. Franklin is justly held in great reverence, particularly in France, where a waxen effigy of him was recently on exhibition, bearing the following touching account of his life and services to science:
Monsieur Franqulin, inventor of electricity. This illustrious savant, after having made several voyages around the world, died on the Sandwich Islands and was devoured by savages, of whom not a single fragment was ever recovered.
Electricity seems destined to play a most important part in the arts and industries. The question of its economical application to some purposes is still unsettled, but experiment has already proved that it will propel a street car better than a gas jet and give more light than a horse.

Except for the rare cases of plastid inheritance, the inheritance of all known characters can be sufficiently accounted for by the presence of genes in the chromosomes. In a word the cytoplasm may be ignored genetically.

Facts alone, no matter how numerous or verifiable, do not automatically arrange themselves into an intelligible, or truthful, picture of the world. It is the task of the human mind to invent a theoretical framework to account for them.

Finally in a large population, divided and subdivided into partially isolated local races of small size, there is a continually shifting differentiation among the latter (intensified by local differences in selection but occurring under uniform and static conditions) which inevitably brings about an indefinitely continuing, irreversible, adaptive, and much more rapid evolution of the species. Complete isolation in this case, and more slowly in the preceding, originates new species differing for the most part in nonadaptive parallel orthogenetic lines, in accordance with the conditions. It is suggested, in conclusion, that the differing statistical situations to be expected among natural species are adequate to account for the different sorts of evolutionary processes which have been described, and that, in particular, conditions in nature are often such as to bring about the state of poise among opposing tendencies on which an indefinitely continuing evolutionary process depends.

Finally, two days ago, I succeeded - not on account of my hard efforts, but by the grace of the Lord. Like a sudden flash of lightning, the riddle was solved. I am unable to say what was the conducting thread that connected what I previously knew with what made my success possible.

Form may be of more account than substance. A lens of ice will focus a solar beam to a blaze.

From my earliest childhood I nourished and cherished the desire to make a creditable journey in a new country, and write such a respectable account of its natural history as should give me a niche amongst the scientific explorers of the globe I inhabit, and hand my name down as a useful contributor of original matter.

Generally speaking, geologists seem to have been much more intent on making little worlds of their own, than in examining the crust of that which they inhabit. It would be much more desirable that facts should be placed in the foreground and theories in the distance, than that theories should be brought forward at the expense of facts. So that, in after times, when the speculations of the present day shall have passed away, from a greater accumulation of information, the facts may be readily seized and converted to account.

Genius is rarely able to give any account of its own processes.

Geologists have not been slow to admit that they were in error in assuming that they had an eternity of past time for the evolution of the earth’s history. They have frankly acknowledged the validity of the physical arguments which go to place more or less definite limits to the antiquity of the earth. They were, on the whole, disposed to acquiesce in the allowance of 100 millions of years granted to them by Lord Kelvin, for the transaction of the whole of the long cycles of geological history. But the physicists have been insatiable and inexorable. As remorseless as Lear’s daughters, they have cut down their grant of years by successive slices, until some of them have brought the number to something less than ten millions. In vain have the geologists protested that there must somewhere be a flaw in a line of argument which tends to results so entirely at variance with the strong evidence for a higher antiquity, furnished not only by the geological record, but by the existing races of plants and animals. They have insisted that this evidence is not mere theory or imagination, but is drawn from a multitude of facts which become hopelessly unintelligible unless sufficient time is admitted for the evolution of geological history. They have not been able to disapprove the arguments of the physicists, but they have contended that the physicists have simply ignored the geological arguments as of no account in the discussion.

Good methods can teach us to develop and use to better purpose the faculties with which nature has endowed us, while poor methods may prevent us from turning them to good account. Thus the genius of inventiveness, so precious in the sciences, may be diminished or even smothered by a poor method, while a good method may increase and develop it.

