History of science

"Every publication I have frankly acknowledged to be very imperfect, and the present, I am as ready to acknowledge, is so. But, paradoxical as it may seem, this will ever be the case in the progress of natural science, so long as the works of God are, like himself, infinite and inexhaustible. In completing one discovery, we never fail to get an imperfect knowledge of others, of which we could have had no idea before; so that we cannot solve one doubt without creating several new ones."

"The greater is the circle of light, the greater is the boundary of the darkness by which it is confined. But notwithstanding this, the more light we get, the more thankful we ought to be. For by this means we have the greater range for satisfactory contemplation. In time the bounds of light will be still farther extended; and from the infinity of the divine nature, and the divine works, we may promise ourselves an endless progress in our investigation of them: a prospect truly sublime and glorious. The works of the greatest and most successful philosophers are, on this account, open to our complaints of their being imperfect."

"Newton, as he had very little knowledge of air, so he had few doubts concerning it."

"If a man be not mistaken in the principal object of his pursuits, he has no occasion to distress himself about lesser things."

"In the progress of his inquiries he will generally be able to rectify his own mistakes; or if little and envious minds should take a malignant pleasure in detecting them for him, and endeavouring to expose him, he is not worthy of the name of a philosopher, if he has not strength of mind sufficient to enable him not to be disturbed at it. He who does not foolishly affect to be above the failings of humanity, will not be mortified when it is proved that he is but a man."

"The man who believes that there is a governor as well as a maker of the world (and there is certainly equal reason to believe both) will acknowledge his providence and favour at least as much in a successful pursuit of knowledge, as of wealth; which is a sentiment that entirely cuts off all boasting with respect to ourselves, and all envy and jealousy with respect to others; and disposes us mutually to rejoice in every new light that we receive, through whose hands soever it be conveyed to us."

"This rapid process of knowledge, which, like the progress of a wave of the sea, of sound, or of light from the sun, extends itself not this way or that way only, but in all directions, will, I doubt not, be the means, under God, of extirpating all error and prejudice, and of putting an end to all undue and usurped authority in the business of religion, as well as of science; and all the efforts of the interested friends of corrupt establishments of all kinds, will be ineffectual for their support in this enlightened age; though, by retarding their downfall, they may make the final ruin of them more complete and glorious."

"Men of leisure, spirit, and ingenuity, in the middle ranks of life... is a circumstance that promises better for the continuance of this progress in useful knowledge than any noble or royal patronage."

"The system of nature is superior to any political system upon earth. If extensive usefulness be the object, science has the same advantage over politics. The greatest success in the latter seldom extends farther than one particular country, and one particular age; whereas a successful pursuit of science makes a man the benefactor of all mankind, and of every age. How trifling is the fame of any statesman that this country has ever produced to that of Lord Bacon, of Newton, or of Boyle; and how much greater are our obligations to such men as these, than to any other in the whole Biographia Britannica; and every country, in which science has flourished, can furnish instances for similar observations."

"I have... repeatedly cautioned my readers... that they are to consider new facts only as discoveries and mere deductions from those facts, as of no kind of authority; but to draw all conclusions, and form all hypotheses, for themselves."

"It is enough for us to see that nature is inexhaustible, that it is a rich mine, in which we shall never dig in vain, and that it is open to infinitely more labourers than are now employed in exploring its contents, or in digging for them."

"Persons who have only one object of pursuit, never fail to over-rate it, and of course to undervalue other things. ...the attention I have given to theology ...does not engross so much of my time as some persons may imagine ...these different studies so relieve one another, that I believe I do more in each of them, by applying to them alternately, than I should do, if I gave my whole attention to one of them only. But my principal defence rests on the superior dignity and importance of theological studies to any other whatever, and with some observations of this kind I shall chuse to conclude this long Preface."

"I... address my brother philosophers on a subject equally interesting to us as philosophers, and as men. Do not disregard a question of infinite moment. Give it that degree of attention to which it is naturally intitled; and especially do not so far abandon the serious character of philosophers, as to laugh where you ought to reason. At least, do this great subject [theology], and yourselves, the justice to consider the facts, and endeavour to frame some hypothesis by which to account for them; and do not decide in half an hour, on an inquiry which well deserves the study of a great part of your lives."

"Could I imagine that the knowledge of nature would ever be exhausted, and that we were approaching to a termination of our enquiries, I could more contentedly shut my eyes on a scene in which nothing more was to be seen, or done. But to quit the stage at present (and I believe the aspect of things will be exactly similar in any future period of our existence) without the hope of re-visiting it, would fill me with the deepest regret. The general who, like Epaminondas, or Wolfe, dies in the arms of victory, dies with satisfaction; but not so he that is cut off in the beginning of a doubtful, though promising, engagement. Thus I feel on the idea of ceasing to breathe, when I have but just begun to know what it is that I breathe."

"Till I hear better reasons than have yet been offered to me for changing my conduct, I shall continue to give my attention to my different pursuits, according to my own ideas of their respective importance; and my friends have no reason to fear that I shall neglect philosophy. It has, perhaps, but too strong charms for me. I shall endeavour, however, to keep it in its proper place, and not so much attach myself to the study of the laws, which govern this world, as to lose sight of the subserviency of this world, and of all things in it, to another and a better; in which I hope to resume these pleasing philosophical pursuits, and to see, in a comprehensive view, those detached discoveries which we are now making here."

"When a sufficient number of new facts shall be discovered (towards which even imperfect hypotheses will contribute) a more general theory will soon present itself; and perhaps to the most incurious and least sagacious eye. Thus, when able navigators have, with great labour and judgment, steered towards an undiscovered country, a common sailor, placed at the mast head, may happen to get the first sight of the land."

"Let us not... contend about merit, but let us all be intent on forwarding the common enterprize, and equally enjoy any progress we may make towards succeeding in it; and above all, let us acknowledge the guidance of that Great Being, who has put a spirit in man, and whose inspiration giveth him understanding."

"It will be seen that my apparatus for experiments on air is in fact nothing more than that of Dr. Hales, Dr. Brownrigg, and Mr. Cavendish, diversified and made a little more simple."

"It was in consequence of living for some time in the neighbourhood of a public brewery, a little after Midsummer in 1767, that I was induced to make experiments on fixed air, of which there is always a large body, ready formed, on the surface of the fermenting liquor, generally about nine inches, or a foot, in depth, within which any kind of substance may be very conveniently placed; and though, in these circumstances, the fixed air must be continually mixing with the common air and is therefore far from being perfectly pure, yet there is a constant fresh supply from the fermenting liquor, and it is pure enough for many purposes."

"When this fixed air is very strong, the smoke of a small quantity of gunpowder fired in it will be wholly retained by it, no part escaping into the common air. ...if ...any of the fixed air be thrown over the side of the vessel the smoke, which is mixed with it will fall to the ground, as if it was so much water, the fixed air being heavier than common air."

"Considering the near affinity between water and fixed air, I concluded that if a quantity of water was placed near the yeast of the fermenting liquor, it could not fail to imbibe that air, and thereby acquire the principal properties of Pyrmont, and some other medicinal mineral waters. Accordingly, I found, that when the surface of the water was considerable, it always acquired the pleasant acidulous taste that Pyrmont water has. The readiest way of impregnating water with this virtue, in these circumstances, is to take two vessels, and to keep pouring the water from one into the other, when they are both of them held as near the yeast as possible; for by this means a great quantity of surface is exposed to the air, and the surface is also continually changing. In this manner, I have sometimes, in the space of two or three minutes, made a glass of exceedingly pleasant sparkling water, which could hardly be distinguished from very good Pyrmont, or rather Seltzer water."

"I had acquainted all my friends with what I had done, and frequently expressed my wishes that persons who had the care of large distilleries (where I was told that fermentation was much stronger than in common breweries) would contrive to have vessels of water suspended within the fixed air which they produced, with a fardier contrivance for agitating the surface of the water; as I did not doubt but that, by this means, they might, with little or no expence, make great quantities of Pyrmont water; by which they might at the same time both serve the public, and benefit themselves. For I never had the most distant thought of making any advantage of the scheme myself."

"All calcareous substances contain fixed air, and any acids may be used in order to set it loose from them; but pounded lime stone, or the sawings of marble, and oil of vitriol are, both of them the cheapest, and upon the whole, the best for die purpose."

"It is something remarkable, that all the acids that produce any air by the solution of metals give inflammable air, except spirit of nitre only, which forms a different kind of union with the inflammable principle; making nitrous air, more or less modified. Besides oil of vitriol and spirit of salt, I have observed that the vegetable acid also produces inflammable air, by the solution of metals, though in a much less quantity. Perhaps the proportion of the strength of the acids may be ascertained by this means. The concentrated vinegar which I made use of in my experiments on the vegetable acid air, dissolved zinc almost as rapidly as spirit of salt, and produced inflammable air; and radical vinegar, which is unquestionably a pure vegetable acid, had the same effect when applied both to zinc and iron."

"More is owing to what we call chance, that is, philosophically speaking, to the observation of events arising from unknown causes, than to any proper design, or preconceived theory in this business [of science]. This does not appear in the works of those who write synthetically upon these subjects; but would, I doubt not, appear very strikingly in those who are the most celebrated for their philosophical acumen, did they write analytically and ingenuously."

"I will frankly acknowledge, that, at the commencement of the experiments recited in this section, I was so far from having formed any hypothesis that led to the discoveries I made in pursuing them, that they would have appeared very improbable to me had I been told of them; and when the decisive facts did at length obtrude themselves upon my notice, it was very slowly, and with great hesitation, that I yielded to the evidence of my senses. And yet, when I re-consider the matter, and compare my last discoveries relating to the constitution of the atmosphere with the first, I see the closest and the easiest connexion between them, so as to wonder that I should not have been led immediately from the one to the other. That this was not the case, I attribute to the force of prejudice, which, unknown to ourselves, biasses not only our judgments, properly so called, but even the perceptions of our senses; for we may take a maxim so strongly for granted, that the plainest evidence of sense will not entirely change, and often hardly modify, our persuasions; and the more ingenious a man is, the more effectually he is entangled in his errors; his ingenuity only helping him to deceive himself, by evading the force of truth."

"There are, I believe, very few maxims in philosophy that have laid firmer hold upon the mind, than that air, meaning atmospherical air, (free from various foreign matters, which were always supposed to be dissolved, and intermixed with it) is a simple elementary substance, indestructible, and unalterable, at least as much so as water is supposed to be."

"In the course of my inquiries I was... soon satisfied that atmospherical air is not an unalterable thing; for that, according to my first hypothesis, the phlogiston with which it becomes loaded from bodies burning in it, and animals breathing it, and various other chemical processes, so far alters and depraves it, as to render it altogether unfit for inflammation, respiration, and other purposes to which it is subservient; and I had discovered that agitation in water, the process of vegetation, and probably other natural processes, restore it to its original purity."

"At the time of my first publication, I was not possessed of a burning lens of any considerable force; and for want of one, I could not possibly make many of the experiments that I had projected, and which, in theory, appeared very promising. I had, indeed, a mirror of force sufficient for my purpose. But the nature of this instrument is such, that it cannot be applied, with effect, except upon substances that are capable of being suspended, or resting on a very slender support. It cannot be directed at all upon any substance in the form of powder, nor hardly upon any thing that requires to be put into a vessel of quicksilver; which appears to me to be the most accurate method of extracting air from a great variety of substances..."

"But having afterwards procured a lens of twelve inches diameter, and twenty inches focal distance, I proceeded with great alacrity to examine, by the help of it, what kind of air a great variety of substances, natural and factitious, would yield, putting them into the vessels represented fig. a, Plate IV. which I filled with quicksilver, and kept inverted in a bason of the same."

"On the 1st of August, 1774, I endeavoured to extract air from mercurius calcinatus per se; and I presently found that, by means of this lens, air was expelled from it very readily. Having got about three or four times as much as the bulk of my materials, I admitted water to it, and found that it was not imbibed by it. But what surprized me more than I can well express, was, that a candle burned in this air with a remarkably vigorous flame, very much like that enlarged flame with which a candle burns in nitrous air, exposed to iron or liver of sulphur; but as I had got nothing like this remarkable appearance from any kind of air besides this particular modification of nitrous air, and I knew no nitrous acid was used in the preparation of mercurius calcinatus, I was utterly at a loss how to account for it."

"This experiment might have satisfied any moderate sceptic, but, however, being at Paris in the October following, and knowing that there were several very eminent chymists in that place, I did not omit the opportunity... to get an ounce of mercurius calcinatus prepared by Mr. Cadet, of the genuineness of which there could not possibly be any suspicion; and at the same time, I frequently mentioned my surprise at the kind of air which I had got from this preparation to Mr. Lavoisier Mr. le Roy, and several other philosophers who honoured me with their notice in that city; and who I dare say cannot fail to recollect the circumstance."

"On the 8th of this month [March, 1775] I procured a mouse, and put it into a glass vessel, containing two ounce measures of the air from mercurius calcinatus. Had it been common air, a full grown mouse, as this was, would have lived in it about a quarter of an hour. In this air, however, my mouse lived a full half hour; and though it was taken out seemingly dead, it appeared to have been only exceedingly chilled; for, upon being held to the fire, it presently revived, and appeared not to have received any harm from the experiment."

"I have been so happy, as by accident to have hit upon a method of restoring air, which has been injured by the burning of candles, and to have discovered at least one of the restoratives which nature employs for this purpose. It is vegetation. This restoration of vitiated air, I conjecture, is effected by plants imbibing the phlogistic matter with which it is overloaded."

"One might have imagined that, since common air is necessary to vegetable, as well as to animal life, both plants and animals had affected it in the same manner; and I own I had that expectation, when I first put a sprig of mint into a glass jar, standing inverted in a vessel of water; but when it had continued growing there for some months, I found that the air would neither extinguish a candle, nor was it at all inconvenient to a mouse, which I put into it."

"On the 17th of August 1771, I put a sprig of mint into a quantity of air, in which a wax candle had burned out, and found that, on the 27th of the same month, another candle burned perfectly well in it."

"Fluctuating... as the present state of this branch of knowledge is, I shall not decline to give my present views of it; nor shall I find any more difficulty in retracting any opinion I shall now advance, than I have hitherto done in retracting what I have advanced before. The sketch that I shall now give may at least serve, like former theories, to amuse us when we look back upon it, after having gained a more perfect knowledge of the subject."

"That the vegetable creation should restore the air which is spoiled by the animal part of it, looks like a rational system, and seems to be of a piece with the rest. Thus fire purifies water all the world over. It purifies it by distillation, when it raises it in vapours, and lets it fall in rain; and farther still by filtration, when keeping it fluid, it suffers that rain to percolate the earth. We knew before that putrid animal substances were converted into sweet vegetables when mixed with the earth and applied as manure; and now, it seems, that the same putrid substances, mixed with the air, have a similar effect. The strong, thriving state of your mint, in putrid air, seems to show that the air is mended by taking something from it, and not by adding to it. I hope this will give some check to the rage of destroying trees that grow near houses, which has accompanied our late improvements in gardening, from an opinion of their being unwholesome. I am certain, from long observation, that there is nothing unhealthy in the air of woods; for we Americans have everywhere our country habitations in the midst of woods, and no people on earth enjoy better health or are more prolific."

"Why were Priestley, Boyle and Black able to see the question clearly enough to begin trying to answer it? ...because they had new tools. The air pump designed by Otto von Guericke and Boyle (...in collaboration with his assistant Robert Hooke...) were essential to Priestley's lab in Leeds. ...In a way, the air pump had enabled the entire field of pneumatic chemistry in the seventeenth century."

"The Royal Society... voted to award him the Copley Medal, the most prestigious scientific prize of its day, "on account of the many curious and useful Experiments contained in his observations on different kinds of Air." In receiving the prize, Priestley was joining the ranks of his friends Canton and Franklin, who had three medals between them. Only five years after they had encouraged him to turn his experimental hobbies into a serious vocation, Priestly had reached the highest pinnacle of scientific achievement."

"In 1774 he thought he had obtained nitrous oxide... in 1775 he saw the gas as dephlogisticated air... If we refuse the palm to Priestley, we cannot award it to Lavoisier for the work of 1775... Lavoisier insisted that oxygen was an atomic "principle of acidity"... formed only when that "principle" united with "caloric"... Ignoring Scheele, we can safely say that oxygen had not been discovered before 1774, and we would probably say that it had been discovered by 1777 or shortly thereafter. But... any attempt to date the discovery must inevitably be arbitrary because discovering a new sort of phenomenon is necessarily a complex event, one which involves recognizing both that something is and what it is."

"Priestley had discovered in 1772 that metals on calcination absorbed at most one-fifth of the volume of air in which they were enclosed."

"In... "The Portuguese Discoveries and the Rise of Modern Science", Prof. Hooykaas supported the thesis "That the Portuguese seafarers and scientists of the 15th and 16th centuries made an important contribution to the rise of modern science by unintentionally undermining the belief in scientific authorities and by strengthening the confidence in the empirical, natural-historic method". ...Prof. Hooykaas analyzed the meaning of "natural science" in Antquity and the Middle Ages... characterized by too great a confidence in human reason and a sacred respect for what the authorities in the ancient world had written. ...In 1956, Prof. Hooykaas had already affirmed that "the discovery of the New World caused many difficulties to naturalists and historians..." …botanical species of medical interest warned that Dioscorides and Galen had not known everything; ...Portuguese seamen had clarified many doubts and shown the existence of the antipodes etc.."

"The modern origins of empirical scientific knowledge lie in the sixteenth and seventeenth centuries. This time period, known as the Scientific Revolution, saw advances such as Newton's theory of gravitation, Boyle's gas laws, Hooke's recognition that all living things are made of cells, and the beginning of the Royal Society... The spirit that infused this time period brought forth a whole host of new knowledge, and the disproving of facts that had existed for centuries, if not millennia. ...some of the most important components of this endeavor were to try to eliminate errors and create a means of spreading correct facts. Many of the papers presented in the early years of the Royal Society were devoted to trying to understand errors, to root out misunderstandings, or to test the veracity of tales told to them that often seemed too good to be true. ...Most important, they didn't keep this new knowledge secret. They spread it far and wide, publishing it and disseminating it through the loose network of natural philosophers of Europe."

"Concerning ourselves we speak not; but as touching the matter which we have in hand, this we ask;—that men deem it not to be the setting up of an Opinion, but the performing of a Work; and that they receive this as a certainty; that we are not laying the foundations of any sect or doctrine, but of the profit and dignity of mankind:—Furthermore, that being well disposed to what shall advantage themselves, and putting off factions and prejudices, they take common counsel with us, to the end that being by these our aids and appliances freed and defended from wanderings and impediments, they may lend their hands also to the labours which remain to be performed:—And yet, further, that they be of good hope; neither feign and imagine to themselves this our Reform as something of infinite dimension and beyond the grasp of mortal man, when, in truth, it is of infinite errour, the end and true limit; and is by no means unmindful of the condition of mortality and humanity, not confiding that such a thing can be carried to its perfect close in the space of one single age, but assigning it as a task to a succession of generations."

"[L]ong ago have those doctrines been exploded of the Force of the First Mover and the Solidity of the Heaven,—the stars being supposed to be fixed in their orbs like nails in a roof. And with no better reason is it affirmed, that there are different poles of the zodiac and of the world; that there is a Second Mover of counteraction to the force of the first; that all the heavenly bodies move in perfect circles; that there are eccentrics and epicycles whereby the constancy of motions in perfect circles is preserved; that the moon works no change or violence in the regions above it: and the like. And it is the absurdity of these opinions that has driven men to the of the earth; which I am convinced is most false. But there is scarce any one who has made inquiries into the physical causes, as well of the substance of the heavens both stellar and interstellar..."

"Though Lavoisier generally gets credit for the authorship of this principle [ conservation of mass ], others had conceived it before him. The seventeenth century chymists, notably Helmont, Starkey, and Boyle, had a dawning awareness of the importance of weighing and measuring materials before and after an experimental process, though their methods and measurement devices were not so precise. In 1623, Francis Bacon declared, "[…]when they perceive that a body which was before manifest to the senses has escaped and disappeared, they should not admit or liquidate the account before it has been shown to them where the body has gone to and into what it has been received." And as early as 450 B.C., Anaxagoras argued, "Wrongly do the Greeks suppose that aught begins or ceases to be; for nothing comes into being or is destroyed; but all is an aggregation or secretion of preexisting things; so that all becoming might more correctly be called becoming mixed, and all corruption, becoming separate.""

"In Newton's time only two kinds of force were available for quantitative investigation. One was the force of gravity; the other the forces of push and pull encountered in everyday life... Newton endeavored to construct a general theory of all forces, both those known in his time and those that might be discovered and investigated later. He intended his theory of gravitation to be one example that he himself could work out fully... Newton formulated his celebrated three laws: (1) In the absence of force, a body will continue at rest or in its present state of uniform rectilinear motion. (2) In the presence of force, a body will be accelerated in the direction of that force, the product of its mass by its acceleration being equal to the force (f = ma). (3) To every force there corresponds an equal counterforce, acting in a direction opposite to that of the force... According to the third law, then, each planet exerts an attractive counterforce to the sun, accelerating it toward the planet... a relatively small acceleration, because the mass of the sun so vastly exceeds... every planet..."

"During medieval times, men accepted Ptolemy's view that the earth was the natural center of the universe. ...[A]dapting earth as a universal ' (standard to which all motions are referred) was justified... Once the Ptolemaic point of view was abandoned, the choice... was reopened. Copernicus substituted the sun... as the "natural" frame of reference, and his choice was indeed excellent for describing the motions within the solar system. Today, however, it is understood that the sun is but one of millions of fixed stars in the galaxy... one of innumerable galaxies... Newton was well aware of the profundities involved in the choice of a proper frame of reference. All of his fundamental laws of mechanics involved statements concerning accelerations, changes to velocities... rather than the velocities themselves. The accelerations were tied to distances between the bodies... The choice of the frame of reference had no effect on the determination of distances... but the accelerations which resulted from the mutual attractions and repulsions of bodies were to be reckoned in relation to a universal norm... intimately bound up with the choice of a frame of reference. ...[T]here was no such thing as absolute rest, or absolute motion, for that matter, but only absolute acceleration... governed by the forces resulting from the proximity of other bodies."

"The credit of first using the telescope for astronomical purposes is almost invariably attributed to Galilei, though his first observations were in all probability slightly later in date than those of Harriot and Marius, is to a great extent justified by the persistent way in which he examined object after object, whenever there seemed any reasonable prospect of results following, by the energy and acuteness with which he followed up each clue, by the independence of mind with which he interpreted his observations, and above all by the insight with which he realised their astronomical importance."

"Let me close by reminding you of what Newton actually did on the day that he conceived G = k \frac{mm'}{r^2}. ...Newton did not have any subsidies, grants, funds, Secret Service money. But he had the moon. He said, "... I cannot throw a ball round the world, but let me picture the moon as if it were a ball which has been flung around the world... How long will it take to go round the world?" ...He knew the value of gravity at the earth's surface ...but he did not know the value of the earth's gravity for the moon. He said, "Let us suppose that it is given by an inverse square law. Now, how long will it take the moon to go around?" It comes out at twenty-eight days. As Newton said, "They agreed pretty nearly.""

"The gloriously romantic universe of Dante and Milton, that set no bounds to the imagination of man as it played over space and time, had now been swept away. Space was identified with the realm of geometry, time with the continuity of number. The world that people had thought themselves living in—a world rich with colour and sound, redolent with fragrance, filled with gladness, love and beauty, speaking everywhere of purposive harmony and creative ideals—was crowded now into minute corners in the brains of scattered organic beings. The really important world outside was a world hard, cold, colourless, silent, and dead; a world of quantity, a world of mathematically computable motions in mechanical regularity. The world of qualities as immediately received by man became just a curious and quite minor effect of that infinite machine beyond."

"[T]he supremely important field for the ordinary purposes of education... perhaps more in need of the intervention of the historian... is the so-called "scientific revolution," popularly associated with the sixteenth and seventeenth centuries, but reaching back in an unmistakably continuous line...much earlier still. Since the revolution overturned the authority in science not only in the middle ages but of the ancient world—since it ended not only in the eclipse of Aristotelian physics—it outshines everything since the rise of Christianity and reduces the Renaissance and Reformation to the rank of mere episodes, mere internal displacements, within the system of medieval Christendom. Since it changed the character of men's habitual mental operations even in the conduct of the non-material sciences, while transforming the whole diagram of the physical universe and the very texture of human life itself. It looms so large as the real origin both of the modern world and of the modern mentality that our customary periodisation of European history has become an anachronism and an encumbrance."

"William Gilbert published a famous book on the magnet in 1600 and laid himself open to the gibes of Sir Francis Bacon for being one of those people so taken by their pet subject of research that they could only see the whole universe transposed into terms of it. Having made a spherical magnet called a ', and having found that it revolved when placed in a magnetic field, he decided that the whole earth was a magnet, that gravity was a form of magnetic attraction, and that the principles of the magnet accounted for the workings of the Copernican system as a whole. Kepler and Galileo were both influenced by this view, and with Kepler, it became an integral part of his system, a basis for the doctrine of almost universal gravitation."

"In mechanics, Descartes can hardly be said to have advanced beyond Galileo. The latter had overthrown the ideas of Aristotle on this subject and Descartes simply "threw himself upon the enemy" that had already been "put to the rout." His statement of the first and second laws of motion was an improvement in form, but his third law is false in substance. The motions of bodies in their direct impact was imperfectly understood by Galileo erroneously given by Descartes and first correctly stated by C. Wren, J. Wallis, and C. Huygens."

"In the sixteenth and seventeenth centuries the medieval world view, based on Aristotelian philosophy and Christian theology, changed radically. The notion of an organic, living, and spiritual universe was replaced by that of a world as a machine, and the world machine became the dominant metaphor of the modern era. This radical change was brought about by the new discoveries in physics, astronomy, and mathematics known as the Scientific Revolution and associated with the names of Copernicus, Galileo, Descartes, Bacon, and Newton."

"From the thick darkness of the middle ages man's struggling spirit emerged as in new birth; breaking out of the iron control of that period; growing strong and confident in the tug and din of succeeding conflict and revolution, it bounded forwards and upwards with restless vigour to the investigation of physical and moral truth; ascending height after height; sweeping afar over the earth, penetrating afar up into the heavens; increasing in endeavour, enlarging in endowment; every where boldly, earnestly out-stretching, til, in the AUTHOR of the PRINCIPIA, one arose, who, grasping the master-key of the universe and treading its celestial paths, opened up to the human intellect the stupendous realities of the material world, and, in the unrolling of its harmonies, gave to the human heart a new song to the goodness, wisdom, and majesty of the all-creating, all-sustaining, all-perfect God."

"In the century from Copernicus to Newton, the understanding of the universe had been transformed. The Earth had been firmly dislodged from its position of celestial preeminence at the center of the Ptolemaic universe. The nature of the orbits of the planets had been revealed by the masterful observations of Tycho and their ingenious interpretation by Kepler. The failure to detect parallax in stars was accepted as an indication that they must be at vast distances beyond the solar system, such that any parallax would be too small to be measurable with current instruments. Galileo introduced the telescope and produced observations that provided validations of the new ideas. And the genius of Newton brought forth the reflecting telescope, new laws of motion, and an understanding of the fundamentals of optics. It also delivered the theory of universal gravitation, which explained the motions of the planets and identified the primary force in shaping the universe. Real science now had its firm foundation."

"The clash between reason and Portuguese experience. Hooykaas' starting point is the intellectual challenge which, from the early 15th century onward, was posed by the discoveries of the Portuguese mariners... There follows an array of fascinating accounts of, and quotations from, works by contemporary authors who were compelled to face as facts numerous phenomena the ancients had been quite sure could not possibly be observed because they were bound not to exist. Examples are Aristotle's denial that the tropics could be inhabited; Ptolemy's mathematically derived conviction that all dry land is confined to part of the Northern Hemisphere, and so on. ...In Hooykaas' view we are witnessing here a birth of 'natural history' in the domain of the hard and given fact... The narrow world of sense-data to which the ancient natural philosophers had confined their all-too-rational speculations was now being blown to pieces. And this was not being done by fellow natural philosophers, but rather at the urging of scarcely literate sailors!"

"Galileo had the experience of beholding the heavens as they actually are for perhaps the first time, and wherever he looked he found evidence to support the Copernican system against the Ptolemaic, or at least weaken the authority of the ancients. This shattering experience—of observing the depths of the universe, of being the first mortal to know what the heavens are actually like—made so deep an impression... that it is only by considering the events of 1609... that one can understand the subsequent direction of his life."

"His conflict with the Catholic Church arose because deep in his heart Galileo was a believer. There was for him no path of compromise, no way to have separate secular and theological cosmologies. If the Copernican system was true as he believed, what else could Galileo do but fight with every weapon he had in his arsenal... to make his Church accept a new system of the universe. ...In the contrast between Galileo's heroic stand when he tried to reform the cosmological basis of orthodox theology and his humbled, kneeling surrender when he disavowed his Copernicanism, we may sense the tremendous forces attendant on the birth of modern science."

"The seventeenth century witnessed the birth of modern science as we know it today. The science was something new, based on a direct confrontation of nature by experiment and observation. But there was another feature of the new science—a dependence on numbers, on real numbers of actual experience. ...The ancients knew a few numerical laws... But prior to the Scientific Revolution, the goal of science (or the study of nature) was not to seek laws of nature expressed in terms of numbers or number relations. ...the new science ...not only found laws based on numbers but they were also willing to express these laws in terms of higher powers of numbers—squares and cubes."

"The pioneering practitioners of the new science knew that they were producing a new kind of knowledge and so they declared this newness in the titles of their books and articles. Thus we have Galileo's Two New Sciences, Boyle's New Experiments, Kepler's New Astronomy, and Tartaglia's New Science. When Ben Jonson presented a masque entitled "News from the New World," his new world was not the newly found continent of North America, but the new world of science, the world revealed by the telescope of Galileo."

"Although the authority of the ancient authors as the arbiters of all scientific knowledge had obviously been severely weakened, it did not immediately crumble. Too many professional, medical, ecclesiastical, and legal careers were founded on that authority for it to simply disappear without a struggle. The scientific elite resisted the infusion of new natural knowledge with all its might, but in the long run, its rearguard efforts were futile. ...The common sense of the working people prevailed and brought about the changes in worldview that have come to be known as the Scientific Revolution."

"Koyré's exaltation of the "Platonic and Pythagorean" elements of the Scientific Revolution... was based on a demonstrably false understanding of how Galileo reached his conclusions. Koyré asserted that Galileo merely used experiments as a check on the theories he devised by mathematical reasoning. But later research has definitively established that Galileo's experiments preceded his attempts to give a mathematical account of their results."

"Growing skill in the working of metals is... exemplified by the development of the instrument-maker's craft. To many... we make reference elsewhere—for example, clocks, navigational instruments and balances. ...Brass, ivory, and closed-grained woods, such as box and pear, were the principal materials of the instrument-makers, with brass becoming increasingly favoured because of its rigidity and permanence. For the shaping of metal the lathe was a valuable tool, and the clock-makers in particular developed it greatly for precision work. The engraving of scales was, of course, a most important part of the work: until the advent of mechanical devices, this was done with simple engraving tools and punches, the design being first set out by geometrical methods. The earliest products of the instrument-makers were made mainly for astronomical purposes or to apply astronomical methods in navigation: they included astrolabes, cross-staffs, quadrants, sundials, and orreries, as well as basic geometrical instruments such as compasses and rules. From the seventeenth century, however, a variety of new instruments, or much improved versions of old ones, began to appear. The needs of surveyors led to the elaboration of the hodometer... enabling distances to be measured... Improvements in artillary called for more accurate sighting of cannon, and by the beginning of the seventeenth century the gunner's level had been highly developed. The invention of the telescope and microscope introduced new problems both in the making of lenses and of the instruments in which they were mounted: the new instruments were a regular part of the instrument-maker's trade from about 1660. From 1700 the revolution in science was making still further demands on the craft, and air-pumps, thermometers, barometers, electrical machines, and other instruments were called for in constantly increasing quantities."

"After sketching his program for the scientific revolution that he foresaw, Bacon ends his account with a prayer: "Humbly we pray that this mind may be steadfast in us, and that through these our hands, and the hands of others to whom thou shalt give the same spirit, thou wilt vouchsafe to endow the human family with new mercies". That is still a good prayer for all of us as we begin the twenty-first century."

"The great question for our time is, how to make sure that the continuing scientific revolution brings benefits to everybody rather than widening the gap between rich and poor. To lift up poor countries, and poor people in rich countries, from poverty, to give them a chance of a decent life, technology is not enough. Technology must be guided and driven by ethics if it is to do more than provide new toys for the rich."

"Science as subversion has a long history. ...Davis and Sakharov belong to an old tradition in science that goes all the way back to the rebels Benjamin Franklin and Joseph Priestley in the eighteenth century, to Galileo and Giordano Bruno in the seventeenth and sixteenth. If science ceases to be a rebellion against authority, then it does not deserve the talents of our brightest children. ...We should try to introduce our children to science today as a rebellion against poverty and ugliness and militarism and economic injustice."

"There is an enormous variety of things that we never dreamed of, like... black holes, s, quasars, all these unbelievably active goings-on in the universe... [I]n Aristotle's time the universe... was supposed to be quiescent, it was supposed to be perfect and peaceful, and nothing ever happened in the ; and that remained true... throughout all of the revolutions... It remained the general view of astronomers... through Copernicus, and Galileo, and Newton, and everybody else... until just the last 30 years, and now we know it's not like that at all. In fact the universe is full of violent events, and fantastic strong gravitational fields, and collapsed objects, and huge outpourings of energy."

"I want now to glance for a moment at the development of the theoretical method, and while doing so especially to observe the relation of pure theory to the totality of the data of experience. Here is the eternal antithesis of the two inseparable constituents of human knowledge, Experience and Reason, within the sphere of physics. We honour ancient Greece as the cradle of western science. She for the first time created the intellectual miracle of a logical system, the assertions of which followed one from another with such rigor that not one of the demonstrated propositions admitted of the slightest doubt—Euclid's geometry. This marvellous accomplishment of reason gave to the human spirit the confidence it needed for its future achievements. ...But yet the time was not ripe for a science that could comprehend reality, was not ripe until a second elementary truth had been realized, which only became the common property of philosophers after Kepler and Galileo. Pure logical thinking can give us no knowledge whatsoever of the world of experience; all knowledge about reality begins with experience and terminates in it."

"Although many historians of the new millennium now take issue with the notion of a Scientific Revolution, it is generally agreed that Newton's work culminated the long development of European science, creating a synthesis that opened the way for the scientific culture of the modern age."

"I mentally conceive of some moveable [sphere] projected on a horizontal plane, all impediments being put aside. Now it is evident... that equable motion on this plane would be perpetual if the plane were of infinite extent, but if we assume it to be ended, and [situated] on high, the movable, driven to the end of this plane and going on further, adds on to its previous equable and indelible motion, that downward tendency which it has from its heaviness. Thus, there emerges a certain motion, compounded..."

"It seems to me proper to adorn the Author's thought here with its conformity to a conception of Plato's regarding the determination of the various speeds of equable motion in the celestial motions of revolution. ...he said that God, after having created the movable celestial bodies, in order to assign to them those speeds with which they must be moved perpetually in equable circular motion, made them depart from rest and move through determinate spaces in that natural straight motion in which we sensibly see our moveables to be moved from the state of rest, successively accelerating. And he added that these having been made to gain that degree [of speed] which it pleased God that they should maintain forever, He turned their straight motion into circulation, the only kind [of motion] that is suitable to be conserved equably, turning always without retreat from or approach toward any pre-established goal desired by them. The conception is truly worthy of Plato, and it is to be more esteemed to the extent that its foundations, of which Plato remained silent, but which were discovered by our Author in removing their poetical mask or semblance, show it the guise of a true story."

"On the authority of Aristotle... motion in the planetary world was somehow directed by the more perfect motion in higher spheres, and so on, up to the outermost sphere of fixed stars, indistinguishable from the prime mover. This implied a refined animistic and pantheistic world view, incomparably more rational than the ancient world views of Babylonians and Egyptians, among others, but a world view, nonetheless, hardly compatible with the idea of "inertial motion" which is implied in Buridan's concept of "impetus"… a momentous breaking point... which was to bear fruit... in the hands, first of Copernicus and then of Newton."

"J. Kepler was the first (that I know of) that discover'd the true cause of the Tide, and he explains it largely in his Introduction to the Physics of the Heavens, given in his Commentaries to the Motion of the Planet Mars, where after he has shewn the Gravity or Gravitation of all Bodies towards another, he thus writes: "The Orb of the attracting Power, which is in the Moon is extended as far as the Earth, and draws the Waters under the Torrid Zone, acting upon places where it is vertical, insensibly on included Seas, but sensibly on the Ocean, whose Beds are large, and the Waters have the liberty of reciprocation, that is, of rising and falling"; and in the 70th Page of his Lunar Astronomy,—"But the cause of the Tides of the Sea appear to be the Bodies of the Sun and Moon drawing the Waters of the Sea.""

"The Scientific Revolution has not been a revolution of knowledge. It has been above all a revolution of ignorance. The great discovery that launched the Scientific Revolution was the discovery that humans do not know the answers to their most important questions."

"Until the Scentific Revolution most human cultures did not believe in progress. They thought that the golden age was the past, and that the world was stagnant, if not deteriorating."

"the Scientific Revolution might prove itself far greater than a mere historical revolution. It may turn out to be the most important bological revolution since the appearance of life on earth."

"To reassert the reign of beauty, Copernicus goes back to what he had once called "the first principles of uniform motion." He rejects non-uniformities and inconsistancies of motion - his "mind shudders" at the very consideration of them - and even at the cost of setting the earth in motion, he arrives at a system that has all the earmarks of divine handicraft; the s are gone, the phenomena are saved; the whole system has symmetry, parsimony, necessity. ... The device of uniform motion in a circle was not forced by the data; and as Kepler's ellipses showed later, it was not even the most functional device from the mathematical point of view. Yet the metaphor of uniform circular motion as the divine key... - even as in antiquity - had infected the thinking from which the scientific revolution of the seventeenth century came. ...the function of a metaphor ..."can be a restructuring of the world," in the words of Sir Ernst Gombrich."

"The Portuguese had undertaken their voyages towards the southern hemisphere in spite of the science of their day... they followed an irresistible urge, which went against their scientific and religious convictions."

"Our thesis now is that the Portuguese seafarers and scientists of the 15th and 16th centuries made an important contribution to the rise of modern science by unintentionally undermining the belief in scientific authorities and by strengthening the confidence in an empirical, natural, historical method."

"Perhaps there is no literature in Europe that mirrors so clearly as the Portuguese, the painful conflict in the minds of people who, on the one hand, by their humanistic education, not only knew better but also more uncritically admired, ancient learning than their medieval predecessors, and, who, on the other hand, in the same epoch, were confronted with abundant proofs of the insufficiency and fallibility of that same Antiquity."

"In the early decades of the seventeenth century, the men of the Renaissance could show that they had already put out to good interest the treasure bequeathed to them by the Greeks. They had produced the astronomical system of Copernicus, with Kepler's great additions; the astronomical discoveries and the physical investigations of Galileo; the mechanics of Stevinus and the 'De Magnete' of Gilbert; the anatomy of the great French and Italian schools and the physiology of Harvey. In Italy, which had succeeded Greece in the hegemony of the scientific world, the Accademia dei Lyncei and sundry other such associations for the investigation of nature, the models of all subsequent academies and scientific societies, had been founded; while the literary skill and biting wit of Galileo had made the great scientific questions of the day not only intelligible, but attractive to the general public."

"Sixty years after Bacon's death Newton had crowned the long labors of the astronomers and the physicists, by coordinating the phenomena of molar motion throughout the visible universe into one vast system, but the 'Principia' helped no man to either wealth or comfort. Descartes, Newton, and Leibnitz had opened up new worlds to the mathematician, but the acquisitions of their genius enriched only man's ideal estate. Descartes had laid the foundations of rational cosmogony and of physiological psychology; Boyle had produced models of experimentation in various branches of physics and chemistry; Pascal and Torricelli had weighed the air; Malpighi and Grew, Ray and Willoughby had done work of no less importance in the biological sciences; but weaving and spinning were carried on with the old appliances; nobody could travel faster by sea or by land than at any previous time in the world's history, and King George could send a message from London to York no faster than King John might have done. Metals were worked from their ores by immemorial rule of thumb, and the centre of the iron trade of these islands was still among the oak forests of Sussex. The utmost skill of our mechanicians did not get beyond the production of a coarse watch."

"Science... has ended by utterly repudiating the personal point of view. She catalogues her elements and records her laws indifferent as to what purpose may be shown forth by them, and constructs her theories quite careless of their bearing on human anxieties and fates. Though the scientist may individually nourish a religion, and be a theist in his irresponsible hours, the days are over when it could be said that for Science herself the heavens declare the glory of God and the firmament showeth his handiwork. Our solar system, with its harmonies, is seen now as but one passing case of a certain sort of moving equilibrium in the heavens, realized by a local accident in an appalling wilderness of worlds where no life can exist. In a span of time which as a cosmic interval will count but as an hour, it will have ceased to be. The Darwinian notion of chance production, and subsequent destruction, speedy or deferred, applies to the largest as well as to the smallest facts. It is impossible, in the present temper of the scientific imagination, to find in the driftings of the cosmic atoms, whether they work on the universal or on the particular scale, anything but a kind of aimless weather, doing and undoing, achieving no proper history, and leaving no result. Nature has no one distinguishable ultimate tendency with which it is possible to feel a sympathy. In the vast rhythm of her processes... she appears to cancel herself. The books of natural theology which satisfied the intellects of our grandfathers seem to us quite grotesque, representing, as they did, a God who conformed the largest things of nature to the paltriest of our private wants. The God whom science recognizes must be a God of universal laws exclusively, a God who does a wholesale, not a retail business. He cannot accommodate his processes to the convenience of individuals. The bubbles on the foam which coats a stormy sea are floating episodes, made and unmade by the forces of the wind and water. Our private selves are like those bubbles—epiphenomena, as Clifford, I believe, ingeniously called them; their destinies weigh nothing and determine nothing in the world's irremediable currents of events."

"When Galilei let balls of a particular weight, which he had determined himself, roll down an inclined plain, or Torricelli made the air carry a weight, which he had previously determined to be equal to that of a definite volume of water; or when, in later times, Stahl changed metal into lime, and lime again into metals, by withdrawing and restoring something, a new light flashed on all students of nature. They comprehended that reason has insight into that only, which she herself produces on her own plan, and that she must move forward with the principles of her judgments, according to fixed law, and compel nature to answer her questions, but not let herself be led by nature, as it were in leading strings, because otherwise accidental observations made on no previously fixed plan, will never converge towards a necessary law, which is the only thing that reason seeks and requires. Reason, holding in one hand its principles, according to which concordant phenomena alone can be admitted as laws of nature, and in the other hand the experiment, which it has devised according to those principles, must approach nature, in order to be taught by it: but not in the character of a pupil, who agrees to everything the master likes, but as an appointed judge, who compels the witnesses to answer the questions which he himself proposes. Therefore even the science of physics entirely owes the beneficial revolution in its character to the happy thought, that we ought to seek in nature (and not import into it by means of fiction) whatever reason must learn from nature, and could not know by itself, and that we must do this in accordance with what reason itself has originally placed into nature. Thus only has the study of nature entered on the secure method of a science, after having for many centuries done nothing but grope in the dark."

"Galileo had provided the methodology for the analysis of motions on and near the earth and had applied it successfully. Copernicus and Kepler had previously obtained the laws of motion of the planets and their satellites. ...But Galileo had succeeded in deriving numerous laws from a few physical principles and... the axioms and theorems of mathematics. ...The Keplerian laws ...were not logically related to each other. Each was an independent inference from observations. ...They seemed to be suspended in the same vacuum in which the planets moved. Galileo's laws had the additional advantage of supplying physical insight. The first law of motion and the law that the force of graviation gives... a downward acceleration of 32 ft/sec2... explain the vertrical rise and fall of bodies, motion on slopes, and projectile motion. Kepler's laws... had no physical basis. ...Kepler tried to introduce the idea of a magnetic force which the sun exerted... But he failed to related the behavior of the planets to the precise laws of planetary motion. ... The new astronomical theory was completely isolated from the theory of motion on earth. ...it bothered mathematicians and scientists who believed that all the phenomena of the universe were governed by one master plan instituted by the master planner—God."

"The goal of deriving all the phenomena of nature from a few basic physical laws and the axioms of mathematics had been set by Galileo... In studying curvilinear motions on the earth Galileo had found the parabola to be the basic curve. In the heavens... Kepler... had found the ellipse to be the basic curve. Why this difference? ...since parabola and ellipse are both conic sections there was the provocative suggestion that perhaps some physical law unified these related paths of motion. ... It has often happened in the history of mathematics and science that major problems remained outstanding... great minds... succeeded only in revealing the true difficulties... and in generating an atmosphere of dispair... Then a genius appeared... with ideas that seemed remarkably simple once propounded, clarified the entire situation, dispelled the confusion, restored order, and produced a new synthesis that embraced far more even than the phenomena under consideration. The genius who... picked up the torch of science dropped by Galileo, was Isaac Newton."

"I shall try to sum up the main obstacles which arrested the progress of science for such an immeasurable time. The first was the splitting of the world into two spheres, and the mental split which resulted from it. The second was the geocentric dogma, the blind eye turned on the promising line of thought which had started with the Pythagoreans and stopped abruptly with Aristarchus of Samos. The third was the dogma of uniform motion in perfect circles. The fourth was the divorcement of science from mathematics. The fifth was the inability to realize that a body at rest tended to stay at rest, a body in motion tended to stay in motion. The main achievement of the first part of the scientific revolution was the removal of these five cardinal obstacles. This was done chiefly by three men: Copernicus, Kepler and Galileo. After that, the road was open to the Newtonian synthesis; from there on the journey led with rapidly gaining speed to the atomic age."

"The uomo universale of the Renaissance, who was artist and craftsman, philosopher and inventor, humanist and scientist, astronomer and monk, all in one, split up into his component parts. Art lost its mythical, science its mystical inspiration; man became again deaf to the harmony of the spheres. The Philosophy of Nature became ethically neutral, and "blind" became the favourite adjective for the working of natural law. The space-spirit hierarchy was replaced by the space-time continuum. ...man's destiny was no longer determined from "above" by a super-human wisdom and will, but from "below" by the sub-human agencies of glands, genes, atoms, or waves of probability. ...they could determine his fate, but could provide him with no moral guidance, no values and meaning. A puppet of the Gods is a tragic figure, a puppet suspended on his chromosomes is merely grotesque."

"What the founders of modern science … had to do, was not criticize and to combat certain faulty theories, and to correct or to replace them by better ones. They had to do something quite different. They had to destroy one world and replace it by another. They had to reshape the framework of our intellect itself, to restate and to reform its concepts, to evolve a new approach to Being, a new concept of knowledge, and a new concept of science — and even to replace a pretty natural approach, that of common sense, by another which is not natural at all."

"The infinite Universe of the New Cosmology, infinite in Duration as well as Extension, in which eternal matter in accordance with eternal and necessary laws moves endlessly and aimlessly in eternal space, inherited all the ontological attributes of Divinity. Yet only those — all the others the departed God took with him... The Divine Artifex had therefore less and less to do in the world. He did not even have to conserve it, as the world, more and more, became able to dispense with this service..."

"There is something for which Newton — or better to say not Newton alone, but modern science in general — can still be made responsible: it is splitting of our world in two. I have been saying that modern science broke down the barriers that separated the heavens and the earth, and that it united and unified the universe. And that is true. But, as I have said, too, it did this by substituting for our world of quality and sense perception, the world in which we live, and love, and die, another world — the world of quantity, or reified geometry, a world in which, though there is place for everything, there is no place for man. Thus the world of science — the real world — became estranged and utterly divorced from the world of life, which science has been unable to explain — not even to explain away by calling it "subjective"."