He (Anaxagoras) is said to have been twenty years old at the time of Xerxes' crossing, and to have lived to seventy-two. Apollodorus says in his Chronicles that he was born in the seventieth Olympiad (500-497 B.C.) and died in the first year of the eighty-eighth (428/7). He began to be a philosopher at Athens in the archonship of Callias (456/5), at the age of twenty, as Demetrius Phalereus tells us in his Register of Archons, and they say he spent thirty years there. … There are different accounts given of his trial. Sotion, in his Succession of Philosophers, says that he was prosecuted by Cleon for impiety, because he maintained that the sun was a red hot mass of metal, and after that Pericles, his pupil, had made a speech in his defence, he was fined five talents and exiled. Satyrus in his Uves, on the other hand, says that the charge was brought by Thucydides in his political campaign against Pericles; and he adds that the charge was not only for the impiety but for Medism as well; and he was condemned to death in his absence. ... Finally he withdrew to Lampsacus, and there died. It is said that when the rulers of the city asked him what privilege he wished to be granted, he replied that the children should be given a holiday every year in the month in which he died. The custom is preserved to the present day. When he died the Lampsacenes buried him with full honours.

Her [Nettie Stevens] single-mindedness and devotion, combined with keen powers of observation; her thoughtfulness and patience, united to a well-balanced judgment, account, in part, for her remarkable accomplishment.

Hofstadter’s Law: It always takes longer than you expect, even when you take into account Hofstadter’s Law.

I am persuaded that there is not in the nature of science anything unfavourable to religious feelings, and if I were not so persuaded I should be much puzzled to account for our being invested, as we so amply are, with the facilities that lead us to the discovery of scientific truth. It would be strange if our Creator should be found to be urging us on in a career which tended to be a forgetfulness of him.

I argued that it was important not to place too much reliance on any single piece of experimental evidence. It might turn out to be misleading, as the 5.1 Å reflection undoubtedly was. Jim was a little more brash, stating that no good model ever accounted for all the facts, since some data was bound to be misleading if not plain wrong. A theory that did fit all the data would have been “carpentered” to do so and would thus be open to suspicion.

I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office at Madras on a salary of only £20 per annum. I am now about 23 years of age. … After leaving school I have been employing the spare time at my disposal to work at Mathematics.

I cannot find anything showing early aptitude for acquiring languages; but that he [Clifford] had it and was fond of exercising it in later life is certain. One practical reason for it was the desire of being able to read mathematical papers in foreign journals; but this would not account for his taking up Spanish, of which he acquired a competent knowledge in the course of a tour to the Pyrenees. When he was at Algiers in 1876 he began Arabic, and made progress enough to follow in a general way a course of lessons given in that language. He read modern Greek fluently, and at one time he was furious about Sanskrit. He even spent some time on hieroglyphics. A new language is a riddle before it is conquered, a power in the hand afterwards: to Clifford every riddle was a challenge, and every chance of new power a divine opportunity to be seized. Hence he was likewise interested in the various modes of conveying and expressing language invented for special purposes, such as the Morse alphabet and shorthand. … I have forgotten to mention his command of French and German, the former of which he knew very well, and the latter quite sufficiently; …

I consider the differences between man and animals in propensities, feelings, and intellectual faculties, to be the result of the same cause as that which we assign for the variations in other functions, viz. difference of organization; and that the superiority of man in rational endowments is not greater than the more exquisite, complicated, and perfectly developed structure of his brain, and particularly of his ample cerebral hemispheres, to which the rest of the animal kingdom offers no parallel, nor even any near approximation, is sufficient to account for.

I do not profess to be able thus to account for all the [planetary] motions at the same time; but I shall show that each by itself is well explained by its proper hypothesis.

I have always consistently opposed high-tension and alternating systems of electric lighting, not only on account of danger, but because of their general unreliability and unsuitability for any general system of distribution.

I heard Professor Cannon lecture last night, going partly on your account. His subject was a physiological substitute for war—which is international sports and I suppose motorcycle races—to encourage the secretion of the adrenal glands!

I look upon statistics as the handmaid of medicine, but on that very account I hold that it befits medicine to treat her handmaid with proper respect, and not to prostitute her services for controversial or personal purposes.

I maintain that the human mystery is incredibly demeaned by scientific reductionism, with its claim in promissory materialism to account eventually for all of the spiritual world in terms of patterns of neuronal activity. This belief must be classed as a superstition. ... We have to recognize that we are spiritual beings with souls existing in a spiritual world as well as material beings with bodies and brains existing in a material world.

I ought to call myself an agnostic; but, for all practical purposes, I am an atheist. I do not think the existence of the Christian God any more probable than the existence of the Gods of Olympus or Valhalla. To take another illustration: nobody can prove that there is not between the Earth and Mars a china teapot revolving in an elliptical orbit, but nobody thinks this sufficiently likely to be taken into account in practice. I think the Christian God just as unlikely.

I shall no doubt be blamed by certain scientists, and, I am afraid, by some philosophers, for having taken serious account of the alleged facts which are investigated by Psychical Researchers. I am wholly impenitent about this. The scientists in question seem to me to confuse the Author of Nature with the Editor of Nature; or at any rate to suppose that there can be no productions of the former which would not be accepted for publication by the latter. And I see no reason to believe this.

I will try to account for the degree of my aesthetic emotion. That, I conceive, is the function of the critic.

If any layman were to ask a number of archaeologists to give, on the spur of the moment, a definition of archaeology, I suspect that such a person might find the answers rather confusing. He would, perhaps, sympathize with Socrates who, when he hoped to learn from the poets and artisans something about the arts they practised, was forced to go away with the conviction that, though they might themselves be able to accomplish something, they certainly could give no clear account to others of what they were trying to do.

If in a discussion of many matters … we are not able to give perfectly exact and self-consistent accounts, do not be surprised: rather we would be content if we provide accounts that are second to none in probability.

If one of these people, in whom the chance-worship of our remoter ancestors thus strangely survives, should be within reach of the sea when a heavy gale is blowing, let him betake himself to the shore and watch the scene. Let him note the infinite variety of form and size of the tossing waves out at sea; or against the curves of their foam-crested breakers, as they dash against the rocks; let him listen to the roar and scream of the shingle as it is cast up and torn down the beach; or look at the flakes of foam as they drive hither and thither before the wind: or note the play of colours, which answers a gleam of sunshine as it falls upon their myriad bubbles. Surely here, if anywhere, he will say that chance is supreme, and bend the knee as one who has entered the very penetralia of his divinity. But the man of science knows that here, as everywhere, perfect order is manifested; that there is not a curve of the waves, not a note in the howling chorus, not a rainbow-glint on a bubble, which is other than a necessary consequence of the ascertained laws of nature; and that with a sufficient knowledge of the conditions, competent physico-mathematical skill could account for, and indeed predict, every one of these 'chance' events.

If the Humours of the Eye by old Age decay, so as by shrinking to make the Cornea and Coat of the Crystalline Humour grow flatter than before, the Light will not be refracted enough, and for want of a sufficient Refraction will not converge to the bottom of the Eye but to some place beyond it, and by consequence paint in the bottom of the Eye a confused Picture, and according to the Indistinctuess of this Picture the Object will appear confused. This is the reason of the decay of sight in old Men, and shews why their Sight is mended by Spectacles. For those Convex glasses supply the defect of plumpness in the Eye, and by increasing the Refraction make the rays converge sooner, so as to convene distinctly at the bottom of the Eye if the Glass have a due degree of convexity. And the contrary happens in short-sighted Men whose Eyes are too plump. For the Refraction being now too great, the Rays converge and convene in the Eyes before they come at the bottom; and therefore the Picture made in the bottom and the Vision caused thereby will not be distinct, unless the Object be brought so near the Eye as that the place where the converging Rays convene may be removed to the bottom, or that the plumpness of the Eye be taken off and the Refractions diminished by a Concave-glass of a due degree of Concavity, or lastly that by Age the Eye grow flatter till it come to a due Figure: For short-sighted Men see remote Objects best in Old Age, and therefore they are accounted to have the most lasting Eyes.

If the task of scientific methodology is to piece together an account of what scientists actually do, then the testimony of biologists should be heard with specially close attention. Biologists work very close to the frontier between bewilderment and understanding.
Biology is complex, messy and richly various, like real life; it travels faster nowadays than physics or chemistry (which is just as well, since it has so much farther to go), and it travels nearer to the ground. It should therefore give us a specially direct and immediate insight into science in the making.