"Here, then: a revolution [in science and chemistry] has taken place in an important part of human knowledge since your departure from Europe... I will consider this revolution to be well advanced and even completely accomplished if you range yourself with us. ...After having brought you up to date on what is happening in chemistry, it would be well to speak to you about our political revolution. We regard it as done and without any possibility of return to the old order."

"He [ Kepler ] supposes, in that treatise [epitome of astronomy], that the motion of the sun on his axis is preserved by some inherent vital principle; that a certain virtue, or immaterial image of the sun, is diffused with his rays into the ambient spaces, and, revolving with the body of the sun on his axis, takes hold of the planets and carries them along with it in the same direction; as a load-stone turned round in the neighborhood of a magnetic needle makes it turn round at the same time. The planet, according to him, by its inertia endeavors to continue in its place, and the action of the sun's image and this inertia are in a perpetual struggle. He adds, that this action of the sun, like to his light, decreases as the distance increases; and therefore moves the same planet with greater celerity when nearer the sun, than at a greater distance. To account for the planet's approaching towards the sun as it descends from the aphelium to the perihelium, and receding from the sun while it ascends to the aphelium again, he supposes that the sun attracts one part of each planet, and repels the opposite part; and that the part which is attracted is turned towards the sun in the descent, and that the other part is towards the sun in the ascent. By suppositions of this kind he endeavored to account for all the other varieties of the celestial motions."

"In the opinion of one of the most eminent modem naturalists, it was Boyle who opened up those chemical inquiries, which went on accumulating until, a century later, they supplied the means by which Lavoisier and his contemporaries fixed the real basis of chemistry, and enabled it for the first time to take its proper stand among those sciences that deal with the external world."

"We offer this work as mathematical principles of philosophy; for all the difficulty of philosophy seems to consist in this—from the phænomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phænomena; and to this end the general propositions in the first and second book are directed. In the third book we give an example of this in the explication of the System of the World; for by the propositions mathematically demonstrated in the first book, we there derive from the celestial phænomena the forces of gravity with which bodies tend to the sun and the several planets. Then from these forces, by other propositions which are also mathematical, we deduce the motions of the planets, the comets, the moon, and the sea."

"The researches of Galileo, followed up by Huygens and others, led to those modern conceptions of Force and Law, which have revolutionized the intellectual world. The great attention given to mechanics in the seventeenth century soon so emphasized these conceptions as to give rise to the Mechanical Philosophy, a doctrine that all the phenomena of the physical universe are to be explained upon mechanical principles. Newton's great discovery imparted a new impetus to this tendency. The old notion that heat consists in an agitation of corpuscles was now applied as an explanation to the chief properties of gases. The first suggestion in this direction was that the pressure of gases is explained by the battering of the particles against the walls of the containing vessel, which explained Boyle's law of the compressibility of air. Later, the expansion of gases, Avogadro's chemical law, the diffusion and viscosity of gases, and the action of Crooke's radiometer were shown to be consequences of the same kinetical theory; but other phenomena, such as the ratio of the specific heat at constant volume to that at constant pressure, require additional hypotheses, which we have little reason to suppose are simple, so that we find ourselves quite afloat. In like manner with regard to light..."

"Most authors were led to identify the birth of scientific method with what, not by accident, is called the Scientific Renaissance, and that until the nineteenth century the civilization that gave us science was not even considered worthy of that name: it was just a "period of decadence" of Greek civilization."

"The age-long history of thinking on gravitation, too, was erased from the collective consciousness, and that force somehow became the serendipitous child of Newton's genius. The new attitude is well illustrated by the anecdote of the apple, a legend spread by Voltaire, one of the most active and vehement erasers of the past. … The need to build the myth of an ex nihilo creation of modern science gave rise to much impassioned rhetoric."

"Not only can any given theory be proven wrong... sooner or later it probably will be. And when it is, the occasion will mark the success of science, not its failure. This was the pivotal insight of the Scientific Revolution: that the advancement of knowledge depends on current theories collapsing in the face of new insights and discoveries. In this model of progress, errors do not lead us away from truth. Instead, they edge us incrementally toward it."

"This is another important dispute in the history of how we think about being wrong: whether error represents an obstacle in the path toward truth, or the path itself. The former idea is a conventional one. The latter... emerged during the Scientific Revolution and continued to evolve throughout the Enlightenment. But it didn't really reach its zenith until the early nineteenth century, when... Pierre Simon Laplace refined the distribution of errors, illustrated by the now-familiar bell curve. ...Laplace used the bell curve to determine the precise orbit of the planets. ...By using the normal distribution to graph... individually imperfect data points, Laplace was able to generate a far more precise picture of the galaxy. ...aggregate enough flawed data, and you get a glimpse of the truth."

"Newton proposed that the particles of the air (we would call them molecules), were motionless in space and were held apart by repulsive forces between them... He assumed that the repulsive force was inversely proportional to the distance between the particles...He showed that, on the basis of this assumption, a collection of static particles in a box would behave exactly as Boyle had found. His model led directly to Boyle's law. Probably the greatest scientist ever, Newton managed to get the right answer from a model that was wrong in every possible way."

"The Hon. Robert Boyle... in the third volume of the folio edition of his work, is a paper having the following title, "That the Goods of Mankind may be much Increased by the Naturalist's Insight into Trades." This paper contains... the first attempt at a philosophical recognition of the value and importance of the industrial arts of mankind. In it we recognise the early effort of a man of science seeking to call the attention of the learned and great of his time to what he aptly denominates the Natural History of Trades. ...He contends that the benefit accruing from such an inquiry would be mutual, both to the learned in natural knowledge, and to the skilled in industrial art."

"The founders of modern science - for instance, Galileo, Kepler, and Newton - were mostly pious men who did not doubt God’s purposes. Nevertheless they took the revolutionary step of consciously and deliberately expelling the idea of purpose as controlling nature from their new science of nature. They did this on the ground that inquiry into purposes is useless for what science aims at: namely, the prediction and control of events. To predict an eclipse, what you have to know is not its purpose but its causes. Hence science from the seventeenth century onwards became exclusively an inquiry into causes. The conception of purpose in the world was ignored and frowned on. This, though silent and almost unnoticed, was the greatest revolution in human history, far outweighing in importance any of the political revolutions whose thunder has reverberated through the world."

"By analyzing the measurements of , Johannes Kepler established that planetary motions weren't circles but ellipses... Through his telescopes, Galileo saw that the Sun had its perfection tarnished by ugly black spots. And the Moon wasn't a perfect sphere but looked like a place, complete with mountains and giant craters. So why didn't it fall down? Isaac Newton finally answered... by exploring... [a radical] idea... that heavenly objects obey the same laws as objects here on Earth. ...Newton ...realized that ...the fate of a horizontally fired cannon ball depends on its speed: it crashes to the ground only if its speed is below some magic value. ...[W]ith ever higher speeds, they'll travel farther ...before landing ...until ...they keep their height over the ground ...constant and never land, merely orbiting ...just like the Moon! Since he knew the strength of gravity near the Earth's surface... he was able to calculate the magic speed... 7.9 kilometers per second. Assuming the Moon... was obeying the same laws... he could similarly predict what speed it needed... Moreover, since the Moon took one month to travel around a circle whose circumference Aristarchos had figured out, Newton already knew its speed... Now he made a remarkable discovery: if he assumed that the force of gravity weakened like the inverse square... then this magical speed that would give the Moon a circular orbit exactly matched its measured speed! He had discovered the law of gravity... applying not merely here on Earth, but in the heavens as well. ...People boldly extrapolated not only to the macrocosmos... but also to the microcosmos, finding that many properties... could be explained by applying to... atoms... The scientific revolution had begun."

"Newton did not show the cause of the apple falling, but he shewed a similitude between the apple and the stars. By doing so he turned old facts into new knowledge; and was well content if he could bring diverse phenomenon under "two or three Principles of Motion" even "though the Causes of these Principles were not yet discovered.""

"Gilbert, in his work, De Magnete printed in 1600 has only some vague notions that the magnetic virtue of the earth in some way determines the direction of the earth's axis, the rate of its diurnal rotation, and that of the revolution of the moon about it. Gilbert died in 1603, and in his posthumous work (De Mundo nostro Sublunari Philosophia nova, 1631) we have already a more distinct statement of the attraction of one body by another. "The force which emanates from the moon reaches to the earth, and, in like manner, the magnetic virtue of the earth pervades the region of the moon: both correspond and conspire by the joint action of both, according to a proportion and conformity of motions, but the earth has more effect in consequence of its superior mass; the earth attracts and repels, the moon, and the moon within certain limits, the earth; not so as to make the bodies come together, as magnetic bodies do, but so that they may go on in a continuous course." Though this phraseology is capable of representing a good deal of the truth, it does not appear to have been connected... with any very definite notions of mechanical action in detail."

"The inquiry into Nature having thus been pursued nearly two thousand years theologically, we find by the middle of the sixteenth century some promising beginnings of a different method—the method of inquiry into Nature scientifically—the method which seeks not plausibilities but facts."

"The way in which the persecution of Galileo has been remembered is a tribute to the quiet commencement of the most intimate change in outlook which the human race had yet encountered. Since a babe was born in a manger, it may be doubted whether so great a thing has happened with so little stir."

"The main importance of Francis Bacon’s influence does not lie in any peculiar theory of inductive reasoning which he happened to express, but in the revolt against second-hand information of which he was a leader."

"During the Middle Ages the universe was regarded as finite, with the earth at its centre. The idea was abandoned during the Scientific Renaissance, and the universe came to be pictured as an indefinitely large number of stars scattered throughout infinite Euclidean space. This conception appeared to be a necessary consequence of the theory of gravitation; for, as Newton pointed out, a finite material universe in infinite space would tend to concentrate in one massive lump."

"The Propositions that are insisted on in this Discourse. PROP. I. That the seeming Novelty and Singularity of this Opinion, can be no sufficient Reason to prove it Erroneus. PROP. II. That the places of Scripture, which seem to intimate the Diurnal Motion of the Sun, or Heavens, are fairly capable of another interpretation. PROP. III. That the Holy Ghost, in many places of Scripture, does plainly conform his Expressions to the Error of our Conceits, and does not speak of sundry things as they are in themselves, but as they appear unto us. PROP. IV. That divers learned Men have fallen into great Absurdities, whilst they have looked for the Grounds of Philosophy from the Words of Scripture. PROP. V. That the words of Scripture, in their proper and strict construction, do not any where affirm the Immobility of the Earth. PROP. VI. That there is not any Argument from the words of Scripture, Principles of Nature, or Observations in Astronomy, which can sufficiently evidence the Earth to be in the Centre of the Universe. PROP. VII. 'Tis probable that the Sun is the Centre of the World. PROP. VIII. That there is not any sufficient reason to prove the Earth incapable of those Motions which Copernicus ascribes unto it. PROP. IX. That it is more probable that the Earth does move, than the Heavens. PROP. X. That this Hypothesis is exactly agreeable to common Appearances."

"'Tis in Philosophy, and that is made up of nothing else; but receives addition from every days experiment. True indeed, for Divinity we have an infallible rule that do's plainly inform us of all necessary Truths; and therefore the Primitive Times are of greater Authority, because they were nearer to those holy Men who were the Pen-Men of Scripture. But now for Philosophy, there is no such reason: What ever the School Men may talk; yet Aristotles works are not necessarily true, and he himself hath by sufficient Arguments proved himself to be liable unto errour. Now in this case, if we should speak properly, Antiquity do's consist in the old age of the World, not in the youth of it. In such Learning as may be increased by fresh experiments and new discoveries: 'Tis we are the Fathers, and of more Authority than former Ages; because we have the advantage of more time than they had, and Truth (we say) is the Daughter of Time."

"Reason may be employed in two ways to establish a point: firstly, for the purpose of furnishing sufficient proof of some principle, as in natural science, where sufficient proof can be brought to show that the movement of the heavens is always of uniform velocity. Reason is employed in another way, not as furnishing a sufficient proof of a principle, but as confirming an already established principle, by showing the congruity of its results, as in astrology the theory of eccentrics and epicycles is considered as established, because thereby the sensible appearances of the heavenly movements can be explained; not, however, as if this proof were sufficient, forasmuch as some other theory might explain them."

"Five geometers—Clairaut, Euler, D'Alembert, Lagrange and Laplace—shared among them the world of which Newton had revealed the existence. They explored it in all directions, penetrated into regions believed inaccessible, pointed out countless phenomena in those regions which observation had not yet detected, and finally—and herein lies the imperishable glory—they brought within the domain of a single principle, a unique law, all that is most subtle and mysterious in the motions of the celestial bodies. Geometry also had the boldness to dispose of the future; when the centuries unroll themselves they will scrupulously ratify the decisions of science."

"Studies serve for delight, for ornament, and for ability. Their chief use for delight, is in privateness and retiring; for ornament, is in discourse; and for ability, is in the judgment and disposition of business. For expert men can execute, and perhaps judge of particulars, one by one; but the general counsels, and the plots and marshalling of affairs, come best from those that are learned. To spend too much time in studies, is sloth; to use them too much for ornament, is affectation; to make judgment wholly by their rules, is the humour of a scholar scholastic]. They perfect nature, and are perfected by experience. For natural abilities are like natural plants, that need proyning by study; and studies themselves do give forth directions too much at large, except they be bounded in by experience. Crafty men contemn studies; simple men admire them; and wise men use them. For they teach not their own use; but that is a wisdom without [outside of] them, and above them, won by observation. Read not to contradict and confute, nor to believe and take for granted, nor to find talk and discourse, but to weigh and consider. Some books are to be tasted, others to be swallowed, and some few to be chewed digested. That is, some books are to be read only parts; others to be read, but not curiously; and some few to be read wholly, and with diligence and attention. Some books also may be read by deputy, and extracts made of them by others; but that would be only in less important arguments, and the meaner sort of books: else distilled books are, like common distilled waters, flashy things. Reading maketh a full man; conference a ready man; and writing an exact man. And, therefore, if a man write little, he had need have a great memory; if he confer little, he had need have a present wit; and if he read little, he had need have much cunning, to seem to know that he doth not."

"The more man inquires into the laws which regulate the material universe, the more he is convinced that all its varied forms arise from the action of a few simple principles. These principles themselves converge, with accelerating force, towards some still more comprehensive law to which all matter seems to be submitted. Simple as that law may possibly be, it must be remembered that it is only one amongst an infinite number of simple laws: that each of these laws has consequences at least as extensive as the existing one, and therefore that the Creator who selected the present law must have foreseen the consequences of all other laws."

"Let such a history be once provided and well set forth, and let there be added to it such auxiliary and light-giving experiments... and the investigation of nature and of all sciences will be the work of a few years. ...In this way, and in this way only, can the foundations of a true and active philosophy be established; and then will men wake as from deep sleep."

"This history I call Primary History, or the Mother History."

"Atomism began life as a philosophical idea that would fail virtually every contemporary test of what should be regarded as 'scientific'; yet, eventually, it became the cornerstone of physical science."

"Scanning the past millennia of human achievement reveals just how much has been achieved during the last three hundred years since Newton set in motion the effective mathematization of Nature. We found that the world is curiously adapted to a simple mathematical description. It is enigma enough that the world is described by mathematics; but by simple mathematics, of the sort that a few years energetic study now produces familiarity with, this is an enigma within and enigma."

"Maxwell in particular noted that the phenomena of electromagnetism did not fit into the scheme of Newtonian mechanics. Whereas it had been thought that only the distance between two objects determined the force one exerted on the other, electric charges in motion, such as are met with in electric currents, were found to produce effects not encountered when charges are at rest. Celestial bodies will only attract each other; electric charges at rest will either attract or repel... they will exert forces only in the direction of the connecting straight line. Oersted discovered that an electric current (...charges in motion) will exert a force on a magnetic needle at right angles to the connecting straight line. Previous observations in astronomy had tended to show that the force between two bodies depended only on their instantaneous configuration, but Hertz showed by experiment that electromagnetic disturbances propagate as waves, at a finite rate of speed. Hence the force experienced by one body can be understood and explained only in terms of the history of the other."

"Maxwell succeeded in casting all known electromagnetic effects into a mathematical form that has endured to this day... known as Maxwell's field equations. Based on Faraday's earlier work, Maxwell stressed the notion of fields, in contrast to Newton's emphasis on the direct action of bodies on each other across empty space ('). Faraday and Maxwell regarded the effect on an electrically charged body as giving rise to stresses in its immediate surroundings. These in turn produce stresses in ever widening circles, gradually diminishing... These stresses... thought of as capable of existence in otherwise empty space, are called fields... intermediaries between material particles and which assume the burden of Newton's action at a distance."

"The old contrast, often amounting to hostility, between scientific and humane subjects needs to be broken down and replaced by a scientific humanism. At the same time, the teaching of science proper requires to be humanized. The dry and factual presentation requires to be transformed... by emphasizing the living and dramatic character of scientific advance... Here the teaching of the history of science, not isolated as at present, but in close relation to general history teaching, would serve to correct the existing atmosphere of scientific dogmatism. It would show at the same time how secure are the conquests of science in the control they give over natural processes and how insecure and provisional, however necessary, are the rational interpretations, the theories and hypotheses put forward at each stage. Past history by itself is not enough, the latest developments of science should not be excluded because they have not yet passed the test of time. It is absolutely necessary to emphasize the fact that science not only has changed but is continually changing, that it is an activity and not merely a body of facts. Throughout, the social implications of science, the powers that it puts into men’s hands, the uses... should be brought out and made real by a reference to immediate experience of ordinary life. ...[I]t should be possible to introduce the teaching of practical scientific methods by making students find out for themselves new relationships in things that already concern them and not in artificially simplified and unnecessarily abstract experiment."

"In every age there is a turning point, a new way of seeing and asserting the coherence of the world. It is frozen in the statues of Easter Island that put a stop to time—and in the medieval clocks of Europe that once also seemed to say the last word about the heavens for ever. Each culture tries to fix its visionary moment, when it was transformed by a new conception either of nature or of man. But in retrospect, what commands our attention as much are the continuities—the thoughts that run or recur from one civilization to another."

"If I were giving this lecture fifty years from now, the word "gravitation" would be as old-fashioned as the word "phlogiston" is to us. Relativity has certainly demoted gravitation as a real explanation, just as Priestley's and Lavoisier's analyses and decoding of chemical reactions destroyed the word "phlogiston.""

"An invention acts rather like a trigger, because, once it's there, it changes the way things are, and that change stimulates the production of another invention, which in turn, causes change, and so on. Why those inventions happened, between 6,000 years ago and now, where they happened and when they happened, is a fascinating blend of accident, genius, craftsmanship, geography, religion, war, money, ambition... Above all, at some point, everybody is involved in the business of change, not just the so-called "great men." Given what they knew at the time, and a moderate amount of what's up here [pointing to head], I hope to show you that you or I could have done just what they did, or come close to it, because at no time did an invention come out of thin air into somebody's head, [snaps fingers] like that. You just had to put a number of bits and pieces, that were already there, together in the right way."

"How curious, after all, is the way in which we moderns think about our world! And it is all so novel, too. The cosmology underlying our mental processes is but three centuries old—a mere infant in the history of thought—and yet we cling to it with the same embarrassed zeal with which a young father fondles his new-born baby."

"Considering the part played by the sciences in the story of our Western civilization, it is hardly possible to doubt the importance which the history of science will sooner or later acquire both in its own right and as the bridge which has been so long needed in between the Arts and the Sciences."

"In spite of all the allegations of self-love, the facts at first associated with the name of a particular man end by being anonymous, lost forever in the ocean of Universal Science. Thus the monograph imbued with individual human quality becomes incorporated, stripped of sentamentalisms, in the abstract doctrine of the general treatise. To the hot sun of actuality will succeed—if they do succeed—the cold beams of the history of learning."

"A law explains a set of observations; a theory explains a set of laws. The quintessential illustration of this jump in level is the way in which Newton’s theory of mechanics explained Kepler’s law of planetary motion. Basically, a law applies to observed phenomena in one domain (e.g., planetary bodies and their movements), while a theory is intended to unify phenomena in many domains. Thus, Newton’s theory of mechanics explained not only Kepler’s laws, but also Galileo’s findings about the motion of balls rolling down an inclined plane, as well as the pattern of oceanic tides. Unlike laws, theories often postulate unobservable objects as part of their explanatory mechanism. So, for instance, Freud’s theory of mind relies upon the unobservable ego, superego, and id, and in modern physics we have theories of elementary particles that postulate various types of quarks, all of which have yet to be observed."

"This statistical regularity in moral affairs fully establishes their being under the presidency of law. Man is now seen to be an enigma only as an individual; in the mass he is a mathematical problem."

"The book, as far as I am aware, is the first attempt to connect the natural sciences into a history of creation."

"The progress of knowledge is very irregular, somewhat resembling the movements of an army, of which some battalions are in vigorous health, while others are sickly or overburdened with baggage. The experimental marches on at a good pace; the observational proceeds but slowly; the speculative is left far in the rear."

"History of science played a very important role for me. Before I knew well how to do an experiment, I knew why Joliot has missed the neutron, why his wife missed the fission, why they succeeded in having artificial radioactivity, and even why they almost missed the other things, by doing very nice experiments, but didn't come to the conclusion. That is science. Science is doubt, is research. It is not something which is—and that is the danger of teaching—which is too academic and which the people explain [to] you... it is like the logic thing that comes out of the computer, which is not true. You have intuition, you have passion."

"Every science may be exhibited under two methods or procedures, the Historical and the Dogmatic. ...The more discoveries are made, the greater becomes the labour of the historical method of study, and the more effectual the dogmatic, because the new conceptions bring forward the earlier ones in a fresh light. ...By the dogmatic method, therefore, must every advanced science be attained, with so much of the historical combined with it as is rendered necessary ..."

"The most important ploy that nineteenth-century European scholars devised to avoid acknowledging that the roots of civilization are Afroasiatic was to minimize the importance of Egyptian, Sumerian, and Semitic contributions and to focus instead almost entirely on the Greeks. According to this idea, the Egyptians, Sumerians, and Semites established rather static and uninteresting cultures, while the really worthwhile developments in the rise of civilization were the work of the dynamic and sophisticated Greeks, who were considered to be of Aryan stock because their language is part of the Indo-European family. ...It was claimed that the Greeks developed their culture all on their own, with virtually no contribution from the earlier civilizations."

"In the nineteenth century C.E., a small but influential group of German scholars led by Karl Otfried Müller decided that the ancient Greek authors did not know what they were talking about—that their traditions of external influences were simply "myths." …They were convinced that the principle of historical explanation was race, and they believed they had discovered the "scientific laws of race." …only the white race ...had the natural ability to create advanced civilizations. ...This "racial science" …served as a useful ideology to explain the "natural right" of white Europeans to dominate the darker peoples of the world."

"Modern science will continue to be blindly destructive as long as its operations are determined by the anarchism of market economic forces. The problem to be solved is whether science, technology, and industry can be brought under genuinely democratic control in the context of a global planned economy, so that all of us can collectively put our hard-won scientific knowledge to mutually beneficial use. I am confident it can be accomplished, but will it? If so, there is reason for optimism. If not... well, to paraphrase Keynes, "in the not-so-long run we're all dead.""

"The strategic act by which Grosseteste and his thirteenth- and fourteenth-century successors created modern experimental science was to unite the experimental habit of the practical arts with the rationalism of twelfth-century philosophy."

"Before the eighth century [B.C.] no scientific astronomy was possible owing to the absence of one indispensable condition, namely, the possession of an exact system of chronology. The old calendar already in use about the year 2500, and perhaps earlier, was composed of twelve s. But as twelve lunar periods make only 354 days, a thirteenth month was from time to time inserted to bring the date at which the festivals recurred each year, into harmony with the seasons. It was only little by little that greater precision was attained by observing at what date the heliac rising of certain fixed stars took place. ...By degrees, direct observation of celestial phenomena, intended either to enable soothsayers to make predictions or to fix the calendar, led to the establishment of the fact that certain... phenomena recurred at regular intervals, and the attempt was then made to base predictions on the calculation of this recurrence or periodicity. This necessitated a strict chronology, at which the Babylonians did not arrive till the middle of the eighth century B.C.: in 747 they adopted the so-called "era of ." ...the moment when, doubtless owing to the establishment of a lunisolar cycle, they kept properly constructed chronological tables. Farther back there was no certainty in regard to the calculation of time. It is from that moment that the records of eclipses begin which Ptolemy used, and which are still sometimes employed by men of science for the purpose of testing their lunar theories."

"When we realize the important rôle played by space-time in our attempts to avoid a belief in absolute rotation, we can well understand that the doctrine of the relativity of all motion would have been absurd in Newton's day. ...any speaker prior to, say, the year 1900 could never have anticipated the discovery of space-time, for its sole justification arose from the negative experiments in optics and electrodynamics attempted at about that time. As for Newton, not only did he not know nothing of the non-mechanical negative experiments, but in addition, the equations of electrodynamics had not been discovered... even if he had conceived of space-time through some divine inspiration, he could never have utilised it for the purpose of establishing the relativity of all motion. His ignorance of non-Euclidean geometry would have rendered the task impossible. In fact, space-time, in the seventeenth century, would have been a hindrance, and the sole result of its premature introduction into science would have been to muddle everything up and render the discovery of Newton's law of gravitation well-nigh impossible. And this brings us to another point which is often true in physical science. Premature discoveries are apt to do more harm than good. ...had the astronomers of the seventeenth century possessed more perfect telescopes, had they recognized that the planets (Mercury, in particular) did not obey Kepler's laws rigorously, Newton's law might never have been discovered. At all events, its correctness would have been questioned seriously and mathematicians might have lost courage and doubted their ability to discover natural laws. Leverrier, for example, might have lacked the necessary assurance to carry out his lengthy calculations leading to the discovery of Neptune. In short, physical science proceeds by successive approximations, and too rapid jumps in the accretion of knowledge are liable to be disastrous."

"The present century has witnessed the emergence of two grand theories of mathematical physics: the Theory of Relativity and the Quantum Theory. Both theories were conceived for coordinating certain bodies of facts which the classical theories were unable to interpret; and neither theory would have seen the day had it not been for the increased refinement of experimental measurements which rendered the disclosure of these facts possible. But although the two theories were born under similar circumstances, they soon branched in opposite directions. The theory of relativity has developed into a doctrine whose principle field of application is found in the world of large-scale phenomena, whereas the quantum theory has become identified with the atomic and subatomic worlds. To this extent the theories are complimentary."

"Inasmuch as both Rayleigh's and Wien's laws of radiation, though incorrect, appear to express facts correctly at opposite limits of temperature and frequency, we may presume that the correct law must have an intermediary form, passing over into Rayleigh's when [temperature] T is large and [frequency] ν small, and into Wein's when the reverse situation... Planck, guided by these considerations, devised a new theory of radiation which he called the "Quantum Theory." From this theory Planck was able to derive a radiation law which satisfied Wien's relation, ...the displacement law [when the temperature is increased, intensities of all the frequencies increase, while the radiation of maximum intensity is directly proportional to the absolute temperature] and Stefan's law, and which was in excellent agreement with experimental measurements at all temperatures."

"1. Small particles called atoms exist and compose all matter; 2. They are indivisible and indestructible; 3. Atoms of the same chemical element have the same chemical properties and do not transmute or change into different elements."

"The genesis of all science can be traced to the contemplation of... occult influences. Astrology preceded astronomy, chemistry grew out of alchemy, and the theory of numbers had its precursor in a sort of numerology which to this day persists in otherwise unaccountable omens and superstitions."

"While we cannot place Pythagoras among the great or event near-great mathematicians, his position in the history of scientific thought remains unchallenged. ...dictum "Number rules the universe" ...in the broad modern sense ...is there anything in the dictum to which a modern scientist could not or would not subscribe? The theories of relativity and quanta have shaken the physical sciences to the very foundation, forcing the physicist to cast overboard such principles as conservation of energy or economy of action, and to revise the very concepts of space, time, matter, cause and effect. Still, number reigns as firmly in the new physics as it did in the old."

"Great is the power of steady misrepresentation; but the history of science shows that fortunately this power does not long endure."

"The rise of the scientific spirit was a notable feature of the Renaissance: men no longer accepted without question the opinions of the ancients about the universe and the laws governing the natural world; dogma was subjected to experiment, and when it failed to survive the test it was rejected and new theories were formulated. Thus science in the modern sense was born, and rapid progress was made in mathematics, physics, chemistry, and biology. But the immediate consequences for technology were confined to a few specialized fields; in the main, technological progress still depended upon the empirical methods by practical men. On the whole, up to 1750 science probably gained more from technology than vice versa. Among the notable exceptions... were the navigational instruments that played so important a part in the great voyages of exploration and in surveying and cartography; the application of the principle of the pendulum to time-measurement; and, particularly, the growing exploitation of chemistry. However, the new outlook on natural phenomena was only one manifestation of a healthy scepticism: technological processes which often had changed very little for centuries were carefully scrutinized to see what improvements could usefully be made. The Royal Society, founded in 1660 to further the investigation of natural phenomena by observation and experiment, in its early days directed at least as much of its attention to the improvement of existing arts and industries as to the advancement of fundamental scientific knowledge. Among the Society's early activities was the founding of Greenwich Observatory in 1675 for the strictly practical purpose of 'finding out the longitude for perfecting navigation'."

"Growing skill in the working of metals is... exemplified by the development of the instrument-maker's craft. To many... we make reference elsewhere—for example, clocks, navigational instruments and balances. ...Brass, ivory, and closed-grained woods, such as box and pear, were the principal materials of the instrument-makers, with brass becoming increasingly favoured because of its rigidity and permanence. For the shaping of metal the lathe was a valuable tool, and the clock-makers in particular developed it greatly for precision work. The engraving of scales was, of course, a most important part of the work: until the advent of mechanical devices, this was done with simple engraving tools and punches, the design being first set out by geometrical methods. The earliest products of the instrument-makers were made mainly for astronomical purposes or to apply astronomical methods in navigation: they included astrolabes, cross-staffs, quadrants, sundials, and orreries, as well as basic geometrical instruments such as compasses and rules. From the seventeenth century, however, a variety of new instruments, or much improved versions of old ones, began to appear. The needs of surveyors led to the elaboration of the hodometer... enabling distances to be measured... Improvements in artillary called for more accurate sighting of cannon, and by the beginning of the seventeenth century the gunner's level had been highly developed. The invention of the telescope and microscope introduced new problems both in the making of lenses and of the instruments in which they were mounted: the new instruments were a regular part of the instrument-maker's trade from about 1660. From 1700 the revolution in science was making still further demands on the craft, and air-pumps, thermometers, barometers, electrical machines, and other instruments were called for in constantly increasing quantities."

"Greek and medieval knowledge accepted the world in its qualitative variety, and regarded nature's processes as having ends, or in technical phrase as teleological. New science was expounded so as to deny the reality of all qualities in real, or objective, existence. Sounds, colors, ends, as well as goods and bads, were regarded as purely subjective — as mere impressions in the mind. Objective existence was then treated as having only quantitative aspects — as so much mass in motion, its only differences being that at one point in space there was a larger aggregate mass than at another, and that in some spots there were greater rates of motion than at others. Lacking qualitative distinctions, nature lacked significant variety. Uniformities were emphasized, not diversities; the ideal was supposed to be the discovery of a single mathematical formula applying to the whole universe at once from which all the seeming variety of phenomena could be derived. This is what a mechanical philosophy means."

"Les hypothèses ne sont point le produit d'une création soudaine, mais le résultat d'une évolution progressive. [Hypotheses are not the product of sudden creation, but the result of progressive évolution.]"

"Science and religion are two human enterprises sharing many common features. They share these features also with other enterprises such as art, literature and music. The most salient features of all these enterprises are discipline and diversity. Discipline to submerge the individual fantasy in a greater whole. Diversity to give scope to the infinite variety of human souls and temperaments. Without discipline there can be no greatness. Without diversity there can be no freedom. Greatness for the enterprise, freedom for the individual—these are the two themes, contrasting but not incompatible, that make up the history of science and the history of religion."

"Science as subversion has a long history. ...Davis and Sakharov belong to an old tradition in science that goes all the way back to the rebels Benjamin Franklin and Joseph Priestley in the eighteenth century, to Galileo and Giordano Bruno in the seventeenth and sixteenth. If science ceases to be a rebellion against authority, then it does not deserve the talents of our brightest children. ...We should try to introduce our children to science today as a rebellion against poverty and ugliness and militarism and economic injustice."

"The two great conceptual revolutions of twentieth-century science, the overturning of classical physics by Werner Heisenberg and the overturning of the foundations of mathematics by Kurt Gödel, occurred within six years of each other within the narrow boundaries of German-speaking Europe. ...A study of the historical background of German intellectual life in the 1920s reveals strong links between them. Physicists and mathematicians were exposed simultaneously to external influences that pushed them along parallel paths. ...Two people who came early and strongly under the influence of Spengler's philosophy were the mathematician Hermann Weyl and the physicist Erwin Schrödinger. ...Weyl and Schrödinger agreed with Spengler that the coming revolution would sweep away the principle of physical causality. The erstwhile revolutionaries David Hilbert and Albert Einstein found themselves in the unaccustomed role of defenders of the status quo, Hilbert defending the primacy of formal logic in the foundations of mathematics, Einstein defending the primacy of causality in physics. In the short run, Hilbert and Einstein were defeated and the Spenglerian ideology of revolution triumphed, both in physics and in mathematics. Heisenberg discovered the true limits of causality in atomic processes, and Gödel discovered the limits of formal deduction and proof in mathematics. And, as often happens in the history of intellectual revolutions, the achievement of revolutionary goals destroyed the revolutionary ideology that gave them birth. The visions of Spengler, having served their purpose, rapidly became irrelevant."

"Progress in science is often built on wrong theories that are later corrected. It is better to be wrong than to be vague."

"According to Descartes, scientists should stay at home and deduce the laws of Nature by pure thought... scientists will need only the rules of logic and knowledge of the existence of God. For four hundred years since Bacon and Descartes... science has raced ahead by following both paths simultaneously. Neither Baconian empiricism nor Cartesian dogmatism has the power to elucidate Nature's secrets by itself, but both together have been amazingly successful. For four hundred years English scientists have tended to be Baconian and French scientists Cartesian. Faraday and Darwin and Rutherford were Baconians; Pascal and Laplace and Poincaré were Cartesians. Newton was at heart a Cartesian, using pure thought... to demolish the Cartesian dogma of vortices. Marie Curie was at heart a Baconian, boiling tons of crude uranium ore to demolish the dogma of the indestructibility of atoms."

"The present revolution of scientific thought follows in natural sequence on the great revolutions at earlier epochs in the history of science."

"...The present revolution of scientific thought follows in natural sequence on the great revolutions at earlier epochs in the history of science. Einstein's special theory of relativity, which explains the indeterminateness of the frame of space and time, crowns the work of Copernicus who first led us to give up our insistence on a geocentric outlook on nature; Einstein's general theory of relativity, which reveals the curvature or non-Euclidean geometry of space and time, carries forward the rudimentary thought of those earlier astronomers who first contemplated the possibility that their existence lay on something which was not flat. These earlier revolutions are still a source of perplexity in childhood, which we soon outgrow; and a time will come when Einstein's amazing revelations have likewise sunk into the commonplaces of educated thought."

"If the idea of physical reality had ceased to be purely atomic, it still remained for the time being purely mechanistic; people still tried to explain all events as the motion of inert masses; indeed no other way of looking at things seemed conceivable. Then came the great change, which will be associated for all time with the names of Faraday, Clerk Maxwell, and Hertz."

"Scientific thought is a development of pre-scientific thought."

"I fully agree with you about the significance and educational value of methodology as well as history and philosophy of science. So many people today—and even professional scientists—seem to me like someone who has seen thousands of trees but has never seen a forest. A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is—in my opinion—the mark of distinction between a mere artisan or specialist and a real seeker after truth."

"What Luther's burning of the Papal Bull was in the religious field, in the field of natural science was the great work of Copernicus, in which he, although timidly... threw down a challenge to ecclesiastical superstition. From then on natural science was in essence emancipated from religion, although the complete settlement of accounts in all details has gone on to the present day and in many minds is still far from being complete. But from then on the development of science went forward with giant strides, increasing, so to speak, proportionately to the square of the distance in time from its point of departure, as if it wanted to show the world that for the motion of the highest product of organic matter, the human mind, the law that holds good is the reverse of that for the motion of inorganic matter."

"The impression that science is over has occurred many times in various branches of human knowledge, often because of an explosion of discoveries made by a genius or a small group of men in such a short time that average minds could hardly follow and had the unconscious desire to take breath, to get used to the unexpected things that came to be revealed. Dazzled by these new truths, they could not see beyond. Sometimes an entire century did not suffice to produce this accommodation."

"Christians believed in a teleological cosmos, one created by an omniscient God, a Grand Designer, for a specific purpose. This comforting view was threatened by the new statistical methods in physics, and also by Darwin's theory of evolution, which assumes that chance may intervene between generations to introduce new characteristics."

"The Egyptians were also busy with agriculture, dairying, pottery, glass-making, weaving, ship-building, and carpentry of every sort. This technical activity rested upon a basis of empirical knowledge... To deny it the name of science because it was, perhaps, handed down by tradition to apprentices instead of being written in a book is not wholly just. Technical problems also certainly clamoured for solution in connection with their gold-work, weaving, pottery, hunting, fishing, navigation, basket-work, culture of cereals, culture of flax, baking and brewing, vine-growing and wine-making, stone-cutting and stone-polishing, carpentry, joinery, boat-building, and the many other processes so accurately figured on the walls of the tombs of the nobles at Sakara. In all these techniques lay the germ of science."

"Progress was often achieved by a "criticism from the past"… After Aristotle and Ptolemy, the idea that the earth moves - that strange, ancient, and "entirely ridiculous", Pythagorean view was thrown on the rubbish heap of history, only to be revived by Copernicus and to be forged by him into a weapon for the defeat of its defeaters. The Hermetic writings played an important part in this revival, which is still not sufficiently understood, and they were studied with care by the great Newton himself. Such developments are not surprising. No idea is ever examined in all its ramifications and no view is ever given all the chances it deserves. Theories are abandoned and superseded by more fashionable accounts long before they have had an opportunity to show their virtues. Besides, ancient doctrines and "primitive" myths appear strange and nonsensical only because their scientific content is either not known, or is distorted by philologists or anthropologists unfamiliar with the simplest physical, medical or astronomical knowledge."

"Our freedom to doubt was born out of a struggle against authority in the early days of science. It was a very deep and strong struggle: permit us to question — to doubt — to not be sure. I think that it is important that we do not forget this struggle and thus perhaps lose what we have gained."

"By the way, what I have just outlined is what I call a “physicist’s history of physics,” which is never correct. What I am telling you is a sort of conventionalized myth-story that the physicists tell to their students, and those students tell to their students, and is not necessarily related to the actual historical development, which I do not really know!"

"For indeed it is one of the lessons of the history of science that each age steps on the shoulders of the ages which have gone before. The value of each age is not its own, but is in part, in large part, a debt to its forerunners. And this age of ours if, like its predecessors, it can boast of something of which it is proud, would, could it read the future, doubtless find also much of which it would be ashamed."

"Fundamental changes in science have always been accompanied by deeper digging toward the philosophical foundations. Changes like the transition from the Ptolemaic to the Copernican system, from Euclidean to non-Euclidean geometry, from Newtonian to relativistic mechanics... have brought about a radical change in our common-sense explanation of the world. From all these considerations everyone who is to get a satisfactory understanding of twentieth century science will have to absorb a good deal of philosophical thought. But he will soon feel the same thing holds for a thorough understanding of the science which originated in any period of history."

"Toward the last quarter of the nineteenth century, it was accepted more and more that the phenomena of electromagnetism were not to be reduced to Newtonian mechanics, but were to be reduced from a separate system of principles, of which, in turn, the Newtonian laws were a special case. The "state of a system" is no longer described by the velocity at a certain point x, y, z and at a time t, but by the electric and magnetic field strengths at x, y, z and at a time t. A causal law in the theory of the electromagnetic field is now an equation that allows us to compute from the present distribution of field strengths the future value of field strengths. Mathematically, the causal laws look exactly like those in mechanics except that the velocities u, v, w are replaced by the field strengths. This theory... has been generalized into a "general field theory.""

"[A]mong several theories that are set up to account for a certain domain of observed facts, one will stand out as the best... the theory should be accepted which shows "more" agreement with observed facts... However, this... cannot be the only criterion... If this were so, the best theory would be the mere description of facts; but this would be no theory at all. ...the actual advance of science has always been engineered by a criterion of economy and simplicity. The criteria of Reichenbach and Carnap, which are based, like John Stuart Mill's inductive logic, upon agreement with observations, have to be complemented by the criterion of economy and simplicity which was advanced in the history of science by men like William Ockham, Isaac Newton, and Ernst Mach. In our twentieth century, the importance of crieteria other than mere agreement with observation was stressed by von Mises and Bronowski."

"[F]itness to support desirable conduct on the part of citizens or, briefly, to support moral behavior, has served through the ages as a reason for the acceptance of a theory. In antiquity, the physics of Aristotle and Plato seemed to be fitter, in this respect, than the physics of Epicurus. According to the first, the celestial bodies were made of a nobler material than our earth, while according to the "materialistic" doctrine of Epicurus, all these bodies consisted of the same elements. This latter doctrine, however, made it more difficult to teach the existence of a difference between material and spiritual beings. Since a great many educators and statesmen have been convinced that the belief in this difference is important for the education of good citizens, the Epicurean doctrine was rejected by powerful groups. ...Plato ...in his description of "good government" included the requirement that the followers of Epicurean philosophy should be silenced."

"Included in this “almost nothing,” as a kind of geological afterthought of the last few million years, is the first development of self-conscious intelligence on this planet—an odd and unpredictable invention of a little twig on the mammalian evolutionary bush. Any definition of this uniqueness, embedded as it is in our possession of language, must involve our ability to frame the world as stories and to transmit these tales to others. If our propensity to grasp nature as story has distorted our perceptions, I shall accept this limit of mentality upon knowledge, for we receive in trade both the joys of literature and the core of our being."

"I... praise the newly opened halls of fossil mammals at the . ...teaching us about evolutionary trees by organizing the entire hall as a central trunk and set of branches... placing our brains in our feet and letting us learn by walking. ...the chosen geometry of evolutionary organization... violates the traditional picture of life's history, thus illustrating... an important principle in the history of science: the central role of pictures, graphs, and other forms of visual representation in channeling and constraining our thought. ...Words are an evolutionary afterthought. ...My colleagues have actually done it. ...They have ordered all the fossils into an unconventional iconographic tree that fractures the bias of progress. ...so that we can preambulate along the tree of life and absorb the new scheme viscerally by walking... They have taken Colbert's radical idea and arranged all the fossils by their branching order, not by their later "success" or "advancement." Groups that branch early, appear early in the hall... Sea cows and elephants are at the end of the hall, horses in the middle, and primates near the beginning."

"In this oversimplified view of scientific progress, we advance along a pathway of accumulating knowledge, guided by a timeless method of accurate observation and relentless logic. ... T. H. Huxley's The Crayfish... argues that the study of organisms has progressed through the same three stages followed by all sciences... an initial phase of gathering information without theoretical guidance (Huxley calls this... Natural History... "accurate, but necessarily incomplete and unmethodized knowledge"); a second stage of systemizing and organization... still without guiding theory (called Natural Philosophy); and... the... synthetic climax... Physical Science, "this final stage of knowledge, [where] the phenomena of nature are regarded as one continuous series of causes and effects." ...In this system... Linnaeus occupies the middle rung. ...I would agree with most modern historians of science in branding this... as misleading, and unfair... [T]wo aspects of this older positivist view... lack validity and impede understanding: ...the notion of a timeless based on rigorously objective observation and logic, and ...that earlier systems were either theory-free or theory-poor because explanation can only follow accurate description. Theory-free science makes about as much sense as value-free politics. Both... are oxymoronic. All thinking about the natural world must be informed by theory... The old... theories may have been wrong, but they were as persuasive (and restrictive) in the structuring of knowledge as any more accurate and later system... [W]e cannot collect information without a theory to organize our searches and observations."

"Henry Fairfield Osborn, the dominant paleontologist of his era, and long time director of the American Museum of Natural History, gave the "standard version in his popular book of 1918, The Origin and Evolution of Life... "Lamarck attributed the lengthening of the [giraffe's] neck to the inheritance of bodily modifications caused by the neck-stretching habit. Darwin attributed the lengthening of the neck to the constant selection of individuals and races which were born with the longest necks. Darwin was probably right." …The version has held ever since."

"Progress in science proceeds in fits and starts. Some periods are filled with great breakthroughs; at other times researchers experience dry spells. Scientists put forward results... theoretical and experimental. The results are debated... sometimes... discarded, sometimes... modified, and sometimes they provide inspirational jumping-off points for new and more accurate ways of understanding... a zig zag path toward what we hope will be ultimate truth, a path that began with humanity's earliest attempts to fathom the cosmos and whose end we cannot predict. Whether string theory is an incidental rest stop... a landmark turning point, or... the final destination we do not know. But the last two decades of research by hundreds of... physicists and mathematicians from numerous countries have given us well-founded hope that we are on the right and possibly final track."

"Kuhn... (like Popper and many other predecessors) thought the primary work of science was theoretical. He esteemed theory, and although he had a good sense of experimentation, presented it as of secondary importance. Since the 1980s there has been a substantial shift in emphasis, with historians, sociologists, and philosophers attending seriously to experimental science."

"The whole history of science has been the gradual realization that events do not happen in an arbitrary manner, but that they reflect a certain underlying order, which may or may not be divinely inspired."

"Everything is theoretically impossible, until it is done. One could write a history of science in reverse by assembling the solemn pronouncements of highest authority about what could not be done and could never happen."

"There is an enormous difference between modern science and Greek philosophy, and that is just the empiristic attitude... Since the time of Galileo and Newton, modern science has been based upon a detailed study of nature and upon the postulate that only such statements should be made, as have been verified or at least can be verified by experiment. The idea that one can single out some events from nature by an experiment... to find out what is the constant law in the continuous change, did not occur to the Greek philosophers. Therefore, modern science has from its beginning stood on a much more modest, but at the same time much firmer, basis than ancient philosophy. Therefore, the statements of modern physics are in some way meant much more seriously than the statements of Greek philosophy."

"[E]normous activity, the new spirit... had come... through the Renaissance. ...[A] new authority appeared... independent of Christian religion or philosophy or... the Church, the authority of experience, of the empirical fact. One may trace this... into the philosophy of Occam and Duns Scotus, but it became a vital force... only from the sixteenth century onward. Galileo did not only think about... the pendulum and the falling stone, he tried out by experiments, quantitatively, how these motions took place. ...[E]mphasis on experience was connected with a slow and gradual change in the aspect of reality. While in the Middle Ages... the symbolic meaning of a thing was... its primary reality, the aspect of reality changed... What we can see and touch became primarily real. And this... could be connected with... experiment... [T]his... meant a departure... into an immense new field of... possibilities, and... the Church saw in the new movement the dangers rather than the hopes. ...[R]epresentatives of natural science could argue that experience offers an undisputable truth... made by nature or...in this sense, by God. ...[T]raditional religion ...could argue that... we lose the connection with the essential values... that part of reality beyond the material world. These two arguments do not meet and therefore the problem could not be settled by any... agreement or decision."

"Of the splendid constellation of great names... we admire the living and revere dead far too warmly and too deeply to suffer us sit in judgment on their respective claims to in this or that particular discovery; to balance mathematical skill of one against the experimental dexterity of another, or the philosophical acumen a third. So long as "one star differs from another in glory,"—so long as there shall exist varieties, or even incompatibilities of excellence,—so long will the admiration of mankind be found sufficient for all who merit it."

"In former times the Mathematician and the Physicist were usually one and the same man. Even as late as the eighteenth century this was very generally the case; it was in the nineteenth century that the increasing complexity of both Sciences produced that separation of the two departments which has become continually more marked, and has reached its extreme point in our own time. ...The chief drawback is that each specialist, from lack of interest in, and knowledge of, the progress of the other great department, is apt to miss that large source of inspiration in his own study which is supplied by the other one."