If we wish to give an account of the atomic constitution of the aromatic compounds, we are bound to explain the following facts:
1) All aromatic compounds, even the most simple, are relatively richer in carbon than the corresponding compounds in the class of fatty bodies.
2) Among the aromatic compounds, as well as among the fatty bodies, a large number of homologous substances exist.
3) The most simple aromatic compounds contain at least six atoms of carbon.
4) All the derivatives of aromatic substances exhibit a certain family likeness; they all belong to the group of 'Aromatic compounds'. In cases where more vigorous reactions take place, a portion of the carbon is often eliminated, but the chief product contains at least six atoms of carbon These facts justify the supposition that all aromatic compounds contain a common group, or, we may say, a common nucleus consisting of six atoms of carbon. Within this nucleus a more intimate combination of the carbon atoms takes place; they are more compactly placed together, and this is the cause of the aromatic bodies being relatively rich in carbon. Other carbon atoms can be joined to this nucleus in the same way, and according to the same law, as in the case of the group of fatty bodies, and in this way the existence of homologous compounds is explained.

In 1684 Dr Halley came to visit him at Cambridge, after they had been some time together, the Dr asked him what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of their distance from it. Sr Isaac replied immediately that it would be an Ellipsis, the Doctor struck with joy & amazement asked him how he knew it, why saith he I have calculated it, whereupon Dr Halley asked him for his calculation without any farther delay. Sr Isaac looked among his papers but could not find it, but he promised him to renew it, & then to send it him.
[Recollecting Newton's account of the meeting after which Halley prompted Newton to write The Principia. When asking Newton this question, Halley was aware, without revealing it to Newton that Robert Hooke had made this hypothesis of plantary motion a decade earlier.]

In all spheres of science, art, skill, and handicraft it is never doubted that, in order to master them, a considerable amount of trouble must be spent in learning and in being trained. As regards philosophy, on the contrary, there seems still an assumption prevalent that, though every one with eyes and fingers is not on that account in a position to make shoes if he only has leather and a last, yet everybody understands how to philosophize straight away, and pass judgment on philosophy, simply because he possesses the criterion for doing so in his natural reason.

In general I would be cautious against … plays of fancy and would not make way for their reception into scientific astronomy, which must have quite a different character. Laplace’s cosmogenic hypotheses belong in that class. Indeed, I do not deny that I sometimes amuse myself in a similar manner, only I would never publish the stuff. My thoughts about the inhabitants of celestial bodies, for example, belong in that category. For my part, I am (contrary to the usual opinion) convinced … that the larger the cosmic body, the smaller are the inhabitants and other products. For example, on the sun trees, which in the same ratio would be larger than ours, as the sun exceeds the earth in magnitude, would not be able to exist, for on account of the much greater weight on the surface of the sun, all branches would break themselves off, in so far as the materials are not of a sort entirely heterogeneous with those on earth.

In its earliest development knowledge is self-sown. Impressions force themselves upon men’s senses whether they will or not, and often against their will. The amount of interest in which these impressions awaken is determined by the coarser pains and pleasures which they carry in their train or by mere curiosity; and reason deals with the materials supplied to it as far as that interest carries it, and no further. Such common knowledge is rather brought than sought; and such ratiocination is little more than the working of a blind intellectual instinct. It is only when the mind passes beyond this condition that it begins to evolve science. When simple curiosity passes into the love of knowledge as such, and the gratification of the æsthetic sense of the beauty of completeness and accuracy seems more desirable that the easy indolence of ignorance; when the finding out of the causes of things becomes a source of joy, and he is accounted happy who is successful in the search, common knowledge passes into what our forefathers called natural history, whence there is but a step to that which used to be termed natural philosophy, and now passes by the name of physical science.
In this final state of knowledge the phenomena of nature are regarded as one continuous series of causes and effects; and the ultimate object of science is to trace out that series, from the term which is nearest to us, to that which is at the farthest limit accessible to our means of investigation.
The course of nature as it is, as it has been, and as it will be, is the object of scientific inquiry; whatever lies beyond, above, or below this is outside science. But the philosopher need not despair at the limitation on his field of labor; in relation to the human mind Nature is boundless; and, though nowhere inaccessible, she is everywhere unfathomable.

In its essence, the theory of natural selection is primarily an attempt to give an account of the probable mechanism of the origin of the adaptations of the organisms to their environment, and only secondarily an attempt to explain evolution at large. Some modern biologists seem to believe that the word 'adaptation' has teleological connotations, and should therefore be expunged from the scientific lexicon. With this we must emphatically disagree. That adaptations exist is so evident as to be almost a truism, although this need not mean that ours is the best of all possible worlds. A biologist has no right to close his eyes to the fact that the precarious balance between a living being and its environment must be preserved by some mechanism or mechanisms if life is to endure.

In order to discover Truth in this manner by observation and reason, it is requisite we should fix on some principles whose certainty and effects are demonstrable to our senses, which may serve to explain the phenomena of natural bodies and account for the accidents that arise in them; such only are those which are purely material in the human body with mechanical and physical experiments … a physician may and ought to furnish himself with, and reason from, such things as are demonstrated to be true in anatomy, chemistry, and mechanics, with natural and experimental philosophy, provided he confines his reasoning within the bounds of truth and simple experiment.

In so far as such developments utilise the natural energy running to waste, as in water power, they may be accounted as pure gain. But in so far as they consume the fuel resources of the globe they are very different. The one is like spending the interest on a legacy, and the other is like spending the legacy itself. ... [There is] a still hardly recognised coming energy problem.

In the 1920s, there was a dinner at which the physicist Robert W. Wood was asked to respond to a toast … “To physics and metaphysics.” Now by metaphysics was meant something like philosophy—truths that you could get to just by thinking about them. Wood took a second, glanced about him, and answered along these lines: The physicist has an idea, he said. The more he thinks it through, the more sense it makes to him. He goes to the scientific literature, and the more he reads, the more promising the idea seems. Thus prepared, he devises an experiment to test the idea. The experiment is painstaking. Many possibilities are eliminated or taken into account; the accuracy of the measurement is refined. At the end of all this work, the experiment is completed and … the idea is shown to be worthless. The physicist then discards the idea, frees his mind (as I was saying a moment ago) from the clutter of error, and moves on to something else. The difference between physics and metaphysics, Wood concluded, is that the metaphysicist has no laboratory.

In the conception of a machine or the product of a machine there is a point where one may leave off for parsimonious reasons, without having reached aesthetic perfection; at this point perhaps every mechanical factor is accounted for, and the sense of incompleteness is due to the failure to recognize the claims of the human agent. Aesthetics carries with it the implications of alternatives between a number of mechanical solutions of equal validity; and unless this awareness is present at every stage of the process … it is not likely to come out with any success in the final stage of design.

In the discussion of the. energies involved in the deformation of nuclei, the concept of surface tension of nuclear matter has been used and its value had been estimated from simple considerations regarding nuclear forces. It must be remembered, however, that the surface tension of a charged droplet is diminished by its charge, and a rough estimate shows that the surface tension of nuclei, decreasing with increasing nuclear charge, may become zero for atomic numbers of the order of 100. It seems therefore possible that the uranium nucleus has only small stability of form, and may, after neutron capture, divide itself into two nuclei of roughly equal size (the precise ratio of sizes depending on liner structural features and perhaps partly on chance). These two nuclei will repel each other and should gain a total kinetic energy of c. 200 Mev., as calculated from nuclear radius and charge. This amount of energy may actually be expected to be available from the difference in packing fraction between uranium and the elements in the middle of the periodic system. The whole 'fission' process can thus be described in an essentially classical way, without having to consider quantum-mechanical 'tunnel effects', which would actually be extremely small, on account of the large masses involved.
[Co-author with Otto Robert Frisch]