"Mathematical thinking has played a very important part in the formation of the fundamental concepts of the Physicist; very often this part has been a dominant one. Many of these concepts could only have received a precise meaning and... taken definite forms as the result of the work of Mathematicians... For example, the conception of Energy, and the exact meaning of the... law of the Conservation of Energy, emerged as results of the development of the abstract side of molar mechanics, which determined the mode in which the of moving bodies and as work are defined as measurable quantities. Only by the transference and extension of these notions to the molecular domain did the conception involved in the modern doctrine become possible. The doctrine... had been established before Joule and Mayer commenced their work, and was a necessary presupposition of their further development. Joule was able to determine the only owing to the fact that mechanical work was already regarded as a measurable quantity, measured in a manner which had been fixed in the course of the development of the older Mathematical Mechanics. The notion of Potential, fundamental in Electrical Science, and which every Physicist, and every Electrical Engineer, constantly employs, was first developed as a Mathematical conception during the eighteenth century in connection with the theory of the attractions of gravitating bodies. It was transferred to the electrical domain by George Green and others, together with a good deal of detailed mathematics connected with it which had previously been applied to the function."

"Science has only existed for a few hundred years, and its most spectacular achievements have occurred within the last century. Viewed from a historical perspective, the modern era of rapid scientific and technological progress appears to be not a permanent feature of reality, but an abberation, a fluke, a product of a singular convergence of social, intellectual, and political factors."

"The history of civilization details the steps by which men have succeeded in building up an artificial world within the cosmos. Fragile reed as he may be, man, as Pascal says, is a thinking reed: there lies within him a fund of energy, operating intelligently and so far akin to that which pervades the universe, that it is competent to influence and modify the cosmic process. In virtue of his intelligence the dwarf bends the Titan to his will. In every family, in every polity that has been established, the cosmic process in man has been restrained and otherwise modified by law and custom; in surrounding nature, it has been similarly influenced by the art of the shepherd, the agriculturist, the artisan. As civilization has advanced, so has the extent of this interference increased; until the organized and highly developed sciences and arts of the present day have endowed man with a command over the course of non-human nature greater than that once attributed to the magicians. ...a right comprehension of the process of life and of the means of influencing its manifestations is only just dawning upon us. We do not yet see our way beyond generalities; and we are befogged by the obtrusion of false analogies and crude anticipations. But Astronomy, Physics, Chemistry, have all had to pass through similar phases, before they reached the stage at which their influence became an important factor in human affairs. Physiology, Psychology, Ethics, Political Science, must submit to the same ordeal. Yet it seems to me irrational to doubt that, at no distant period, they will work as great a revolution in the sphere of practice."

"In the history of sciences, important advances often come from... the recognition that two hitherto separate observations can be viewed from a new angle and seen to represent nothing but different facets of one phenomenon. Thus, terrestrial and celestial mechanisms became a single science with Newton's laws. Thermodynamics and mechanics were unified through statistical mechanics, as were optics and electromagnetism through Maxwell's theory of magnetic field, or chemistry and through quantum mechanics. Similarly different combinations of the same atoms, obeying the same laws, were shown by biochemists to compose both the inanimate and animate worlds. ... Despite such generalizations, however, large gaps remain... Following the line from physics to sociology, one goes from simpler to the more complex objects... from the poorer to the richer empirical content, as well as from the harder to the softer system of hypotheses and experimentation. ...Because of the hierarchy of objects, the problem is always to explain the more complex in terms and concepts applying to the simpler. This is the old problem of reduction, emergence, whole and parts... an understanding of the simple is necessary to understand the more complex, but whether it is sufficient is questionable. ...the appearance of life and later of thought and language—led to phenomena that previously did not exist... To describe and to interpret these phenomena new concepts, meaningless at the previous level, are required. ...At the limit total reductionism results in absurdity. ...explaining democracy in terms of the structure and properties of elementary particles... is clearly nonsense."

"Great courageous spirits like Abelard and Saint Thomas Aquinas dared to introduce into Catholicism the concepts of Aristotelian logic, and thus founded scholastic philosophy. But when the Church took the sciences under her wing, she demanded that the forms in which they moved be subjected to the same unconditioned faith in authority as were her own laws. And so it happened that scholasticism, far from freeing the human spirit, enchained it for many centuries to come, until the very possibility of free scientific research came to be doubted. At last, however, here too daylight broke, and mankind, reassured, determined to take advantage of its gifts and to create a knowledge of nature based on independent thought. The dawn of the day in history is known as the Renaissance or the Revival of Learning."

"The Copernican revolution... revealed that the earth is not the center of the universe... The second, the Darwinian revolution... revealed that we are not created divinely or uniquely but instead evolved from simpler animals by a process of natural selection. The third great revolution, the Freudian revolution of Vienna 1900, revealed that we do not consciously control our own actions but are instead driven by unconscious motives. This... later led to the idea that human creativity... stems from conscious access to underlying, unconscious forces."

"When Galilei let balls of a particular weight, which he had determined himself, roll down an inclined plain, or Torricelli made the air carry a weight, which he had previously determined to be equal to that of a definite volume of water; or when, in later times, Stahl changed metal into lime, and lime again into metals, by withdrawing and restoring something, a new light flashed on all students of nature. They comprehended that reason has insight into that only, which she herself produces on her own plan, and that she must move forward with the principles of her judgments, according to fixed law, and compel nature to answer her questions, but not let herself be led by nature, as it were in leading strings, because otherwise accidental observations made on no previously fixed plan, will never converge towards a necessary law, which is the only thing that reason seeks and requires. Reason, holding in one hand its principles, according to which concordant phenomena alone can be admitted as laws of nature, and in the other hand the experiment, which it has devised according to those principles, must approach nature, in order to be taught by it: but not in the character of a pupil, who agrees to everything the master likes, but as an appointed judge, who compels the witnesses to answer the questions which he himself proposes. Therefore even the science of physics entirely owes the beneficial revolution in its character to the happy thought, that we ought to seek in nature (and not import into it by means of fiction) whatever reason must learn from nature, and could not know by itself, and that we must do this in accordance with what reason itself has originally placed into nature. Thus only has the study of nature entered on the secure method of a science, after having for many centuries done nothing but grope in the dark."

"It is not an unusual phenomenon in the history of science that views which were once considered antiquated and out of date suddenly come into favor again, though in a more or less modified form. An extremely interesting case of this kind is presented by the revolution in our ideas of electric phenomena which has taken place within the last 10 years... The modern theory of electrical and allied optical phenomena... [i.e.,] the "electron theory," means practically a return to views as laid down in the sixties and seventies by Wilhelm Weber and Zöllner, but modified by the results of Maxwell's and Hertz's researches. W. Weber imagined electric phenomena as the actions of elementary electrical particles—so called "electric atoms"—whose mutual influence depended not only upon their positions but also upon their relative velocities and accelerations. ...most of the laws of electrodynamics when expressed from the standpoint of pure phenomenology in the shape of differential equations, are much more simple and convenient than Weber's formulæ. ...Faraday and Maxwell brought about a general feeling that... a finite rate of propagation would have to take the place of action at a distance. ...Maxwell's formulæ [were] wholly void ...of atomistic conceptions ...According to Maxwell... the vibrations of light were not mechanical, but electrical vibrations of the ether, and the two constants by which Maxwell defined the electric and magnetic behaviour of every body (the dielectric constant and the magnetic permeability) had also to be the determining elements in its refractive power. Although the condition... was well fulfilled in a number of bodies, ...many bodies, notably water...sufficed to prove the inadequacy of the theory... To this was added the dependence of the refractive index upon the colour [frequency], for which the original theory gave no explanation whatever. H. A. Lorentz showed that the foundations of an electromagnetic theory of dispersion could be laid in a manner quite analogous to the mechanical theory, by regarding every molecule as the origin of electric vibrations of a definite period. He says:—"Let there be in every material particle several material points charged with electricity, of which, however, only one be movable, and have the charge e and the mass μ." Lorentz derives the equations of dispersion from this fundamental assumption of vibrating charged particles. ... In his Faraday Memorial Address of 1881 Helmholtz points out that Faraday's law necessarily implies the existence of electric atoms. ...when a neutral molecule—say NaCl—splits up in +Na and -CI when dissolved in water, it is most probable that both the sodium and the chlorine atom had their charges beforehand... equal and opposite. But if we consider a ray of light traversing a crystal of salt, the charges and the atoms they accompany must be thrown into vibrations, and must influence the propagation of the light. ... In the years 1890-93 a number of works appeared by F. Richarz, H. Ebert and G. Johnstone Stoney, mostly dealing with the mechanism of the emission of luminous vapours, and in which attempts are made, on the basis of the kinetic theory of gases, to determine the magnitude of the elementary electrical quantity, called by Stoney... the now universally accepted name of electron. ...that one electron contains about 10-10 electrostatic units. ...a whole series of other methods... tend to very similar values. ... In 1896 a pupil of Lorentz, P. Zeeman, discovered a phenomenon whose existence Faraday had vainly sought for in 1862. If a luminous vapour, say a sodium flame, is brought into a strong magnetic field, the spectrum lines of the vapour show peculiar changes, consisting of a doubling or trebling, according to the line of vision. These changes are predicted by Lorentz's theory. The Zeeman phenomenon further permitted a determination of the inert mass connected with the vibrating charges, and then a striking result was obtained: the vibrating electron is always negatively charged, while the positive charge is stationary. ...The original and almost tacit assumption that the whole ion—i.e., the chemical atom plus its valency charge—was in oscillation must, therefore, be abandoned. We must suppose that the charge, just as is the case in electrolysis, has also an independent mobility in the light-emitting molecule, and that the mass concerned in the Zeeman phenomenon is that of the electron itself. We thus arrive at a view which nearly coincides with the old conception of Weber, but with the important difference that instead of a direct action at a distance we have an action transmitted by the ether, and further, that we have now a perfectly distinct numerical estimate of the magnitude of the electric atoms."

"Historically, the investigations of oscillatory motions was motivated by the desire to improve methods of telling time. ...In the seventeenth century the need to measure small periods of time accurately for the purpose of telling longitude at sea caused scientists to search for increasingly accurate clocks. The search resulted in some major successes that were at least as valuable for the advancement of mathematics and the study of other phenomena of nature, such as light and sound, as they were for the specific problem of measuring time. Scientists naturally concentrated on any physical phenomena that seemed to be periodic or repetitive and might therefore be related to the periodic motion of the planets. Two phenomena recommended themselves for closer investigation, the motion of an object or bob... on a spring, and the motion of a pendulum. The first of those attracted the attention of Robert Hooke... Suppose d is the increase or decrease in the length of the spring resulting from extension or contraction. Hooke found that the restoring force the spring exerts is proportional to d; that is, the force is a constant k, say, times d. This is the meaning of [Ut tensio, sic vis ("as the extension, so the force")]..."

"All "if" statements about the past are as dubious as prophecies of the future are. It seems fairly plausible that if Alexander or Ghengis Khan had never been born, some other individual would have filled his place and executed the design of the Hellenic or Mongolic expansion; but the Alexanders of philosophy and religion, of science and art, seem less expendable; their impact seems less determined by economic challenges and social pressures; and they seem to have a much wider range of possibilities to influence the direction, shape and texture of civilizations."

"If conquerors be regarded as the engine-drivers of History, then the conquerors of thought are perhaps the pointsmen who, less conspicuous to the traveller's eye, determine the direction of the journey."

"We are tempted to... fall into the mistaken belief that the advance of knowledge has always been a continuous, cumulative process along a road which steadily mounts from the beginnings of civilization to our present dizzy height. This, of course, is not the case. In the sixth century B.C., educated men knew that the earth was a sphere; in the sixth century A.D., they again thought it was a disc, or resembling in shape the Holy Tabernacle. In looking back... There are tunnels on the road, whose length is measured in miles, alternating with stretches in full sunlight of no more than a few yards. Up to the sixth century B.C., the tunnel is filled with mythological figures; then for three centuries there is a shrill light; then we plunge into another tunnel, filled with different dreams."

"Rationality is very much connected with the tradition in science for the last 300 years, when you're going to end up with some sort of understandable explanation of something. And I would be disappointed if that were the case."

"Science as we now understand the word is of later birth. If its germinal origin may be traced to the early period when Observation, Induction, and Deduction were first employed, its birth must be referred to that comparatively recent period when the mind,—rejecting the primitive tendency to seek in supernatural agencies for an explanation of all external phenomena,—endeavoured, by a systematic investigation of the phenomena themselves to discover their invariable order and connection."

"The separation of Science from Knowledge was effected step by step as the Subjective Method was replaced by the Objective Method: i.e., when in each inquiry the phenomena of external nature ceased to be interpreted on premisses suggested by the analogies of human nature."

"Although modern Science includes ideas not less transcendental than those included in ancient Science... As abstract expressions of the observed order of nature they are liable at any moment to be displaced in favour of expressions more accurate. They serve as guides and starting-points in research. They are not believed in as absolute existences. In ancient science they were held to be absolute existences, which it was the primary object of research to find, and which, when disclosed to the imagination, required no confrontation with reality."

"He who is ignorant of Motion, says Aristotle, is necessarily ignorant of all natural things. ...Not only was he entirely in the dark respecting the Laws, he was completely wrong in his conception of the nature of Motion. ...He thought that every body in motion naturally tends to rest."

"The gist and kernel of mechanical ideas has in almost every case grown up in the investigation of very simple and special cases of mechanical processes; and the analysis of the history of the discussions concerning these cases must ever remain the method at once the most effective and the most natural for laying this gist and kernel bare. ...[I]t is the only way in which a real comprehension of the general upshot of mechanics is to be attained."

"The history of the development of mechanics, is... indispensable to a full comprehension of the science in its present condition. It also affords a simple and instructive example of the processes by which natural science generally is developed."

"We now propose to enter more minutely into subject of our inquiries, and at the same time, without making the history of mechanics the chief topic discussion, to consider its historical development so far as this is requisite to an understanding of the present state of mechanical science... Apart from the consideration that we cannot afford to neglect the great incentives that it is in our power to derive from the foremost intellects of all epochs, incentives which taken as a whole are more fruitful than the greatest men of the present day are able to offer, there is no grander, no more intellectually elevating spectacle than that of the utterances of the fundamental investigators in their gigantic power. Possessed as yet of no methods, for these were created by their labors, and are only rendered comprehensible to us by their performances, they grapple with and subjugate the object of their inquiry, and imprint upon it the forms of conceptual thought. They that know the entire course of the development of science, will, as a matter of course, judge more freely and more correctly of the significance of any present scientific movement than they, who limited in their views, to the age in which their own lives have been spent, contemplate merely the momentary trend that the course of intellectual events takes at the present moment."

"The acquisition of the most elementary truth does not devolve upon the individual alone: it is pre-effected in the development of the race."

"Know that this Universe, in its entirety, is nothing else but one individual being; that is to say, the outermost heavenly sphere, together with all included therein, is as regards individuality beyond all question a single being like Said and Omar. The variety of its substances—I mean the substances of that sphere and all its component parts—is like the variety of the substances of a human being: just as, e.g., Said is one individual, consisting of various solid substances, such as flesh, bones, sinews of various humours, and of various spiritual elements; in like manner this sphere in its totality is composed of the celestial orbs, the four elements and their combinations; there is no vacuum whatever therein, but the whole space is filled up with matter. Its centre is occupied by the earth, earth is surrounded by water, air encompasses the water, fire envelopes the air, and this again is enveloped by the fifth substance (quintessence). These substances form numerous spheres, one being enclosed within another so that no intermediate empty space, no vacuum, is left. One sphere surrounds and closely joins the other. All the spheres revolve with constant uniformity, without acceleration or retardation; that is to say, each sphere retains its individual nature as regards its velocity and the peculiarity of its motion; it does not move at one time quicker, at another slower. Compared with each other, however, some of the spheres move with less, others with greater velocity. The outermost, all-encompassing sphere, revolves with the greatest speed; it completes its revolution in one day, and causes every thing to participate in its motion, just as every particle of a thing moves when the entire body is in motion; for all existing beings stand in the same relation to that sphere as a part of a thing stands to the whole. These spheres have not a common centre; the centres of some of them are identical with the centre of the Universe, while those of the rest are different from it. Some of the spheres have a motion independent of that of the whole Universe, constantly revolving from East to West, while other spheres move from West to East. The stars contained in those spheres are part of their respective orbits; they are fixed in them, and have no motion of their own, but participating in the motion of the sphere of which they are a part, they themselves appear to move. The entire substance of this revolving fifth element is unlike the substance of those bodies which consist of the other four elements, and are enclosed by the fifth element."

"Through the constant revolution of the fifth element, with all contained therein, the four elements are forced to move and to change their respective positions, so that fire and air are driven into the water, and again these three elements enter the depth of the earth. Thus are the elements mixed together; and when they return to their respective places, parts of the earth, in quitting their places, move together with the water, the air and the fire. In this whole process the elements act and react upon each other. The elements intermixed, are then combined, and form at first various kinds of vapours; afterwards the several kinds of minerals, every species of plants, and many species of living beings, according to the relative proportion of the constituent parts. All transient beings have their origin in the elements, into which again they resolve when their existence comes to an end. The elements themselves are subject to being transformed from one into another; for although one substance is common to all, substance without form is in reality impossible, just as the physical form of these transient beings cannot exist without substance."

"[T]he principal part in the human body, namely, the heart, is in constant motion, and is the source of every motion noticed in the body; it rules over the other members, and communicates to them through its own pulsations the force required for their functions. The outermost sphere by its motion rules in a similar way over all other parts of the universe, and supplies all things with their special properties. Every motion in the universe has thus its origin in the motion of that sphere; and the soul of every animated being derives its origin from the soul of that same sphere."

"The history of science shews that even during the phase of her progress in which she devotes herself to improving the accuracy of the numerical measurement of quantities with which she has long been familiar, she is preparing the materials for the subjugation of the new regions, which would have remained unknown if she had been contented with the rough methods of her early pioneers. I might bring forward instances gathered from every branch of science... But the history of the science of terrestrial magnetism affords us a sufficient example of what may be done by experiments in concert, such as we hope some day to perform in our Laboratory."

"[T]he application of algebra to geometry... far more than any of his metaphysical speculations, has immortalized the name of Descartes, and constitutes the greatest single step ever made in the progress of the exact sciences."

"Do what we will, we always, more or less, construct our own universe. The history of science may be described as the history of the attempts, and the failures, of men " to see things as they are.""

"With the development of the sciences and with the articulation of the machine in practical life, the realm of order was transferred from the absolute rulers, exercising a personal control, to the universe of impersonal nature and to a particular group of artifacts and customs we call the machine. The royal formula of purpose—"I will"—was translated into the causal terms of science—"It must." By partly supplanting the crude desire for personal dominion by an impersonal curiosity and by the desire to understand, science prepared the way for a more effective conquest of the external environment and ultimately for a more effective control of the agent, man, himself."

"These independent objects of Newtonian physics might move, touch each other, collide, or even, by a certain stretch of the imagination, act at a distance: but nothing could penetrate them except in the limited way that light penetrated translucent substances. This world of separate bodies, unaffected by the accidents of history or geographic location, underwent a profound change with the elaboration of the new concepts of matter and energy that went forward from Faraday and von Mayer through Clerk-Maxwell and Willard Gibbs and Ernest Mach to Planck and Einstein. The discovery that solids, liquids, and gases were phases of all forms of matter modified the very conceptions of substance, while the identification of electricity, light, and heat as aspects of a protean energy, and the final break-up of "solid" matter into particles of this same ultimate energy lessened the gap, not merely between various aspects of the physical world, but between the mechanical and the organic. Both matter in the raw and the more organized and internally self-sustaining organisms could be described as systems of energy in more or less stable, more or less complex, states of equilibrium."

"The history of science is rich in the example of the fruitfulness of bringing two sets of techniques, two sets of ideas, developed in separate contexts for the pursuit of new truth, into touch with one another."

"While, by the present methods of teaching, a knowledge of science in its present state of advancement is imparted very successfully, eminent and far-sighted men have repeatedly been obliged to point out a defect which too often attaches to the present scientific education of our youth. It is the absence of the historical sense and the want of knowledge of the great researches upon which the edifice of science rests."

"If we study the history of science we see happen two inverse phenomena, so to speak. Sometimes simplicity hides under complex appearances; sometimes it is the simplicity which is apparent, and which disguises extremely complicated realities. ...What is more complicated than the confused movements of the planets? What simpler than Newton's law? ...In the kinetic theory of gases, one deals with molecules moving with great velocities, whose paths, altered by incessant collisions, have the most capricious forms... The observable result is Mariotte's simple law. ...The law of great numbers has reestablished simplicity in the average. ...No doubt, if our means of investigation should become more and more penetrating, we should discover the simple under the complex, then the complex under the simple, then again the simple under the complex, and so on, without our being able to foresee what will be the last term. We must stop somewhere, and that science may be possible, we must stop when we have found simplicity. This is the only ground on which we can rear the edifice of our generalizations."

"Zoologists maintain that the embryonic development of an animal recapitulates in brief the whole history of its ancestors throughout geologic time. It seems it is the same in the development of minds. The teacher should make the child go over the path his fathers trod; more rapidly, but without skipping stations. For this reason the history of science should be our first guide."

"In my presentation I... follow the genetic method. The essential idea... is that the order in which knowledge has been acquired by the human race will be a good teacher for its acquisition by the individual. The sciences came in a certain order; an order determined by human interest and inherent difficulty. Mathematics and astronomy were the first sciences really worth the name; later came mechanics, optics, and so on. At each stage of its development the human race has had a certain climate of opinion, a way of looking, conceptually, at the world. The next glimmer of fresh understanding had to grow out of what was already understood. The next move forward, halting shuffle, faltering step, or stride with some confidence, was developed upon how well the [human] race could then walk. As for the human race, so for the human child. But this is not to say that to teach science we must repeat the thousand and one errors of the past, each ill-directed shuffle. It is to say that the sequence in which the major strides forward were made is a good sequence in which to teach them. The genetic method is a guide to, not a substitute for, judgement."

"The history of science, like the history of all human ideas, is a history of irresponsible dreams, of obstinacy, and of error. But science is one of the very few human activities — perhaps the only one — in which errors are systematically criticized and fairly often, in time, corrected. This is why we can say that, in science, we often learn from our mistakes, and why we can speak clearly and sensibly about making progress there."

"The History of Electricity is a field full of pleasing objects, according to all the genuine and universal principles of taste, deduced from a knowledge of human nature. Scenes like these, in which we see a gradual rise and progress in things, always exhibit a pleasing spectacle to the human mind. Nature, in all her delightful walks, abounds with such views, and they are in a more especial manner connected with every thing that relates to human life and happiness; things, in their own nature, the most interesting to us. Hence it is, that the power of association has annexed crouds of pleasing sensations to the contemplation of every object, in which this property is apparent. This pleasure, likewise, bears a considerable resemblance to that of the sublime, which is one of the most exquisite of all those that affect the human imagination. For an object in which we see a perpetual progress and improvement is, as it were, continually rising in its magnitude; and moreover, when we see an actual increase, in a long period of time past, we can not help forming an idea of an unlimited increase in futurity; which is a prospect really boundless, and sublime."

"Let us not... contend about merit, but let us all be intent on forwarding the common enterprize, and equally enjoy any progress we may make towards succeeding in it; and above all, let us acknowledge the guidance of that Great Being, who has put a spirit in man, and whose inspiration giveth him understanding."

"It is a remarkable fact in the history of science, that the more extended human knowledge has become, the more limited human power, in that respect, has constantly appeared. This globe, of which man imagines the haughty possessor, becomes, in the eyes of astronomer, merely a grain of dust floating in immensity of space: an earthquake, a tempest, an inundation, may destroy in an instant an entire people, or ruin the labours of twenty ages. ...But if each step in the career of science thus gradually diminishes his importance, his pride has a compensation in the greater idea of his intellectual power, by which he has been enabled to perceive those laws which seem to be, by their nature, placed for ever beyond his grasp."

"The more advanced the sciences have become, the more they have tended to enter the domain of mathematics, which is a sort of center towards which they converge. We can judge of the perfection to which a science has come by the facility, more or less great, with which it may be approached by calculation."

"[S]cientific physics dates its existence from the discovery of the differential calculus. Only when it was learned how to follow continuously the course of natural events, attempts, to construct by means of abstract conceptions the connection between phenomena, met with success. To do this two things are necessary: First, simple fundamental concepts with which to construct; second, some method by which to deduce, from the simple fundamental laws of the construction which relate to instants of time and points in space, laws for finite intervals and distances, which alone are accessible to observation..."

"Up until the publication of Thomas Kuhn's The Structure of Scientific Revolutions in 1962, the history, philosophy, and sociology of science maintained an internalist approach to scientific knowledge claims. Science was seen as somehow above any social, political, or cultural influences, and therefore, the examinations of scientific knowledge focused on areas such as 'discoveries,' 'famous men,' and 'the scientific revolution in the West.' When Kuhn opened the door to the possibility that external factors were involved in the development of scientific paradigms, science studies assumed a more critical tone."

"Histories of scientific thought tend to obscure the revolutionary state of knowledge in the age of Archimedes—the Hellenistic period—toning down the differences between it, the natural philosophy of classical Greece two centuries earlier, and even the prescientific knowledge of ancient Egypt and Mesopotamia."

"Humans may crave absolute certainty; they may aspire to it; they may pretend, as partisans of certain religions do, to have attained it. But the history of science — by far the most successful claim to knowledge accessible to humans — teaches that the most we can hope for is successive improvement in our understanding, learning from our mistakes, an asymptotic approach to the Universe, but with the proviso that absolute certainty will always elude us."

"The history of science—especially physics—has in part been the tension between the natural tendency to project our everyday experience on the universe and the universe's noncompliance..."

"The relativity and quantum theories provide good examples of one of the most characteristic features in the development of scientific ideas—namely the fact that every major advance, resulting in a new representation which post factum can be seen to have reduced the earlier picture to one whose results approximate closely to those of the newer one in special cases, has been connected with a revolutionary change in outlook, and with a radical revision of the epistemological and metaphysical foundations of the earlier picture. It is at such turning-points that scientific thought is most clearly revealed as creative speculation, kept within certain boundaries, and corrected, by facts and experimental evidence... akin to that sphere of inspiration which brings about the great creations of art: both constitute sudden and unpredictable insights into reality which no artificial and mechanical devices, such as computers, could ever achieve. ...science in the making can be seen to be as much an experiment with ideas as a search after significant experimental data."

"The history of science should be the leading thread in the history of civilization."

"The history of science familiarizes us with the ideas of evolution and the continuous transformation of human things... It shows us that if the accomplishments of mankind as a whole are grand, the contributions of each is small."

"It is childish to assume that science began in Greece; the Greek "miracle" was prepared by millenia of work in Egypt, Mesopotamia and possibly in other regions. Greek science was less an invention than a revival."

"Hellenic science is a victory of rationalism, which appears greater, not smaller, when one is made to realize that it had been won in spite of the irrational beliefs of the Greek people; all in all, it was a triumph of reason in the face of unreason. Some knowledge of Greek superstitions is needed not only for a proper appreciation of that triumph but also for the justification of occasional failures, such as the many Platonic aberrations."

"The historical order is very interesting, but accidental and capricious; if we would to understand the growth of knowledge, we cannot be satisfied with accidents, we must explain how knowledge was gradually built up."

"The history of science should not be an instrument to defend any kind of social or philosophic theory; it should be used only for its own purpose, to illustrate impartially the working of reason against unreason, the gradual unfolding of truth, in all its forms, whether pleasant or unpleasant, useful of useless, welcome or unwelcome."

"Men of science have made abundant mistakes of every kind; their knowledge has improved only because of their gradual abandonment of ancient errors, poor approximations, and premature conclusions."

"Science, especially evolutionary sciences, can only proceed from learning about theories of hypotheses that do not stand the test of time."

"That the Babylonians were Syrians, I believe that nobody will deny. Consequently, they are greatly mistaken who say that it is not possible that the Syrians know something of such matters (astronomy), since these Syrians were the inventors and the first Masters in these matters. Ptolemy again renders witness to this in the "Syntax" (Almageste), because when he chooses an origin for the computation of the Sun, the Moon and the five planets, he does not start with the years of Greek kings, but with those of the kings of Babylon, that is, Nebuchadnezzar, king of the Assyrians. I said Nebuchadnezzar, not the one of whom the prophet Daniel was the contemporary, but another more ancient. Ptolemy has thus given in the "Syntax" that the years that have passed since this first Nebuchadnezzar ---- i.e. of the Babylonian and Persian kings ---- until Philip (Arrhidaeus) the Macedonian, the successor of Alexander the founder of Alexandria, (are in the number of) four hundred and twenty-four years. There he rightly shows that he found among the Babylonians, and not among the Greeks, the beginning and foundation of the calculations which he made. It is thus on this foundation that he built and that he piled up the many calculations that he made."

"The history of science on the part of students will give them a better understanding of the broad tendencies which have determined the general course of scientific progress, will enlarge their appreciation of the work of successive generations, and tend to guard them against falling into those ancient pitfalls which have bordered the paths of progress."

"Two points should be specially emphasized in connection with the general theory of relativity. First, it is a purely physical theory, invented to explain empirical physical facts, especially the identity of gravitational and inertial mass, and to coordinate and harmonize different chapters of physical theory, especially mechanics and electromagnetic theory. It has nothing metaphysical about it. Its importance from a metaphysical or philosophical point of view is that it aids us to distinguish in the observed phenomena what is absolute, or due to the reality behind the phenomena, from what is relative, i.e. due to the observer. Second, it is a pure generalization, or abstraction, like Newton's system of mechanics and law of gravitation. It contains no hypothesis, as contrasted with the atomic theory or the theory of quanta, which are based on hypothesis. It may be considered as the logical sequence and completion of Newton's Principia. The science of mechanics was founded by Archimedes, who had a clear conception of the relativity of motion, and may be called the first relativist. Galileo, who was inspired by the reading of the works of Archimedes, took the subject up where his great predecessor had left it. His fundamental discovery is the law of inertia, which is the backbone of Newton's classical system of mechanics, and retains the same central position in Einstein's relativistic system. Thus one continuous line of thought can be traced through the development of our insight into the mechanical processes of nature... characterized by the sequence... Archimedes, Galileo, Newton, Einstein."

"Descartes's so-called dualism is often taken to represent a fundamental revolution in ideas and the starting point of modern philosophy. ...but in substance his work is... better understood as an attempt to conserve the old truths in the face of new threats. His dualism was in essence an armistice... between the established religion and the emerging science of his time. ...isolating the mind from the physical world... ensured that many of the central doctrines of orthodoxy—immortality of the soul, the freedom of will, and, in general, the "special" status of humankind—were rendered immune to any possible contravention by the scientific investigation of the physical world. ... For men such as Descartes, Malebranche, and Leibniz, solving the mind-body problem was vital to preserving the theological and political order inherited from the Middle Ages... For Spinoza, it was a means of destroying that same order and discovering a new foundation for human worth."

"No scientific discovery is named after its original inventor."

"Lagrange's "" is perhaps his most valuable work and still amply repays careful study. ...the full power of the newly developed analysis was applied to the mechanics of points and rigid bodies. The results of Euler, of D'Alembert, and of the other mathematicians of the Eighteenth Century were assimilated and further developed from a consistent point of view. Full use of Lagrange's own made the unification of the varied principles of statistics and dynamics possible... Newton's geometrical approach was now fully discarded; Lagrange's book was a triumph of pure analysis."

"The development of human thought and achievement, as a whole, has not been, as commonly supposed, a continual upward progression, nor even the equivalent of a continuous series of ascertained results. Thoughts and inventions, which seemed on the verge of practical fruition, have often been reduced to nothingness, even at the most decisive moment, through some combination of untoward circumstances; yes, even the very memory of a pathway broken into the Land of Promise is often obliterated and what seemed accomplished fact has had to be recreated by laborious work covering years, decades and even centuries. Just the simplest, most natural and, in the end, almost self-evident facts are the hardest to evolve and elucidate, just what was most decisive and potent of result has been time and again overlooked by the seeker after truth. ...The gold of historic thought, indeed, is as little to be found in the street as the gold of actual daily strife, and it is by no means the task of the historian of broad general scope to give the initial clew to its discovery. He, indeed, can only reproduce the past with fidelity and exactitude. The intuition of the true investigator and pathfinder of today and tomorrow must find its own way to new guiding principles from the work of yesterday, before yesterday, and the distant past."

"David Hume posed the issue in the following way (as rephrased in the black swan problem by... John Stuart Mill) No amount of observations of white swans can allow the inference that all swans are white, but the observation of a single black swan is sufficient to refute that conclusion."

"Science had shifted, thanks to Bacon, into an emphasis on empirical observation. The problem is that, without a proper method, empirical observations can lead you astray. Hume came to... stress the need for some rigor in the gathering and interpretation of knowledge... epistemology... Hume is the first modern epistemologist... he was an obsessive skeptic and never believed... that a link between two items could be established as being causal."

"[T]he ancients possessed a considerable acquaintance with many operations of technical chemistry... Their methods were probably jealously guarded and handed down by successive members of the crafts as precious secrets. ...But, under the conditions in which their industries were prosecuted, the scientific spirit was not free to develop, for science depends essentially upon free inter-communication of facts ...Moreover, the great intellects of antiquity, for the most part, had little sympathy with the operations of artisans, who, at least among the Greeks and Romans, were, for the most part, slaves. Philosophers taught that industrial work tended to lower the standard of thought. The priests, in most ages, have looked more or less askance at attempts, on the part of the laity, to inquire too closely into the causes of natural phenomena. The investigation of nature in early times was impossible for religious reasons. There was an outcry in Athens when the thunderbolts of Zeus were ascribed to the collision of clouds. Anaxagoras, , Plato, Aristotle, Diagoras, and Protagoras were charged by the priests with blasphemy and driven into exile. Prodikos, who deified the natural forces, as did Empedokles the primal elements, was executed for impiety. Sacerdotalism in Athens had no more sympathy with science than had the Holy Congregation in Italy when it banned the writings of Copernicus, Kepler, and Galileo, and sent Giordano Bruno to the stake. The educated Greeks had no interest in observing or in explaining the phenomena of technical processes. However prone they might be to speculation, they had no inclination to experiment or to engage in the patient accumulation of the knowledge of physical facts. ...The influence of a spurious , which lasted through many centuries and even beyond the time of Boyle, was wholly opposed to the true methods of science, and it was only when philosophy had shaken itself free from that chemistry, as a science, was able to develop."

"Where Francis Bacon had provided the manifesto for experimental science, René Descartes... did the same for scientific theory. And though in the three hundred years since 1650, there have been occasional conflicts between the Baconian and Cartesian tendencies in modern science, their opposition has been creative, and out of it have come many of our most profound insights."

"This subject crosses most cultures and places... It might even be argued that this discipline was the link that brought geometric models of the cosmos together with numerical computation in a synthesis that allowed theory to be converted into prediction: the birth of the exact sciences. All this makes it hard to believe that trigonometry has never been given a proper book-length historical treatment in English."

"One cannot genuinely practice the history of a scientific subject without also living and breathing the science itself."

"Our technology is based entirely on mathematics and physics. ...The unprecedented growth of natural science in the 17th century was followed ineluctably by the rationalism of the 18th, by the deification of reason... Science is the most significant phenomenon of modern times, the principal ingredient of our civilization — alas! ...the most important question for the history of culture is: How did our modern natural science come about? It will be conceded that most historical writings either do not consider this question at all, or else deal with it in a very unsatisfactory manner. For example, which are the histories of Greek culture that mention the names of Theaetetus and of Eudoxus, two of the greatest mathematicians of all times? Who realizes that, from the historical point of view, Newton was the most important figure of the 17th century?"

"Without the stupendous work of Ptolemy, which completed and closed antique astronomy, Kepler's , and hence the mechanics of Newton, would have been impossible. Without the conic sections of Apollonius, which Newton knew thoroughly, his development of the law of gravitation is equally unthinkable. And Newton's integral calculus can be understood only as a continuation of Archimedes' determination of areas and volumes. The history of mechanics as an exact science begins with the law of the lever, the laws of hydrostatics and the determination of mass centers by Archimedes. ...all the developments which converge in the work of Newton, those of mathematics, of mechanics and of astronomy, begin in Greece."

"The treatment of the kinetics of a material system by the method of generalised coordinates was first introduced by Lagrange, and has since his time been greatly developed by the investigations of different mathematicians. Independently of the highly interesting, although purely abstract science of theoretical dynamics which has resulted from these investigations, they have proved of great and continually increasing value in the application of mechanics to thermal, electrical and chemical theories, and the whole range of ."

"The important thing for the progress of physics is not the decision that a theory is true, but the decision that it is worth taking seriously—worth teaching to graduate students, worth writing textbooks about, above all, worth incorporating into one’s own research."

"The effect of these researches has been, a persuasion, that we need not despair of seeing, even in our own time, a renovation of sound philosophy, directed by the light which the History of Science sheds. Such a reform, when its Epoch shall arrive, will not be the work of any single writer, but the result of the intellectual tendencies of the age."

"Our species, from the time of its creation, has been travelling onwards in pursuit of truth; and now that we have reached a lofty and commanding position, with the broad light of day around us, it must be grateful to look back on the line of our past progress;—to review the journey."

"The main object of the work was to present such a survey of the advances already made in physical knowledge, and of the mode in which they have been made, as might serve as a real and firm basis for our speculations concerning the progress of human knowledge, and the processes by which sciences are formed."

"The present generation finds itself the heir of a vast patrimony of science; and it must needs concern us to know the steps by which these possessions were acquired, and the documents by which they are secured to us and our heirs for ever."

"The earlier truths are not expelled but absorbed, not contradicted but extended; and the history of each science, which may thus appear like a succession of revolutions, is, in reality, a series of developements."

"In all modern history, interference with science in the supposed interest of religion, no matter how conscientious such interference may have been, has resulted in the direst evils both to religion and to science, and invariably; and, on the other hand, all untrammelled scientific investigation, no matter how dangerous to religion some of its stages may have seemed for the time to be, has invariably resulted in the highest good both of religion and of science."

"Herein lies the truth of all bibles, and especially of our own. ...they are eminently precious, not as a record of outward fact, but as a mirror of the evolving heart, mind, and soul of man. They are true because they have been developed in accordance with the laws governing the evolution of truth in human history, and because in poem, chronicle, code, legend, myth, apologue, or parable they reflect this development of what is best in the onward march of humanity. To say that they are not true is as if one should say that a flower or a tree or a planet is not true; to scoff at them is to scoff at the law of the universe. In welding together into noble form, whether in the book of Genesis, or in the Psalms, or in the book of Job, or elsewhere, the great conceptions of men acting under earlier inspiration, whether in Egypt, or Chaldea, or India, or Persia, the compilers of our sacred books have given to humanity a possession ever becoming more and more precious; and modern science, in substituting a new heaven and a new earth for the old—the reign of law for the reign of caprice, and the idea of evolution for that of creation..."

"The physical doctrine of the atom has got into a state which is strongly suggestive of the epicycles of astronomy before Copernicus."

"We are indeed a blind race, and the next generation, blind to its own blindness, will be amazed at ours."

"Understanding what M-theory really is—the physics it embodies—would transform our understanding of nature at least as radically as occurred in any of the major scientific upheavals of the past."

"This statement appears to us to be conclusive with respect to the insufficiency of the undulatory theory, in its present state, for explaining all the phenomena of light. But we are not therefore by any means persuaded of the perfect sufficiency of the projectile system: and all the satisfaction that we have derived from an attentive consideration of the accumulated evidence, which has been brought forward, within the last ten years, on both sides of the question, is that of being convinced that much more evidence is still wanting before it can be positively decided. In the progress of scientific investigation, we must frequently travel by rugged paths, and through valleys as well as over mountains. Doubt must necessarily succeed often to apparent certainty, and must again give place to a certainty of a higher order; such is the imperfection of our faculties, that the descent from conviction to hesitation is not uncommonly as salutary, as the more agreeable elevation from uncertainty to demonstration. An example of such alternations may easily be adduced from the history of chemistry. How universally had phlogiston once expelled the aërial acid of Hooke and Mayow. How much more completely had phlogiston given way to oxygen! And how much have some of our best chemists been lately inclined to restore the same phlogiston to its lost honours! although now again they are beginning to apprehend that they have already done too much in its favour. In the mean time, the true science of chemistry, as the most positive dogmatist will not hesitate to allow, has been very rapidly advancing towards ultimate perfection."

"Notwithstanding the broad foundation for mechanics laid by Newton in his Principia, and notwithstanding the indefatigable labors of Clairaut, d'Alembert, the Bernoullis, and Euler, there was near the end of the eighteenth century no comprehensive treatise on the science. Its leading principles and methods were fairly well known, but scattered through many works, and presented from divers points of view. It remained for Lagrange to unite them into one harmonious system. Mechanics had not yet freed itself from the restrictions of geometry, though progress since Newton's time had been constantly toward analytical... methods. The emancipation came with Lagrange's Mécanique Analytique published one hundred and one years after the Principia."

"The history of the rainbow from the age of myth to contemporary optics is an example wrought in miniature of our unfolding penetration of and relation to natural phenomena. ...Yet while engaging in itself, the history of the rainbow hides within it another story far more significant than an external history of science. For the changing images of the rainbow reflect to us momentous changes in the fabric of consciousness itself. The history of light, the rainbow, and more generally the history of science continue to act as a text in which we read the psychogenesis of the mind."

"To recap, I had four numbers to add together. If the total came to under 2, then Einstein’s version of quantum reality was correct and the world is deterministic, rather than probabilistic, with quantum entities existing prior to being observed. But if the total came to over 2, then Niels Bohr was right and there is no objective reality out there in the absence of measurement and the subatomic world is ruled by chance and probability. [...] So, sorry Einstein, victory goes to Bohr instead."

"The discomfort that I feel is associated with the fact that the observed perfect quantum correlations seem to demand something like the ‘genetic’ hypothesis [identical twins, carrying with them identical genes]. For me, it is so reasonable to assume that the photons in those experiments carry with them programs, which have been correlated in advance, telling them how to behave. This is so rational that I think that when Einstein saw that, and the others refused to see it, he was the rational man. The other people, although history has justified them, were burying their heads in the sand. I feel that Einstein’s intellectual superiority over Bohr, in this instance, was enormous; a vast gulf between the man who saw clearly what was needed, and the obscurantist. So for me, it is a pity that Einstein’s idea doesn’t work. The reasonable thing just doesn’t work."

"Bohr was inconsistent, unclear, willfully obscure and right. Einstein was consistent, clear, down-to-earth and wrong."

"The EPR paper came out in 1935 and for at least two decades no one paid much attention to it. However, in 1964, the late John Bell published a paper that changed everything. He showed that Einstein’s idea that the results of quantum mechanics could be reproduced by a theory in which Einstein’s notions of realism were included could be tested in the laboratory. Having spent a good deal of time talking to Bell I can tell you that his heart was with Einstein. He often referred to Bohr as an “obscurantist.” But the experiments were carried out by Alain Aspect and others and showed that Einstein was wrong and Bohr was right. I cannot believe that anyone familiar with this would still agree with Einstein."

"His thought experiment with photon and film had not challenged Heisenberg's principle, but now Einstein did turn his attention there. He began looking for an experiment that would allow a more complete collection of data than the Heisenberg team thought possible. If he could find a technique that allowed the simultaneous discovery of position and momentum or time and energy, he would prove the quantum mechanics had indeed not yet brought us to the the secret of the Old One. This effort led the most famous set-pieces of the Einstein "debate" with Bohr over quantum mechanics. Einstein, Bohr, and Ehrenfest would meet in the hotel dining room for breakfast. Einstein would propose a thought experiment. Bohr would think about it. ... During the day's program at Solvay, Heisenberg and Pauli would analyze the experiment that Einstein had proposed. They would find some point where the uncertainty principle fought back, and over dinner, Bohr wold refute the experimental effort while Ehrenfest looked on."

"The mid-twentieth century “Bohr-Einstein debate” about quantum theory is often misinterpreted as a personal clash between wizards. So counter-intuitive are quantum theory’s predictions that, under the leadership of one of its pioneers, Neils Bohr, a myth grew that there is no underlying reality that explains them. Particles get from A to B without passing through the intervening space, where they have insufficient energy to exist; they briefly “borrow” the energy, because we are “uncertain” about what their energy is. Information gets from A to B without anything passing in between – what Einstein called “spooky action at a distance.” And so on....So, while most accounts say that Bohr won the debate, my view is that Einstein, as usual, was seeking an explanation of reality, while his rivals were advocating nonsense. Everett’s interpretation doesn’t make Einstein a demigod. But it does make him right."

"Einstein was not prepared to let us do what, to him, amounted to pulling the ground from under his feet. Later in life, also, when quantum theory had long since become an integral part of modern physics, Einstein was unable to change his attitude—at best, he was prepared to accept the existence of quantum theory as a temporary expedient. "God does not throw dice" was his unshakable principle, one that he would not allow anybody to challenge. To which Bohr could only counter with: "Nor is it our business to prescribe to God how He should run the world.""

"Their dispute went to the fundamental heart of the design of the cosmos. Was there an objective reality that existed whether or not we could ever observe it? Were there laws that restored strict causality to phenomena that seemed inherently random? Was everything in the universe predetermined?"

"Einstein's thinking is always on the ontological level traditional in physics; trying to describe the realities of Nature. Bohr's thinking is always on the epistemological level, describing not reality but only our information about reality."

"The famous debate between Einstein and Bohr began at the Solvay Council in 1927. The debate was about the interpretation of quantum mechanics, but also addressed the fundamental question of what the purpose and aim of a physical theory should be. Their conflicting positions were based on two diametrically opposed philosophical approaches to the fundamental problems of physics. The many books popularising quantum mechanics quite rightly place the emphasis on the problem of interpretation: they discuss the opposing positions of Einstein’s “realism” and the “Copenhagen interpretation” of which Bohr is seen as the leading protagonist."

"We, of course, were sure that on that particular debate Bohr was right and Einstein was wrong."

"The refutation of Einstein’s criticism does not add any new element to the conception of complementarity, but it is of great importance in laying bare a very deep-lying opposition between Bohr’s general philosophical attitude and the still widespread habits of thought belonging to a glorious but irrevocably bygone age in the evolution of science."

"Albert Einstein, who was in many ways the father of quantum mechanics, had a notorious love-hate relation with the subject. His debates with Niels Bohr—Bohr completely accepting of quantum mechanics and Einstein deeply skeptical— are famous in the history of science. It was generally accepted by most physicists that Bohr won and Einstein lost. My own feeling, I think shared by a growing number of physicists, is that this attitude does not do justice to Einstein’s views. Both Bohr and Einstein were subtle men. Einstein tried very hard to show that quantum mechanics was inconsistent; Bohr, however, was always able to counter his arguments. But in his final attack Einstein pointed to something so deep, so counterintuitive, so troubling, and yet so exciting, that at the beginning of the twenty-first century it has returned to fascinate theoretical physicists. Bohr’s only answer to Einstein’s last great discovery—the discovery of entanglement—was to ignore it."

"To this day, many researchers agree with Bohr's pragmatic attitude. The history books say that Bohr has proved Einstein wrong. But others, including myself, suspect that, in the long run, the Einsteinian view might return: that there is something missing in the Copenhagen interpretation. Einstein's original objections could be overturned, but problems still arise if one tries to formulate the quantum mechanics of the entire universe (where measurements can never be repeated), and if one tries to reconcile the laws of quantum mechanics with those of gravitation. But I am running far ahead in my story (I will return to this point in chapter 28). For a correct description of atoms and molecules, quantum mechanics is a perfect theory."

"The other mistake that is widely attributed to Einstein is that he was on the wrong side in his famous debate with Niels Bohr over quantum mechanics, starting at the Solvay Congress of 1927 and continuing into the 1930s. In brief, Bohr had presided over the formulation of a “Copenhagen interpretation” of quantum mechanics, in which it is only possible to calculate the probabilities of the various possible outcomes of experiments. Einstein rejected the notion that the laws of physics could deal with probabilities, famously decreeing that God does not play dice with the cosmos. But history gave its verdict against Einstein—quantum mechanics went on from success to success, leaving Einstein on the sidelines. All this familiar story is true, but it leaves out an irony. Bohr’s version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe."