In the modern interpretation of Mendelism, facts are being transformed into factors at a rapid rate. If one factor will not explain the facts, then two are involved; if two prove insufficient, three will sometimes work out. The superior jugglery sometimes necessary to account for the results may blind us, if taken too naively, to the common-place that the results are often so excellently 'explained' because the explanation was invented to explain them. We work backwards from the facts to the factors, and then, presto! explain the facts by the very factors that we invented to account for them. I am not unappreciative of the distinct advantages that this method has in handling the facts. I realize how valuable it has been to us to be able to marshal our results under a few simple assumptions, yet I cannot but fear that we are rapidly developing a sort of Mendelian ritual by which to explain the extraordinary facts of alternative inheritance. So long as we do not lose sight of the purely arbitrary and formal nature of our formulae, little harm will be done; and it is only fair to state that those who are doing the actual work of progress along Mendelian lines are aware of the hypothetical nature of the factor-assumption.

In the world of science, however, these sentiments have never been of much account. There everything depends on making opinion prevail and dominate; few men are really independent; the majority draws the individual after it.

In the world’s history certain inventions and discoveries occurred of peculiar value, on account of their great efficiency in facilitating all other inventions and discoveries. Of these were the art of writing and of printing, the discovery of America, and the introduction of patent laws. The date of the first … is unknown; but it certainly was as much as fifteen hundred years before the Christian era; the second—printing—came in 1436, or nearly three thousand years after the first. The others followed more rapidly—the discovery of America in 1492, and the first patent laws in 1624.

In the year 1666 he retired again from Cambridge... to his mother in Lincolnshire & whilst he was musing in a garden it came into his thought that the power of gravity (wch brought an apple from the tree to the ground) was not limited to a certain distance from the earth but that this power must extend much farther than was usually thought. Why not as high as the moon said he to himself & if so that must influence her motion & perhaps retain her in her orbit, whereupon he fell a calculating what would be the effect of that supposition but being absent from books & taking the common estimate in use among Geographers & our seamen before Norwood had measured the earth, that 60 English miles were contained in one degree of latitude on the surface of the Earth his computation did not agree with his theory & inclined him then to entertain a notion that together with the force of gravity there might be a mixture of that force wch the moon would have if it was carried along in a vortex.
[The earliest account of Newton, gravity and an apple.]

Infinities and indivisibles transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness; Imagine what they are when combined.

It has been pointed out already that no knowledge of probabilities, less in degree than certainty, helps us to know what conclusions are true, and that there is no direct relation between the truth of a proposition and its probability. Probability begins and ends with probability. That a scientific investigation pursued on account of its probability will generally lead to truth, rather than falsehood, is at the best only probable.

It is a test of true theories not only to account for but to predict phenomena.

It is change, continuing change, inevitable change, that is the dominant factor in society today. No sensible decision can be made any longer without taking into account not only the world as it is, but the world as it will be … This, in turn, means that our statesmen, our businessmen, our everyman must take on a science fictional way of thinking.

It is curious to observe how differently these great men [Plato and Bacon] estimated the value of every kind of knowledge. Take Arithmetic for example. Plato, after speaking slightly of the convenience of being able to reckon and compute in the ordinary transactions of life, passes to what he considers as a far more important advantage. The study of the properties of numbers, he tells us, habituates the mind to the contemplation of pure truth, and raises us above the material universe. He would have his disciples apply themselves to this study, not that they may be able to buy or sell, not that they may qualify themselves to be shop-keepers or travelling merchants, but that they may learn to withdraw their minds from the ever-shifting spectacle of this visible and tangible world, and to fix them on the immutable essences of things.
Bacon, on the other hand, valued this branch of knowledge only on account of its uses with reference to that visible and tangible world which Plato so much despised. He speaks with scorn of the mystical arithmetic of the later Platonists, and laments the propensity of mankind to employ, on mere matters of curiosity, powers the whole exertion of which is required for purposes of solid advantage. He advises arithmeticians to leave these trifles, and employ themselves in framing convenient expressions which may be of use in physical researches.

It is more important to have beauty in one's equations than to have them fit experiment... It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory.

It is not easy to name another Voyager or Traveller who has given more useful information to the world; to whom the Merchant and Mariner are so much indebted; or who has communicated his information in a more unembarrassed and intelligible manner. And this he has done in a style perfectly unassuming, equally free from affectation and from the most distant appearance of invention.