"In the famous Einstein–Bohr debates, Bohr defended quantum mechanics against Einstein's yearning for a more classical theory; but some of us are coming to feel in defending his hard-won ground he compromised too much. Quantum mechanics should be pushed as hard as possible, to the point where it can describe within itself a recognizable caricature of the world as it is experienced, and thus begin to provide its own self-consisted interpretation — or else there should be some definite change in its equations. As yet this task has not been accomplished."

"Einstein’s great friend and intellectual sparring partner Niels Bohr had a nuanced view of truth. Whereas according to Bohr, the opposite of a simple truth is a falsehood, the opposite of a deep truth is another deep truth. In that spirit, let us introduce the concept of a deep falsehood, whose opposite is likewise a deep falsehood. It seems fitting to conclude this essay with an epigram that, paired with the one we started with, gives a nice example:“Naïveté is doing the same thing over and over, and always expecting the same result.”"

"Willis combined the physician's expert anatomical sophistication with the fluent use of an interpretive apparatus that see-sawed between novelty and tradition, Galenism and Gassendist , and mechanism."

"The history of medicine, of all the branches of that art, is the one to which least attention is devoted by physicians; and yet its study not only possesses great scientific value, but likewise includes an important germ of practical information."

"Medicine and theology, now it would seem irreconcilably at variance, were in their early periods of development most intimately united, like twin sisters in the womb, whom we are unable for a long period to recognize as distinct beings, and of whom even after birth we cannot say which is the elder, since both were born at the same time."

"To the naturalist, it [the history of medicine] teaches how the branches of his science, which lift their heads so proudly to-day, were originally mere offshoots of medicine, and have been only recently planted as independent growths upon a soil of their own."

"An acquaintance with the history of his science is... especially indispensable to the practical physician, if he would thoroughly comprehend and penetrate the secrets of his profession. To him, indeed, it is the bright and polar star, since undoubtedly it alone can teach him the principles of a medical practice independent of the currents, the faith and the superstition of the present. Moreover, it offers him as scientific gain, through the knowledge of the past, the measure for a just and well-founded criticism of the doings of his own time, places in his hand the thread by which he unites past conditions and efforts with those of the present, and sets before him the mirror in which he may observe and compare the past and present, in order to draw therefrom well-grounded conclusions for the future."

"We prize infinitely less the fact that history, among almost all people, presents to our eyes the immortal gods as the authors of medical art, than that it teaches us how mortal men have struggled continually after god-like aims—the prevention, the cure, or at least the alleviation of the woe and suffering imposed as an unavoidable heritage, and in a thousand different forms, upon us created beings—even though to-day, as in the past, these aims have been only imperfectly attained."

"Medicine is a science which hath been... more professed than laboured, and yet more laboured than advanced: the labour having been, in my judgment, rather in circle than in progression. For I find much iteration but small addition. It considereth causes of diseases, with the occasions or impulsions; the diseases themselves, with the accidents; and the cures with the preservations. The deficiencies which I think good to note being a few of many, and those such as are of a more open and manifest nature, I will enumerate, and not place."

"To attempt to isolate the history of medicine, and to comprehend its curious ebbs and flows of doctrine from medical writings only, is like cutting a narrow strip from the center of a piece of tapestry and speculating upon the origin and purpose of the cut threads of patterns that may be found in it."

"When we take an extended view of the progress of medicine, tracing it from its scanty sources, in the most remote periods of society, and observe its course, as gradually augmented by the stores of Grecian and Roman learning, obscured by the darkness of the middle ages, and again bursting forth in the copious and almost overwhelming streams of modern literature, we are naturally led to separate the narrative into three divisions, corresponding to the three great chronological periods. The first of these will comprehend the history of practical medicine, from the earliest records which we possess, to the decline of Roman literature; the second will contain an account of the state of the science, through what are termed the dark ages, until the revival of letters; the third will commence with the establishment of the inductive philosophy, and be continued to the commencement of the nineteenth century."

"The improvement in the healing art has been nearly in proportion to the advancement of the other arts of life, and to the gradual progress of knowledge on all subjects intimately connected with our existence or welfare."

"The probability... is that the priests of the Egyptians were at the same time their physicians. This appears to have been the case among the Jews and the Greeks, who are supposed to have borrowed from the Egyptians many of their institutions; and indeed it seems to be the natural progress of society in its earlier periods, when the priests were generally the depositaries of knowledge."

"The Greeks soon excelled the Egyptians in medicine, so late as the time of Plato, the Pastopheri, or medical division of the hierarchy, are found not altogether to have lost their former celebrity. Some of the distinguished Greek physicians went to Egypt, in order to study medicine under the Egyptian priesthood. The Pastopheri were keepers of the temples, and the sick who resorted there for aid came in the first instance into their hands, and they were thus called upon more frequently than others, both to examine the patient and to prescribe a remedy. That the upper ranks of the hierarchy, the higher orders of the sacred colleges also, attended to medical practice, we have positive proof. Plato and Euripedes, during their residence in Egypt, were both cured of an attack of illness by such."

"If we examine the great eras in civilization, Medicine will be found to have progressed as rapidly as the physical sciences generally. The discoveries of Columbus and successive navigators, were not earlier nor more important in geography, than those of Mondini, Beranger, Vesalius, and Sylvius, in anatomy. Copernicus did not earlier conceive the errors of the Ptolemaic astronomy, than Servetus, R. Columbus, and Cesalpine the errors of Galenic physiology; and Galileo, who demonstrated the movements of the earth and planets around the sun, was a cotemporary with Harvey, who demonstrated the circulation of the blood. The universal law of Newton for the solar system, was not greatly in advance of that of Haller of the laws and special forces of life. If the great philosopher established that the force manifested in the fall of an apple to earth, is the same as that which keeps the planets in their orbits, so the pathologist has shown that the laws of inflammation in the deep-seated and vital organs are identical with those that are seen in the smallest inflammatory point on the skin. And how much might be added on the application of physical laws in diagnosis, the prevention of small pox, the easy cure of autumnal fever, etc., to show that in point of progress Medicine marches hand in hand with kindred sciences."

"The epidemics that formerly terrified the nations leaving in their trail desolations worse than the tornado have been shorn of their terrors. The prevalence of small pox has been almost prevented by Jenner's discovery of vaccination. The treatment of cholera is now so well understood that it has lost its former desolating power. Human life has been greatly lengthened in the last hundred years. The reports of the Parisian hospitals show that while in 1805 one died in seven who were admitted, now only one dies in twelve... In surgical practice, the saving of life at present exceeds by more than thirty five per cent. ...In midwifery practice, one hundred and fifty years ago, according to Dr. Merriman, one in forty died. At the close of his tables, (1828) only one in one hundred and seven died, and at this time perhaps not one in two hundred and fifty dies."

"The message of medical history to the future is: "Come clean.""

"The history of medicine is... the history of humanity itself, with its ups and downs, its brave aspirations after truth and finality, its pathetic failures. The subject may be treated variously as a pageant, an array of books, a procession of characters, a succession of theories, an exposition of human ineptitudes, or as the very bone and marrow of cultural history."

"Under different aspects of space and time, all phases of folk-medicine and ancient medicine have been essentially alike in tendency, differing only in unimportant details. In the light of anthropology, this proposition may be taken as proved. Cuneiform, hieroglyphic, runic, and palm-leaf inscriptions all indicate that the folk-ways of early medicine, whether Accadian or Scandinavian, Slavic or Celtic, Roman or Polynesian, have been the same—in each case an affair of charms and spells, plant lore and psychotherapy, to stave off the effects of supernatural agencies."

"The history of Medicine is largely the history of science and philosophy. It is not a narrative of events simply, but more a tracing of the evolution of the various branches of the sciences, the ensemble of which comprises Medicine."

"The history of Medicine is... a study of the progress of the science and art of caring for living beings in health and disease, and of ideas fundamental to them, and only incidentally of men who distinguished themselves in their advancement."

"Physicians have, as a rule, taken their theories from the philosophers. ...seeking by a show of great words and learned phrases to give to their statements an evidence of truth that they did not have, and that they could never acquire. When the philosophers began introduce a critical spirit into human knowledge, physicians were also the first not to admit any principle which was not the result of accurate observation. Nothing could be more natural, therefore, than that physicians, in their search for data that were demonstrable, should often find themselves unwittingly in conflict with deductions predicated upon imaginary, revealed, or supernatural sources; the more so, since... the philosophy of man both in health and disease, physiologically and pathologically, and in his twofold nature—conscious and sub-conscious,—allies him with both systems of thought, the Physical and the Psychical."

"However arid and uninviting the prospect of a History of Medicine may appear at a distance, it will be found gradually to improve, and become full of interest wonder and animation as we proceed. ...The History of Medicine is ...the history of the human species, uncontaminated by those civil discords and fearful atrocities, those crimes and disorders which blot the page of other histories, and stamp man, created in the image of his maker, with the visage of a fiend and the heart of a brute. The History of Medicine, on the contrary, is the history of peace and good will, of endless harmony, and unceasing philanthropy. Instead of recording the desolations of war, and the growth of immorality—the deadly effects of human passions, and the bloody triumphs of senseless ambition—her province is to note the diminution of mortal suffering; and the only triumphs which she records are those obtained over sickness, death, and Sorrow."

"It is hardly an exaggeration to summarize the history of four hundred years by saying that the leading idea of a conquering nation in relation to the conquered was, in 1600, to change their religion; in 1700, to change their trade; in 1800, to change their laws; and in 1900, to change their drainage. May we not then say, that on the prow of the conquering ship in these four centuries first stood the priest, then the merchant, then the lawyer, and finally the physician?"

"Disease is almost as old as man himself; and so must have been medicine."

"Medicine appears to have been very early seized upon by the priests, as an instrument of great power; and thus mixed up and blended with religious superstitions, it was practised by a sect of the Egyptian priesthood, under the denomination of Pastopheri."

"[W]hen they write incantations, and utter them as to the stars, not only to [the bodies and] souls of these, but also to things superior to soul, what do they effect? They answer, charms, allurements, and persuasions, so that the stars hear the words addressed to them, and are drawn down; if any one of us knows how in a more artificial manner to utter these incantations, sounds, aspirations of the voice, and hissings, and such other particulars as in their writings are said to possess a magical power. ...They likewise pretend that they can expel disease. And if, indeed, they say that they effect this by temperance and an orderly mode of life, they speak rightly, and conformably to philosophers. But now when they assert that diseases are daemons, and that they are able to expel these by words, and proclaim that they possess this ability, they may appear to the multitude to be more venerable, who admire the powers of magicians; but they will not persuade intelligent men that diseases have not their causes either from labours, or satiety, or indigence, or putrefaction, and in short from mutations which either have an external or internal origin. This, however, is manifest from the cure of diseases. For disease is deduced downward, so as to pass away externally, either through a flux of the belly, or the operation of medicine. Disease, also, is cured by letting of blood and fasting. ...The disease ...was something different from the daemon. ...The manner, however, in which these things are asserted by the Gnostics, and on what account is evident; since for the sake of this, no less than of other things, we have mentioned these daemons. ...And this must every where be considered, that he who pursues our form of philosophy, will, besides all other goods, genuinely exhibit simple and venerable manners, in conjunction with the possession of wisdom, and will not endeavour to become insolent and proud; but will possess confidence accompanied with reason, much security and caution, and great circumspection."

"It is evident, indeed, that the practitioner who has no faith in the eflicacy of his art, can not devote himself to the study and practice of it, with the necessary zeal and perseverance. But, it will not suffice for the physician only to be convinced of the utility of the remedies he prescribes; it is also very advantageous to the success of the treatment, if the patient share his confidence in them. It is, then, important to all of us, to form early a reasonable opinion on the degree of efficacy and certainty that may be attained in medicine. Now we shall not be able to draw the motives of such an opinion from any better source than the history of this science."

"Medicine... was called in its origin the Art of Healing. It consisted at that time, in a succinct description of diseases, which had been observed, and the indication of the remedies employed to combat them. These two parts... relate to man in a state of disease only. Subsequently, those who devoted themselves to the practice of Medicine, enlarged, gradually, the field of their observations. Nosological descriptions became more extended and numerous, and the therapeutical indications more precise. They became convinced, that to understand diseases well, it was necessary to study man in a state of health. Thus Anatomy... and Physiology... became important branches of medical science. Experience, also, taught men that it is always more important, and often easier, to prevent the development of certain diseases, than to arrest their progress when once developed. Consequently physicians... traced the rules for the preservation of health, and the collection of these rules constituted a new branch of the art called Hygiene. These successive additions necessitated a change in the definition of Medicine; the first, not embracing any longer all the departments of the science, the following was then nearly unanimously adopted: "Medicine is a science which has for its aim, the promotion of Health, and the cure of Disease.""

"Two interesting ramifications are developed recently, from this majestic trunk of science devoted to physical man. The first named Orthopaedia, teaches how to correct certain exterior deformities, whether accidental or congenital; the success it has attained, and the extension it has acquired, make it already a special branch of Medicine. The second ramification is called Phrenology, a Greek word, which signifies, literally, a discourse on thought, or on the faculties of the soul. But, by thought, here, is meant the organ which serves, more particularly, for its manifestation. It is then the organ of thought, that is to say, the encephalon, of which Phrenology treats. Those who have made a special study of this branch, believe that the development of the faculties of the soul, or rather, the manifestation of these faculties, depends on the volume and the form of certain parts of the encephalon... the last definition that we have given to Medicine, appears to me a little too restrained, and it may be advantageously replaced, I think, by the following:—"Medicine is a Science, which aims at the Preservation of Health, the cure of Diseases, and the Physical perfection of Man.""

"To the historian, Medicine presents itself in three principal phases, viz: as a Profession, as an Art, and as a Science."

"In the point of view of an Art... Medicine appears to me to have followed a constantly progressive march from its origin to the death of Galen. Then it remained stationary, or even retrograded, at least in Europe, until the end of the fourteenth century... But from this epoch, the Healing Art took a new bound, and acquired, from generation to generation, remarkable perfection. Those who deny the progress of Medicine, have never seriously studied its history."

"Whatever this erudite historian in Medicine may say, doubt is not the last word of science, it is only the commencement of it, the point of departure. It is merely a favorable disposition for acquiring knowledge, certainty, or at least conviction. So taught Aristotle, so proclaimed Descartes, and the intimate sense of each one of us confirms the same. When we undertake the search for truth, it is with the desire and hope of attaining it, and if persuaded in advance that this desire and hope are vain... we would rest in careless repose, rather than uselessly fatigue ourselves in the pursuit of a chimera."

"Celebrated physicians influence the progress of their Science and the value of their Art, not by their writings only, but by their oral teachings, character, and conduct. Their lives offer, often, models for imitation, and sometimes, also, faults and errors to be avoided. Often, too, the early education of a man, and the circumstances in the midst of which he was reared, explain the peculiarity of his genius, and give the key to his successes and reverses. For these reasons, I could not neglect entirely some biographic details relative to the most famous physicians, especially when these details had some connection with the general history of the Art, or embraced some moral considerations."

"Of capital interest in the history of medical theories is, that they are all derived more or less directly, from some system of philosophy; so that only an incomplete idea of them could be obtained if the philosophic sources from which they were drawn were unknown. But too much importance must not be attached to these analogies, nor must the value of medical theories be judged by them... a philosophic system may be false as a whole and yet true in its particular application to Medicine. On the other hand, we may, by false logic, deduce an erroneous medical theory from an irreproachable philosophic system. Thus, then, after having indicated the philosophic ideas with which each medical doctrine may seem to be related, we shall judge this in itself, and relative to its practical consequences."

"Rome at an early period gave birth to several philosophers and practitioners in the art of healing. Cornelius Celsus['s] ...works on medicine show the advanced state of surgery and medicine during the Roman Empire. ...Of the methods of administration employed in early Roman pharmacy, the malagma was commonly used. It was a kind of soft mass composed of herbs and grass beaten up to the consistency of a thick paste, and applied to the skin. Numerous formulae for malagmas are given, in which pellitory, , resin, s, , , etc., are included. Their malagmas corresponded with our ointments. They also used plasters, of which the of galbanum, pitch, resin, and oil, in an improved form, has survived two thousand years. Troches, for healing wounds, were composed of dry medicines held in suspension by some liquid such as wine or oil. Pessaries (vaginal) were originated by the Greeks, who called them pessi. The ingredients were placed in a piece of wool, and thus used. Powders and snuffs were also common methods of administration. ...The Greeks called their embrocations or ointments euchrista. The catapotia was the method used for internal administration in liquid form, for which many recipes are given by Celsus."

"The history of medicine from Hippokrates and Galen till the present time has been replete with innovations, new teachers, new schools, new procedures. There has been no one school, no single medical profession, outside of the priesthoods, extending in an unbroken chain from the indefinite Past to our own Twentieth Century. New phases have manifested themselves as regularly almost as those of the moon in the sky. We may not be astonished at Paracelsus for burning the writings of Galen as no longer suitable for the student of the Healing Art. A distinguished physician of Edinburg upon taking charge of the Library of the University, commanded all books of reference that were ten years old to be removed as obsolete. If any would conjure with old names, like Galen, Rhasis, Ibn Sina, or later ones that have been distinguished, the fact is nevertheless unquestionable, that they have had their time. We may profit by their counsel and examples, but we can not be bound to employ their formulas and procedures."

"The earlier faiths of the world which ascribed the origin of mankind to Divinity, also associated the technique of medicine with the offices of religious worship. They named gods as the first physicians; these famous hero-chieftains, gifted men who were instinct with enthusiastic fervor, the Rephaim and giant-minds among the tribes and peoples of the earth. The temples were often hospitals to which the sick resorted for counsel and healing medicines, believing that the means of cure had been revealed there by the guardian divinity of the shrine. The priests were regarded as physicians for disorders of the body; prophets and diviners were consulted for those who suffered from disease, and the wisdom of the philosophers included the knowledge of treating physical maladies. ...Pythagoras, Aristotle, Athenæos, the early Christian teachers, the mystics of later centuries, down to our own times, not only gave instructions to their disciples in arcane, metaphysical and other learning, but also treated the sick and ministered to their bodily injuries."

"Indeed, we may regard it as an axiom, that the knowledge which is anywhere possessed of the art of healing, is the measure of the refinement and civilization to which the people have attained. Man is civilized by virtue of social relations; and refinement is the becoming divested from grossness, vulgarity, and the evil manners which are characteristic and incident to a living for one's self alone. Selfishness is savagery; and a state of society in which self-interest is the ruling element is hardly yet reclaimed from the state of barbarism. It is of little avail to appeal to skill in mechanics, engineering, and other attainments in the plane of material evolution. These are not adequate proof of spiritual advancement. Kindly sentiment toward others, sincere regard for their welfare, charity in will and act, make the only real culture and civilization. The art and technique of healing proceed from these qualities, and cannot flourish apart from them."

"The History of the Healing Art is as old as the history of the human race. The amber of antiquity has not preserved the name or any monument of the benefactor who first ventured upon the attempt to relieve the maladies of his fellow beings. To know so much would be equivalent to knowing the origins of civilization... What is regarded as learning, erudition, or wisdom, is a treasure which others have won and possessed before us. Every great thought has had a precursor, every great man a predecessor. ...We have no Father of Medicine, no Founder of the Healing Art, except in eponym."

"The more man inquires into the laws which regulate the material universe, the more he is convinced that all its varied forms arise from the action of a few simple principles. These principles themselves converge, with accelerating force, towards some still more comprehensive law to which all matter seems to be submitted. Simple as that law may possibly be, it must be remembered that it is only one amongst an infinite number of simple laws: that each of these laws has consequences at least as extensive as the existing one, and therefore that the Creator who selected the present law must have foreseen the consequences of all other laws."

"It appears... that the elastic theories of light, if Kelvin's gyrostatic adynamic ether be admitted, have not been wholly routed. Nevertheless the great electromagnetic theory of light propounded by Maxwell (1864, 'Treatise,' 1873) has been singularly apt not only in explaining all the phenomena reached by the older theories and in predicting entirely novel results, but in harmoniously uniting as parts of a unique doctrine, both the electric or photographic light vector of Fresnel and Cauchy and the magnetic vector of Neumann and MacCullagh. Its predictions have, moreover, been astonishingly verified by the work of Hertz (1890), and it is to-day acquiring added power in the convection theories of Lorentz (1895) and others."

"At first the mathematical disciplines were not sharply defined. As knowledge increased, individual subjects split off from the parent mass and became autonomous. Later, some were overtaken and reabsorbed in vaster generalizations of the mass from which they sprang. Thus trigonometry issued from surveying, astronomy, and geometry only to be absorbed, centuries later, in the analysis which had generalized geometry. This recurrent escape and recapture has inspired some to dream of a final, unified mathematics which shall embrace all. Early in the twentieth century it was believed by some for a time that the desired unification had been achieved in mathematical logic. But mathematics, too irrepressibly creative to be restrained by any formalism, escaped."

"Whatever its source, mathematics has come down to the present by the two main streams of number and form. The first carried along arithmetic and algebra, the second, geometry. In the seventeenth century these two united, forming the ever-broadening river of mathematical analysis."

"If the early Greeks were cognizant of Babylonian algebra, they made no attempt to develop or even to use it, and thereby they stand convicted of the supreme stupidity in the history of mathematics. ...The ancient Babylonians had a rare capacity for numerical calculation; the majority of Greeks were either mystical or obtuse in their first approach to number. What the Greeks lacked in number, the Babylonians lacked in logic and geometry, and where the Babylonians fell short, the Greeks excelled. Only in the modern mind of the seventeenth and succeeding centuries were number and form first clearly perceived as different aspects of one mathematics."

"Science is an attempt to represent the known world as a closed system with a perfect formalism. Scientific discovery is a constant maverick process of breaking out at the ends of the system... and then hastily closing it... The act of the imagination is the opening of the system so that it shows new connections. ...every act of imagination is the discovery of likenesses between two things which were thought unlike. ...they introduce new likenesses, whether it is Shakespeare... or Newton saying that the moon in essence is exactly like a thrown apple."

"Up to this point mathematics alone appeared to Descartes worthy of being called a science. ...in order to establish the science or philosophy sought by Descartes, it was sufficient to find a method that should be to philosophy what the method of mathematical deduction is to arithmetic, algebra and geometry. ...How could one pass from these processes, which are especially adapted to particular sciences, to the general method required by general science or philosophy? Descartes would undoubtedly never have conceived such an audacious hope, had not a great discovery of his set him on this track. He had invented analytical geometry... In this way, Descartes substituted for the old methods, which were especially adapted to algebra and geometry as distinct branches, a general method, applicable to what he called the "universal mathematical science," viz., to the study of "the various ratios or proportions to be found between the objects of the mathematical sciences, hitherto regarded as distinct." Not only did this discovery mark a decisive epoch in the history of mathematics, which it provided with an instrument of incomparable simplicity and power, but it furthermore gave Descartes a right to hope for the philosophical method he was seeking. Ought not a last generalization to be possible, by means of which the method he had so happily discovered should become applicable, not only to the "universal mathematical science," but also to the systematic combination of all the truths which our finite minds may permit us to attain?"

"[A]s the great extreme of dimension is sublime, so the last extreme of littleness is in the same measure sublime... when we attend to the infinite divisibility of matter, when we pursue animal life into these excessively small, and yet organized beings... when we push our discoveries yet downward... in tracing which the imagination is lost as well as the sense; we become amazed and confounded at the wonders of minuteness; nor can we distinguish in its effects this extreme of littleness from the vast itself. For division must be infinite as well as addition; because the idea of a perfect unity can no more be arrived at, than that of an complete whole, to which nothing can be added."

"Edmund Burke, ' (1757) p. 81 of the 1898 edition."

"Copernicus had taken one course in treating the earth as virtually a celestial body in the Aristotelian sense—a perfect sphere governed by the laws which operated in the higher reaches of the skies. Galileo complemented this by taking now the opposite course—rather treating the heavenly bodies as terrestrial ones, regarding the planets as subject to the very laws which applied to balls sliding down inclined planes. There was something in all this which tended to the reduction of the whole universe to uniform physical laws, and it is clear that the world was coming to be more ready to admit such a view."

"[T]he attempt to embrace the whole course of things in time and to relate the successive epochs to one another—the transition to the view that time is actually aiming at something, that temporal succession has meaning and that the passage of ages is generative—was greatly influenced by the fact that the survey became wider than that of human history, that the mind gradually came to see geology, pre-history and history in due succession to one another. The new science and the history joined hands and each acquired a new power as a result of their mutual reinforcement. The idea of progress itself gained additional implications when there gradually emerged a wider idea of evolution."

"Let us assert, as our original postulate, that, the multiple (that is, non-being, if taken in the pure state) being the only rational form of a creatable (creabile) nothingness, the creative act is comprehensible only as a gradual process of arrangement and unification, which amounts to accepting that to create is to unite. And, indeed, there is nothing to prevent our holding that union creates. To the objection that union presupposes already existing elements, I shall answer that physics has just shown us (in the case of mass) that experientially (and for all the protests of "common sense") the moving object exists only as the product of its motion."

"The scientific spirit must then lose its present tendency to speciality, and be impelled towards a logical generality; for all the branches of natural philosophy must furnish their contingent to the common doctrine; in order to which they must first be completely condensed and co-ordinated. When the savans have learned that active life requires the habitual and simultaneous use of the various positive ideas that each of them isolates from all the rest, they will perceive that their social ascendency supposes the prior generalization of their common conceptions, and consequently the entire philosophical reformation of their present practice. Even in the most advanced sciences... the scientific character at present fluctuates between the abstract expansion and the partial application, so as to be usually neither thoroughly speculative nor completely active; a consequence of the same defect of generality which rests the ultimate utility of the positive spirit on minor services, which are as special as the corresponding theoretical habits. But this view, which ought to have been long outgrown, is a mere hindrance in the way of the true conception,—that positive philosophy contemplates no other immediate application than the intellectual and moral direction of civilized society; a necessary application, presenting nothing that is incidental or desultory, and imparting the utmost generality, elevation, unity, and consistency, to the speculative character. Under such a homogeneousness of view and identity of aim, the various positive philosophers will naturally and gradually constitute a European body, in which the dissensions that now break up the scientific world into coteries will merge; and with the rivalries of struggling interests will cease the quarrels and coalitions which are the opprobrium of science in our day."

"Prior to Newton, mathematics, chiefly in the form of geometry, had been studied as a fine art without any view to its physical applications other than in very trivial cases. But with Newton all the resources of mathematics were turned to advantage in the solution of physical problems. Thenceforth mathematics appeared as an instrument of discovery, the most powerful one known to man, multiplying the power of thought... It is this application of mathematics to the solution of physical problems, this combination of two separate fields of investigation, which constitutes the essential characteristic of the Newtonian method. Thus problems of physics were metamorphosed into problems of mathematics. ...Newton showed the mark of genius by inventing the integral calculus. As a result... problems which would have baffled Archimedes were solved with ease. ...this new departure in scientific method led to the discovery of the law of gravitation. ...the real significance in Newton's achievement lay ...in his having established the presence of law and order at least in one realm of nature ...the motions of the heavenly bodies. Nature thus exhibited rationality and was not mere blind chaos and uncertainty."

"Newton, in his application of mathematics to physics, had been concerned only with... planetary motions, mechanics, propagation of sound, etc. But when it came to applying the mathematical method to the more intricate physical problems, a considerable advance was necessary... both mathematical and empirical. Thanks to the gradual accumulation of physical data, and... to the efforts of Newton's great successors in the field of pure mathematics (Euler, Lagrange, Laplace), conditions were ripe in the first half of the nineteenth century for a systematic attack on many of nature's secrets. The mathematical theories constructed were known under the general name of theories of mathematical physics. ...they had their prototype in Newton's celestial mechanics. ...they dealt with a wide variety of physical phenomena (electric, hydrostatic, etc.) ...The most celebrated of these theories (such as those of Maxwell, Boltzmann, Lorentz and Planck) were concerned with very special classes of phenomena. But with Einstein's theory of relativity... the scope of our investigations is so widened that we are appreciably nearer than ever before to the ideal of a single mathematical theory embracing all of physical knowledge."

"The equations of gravitation... signify that whenever we recognise the existence of one of these physical magnitudes it is always accompanied by corresponding curvatures of space-time. It is usual to assume that the curvatures are produced by those concrete somethings which we call mass, momentum, energy, pressure. In this way, we must concede a duality to nature; there would exist both matter and space-time, or, better still, matter and the metrical field of space-time. Einstein... attempted to remove this duality by proving that it was possible to attribute the entire existence of the metrical field, hence of space-time, to the presence of matter. This attitude led to a matter-moulding conception of the universe... And... only when this attitude was adhered to could Mach's belief in the relativity of all motion be accepted. Eddington's attitude is just the reverse. He prefers to assume that the equations of gravitation are not equations in the ordinary sense of something being equal to something else. In his opinion they are identities. They merely tell us how our senses will recognize the existence of certain curvatures of space-time by interpreting them as matter, motion, and so on. In other words, there is no matter; there is nothing but a variable curvature of space-time. Matter, momentum, vis viva, are the names we give to those curvatures on account of the varying ways they affect our senses."

"Passing to the laws of motion, we remember that there is but one law: All free bodies (when reduced to point-masses) follow time-geodesics in space-time regardless of whether space-time be flat, as it is (at least approximately) in interstellar space, or whether it be curved by the presence of matter. If space-time is flat, the geodesics are straight and the bodies describe straight courses with constant speeds as referred to a Galilean frame. Thus Newton's law of inertia is seen to express the flatness of space-time. When space-time, and hence its geodesics, are curved by the presence of matter, the courses of free bodies appear to be curved, or else their motion to be accelerated. But whereas, under those conditions, the law of inertia was at fault in classical science, and an additional gravitational influence had to be introduced, in Einstein's theory the general law of geodesic motion still holds good. Inasmuch as the structure of space-time determines the laws of our geometry, the beatings of natural clocks (atoms) and the motion of free bodies, we see that the theory has brought about a fusion between geometry and physics."

"The age-old conflict between our notions of continuity and the scientific concept of number ended in a decisive victory for that latter. This victory was brought about by the necessity of vindicating, of legitimizing... a procedure which ever since the days of Fermat and Descartes had been an indispensable tool of analysis. ...analytic geometry ...this discipline which was born of the endeavors to subject problems of geometry to arithmetical analysis, ended by becoming the vehicle through which the abstract properties of number are transmitted to the mind. It furnished analysis with a rich, picturesque language and directed it into channels of generalization hitherto unthought of. Now, the tacit assumption on which analytic geometry operated was that it was possible to represent the points on a line, and therefore points in a plane and in space, by means of numbers. ...The great success of analytic geometry... gave this assumption an irresistible pragmatic force. ...Under such circumstances mathematics proceeds by fiat. It bridges the chasm between intuition and reason by a convenient postulate. On the one hand, there was the logically consistent concept of real number and its aggregate, the arithmetic continuum; on the other, the vague notions of the point and its aggregate, the linear continuum. All that was necessary was to declare the identity of the two, or, what amounted to the same thing, to assert that: It is possible to assign to any point on a line a unique real number, and, conversely, any real number can be represented in a unique manner by a point on a line. This is the famous Dedekind-Cantor axiom."

"[W]ith a view to summon myself to the search for a science of mathematics in general, I asked myself... what precisely was the meaning of this word mathematics, and why arithmetic and geometry only, and not also astronomy, music, optics, mechanics, and so many other sciences, should be considered as forming a part of it; for it is not enough here to know the etymology of the word. In reality the word mathematics meaning nothing but science, those which I have just named have as much right as geometry to be called mathematics; and nevertheless there is no one, however little instructed, who cannot distinguish at once what belongs to mathematics... from what belongs to the other sciences. But... all the sciences which have for their end investigations concerning order and measure, are related to mathematics, it being of small importance whether this measure be sought in numbers, forms, stars, sounds, or any other object; that, accordingly, there ought to exist a general science which should explain all that can be known about order and measure, considered independently of any application to a particular subject, and that, indeed, this science has its own proper name, consecrated by long usage, to wit, mathematics... And a proof that it surpasses in facility and importance the sciences which depend upon it is that it embraces at once all the objects to which these are devoted and a great many others besides; and consequently, if it contain any difficulties, these exist in the rest, which have themselves the peculiar ones arising from their particular subject-matter, and which do not exist for the general science."

"I think that the correct connection between quantum theory and relativity has not yet been discovered. ...I think that the present methods which theoretical physicists are using are not the correct methods. They use... a renormalization technique which involves handling infinite quantities, and this is not really a mathematically logical process. ...[I]t is just a set of working rules rather than a correct mathematical theory and I don't like this whole development at all. I think that some other important discoveries will have to be made before these questions are put into order. In particular, there is the problem of explaining the , the number 137, which plays an important role in physics, and the question is, why should it be 137 instead of some other number. That has not been explained at all, and I feel that it is necessary to get an explanation of that before one would make an important advance in understanding atomic theory. ...There is quite a different problem with the ratio of the mass of the proton to the mass of the electron, and the question is whether the ratio of these masses remains constant or whether it develops slowly with time."

"You could not imagine the sum-over-histories picture being true for a part of nature and untrue for another part. You could not imagine it being true for electrons and untrue for gravity. It was a unifying principle that would either explain everything or explain nothing. And this made me profoundly skeptical. I knew how many great scientists had chased this will-o’-the-wisp of a unified theory. The ground of science was littered with the corpses of dead unified theories. Even Einstein had spent twenty years searching for a unified theory and had found nothing that satisfied him. I admired Dick tremendously, but I did not believe he could beat Einstein at his own game."

"From the present state of theory it looks as if the electromagnetic field, as opposed to the gravitational field, rests upon an entirely new formal motif, as though nature might just as well have endowed the gravitational ether with fields of quite another type, for example, with fields of a scalar potential, instead of fields of the electromagnetic type. Since according to our present conceptions the elementary particles of matter are also, in their essence, nothing else than condensations of the electromagnetic field, our present view of the universe presents two realities which are completely separated from each other conceptually, although connected causally, namely, gravitational ether and electromagnetic field, or — as they might also be called — space and matter. Of course it would be a great advance if we could succeed in comprehending the gravitational field and the electromagnetic field together as one unified conformation. Then, for the first time, the epoch of theoretical physics founded by Faraday and Maxwell would reach a satisfactory conclusion. The contrast between ether and matter would fade away, and, through the general theory of relativity, the whole of physics would become a complete system of thought, like geometry, kinematics, and the theory of gravitation."

"The basic concepts and laws which are not logically further reducible constitute the indispensable and not rationally deducible part of the theory. ...The conception... of the purely fictitious character of the basic principles of theory was in the eighteenth and nineteenth centuries still far from being the prevailing one. But it continues to gain more and more ground because of the ever-widening logical gap between the basic concepts and laws on the one side and the consequences to be correlated with our experiences on the other—a gap which widens progressively with the developing unification of the logical structure, that is with the reduction in the number of the logically independent conceptual elements required for the basis of the whole system."

"Although it is true that it is the goal of science to discover rules which permit the association and foretelling of facts, this is not its only aim. It also seeks to reduce the connections discovered to the smallest possible number of mutually independent conceptual elements. It is in this striving after the rational unification of the manifold that it encounters its greatest successes, even though it is precisely this attempt which causes it to run the greatest risk of falling a prey to illusions."

"We have to realize that a unified theory of the physical world simply does not exist. We have theories that work in restricted regions, we have purely formal attempts to condense them into a single formula, we have lots of unfounded claims (such as the claim that all of chemistry can be reduced to physics), phenomena that do not fit into the accepted framework are suppressed; in physics, which many scientists regard as the one really basic science, we have now at least three different points of view (relativity, dealing with the very large, quantum theory for an intermediate domain and various particle models for the very small) without a promise of conceptual (and not only formal) unification; perceptions are outside of the material universe (the mind-body problem is still unsolved) - from the very beginning the salesman of a universal truth cheated people into admissions instead of clearly arguing for their philosophy. And let us not forget that it was they and not the representatives of the traditions they attacked who introduced argument as the one and only universal arbiter. They praised argument - they constantly violated its principles."

"People are always asking for the latest developments in the unification of this theory with that theory, and they don't give us a chance to tell them anything about what we know pretty well. They always want to know the things we don't know."

"Unlike the chess game... in which the rules become more complicated as you go along, in physics, when you discover new things, it looks more simple. It appears on the whole to be more complicated because we learn about a greater experience—that is, we learn more about more particles and new things—and so the laws look more complicated again. But if you realize all the time what's kind of wonderful—that is, if we expand our experience into wilder and wilder regions of experience—every once in a while we have these integrations when everything's pulled together into a unification, in which it turns out to be simpler than it was before."

"In some ways, science today is less specialized... Consider... physics and chemistry; fifty years ago they were regarded as separate fields. ...Philosophers even gave an "intelligible" reason why physics and chemistry would always be separate... Physics had to do with quantity, chemistry with quality. Then there developed the field of , later the field of . Today it would be difficult to say what the difference is between physics and chemistry... now the laws of chemistry are derived from physics, from thermodynamics, electrodynamics, and from quantum mechanics. ...The same exists between physics and biology, or between economics and anthropology. ...Today we must understand economics as a tribal custom, and tribal customs from the economic point of view. ...The disappearance of the old unity between science and philosophy can hardly be ascribed to the increasing specialization in science."

"The decisive steps toward a clear understanding of non-Euclidean geometry were taken by Riemann, Helmholtz, and Poincaré, who recognized the essential unity of geometry and physics. However, the understanding did not come into its own until Einstein showed that such a combination of geometry and physics was really necessary for the derivation of phenomena which had actually been observed."

"Our understanding of the four basic concepts of Physics—space, time, matter and force—has undergone radical change in the course of work on unification, starting with Maxwell's unification of electricity with magnetism, all the way to present day string theory. What started as four independent concepts, with space and time postulated and the possible forms of matter and force arbitrarily chosen, now appear as different aspects of a rich and novel dynamically determined structure."

"In general the position as regards all such new calculi is this — That one cannot accomplish by them anything that could not be accomplished without them. However, the advantage is, that, provided such a calculus corresponds to the inmost nature of frequent needs, anyone who masters it thoroughly is able — without the unconscious inspiration of genius which no one can command — to solve the respective problems, yea to solve them mechanically in complicated cases in which, without such aid, even genius becomes powerless. Such is the case with the invention of general algebra, with the differential calculus, and in a more limited region with Lagrange's calculus of variations, with my calculus of congruences, and with Mobius's calculus. Such conceptions unite, as it were, into an organic whole countless problems which otherwise would remain isolated and require for their separate solution more or less application of inventive genius."

"Geoffrey also recognized that the opposite orientations of gut and nervous system posed a problem for his claim that insects and vertebrates represent different versions of the same archetypal animal - and he proposed the first account of the inversion theory to resolve this threat to unification. ...Geoffroy pursued the... aim of establishing a "unity of type" that could generate both s and vertebrates from the same basic blueprint. ...The single grand design includes a gut in the middle and the main nerve cords somewhere on the periphery."

"[A]fter a close study of the experimental work of Michael Faraday,... James Clerk Maxwell succeeded in uniting electricity and magnetism in the framework of the '. ...Beyond uniting... all... electric and magnetic phenomena in one mathematical framework, Maxwell's theory showed—quite unexpectedly, that electromagnetic disturbances travel at a fixed and never-changing speed that turns out to equal that of light. From this, Maxwell realized that visible light itself is nothing but a particular kind of electromagnetic wave... Maxwell's theory also showed that all electromagnetic waves—visible light among them—are the epitome of the peripatetic traveler. They never stop. They never slow down. Light always travels at light speed."

"The notion of a smooth spatial geometry, the central principle of general relativity, is destroyed by the violent fluctuations of the quantum world on short distance scales. ...The equations of general relativity cannot handle the rolling frenzy of the quantum foam. ...There are ...physicists ...who are deeply unsettled by the fact that the two foundational pillars of physics as we know it are at their core fundamentally incompatible, regardless of the ultramicroscopic distances that must be probed to expose the problem. This incompatibility, they argue, points to an essential flaw in our understanding of the physical universe. This opinion rests on an unprovable but profoundly felt view that the universe, if understood at its deepest and most elementary level, can be described by a logically sound theory whose parts are harmoniously united. Physicists have made numerous attempts at modifying either general relativity or quantum mechanics in some manner so as to avoid the conflict, but the attempts... have been met with failure after failure. That is, until the discovery of superstring theory."

"In a paper he sent to Einstein in 1919, Kaluza made an astounding suggestion. He proposed that the spatial fabric of the universe might possess more than the three dimensions... it provided an elegant and compelling framework for weaving together Einstein's general relativity and Maxwell's electromagnetic theory into a single, unified conceptual framework. ...implicit in Kaluza's work and subsequently made explicit and refined by... Oskar Klein in 1926... the spatial fabric of our universe may have both extended and curled-up dimensions. ... Einstein had formulated general relativity in the familiar setting of a universe with three spatial dimensions and one time dimension. The mathematical formalism... however, could be extended fairly directly to write down analogous equations for a universe with additional space dimensions. Under the "modest" assumption of one additional space dimension, Kaluza... derived the new equations. ...Kaluza found extra equations... those Maxwell had written down in the 1880s for deriving the electromagnetic force! ...Kaluza had united Einstein's theory of gravity with Maxwell's theory of light."

"Although the first principles of a science are the first in logical order, they are generally the last in order of discovery. They are arrived at by generalisations of extended experience. They mark the attainment of true scientific inductions, and manifest their correctness by the explanations they are able to afford. They enable us to discern the coherence of large classes of facts, and give us the power to forecast a line of sequences whereby we may direct them to the accomplishment of desired ends, or shape our actions to those coming events which are beyond our control. As an instrument of discovery, first principles are of very little value, and on account of the many chances of error, and of the fascination which the idea of a completed system exercises over the imagination of great minds, the search after them has been fruitful of error. The present undertaking, therefore, is to be regarded not as an attack upon the evolutionism of Lamarck, nor as an attack upon the evolutionism of Lyell or Darwin, nor yet upon the evolutionism of Spencer as regards the development of intelligence, but as an attack upon the theory which attempts to combine all these into one continuous process."

"All knowledge... is unification of the multiple."

"[I]n the nineteenth century, even the could be reduced to mechanics by the assumption that heat really consists of a complicated statistical motion of the smallest parts of matter. By combining the concepts of the mathematical theory of probability with the concepts of Newtonian mechanics Clausius, Gibbs and Boltzmann were able to show that the fundamental laws in the theory of heat could be interpreted as statistical laws following from Newton's mechanics when applied to very complicated mechanical systems."

"Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics."

"Science attempts to confront the possible with the actual. The price to be paid for this outlook, however, turned out to be high. It was... renouncing a unified world view. ...Most other systems of explanation—mythic, magic, or religious—generally encompass everything. They apply to every domain. They answer any possible question. They account for the origin, the present, and the end of the universe. Science proceeds differently. It operates by detailed experimentation... it looks for partial and provisional answers about those phenomena that can be isolated and well defined. ...the beginning of modern science can be dated from the time when such general questions as, "How was the universe created? What is matter made of? What is the essence of life?" were replaced by such limited questions as "How does a stone fall? how does water flow in a tube? How does blood circulate in vessels?" ...While asking general questions led to limited answers, asking limited questions turned out to provide more and more general answers."

"In the history of sciences, important advances often come from... the recognition that two hitherto separate observations can be viewed from a new angle and seen to represent nothing but different facets of one phenomenon. Thus, terrestrial and celestial mechanisms became a single science with Newton's laws. Thermodynamics and mechanics were unified through statistical mechanics, as were optics and electromagnetism through Maxwell's theory of magnetic field, or chemistry and atomic physics through quantum mechanics. Similarly different combinations of the same atoms, obeying the same laws, were shown by biochemists to compose both the inanimate and animate worlds. ... Despite such generalizations, however, large gaps remain... Following the line from physics to sociology, one goes from simpler to the more complex objects... from the poorer to the richer empirical content, as well as from the harder to the softer system of hypotheses and experimentation. ...Because of the hierarchy of objects, the problem is always to explain the more complex in terms and concepts applying to the simpler. This is the old problem of reduction, emergence, whole and parts... an understanding of the simple is necessary to understand the more complex, but whether it is sufficient is questionable. ...the appearance of life and later of thought and language—led to phenomena that previously did not exist... To describe and to interpret these phenomena new concepts, meaningless at the previous level, are required. ...At the limit total reductionism results in absurdity. ...explaining democracy in terms of the structure and properties of elementary particles... is clearly nonsense."

"But even the distant reader must allow that Clifford's mental personality belonged to the highest possible type to say no more. The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal. And if in these modern days we are to look for any prophet or saviour who shall influence our feelings towards the universe as the founders and renewers of past religions have influenced the minds of our fathers, that prophet, if he ever come, must, like Clifford, be no mere sentimental worshipper of science, but an expert in her ways. And he must have what Clifford had in so extraordinary a degree—that lavishly generous confidence in the worthiness of average human nature to be told all truth, the lack of which in Goethe made him an inspiration to the few but a cold riddle to the many."

"Reduced to their most pregnant difference, empiricism means the habit of explaining wholes by parts, and rationalism means the habit of explaining parts by wholes. Rationalism thus preserves affinities with monism, since wholeness goes with union, while empiricism inclines to pluralistic views. No philosophy can ever be anything but a summary sketch, a picture of the world in abridgment, a foreshortened bird's-eye view of the perspective of events."

"Giacomo Rizzolatti... calls these "mirror neurons" and suggests that they provide the first insight into imitation, identification, empathy, and possibly the ability to mime vocalization—the mental processes intrinsic to human interaction. Vilayanur Ramachandran has found evidence of comparable neurons in the premotor cortex of people. ...one can see a whole new area of biology opening up... that can give us a sense of what makes us social, communicating beings. An ambitious undertaking of this sort might... teach us something about the factors that give rise to tribalism, which is so often associated with fear, hatred, and intolerance of outsiders."

"The remarkable insight that characterized Klimpt's later work was contemporaneous with Freud's psychological studies and presaged the inward turn that would pervade all fields of inquiry in Vienna in 1900. This period... was characterized by the attempt to make a sharp break with the past and to explore new forms of expression in art, architecture, psychology, literature, and music. It spawned an ongoing pursuit to link these disciplines. ...Viennese life at the turn of the century provided opportunities in salons and coffeehouses for scientists, writers, and artists to come together in an atmosphere that was at once inspiring, optimistic, and politically engaged. ...science was no longer the narrow and restrictive province of scientists but had become an integral part of Viennese culture. ...a paradigm for how an open dialogue can be achieved."

"Galileo and Newton swept away the last traces of mysticism and superstition that had always been associated with the heavens. The heliocentric theory of Copernicus and Kepler had classed the earth among the other planets, so that there was good reason to believe that the heavens were made of the stuff of earth rather than, as Greek and medieval philosophers had maintained, of some light, perfect, indestructible substance. But the heliocentric theory... was regarded by many as a mathematical contrivance... not physically true. Moreover... the heliocentric theory created difficulties in accounting for the phenomena of motion readily observed here on earth, and hence encountered legitimate objections. The work of Galileo and Newton resolved these difficulties... and incorporated the theory of the heavenly motions in the very same physical theory that treated motions on earth. There could be no doubt now... that the substance of the other planets could be identified with the rock and clay beneath man's feet, for this affirmation is the very essence of the law of gravitation. The identification... wiped out libraries of speculation and dogma..."

"The mathematician and versatile scientist Pierre L. M. de Maupertuis, a keen student if Newton's work on gravitation, made the next decisive step. Like Euler, Maupertuis studied under John Bernoulli. ...After having worked in the theory of light and gravitation, he announced, in 1744, a new minimum principle, the Principle of Least Action, from which he claimed he could deduce the behavior of light and masses in motion. The principle asserts that nature always behaves so as to minimize an integral known technically as action, and amounting to the integral of the product of mass, velocity, and distance traversed by a moving object. From this principle he deduced the Newtonian laws of motion. With sometimes suitable and sometimes questionable interpretation of the quantities involved, Maupertuis managed to show that optical phenomena, too, could be deduced from this principle. Hence, to an extent at least, he succeeded in uniting the optics of the eighteenth century and mechanical phenomena."