It is not only a decided preference for synthesis and a complete denial of general methods which characterizes the ancient mathematics as against our newer Science [modern mathematics]: besides this extemal formal difference there is another real, more deeply seated, contrast, which arises from the different attitudes which the two assumed relative to the use of the concept of variability. For while the ancients, on account of considerations which had been transmitted to them from the Philosophie school of the Eleatics, never employed the concept of motion, the spatial expression for variability, in their rigorous system, and made incidental use of it only in the treatment of phonoromically generated curves, modern geometry dates from the instant that Descartes left the purely algebraic treatment of equations and proceeded to investigate the variations which an algebraic expression undergoes when one of its variables assumes a continuous succession of values.

It is not, indeed, strange that the Greeks and Romans should not have carried ... any ... experimental science, so far as it has been carried in our time; for the experimental sciences are generally in a state of progression. They were better understood in the seventeenth century than in the sixteenth, and in the eighteenth century than in the seventeenth. But this constant improvement, this natural growth of knowledge, will not altogether account for the immense superiority of the modern writers. The difference is a difference not in degree, but of kind. It is not merely that new principles have been discovered, but that new faculties seem to be exerted. It is not that at one time the human intellect should have made but small progress, and at another time have advanced far; but that at one time it should have been stationary, and at another time constantly proceeding. In taste and imagination, in the graces of style, in the arts of persuasion, in the magnificence of public works, the ancients were at least our equals. They reasoned as justly as ourselves on subjects which required pure demonstration.

It is presumed that there exists a great unity in nature, in respect of the adequacy of a single cause to account for many different kinds of consequences.

It is the task of science, as a collective human undertaking, to describe from the external side, (on which alone agreement is possible), such statistical regularity as there is in a world “in which every event has a unique aspect, and to indicate where possible the limits of such description. It is not part of its task to make imaginative interpretation of the internal aspect of reality—what it is like, for example, to be a lion, an ant or an ant hill, a liver cell, or a hydrogen ion. The only qualification is in the field of introspective psychology in which each human being is both observer and observed, and regularities may be established by comparing notes. Science is thus a limited venture. It must act as if all phenomena were deterministic at least in the sense of determinable probabilities. It cannot properly explain the behaviour of an amoeba as due partly to surface and other physical forces and partly to what the amoeba wants to do, with out danger of something like 100 per cent duplication. It must stick to the former. It cannot introduce such principles as creative activity into its interpretation of evolution for similar reasons. The point of view indicated by a consideration of the hierarchy of physical and biological organisms, now being bridged by the concept of the gene, is one in which science deliberately accepts a rigorous limitation of its activities to the description of the external aspects of events. In carrying out this program, the scientist should not, however, deceive himself or others into thinking that he is giving an account of all of reality. The unique inner creative aspect of every event necessarily escapes him.

It would be an easy task to show that the characteristics in the organization of man, on account of which the human species and races are grouped as a distinct family, are all results of former changes of occupation, and of acquired habits, which have come to be distinctive of individuals of his kind. When, compelled by circumstances, the most highly developed apes accustomed themselves to walking erect, they gained the ascendant over the other animals. The absolute advantage they enjoyed, and the new requirements imposed on them, made them change their mode of life, which resulted in the gradual modification of their organization, and in their acquiring many new qualities, and among them the wonderful power of speech.

Just as Americans have discovered the hidden energy costs in a multitude of products—in refrigerating a steak, for example, on its way to the butcher—they are about to discover the hidden water costs. Beginning with the water that irrigated the corn that was fed to the steer, the steak may have accounted for 3,500 gallons. The water that goes into a 1,000-pound steer would float a destroyer. It takes 14,935 gallons of water to grow a bushel of wheat, 60,000 gallons to produce a ton of steel, 120 gallons to put a single egg on the breakfast table.

Just as the introduction of the irrational numbers … is a convenient myth [which] simplifies the laws of arithmetic … so physical objects are postulated entities which round out and simplify our account of the flux of existence… The conceptional scheme of physical objects is [likewise] a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part.