"To the scientists of 1850, Hamilton's principle was the realization of a dream. ...from the time of Galileo scientists had been striving to deduce as many phenomena of nature as possible from a few fundamental physical principles. ...they made striking progress ...But even before these successes were achieved Descartes had already expressed the hope and expectation that all the laws of science would be derivable from a single basic law of the universe. This hope became a driving force in the late eighteenth century after Maupertuis's and Euler's work showed that optics and mechanics could very likely be unified under one principle. Hamilton's achievement in encompassing the most developed and largest branches of physical science, mechanics, optics, electricity, and magnetism under one principle was therefore regarded as the pinnacle of mathematical physics."

"The decisive step leading to the construction of precise and verifiable scientific theories in place of vague and largely speculative accounts was the involvement of mathematics. This step was made by the Pythagoreans. ...In their philosophy of nature the Pythagoreans began with the principle that number is the essence of all substance. ...forms reduced to numbers. Since number is the essence of any object, the explanation of natural phenomena could be achieved only through number. ...Whether by a lucky stroke or by intuitive genius the Pythagoreans did hit upon two doctrines which later proved to be all important. The first is that nature is built in accordance with mathematical principles, and the second that number relationships reveal the order in nature. They underlie and unify the seeming diversity exhibited by nature."

"To define distance in their non-Euclidean geometries, Cayley and Klein proceeded by analogy with a discovery of Laguerre... who had shown that the distances and angles of ordinary Euclidean geometry can be expressed as cross ratios, in other words, that the Euclidean metric geometry is clearly a specialization of projective geometry. The concept of the "absolute" and the definition of distance unified Euclidean and non-Euclidean geometries into a single all-embracing theory."

"Klein showed that the Reimannian species of non-Euclidean geometry can be developed in a fashion completely analogous to the Lobachevskian type by choosing an "imaginary" absolute, that is, an "imaginary" point pair or conic, and an imaginary value of the constant k. Euclidean geometry can also be treated in the same way by choosing a "degenerate" point pair or conic."

"As long as algebra and geometry travelled separate paths their advance was slow and their applications limited. But when these two sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace towards perfection. It is to Descartes that we owe the application of algebra to geometry,—an application which has furnished the key to the greatest discoveries in all branches of mathematics."

"Group theory is the mathematical language of symmetry, and it... seems to play a fundamental role in the very structure of nature. ...In the midst of the fomenting of the new twentieth century physics was the... life of the greatest female mathematician who ever lived, Emmy Noether. ...At Göttingen, Noether achieved fame for her research into the fundamental structure of mathematics. However, she stepped briefly into the realm of theoretical physics... is a profound statement, perhaps running as deeply into the fabric of our psyche as the famous theorem of Pythagoras. Noether's theorem directly connects symmetry to physics, and vice versa. It frames our modern concepts about nature and rules modern scientific methodology. ...For scientists it is the guiding light to unraveling nature's mysteries, as they delve into the innermost fabric of matter ...To this task scientists apply ...the great s ...Emmy Noether's work interweaves our understanding of nature—through physics and mathematics—with the beauty and harmony that surrounds us... Noether's theorem provides a natural centerpiece for any discussion that unifies physics and mathematics, such as in the teaching of these... in a way that enlivens them both."

"I feel that controversies can never be finished, nor silence imposed upon the Sects, unless we give up complicated reasonings in favour of simple calculations, words of vague and uncertain meaning in favour of fixed symbols [characteres]. Thus it will appear that 'every paralogism is nothing but an error of calculation. When controversies arise, there will be no more necessity for disputation between two philosophers than between two accountants. Nothing will be needed but that they should take pen in hand, sit down with their counting-tables and (having summoned a friend, if they like) say to one another: Let us calculate.'"

"Theoretical physicists today have some ideas on how to combine the strong and electroweak forces, and hope eventually to include gravity in a single unified theory of all forces. The very meaning of "unification" in this context is that one harmonizing theoretical structure, mathematical in form, should be made to accommodate formerly distinct theories under one roof. Unification is the theme, the backbone of modern physics, and for most physicists what unification means in practice is the uncovering of tidier, more comprehensive mathematical structures linking separate phenomena."

"During the 1970s Sheldon Glashow, Abdus Salam, and Steven Weinberg... came up with a theory in which there have to be three separate particles carrying the weak force... the three weak carriers are recognized as heavy photons and the weak force is seen as a modified form of electromagnetism. The obvious differences between... interactions are ascribed to the fact that the photon has no mass and the weak carriers have a lot. ... The role of the electroweak theory in the effort to streamline fundamental physics is in some respects debatable. More [three] particles are needed and the mathematical structure... is not entirely beyond reproach. But it ties two separate forces into a single theoretical device... In 1983, physicists... found the W and Z particles. The electroweak theory was thereupon deemed correct, and the number of distinct forces in the world was officially reduced to three—electroweak, strong, and gravitational. Electroweak unification has organized another corner of theoretical physics, as did the quark model before it."

"Functions are the bread and butter of modern scientists, statisticians, and economists. Once many repeated... experiments and observations produce the same functional interrelationships, those may acquire the... status of laws of nature—mathematical descriptions... Descartes' ideas... opened the door for a systematic mathematization of everything—the very essence of the notion that God is a mathematician. ...[B]y establishing the equivalence of two perspectives of mathematics (algebraic and geometric) previously considered disjoint, Descartes expanded the horizons of mathematics and paved the way to the modern era of analysis, which allows [us] to comfortably cross from one mathematical discipline to another."

"While Descartes' theory of vortices was spectacularly wrong (as Newton ruthlessly pointed out later), it was still interesting, being the first serious attempt to formulate a theory of the universe as a whole based upon the same laws that apply on the Earth's surface. In other words, to Descartes there was no difference between terrestrial and celestial phenomena—the Earth was part of a universe that obeyed uniform physical laws."

"In the late 1960s... Steven Weinberg, Sheldon Glashow, and Abdus Salam developed a theory that treats the electromagnetic force and the weak nuclear force in a unified manner. ...the electroweak theory, predicted the existence of three particles (...W+, W-, and Z bosons) that had never before been observed. The particles were unambiguously detected in 1983 in accelerator experiments... led by... Carlo Rubbia and Simon van der Meer."

"The more sluggish positive charges are at first of less interest,—but the behaviour of electrons cannot be fully and properly understood without a knowledge of the nature and properties of the positive constituent too. According to Larmor, positive charge must be the mirror-image of negative charge, in essential constitution. The positive electron has not, as far as I know, been as yet observed free. Some think it cannot exist in a free state, that it is in fact the rest of the atom of matter from which a negative unit charge has been removed; or, to put it crudely, that "electricity" repels "electricity," and "matter" repels "matter," but that Electricity and Matter in combination form a neutral substance which is the atom of matter as we know it. Such a statement is an extraordinary and striking return to the views expressed by that great genius, Benjamin Franklin."

"My purpose is merely to illustrate the issue involved in our question about the unification of science. A complete unification... would be a unification downward, finding its ultimate and universal laws in mechanics; and it would include in its scope all the movements of human bodies. Those who assert the possibility of a rigorously complete unification thus imply a denial of all physical efficacy to thoughts and feelings as such. Those, on the contrary, who assert such efficacy deny by implication the possibility of a complete unification of even the laws of the motion of matter. They tacitly or explicitly introduce a real discontinuity into the fabric of science."

"The significance of the contention that the laws of the several sciences are discontinuous appears chiefly when you thus regard the sciences as corresponding to stages in the process of evolution. ...that means that at certain points in the evolutionary sequence matter begins to behave in essentially new ways, develops novel properties and methods of action which were in no true sense contained in or implied by its earlier characteristics and performances. If, on the other hand, all the laws of biology and chemistry are ultimately reducible to, and deducible from, the laws of some fundamental branch of physics, that means that, in a very thorough-going sense, the first morning of creation wrote what the last dawn of reckoning shall read."

"Heraclitus. ...change and incessant movement is the basis, and the only basis, of all things and that what is illusory is the idea of a central, or indeed of any other, unity: the Universe is a stream of incessant and infinitely minute changes. The Atomists. From this springs naturally the atomistic theory of Leucippus and Democritus. This theory is an endeavour to give a sort of solidity and reality to the mutability of Heraclitus, whilst retaining his controversial advantages in the denial of an all-embracing One. The veritable original of things is taken by these Atomists to be, not one, but innumerable, indefinitely minute, homogeneous atoms, the mere mechanical combination of which makes up the variety of nature."

"Nature does not begin with elements, as we are obliged to begin with them. It is certainly fortunate... that we can... turn aside our eyes from the over powering unity of the All, and allow them to rest on individual details. But we should not omit, ultimately, to complete and correct our views by a thorough consideration of the things which for the time being we left out of account."

"Velocity of transverse undulations in our hypothetical medium, calculated from the electromagnetic experiments of 'MM'. Kohlrausch and Weber, agrees so exactly with the velocity of light calculated from the optical experiments of M. Fizeau, that we can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena."

"The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws."

"The object of the book is philosophical, in the sense now accepted by many and by divergent schools—i.e., it desires to contribute something towards a unification of thought."

"In both Newton's theory and Maxwell's theory the unification consists, partly, in showing that two different processes or phenomena can be identified, in some way, with each other—that they belong to the same class or are the same kind of thing. Celestial and terrestrial objects are both subject to the same gravitational-force law, and optical and electromagnetic processes are one and the same. Because each of these theories unifies such a diverse range of phenomena, they have traditionally been thought to possess a great deal of explanatory power."

"In whatever they focus on, physicists seek the simplicity in complexity and the unity in diversity. Like philosophers, their intellectual siblings, they are driven by the conviction that the universe is within the human power to understand and that if you look beneath its variety and intricacy, you will find comprehensible rules."

"Since the ancients made great account of the science of Mechanics in the investigation of natural things; and the moderns, laying aside substantial forms and occult qualities, have endeavoured to subject the phænomena of nature to the laws of mathematics; I have in this treatise cultivated Mathematics... The ancients considered Mechanics in a twofold respect; as rational, which proceeds accurately by demonstration, and practical. To practical Mechanics all the manual arts belong, from which Mechanics took its name. But as artificers do not work with perfect accuracy, it comes to pass that Mechanics is so distinguished from Geometry, that what is perfectly accurate is called Geometrical, what is less so is called Mechanical. But the errors are not in the art, but in the artificers. ...the description of right lines and circles, upon which Geometry is founded, belongs to Mechanics. ...To describe right lines and circles are problems, but not geometrical problems. The solution of these problems is required from Mechanics; and by Geometry the use of them, when so solved, is shewn. And it is the glory of Geometry that from those few principles, fetched from without, it is able to produce so many things. Therefore Geometry is founded in mechanical practice, and is nothing but that part of universal Mechanics which accurately proposes and demonstrates the art of measuring. But since the manual arts are chiefly conversant in the moving of bodies, it comes to pass that Geometry is commonly referred to their magnitudes, and Mechanics to their motion. In this sense Rational Mechanics will be the science of motions resulting from any forces whatsoever and of the forces required to produce any motions, accurately proposed and demonstrated. ...we consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces whether attractive or impulsive. And therefore we offer this work as mathematical principles of philosophy. For all the difficulty of philosophy seems to consist in this, from the phenomena of motions to investigate the forces of Nature, and then from these forces to demonstrate the other phenomena."

"The most immediate result of this unbalanced specialisation has been that to-day, when there are more "scientists" than ever, there are much less "cultured" men than, for example, about 1750. And the worst is that with these turnspits of science not even the real progress of science itself is assured. For science needs from time to time, as a necessary regulator of its own advance, a labour of reconstitution, and, as I have said, this demands an effort towards unification, which grows more and more difficult, involving, as it does, ever-vaster regions of the world of knowledge. Newton was able to found his system of physics without knowing much philosophy, but Einstein needed to saturate himself with Kant and Mach before he could reach his own keen synthesis."

"In early physical systems we have optics dealing with phenomena perceived by the eye; acoustics treating of auditory percepts, and so on. The subjective concepts of "tone" and "colour" have now been replaced by the objectified concepts of frequency of vibration; and wave-length. The object of this process of elimination is, according to Planck, the striving towards a unification of the whole theoretical system, so that it shall be equally significant for all intelligent beings."

"The unification of knowledge is the natural consequence of the intellectual and moral development of the race."

"The Pythagoreans were the first who attempted a complete classification of the facts of the universe. Their effort, though feeble, was in the right direction; for the first principle of perception is analysis, or classification; and knowledge can never be unified until an ultimate or complete analysis has been performed."

"All the early thinkers sought with wonderful perseverance the knowledge of the First Cause. The of Aristotle, though they had been separately recognized, had not all been proclaimed necessary. Aristotle... gave his chief attention to the solution of the problem of First Causes. He maintained that there were four, as follows: First, the Material Cause, or Essence; second, the Substantial [or Formal] Cause; third, the Efficient Cause, or the principle of motion; fourth, the Final Cause, or the Purpose and End."

"It is the opinion of all competent authorities that the fundamental principles of Kant's philosophy declare against the possibility of a unification of knowledge."

"Ever since Hermann Minkowski's now infamous comments in 1908 concerning the proper way to view space-time, the debate has raged as to whether or not the universe should be viewed as a four-dimensional, unified whole wherein the past, present, and future are regarded as equally real or whether the views espoused by the possibilists, historicists, and presentests regarding the unreality of the future (and, for presentests, the past) are more accurate. Now, a century after Minkowski's proposed block universe first sparked debate, we present a new, more conclusive argument in favor of eternalism."

"A third stage appears between 7 and 8, which we shall call the stage of incipient cooperation. Each player now tries to win, and all, therefore, begin to concern themselves with the question of mutual control and of unification of the rules. But while a certain agreement may be reached in the course of one game, ideas about the rules in general are still rather vague. In other words, children of 7-8, who belong to the same class at school and are therefore constantly playing with each other, give, when they are questioned separately, disparate and often entirely contradictory accounts of the rules observed in playing marbles."

"Now what is science? ...it is before all a classification, a manner of bringing together facts which appearances separate, though they are bound together by some natural and hidden kinship."

"Maxwell got a huge bonus for understanding the unification of electricity and magnetism. He understood the nature of light! When I first heard about this in high school I thought this was the coolest thing, and I still do. It's what we're all trying to do."

"Mathematics and logic, historically speaking, have been entirely distinct studies. Mathematics has been connected with science, logic with Greek. But both have developed in modern times: logic has become more mathematical and mathematics has become more logical. The consequence is that it has now become wholly impossible to draw a line between the two; in fact, the two are one. They differ as boy and man: logic is the youth of mathematics and mathematics is the manhood of logic. This view is resented by logicians who, having spent their time in the study of classical texts, are incapable of following a piece of symbolic reasoning, and by mathematicians who have learnt a technique without troubling to inquire into its meaning or justification. Both types are now fortunately growing rarer. So much of modern mathematical work is obviously on the border-line of logic, so much of modern logic is symbolic and formal, that the very close relationship of logic and mathematics has become obvious to every instructed student. The proof of their identity is, of course, a matter of detail: starting with premises which would be universally admitted to belong to logic, and arriving by deduction at results which as obviously belong to mathematics, we find that there is no point at which a sharp line can be drawn, with logic to the left and mathematics to the right. If there are still those who do not admit the identity of logic and mathematics, we may challenge them to indicate at what point, in the successive definitions and deductions of Principia Mathematica, they consider that logic ends and mathematics begins. It will then be obvious that any answer must be quite arbitrary."

"Science itself is badly in need of integration and unification. The tendency is more and more the other way … Only the graduate student, poor beast of burden that he is, can be expected to know a little of each. As the number of physicists increases, each specialty becomes more self-sustaining and self-contained. Such Balkanization carries physics, and indeed, every science further away, from natural philosophy, which, intellectually, is the meaning and goal of science."

"There is obviously only one alternative, namely the unification of minds or consciousnesses. Their multiplicity is only apparent, in truth there is only one mind."

"In Newton's system of mechanics... there is an absolute space and an absolute time. In Einstein's theory time and space are interwoven, and the way in which they are interwoven depends on the observer. Instead of three plus one we have four dimensions."

"Einstein’s dissent from quantum mechanics and immersion in the search for a unified field theory were not failures but anticipations. After all, even if many string theorists would disagree with Einstein about the incompleteness of quantum mechanics, much of what goes on in string theory these days looks a lot like what Einstein was doing in his Princeton years, which was trying to find new mathematics that might extend general relativity to a unification of all the forces and particles in nature."

"In both quantum theory and general relativity, we encounter predictions of physically sensible quantities becoming infinite. This is likely the way that nature punishes impudent theorists who dare to break her unity. ...If infinities are signs of missing unification, a unified theory will have none. It will be what we call a finite theory."

"A scientific hypothesis may be defined in general terms as a provisional or tentative explanation of physical phenomena. But what is an explanation in the true scientific sense? The answers to this question which are given by logicians and men of science, though differing in their phraseology, are essentially of the same import. Phenomena are explained by an exhibition of their partial or total identity with other phenomena. Science is knowledge; and all knowledge, in the language of Sir William Hamilton is a "unification of the multiple." "The basis of all scientific explanation," says Bain, "consists in assimilating a fact to some other fact or facts. It is identical with the generalizing process." And "generalization is only the apprehension of the One in the Many." Similarly Jevons: "Science arises from the discovery of identity amid diversity," and "every great advance in science consists in a great generalization pointing out deep and subtle resemblances." ...the author just quoted in another place: "Every act of explanation consists in detecting and pointing out a resemblance between facts, or in showing that a greater or less degree of identity exists between apparently diverse phenomena." All this may be expressed in familiar language thus: When a new phenomenon presents itself to the man of science or to the ordinary observer, the question arises in the mind of either: What is it?—and this question simply means: Of what known, familiar fact is this apparently strange, hitherto unknown fact a new presentation—of what known, familiar fact or facts is it a disguise or complication? Or, inasmuch as the partial or total identity of several phenomena is the basis of classification (a class being a number of objects having one or more properties in common), it may also be said that all explanation, including explanation by hypothesis, is in its nature classification. Such being the essential nature of a scientific explanation of which an hypothesis is a probatory form, it follows that no hypothesis can be valid which does not identify the whole or a part of the phenomenon, for the explanation of which it is advanced, with some other phenomenon or phenomena previously observed. This first and fundamental canon of all hypothetical reasoning in science is formally resolvable into two propositions, the first of which is that every valid hypothesis must be an identification of two terms—the fact to be explained and a fact by which it is explained; and the second that the latter fact must be known to experience."

"The theories that we describe here provide the basis of progress toward a unification of macroeconomics and microeconomics."

"Lagrange's "" is perhaps his most valuable work and still amply repays careful study. ...the full power of the newly developed analysis was applied to the mechanics of points and rigid bodies. The results of Euler, of D'Alembert, and of the other mathematicians of the Eighteenth Century were assimilated and further developed from a consistent point of view. Full use of Lagrange's own made the unification of the varied principles of statistics and dynamics possible..."

"In the year 1749 he first suggested his idea of explaining the phenomena of thunder-gusts and of the aurora borealis, upon electrical principles. He points out many particulars in which lightning and electricity agree; and he adduces many facts, and reasonings from facts, in support of his positions. In the same year he conceived the astonishingly bold and grand idea of ascertaining the truth of his doctrine, by actually drawing down the lightning, by means of sharp pointed iron rods raised into the region of the clouds. Even in this uncertain state, his passion to be useful to mankind displays itself in a powerful manner. Admitting the identity of electricity and lightning, and knowing the power of points in repelling bodies charged with electricity, and in conducting their fire silently and imperceptibly, he suggested the idea of securing houses, ships, &c. from being damaged by lightning, by erecting pointed rods, that should rise some feet above the most elevated part, and descend some feet into the ground or the water."

"We only call an elephant or a bacterium an 'organism' because, by analogy we attribute to those beings a similar unification of sensation and of consciousness to that we are conscious of in ourselves; but in human societies and in humanity this essential indication is lacking, and therefore, however many other indications we may detect that are common to humanity and to an organism, in the absence of that essential indication, the acknowledgement of humanity as an organism is incorrect."

"Plato wove together separate threads from three earlier philosophers: the mathematics of Pythagoras, the atomism of Demokritos, and the four elements of Empedokles. As happens with the best scientific syntheses, the resulting theory transformed the components from which it started, and was intellectually more powerful than any of them. For these geometrical atoms differed from those of Demokritos in having a limited number of definite shapes, governed by precise mathematical theorems; and furthermore, they were no longer immutable, but could change into one another in ways that could be related back to their geometrical compositions. As a result, Plato could envisage transmutations of a kind that Demokritos did not allow for, and so introduced a new, quantitative element into the analysis of material change. ...For the regular solids can all be built up from two simple triangles... the fundamental elements of his theory."

"In matter-theory, as in astronomy, the Church's commitment to Aristotle was in due course to prove an embarassment. In both branches of science his speculative distinction between terrestrial and celestial matter was insecure from the very beginning. His own most loyal commentator, ... had already dreamt of a theory unifying all things, and John Philoponos... had rejected the distinction between terrestrial and celestial matter outright. Nevertheless, it was still an axiom of almost a thousand years later."

"Descartes' importance for science does not lie in the details of his cosmology. His decipherment of Nature might be crude, yet he had the courage to insist that mechanical sense could be made of the workings of Nature, throughout the realms of physics, chemistry, and even physiology. By reasserting the unity and rationality of Nature, he did as much as any man to put seventeenth-century scientists back on the intellectual road first trodden by the Greeks."

"From Pappus it appears, however, that the early Mathematicians had at first some reluctance in admitting either the Conic Sections or superior curves in the solution of problems, considering them as not strictly geometrical; but afterwards these lines became objects of much curious investigation, even among the ancients; and in modern times ultimately were of the most extensive utility, both in abstract and in physical science."

"More than a hundred years have elapsed since Benjamin Franklin, employing a phraseology now superseded, put forth a theory of matter. It was pronounced "a delusion" by the physicists of the nineteenth century, but the scientists of the twentieth century, according to Sir Oliver Lodge, may be forced to rehabilitate it as the only means of issue from the labyrinth in which all physical study is now involved. ...the Franklin theory is that electricity and matter in combination form a neutral substance, which is the atom of matter as we know it. The most interesting part of the problem for ourselves, says Sir Oliver, is the explanation of matter in terms of electricity, the view that electricity is, as Franklin seems to have supposed, the fundamental "substance." What we men of to-day have been accustomed to regard as an indivisible atom of matter is thus built up out of electricity. All atoms—atoms of all sorts of "substances"—are built up of the same thing. In our day... the theoretical and proximate achievement of what philosophers from Franklin's day to ours have always sought—a unification of matter—is offering itself to physical inquiry."

"To see what is general in what is particular and what is permanent in what is transitory is the aim of scientific thought. ...[W]e ...endeavour to imagine the world as one connected set of things which underlies all the perceptions of all people."

"We can describe general relativity using either of two mathematically equivalent ideas: curved space-time or metric field. Mathematicians, mystics and specialists in general relativity tend to like the geometric view because of its elegance. Physicists trained in the more empirical tradition of high-energy physics and quantum field theory tend to prefer the field view, because it corresponds better to how we (or our computers) do concrete calculations. ...the field view makes Einstein's theory of gravity look more like the other successful theories of fundamental physics, and so makes it easier to work toward a fully integrated, unified description of all the laws. ...I'm a field man."

"I feel that we are so close with string theory that—in my moments of greatest optimism—I imagine that any day, the final form of the theory may drop out of the sky and land in someone's lap. But more realistically, I feel that we are now in the process of constructing a much deeper theory than anything we have had before and that well into the twenty-first century, when I am too old to have any useful thoughts on the subject, younger physicists will have to decide whether we have in fact found the final theory."

"Ether theories after the middle of the nineteenth century tended to posit that matter was not, in fact, material at all. ...matter was no longer understood as Lucretius had formulated it: as made up of strong and rigid atoms moving through empty space. Instead, physicists now believed that space was filled with the luminiferous ether, and matter, physicists hypothesized, was simply movement within the ether. Matter was thus etherealized."

"The spooky ether was persistent. It took an Einstein to remove it from the Universe. ...Gradually, over the last twenty years, the vacuum has turned out to be more unusual, more fluid, less empty, and less intangible than even Einstein could have imagined. Its presence is felt on the very smallest and largest dimensions over which the forces of Nature act."

"The physicist's concept of nothing—the vacuum... began as empty space—the void... turned into a stagnant ether through which all the motions of the Universe swam, vanished in Einstein's hands, then re-emerged in the twentieth-century quantum picture of how Nature works."

"The difficult surface conditions met with when light passes from one medium to another, including such subjects as ellipticity, total reflection, etc., have been critically discussed among others by Neumann (1835) and Rayleigh (1888) but the discrimination between the Fresnel and the Neumann vector was not accomplished without misgiving before the advent of the work of Hertz. It appears... that the elastic theories of light, if Kelvin's gyrostatic adynamic ether be admitted, have not been wholly routed. Nevertheless the great electromagnetic theory of light propounded by Maxwell (1864, 'Treatise,' 1873) has been singularly apt not only in explaining all the phenomena reached by the older theories and in predicting entirely novel results, but in harmoniously uniting as parts of a unique doctrine, both the electric or photographic light vector of Fresnel and Cauchy and the magnetic vector of Neumann and MacCullagh. Its predictions have, moreover, been astonishingly verified by the work of Hertz (1890), and it is to-day acquiring added power in the convection theories of Lorentz (1895) and others."

"I hold in fact (1) That small portions of space are in fact of a nature analogous to little hills on a surface which is on the average flat; namely, that the ordinary laws of geometry are not valid in them. (2) That this property of being curved or distorted is continually being passed on from one portion of space to another after the manner of a wave. (3) That this variation of the curvature of space is what really happens in that phenomenon which we call the motion of matter, whether ponderable or etherial. (4) That in the physical world nothing else takes place but this variation, subject possibly to the law of continuity."

"Einstein's definition... does not differ in spirit from the definitions in classical science; its sole advantage is that it entails a minimum of assumptions, and is susceptible of being realised in a concrete way permitting a high degree of accuracy in our measurements. Einstein's definition, is then, as follows: If we consider a ray of light passing through a Galilean frame, its velocity in the frame will be the same regardless of the relative motion of the luminous source and frame, and regardless of the direction of the ray. ...when it was found that contrary to the anticipations of classical science not the slightest trace of anisotropy could be detected even by ultra-precise experiment, the objections which classical science may might have presented... lost all force. ...ether drift appeared to exert no influence one way or the other. ... Isotropy signifies that the velocity of light is the same in all directions. And how can we ascertain the equality of a velocity in all directions when we do not yet know how to measure time? Experimenters solved the difficulty by appealing to the observation of coincidences. ... Waves of light leaving the centre of a sphere simultaneously are found to return to the centre also in concidence, after having suffered a reflection against a highly polished inner surface of the sphere. ...the light waves have thus covered equal distances in the same time; whence we conclude that their speed is the same in all directions. Inasmuch as this experiment has been performed, yielding the results we have just described, even though the ether drift caused by the earth's motion should have varied in direction and intensity, the isotropy of space to luminous propogations was thus established. (The experiment described constitutes but a schematic form of Michelson's.) It is to be noted that in this experiment the observation of coincidences is alone appealed to (even spatial measurements can be eliminated). This is because in Michelson's experiment it is not necessary to consider a sphere. The two arms of the apparatus may be of different lengths; and all that is observed is the continued coincidence of the interference-bands with markings on the instrument. When it is realised that coincidences constitute the most exact form of observation, we understand why it is that Einstein's definition is justified."

"These last two equations connote that varying electric and magnetic intensities will be propagated through the ether in wave form with a velocity c... This discovery removed all possibility of action at a distance, since the field perturbations now appeared to be propagated from place to place with a finite velocity. It was... of interest to determine the precise value of c. ...Physicists ...were unable, in Maxwell's day, to devise a means of performing such delicate experiments. ...Maxwell remarked that it would be given by the ratio of the magnitude of any electric charge, measured in terms of electrostatic units (based on electricity), and then of electromagnetic units (based on magnetism). If two magnetic poles of equal strength, situated in empty space... one centimetre apart, attract or repel each other with a force of one dyne, either pole is said to represent one unit of magnetic pole strength in the electromagnetic system of units. Owing to the interconnections between magnetism and electricity, we can deduce therefrom the unit of electric charge also in the electromagnetic system. Likewise, if two electric charges of equal strength... in empty space at a distance of one centimetre apart, attract or repel each other with a force of one dyne, either charge is said to represent one unit of electric charge in the electrostatic system of units. From this we can derive the unit of magnetic pole strength in the electrostatic system. Precise measurements... then proved that the value of this ratio was about 186,000 miles per second; whence it became necessary to assume that periodic perturbations in the strains and stresses of the field would be propagated in the form of waves moving through the ether with this particular speed. But this velocity was precisely that of light waves propagated through the luminiferous ether."

"The most precise experiments have proved the correctness of the Einsteinian laws of mechanics and...Bucherer's experiment proving the increase in mass of an electron in rapid motion is a case in point. Very important differences distinguish the theory of Einstein from that of Lorentz. Lorentz also had deduced from his theory that the mass of the electron should increase and grow infinite when its speed neared that of light; but the speed in question was the speed of the electron through the stagnant ether; whereas in Einstein's theory it is merely the speed with respect to the observer. According to Lorentz, the increase in mass of the moving electron was due to its deformation of Fitzgerald contraction. The contraction modified the lay of the electromagnetic field round the electron; and it was from this modification that the increase in mass observed by Bucherer was assumed to arise. In Einstein's theory, however, the increase in mass is absolutely general and need not be ascribed to the electromagnetic field of the electron in motion. An ordinary unelectrified lump of matter like a grain of sand would have increased in mass in exactly the same proportion; and no knowledge of the microscopic constitution of matter is necessary in order to predict these effects, which result directly from the space and time transformations themselves. Furthermore, the fact that this increase in mass of matter in motion is now due to relative motion and not to motion through the stagnant ether, as in Lorentz's theory, changes the entire outlook considerably. According to Lorentz, the electron really increased in mass, since its motion through the ether remained a reality. According to Einstein, the electron increases in mass only in so far as it is in relative motion with respect to the observer. Were the observer to be attached to the flying electron no increase in mass would exist; it would be the electron left behind which would now appear to have suffered the increase. Thus mass follows distance, duration and electromagnetic field in being a relative and having no definite magnitude of itself and being essentially dependent on the conditions of observation. Owing to the general validity of the Lorentz-Einstein transformations, it becomes permissible to apply them to all manner of phenomena.. ...temperature, pressure and many other physical magnitudes turned out to be relatives. ...entropy, electric charge and the velocity of light in vacuo were absolutes transcending the observer's motion. ...a number of other entities are found to be absolutes, the most important of which is that abstract mathematical quantity called the Einsteinian interval, which plays so important a part in the fabric of the new objective world of science, the world of four-dimensional space-time."

"We may assume the existence of an aether; only we must give up ascribing a definite state of motion to it, i.e. we must by abstraction take from it the last mechanical characteristic which Lorentz had still left it. … But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it."

"Can we represent the electric field by something more like a temperature, say like the displacement of a piece of jello? Suppose that we were to begin by imagining that the world was filled with thin jello and that the fields represented some distortion—say a stretching or twisting—of the jello. Then we could visualize the field. After we “see” what it is like we could abstract the jello away. For many years that’s what people tried to do. Maxwell, Ampère, Faraday, and others tried to understand electromagnetism this way. (Sometimes they called the abstract jello “ether.”) But it turned out that the attempt to imagine the electromagnetic field in that way was really standing in the way of progress. We are unfortunately limited to abstractions, to using instruments to detect the field, to using mathematical symbols to describe the field, etc. But nevertheless, in some sense the fields are real, because after we are all finished fiddling around with mathematical equations—with or without making pictures and drawings or trying to visualize the thing—we can still make the instruments detect the signals from Mariner II and find out about galaxies a billion miles away, and so on."

"The strangest explanation [for the Michelson–Morley experiment] was put forth by an Irish physicist, George Francis Fitzgerald. Perhaps, he said, the ether wind puts pressure on a moving object, causing it to shrink a bit in the direction of motion. To determine the length of a moving object, its length at rest must be multiplied by the following simple formula, in which \scriptstyle v^2 is the velocity of the object multiplied by itself, \scriptstyle c^2 is the velocity of light multiplied by itself: \scriptstyle \sqrt{1-\frac{v^2}{c^2}}."

"Lorentz made an important addition to his original theory. He introduced changes in time. Clocks, he said, would be slowed down by the ether wind, and in just such a way as to make the velocity of light always measure 299,800 meters per second."

"Einstein, following the steps of Ernst Mach, took a bolder view. The reason Michelson and Morley were unable to detect an ether wind, Einstein said, is simple: There is no either wind. He did not say that there was no ether; only... [that the ether] is of no value in measuring uniform motion."

"The ether occupies a highly anomalous position in the world of science. It may be described as a half-discovered entity. ...it would be a great exaggeration of our knowledge if l were to speak of it as a body or even as a substance. When nearly a century ago, Young and Fresnel discovered that the motions of an incandescent particle were conveyed to our eyes by undulation, it followed that between our eyes and the particle there must be something to undulate. In order to furnish that something, the notion of the ether was conceived, and for more than two generations the main, if not the only, function of the word ether has been to furnish a nominative case to the verb "to undulate." Lately, our conception of this entity has received a notable extension. One of the most brilliant of the services which Professor Maxwell has rendered to science has been the discovery that the figure which expressed the velocity light, also expressed the multiplier required to change the measure of static or passive electricity into that dynamic or active electricity. The interpretation reasonably affixed to this discovery is that, as light and the electric impulse move approximately at the same rate through space, it is probable that the undulations which convey them are undulations of the same medium. And as induced electricity penetrates through everything, or nearly everything, it follows that the ether through which its undulations are propagated must pervade all space, whether empty or full, whether occupied by opaque matter or transparent matter, or by no matter at all. The attractive experiments by which the late Professor Herz illustrated the electric vibrations of the ether will only alluded to by me... But the mystery of the ether, though it has been made more fascinating by these discoveries, remains even more inscrutable than before. Of this all-pervading entity we know absolutely nothing except this one fact, that it can be made to undulate. Whether outside the influence of matter on the motion of its waves, ether has any effect on matter or matter upon it, is absolutely unknown. And even [in] its solitary function of undulating ether performs in an abnormal fashion which has caused infinite perplexity. All fluids that we know transmit any blow they have received by waves which undulate backwards and forwards in the path of their own advance. The ether undulates athwart the path of the wave's advance. The genius of Lord Kelvin has recently discovered what he terms a labile state of equilibrium, in which a fluid that is infinite in its extent may exist, and may undulate in this eccentric fashion without outraging the laws of mathematics. I am no mathematician, and l cannot judge whether this reconciliation of the action of the ether with mechanical law is to be looked upon as a permanent solution of the question, or is only what diplomatists call a modus vivendi. In any case it leaves our knowledge of the ether in a very rudimentary condition. It has no known qualities except one, and that quality is in the highest degree anomalous and inscrutable... It is not easy to fit in the theory of electrical ether waves with the phenomena of positive and negative electricity, and as to the true significance and cause of those counteracting and complementary forces, to which we give the provisional names of negative and positive, we know about as much now as Franklin knew a century and a half ago."

"The subjects of change in the vibrations are the electric or magnetic polarisations of the medium in which they take place. In order to explain the propagation of light in space between the stars, which is free from all trace of ponderable matter, the electromagnetic theory of light also must assume a medium, which fills the world-space even where no ponderable matter is to be found. It must so far make the same assumption as the undulatory theory (of light); but while the latter has to ascribe the properties of a solidly-elastic body to the ether, no assumption at all need be made by the electromagnetic theory as to the mode of its inner consistence. It is enough, that the ether is capable of being magnetised, and electrified in the fashion of an insulator, that is, in such a way that in its smallest parts a certain electric distribution, a so-called dielectric polarisation, as Faraday named it, is possible."

"I adopt Mr. Darwin's hypothesis, therefore, subject to the production of proof that physiological species may be produced by selective breeding; just as a physical philosopher may accept the undulatory theory of light, subject to the proof of the existence of the hypothetical ether; or as the chemist adopts the atomic theory, subject to the proof of the existence of atoms; and for exactly the same reasons, namely, that it has an immense amount of primâ facie probability: that it is the only means at present within reach of reducing the chaos of observed facts to order; and lastly, that it is the most powerful instrument of investigation which has been presented to naturalists since the invention of the natural system of classification and the commencement of the systematic study of embryology."

"The gradual reception of the undulatory theory of light necessitated the assumption of the existence of an 'ether' filling all space. But whether this ether was to be regarded as a strictly material and continuous substance was an undecided point, and hence the revived atomism escaped strangling in its birth. For it is clear, that if the ether is admitted to be a continuous material substance, Democritic atomism is at an end and Cartesian continuity takes its place."

"The primitive atomic theory, which has served as the scaffolding for the edifice of modern physics and chemistry, has been quietly dismissed. I cannot discover that any contemporary physicist or chemist believes in the real indivisibility of atoms, or in an interatomic matterless vacuum. Atoms appear to be used as mere names for physico-chemical units which have not yet been subdivided, and 'molecules' for physico-chemical units which are aggregates of the former. And these individualised particles are supposed to move in an endless ocean of a vastly more subtle matter—the ether."

"If this ether is a continuous substance... we have got back from the hypothesis of Dalton to that of Descartes. But there is much reason to believe that science is going to make a still further journey, and, in form, if not altogether in substance, to return to the point of view of Aristotle."

"The so called vortex-ring' hypothesis is a very serious and remarkable attempt to deal with material units from a point of view which is consistent with the doctrine of evolution. It supposes the ether to be a uniform substance, and that the 'elementary' units are, broadly speaking, permanent whirlpools, or vortices, of this ether, the properties of which depend on their actual and potential modes of motion. It is curious and highly interesting to remark that this hypothesis reminds us not only of the speculations of Descartes, but of those of Aristotle."

"The resemblance of the 'vortex rings' to the 'tourbillons' of Descartes is little more than nominal; but the correspondence between the modern and the ancient notion of a distinction between primary and derivative matter is, to a certain extent, real. For this ethereal 'Urstoff' of the modern corresponds very closely with the πρώτη ΰλη of Aristotle, the materia prima of his mediæval followers; while matter, differentiated into our elements, is the equivalent of the first stage of progress towards the έσχάτη ΰλη, or finished matter, of the ancient philosophy."

"At this time, space was supposed to be filled with an ether, a substance which might well serve, among other functions, to transmit forces across space. So long as such an ether could be called on, the transmission of force to a distance was easy to understand; it was like ringing a distant bell by pulling a bell-rope."

"Faraday, Maxwell, Larmor and a great number of others tried to explain electromagnetic action on these lines, but all attempts failed, and it began to seem impossible that any properties of ether could explain the observed pattern of events."

"Then the theory of relativity came and explained the cause of the failure. Electric action requires time to travel from one point of space to another, the simplest instance of this being the finite speed of travel of light... Thus electromagnetic action may be said to travel through space and time jointly. But by filling space and space alone [excluding time] with an ether, the pictorial representations had all supposed a clear-cut distinction between space and time."

"...when the experiment was attempted by Michelson and Morley it failed, thus showing that space and time assumed in the picture were not true to the facts of nature. ...the pattern of events was the same whether the world stood at rest in the supposed ether, or had an ether wind blowing through it at a million miles an hour. It began to look as though the supposed ether was not very important in the scheme of things... and so might as well be abandoned. But if the bell-rope is to be discarded, what is to ring the bell?"

"When he proved that electromagnetic waves travel with the speed of light, Maxwell concluded that these waves travel in ether, because since Newton's days ether had been accepted as the medium in which light moved. But since electromagnetic waves travel through all substances this means that ether must pervade all substances, including empty space. ...since the waves move with enormous velocity the ether has to be highly rigid, for the more rigid a body the faster the waves travel through it. On the other hand if ether pervades space it must be completely transparent and the planets must move through it with no friction. These conditions... are contradictory. ...We must conclude that it is a fiction, a mere word satisfying only those minds that do not look behind words."

"Under the influence of the elastic forces, the electrons can vibrate about their positions of equilibrium. In doing so, and perhaps also on account of other more irregular motions, they become the centres of waves that travel outwards in the surrounding ether and can be observed as light if the frequency is high enough. In this manner we can account for the emission of light and heat."

"I cannot speak here of the many highly interesting applications which Einstein has made of this principle. His results concerning electromagnetic and optical phenomena ...agree in the main with those which we have obtained... the chief difference being that Einstein simply postulates what we have deduced, with some difficulty and not altogether satisfactorily, from the fundamental equations of the electromagnetic field. By doing so, he may certainly take credit for making us see in the negative result of experiments like those of Michelson, Rayleigh and Brace, not a fortuitous compensation of opposing effects, but the manifestation of a general and fundamental principle. Yet, I think, something may also be claimed in favour of the form in which I have presented the theory. I cannot but regard the ether, which can be the seat of an electromagnetic field with its energy and vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter. ...it seems natural not to assume at starting that it can never make any difference whether a body moves through the ether or not, and to measure distances and lengths of time by means of rods and clocks having a fixed position relatively to the ether. It would be unjust not to add that, besides the fascinating boldness of its starting point, Einstein's theory has another marked advantage over mine. Whereas I have not been able to obtain for the equations referred to moving axes exactly the same form as for those which apply to a stationary system, Einstein has accomplished this by means of a system of new variables slightly different from those which I have introduced."

"The most obvious mechanical phenomenon in electrical and magnetical experiments is the mutual action by which bodies in certain states set each other in motion while still at a sensible distance from each other. ...mathematical theories of statical electricity, of magnetism, of the mechanical action between conductors carrying currents, and of the induction of currents have been formed. In these theories the force acting between the two bodies is treated with reference only to the condition of the bodies and their relative position, and without any express consideration of the surrounding medium. These theories assume, more or less explicitly, the existence of substances the particles of which have the property of acting on one another at a distance by attraction or repulsion. The most complete development of a theory of this kind is that of... MM. W. Weber and C. Neumann... The mechanical difficulties, however, which are involved in the assumption of particles acting at a distance with forces which depend on their velocities are such as to prevent me from considering this theory as an ultimate one... I have, therefore, preferred to seek an explanation of the fact in another direction, by supposing them to be produced by actions which go on in the surrounding medium as well as in the excited bodies, and endeavouring to explain the action between distant bodies without assuming the existence of forces capable of acting directly at sensible distances."

"To those who maintained the existence of a plenum as... principle, nature's abhorrence of a vacuum was a sufficient reason for imagining an all-surrounding aether, even though every other argument should be against it. ...Descartes ...made ...matter a necessary condition of extension... It is only when we remember the extensive and mischievous influence on science... that we can appreciate the horror of aethers which sober-minded men had during the 18th century, and which... descended even to... John Stuart Mill. ...Newton himself... endeavoured to account for gravitation by differences of pressure in an aether... but he did not publish his theory, "because he was not able from experiment and observation to give a satisfactory account..." ...The only aether which has survived is that which was invented by Huygens to explain the propagation of light. The evidence for... the luminiferous aither has accumulated as additional phenomena of light and other radiations have been discovered; and the properties of this medium... have been found to be... those required to explain electromagnetic phenomena. ...the interplanetary and interstellar spaces are not empty, but are occupied by a material substance or body, which is certainly the largest, and probably the most uniform body of which we have any knowledge. ...Whether this vast homogeneous expanse of isotropic matter is fitted not only to be a medium of physical interaction between distant bodies, and to fulfil other physical functions... but also, as the authors [ and Peter Tait] of the Unseen Universe seem to suggest, to constitute the material organism of beings exercising functions of life and mind as high or higher than ours are at present, is a question far transcending the limits of physical speculation."

"It appears, from all that precedes, reasonably certain that if there be any relative motion between the earth and the luminiferous ether, it must be small; quite small enough entirely to refute Fresnel's explanation of aberration."

"Suppose that an ether strain corresponds to an electric charge, an ether displacement to the electric current, these ether vortices to the atoms—if we continue these suppositions, we arrive at what may be one of the grandest generalizations of modern science—of which we are tempted to say that it ought to be true even if it is not—namely, that all the phenomena of the physical universe are only different manifestations of the various modes of motions of one all pervading substance—the ether."

"It may be that ultimately the search for dark matter will turn out to be the most expensive and largest null result experiment since the Michelson-Morely experiment, which failed to detect the ether."

"Were I to assume an hypothesis, it should be this, if propounded more generally, so as not to assume what light is further than that it is something or other capable of exciting vibrations of the ether. First, it is to be assumed that there is an ethereal medium, much of the same constitution as air, but far rarer, subtiller, and more strongly elastic. ...In the second place, it is to be supposed that the ether is a vibrating medium, like air, only the vibrations much more swift and minute; those of air made by a man's ordinary voice succeeding at more than half a foot or a foot distance, but those of ether at a less distance than the hundredth-thousandth part of an inch. And as in air the vibrations are some larger than others, but yet all equally swift... so I suppose the ethereal vibrations differ in bigness but not in swiftness. ...In the fourth place, therefore, I suppose that light is neither ether nor its vibrating motion, but something of a different kind propagated from lucid bodies. They that will may suppose it an aggregate of various peripatetic qualities. Others may suppose it multitudes of unimaginable small and swift corpuscles of various sizes springing from shining bodies at great distances one after the other, but yet without any sensible interval of time. ...To avoid dispute and make this hypothesis general, let every man here take his fancy; only whatever light be, I would suppose it consists of successive rays differing from one another in contingent circumstances, as bigness, force, or vigour, like as the sands on the shore... and, further, I would suppose it diverse from the vibrations of the ether. ...Fifthly, it is to be supposed that light and ether mutually act upon one another. ...æthereal vibrations are therefore the best means by which such a subtile agent as light can shake the gross particles of solid bodies to heat them."

"And so, supposing that light impinging on a refracting or reflecting ethereal superficies puts it into a vibrating motion, that physical superficies being by the perpetual applause of rays always kept in a vibrating motion, and the ether therein continually expanded and compressed by turns, if a ray of light impinge on it when it is much compressed, I suppose it is then too dense and stiff to let the ray through, and so reflects it; but the rays that impinge on it at other times, when it is either expanded by the interval between two vibrations or not too much compressed and condensed, go through and are refracted."

"And now to explain colours. I suppose that as bodies excite sounds of various tones and consequently vibrations, in the air of various bignesses, so when rays of light by impinging on the stiff refracting superficies excite vibrations in the ether, these rays excite vibrations of various bignesses... therefore, the ends of the capillamenta of the optic nerve which front or face the retina being such refracting superficies, when the rays impinge on them they must there excite these vibrations, which vibrations (like those of sound in a trumpet) will run along the pores or crystalline pith of the capillamenta through the optic nerves into the sensorium (which light itself cannot do), and there, I suppose, affect the sense with various colours, according to their bigness and mixture—the biggest with the strongest colours, reds and yellows; the least with the weakest, blues and violets; middle with green; and a confusion of all with white, much after the manner, that in the sense of hearing, nature makes use of aereal vibrations of several bignesses to generate sounds of divers tones; for the analogy of nature is to be observed."