Just now nuclear physicists are writing a great deal about hypothetical particles called neutrinos supposed to account for certain peculiar facts observed in β-ray disintegration. We can perhaps best describe the neutrinos as little bits of spin-energy that have got detached. I am not much impressed by the neutrino theory. In an ordinary way I might say that I do not believe in neutrinos… But I have to reflect that a physicist may be an artist, and you never know where you are with artists. My old-fashioned kind of disbelief in neutrinos is scarcely enough. Dare I say that experimental physicists will not have sufficient ingenuity to make neutrinos? Whatever I may think, I am not going to be lured into a wager against the skill of experimenters under the impression that it is a wager against the truth of a theory. If they succeed in making neutrinos, perhaps even in developing industrial applications of them, I suppose I shall have to believe—though I may feel that they have not been playing quite fair.

Knowledge of Nature is an account at bank, where each dividend is added to the principal and the interest is ever compounded; and hence it is that human progress, founded on natural knowledge, advances with ever increasing speed.

Lawyers have to make a living and can only do so by inducing people to believe that a straight line is crooked. This accounts for their penchant for politics, where they can usually find everything crooked enough to delight their hearts.

My profession often gets bad press for a variety of sins, both actual and imagined: arrogance, venality, insensitivity to moral issues about the use of knowledge, pandering to sources of funding with insufficient worry about attendant degradation of values. As an advocate for science, I plead ‘mildly guilty now and then’ to all these charges. Scientists are human beings subject to all the foibles and temptations of ordinary life. Some of us are moral rocks; others are reeds. I like to think (though I have no proof) that we are better, on average, than members of many other callings on a variety of issues central to the practice of good science: willingness to alter received opinion in the face of uncomfortable data, dedication to discovering and publicizing our best and most honest account of nature’s factuality, judgment of colleagues on the might of their ideas rather than the power of their positions.

My view, the skeptical one, holds that we may be as far away from an understanding of elementary particles as Newton's successors were from quantum mechanics. Like them, we have two tremendous tasks ahead of us. One is to study and explore the mathematics of the existing theories. The existing quantum field-theories may or may not be correct, but they certainly conceal mathematical depths which will take the genius of an Euler or a Hamilton to plumb. Our second task is to press on with the exploration of the wide range of physical phenomena of which the existing theories take no account. This means pressing on with experiments in the fashionable area of particle physics. Outstanding among the areas of physics which have been left out of recent theories of elementary particles are gravitation and cosmology

Ninety-nine and nine-tenths of the earth’s volume must forever remain invisible and untouchable. Because more than 97 per cent of it is too hot to crystallize, its body is extremely weak. The crust, being so thin, must bend, if, over wide areas, it becomes loaded with glacial ice, ocean water or deposits of sand and mud. It must bend in the opposite sense if widely extended loads of such material be removed. This accounts for … the origin of chains of high mountains … and the rise of lava to the earth’s surface.

Nothing is useless for the man of sense; he turns everything to account.

Now having (I know not by what accident) engaged my thoughts upon the Bills of Mortality, and so far succeeded therein, as to have reduced several great confused Volumes into a few perspicuous Tables, and abridged such Observations as naturally flowed from them, into a few succinct Paragraphs, without any long Series of multiloquious Deductions, I have presumed to sacrifice these my small, but first publish'd, Labours unto your Lordship, as unto whose benign acceptance of some other of my Papers even the birth of these is due; hoping (if I may without vanity say it) they may be of as much use to persons in your Lordships place, as they are of none to me, which is no more than fairest Diamonds are to the Journeymen Jeweller that works them, or the poor Labourer that first digg'd them from Earth.
[An early account demonstrating the value of statistical analysis of public health data. Graunt lived in London at the time of the plague epidemics.]

Oersted would never have made his great discovery of the action of galvanic currents on magnets had he stopped in his researches to consider in what manner they could possibly be turned to practical account; and so we would not now be able to boast of the wonders done by the electric telegraphs. Indeed, no great law in Natural Philosophy has ever been discovered for its practical implications, but the instances are innumerable of investigations apparently quite useless in this narrow sense of the word which have led to the most valuable results.