"To make way for the regular and lasting Motions of the Planets and Comets, it's necessary to empty the Heavens of all Matter, except perhaps some very thin Vapours, Steams or Effluvia, arising from the Atmospheres of the Earth, Planets and Comets, and from such an exceedingly rare Æthereal Medium … A dense Fluid can be of no use for explaining the Phænomena of Nature, the Motions of the Planets and Comets being better explain'd without it. It serves only to disturb and retard the Motions of those great Bodies, and make the frame of Nature languish: And in the Pores of Bodies, it serves only to stop the vibrating Motions of their Parts, wherein their Heat and Activity consists. And as it is of no use, and hinders the Operations of Nature, and makes her languish, so there is no evidence for its Existence, and therefore it ought to be rejected. And if it be rejected, the Hypotheses that Light consists in Pression or Motion propagated through such a Medium, are rejected with it. And for rejecting such a Medium, we have the authority of those the oldest and most celebrated philosophers of ancient Greece and Phoenicia, who made a vacuum and atoms and the gravity of atoms the first principles of their philosophy, tacitly attributing Gravity to some other Cause than dense Matter. Later Philosophers banish the Consideration of such a Cause out of natural Philosophy, feigning Hypotheses for explaining all things mechanically, and referring other Causes to Metaphysicks: Whereas the main Business of natural Philosophy is to argue from Phenomena without feigning Hypotheses, and to deduce Causes from Effects, till we come to the very first Cause, which certainly is not mechanical."

"Planck ...devised his quanta theory, according to which the exchange of energy between the matter and the ether—or rather between ordinary matter and the small resonators whose vibrations furnish the light of incandescent matter—can take place only intermittently. A resonator can not gain energy or lose it in a continuous manner. It can not gain a fraction of a quantum; it must acquire a whole quantum or none at all."

"The earth moves—if it does move—so quietly and silently that we feel no jar or engine-beat to tell us of its motion. If the earth were perpetually shrouded by clouds could we find out its motion through space or even its rotation? And do we actually get any proof on this point from observation of the heavenly bodies? ...who knows if the solar system and all the visible stars are not altogether moving off through space at the rate of a mile or a thousand miles a second? How can we tell unless we have something that is still and fixed to measure the motion by? It seemed until recently that we had such a fixture, the ether. We know of the sun and stars only from the light that comes from them to us. Light, as we can prove by simple experiments, consists of wave motion. Now, can you have wave motion without something to wave? Sound waves are conveyed by air but there is no air between the earth and the sun. So as nothing could be found to fill this empty space scientists had to invent something to satisfy their sense of the fitness of things. The ether was the product of their excogitations. It was a British invention, devised in the , whence have come so many useful theories and discoveries. The ether, as Salisbury, said is simply the nominative of the verb "to undulate." It was conceived of as a sort of transparent jelly filling all space, more rigid than any solid, more frictionless than any fluid, more easily penetrated than any gas. It must be more elastic than steel and yet so rarefied that ordinary matter passes through it without the slightest effort. The ether is supposed to slip between the particles of the rushing earth as the wind blows through the branches of a tree."

"For many years after its invention the ether had nothing to do except to carry light about from one place to another. But when the electro-magnetic waves of the wireless telegraph were produced something was needed also to carry them and this new task was laid upon the shoulders of the uncomplaining ether. When Röntgen discovered the X-rays, whose waves are 10,000 times shorter than the shortest light waves, these were turned over to the ether to run. In fact, it got so that whenever a physicist found any action that he could not explain by ordinary matter he said: "Let the ether do it," and that hypothetical substance apparently answered every purpose until it came to this question of relative motion."

"Now whatever we may think about the ether it would seem that if there is any such thing filling all "empty" space we might use it for measuring the motion of the earth through it as we did the air current in the car. If the earth is really revolving around the sun the ether must be whizzing through its pores at the rate of about nineteen miles a second. But wait—there is the possibility that the earth carries along with it in its flight through space a sort of atmosphere of ether as it does of air. We must first get rid of this possibility by a preliminary experiment to see if a swiftly moving mass of matter does catch up and carry along with it a little of the ether. This would cause a sort of an eddy or disturbance in the ether in the neighborhood of the moving mass as a boat disturbs the water. For instance a ray of light passing close to a rapidly revolving wheel would be a little deflected and show a distorted image. Sir Oliver Lodge tried this experiment and got negative results. That is, moving matter does not disturb or carry with it the ether. Consequently, it would seem, we are left to the only other logical alternative, that the ether drifts through matter and we should expect to detect this drift by measuring the speed of light in the direction of the earth's motion."

"According to an adopted theory, every ponderable atom is differentiated from a tenuous fluid, filling all space merely by spinning motion, as a whirl of water in a calm lake. By being set in movement this fluid, the ether, becomes gross matter. Its movement arrested, the primary substance reverts to its normal state. It appears, then, possible for man through harnessed energy of the medium and suitable agencies for starting and stopping ether whirls to cause matter to form and disappear. At his command, almost without effort on his part, old worlds would vanish and new ones would spring into being. He could alter the size of this planet, control its seasons, adjust its distance from the sun, guide it on its eternal journey along any path he might choose, through the depths of the universe. He could make planets collide and produce his suns and stars, his heat and light; he could originate life in all its infinite forms. To cause at will the birth and death of matter would be man's grandest deed, which would give him the mastery of physical creation, make him fulfill his ultimate destiny."

"The beauty and clearness of the dynamical theory, which asserts heat and light to be modes of motion, is at present obscured by two clouds. I. The first came into existence with the undulatory theory of light, and was dealt with by Fresnel and Dr. Thomas Young; it involved the question, how could the earth move through an elastic solid, such as essentially is the luminiferous ether? II. The second is the Maxwell–Boltzmann doctrine regarding the partition of energy."

"But if ether is nothing but an hypothesis explanatory of light, air on the other hand, is a thing that is directly felt; and even if it did not enable us to explain the phenomenon of sound, we should nevertheless always be directly aware of it, and above all, of the lack of it in moments of suffocation or air-hunger. And in the same way God Himself, not the idea of God, may become a reality that is immediately felt; and even though the idea of God does not enable us to explain either the existence or essence of the Universe, we have at times the direct feeling of God, above all in moments of spiritual suffocation. And the feeling, mark it well, for all that is tragic in it and the whole tragic sense of life is founded upon this — this feeling is a feeling of hunger for God, of the lack of God. To believe in God is, in the first instance... to wish that there may be a God, to be unable to live without Him."

"The conception of lines of force was introduced by Faraday to form a mental picture of the processes going on in the electric field. To him these lines were not mere mathematical abstractions. He ascribed to them properties that gave them a real physical significance. They terminate on opposite charges, are always in a state of tension, tending to shorten themselves, and are mutually repellent. The direction of a line of force at any point gives the direction of the field at that point. With the help of these properties of lines of force it is possible to obtain an idea of the distribution of the intensity of the field surrounding electrically charged bodies. The idea of tubes of force has been introduced to make the method of Faraday metrical rather than merely descriptive. A tube of force is obtained by drawing a number of lines of force through the boundary of any small closed curve. The lines then form a tubular surface, which, it can be proved, will never be cut by any lines of force, and the extremities of which enclose equal and opposite charges. By properly choosing the area of the surface enclosed by the curve through which the lines are drawn the extremities of the tube can be made to enclose unit charge. Such a unit tube is called a Faraday tube. Maxwell and J. J. Thomson have made an exhaustive study of these tubes of force and expressed their properties in mathematical terms. The result that interests us here is that a tube of force behaves as though it had inertia, so that in order to move a tube work must be done. This explains why a charge behaves as if it had mass. It must be remarked that the conception of tubes of forces is used here merely to aid in understanding the phenomena. Whether or not tubes of force, or even the ether, possess any physical significance is a question. Modern developments seem to indicate that this question must be answered in the negative."

"Quite undeservedly, the ether has acquired a bad name."

"The absence of effects due to the earth's motion relative to the ether can be explained on the electromagnetic theory if it is supposed that this theory covers all phenomena. This appears to be a strong argument in favor of the purely electrical nature of matter. It will be convenient now to mention the chief electrical theories of atomic structure which have been proposed."

"We should remember that there was once a discipline called natural philosophy. Unfortunately, this discipline seems not to exist today. It has been renamed science, but science of today is in danger of losing much of the natural philosophy aspect."

"As we divided natural philosophy in general into the inquiry of causes, and productions of effects: so that part which concerneth the inquiry of causes we do subdivide according to the received and sound division of causes. The one part, which is physic, inquireth and handleth the material and efficient causes; and the other, which is metaphysic, handleth the formal and final causes."

"The natural philosophy of Democritus and some others, who did not suppose a mind or reason in the frame of things, but attributed the form thereof able to maintain itself to infinite essays or proofs of nature, which they term fortune, seemeth to me... in particularities of physical causes more real and better inquired than that of Aristotle and Plato; whereof both intermingled final causes, the one as a part of theology, and the other as a part of logic, which were the favourite studies respectively of both those persons. Not because those final causes are not true, and worthy to be inquired, being kept within their own province; but because their excursions into the limits of physical causes hath bred a vastness and solitude in that tract."

"Histories make men wise; poets witty; the mathematics subtile; natural philosophy deep; moral grave; logic and rhetoric able to contend."

"Nature, as well as human affairs, seems to be subject to both necessity and accident. Yet even accident is not completely arbitrary, for there are laws of chance, formulated in the mathematical theory of probability, nor can the cause-effect relation be used for predicting the future with certainty, as this would require a complete knowledge of the relevant circumstances, present, past, or both together, which is not available. There seems to be a hopeless tangle of ideas. ...if you look through the literature ...you will find no satisfactory solution, no general agreement. Only in physics has a systematic attempt been made to use the notions of cause and chance in a way free from contradictions. Physicists form their notions through the interpretation of experiments. This method may rightly be called Natural Philosophy, a word still used for physics at the Scottish universities. ...My material will be taken mainly from physics, but I shall try to regard it with the attitude of the philosopher... I know that such an attempt will not find favour with some philosophers, who maintain that science teaches only a narrow aspect of the world, and one which is of no great importance to man's mind. It is true that many scientists are not philosophically minded and have hitherto shown much skill and ingenuity but little wisdom. ...Wise men would have considered the consequences of their activities before starting on them ; scientists have failed to do so, and only recently have they become conscious of their responsibilities to society. They have gained prestige as men of action, but they have lost credit as philosophers. Yet history shows that science has played a leading part in the development of human thought. It has not only supplied raw material to philosophy by gathering facts, but also evolved the fundamental concepts on how to deal with them. It suffices to mention the Copernican system of the universe, and the Newtonian dynamics which sprang from it. These originated the conceptions of space, time, matter, force, and motion for a long time to come, and had a mighty influence on many philosophical systems. It has been said that the metaphysics of any period is the offspring of the physics of the preceding period. ...more than 200 years after Newton there should be some progress in the assimilation of mathematics by those who are interested in natural philosophy. So I shall use ordinary language and formulae in a suitable mixture; but I shall not give proofs of theorems (they are collected in the Appendix)."

"An unrestricted belief in causality leads necessarily to the idea that the world is an automaton of which we ourselves are only little cog-wheels. This means materialistic determinism. It resembles very much that religious determinism accepted by different creeds, where the actions of men are believed to be determined from the beginning by a ruling of God. ...The notion of divine predestination clashes with the notion of free will, in the same way as the assumption of an endless chain of natural causes. On the other hand, an unrestricted belief in chance is impossible, as it cannot be denied that there are a great many regularities in the world; hence there can be, at most, 'regulated accident'. One has to postulate laws of chance which assume the appearance of laws of nature or laws for human behaviour. ...Our philosophy is dualistic in this respect; nature is ruled by laws of cause and laws of chance in a certain mixture. How is this possible? Are there no logical contradictions? Can this mixture of ideas be cast into a consistent system in which all phenomena can be adequately described or explained? What do we mean by such an explanation if the feature of chance is involved ? What are the irreducible or metaphysical principles involved? Is there any room in this system for free will or for the interference of deity? ...The statement, frequently made, that modern physics has given up causality is entirely unfounded. Modern physics, it is true, has given up or modified many traditional ideas; but it would cease to be a science if it had given up the search for the causes of phenomena. ...I shall survey the development of physical thought, dwelling here and there on special points of interest, and I shall try to apply the results to philosophy in general."

"Since the word "knowledge" occurs in my general title... I am going to be talking about epistemology, although I prefer to use the eighteenth-century, indeed, medieval phrase, "natural philosophy." ...that enterprise of the human mind which attempts to trace lawfulness to nature, dead and living, but which is not directed to specific inquiries into how this or that law works. Philosophy in the sense in which I practice it, natural philosophy, is concerned with lawfulness rather than with laws and the general nature of laws rather than with the specific structure of this or that law. Natural philosophy was one of the three topics (moral philosophy and metaphysical philosophy were the others) to which one graduated in medieval universities after having studied the seven liberal arts. I believe that we need to review the whole of our natural philosophy in the light of scientific knowledge that has arisen in the last fifty years."

"Those who have treated of natural philosophy may be nearly reduced to three classes. Of these, some have attributed to the several species of things specific and occult qualities, on which, in a manner unknown, they make the operations of the several bodies to depend. The sum of the doctrine of the schools derived from Aristotle and the Peripatetics is herein contained. They affirm that the several effects of bodies arise from the particular natures of those bodies; but whence it is that bodies derive those natures they do not tell us, and therefore they tell us nothing. And being entirely employed in giving names to things, and not in searching into things themselves, we may say, that they have invented a philosophical way of speaking, but not that they have made known to us true philosophy. Others, therefore, by laying aside that useless heap of words, thought to employ their pains to better purpose. These supposed all matter homogeneous, and that the variety of forms which is seen in bodies arises from some very plain and simple affections of the component particles; and by going on from simple things to those which are more compounded, they certainly proceed right, if they attribute no other properties to those primary affections of the particles than nature has done. But when they take a liberty of imagining at pleasure unknown figures and magnitudes, and uncertain situations and motions of the parts; and, moreover, of supposing occult fluids, freely pervading the pores of bodies, endued with an all-performing subtilty, and agitated with occult motions; they now run out into dreams and chimeras, and neglect the true constitution of things; which certainly is not to be expected from fallacious conjectures, when we can scarcely reach it by the most certain observations. Those who fetch from hypotheses the foundation on which they build their speculations, may form, indeed, an ingenious romance; but a romance it will still be. There is left, then, the third class, which profess experimental philosophy. These, indeed, derive the causes of all things from the most simple principles possible; but, then, they assume nothing as a principle that is not proved by phænomena. They frame no hypotheses, nor receive them into philosophy otherwise than as questions whose truth may be disputed. They proceed, therefore, in a twofold method, synthetical and analytical. From some select phænomena they deduce by analysis the forces of nature, and the more simple laws of forces; and from thence by synthesis shew the constitution of the rest. This is that incomparably best way of philosophizing which our renowned author most justly embraced before the rest, and thought alone worthy to be cultivated and adorned by his excellent labours. Of this he has given us a most illustrious example by the explication of the System of the World, most happily deduced from the theory of gravity. That the virtue of gravity was found in all bodies, others suspected or imagined before him; but he was the only and the first philosopher that could demonstrate it from appearances, and make it a solid foundation to the most noble speculations."

"Since they are neither great mathematicians nor able experimenters, what are we to call such men as Maxwell, Lorentz and Einstein? If we concede that the name philosopher should apply to those who are concerned with a harmonisation of the whole than with individual facts, or, again, with a general view of things rather than with a restricted view, we must agree that the theoretical physicists must be called philosophers. They are, then, the philosophers of the inorganic world, just as the pure mathematicians might be called the philosophers of abstract relations. Now... the facts which these scientific philosophers are seeking to co-ordinate are of a restricted species; they are mathematical, physical and chemical in nature; hence it is clear that there is room for a more general type of philosopher—a super-philosopher, as it were—whose facts would comprise all the spheres of human knowledge, including consciousness, emotions and the relationships between mind and matter. The traditional philosophers—or shall we say lay philosophers, since we are discussing scientific matters?—aspire to be placed in this category of thinkers. It would appear, then, that theoretical scientists, and lay philosophers have much in common; they differ only in the scope of the facts they are seeking to co-ordinate. But here is where the first breach arises. The theoretical scientist proceeds with the utmost caution and considers himself at liberty to theorise only after a sufficient number of facts have been established by experiment and observation; till then he remains silent. ...It was not one, nor two, nor even three of the negative experiments in electromagnetics that drove Einstein towards his revolutionary theory; it was the whole body of electrodynamics. ... But when we examine the procedure of the lay philosopher who discusses scientific matters, we see that his procedure is entirely different."

"Les causes primordiales ne nous sont point connues; mais elles sont assujetties à des lois simples et constantes, que l'on peut découvrir par l'observation, et dont l'étude est l'objet de la philosophie naturelle."

"Natural Philosophy is placed among those Parts of Mathematics, whose Object is Quantity in general. Mathematics are divided into pure and mixed. Pure Mathematics enquire into the general Properties of Figures and abstracted Ideas. Mixed Mathematics examine Things themselves, and will have our Notions and Deductions to agree both with Reason and Experience. Physics belong to mix'd Mathematics. The Properties of Bodies, and the Laws of Nature, are the foundations of mathematical Reasoning, as all that have examined the Scope of the Science will freely confess. But Philosophers do not equally agree upon what is to pass for a Law of Nature, and what Method is to be followed in quest of those Laws. I have therefore thought fit... to make good the Newtonian Method... Physics do not meddle with the first Foundation of Things. That the World was created by God, is a Position wherein Reason so perfectly agrees with Scripture, that the least Examination of Nature will shew plain Footsteps of supreme Wisdom. It is confounding and oversetting all our clearest Notions, to assert that the World may have taken its Rise from some general Laws of Motion, and that it imports not what is imagined concerning the first Division of Matter. And that there can hardly be anything supposed, from which the same Effect may not be deduced by the same Laws of Nature: and that for this Reason; That since Matter successively assumes all the Forms it is capable of by means of those Laws, if we consider all those Forms in order, we must at last come to that Form wherein this present World was framed; so that we have no Reason in this Case to fear any Error from a wrong Supposition. This Assertion, I say, overthrows all our clearest Notions, as has been fully proved by many learned Men; and is indeed so unreasonable, and so injurious to the Deity, that it will seem unworthy of an Answer to any one that does not know that it has been maintain'd by any antient and modern Philosophers, and some of them of the first Rank, and far removed from any Suspicion of Atheism. Then first laying it down as an undoubted Truth, that God has created all Things, we must afterwards explain by what Laws every thing is governed."

"Neither in science itself, nor in that lower class of the arts which arise out of its practical application, has any individual work an enduring ultimate value, unless from its execution: and this would be altogether independent of its scientific value, and would belong to it solely as a work of art. In science its main worth is temporary, as a stepping-stone to something beyond. Even the Principia, as Newton, with characteristic modesty entitled his great work, is truly but the beginning of a natural philosophy, and no more an ultimate work than Watt's steam-engine, or Arkwright's spinning-machine. ...Thus in science there is a continual progress, a pushing onward: no ground is lost; and the lines keep on advancing. We know all that our ancestors knew, and more: the gain is clear, palpable, indisputable. The discoveries made by former ages have become a permanent portion of human knowledge, and serve as a stable groundwork to build fresh discoveries atop of them; as these in their turn will build up another story, and this again another."

"If we examine the mere signification of the two words Natural Philosophy, we find that natural means something that is produced by nature; and philosophy, from the Greek, is literally "love of wisdom or knowledge." Thus, then, the words imply love of a knowledge of the productions of nature or God. Knowledge, in its true sense, is an accumulation of facts; these man carefully collects, and reasoning thereupon, is capable of penetrating many of the secret workings of nature, and turning such acquisition to his peculiar advantage. Natural Philosophy is also termed Physics, that is, a study of nature by means of the strictest modes of investigation the intellect of man has at command."

"Wide is the scope of Natural Philosophy. It leads to an acquaintance with the laws that keep the planets in their undeviating path; it treats of the phenomena of the earth, the air, and the ocean; of the simple principles of mechanism that man employs; of the falling of the silent dew or the rushing of the roaring cataract; of the heat of summer and the frost of winter; of the zephyr-breeze or the destructive tornado; of the swimming of fishes or the flying of birds; of the ripple of the placid lake or the mountain waves of the ocean; of the grace, motion, and powers of the human form; of the mechanism of the voice, the ear, and the eye. By an acquaintance with its first principles—the embellishments of a palace, the necessities of a cottage, the swinging of a carriage, and the management of a dray, are all better accomplished. The elasticity of air and steam, that drives the vessel despite of tide or wind, or sends tons of merchandise with surprising velocity to the extremes of a kingdom, are by its teaching comprehended. Knowing the cause of the awful voice of thunder, of the terrific destruction of lightning, and of the peaceful beauties of the rainbow, much ignorant teaching is dispelled. Man has so advanced in his comprehension of nature, that he chains one of the most fearful elements to his use, which he guides and directs as if it were possessed of the feebleness of a helpless babe; with it he sends his thoughts with a speed surpassing the rapid flight of time. No one can feel but abashed at not understanding the simple principles that produce such seemingly miraculous effects. Natural Philosophy aids, then, our commerce, wealth, happiness, luxuries, necessities, and civilisation."

"Our imagination is struck only by what is great; but the lover of natural philosophy should reflect equally on little things. We have just seen that winged insects, collected in society, and concealing in their sucker a liquid that irritates the skin, are capable of rendering vast countries almost uninhabitable. Other insects equally small, the termites (comejen), create obstacles to the progress of civilization, in several hot and temperate parts of the equinoctial zone, that are difficult to be surmounted. They devour paper, pasteboard, and parchment with frightful rapidity, utterly destroying records and libraries. Whole provinces of Spanish America do not possess one written document that dates a hundred years back. What improvement can the civilization of nations acquire if nothing link the present with the past; if the depositaries of human knowledge must be repeatedly renewed; if the records of genius and reason cannot be transmitted to posterity?"

"It is the object of Natural Philosophy to make us acquainted with the various qualities or properties of matter, and the manner in which different masses of it affect each other."

"Induction, analogy, hypotheses founded upon facts and rectified continually by new observations, a happy tact given by nature and strengthened by numerous comparisons of its indications with experience, such are the principal means for arriving at truth. If one considers a series of objects of the same nature one perceives among them and in their changes ratios which manifest themselves more and more in proportion as the series is prolonged, and which, extending and generalizing continually, lead finally to the principle from which they were derived. But these ratios are enveloped by so many strange circumstances that it requires great sagacity to disentangle them and to recur to this principle: it is in this that the true genius of sciences consists. Analysis and natural philosophy owe their most important discoveries to this fruitful means, which is called induction. Newton was indebted to it for his theorem of the binomial and the principle of universal gravity. It is difficult to appreciate the probability of the results of induction, which is based upon this that the simplest ratios are the most common; this is verified in the formulae of analysis and is found again in natural phenomena, in crystallization, and in chemical combinations. This simplicity of ratios will not appear astonishing if we consider that all the effects of nature are only mathematical results of a small number of immutable laws. Yet induction, in leading to the discovery of the general principles of the sciences, does not suffice to establish them absolutely. It is always necessary to confirm them by demonstrations or by decisive experiences; for the history of the sciences shows us that induction has sometimes led to inexact results."

"A true philosopher does not engage in vain disputes about the nature of motion; rather, he wishes to know the laws by which it is distributed, conserved or destroyed, knowing that such laws are the basis for all natural philosophy."

"To make way for the regular and lasting Motions of the Planets and Comets, it's necessary to empty the Heavens of all Matter, except perhaps some very thin Vapours, Steams or Effluvia, arising from the Atmospheres of the Earth, Planets and Comets, and from such an exceedingly rare Æthereal Medium … A dense Fluid can be of no use for explaining the Phænomena of Nature, the Motions of the Planets and Comets being better explain'd without it. It serves only to disturb and retard the Motions of those great Bodies, and make the frame of Nature languish: And in the Pores of Bodies, it serves only to stop the vibrating Motions of their Parts, wherein their Heat and Activity consists. And as it is of no use, and hinders the Operations of Nature, and makes her languish, so there is no evidence for its Existence, and therefore it ought to be rejected. And if it be rejected, the Hypotheses that Light consists in Pression or Motion propagated through such a Medium, are rejected with it. And for rejecting such a Medium, we have the authority of those the oldest and most celebrated philosophers of ancient Greece and Phoenicia, who made a vacuum and atoms and the gravity of atoms the first principles of their philosophy, tacitly attributing Gravity to some other Cause than dense Matter. Later Philosophers banish the Consideration of such a Cause out of natural Philosophy, feigning Hypotheses for explaining all things mechanically, and referring other Causes to Metaphysicks: Whereas the main Business of natural Philosophy is to argue from Phenomena without feigning Hypotheses, and to deduce Causes from Effects, till we come to the very first Cause, which certainly is not mechanical."

"As in Mathematicks, so in Natural Philosophy, the Investigation of difficult Things by the Method of Analysis, ought ever to precede the Method of Composition."

"And thus much concerning God; to discourse of whom from the appearances of things, does certainly belong to Natural Philosophy."

"That which is now called natural philosophy, embracing the whole circle of science, of which astronomy occupies the chief place, is the study of the works of God, and of the power and wisdom of God in his works, and is the true theology."

"The term Natural Philosophy was used by Newton, and is still used in British Universities, to denote the investigation of laws in the material world, and the deduction of results not directly observed. Observation, classification, and description of phenomena necessarily precede Natural Philosophy in every department of natural science. The earlier stage is in some branches commonly called Natural History; and it might with equal propriety be so called in all others."

"There are many properties of motion, displacement, and deformation, which may be considered altogether independently of such physical ideas as force, mass, elasticity, temperature, magnetism, electricity. The preliminary consideration of such properties in the abstract is of very great use for Natural Philosophy, and we devote to it, accordingly... the Geometry of our subject, embracing what can be observed or concluded with regard to actual motions, as long as the cause is not sought."

"It is certain that either the earth is becoming on the whole cooler from age to age, or the heat conducted out is generated in the interior by temporary dynamical (that is, in this case, chemical) action. To suppose, as Lyell, adopting the chemical hypothesis, has done, that the substances, combining together, may be again separated electrolytically by thermo-electric currents, due to the heat generated by their combination, and thus the chemical action and its heat continued in an endless cycle, violates the principles of natural philosophy in exactly the same manner, and to the same degree, as to believe that a clock constructed with a self-winding movement may fulfil the expectations of its ingenious inventor by going for ever."

"About the year 1645 while, I lived in London (at a time, when, by our Civil Wars, Academical Studies were much interrupted in both our Universities:) beside the Conversation of divers eminent Divines, as to matters Theological; I had the opportunity of being acquainted with divers worthy Persons, inquisitive into Natural Philosophy, and other parts of Humane Learning; And particularly of what hath been called the New Philosophy or Experimental Philosophy. We did by agreement, divers of us, meet weekly in London on a certain day, to treat and discourse of such affairs. ...The meetings we held sometimes at Dr. Goddard's lodgings...on occasion of his keeping an Operator in his house, for grinding Glasses for Telescopes and Microscopes... and sometime... at ' or some place near adjoyning. Our business was (precluding matters of Theology and State Affairs) to discourse and consider of Philosophical Enquiries, and such as related thereunto, as Physick, Anatomy, Geometry, Astronomy, Navigation, Staticks, Magneticks, Chymicks, Mechanicks, and Natural Experiments; with the state of these studies, as then cultivated, at home and abroad. We there discoursed of the Circulation of the Blood, the Valves in the Veins, the Venæ Lecteæ, the Lymphatick Vessels, the Copernican Hypothesis, the Nature of Comets, and New stars, the Satellites of Jupiter, the Oval Shape (as it then appeared) of Saturn, the Spots in the Sun, and it's turning on it's own Axis, the Inequalities and Selenography of the Moon, the several phases of Venus and Mercury, the improvement of Telescopes and grinding of Glasses for that purpose, the Weight of Air, the Possibility or Impossibility of Vacuities, and Nature's Abhorrence thereof, the Torricellian Experiment in Quicksilver, the Descent of heavy Bodies, and the degrees of acceleration therein; and divers other things of like nature. Some of which were then but New Discoveries, and others not so generally known and imbraced, as now they are, with other things appertaining to what hath been called The New Philosophy; which, from the times of Galileo at Florence, and Sr. Francis Bacon (Lord Verulam) in England, hath been much cultivated in Italy, France, Germany, and other Parts abroad, as well as with us in England. About the year 1648, 1649, some of our company being removed to Oxford (first Dr. Wilkins, then I, and soon after Dr. Goddard) our company divided. Those in London continued to meet there as before... Those meetings in London continued, and (after the King's Return in 1660) were increased with the accession of divers worthy and Honorable Persons; and were afterwards incorporated by the name of the , &c. and so continue to this day."

"When we reflect on the magnificence of the great picture of the universe... we are lost in the contemplation of the immensity of the prospect, and returning to the comparatively diminutive proportions of our individual persons, and of all the objects with which we are most immediately connected, we cannot help feeling our own insignificance in the material world. The mind, notwithstanding, endeavours to raise itself above the restraints which nature has imposed on the body, and to penetrate the abyss of space in search of congenial existences. But in speculations of this kind, reason and argument must give way to conjecture and imagination; and thus, from natural philosophy, our imaginations wander into the regions of poetry; and it must be confessed that the union of poetical embellishment with natural philosophy is seldom very happy. ...his object is, to say a little, very elegantly, in very circuitous, and somewhat obscure terms. But the information, which the natural philosopher has to impart, is too copious to allow of prolixity in its detail; his subjects are too intricate to be compatible with digressions after amusement, which, besides interrupting, are too likely to enervate the mind; and if he is ever fortunate enough to entertain, it must be by gratifying the love of truth, and satisfying the thirst after knowledge."

"Plato introduced into philosophy a variety of imaginations, which resembled the fictions of poetry much more than the truths of science. He maintained, for example, that ideas existed independently of the human mind, and of the external world, and that they composed beings of different kinds, by their union with an imperfect matter. It is observed by Bacon, in his essay on the opinions of Parmenides, that the most ancient philosophers Empedocles, Anaxagoras, Anaximenes, Heraclitus and Democritus, submitted their minds to things as they found them; but that Plato made the world subject to ideas, and Aristotle made even ideas, as well as all other things, subservient to words; the minds of men beginning to be occupied, in those times, with idle discussions and verbal disputations, and the correct investigation of nature being wholly neglected. Plato entertained, however, some correct notions respecting the distinction of denser from rarer matter by its greater inertia; and it would be extremely unjust to deny a very high degree of merit to Aristotle's experimental researches, in various parts of natural philosophy, and in particular to the vast collection of real information contained in his works on natural history. Aristotle attributed absolute levity to fire, and gravity to the earth, considering air and water as of an intermediate nature. By gravity the ancients appear in general to have understood a tendency towards the centre of the earth, which they considered as identical with that of the universe; and as long as they entertained this opinion, it was almost impossible that they should suspect the operation of a mutual attraction in all matter, as a cause of gravitation. The first traces of this more correct opinion respecting it are found in the works of Plutarch."

"Epicurus appears to have reasoned as justly respecting many particular subjects of natural philosophy, as he did absurdly respecting the origin of the world, and of the animals which inhabit it. He adopted in great measure the principles of Democritus respecting atoms, but attributed to them an innate power of affecting each other's motions, and of declining, in such a manner, as to constitute, by the diversity of their spontaneous arrangements, all the varieties of natural bodies. He considered both heat and cold as material; the heat emitted by the sun he thought not absolutely identical with light, and even went so far as to conjecture that some of the sun's rays might possibly possess the power of heating bodies, and yet not affect the sense of vision. In order to explain the phenomena of magnetism, he supposed a current of atoms, passing, in certain directions, through the magnet and through iron, which produced all the effects by their interference with each other. Earthquakes and volcanos he derived from the violent explosions of imprisoned air."

"Religion has two principal enemies, fanaticism and infidelity, or that which is called atheism. The first requires to be combated by reason and morality, the other by natural philosophy."

"Contemplating the universe, the whole system of creation, in this point of light, we shall discover, that all that which is called natural philosophy is properly a divine study— It is the study of God through his works — It is the best study, by which we can arrive at a knowledge of the existence, and the only one by which we can gain a glimpse of his perfection."

"It has been the error of schools to teach astronomy, and all the other sciences and subjects of natural philosophy, as accomplishments only; whereas they should be taught theologically, or with reference to the Being who is the Author of them: for all the principles of science are of divine origin. Man cannot make, or invent, or contrive principles; he can only discover them, and he ought to look through the discovery to the Author. When we examine an extraordinary piece of machinery, an astonishing pile of architecture, a well-executed statue, or a highly-finished painting where life and action are imitated, and habit only prevents our mistaking a surface of light and shade for cubical solidity, our ideas are naturally led to think of the extensive genius and talent of the artist. When we study the elements of geometry, we think of Euclid. When we speak of gravitation, we think of Newton. How, then, is it that when we study the works of God in creation, we stop short and do not think of God? It is from the error of the schools in having taught those subjects as accomplishments only and thereby separated the study of them from the Being who is the Author of them."

"The evil that has resulted from the error of the schools in teaching natural philosophy as an accomplishment only has been that of generating in the pupils a species of atheism. Instead of looking through the works of creation to the Creator Himself, they stop short and employ the knowledge they acquire to create doubts of His existence. They labor with studied ingenuity to ascribe everything they behold to innate properties of matter and jump over all the rest by saying that matter is eternal."

"The atheist who affects to reason, and the fanatic who rejects reason, plunge themselves alike into inextricable difficulties. The one perverts the sublime and enlightening study of natural philosophy into a deformity of absurdities by not reasoning to the end. The other loses himself in the obscurity of metaphysical theories, and dishonours the Creator, by treating the study of his works with contempt. The one is a half-rational of whom there is some hope, the other a visionary to whom we must be charitable. When at first thought we think of a creator our ideas appear to us undefined and confused; but if we reason philosophically, those ideas can be easily arranged and simplified. It is a Being, whose power is equal to his will."

"History of science"

"Philosophy"

"The first formulation of (part of) mechanics by means of a variational principle... is due to Maupertuis in 1746 in a paper called "Les lois du mouvement et du repos déduites d'un principe métaphysique" (Laws of motion and rest deduced from a metaphysical principle). Maupertuis had first introduced the principle of least action in optics in 1744. ...Through experimentation, he found that this quantity depends on mass, velocity, and distance. He called the product of the three factors "action" and accordingly expressed a "principle of the least quantity of action"..."

"Of no little importance are Euler's labors in analytical mechanics. ...He worked out the theory of the rotation of a body around a fixed point, established the general equations of motion of a free body, and the general equation of hydrodynamics. He solved an immense number and variety of mechanical problems, which arose in his mind on all occasions. Thus on reading Virgil's lines. "The anchor drops, the rushing keel is staid," he could not help inquiring what would be the ship's motion in such a case. About the same time as Daniel Bernoulli he published the Principle of the Conservation of Areas and defended the principle of "least action," advanced by P. Maupertius. He wrote also on tides and on sound."

"Let the mass of the projectile be M, and let its speed be v while being moved over an infinitesimal distance ds. The body will have a momentum Mv that, when multiplied by the distance ds, will give , the momentum of the body integrated over the distance ds. Now I assert that the curve thus described by the body to be the curve (from among all other curves connecting the same endpoints) that minimizes\int Mv\,dsor, provided that M is constant along the path,M\int v\,ds."

"After having worked in the theory of light and gravitation, he announced, in 1744, a new minimum principle, the Principle of Least Action, from which he claimed he could deduce the behavior of light and masses in motion. The principle asserts that nature always behaves so as to minimize an integral known technically as action, and amounting to the integral of the product of mass, velocity, and distance traversed by a moving object. From this principle he deduced the Newtonian laws of motion. With sometimes suitable and sometimes questionable interpretation of the quantities involved, Maupertuis managed to show that optical phenomena, too, could be deduced from this principle. Hence, to an extent at least, he succeeded in uniting the optics of the eighteenth century and mechanical phenomena. ... Maupertuis advocated his principle for theological reasons. ...He ...proclaimed his principle to be not only a universal law of nature but also the first scientific proof of the existence of God, for it was "so wise a principle as to be worthy only of a Supreme Being."

"The minimum principle that unified the knowledge of light, gravitation, and electricity of Hamilton's time no longer suffices to relate these fundamental branches of physics. Within fifty years of its creation, the belief that Hamilton's principle would outlive all other physical laws of physics was shattered. Minimum principles have since been created for separate branches of physics... but these are not only restricted... but seem to be contrived... The hope of revising the principle so that it will achieve the unification... still drives mathematicians. This is the problem to which... Einstein devoted the last years of his life. Stripped of the theological associations, the belief of a minimum principle still activates physical science. ... A single minimum principle, a universal law governing all processes in nature, is still the direction in which the search for simplicity is headed, with the price of simplicity now raised from a mastery of differential equations to a mastery of the calculus of variations."

"Maupertuis really had no principle, properly speaking, but only a vague formula, which was forced to do duty as the expression of different familiar phenomena not really brought under one conception. ...Maupertuis' performance, though it had been unfavorably criticized by all mathematicians, is, nevertheless, sort of invested with a sort of historical halo. It would seem almost as if something of the pious faith of the church had crept into mechanics. However, the mere endeavor to gain a more extensive view... was not altogether without results. Euler, at least, if not also Gauss, was stimulated by the attempt of Maupertuis."

"Euler's view is, that the purposes of the phenomena of nature afford as good a basis of explanation as their causes. If this position is taken, it will be presumed a priori that all natural phenomena present a maximum or a minimum. ...in the solution of mechanical problems... it is possible... to find the expression which in all cases is made maximum or minimum. Euler is thus not led astray... and proceeds much more scientifically than Maupertuis. He seeks an expression whose variation put = 0 gives the ordinary equations of mechanics. For a single body moving under the action of forces Euler finds the requisite expression in the formula ∫vds, where ds denotes the element of the path and v the corresponding velocity. This expression is smaller for the path actually taken... therefore, by seeking the path that makes ∫vds a minimum, we can also determine the path. ...In the simplest cases Euler's principle is easily verified. ... The consideration of the motion of a projectile... will also show that the quantity ∫vds is smaller for the parabola than for any other neighboring curve; smaller, even, than for the straight line... between the same terminal points. ... Jacobi pointed out that we cannot assert that ∫vds for the actual motion is a minimum, but simply that the variation of this expression, in its passage to an infinitely adjacent neighboring path, is = 0. ...unquestionably various other integral expressions may be devised that give by variation the ordinary equations of motion, without its following that the integral expressions in question must possess... any particular physical significance. The striking fact remains, however, that so simple and expression as ∫vds does possess the property mentioned."

"I must now explain what I mean by the quantity of action. A certain action is necessary for the carrying of a body from one point to another: this action depends on the velocity which the body has and the space which it describes; but it is neither the velocity nor the space taken separately. The quantity of action varies directly as the velocity and the length of path described; it is proportional to the sum of the spaces, each being multiplied by the velocity with which the body describes it. It is this quantity of action which is here the true expense (dépense) of nature, and which she economizes as much as possible in the motion of light."

"After so many great men have worked on this subject, I almost do not dare to say that I have discovered the universal principle upon which all these laws are based, a principle that covers both elastic and inelastic collisions and describes the motion and equilibrium of all material bodies. This is the principle of least action, a principle so wise and so worthy of the supreme Being, and intrinsic to all natural phenomena; one observes it at work not only in every change, but also in every constancy that Nature exhibits. In the collision of bodies, motion is distributed such that the quantity of action is as small as possible, given that the collision occurs. At equilibrium, the bodies are arranged such that, if they were to undergo a small movement, the quantity of action would be smallest. The laws of motion and equilibrium derived from this principle are exactly those observed in Nature. We may admire the applications of this principle in all phenomena: the movement of animals, the growth of plants, the revolutions of the planets, all are consequences of this principle. The spectacle of the universe seems all the more grand and beautiful and worthy of its Author, when one considers that it is all derived from a small number of laws laid down most wisely. Only thus can we gain a fitting idea of the power and wisdom of the supreme Being, not from some small part of creation for which we know neither the construction, usage, nor its relationship to other parts. What satisfaction for the human spirit in contemplating these laws of motion and equilibrium for all bodies in the universe, and in finding within them proof of the existence of Him who governs the universe!"

"When a change occurs in Nature, the quantity of action necessary for that change is as small as possible. The quantity of action is the product of the mass of the bodies times their speed and the distance they travel. When a body is transported from one place to another, the action is proportional to the mass of the body, to its speed and to the distance over which it is transported."

"It [science] has as its highest principle and most coveted aim the solution of the problem to condense all natural phenomena which have been observed and are still to be observed into one simple principle, that allows the computation of past and more especially of future processes from present ones. ...Amid the more or less general laws which mark the achievements of physical science during the course of the last centuries, the principle of least action is perhaps that which, as regards form and content, may claim to come nearest to that ideal final aim of theoretical research."

"Fermat making use of the argument that Nature could not be wasteful, and was bound for this reason to cause the rays of light to travel between two points in the shortest time possible, was able to deduce from this proposition the laws of reflexion and refraction. Though we do not now attach any weight to the premise, we accept the conclusion."

"There are certain general principles or theorems in mechanics, such as Lagrange's equations, Hamilton's principle, the principle of least work, and Gauss' principle of least constraint, which afford general solutions of certain types of problems. Such general principles have therefore the advantage over ordinary methods in that once having found the general solution, any particular problem may be solved by merely routine processes."

"We find... that Mie's Electrodynamics exists in a compressed form in Hamilton's Principle—analogously to the manner in which the development of mechanics attains its zenith in the principle of action. Whereas in mechanics, however, a definite function L of action corresponds to every given mechanical system and has to be deducted from the constitution of the system, we are here concerned with a single system, the world. This is where the real problem of matter takes its beginning: we have to determine the "function of action," the world-function L, belonging to the world. For the present it leaves us in perplexity. If we choose an arbitrary L, we get a "possible" world governed by this function of action, which will be perfectly intelligible to us—more so than the actual world—provided that our mathematical analysis does not fail us. We are, of course, then concerned in discovering the only existing world, the real world for us. Judging from what we know of physical laws, we may expect the L which belongs to it to be distinguished by having simple mathematical properties. Physics, this time as a physics of fields, is again pursuing the object of reducing the totality of natural phenomena to a single physical law: it was believed that this goal was almost within reach once before when Newton's Principia, founded on the physics of mechanical point-masses was celebrating its triumphs. But the treasures of knowledge are not like ripe fruits that may be plucked from a tree."

"Above all, the ominous clouds of those phenomena that we are with varying success seeking to explain by means of the quantum of action, are throwing their shadows over the sphere of physical knowledge, threatening no one knows what new revolution."

"The present investigations are concerned with the history of the Principle of Least Action in the hands of Maupertuis, Euler, and others. The subject is of great importance in the history of mechanics, both because the principle of least action became, in the hands of Lagrange, "the mother," as Jacobi expressed it, "of our analytical mechanics," and because the animistic tendency displayed in the search for a maximum or a minimum principle in physics undoubtedly had a great influence on such moulders of mechanical theory as Euler, Lagrange (in his early work), Hamilton, Gauss, and in our own times, Willard Gibbs. ...much in this chapter of the evolution of mechanics—one may even say, of thought in general—has been misquoted or misunderstood by even eminent authorities."

"Besides Lagrange's early printed works, his correspondence with Euler allows us to form some impression of the stimulating effect which the principle of least action had on Lagrange's mind at the beginning of his career. Lagrange's correspondence with Euler extends from 1754... to 1775... Already in 1754 Lagrange announces that he has made "some observations about the maxima and minima which are in the actions of nature." In a letter of August 12, 1755 Lagrange informs Euler that he had a new and simpler method of solving isoperimetrical problems and gives a full statement of it. This discovery of what was afterwards called "the calculus of variations" certainly gave the principle of least action an additional attractiveness to Lagrange; he speaks in a letter of May 19, 1756, of his meditations "on the application of the principle of least action to the whole of dynamics." Lagrange's interest in the principle of least action seems to have evaporated when he observed that, when developed, the integrand is the variational form of d'Alembert's principle, and that it is simpler and equally effective to start with the equations of motion divorced from the integration. This is Lagrange's point of view in 1788. The earliest date at which this change in point of view is... 1764. In a letter of Sept 15, 1782, to Laplace, Lagrange says that he has almost finished a mechanical treatise uniquely founded on "the principle or formula" given in... his memoir of 1780 on the libration of the moon."

"Maupertuis's first enunciation of the law of the least quantity of action was in a memoir read to the French Academy on April 15th, 1744, entitled "Accord de différentes Loix de la Nature qui avoient jusqu'ici paru incompatibles." The laws in question appear to be those of the reflection and of the refraction of light. When a ray of light in a uniform medium travels from one point to another, either without meeting an obstacle or with meeting a reflecting surface, nature leads it by the shortest path and in the shortest time. But when a ray is refracted by passing from a uniform medium to one of different density, the ray neither describes the shortest space nor does it take the shortest time about it. As Fermat showed, the time would be the shortest if light moved more quickly in rarer media, but Newton proved that, as Descartes had believed, light moves more quickly in denser media. Maupertuis's discovery was that light neither takes always the shortest path nor always that path which it describes in the shortest time, but "that for which the quantity of action is the least.""

"In order to understand the significance of Action, let us consider any mechanical system passing from an initial configuration P to a final configuration Q. Classical science defined the action A of this system as the difference between its total kinetic energy... and its total potential energy... taken at every instant and then summated over the entire period of time during which the system passed from the initial state P to the final state Q. Now the total kinetic and potential energies of the system at any instant are given by\iiint\,T\,dx\,dy\,dz~ ~and~ \iiint\,V\,dx\,dy\,dz,where T and V represent the densities of the kinetic and potential energies of every point throughout the space occupied by the system. Accordingly, the expression of the action will be given byA = \iiiint\,(T-V)\,dx\,dy\,dz\,dt~ ~or~ \iiiint\,L\,dx\,dy\,dz\,dt....we have merely replaced (T - V) by a single letter L... referred to as the function of action (also called Lagrangian function). Roughly speaking, action was thus in the nature of the product of a duration by an energy contained in a volume of space. On no account may this action be confused with the action dealt with in Newton's law of action and reaction, also expressible as the principle of conservation of momentum. Still less may it be confused with the term "action" which appears in philosophical writings. ...the laws of mechanics can be expressed in a highly condensed form when the concept of action is introduced. Various forms may be given to the principle of Action; here we consider only the form... called Hamilton's Principle of Stationary Action. If we restrict our attention to the very simplest case, we may state Hamilton's principle as follows: If we consider all the varied paths along which a conservative system may be guided, so that it will pass in a given time from a definite initial configuration P to a definite configuration Q, we shall find that the course the system actually follows, of its own accord, is always such that along it the action is a minimum (or a maximum). ...the principle of action issues ...from the laws of classical mechanics ...A priori, we have no means of deciding whether the laws governing physical phenomena of a non-mechanical nature—those of electromagnetics, for example—would issue from the same principle of action."

"When Maxwell had proved that his equations of electromagnetics could be thrown into a form compatible with the principle of action, and when he succeeded in amalgamating electricity, magnetism and optics into one science, the universal validity of the principle was accepted. Inasmuch as this principle includes that of the conservation of energy, we can understand why the principle of action was often referred to as the supreme principle of physical science. ...when the principle of action is satisfied by a phenomenon, an indefinite of different mechanical interpretations of the phenomenon are theoretically possible. In the case of electrodynamic phenomena, however, in view of the complicated hypotheses which he was compelled to postulate, Maxwell abandoned all attempts to discover the precise mechanical interpretation which would correspond to reality."

"The principle... imposes the condition that the natural evolution of any system must be such as to render the action a maximum or a minimum. Could we but express this condition in terms of the usual physical magnitudes, we should be enabled to map out in advance the series of intermediary states through which the phenomenon would pass. From this knowledge we should derive the expression of the laws which governed the evolution of the phenomenon. Here... a twofold problem presents itself. First, we must succeed in finding the correct mathematical expression for the action; and, secondly, we must be in a position to solve the purely mathematical problem of determining under what conditions the action will be a maximum or a minimum. Now all problems of maxima and minima are solve by means of the calculus of variations, a form of calculus we owe chiefly to Lagrange. According to the methods of this calculus, we establish under what conditions a magnitude is a maximum or minimum by discovering under what conditions it will be stationary. ... When a stone is thrown into the air, it ascends with decreasing speed, then seems to hesitate for a brief period of time as it hovers near the point of maximum height before it starts to fall back again towards the earth. During this brief period of hesitation at the apex of its trajectory, the stone is said to remain "stationary." We can recognize a stationary state by observing that when it is reached no perceptible changes take place over a short period of time. In this way, we understand the connection which exists between the stationary condition and the presence of a maximum or a minimum. In mathematics small variations are represented by the letter δ; hence the stationary condition of the action, or again, the principle of action, is expressed by\partial A = 0,~ ~i.e.,~\partial \iiiint\,L\,dx\,dy\,dz\,dt = 0....Lamor applied this method to the phenomena of electricity and magnetism and showed how Maxwell's laws of electrodynamics could be deduced from a suitable mathematical expression L defining the electromagnetic function of action."

"When the theory of relativity supplanted classical science, it was recognised that the classical equations of mechanics were only approximate, and it became necessary to reformulate the principle of action so as to render it compatible... This work was carried out by the pure mathematicians—by Klein and Hilbert in particular. It was then found that a principle of action differing but slightly from the classical one could be obtained."

"In classical science, it was strange to find that action... should yet present the artificial aspect of an energy in space multiplied by a duration. As soon, however, as we realise that the fundamental continuum of the universe is one of space-time and not one of separate space and time, the reason for the importance of the seemingly artificial combination of space with time in the expression for the action receives a very simple explanation. Henceforth, action is no longer energy in a volume of space multiplied by a duration; it is simply energy in a volume of the world, that is to say, in a volume of four-dimensional space-time. Designating a volume of space-time by d\omega, we haved\omega = dxdydzdt,so that our principle of action, \partial A = 0, becomes\partial \int\,L\,d\omega = 0.Now there is a perfect symmetry between the rôles of space and time."

"From the expression for the atom of energy or quantum hv, where h is a constant and v is the frequency of the radiation, it is obvious that there exist as many different types of quanta of energy as there exist different frequencies of radiation. There is no unique type of quantum of energy in nature. That which is universal is not the quantum of energy hv, but the constant h. It can be shown that Planck's constant h is not a mere number; it represents some definite abstract mathematical entity, and that entity is action. We must assume, therefore, that there exist atoms of action in nature, just as there exist atoms of matter. ...we must possess a fairly thorough understanding of what is meant by action, as also of the part this important entity plays in science. ...the atomicity of action ...suggests that change is always discontinuous ...a series of jerks or jumps."

"History of science"

"Classical mechanics"

"Hindu sciences have retired far away from those parts of the country conquered by us, and have fled to places which our hand cannot yet reach, to Kashmir, Benaras and other places."

"The Hindu systems of astronomy are by far the oldest, and that from which the Egyptians, Greeks, Romans, and even the Jews derived Hindus their knowledge."

"The motion of the stars calculated by the Hindus some 4500 years before vary not even a single minute from the modern tables of Cassini and Meyer."

"The Encyclopaedia of Diderot likewise suggested, in the article on India, that the"sciences may be more ancient in India than in Egypt"."

"Many of the advances in the sciences that we consider today to have been made in Europe were in fact made in India centuries ago."

"The sciences may be more ancient in India than in Egypt."

"INDIA'S work in science is both very old and very young: young as an independent and secular pursuit, old as a subsidiary interest of her priests."

"To make these complex calculations the Hindus developed a system of mathematics superior, in everything except geometry, to that of the Greeks. Among the most vital parts of our Oriental heritage are the “Arabic” numerals and the decimal system, both of which came to us, through the Arabs, from India. The miscalled “Arabic” numerals are found on the Rock Edicts of Ashoka (256 B.C.), a thousand years before their occurrence in Arabic literature."

"The decimal system was known to Aryabhata and Brahmagupta long before its appearance in the writings of the Arabs and the Syrians; it was adopted by China from Buddhist missionaries; and Muhammad Ibn Musa al-Khwarazmi, the greatest mathematician of his age (d. ca. 850 A.D.), seems to have introduced it into Baghdad. The oldest known use of the zero in Asia or EuropeI is in an Arabic document dated 873 A.D., three years sooner than its first known appearance in India; but by general consent the Arabs borrowed this too from India, and the most modest and most valuable of all numerals is one of the subtle gifts of India to mankind."

"Algebra was developed in apparent independence by both the Hindus and the Greeks; but our adoption of its Arabic name (al-jabr, adjustment) indicates that it came to western Europe from the Arabs—i.e., from India—rather than from Greece. The great Hindu leaders in this field, as in astronomy, were Aryabhata, Brahmagupta and Bhaskara. The last (b. 1114 A.D.), appears to have invented the radical sign, and many algebraic symbols. These men created the conception of a negative quantity, without which algebra would have been impossible; they formulated rules for finding permutations and combinations; they found the square root of 2, and solved, in the eighth century A.D., indeterminate equations of the second degree that were unknown to Europe until the days of Euler a thousand years later.14 They expressed their science in poetic form, and gave to mathematical problems a grace characteristic of India’s Golden Age."

"The Hindus were not so successful in geometry. In the measurement and construction of altars the priests formulated the Pythagorean theorem (by which the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the other sides) several hundred years before the birth of Christ. Aryabhata, probably influenced by the Greeks, found the area of a triangle, a trapezium and a circle, and calculated the value of π (the relation of diameter to circumference in a circle) at 3.1416—a figure not equaled in accuracy until the days of Purbach (1423-61) in Europe. Bhaskara crudely anticipated the differential calculus, Aryabhata drew up a table of sines, and the Surya Siddhanta provided a system of trigonometry more advanced than anything known to the Greeks."

"Chemistry developed from two sources—medicine and industry. Something has been said about the chemical excellence of cast iron in ancient India, and about the high industrial development of Gupta times, when India was looked to, even by Imperial Rome, as the most skilled of the nations in such chemical industries as dyeing, tanning, soap-making, glass and cement. As early as the second century B.C. Nagarjuna devoted an entire volume to mercury. By the sixth century the Hindus were far ahead of Europe in industrial chemistry; they were masters of calcination, distillation, sublimation, steaming, fixation, the production of light without heat, the mixing of anesthetic and soporific powders, and the preparation of metallic salts, compounds and alloys. The tempering of steel was brought in ancient India to a perfection unknown in Europe till our own times; King Porus is said to have selected, as a specially valuable gift for Alexander, not gold or silver, but thirty pounds of steel.22 The Moslems took much of this Hindu chemical science and industry to the Near East and Europe; the secret of manufacturing “Damascus” blades, for example, was taken by the Arabs from the Persians, and by the Persians from India."

"The Hindus seem to have been the first people to mine gold.... Much of the gold used in the Persian Empire in the fifth century before Christ came from India. Silver, copper, lead, tin, zinc and iron were also mined-iron as early as 1500 B.C. U The art of tempering and casting iron developed in India long before its known appearance in Europe; Vikramaditya, for example, erected at Delhi (ca. 380 A.D.) an iron pillar that stands untarnished today after fifteen centuries; and the quality of metal, or manner of treatment, which has preserved it from rust or decay is still a mystery to modern metallurgical science." Before the European invasion the smelting of iron in small char- coal furnaces was one of the major industries of India. The Industrial Revolution taught Europe how to carry out these processes more cheaply on a larger scale, and the Indian industry died under the competition... Europe looked upon the Hindus as experts in almost every line of manufacture—wood-work, ivory-work, metal-work, bleaching, dyeing, tanning, soap-making, glass-blowing, gunpowder, fireworks, cement, etc.21 China imported eyeglasses from India in 1260 A.D."

"It is India that gave us the ingenious method of expressing all numbers by ten symbols, each receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit."

"Said the great and magnanimous Laplace: 'It is India that gave us the ingenious method of expressing all numbers by ten symbols, each receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.'"

"In order to instill a proper and well-founded pride in Hindus, it is (once more) most important to restore the truth about Hindu history, especially about Hindu society's glorious achievements. In technology, it cannot match China, which was the world leader until a mere three, four centuries ago. But in abstract sciences like linguistics, logic, mathematics, Hindu culture has been the chief pioneer. In psychology, it is still unsurpassed, though this is not yet fully recognized in the West, the part of the world that still arbitrates on what can count as rational and scientific."

"In the Vedic Age, India was very religious, but it was also ahead of the rest in mathematics and astronomy. Thus, the geometry of the Shulba Sutras, geometrical appendices to the manuals of ritual (Shrauta Sutras), include the oldest known formulation of the theorem named after Pythagoras, developed in the context of Vedic altar-building. Modern Hindus are fond of recalling this scientific element in their tradition, e.g. by quoting Carl Sagan: “Hindu cosmology gives a time-scale for the earth and the universe which is consonant with that of modern scientific cosmology”, as opposed to the limited Biblical-Quranic cosmology, which was protected against more far-sighted alternatives by a vigilant religious orthodoxy."

"Sushruta described many surgical operations cataract, hernia, lithotomy, Caesarian section, etc. and 121 surgical instruments, including lancets, sounds, forceps, catheters, and rectal and vaginal speculums. Despite Brahmanical prohibitions he advocated the dissection of dead bodies as indispensable in the training of surgeons. He was the first to graft upon a torn ear portions of skin taken from another part of the body; and from him and his Hindu successors rhinoplasty the surgical reconstruction of the nose descended into modern medicine. "The ancient Hindus," says Garrison, "performed almost every major opera- tion except ligation of the arteries.""

"In the time of Alexander, says Garrison, "Hindu physicians and surgeons enjoyed a well-deserved reputation for superior knowledge and skill," and even Aristotle is believed by some students to have been indebted to them."

"Although it would seem as if we had already furnished sufficient proofs that modern science has little or no reason to boast of originality, yet before closing this volume we will adduce a few more to place the matter beyond doubt... In the famous and recent work of Christna et le Christ, we find the following tabulation: [...]"Mathematics.--They invented the decimal system, algebra, the differential, integral, and infinitesimal calculi. They also discovered geometry and trigonometry, and in these two sciences they constructed and proved theorems which were only discovered in Europe as late as the seventeenth and eighteenth centuries[...] [...]"Chemistry.--They knew the composition of water, and formulated for gases the famous law, which we know only from yesterday, that the volumes of gas are in inverse ratio to the pressures that they support. They knew how to prepare sulphuric, nitric, and muriatic acids; the oxides of copper, iron, lead, tin, and zinc; the sulphurets of iron, copper, mercury, antimony, and arsenic; the sulphates of zinc and iron; the carbonates of iron, lead, and soda; nitrate of silver; and powder. "Medicine.--Their knowledge was truly astonishing. In Tcharaka and Sousruta, the two princes of Hindu medicine, is laid down the system which Hippocrates appropriated later. Sousruta notably enunciates the principles of preventive medicine or hygiene, which he places much above curative medicine--too often, according to him, empyrical. Are we more advanced to-day? It is not without interest to remark that the Arab physicians, who enjoyed a merited celebrity in the middle ages--Averroes among others--constantly spoke of the Hindu physicians, and regarded them as the initiators of the Greeks and themselves. [...]"Surgery.--In this they are not less remarkable. They made the operation for the stone, succeeded admirably in the operation for cataract, and the extraction of the foetus, of which all the unusual or dangerous cases are described by Tcharaka with an extraordinary scientific accuracy. [...]"Architecture.--They seem to have exhausted all that the genius of man is capable of conceiving. Domes, inexpressibly bold; tapering cupolas; minarets, with marble lace; Gothic towers; Greek hemicycles; polychrome style--all kinds and all epochs are there, betokening the origin and date of the different colonies, which, in emigrating, carried with them their souvenirs of their native art." Such were the results attained by this ancient and imposing Brahmanical civilization.... Beside the discoverers of geometry and algebra, the constructors of human speech, the parents of philosophy, the primal expounders of religion, the adepts in psychological and physical science, how even the greatest of our biologists and theologians seem dwarfed! Name to us any modern discovery, and we venture to say, that Indian history need not long be searched before the prototype will be found of record."

"We catch a glimpse of the great river of science which never ceases to flow in India. For India has carried and scattered the data of intellectual progress for the whole world, ever since the pre-Buddhist period when she produced the Sankhya philosophy and the atomic theory."

"The skill of the Indian in the production of delicate woven fabrics ... in all manner of technical arts has from very early times enjoyed worldwide celebrity."

"Fakhr-i-Mudabbir gives primacy to the bow and the sword as the most effective weapons of the horseman. Both these weapons were of different varieties. Among them all, the Hindu sword was the best and most lustrous (gawhardartar). Their export to such distant areas as Ummayad Spain and Seljuq Anatolia too is attested. He also declares that there is no better lance than the Indian."

"It was India, not Greece, that taught Islam in the impressionable years of its youth, formed its philosophy and esoteric religious ideals, and inspired its most characteristic expression in literature, art and architecture."

"In the West they learnt from Plato and Aristotle and in India “Arab scholars sat at the feet of Buddhist monks and Brahman Pandits to learn philosophy, astronomy, mathematics, medicine, chemistry and other subjects.” Caliph Mansur’s (754-76) zeal for learning attracted many Hindu scholars to the Abbasid court. A deputation of Sindhi representatives in 771 C.E. presented many treatises to the Caliph and the Brahma Siddhanta of Brahmagupta and his Khanda-Khadyaka, works on the science of astronomy, were translated by Ibrahim al-Fazari into Arabic with the help of Indian scholars in Baghdad. The Barmak (originally Buddhist Pramukh) family of ministers who had been converted to Islam and served under the Khilafat of Harun-ur-Rashid (786-808 C.E.) sent Muslim scholars to India and welcomed Hindu scholars to Baghdad. Once when Caliph Harun-ur-Rashid suffered from a serious disease which baffled his physicians, he called for an Indian physician, Manka (Manikya), who cured him. Manka settled at Baghdad, was attached to the hospital of the Barmaks, and translated several books from Sanskrit into Persian and Arabic. Many Indian physicians like Ibn Dhan and Salih, reputed to be descendants of Dhanapti and Bhola respectively, were superintendents of hospitals at Baghdad. Indian medical works of Charak, Sushruta, the Ashtangahrdaya, the Nidana, the Siddhayoga, and other works on diseases of women, poisons and their antidotes, drugs, intoxicants, nervous diseases etc. were translated into Pahlavi and Arabic during the Abbasid Caliphate. Such works helped the Muslims in extending their knowledge about numerals and medicine."

"Indian students should value their religious culture and of course, the classical Indian culture bears importantly on the meaning of life and values. I would not separate the two. To separate science and Indian culture would be harmful … I don’t think it is practical to keep scientific and spiritual culture separate."

"The conclusions of modern science are the very conclusions the Vedanta reached ages ago; only in modern science they are written in the language of matter. Today we find wonderful discoveries of modern science coming upon us like bolts from the blue, opening our eyes to marvels we never dreamt of. But many of these are only re-discoveries of what had been found ages ago. ... All science is bound to this conclusion in the long run. Manifestation, and not creation, is the word of science today, and the Hindu is only glad that what he has been cherishing in his bosom for ages is going to be taught in more forcible language, and with further light from the latest conclusions of science."

"Religious faith in the case of Hindus has never been allowed to run counter to scientific laws; moreover the former is never made a condition for the knowledge they teach, but they are always scrupulously careful to take into consideration the possibility that by reason both the agnostic and atheist may attain truth in their own ways."

"...In manufacture, India was the first to make cotton and purple [dye], it was proficient in all works of jewelry, and the very word 'sugar', as well as the article itself, is the product of India. Lastly she has invented the game of chess and the cards and the dice."

"The Hindus no less than the Greeks have shared in the work of constructing scientific concepts and methods in the investigation of physical phenomena , as well as of building up a body of positive knowledge which has been applied to industrial technique; and Hindu scientific ideas and methodology (e.g. the inductive method or methods of algebraic analysis) have deeply influenced the course of natural philosophy in Asia—in the East as well as the West—in China and Japan, as well as in the Saracen empire."

"After these conversations with Tagore some of the ideas that had seemed so crazy suddenly made much more sense. That was a great help for me."

"Long before it became a scientific aspiration to estimate the age of the earth, many elaborate systems of the world chronology had been devised by the sages of antiquity. The most remarkable of these occult time-scales is that of the ancient Hindus, whose astonishing concept of the Earth's duration has been traced back to Manusmriti, a sacred book."

"Now Mayow, like Boyle, conceived the air as made up of minute particles, while he restricted himself to two varieties, those, namely, which are necessary to life, called by him "spiritus igno-aereus," and those incapable of supporting respiration or combustion, which are left after the removal of this "spiritus." Since a mixture of saltpetre and sulphur continued burning even under water, he assumed that his igno-aereal particles must also be contained in the salt. Acids too contained the new principle. ...Mayow died in 1679 at the age of thirty-four years; had he lived but a little longer, it can scarcely be doubted that he would have forestalled the revolutionary work of Lavoisier, and stifled the theory of phlogiston at its birth. As it was, his work, though rendered in one of the most luminous and convincing scientific publications of the period, was immediately forgotten, and so proved of little effect on the evolution of our modern chemical system."

"If I were giving this lecture fifty years from now, the word "gravitation" would be as old-fashioned as the word "phlogiston" is to us. Relativity has certainly demoted gravitation as a real explanation, just as Priestley's and Lavoisier's analyses and decoding of chemical reactions destroyed the word "phlogiston.""

"From inflammable air and dephlogisticated air water is produced."

"One of the most fundamental principles of Lavoisier's chemistry was the use of numbers, notably in relation to what we often call today the principle of ... The principle implies that the experimenter must not only keep account of all the reacting solids and liquids, but also the gases—that is, all of the products. ...This rule led to quantitative experiments. Lavoisier was not the first person to use numbers in chemistry but he was a pioneer in using such numerical measurements as the basis of his system of chemistry. ...When Lavoisier first announced this law, chemists generally believed in... "phlogiston" which supposedly entered into chemical reactions (such as combustion) but had no weight. It was a radical step, therefore, for Lavoisier to base a system of chemistry on a balance of weights and to maintain that chemistry is not concerned with weightless "substances." ...this was indeed a chemical revolution."

"Intelligent design... is not a scientific argument at all, but a religious one. It might be worth discussing in a class on the history of ideas, in a philosophy class on popular logical fallacies, or in a comparative religion class on origin myths from around the world. But it no more belongs in a biology class than alchemy belongs in a chemistry class, phlogiston in a physics class or the stork theory in a sex education class. In those cases, the demand for equal time for "both theories" would be ludicrous. Similarly, in a class on 20th-century European history, who would demand equal time for the theory that the Holocaust never happened?"

"My thesis, paradoxically, and a little provocatively, but nonetheless genuinely, is simply this:PROBABILITY DOES NOT EXIST.The abandonment of superstitious beliefs about the existence of Phlogiston, the Cosmic Ether, Absolute Space and Time, ... , or Fairies and Witches, was an essential step along the road to scientific thinking. Probability, too, if regarded as something endowed with some kind of objective existence, is no less a misleading misconception, an illusory attempt to exteriorize or materialize our true probabilistic beliefs."

"Some hold that fundamental ideas have changed so often within science—especially within physics—that we should always expect our current views to turn out to be wrong. Sometimes this argument is called the “pessimistic meta-induction.” The prefix “meta” is misleading here, because the argument is not an induction about inductions; it’s more like an induction about explanatory inferences. So let’s call it "the pessimistic induction from the history of science." The pessimists give long lists of previously posited theoretical entities like phlogiston and caloric that we now think do not exist... Optimists reply with long lists of theoretical entities that once were questionable but which we now think definitely do exist—like atoms, germs, and genes."

"Lacan goes wrong by relying (quite uncritically!) on Saussure's signifier-signified conception of language. It is understandable that Lacan, when he began to write in the 1930s, should learn Saussure's turn-of-the-century linguistics. But even at the end of his life he and now his followers write about signifiers and signifieds as though the Chomskyan revolution in linguistics had never happened. Contemporary literary theorists tirelessly quote Saussure. But why? Today's linguists no more use Saussure's model than today's physicists use the concept of phlogiston. ...My point is not that Chomsky is right but that Saussure and Lacan are wrong."

"When Priestley described his discovery... he introduced... an open admission of the role of randomness in his work—even including a subtle dig at the theoretical, synthetic mode of Newton and his followers:More is owing to what we call chance... to the observation of events arising from unknown causes, than to any proper design, or preconceived theory in this business. ......But ...Priestley himself was trapped in a preconceived theory ...almost entirely unfounded, though he clung to it for the rest of his life. ...Priestley seared it directly into the name he gave his pure air: dephlogisticated air. That awkward name came from the closest thing to a dominant research paradigm in... : the phlogiston theory, one of the all-time classics in the history of human error."

"The same point can be made at least equally effectively in reverse: there is no such thing as research without counterinstances. For what is it that differentiates normal science from science in a crisis state? Not, surely, that the former confronts no counterinstances. On the contrary, what we previously called the puzzles that constitute normal science exist only because no paradigm that provides a basis for scientific research ever completely resolves all its problems. The very few that have ever seemed to do so (e.g., geometric optics) have shortly ceased to yield research problems at all and have instead become tools for engineering. Excepting those that are exclusively instrumental, every problem that normal science sees as a puzzle can be seen, from another viewpoint, as a counterinstance and thus as a source of crisis. Copernicus saw as counterinstances what most of Ptolemy’s other successors had seen as puzzles in the match between observation and theory. Lavoisier saw as a counterinstance what Priestley had seen as a successfully solved puzzle in the articulation of the phlogiston theory. And Einstein saw as counterinstances what Lorentz, Fitzgerald, and others had seen as puzzles in the articulation of Newton’s and Maxwell’s theories. Furthermore, even the existence of crisis does not by itself transform a puzzle into a counterinstance. There is no such sharp dividing line. Instead, by proliferating versions of the paradigm, crisis loosens the rules of normal puzzle-solving in ways that ultimately permit a new paradigm to emerge. There are, I think, only two alternatives: either no scientific theory ever confronts a counterinstance, or all such theories confront counterinstances at all times."

"All ['s] calculation is founded on the supposition that the calcination of metals is the result of the loss of phlogiston. But what I have been saying (...well known by now) is that this loss of phlogiston, even in the presence of metals is, according to me, nothing but pure supposition. What is more real, what can be known, by the balance and direct measurements, is that in all metallic s, whether made in the dry or humid way, whether... with the aid of air or water, or by means of acids, there is an augmentation of weight of the metal... due to the addition of vital air, or specifically the oxygen principle."

"Finding air necessary for the of fire, Scheele first turned his attention to its analysis; he found that solution of liver of sulphur, and certain other sulphureous compounds, occasioned a diminution in the bulk of air, to which they were exposed, equal to one part in about five, the flame of hydrogen and that sulphur caused a similar decrease of bulk in air standing over water, and lime-water not being rendered in either case turbid by the residuums, no fixed air was formed. He then obtains empyreal air (oxygen) by the decomposition , and other processes; describes the method of transferring, collecting, and examining the gases, and endeavours to prove that heat is a compound of empyreal air and phlogiston; he also shows by direct experiments, that the absorption occasioned in atmospheric air by liver of sulphur, is referrible to the abstraction of its empyreal portion; that it totally absorbs empyreal air, and that, upon adding to the residuary portion of atmospheric air, a quantity of empyreal air, equal to that absorbed by the sulphureous liquor, an air is again compounded, similar in all respects to that of the atmosphere. The identity of these investigations with those of Priestley will not fail of being observed, but... although Priestley was in the field a little before him, Scheele was unacquainted with his proceedings."

"The state of the science at present more nearly resembles the condition of a hundred years ago than the majority of chemists imagine. The latest development of organic chemistry, especially since the great activity in the dye and colour industries, resembles the last stage of the phlogistic period, when new compounds of great importance were being continually discovered, but the quantitative relations between the bodies used in their preparation were considered only as they influenced the yield of the product sought. As Lavoisier introduced weight and measure into the chemistry of the phlogistians, so will the new doctrine of the action of mass determine the direction of the science in the future."

"In 1774, Scheele obtained a yellow gas by digesting marine acid with manganese (manganese dioxide). As Scheele supposed that the manganese withdrew phlogiston from the acid, he called the new gas dephlogisticated marine acid. When, at a later time, phlogiston was regarded by some chemists as identical with , Scheele's view of the relation between the compositions of marine acid and the gas he obtained by the reaction of that acid with manganese oxide was interpreted to mean that the gas was produced by removing hydrogen from the acid. In accordance with his conception of the composition of acids, Lavoisier regarded muriatic acid to be a compound of oxygen; and in order to trace a likeness between the supposed composition of this acid and the compositions of other acids, he asserted that muriatic acid is formed by the union of oxygen with a hypothetical substance which he named radical muriatique. Lavoisier described the reaction between muriatic acid and manganese oxide as an oxidation of the acid; he said that the addition of a second dose of oxygen made the acid more volatile, but less acidic. He named Scheele's yellow gas acide muriatique oxygéné."

"The extension of Black's method by the physicist Lavoisier led to the downfall of the purely qualitative theory of phlogiston, and gave to chemistry the true methods of investigation, and its first great quantitative law—the law of ."

"The results of a scrutiny of the materials of chemical science from a mathematical standpoint are pronounced in two directions. In the first we observe crude, qualitative notions, such as fire-stuff, or phlogiston, destroyed; and at the same time we perceive definite measurable quantities such as fixed air, or oxygen, taking their place. In the second direction we notice the establishment of generalizations, laws, or theories, in which a mass of quantitative data is reduced to order and made intelligible. Such are the law of , the laws of chemical combination, and the atomic theory."

"In the course of my inquiries I was... soon satisfied that atmospherical air is not an unalterable thing; for that, according to my first hypothesis, the phlogiston with which it becomes loaded from bodies burning in it, and animals breathing it, and various other chemical processes, so far alters and depraves it, as to render it altogether unfit for inflammation, respiration, and other purposes to which it is subservient; and I had discovered that agitation in water, the process of vegetation, and probably other natural processes, restore it to its original purity."

"In aesthetic discourse, no interpretative-critical analysis, doctrine or programme is superseded, is erased, by any later construction. The Copernican theory did correct and supersede that of Ptolemy. The chemistry of Lavoisier makes untenable the early phlogiston theory. Aristotle on mimesis and pathos is not superseded by Lessing or Bergson. The Surrealist manifestos of Breton do not cancel out Pope's Essay on Criticism though they may well be antithetical to it."

"[M]etals remained the alchemists' chief concern... they seemed in their own way alive, whereas the calces (s) from which they were manufactured crumbled to dust and looked like cinders. Theory at once suggested a natural analogy. The metal was formed from the calx by the incorporation of or spirit; and this theory of metal-formation long remained in favour, being revived around 1700 as the 'phlogiston' theory. The central problem about metals was to identify the volitile constituents which combined with the calces to form the finished metal. For a long time, the status of quicksilver was ambiguous... resembling much more the volitile reagents which corrode metallic surfaces: mercury, in fact, forms an amalgam with other metals, and is even capable of dissolving gold... So the Alchemy of Avicenna classed mercury as a 'spirit' rather than a 'body'..."

"This statement appears to us to be conclusive with respect to the insufficiency of the undulatory theory, in its present state, for explaining all the phenomena of light. But we are not therefore by any means persuaded of the perfect sufficiency of the projectile system: and all the satisfaction that we have derived from an attentive consideration of the accumulated evidence, which has been brought forward, within the last ten years, on both sides of the question, is that of being convinced that much more evidence is still wanting before it can be positively decided. In the progress of scientific investigation, we must frequently travel by rugged paths, and through valleys as well as over mountains. Doubt must necessarily succeed often to apparent certainty, and must again give place to a certainty of a higher order; such is the imperfection of our faculties, that the descent from conviction to hesitation is not uncommonly as salutary, as the more agreeable elevation from uncertainty to demonstration. An example of such alternations may easily be adduced from the history of chemistry. How universally had phlogiston once expelled the aërial acid of Hooke and Mayow. How much more completely had phlogiston given way to oxygen! And how much have some of our best chemists been lately inclined to restore the same phlogiston to its lost honours! although now again they are beginning to apprehend that they have already done too much in its favour. In the mean time, the true science of chemistry, as the most positive dogmatist will not hesitate to allow, has been very rapidly advancing towards ultimate perfection."

"The calcination of a body is... the exposing of it to the action of fire, to produce some change upon it."

"The principal effects of fire in chemical operations are to carry off the volatile principles, and to separate them from the fixed, or to occasion the combustion of inflammable matters. Hence it follows that bodies are calcined either to deprive them of some volatile principle, or to destroy their inflammable principle, and sometimes for both of these purposes."

"We have examples of the first kind of calcination, in exposing calcareous earths and stones to the fire, to convert them into quicklime, which is effected by the entire evaporation of the watery principle contained in this kind of earth."

"The calcination of ', of ', of ', and of several other Salts, by fire, which deprives them of the water necessary for their crystallization; the roasting of minerals, by which the fire carries off the sulphur, , and other volatile contents; ought to be referred to the first kind of calcination."

"We have an example of the second kind of calcination, by exposing imperfect metals to fire; by which they lose their inflammable principle, their form, and metallic properties, and are changed into earthy matters called Metallic es."

"It is necessary to observe, that this second calcination differs essentially from the first, as the changes produced by it upon imperfect metals are not effected by evaporation, but by decomposition and destruction of their phlogiston. It is therefore a combustion, and not a volatilisation of their inflammable principle."

"Hence it follows, that the first kind of calcination may succeed without the contact of air and in close vessels, although it is more quick and complete in open vessels, from a property of air, by which it greatly accelerates the evaporation of volatile bodies. ...But as the second kind of calcination is a true combustion, like that of all inflammable bodies, it requires all the conditions necessary for combustion, and particularly the free access of air."

"There are many bodies, in the calcination of which an evaporation of volatile parts happens, and also a destruction or deprivation of their inflammable principle, although without any sensible combustion of this latter. Such particularly are all combinations of imperfect metallic matters with vitriolic and s: when these bodies are exposed to fire, their acid evaporates, and at the same time carries off with it their inflammable principle. We have examples of this kind of calcination in exposing to fire Martial Vitriol and Bezoar Mineral."

"Hitherto chemists are not agreed upon the number of simple principles or elements, of which all corporeal substances are composed. ...Others believe that earth and phlogiston are those principles which are the constituent parts of all corporeal substances. The greatest number seem to admit only the peripatetic elements."

"It appears from all these Experiments, that in each of them phlogiston, the simple inflammable principle, is present. It is well known, that Air attracts the inflammable part of bodies, and deprives them of it: not only this may be seen from the above Experiments, but it also appears that in the transition of what is inflammable principle into the Air, a considerable part of the Air is lost; but that what is inflammable principle is the sole cause of this effect, is evident..."

"It likewise appears that a given quantity of Air can be united to or saturated as it were only by a certain quantity of phlogiston..."

"Air is composed of two different fluids, the one of which attracts not the phlogiston, and the other has the quality of attracting it, and this latter fluid makes between a third and a fourth of the whole bulk of the air."

"These experiments seem to prove, that the transition of phlogiston into the air diminishes not always its bulk; which however other experiments clearly indicate..."

"Certainly it is a remarkable circumstance to observe, that the phlogiston separated from bodies, either without or with a fiery motion, and united with air, always considerably diminishes the bulk of air."

"It might be objected that the lost air is still contained in the residuum of air which could not farther be united with the phlogiston; for finding that kind of air lighter than common air, it might be supposed that the phlogiston when united with this air made it less ponderous, which circumstance is already known from other experiments. However, since phlogiston is a substance, (which always supposes some weight,) I very much doubt whether this hypothesis be founded on truth."

"Many chemists, even at the present day, find it impossible to do without certain collective names, analogous to the word phlogiston, for processes which they regard as belonging to the same class, or determined by the same cause. But instead of choosing for this purpose words which designate things, as was the custom till the end of the seventeenth... century, (phlogiston means, for example, fire, or light, and heat), they employ, since the time of Berthollet, terms which designate what are called "forces.""

"To investigate the essence of a natural phenomenon, three conditions are necessary. We must first study and know the phenomenon itself, from all sides; we must then determine in what relation it stands to other natural phenomena; and, lastly, when we have ascertained all these relations, we have to solve the problem of measuring these relations, and the laws of mutual dependence; that is, of expressing them in numbers. ...In the first period of chemistry, all the powers of men's minds were devoted to acquiring a knowledge of the properties of bodies; it was necessary to discover, observe, and ascertain their peculiarities. This is the alchemistical period. The second period embraces the determination of the mutual relations or connexions of these properties; and this is the period of phlogistic chemistry. In the third period, in which we now are, we ascertain by weight and measure, and express in numbers, the degree in which the properties of bodies are mutually dependent. The inductive sciences begin with the substance itself; then come just ideas; and lastly, mathematics are called in, and, with the aid of numbers, completes the work."

"We are... bound to attach the greatest importance to the preliminary step taken by Lavoisier, who is even more justly called the father of modern chemistry than Kepler is called the father of modern astronomy. The exact claims of Lavoisier to this important place in the history of chemistry have been variously stated: ...since his time, and greatly through his labours, the quantitative method has been established as the ultimate test of chemical facts; the principle of this method being the rule that in all changes of combination and reaction, the total weight of the various ingredients—be they elementary bodies or compounds—remains unchanged. The science of chemistry was thus established upon an exact, a mathematical basis. By means of this method Lavoisier, utilising and analysing the results gained by himself and others before him, notably those of Priestley, Cavendish, and Black, succeeded in destroying the older theory of combustion, the so-called phlogistic theory."

"In the time of Lavoisier, and preeminently through his exertions, this vague and unmeasurable principle phlogiston was eliminated from the laboratory and the textbooks: quantities took the place of indefinable qualities, and numerical determinations increased in frequency and accuracy. The vague phlogistic theory, which contained a germ of truth, but one which at that time could not be put into definite terms, had helped to gather up many valuable facts and observations: these were collected and restated in a new and precise language. It has been said that every science must pass through three periods of development. The first is that of presentiment, or faith; the second is that of sophistry; and the third is that of sober research."

"Even before the appearance of The Sceptical Chemist there was a growing conviction that the old hypotheses as to the essential nature of matter were inadequate and misleading. ...[T]he four "elements" of the Peripatetics had become merged into the tria prima—the "salt," "sulphur," and "mercury"—of the Paracelsians. As the phenomena of chemical action became better known... the conception of the tria prinui, as understood by Paracelsus and his followers, was incapable of being generalised into a theory of chemistry. Becher, while clinging to the conception of three primordial substances as making up all forms of matter, changed the qualities hitherto associated with them. According to the new theory, all matter was composed of a mercurial, a vitreous, and a combustible substance or principle, in varying proportions, depending upon the nature of the particular form of matter. When a body was burnt or a metal calcined, the combustible substance—the terra pinguis of Becher—escaped."

"This attempt to connect the phenomena of combustion and calcination with the general phenomena of chemistry was still further developed by Stahl, and was eventually extended into a comprehensive theory of chemistry, which was fairly satisfactory so long as no effort was made to test its sufficiency by an appeal to the balance."

"The theory of phlogiston was originally broached as a theory of combustion. According to this theory, bodies such as coal, charcoal, wood, oil, fat, etc., burn because they contain a combustible principle, which was assumed to be a material substance and uniform in character. This substance was known as phlogiston."

"All combustible bodies were to be regarded... as compounds, one of their constituents being phlogiston: their different natures depended partly upon the proportion of phlogiston they contain, and partly upon the nature and amount of their other constituents."

"A body, when burning, was parting with its phlogiston; and all the phenomena of combustion—the flame, heat, and light—were caused by the violence of the expulsion of that substance."

"Certain metals—as, for example, —could be caused to burn, and thereby to yield earthy substances, sometimes white in colour, at other times variously coloured. These earthy substances were called calces, from their general resemblance to lime."

"Other metals, like lead and mercury, did not appear to burn; but on heating them they gradually lost their metallic appearance, and became converted into calces. This operation was known as . In the act of burning or of calcination phlogiston was expelled. Hence metals were essentially compound: they consisted of phlogiston and a calx, the nature of which determined the character of the metal. By adding phlogiston to a calx the metal was regenerated. Thus, on heating the calx of zinc or of lead with coal, or charcoal, or wood, metallic zinc or lead was again formed. When a candle burns, its phlogiston is transferred to the air; if burned in a limited supply of air, combustion ceases, because the air becomes saturated with phlogiston."

"Respiration is a kind of combustion whereby the temperature of the body is maintained. It consists simply in the transference of the phlogiston of the body to the air. If we attempt to breathe in a confined space, the air becomes eventually saturated with the phlogiston, and respiration stops."

"The colour of a substance is connected with the amount of phlogiston it contains. Thus, when lead is heated, it yields a yellow substance (); when still further heated, it yields a red substance (red lead). These differences in colour were supposed to depend upon the varying amount of phlogiston expelled."

"The doctrine of phlogiston was embraced by nearly all Stahl's German contemporaries, notably by Marggraf, Neumann, Eller, and [Johann Heinrich] Pott. It spread into Sweden, and was accepted by Bergman and Scheele; into France, where it was taught by Duhamel, Rouelle, and Macquer; and into Great Britain, where its most influential supporters were Priestley and Cavendish. It continued to be the orthodox faith until the last quarter of the eighteenth century, when, after the discovery of oxygen, it was overturned by Lavoisier."

"During the sway of phlogiston chemistry made many notable advances... in spite of it. ...[U]ntil the time of Lavoisier few if any investigations were made with the express intention of testing it, or of establishing its sufficiency. When new phenomena were observed the attempt was no doubt made to explain them by its aid, frequently with no satisfactory result. Indeed, even in the time of Stahl facts were known which it was difficult or impossible to reconcile with his doctrine; but these were either ignored, or their true import explained away."

"It is commonly stated that the exception is a proof of the rule. The history of science can show many instances whereby the rule has been demolished by the exception. Little facts have killed big "theories, even as a pebble has slain a giant. During the reign of phlogiston a few of such facts were not unknown at least to some of the better informed of Stahl's followers."

"Some of the alchemists had discovered that a metal gained, not lost, weight by . This was known as far back as the sixteenth century. It had been pointed out by Cardan and by Libavius. Sulzbach showed that such was the case with mercury. Boyle proved it in the case of tin, and Rey in that of lead. Moreover, as knowledge increased it became certain that Stahl's original conception of the principle of combustion as a ponderable substance he imagined, with Becher, that it was of the nature of an earth was not tenable. The later phlogistians were disposed to regard it as probably identical with . But even hydrogen has weight, and facts seemed to require that phlogiston, if it existed at all, should be devoid of weight."

"Towards the latter half of the eighteenth century clearer views began to be held concerning the relations of atmospheric air to the phenomena of combustion and of calcination; many half-forgotten facts relating to these phenomena were recalled, and the inconsistencies and insufficiency of phlogiston as a dogma became gradually manifest. Three cardinal facts conspired to bring about its overthrow—the isolation of oxygen by Priestley; the recognition by him of the nature of atmospheric air, and of the fact that one of its constituents is oxygen; and, lastly, the discovery by Cavendish that water is a compound, and that its constituents are oxygen and . The significance of these facts was first clearly grasped by Lavoisier, and to him is due the credit of their true interpretation. By reasoning and experiment he proved conclusively that all ordinary phenomena of burning are so many instances of the combination of the oxygen of the air with the combustible substance; that calcination is a process of combination of the oxygen in the air with the metal, which thereby increases in weight by the amount of oxygen combined. Water no longer a simple substance is formed by the union, weight for weight, of oxygen and hydrogen. ...The phlogiston myth was thus exploded."

"Inspired by Lavoisier, a small band of French chemists Berthollet, Fourcroy, Guyton de Morveau thereupon set to work to remodel the system of chemistry and to recast its nomenclature so as to eliminate all reference to phlogiston. The very names "oxygen," "hydrogen," "nitrogen," corresponding respectively to the "dephlogisticated air," "phlogiston," and "phlogisticated air" of Priestley, were coined by the new French school."

"For a time le principe oxygine was regarded by this school in much the same relation as phlogiston was regarded by Stahl and his followers. The one fetich was exchanged for the other. The combustible principle—phlogiston—was renounced for the acidifying principle—oxygen. The new chemistry for a time centred itself round oxygen, just as the old chemistry had centred itself round phlogiston. The views of the French school met with no immediate acceptance in Germany, the home of phlogistonism, or in Sweden or England, possibly owing, to some extent, to national prejudices. The spirit of revolution, even although it might be an intellectual revolution, had not extended to these countries. Priestley, Cavendish, and Scheele could not be induced to accept the new doctrine. It was, however, accepted by Black, and its principles taught by him in Edinburgh; and before the end of the century it had practically supplanted phlogistonism in this country. Some of those who, like Kirwan, had energetically opposed the new theory ended by enthusiastically embracing it. Its introduction into Germany was mainly due to the influence of Klaproth."

"If someone associates with a true Pythagorean, what will he will get from him, and in what quantity? I would say: statesmanship, geometry, astronomy, arithmetic, harmonics, music, medicine, complete and god-given prophecy, and also the higher rewards — greatness of mind, of soul, and of manner, steadiness, piety, knowledge of the gods and not just supposition, familiarity with blessed spirits and not just faith, friendship with both gods and spirits, self-sufficiency, persistence, frugality, reduction of essential needs, ease of perception, of movement, and of breath, good color, health, cheerfulness, and immortality."

"It seems to me that they do well to study mathematics, and it is not at all strange that they have correct knowledge about each thing, what it is. For if they knew rightly the nature of the whole, they were also likely to see well what is the nature of the parts. About geometry, indeed, and arithmetic and astronomy, they have handed us down a clear understanding, and not least also about music. For these seem to be sister sciences; for they deal with sister subjects, the first two forms of being."

"They [the Pythagoreans] say the things themselves are Numbers and do not place the objects of mathematics between forms and sensible things. ...Since again, they saw that the modifications and the ratios of the musical scales were expressible in numbers—since, then, all other things seemed in their whole nature to be modelled on numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number... and the whole arrangement of the heavens they collected and fitted into their scheme; and if there was a gap anywhere, they readily made additions so as to make their whole theory coherent."

"These thinkers seem to consider that number is the principle both as matter for things and as constituting their attributes and permanent states."

"They thought they found in numbers, more than in fire, earth, or water, many resemblances to things which are and become; thus such and such an attribute of numbers is justice, another is soul and mind, another is opportunity, and so on; and again they saw in numbers the attributes and ratios of the musical scales. Since, then, all other things seemed in their whole nature to be assimilated to numbers, while numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number."

"It has fallen to the lot of one people, the ancient Greeks, to endow human thought with two outlooks on the universe neither of which has blurred appreciably in more than two thousand years. ...The first was the explicit recognition that proof by deductive reasoning offers a foundation for the structure of number and form. The second was the daring conjecture that nature can be understood by human beings through mathematics, and that mathematics is the language most adequate for idealizing the complexity of nature into appreciable simplicity. Both are attributed by persistent Greek tradition to Pythagoras in the sixth century before Christ. ...there is an equally persistent tradition that it was Thales... who first proved a theorem in geometry. But there seems to be no claim that Thales... proposed the inerrant tactic of definitions, postulates, deductive proof, theorem as a universal method in mathematics. ...in attributing any specific advance to Pythagoras himself, it must be remembered that the Pythagorean brotherhood was one of the world's earliest unpriestly cooperative scientific societies, if not the first, and that its members assigned the common work of all by mutual consent to their master."

"None of Pythagoras' own work has survived, but the ideas fathered on him by his followers would be the most potent in modern history. Pure knowledge, the Pythagoreans argued, was the purification (catharsis) of the soul... rising above the data of the human senses. The pure essential reality... was found only in the realm of numbers. The simple, wonderful proportion if numbers would explain the harmonies of music... [T]hey introduced the musical terminology of the octave, the fifth, the fourth, expressed as 2:1, 3:1, and 4:3. ..."

"In Copernicus' time Pythagoreans still believed that the only way to truth was by mathematics."

"The Pythagorean mathematical concepts, abstracted from sense impressions of nature, were... projected into nature and considered to be the structural elements of the universe. [Pythagoreans] attempted to construct the whole heaven out of numbers, the stars being... material points. ...they identified the regular geometric solids... with the different sorts of substances in nature. ...This confusion of the abstract and the concrete, of rational conception and empirical description, which was characteristic of the whole Pythagorean school and of much later thought, will be found to bear significantly on the development of the concepts of calculus. It has often been inexactly described as mysticism, but such stigmatization appears to be somewhat unfair. Pythagorean deduction a priori having met with remarkable success in its field, an attempt (unwarranted...) was made to apply it to the description of the world of events, in which the Ionian hylozoistic interpretations a posteriori had made very little headway. This attack on the problem was highly rational and not entirely unsuccessful, even though it was an inversion of the scientific procedure, in that it made induction secondary to deduction."

"Ionian philosophers... had sought to identify a first principle for all things. Thales had thought to find this in water, but others preferred to think of air or fire as the basic element. The Pythagoreans had taken a more abstract direction, postulating that number... was the basic stuff behind phenomena; this numerical atomism... had come under attack by the followers of Parmenides of Elea... The fundamental tenet of the was the unity and permanence of being... contrasted with the Pythagorean ideas of multiplicity and change. Of Parmenides' disciples the best known was Zeno the Eleatic... who propounded arguments to prove the inconsistency in the concepts of multiplicity and divisibility."

"We may... go to our... statement from Aristotle's treatise on the Pythagoreans, that according to them the universe draws in from the Unlimited time and breath and the void. The cosmic nucleus starts from the unit-seed, which generates mathematically the number-series and physically the distinct forms of matter. ...it feeds on the Unlimited outside and imposes form or limit on it. Physically speaking this Unlimited is [potential or] unformed matter... mathematically it is extension not yet delimited by number or figure. ...As apeiron in the full sense, it was... duration without beginning, end, or internal division—not time, in Plutarch's words, but only the shapeless and unformed raw material of time... As soon... as it had been drawn or breathed in by the unit, or limiting principle, number is imposed on it and at once it is time in the proper sense. ...the Limit, that is the growing cosmos, breathed in... imposed form on sheer extension, and by developing the heavenly bodies to swing in regular, repetitive circular motion... it took in the raw material of time and turned it into time itself."

"It is certain that the Theory of Numbers originated in the school of Pythagoras."

"Those who dwelt in the common auditorium adopted this oath: "I swear by the discoverer of the Tetraktys, which is the spring of all our wisdom; The perennial fount and root of Nature.""

"The tetrad was called by the Pythagoreans every number, because it comprehends in itself all the numbers as far as to the decad, and the decad itself; for the sum of 1, 2, 3, and 4, is 10. Hence both the decad and the tetrad were said by them to be every number; the decad indeed in energy, but the tetrad in capacity. The sum likewise of these four numbers was said by them to constitute the tetractys, in which all harmonic ratios are included. For 4 to 1, which is a quadruple ratio, forms the symphony bisdiapason; the ratio of 3 to 2, which is sesquialter forms the symphony diapente; 4 to 3, which is sesquitertian, the symphony diatessaron; and 2 to 1, which is a duple ratio, forms the diapason."

"Nicomachus... mentions the customary Pythagorean divisions of quantum and the science that deals with each. Quantum is either discrete or continuous. Discrete quantum in itself considered, is the subject of Arithmetic; if in relation, the subject of Music. Continuous quantum, if immovable, is the subject of Geometry; if movable, of Spheric (Astronomy). These four sciences formed the of the Pythagoreans. With the (which Nicomachus does not mention) of Grammar, Logic, and Rhetoric, they composed the seven liberal arts taught in the schools of the Roman Empire."

"The Neo-Pythagoreans treated all the divisions of philosophy. In Metaphysics they held that the Unit and the (indeterminate) Two are the basis of all things. the Unit being the form, and the Two the matter. ...The Unit being the prior principle may be identified with Deity, and, as such, was thought of either as the former [creator] of indefinite matter into individual things, or, as in Neo-Platonism, as the transcendent origin of the derivative Unit and Two. Another mode of conception was to identify the numbers with the Platonic Ideas and then to think of the Unit as comprehending them in the same manner as the mind comprehends its thoughts and gives them form. In Logic the Neo-Pythagoreans were for the most part imitators of Aristotle. Their Physics was Aristotelian and Stoic. Their Anthropology was Platonic. In Ethics and Politics they merely reechoed the Academy and the Lyceum with Stoic additions. In all this Neo-Pythagoreanism has little originality."

"Why was the Tetraktys so revered? Because to the eyes of the sixth century BC Pythagoreans, it seemed to outline the entire nature of the universe. In geometry — the springboard to the Greeks' epochal revolution in thought — the number 1 represented a point... 2 represented a line... 3 represented a surface... and 4 represented a three-dimensional tetrahedral solid... The Tetraktys, therefore appeared to encompass all the perceived dimensions of space."

"On the question whether mathematics was discovered or invented, Pythagoras and the Pythagoreans had no doubt — mathematics was real, immutable, omnipresent, and more sublime than anything that could conceivably emerge from the human mind. The Pythagoreans literally embedded the universe into mathematics. In fact, to the Pythagoreans, God was not a mathematician — mathematics was God! ...By setting the stage, and to some extent the agenda, for the next generation of philosophers — Plato in particular — the Pythagoreans established a commanding position in Western thought."

"As a moral philosopher, many of his precepts relating to the conduct of life will be found in the verses which bear the name of the Golden Verses of Pythagoras. It is probable they were composed by some one of his school, and contain the substance of his moral teaching. The speculations of the early philosophers did not end in the investigation of the properties of number and space. The Pythagoreans attempted to find, and dreamed they had found, in the forms of geometrical figures and in certain numbers, the principles of all science and knowledge, whether physical or moral. The figures of Geometry were regarded as having reference to other truths besides the mere abstract properties of space. They regarded the unit, as the point; the duad, as the line; the triad, as the surface; and the tetractys, as the geometrical volume. They assumed the pentad as the physical body with its physical qualities. They seem to have been the first who reckoned the elements to be five in number, on the supposition of their derivation from the five regular solids. They made the cube, earth; the pyramid, fire; the octohedron, air; the icosahedron, water; and the dodecahedron, aether. The analogy of the five senses and the five elements was another favourite notion of the Pythagoreans."

"Almost all the theories, religious philosophical and mathematical, taught by the Pythagoreans, were known in India in the sixth century BCE, and the Pythagoreans, like the Jains and the Buddhists, refrained from the destruction of life and eating meat."

"While most s emphasized the reality of change — in particular, the Atomists, followers of and Democritus — the Pythagoreans stressed the study of the unchangeable elements in nature and society. In their search for the eternal laws of the universe they studied geometry, arithmetic, astronomy, and music (the '). Their most outstanding leader was Archytas of Tarentum...and to whose school, if we follow... E. [Eva] Frank, much of the Pythagorean brand of mathematics may be ascribed. ...Numbers were divided into classes: odd, even, even-times-even, odd-times-odd, prime and composite, perfect, friendly, triangular, square, pentagonal, etc. ...Of particular importance was the ratio of numbers (logos, Lat. ratio). Equality of ratio formed a proportion. They discriminated between an arithmetical (2b = a + c), geometrical (b^2 = ac), and a harmonical (\frac{2}{b} = \frac{1}{a} + \frac{1}{c}) proportion that they interpreted philosophically and socially."

"The Pythagoreans knew some properties of s... how a plane can be filled by... regular triangles, squares, or regular hexagons, and space by cubes... [They] may also have known the regular oktahedron and dodekahedron—the latter figure because pyrite, found in Italy, crystallizes in dodekahedra, and models... date to Etruscan times."

"[T]he most striking result of the Greeks' faith that the world could be understood in terms of rational principles was the invention of abstract mathematics. The most grandiose ambition they conceived was to explain all the properties of Nature in arithmetical terms alone. This was the aim of the Pythagoreans... [T]hey... knew that the phenomena of the Heavens recurred in a cyclical manner; and... discovered ...that the sound of a vibrating string ...is simply related to the length ...and its 'harmonics' always go with simple fractional lengths. ...[S]ince the Pythagoreans were a religious brotherhood... they thought that this search would lead to more than explanations alone. If one discovered the mathematical harmonies in things, one should... discover how to put oneself in harmony with Nature. ...[T]hey had ...positive grounds for thinking that both astronomy and acoustics were at the bottom arithmetical; and the study of simple fractions was called 'music' right down until the late Middle Ages."

"It is usually maintained that the Platonic or Socratic philosophy, like the rest of Greek speculation, was original, indigenous, owing very little to any outside influence. But the quest and life and faith of Socrates were as un-Greek as anything could possibly be: that was one of the reasons why the Greeks killed him: the essence of his life belonged to a world unknown to them, and therefore dangerous in their eyes […] There is only one “philosopher” whose doctrines, both practical and theoretical, appear to have resembled Plato’s in spirit and aim as well as in substance; and that one is Pythagoras. It is noteworthy that Pythagoras is the only great thinker of Greece whom Plato never criticises, but of whom he speaks with the greatest deference and respect […] instancing him as the great example of a teacher whose teaching had in it living truth enough to inspire a band of devoted disciples, and to transform their lives as well as their beliefs. And every one of those doctrines, which we know formed the “gospel” of Pythagoras and of the Pythagorean brotherhood at Crotona, was an almost exact reproduction of the cardinal doctrines of the Indian Vidya and the Indian Yoga—so much so that Indian Vedantists today do not hesitate to claim Pythagoras as one of themselves, one of their great expounders, whose very name was only the Greek form of the Indian title Pitta Guru, or Father-Teacher.’"

"It has been no easy task to revise this volume in such a way as to make it more worthy of the favour with which it has been received. Most of it has had to be rewritten in the light of certain discoveries made since the publication of the first edition, above all, that of the extracts from Menon’s Iατρικά, which have furnished, as I believe, a clue to the history of Pythagoreanism."

"[T]he authority of Anaximenes was so great that both Leukippos and Demokritos adhered to his theory of a disc-like earth. ...This, in spite of the fact that the spherical form of the earth was already a commonplace in circles affected by Pythagoreanism."

"The main purpose of the Orgia was to "purify" the believer’s soul, and so enable it to escape from the "wheel of birth," and it was for... this end that the Orphics were organised in communities. Religious associations must have been known to the Greeks from a fairly early date; but the oldest of these were based... in theory, on the tie of kindred blood. What was new was the institution of communities to which any one might be admitted by initiation. This was, in fact, the establishment of churches, though there is no evidence that these were connected... such... that we could rightly speak of them as a single church. The Pythagoreans came nearer to realising that."

"[T]he religious revival... suggested the view that philosophy was above all a "way of life." Science too was a "purification," a means of escape from the "wheel." This is the view expressed so strongly in Plato’s Phaedo, which was written under the influence of Pythagorean ideas."

"The Phaedo is dedicated... to Echekrates and the Pythagorean society at Phleious, and it is evident that Plato in his youth was impressed by the religious side of Pythagoreanism, though the influence of Pythagorean science is not clearly marked till a later period."

"[A] good many fragments of... Aristoxenos and Dikaiarchos are embedded in the mass. These writers were both disciples of Aristotle; they were natives of Southern Italy, and contemporary with the last generation of the Pythagorean school. Both wrote accounts of Pythagoras; and Aristoxenos, who was personally intimate with the last representatives of scientific Pythagoreanism, also made a collection of the sayings of his friends."

"There is no reason to believe that the detailed statements which have been handed down with regard to the organisation of the Pythagorean Order rest upon any historical basis... The distinction of grades within the Order, variously called Mathematicians and Akousmatics, Esoterics and Exoterics, Pythagoreans and Pythagorists, is an invention designed to explain how there came to be two widely different sets of people, each calling themselves disciples of Pythagoras, in the fourth century B.C. So, too, the statement that the Pythagoreans were bound to inviolable secrecy, which goes back to Aristoxenos, is intended to explain why there is no trace of the Pythagorean philosophy proper before Philolaos."

"The Pythagorean Order was simply, in its origin, a religious fraternity... and not, as has sometimes been maintained, a political league. Nor had it anything to do with the "Dorian aristocratic ideal." Pythagoras was an Ionian, and the Order was originally confined to Achaian states. Nor is there the slightest evidence that the Pythagoreans favoured the aristocratic rather than the democratic party. The main purpose... was to secure for... members a more adequate satisfaction of the religious instinct than... the State religion. It was... an institution for the cultivation of holiness. ...[I]t resembled an Orphic society, though it seems that Apollo, rather than Dionysos, was the chief Pythagorean god. That is doubtless why the Krotoniates identified Pythagoras with Apollo Hyperboreios. ...[H]owever, an independent society within a Greek state was apt to be brought into conflict with the larger body. The only way in which it could then assert its right to exist was... by securing the control of the sovereign power. The history of the Pythagorean Order... is, accordingly, the history of an attempt to supersede the State..."

"When discussing the Pythagorean system, Aristotle always refers it to "the Pythagoreans," not to Pythagoras himself. ...[T]his was intentional ...Pythagoras himself is only thrice mentioned in the whole Aristotelian corpus, and in only one... is any philosophical doctrine ascribed to him. ...Aristotle ...is quite clear that what he knew as the Pythagorean system belonged in the main to the days of Empedokles, Anaxagoras, and Leukippos; for ...he goes on to describe the Pythagoreans as "contemporary with and earlier than them.""

"The Pythagoreans held, [Aristotle] tells us that there was "boundless breath" outside the heavens, and that it was inhaled by the world. In substance, this is the doctrine of Anaximenes, and... it was that of Pythagoras... Xenophanes denied it. ...[F]urther development of the idea is ...due to Pythagoras ...We are told that, after the first unit had been formed ...the nearest part of the Boundless was first drawn in and limited; and... the Boundless thus inhaled... keeps the units separate from each other. It represents the interval between them. This is a... primitive way of describing... discrete quantity."

"In... Aristotle... the Boundless is also... the void or empty. This identification of air and the void is a confusion... in Anaximenes... too. We find also... the other confusion... air and vapour. ...Pythagoras identified the Limit with fire, and the Boundless with darkness. We are told by Aristotle that Hippasos made Fire the first principle... Parmenides... attributes... two primary "forms," Fire and Night. ...Light and Darkness appear in the Pythagorean table of opposites under the heads of the Limit and the Unlimited respectively."

"The identification of breath with darkness ...is a strong proof of the primitive character of the doctrine; for in the sixth century darkness was supposed ...a sort of vapour, while in the fifth, its true nature was ...known. Plato... makes the Pythagorean Timaios describe mist and darkness as condensed air."

"[T]hink, then, of a "field" of darkness or breath marked out by luminous units ...which the starry heavens would naturally suggest."

"It is... probable that we should ascribe to Pythagoras the Milesian view of a plurality of worlds, though... not... infinite ...Petron, one of the early Pythagoreans, said there were ...a hundred and eighty-three worlds arranged in a triangle; and Plato makes Timaios admit, when laying down ...only one world, that something might be urged in favour of ...five, as there are five regular solids."

"Simplicius, with the poem of Parmenides before him, corrects Aristotle by substituting Light and Darkness for Fire and Earth... Parmenides... calls one "form" Light, Flame, and Fire, and the other Night, and we... consider whether these can be identified with the Pythagorean Limit and Unlimited. We have... reason to believe that... the world breathing belonged to the earliest form of Pythagoreanism, and... identifying this "boundless breath" with Darkness, which stands... for the Unlimited. "Air" or mist was always regarded as the dark element. And that which gives definiteness to the vague darkness is... light or fire, and this may account for the prominence given to that element by Hippasos. We may probably conclude... that the Pythagorean distinction between the Limit and the Unlimited... made its first appearance in this crude form. If... we identify darkness with the Limit, and light with the Unlimited, as most critics do, we get into insuperable difficulties."

"In the fourth century, the chief seat of the school is at Taras, and we find the Pythagoreans heading the opposition to Dionysios of Syracuse. ...[In] this period... Archytas... the friend of Plato... almost realised, if he did not suggest, the ideal of the . ...He was also the inventor of mathematical mechanics."

"At the same time, Pythagoreanism had taken root in Hellas. Lysis... remained at Thebes, where Simmias and Kebes had heard Philolaos, and there was an important community of Pythagoreans at Phleious. Aristoxenos was personally acquainted with the last generation of the school, and mentioned by name Xenophilos the Chalkidian from , with Phanton, Echekrates, Diokles, and Polymnestos of Phleious. They were all, he said, disciples of Philolaos and Eurytos. Plato was on friendly terms with these men, and dedicated the Phaedo to them. Xenophilos was the teacher of Aristoxenos..."

"It seems natural to suppose... the Pythagorean elements of Plato’s Phaedo and Gorgias come mainly from Philolaos. Plato makes Sokrates express surprise that Simmias and Kebes had not learnt from him why it is unlawful for a man to take his [own] life, and it seems to be implied that the Pythagoreans at Thebes used the word "philosopher" in the... sense of... seeking to find... release from the burden of this life? It is... probable that Philolaos spoke of the body... as the tomb... of the soul. ...[H]e taught the old Pythagorean religious doctrine in some form, and... likely... laid stress upon knowledge as a means of release. ...Plato ...is by far the best authority ...on the subject."

"We know... Philolaos wrote on "numbers"; for Speusippos followed him in the account he gave of the Pythagorean theories on that subject. It is probable... he busied himself... with arithmetic, and... his geometry was... primitive... Eurytos was his disciple, and... his views were... crude."

"Philolaos wrote on medicine, and... while... influenced by the... Sicilian school, he opposed them from the Pythagorean standpoint. ...[H]e said... our bodies were composed only of the warm... [O]nly after birth... the cold was introduced by respiration. The connexion... with the old Pythagorean theory is obvious. Just as the Fire in the macrocosm draws in and limits the cold dark breath which surrounds the world... so do our bodies inhale cold breath... Philolaos made , blood, and the causes of disease..."

"Philolaos... is a sufficiently remarkable figure... and has... been spoken of as a "precursor of Copernicus.""

"Plato was intimate with these men and was deeply impressed by their religious teaching, though... he did not adopt it... He was still more attracted by the scientific side of Pythagoreanism, and... this exercised a great influence on him. His own system in its final form had many points of contact with it, as he is careful to mark in the ' But... he is apt to develop Pythagoreanism on lines of his own, which may or may not have commended themselves to Archytas, but are no guide to the views of Philolaos and Eurytos. He is not careful... to claim the authorship of his own improvements in the system. He did not believe that cosmology could be an exact science, and he... therefore... credit[s] Timaios the Lokrian, or "ancient sages"... with theories which... had their birth in the Academy."

"Plato had many enemies and detractors, and this literary device enabled them to bring against him the charge of plagiarism. Aristoxenos... made the extraordinary statement that most of the Republic was... found in a work by Protagoras. ...He seems also... the... source of the story that Plato bought "three Pythagorean books" from Philolaos and copied the Timaeus out of them. ...[A]ccounts... imply... Plato bought... either a book by Pythagoras, or... notes of his teaching..."

"We know nothing of Timaios except what Plato tells us... and he may... be a fictitious character like the Eleatic Stranger."

"We are told that the other book which passed under the name of Pythagoras was really by Lysis."

"[W]e have... testimony that the five "Platonic figures,"... were discovered in the Academy. In the to Euclid... Pythagoreans only knew the , the pyramid (), and the , while the and the were discovered by Theaitetos."

"This sufficiently justifies... regarding the "fragments of Philolaos" with... more than suspicion."

"[W]e cannot safely take Plato as our guide to the original meaning of the Pythagorean theory, though... from him alone... we can learn to regard it sympathetically."

"Aristotle... was... out of sympathy with Pythagorean ways of thinking, but took... great... pains to understand them. This was... because they played so great a part in the philosophy of Plato and his successors, and he had to make the relation of the two doctrines as clear as he could to... his disciples."

"[W]e have to... interpret what Aristotle tells us in the spirit of Plato, and... consider how the doctrine... is related to the systems which had preceded it. ...[This] delicate operation... has been made... safer by recent discoveries in the early history of mathematics and medicine."

"Platonic elements which have crept into later accounts... are of two kinds. First... genuine Academic formulae... as... identification of the Limit and the Unlimited with the One and the Indeterminate Dyad; ...secondly ...the Neoplatonic doctrine which represents it as an opposition between God and Matter. ...[N]o one will any longer attribute these doctrines to the Pythagoreans of the fifth century."

"[T]he problem... is still extremely difficult."

"According to Aristotle, the Pythagoreans said Things are numbers, though that does not appear to be the doctrine of the fragments of "Philolaos." According to them, things have number, which make them knowable, while their real essence is... unknowable. ...[B]ut ...things are numbers seems meaningless. We have seen reason for believing that it is due to Pythagoras..., though we did not feel able to say... clearly what he meant..."

"There is no such doubt... [in] his school. Aristotle says they used the formula in a cosmological sense. The world... was made of numbers in the same sense as others had said it was made of "four roots" or "innumerable seeds." It will not do to dismiss this as mysticism."

"Whatever we may think of Pythagoras, the Pythagoreans of the fifth century were scientific men, and they must have meant something... definite. ...[T]hey used the words Things are numbers in a ...non-natural sense, but there is no difficulty in such a supposition."

"The Pythagoreans had... a great veneration for the... words of the Master... but... veneration is often accompanied by a singular licence of interpretation."

"Aristotle is... decided in his opinion that Pythagoreanism was intended to be a cosmological system like the others. "Though the Pythagoreans... made use of less obvious s and elements than the rest, seeing that they did not derive them from sensible objects, yet all their discussions and studies had reference to nature alone. They describe the origin of the heavens, and they observe the phenomena of its parts, all that happens to it and all it does." They apply their first principles entirely to these things, "agreeing... with the other natural philosophers in holding that reality was just what could be perceived by the senses, and is contained within the compass of the heavens," though "the first principles and causes of which they made use were... adequate to explain realities of a higher order than the sensible.""

"The doctrine is more precisely stated by Aristotle to be that the elements of numbers are the elements of things, and... therefore things are numbers. He is equally positive that these "things" are sensible things, and... are... the bodies of which the world is constructed. This construction... out of numbers was a real process in time, which the Pythagoreans described in detail."

"[T]he numbers were intended to be mathematical... though... not separated from... things of sense. ...[T]hey were not mere predicates of something else, but had an independent reality... "They did not hold that the limited and the unlimited and the one were... substances, such as fire, water... [etc.,] but... the unlimited itself and the one itself were the reality of the things of which they are predicated, and that is why they said that number was the reality of everything.""

"Accordingly the numbers are, in Aristotle’s own language, not only the formal, but also the material, cause of things. According to the Pythagoreans, things are made of numbers in the same sense as they were made of fire, air, or water in the theories of their predecessors."

"Aristotle notes that the point in which the Pythagoreans agreed with Plato was in giving numbers an independent reality of their own; while Plato differed from the Pythagoreans in holding that this reality was distinguishable from that of sensible things."

"Aristotle speaks of certain "elements"... of numbers, which were also the elements of things. ...Primarily, the "elements of number" are the Odd and the Even... identified in a somewhat violent way with the Limit and the Unlimited... the original principles of the Pythagorean cosmology. Aristotle tells us... the Even... gives things their unlimited character when... contained in them and limited by the Odd... [C]ommentators... understand... this to mean... the Even is... the cause of infinite divisibility. They get into great difficulties, however..."

"Simplicius... preserved an explanation, in all probability Alexander’s... that they called the even number unlimited "because every even is divided into equal parts, and what is divided into equal parts is unlimited in respect of bipartition; for division into equals and halves goes on '. But, when the odd is added, it limits it; for it prevents its division into equal parts.""

"[W]e must not impute to the Pythagoreans... that even numbers can be halved indefinitely. They had... studied the properties of the decad, and... must have known that... 6 and 10 do not admit of this."

"In this way, then, the Odd and the Even were identified with the Limit and the Unlimited, and it is possible... Pythagoras... had taken this step... by... Unlimited he meant something spatially extended, and... identified... with air, night, or the void, so we are prepared to find... his followers also thought of the Unlimited as extended."

"Aristotle... argues... if the Unlimited is... a reality, and not merely the predicate of some other reality, then every part of it must be unlimited... just as every part of air is air. The same thing is implied in his statement that the Pythagorean Unlimited was outside the heavens. Further than this, it is hardly safe to go."

"Philolaos and his followers cannot have regarded the Unlimited in the old Pythagorean way as Air; for... they adopted the theory of Empedokles as to that "element," and accounted for it otherwise. ...[T]hey can hardly have regarded it as an absolute void; for that conception was introduced by the Atomists. ...[T]hey meant by the Unlimited the ', without analysing that... further."

"As the Unlimited is spatial, the Limit must be spatial too, and we should... expect... the point... line, and... surface were regarded as... forms of the Limit. That was the later doctrine; but the characteristic feature of Pythagoreanism is... that the point was not... a limit, but... the first product of the Limit and the Unlimited, and was identified with the arithmetical unit. According[ly]... the point has one dimension, the line two, the surface three, and the solid four... [i.e.,] Pythagorean points have magnitude... lines breadth, and... surfaces thickness. The whole theory... turns on the definition of the point as a unit “having position." ...[O]ut of such elements ...it seemed possible to construct a world."

"[T]his way of regarding the point... line, and... surface is closely bound... with... representing numbers by dots... in symmetrical patterns... attribut[ed]... to the Pythagoreans."

"The science of geometry had... made considerable advances, but the old view of quantity as a sum of units had not been revised... so... [ such a] doctrine... was inevitable."

"Aristotle is... decided as to Pythagorean points having magnitude. "They construct the whole world out of numbers... but they suppose the units have magnitude. As to how the first unit with magnitude arose, they appear to be at a loss.""

"Aristotle criticises the Pythagoreans. They held, he says, that in one part of the world Opinion prevailed, while a little above it or below it were to be found Injustice or Separation or Mixture, each... a number. But in the very same regions of the heavens were... things having magnitude which were also numbers. How can this be, since Justice has no magnitude? This means... the Pythagoreans... failed to give... clear account of the relation between these... fanciful analogies and their quasi-geometrical construction of the universe."

"[W]hat distinguished the Pythagoreanism of this period from its earlier form was that it sought to adapt... to the new theory of "elements." ...[T]his ...makes it necessary ...to take up ...consideration of the system ...in connexion with the pluralists."

"When the Pythagoreans returned to Southern Italy, they must have found views... there which... demanded a partial reconstruction of their own system. ...Empedokles founded a philosophical society, but ...influence[d] ...the medical school of these regions; and ...Philolaos played a part in the history of medicine."

"The tradition is that the Pythagoreans explained the elements as built up of geometrical figures, a theory... in the more developed form... attained in Plato’s Timaeus. If they were to retain their position as... leaders of medical study... they were bound to account for the elements."

"[T]he Pythagorean construction of the elements was... that... in Plato’s Timaeus. ...[T]here is good reason for believing they only knew three of the regular solids, the , the pyramid (), and the . Plato starts from fire and earth, and... the construction οf the elements proceeds... such... that the and the can easily be transformed into pyramids, while the cube and the dodecahedron cannot. ...[I]t follows that, while air and water pass readily into fire, earth cannot... and the dodecaedron is reserved for another purpose... This would... suit the Pythagorean system; for it would leave room for a dualism... outlined in the Second Part of the poem of Parmenides."

"Hippasos made Fire the first principle, and... from the Timaeus... it would be possible to represent air and water as forms of fire. The other element is... earth, not air, as... it was in early Pythagoreanism. That would be a... result of the discovery of atmospheric air by Empedokles and of his general theory of the elements. It would... explain the... fact... that Aristotle identifies the two "forms" spoken of by Parmenides with Fire and Earth."

"The most interesting point in the theory is... the use... of the ... identified... with the "sphere of the universe," or... in the Philolaic fragment, with the "hull of the sphere." ...[I]t must be taken in close connexion with the word "" applied to the central fire. The structure of the world was compared to the building of a ship..."

"In the Phaedo we read that the "true earth,"... looked at from above, is "many-coloured like the balls that are made of twelve pieces of leather." In the Timaeus... "Further, as there is still one construction left, the fifth, God made use of it for the universe when he painted it." ...[T]he approaches more nearly to the than any other of the regular solids. The twelve pieces of leather used to make a ball would... be s; and, if the material were not flexible like leather, we should have a dodecahedron instead of a sphere. This points to the Pythagoreans having had at least the rudiments of the "" formulated later by Eudoxos."

"They must have studied the properties of circles by means of inscribed polygons and those of spheres by means of inscribed solids. That gives us a high idea of their mathematical attainments; but that it is not too high, is shown by the fact that the famous lunules of Hippokrates date from the middle of the fifth century. The inclusion of straight and curved in the "table of opposites" under the head of Limit and Unlimited points in the same direction."

"The tradition confirms... the importance of the in the Pythagorean system. According to one account, Hippasos was drowned at sea for revealing its construction and claiming the discovery as his οwn."

"[T]he Pythagoreans adopted the pentagram or pentalpha as their symbol. The use... in later magic is well known; and Paracelsus... employed it as a symbol of health, which is... what the Pythagoreans called it."

"The view that the soul is a "harmony," or... attunement, is intimately connected with the theory of the four elements. It cannot have belonged to the earliest... Pythagoreanism; for... in Plato’s Phaedo, it is... inconsistent with the idea that the soul can exist independently of the body. It is... opposite of the belief that "any soul can enter any body." ...[F]rom the Phaedo... it was accepted by Simmias and Kebes, who had heard Philolaos at Thebes, and by Echekrates of Phleious, who was the disciple of Philolaos and Eurytos."

"The account of the doctrine given by Plato is... in accordance with the view that it was of medical origin. Simmias says: "Our body being... strung and held together by the warm and the cold, the dry and the moist... [etc.,] our soul is a sort of temperament and attunement of these, when... mingled... well and in due proportion. If, then, our soul is an attunement,... when the body has been relaxed or strung up out of measure by diseases and other ills, the soul must... perish at once." This is... an application of the theory of Alkmaion, and is in accordance with... the Sicilian school of medicine. It completes the evidence that the Pythagoreanism of the end of the fifth century was an adaptation of the old doctrine to the new principles introduced by Empedokles."

"The planetary system which Aristotle attributes to "the Pythagoreans" and Aetios to Philolaos is... remarkable. The earth is no longer in the middle of the world; its place... taken by a central fire, which is not... the sun. Round this fire revolve ten bodies. First comes the Antichthon or , and next the earth, which thus becomes one of the planets. After the earth comes the moon, then the sun, the five planets, and the heaven of the fixed stars. We do not see the central fire and the antichthon because... [our] side of the earth... is always turned away from them.., explained by the analogy of the moon. ...[M]en living on the other side of it would never see the earth. ...[A]ll these bodies rotate on their axes in the same time as they revolve round the central fire."

"Plato gives a description of the earth and its position... entirely opposed to... [antichthon theory], but is accepted... by Simmias the disciple of Philolaos. It is undoubtedly... Pythagorean... and marks... advance on the Ionian views then current at Athens. ...Plato states it as ...a novelty that the earth does not require ...support ...to keep it in its place. ...Anaxagoras had not been able to shake himself free of that idea, and Demokritos still held it."

"The... inference from the Phaedo would... be that the theory of a spherical earth, kept in the middle of the world by its equilibrium, was that of Philolaos... If so, the doctrine of the central fire would belong to a somewhat later generation of the school, and Plato may have learnt it from Archytas and his friends after he had written the Phaedo."

"[I]t is... incredible that the heaven of the fixed stars should have been regarded as stationary. That would have been the most startling paradox that any scientific man had yet propounded, and we should have expected the comic poets and popular literature generally to raise the cry of atheism... [W]e should have expected Aristotle to say something... He made the circular motion of the heavens the... keystone of his system, and would have regarded... a stationary heaven as blasphemous. ...[H]e argues against those who, like the Pythagoreans and Plato, regarded the earth as in motion; but he does not attribute the view that the heavens are stationary to any one. There is no necessary connexion between the two ideas. All the heavenly bodies may be moving as rapidly as we please, provided that their relative motions are such as to account for the phenomena."

"It seems probable that the... earth’s revolution round the central fire... originated in the account... by Empedokles of the sun's light. The two... are brought into... connexion by Aetios, who says... Empedokles believed in two suns, while Philolaos believed in two or... three. The theory of Empedokles... gives two inconsistent explanations of night."

"The central fire received a number of mythological names. ...[W]e are dealing with a real scientific hypothesis. It was a great thing... that the phenomena could best be "saved" by a central luminary, and that the earth must... be a revolving sphere like the planets. [W]e are almost tempted to say that the identification of the central fire with the sun... suggested for the first time in the Academy, is a mere detail in comparison. The great thing was that the earth should... take its place among the planets... once... done.., we can... search for the true "hearth" of the planetary system... It is probable... that... this theory... made it possible for Herakleides of Pontos and Aristarchos of Samos to reach the heliocentric hypothesis, and it was... Aristotle’s reversion to the geocentric theory which made it necessary for Copernicus to discover the truth afresh. We have his own word for it that the Pythagorean theory put him on the right track."

"The existence of the antichthon was... a hypothesis intended to account for... eclipses. ...Aristotle says that the Pythagoreans invented it... to bring the number of revolving bodies up to ten; but that is a... sally... Aristotle... knew better. In his work on the Pythagoreans... he said... eclipses of the moon were caused sometimes by.... the earth and sometimes by... the antichthon... the same statement was made by Philip of Opous..."

"Aristotle shows... how the theory originated... that some thought there might be a considerable number of bodies revolving round the centre, though invisible because of the intervention of the earth, and... they accounted... for there being more eclipses of the moon than of the sun. ...Aristotle regarded the two hypotheses as of the same nature."

"Anaximenes... assumed... existence of dark planets to account for the frequency of s, and Anaxagoras... revived that view. Certain Pythagoreans had placed these dark planets between the earth and the central fire... to account for their invisibility, and the next stage was to reduce them to a single body. ...[A]gain ...the Pythagoreans tried to simplify the hypotheses of ...predecessors."

"We must not assume ...Pythagoreans made the sun, moon, and planets, including the earth, revolve in the opposite direction to the heaven of the fixed stars. ...Alkmaion is said to have agreed with "some of the mathematicians" in holding this view, but it is never ascribed to Pythagoras or even to Philolaos."

"The old theory was that all... heavenly bodies revolved... from east to west, but that the planets revolved more slowly the further they were removed from the heavens, so... those... nearest the earth are "overtaken" by those that are further away. This view was... maintained by Demokritos, and that it was... Pythagorean... follow[s] from... the "harmony of the spheres." [W]e cannot attribute this theory in... later form to the Pythagoreans of the fifth century, but we have... testimony of Aristotle... that those Pythagoreans whose doctrine he knew believed... heavenly bodies produced s in their courses. ...[V]elocities of these bodies depended on the distances between... [which] corresponded to the intervals of the . He... implies that the heaven of the fixed stars takes part in the concert; for... "the sun, the moon, and the stars, so great in magnitude and in number as they are..." ...[T]he slower bodies give out a deep note and the swifter a high note."

"[P]revailing tradition gives the high note of the octave to the heaven of the fixed stars... [I]t follows that all the heavenly bodies revolve in the same direction, and... their velocity increases in proportion to their distance from the centre."

"The theory that the proper motion of the sun, moon, and planets is from west to east, and that they also share in the motion from east to west of the heaven of the fixed stars, makes its first appearance in the in Plato’s Republic, and is fully worked out in the Timaeus. In the Republic it is still associated with the "harmony of the spheres,"..."

"In the Timaeus... the slowest of the heavenly bodies appear the fastest and vice versa; and, as this... is... a Pythagorean [speaking], we might suppose the theory of a composite movement to have been anticipated by some... [in] that school."

"Pythagoreans were... open to new ideas."

"[T]he theory is... emphatically expressed by the Athenian Stranger in the Laws, who is... Plato... expounding a novel theory."

"[A] view... Aristotle sometimes attributes to the Pythagoreans... things were "like numbers." He does not appear to regard this as inconsistent with the doctrine that things are numbers..."

"Aristoxenos represented the Pythagoreans as teaching that things were like numbers, and there are other traces of an attempt to make... this... the original doctrine. A letter... purporting to be... Theano... wife of Pythagoras... says... she hears many of the Hellenes think Pythagoras said things were made of number, whereas he... said they were made according to number. ...[T]his fourth-century theory had to be explained away... later... and Iamblichos... tells... that it was Hippasos who said number was the of things."

"Aristotle seems to find only a verbal difference between Plato and the Pythagoreans. The metaphor of [numbers'] "participation" was merely substituted for that of [numbers'] "imitation." ...Aristotle’s ascription of the doctrine of "imitation" to the Pythagoreans is... justified by the Phaedo."

"The arguments for immortality ...come from various sources. Those derived from the doctrine of Reminiscence... sometimes... supposed... Pythagorean, are only known to the Pythagoreans by hearsay, and Simmias requires to have the whole psychology of the subject explained... When... we come to the question what it is that our sensations remind us of, his attitude changes. The view that the equal itself is alone real, and that what we call... things are imperfect imitations of it, is... familiar to him. He requires no proof... and is... convinced of the immortality of the soul... because Sokrates makes him see that the theory of forms implies it."

"Sokrates does not introduce the theory as a novelty. The reality of the "ideas" is the... reality "we are always talking about," and they are explained in a peculiar vocabulary... of a school."

"Whose theory is it? It is usually supposed... Plato’s... though nowadays it is... his "early theory of ideas,"... that he modified... profoundly in later life. But there are serious difficulties in this view."

"Plato... was not present at the conversation... in the Phaedo. Did any philosopher ever propound a new theory of his own by representing it as already familiar to... distinguished living contemporaries? It would be rash... to ascribe the theory to Sokrates, and there seems nothing... but to suppose that the doctrine of “forms” originally took shape in Pythagorean circles, perhaps under Sokratic influence. ... Simmias and Kebes were not only Pythagoreans but disciples of Sokrates; for... Xenophon has included them in his list of true Sokratics."

"We have... ground for believing... the Megarians had adopted a like theory under similar influences, and Plato states... that Eukleides and of were present at the conversation recorded in the Phaedo. ...[U]se of the words εἴδη and ἰδέαι to express ultimate realities is pre-Platonic, and it seems most natural to regard it as of Pythagorean origin."

"Parmenides had already called the original Pythagorean "elements" μορφαί, and Philistion called the "elements" of Empedokles ἰδέαι. If the ascription of this terminology to the Pythagoreans is correct, we may say that the Pythagorean "forms" developed into the atoms of Leukippos and Demokritos on the one hand, and into the "ideas" of Plato on the other."

"We... exceeded the limits... by tracing the history of Pythagoreanism... to... where it becomes practically indistinguishable from the earliest form of ; but it was necessary... to put the statements of our authorities in their true light."

"Aristoxenos is not likely... mistaken with regard to the opinions of the men he had known personally, and Aristotle’s statements must have had some foundation."

"We must assume... a later form of Pythagoreanism... was closely akin to early . [T]he fifth-century doctrine was of the more primitive type..."

"Whether or not we accept the hypothesis of direct influence from Persia on the Ionian Greeks in the sixth century, any student of Orphic and Pythagorean thought cannot fail to see that the similarities between it and Persian religion are so close as to warrant out regarding them as expressions of the same view of life, and using the one system to interpret the other. The characteristic preoccupation of Pythagoreanism with astronomy and the contemplation of the heavens becomes transparently clear, when we see it in the light of notions like , , and ."

"The School of Pythagoras, in our opinion, represents the main current of that mystical tradition which we have set in contrast with the scientific tendency. The terms 'mystical' and 'scientific,' ...are ...not to be understood as if ...all the philosophers we class as mystic were unscientific. The fact that we regard Parmenides, the discoverer of Logic, as an offshoot of Pythagoreanism, and Plato... as finding in the Italian philosophy the chief source of his inspiration, will be enough to refute such a misunderstanding. Moreover, the Pythagorean School... developed a scientific doctrine closely resembling the Milesian Atomism; and Empedocles, again, attempted to combine the two types of philosophy."

"Behind the School of Pythagoras, we can discern, in the socalled Orphic revival, one of these reformations of Dionysiac religion. ...[T]the Pythagorean philosophy... is always passing from mysticism to science, as its religion had passed from Dionysus to Apollo. Yet, philosophy and religion alike do not cease to be mystical at the root; and the attempt to hold the two ends together involves religion in certain contradictions, and leads philosophy to corresponding dilemmas..."

"[T]hroughout the mystical systems inspired by Orphism, we... find the fundamental contrast between... principles of Light and Darkness, identified with Good and Evil. This cosmic dualism is the counterpart of the dualism in the... soul; for... physis and soul... are... identical in substance. The soul in its pure state consists of fire, like the divine stars from which it falls; in its impure state, throughout... reincarnation, it... is infected with the baser elements, and weighed down... In the cosmologies... the manifold world of sense will be viewed as a degradation from the purity of real being. Such systems will tend to be other-worldly, putting all value in the unseen unity of God, and condemning the visible world as false and illusive, a turbid medium... obscured in mist and darkness. These characteristics are common to all the systems which came out of the Pythagorean movement—Pythagoreanism proper, and the philosophies of Parmenides, Empedocles, and Plato."

"The doctrines of mysticism are secret, because they are not cold, abstract beliefs, or articles in a creed, which can be taught and explained by intellectual processes... The 'truth' which mysticism guards is... only... learnt by being experienced (παθεῖν μαθεῖν); it is... not an intellectual, but an emotional experience—that invasive, flooding sense of oneness, of reunion and communion with... the life of the world... Being an emotional, non-rational state, it is indescribable, and incommunicable save by suggestion. To induce that state, by the stimulus of collective excitement and all the pageantry of dramatic ceremonial, is the aim of mystic ritual. The 'truth' can only come to those who submit themselves to these... because it is... to be immediately felt, not conveyed by dogmatic instruction. For that reason only... 'mysteries' are reserved to the initiate, who have undergone 'purification,' ...a state of mind which fits them for the consummate experience. Pythagoreanism presents... an attempt to intellectualise... Orphism, while preserving its social form, and... spirit... Orphism ceases to be a cult, and becomes a Way of life. As a revival, Pythagoreanism means a return to an earlier simplicity... simple enough to adapt itself to a new movement of the spirit. Pythagoreanism is... a complex phenomenon, containing the germs of several tendencies... philosophies that emerged from the school... separating towards divergent issues, or intertwined in ingenious reconciliations. Our analysis must take account of three strata, superimposed... Dionysus, Orpheus, Pythagoras. From Dionysus come the unity of all life, in the cycle of death and rebirth, and the conception of the or collective soul, immanent in the group as a whole, and yet something more than any or all... To Orpheus is due the shift of focus from earth to heaven, the substitution for the vivid, emotional experience of the renewal of life in nature, of the worship of a distant and passionless perfection in the region of light, from which the soul, now immortal, is fallen into the body of this death, and which it aspires to regain by the formal observances of asceticism. But the Orphic still clung to the emotional... reunion and... ritual that induced it, and... to the passionate spectacle (theoria) of the suffering God. Pythagoras gave a new meaning to theoria... as the passionless contemplation of rational, unchanging truth... a 'pursuit of wisdom' (philosophia). The way of life is still also a way of death; but now... death to the emotions and lusts... and a release of the intellect to soar into the untroubled of theory... by which the soul can 'follow God' (ἕπεσθαι θεῷ)... beyond the stars. Orgiastic ritual... drives a... nail into the coffin of the soul, and binds it... to its earthly prison-house. ...[O]only certain ascetic prescriptions of the Orphic askesis are retained, to symbolise a turning away from lower desires, that might enthral... reason."

"To this society men and women were admitted without distinction; they had all possessions in common, and a 'common fellowship and mode of life.' ...[N]o individual... was allowed to claim the credit of any discovery... It was vulgarly supposed that the school must have wished to keep its knowledge to itself as a 'mysterious' doctrine, as if there were any conceivable reason for hiding a theorem in geometry or harmonics. ...What is to be gathered from the story of Hippasos is that the pious Pythagoreans believed that the Master’s spirit dwelt continually within his church, and was the source of all its inspiration. ...The impiety lay, not in divulging a discovery in mathematics, but in claiming to have invented what could only have come from... a group-soul... living on after [Pythagoras'] death as the Logos of his disciples."

"[T]he Pythagorean One, or Monad, splits into two principles, male and female, the Even and the Odd, which are the elements of all numbers and so of the universe. ...One is not simply a numerical unit, which gives rise to other numbers by ...addition. That conception belongs to the later atomistic number-doctrine ...In the earlier Pythagoreanism, we must think of the One (which is not itself a number at all) as analogous to Anaximander’s ἄπειρον. It is the primary, undifferentiated group-soul, or physis, of the universe, and numbers must arise from it by a process of differentiation or 'separating out' (ἀπόκρισις). Similarly, each of these numbers is not a collection of units, built up by addition, but itself a sort of minor group-soul—a distinct 'nature,' with various mystical properties. In the same way, it is by dividing up the whole interval of the octave that the harmonic proportions are determined."

"Pythagorean science... will inevitably reproduce the later and inconsistent conception of the atomic, indestructible, individual soul. This... was... present in Orphic religion, fallen from its first Dionysiac faith in the one continuous life in all things, towards the Olympian conception of athanasia. The later Pythagoreans of the fifth century 'construct the whole world out of numbers, but they suppose the units to have magnitude. As to how the first unit with magnitude arose, they appear to be at a loss.' ...at a loss, because they could not realise that this physical doctrine was ...a reflection of the belief in a plurality of immortal souls, which contradicted their older faith that Soul was a Harmony—a bond linking all things in one. This Soul had formerly been the One God manifest in the logos; now it is broken up into a multitude of individual atoms, each claiming an immortal and separate persistence. And the material world suffers a corresponding change. In place of the doctrine of procession from the Monad, bodies are built up out of numbers, now conceived as collections of ultimate units, having position and magnitude. Thus, Pythagoreanism is led... from a temporal monism to a spatial pluralism—a doctrine of number-atoms hardly distinguishable from the atoms of Leukippus and Democritus, who, as Aristotle says, like these Pythagoreans, 'in a sense make all things to be numbers and to consist of numbers.' But the development of this number-atomism was predestined by religious representations of the nature of soul older than Pythagoreanism itself, and already contained in the blend of Dionysiac and Olympian conceptions inherited by Pythagoras from Orphism."

"The tendency which impelled Pythagorean science towards a materialistic atomism is only the recoil of that same tendency which exalted Pythagoras, from his position as the indwelling daemon of his church, to the distant heaven of the immortals. It is the tendency to dualism. When God ceases to be the immanent Soul of the world, living and dying in its ceaseless round of change, and ascends to the region of immutable perfection, it is because man has acquired a soul of his own, a little indestructible atom of immortality, a self-subsistent individual. 'Nature' likewise loses her unity, continuity, and indwelling life, and is remodelled as an aggregate of little indestructible atoms of matter. But note the consequence: she, too, is now self-subsistent. The world of matter becomes the undisputed dominion of Destiny, or Chance, or Necessity—of Moira, ', . There is no place in it for the God who has vanished beyond the stars."

"Not one of the philosophical ideas in Part I of the commentary is peculiarly Neoplatonic. The doctrine of the Threeness of things... is found in Aristotle and goes back to the early Pythagoreans or to Homer even; paragraph 8 is mathematical in content rather than philosophical... although there is an allusion in it to the Monad as the principle of finitudes, again a very early Pythagorean doctrine; and these two paragraphs are the source of [Heinrich] Sitter's suggestion of the authorship of Proclus. As a matter of fact, the philosophical notions in Part I have been borrowed for the most part directly from Plato, with two or three exceptions that are Aristotelian... Plato's Theaetetus, Parmenides, and the Laws, are specifically mentioned. The Timaeus forms the background of much of the thought. And the Platonism of a mathematician of the turn of the third century A. D. need not surprise us, if we but recall Aristotle's accusation that the Academy tended to turn philosophy into mathematics."

"§1. The aim of Book X of Euclid's treatise on the Elements is to investigate the commensurable and incommensurable, the rational and irrational continuous quantities. This science (or knowledge) had its origin in the sect (or school) of Pythagoras, but underwent an important development at the hands of the Athenian, Theaetetus, who had a natural aptitude for this as for other branches of mathematics most worthy of admiration."

"§2. Since this treatise (i. e. Book X of Euclid.) has the aforesaid aim and object, it will not be unprofitable for us to consolidate the good which it contains. Indeed the sect (or school) of Pythagoras was so affected by its reverence for these things that a saying became current in it, namely, that he who first disclosed the knowledge of surds or irrationals and spread it abroad among the common herd, perished by drowning: which is most probably a parable by which they sought to express their conviction that firstly, it is better to conceal (or veil) every surd, or irrational, or inconceivable in the universe, and, secondly, that the soul which by error or heedlessness discovers or reveals anything of this nature which is in it or in this world, wanders [thereafter] hither and thither on the sea of nonidentity (i. e. lacking all similarity of quality or accident), immersed in the stream of the coming-to-be and the passing-away, where there is no standard of measurement. This was the consideration which Pythagoreans and the Athenian Stranger held to be an incentive to particular care and concern for these things and to imply of necessity the grossest foolishness in him who imagined these things to be of no account."

"Van Helmont adds a... criticism to the Paracelsian theory. The tria prima play no role in disease, as they cannot be isolated from the living body. Paracelsus, he believes, was mistaken in assuming that the salt in urine was one of the tria prima, when in fact it is only salt water that has not yet been separated into its components. In fact, the tria prima cannot be obtained from living things at all; only by the destruction of the living principle... Hence diseases cannot be caused by the three principles... Surprisingly... he employs the tria prima in his theory... Van Helmont first postulates that water presents itself in four distinct states: ice, water, vapour and Gas... [and] contends that water is formed of 'atoms', which in turn are made up of the three principles (mercury, salt, and sulphur) in different spatial arrangements within the atom. These... give water both its resiliance and diversity of character."

"Tria Prima. The three elements of the alchemists, their salt, sulphur, and mercury: the first of which appears to have denoted whatever remained fixed in the fire; the second, whatever was inflammable; and the third, whatever was neither fixed nor inflammable, but rose in vapour without being burned."

"Alchemical theory was essentially static throughout the medieval period. ...Paracelsus was the herald of a new era, an era of . His contribution to alchemical theory lay in the addition to sulphur and mercury of a third principle, which he called 'salt.' Materially this was recognised as the principle of uninflammability and fixidity. ...[T]he tria prima, or three 'hypostatical principles' could be interpreted in either a material or a spiritual sense. In the words of Paracelsus himself: 'Know, then, that all the seven metals are born from a threefold matter... Mercury is the spirit, Sulphur is the soul, and Salt is the body... the soul... unites those two contraries, the body and spirit, and changes them into essence.' ...similar to the material effect of the liquid menstruum, or Hermetic Stream, in uniting sophic sulphur and sophic mercury to produce the Philospher's Stone."

"Since a great part of those Learned Men, especially Physicians who have discerned the defects of the vulgar Philosophy, but are not yet come to understand and relish the Corpuscularian, have slid into the Doctrine of the Chymists; and since the Spagyrists are wont to pretend to make out all the Qualities of bodies from the Predominancy of some one of their three Hypostatical Principles, I suppose it may both keep my opinion from appearing too presumptuous, and (which is far more considerable) may make way for the fairer Reception of the Mechanical Hypothesis about Qualities, if I here intimate (though but briefly and in general) some of those defects, that I have observed in Chymists Explications of Qualities."

"Now a man need not be very conversant in the writings of Chymists to observe, in how Laxe, Indefinite, and almost Arbitrary Senses they employ the Terms of Salt, Sulphur and Mercury; of which I could never find that they were agreed upon any certain Definitions or setled Notions; not onely differing Authors, but not unfrequently one and the same, and perhaps in the same Book, employing them in very differing senses."

"And first the Doctrine that all their Theory is grounded on, seems to me Inevident and undemonstrated, not to say precarious."

"It is somewhat strange to me, that neither the Spagyrists themselves, nor yet their Adversaries, should have taken notice that Chymists have rather supposed than evinced, that the Analysis of bodies by fire, or even that at least some Analysis is the onely instrument of investigating what Ingredients mixt bodies are made up of, since in divers cases That may be discovered by Composition as well as by Resolution; as it may appear, that consists of metalline parts (whether Martial, or Venereal, or both) associated by Coagulation with ones, one may, I say, discover this as well by making true Vitriol with Spirit (improperly called Oil) of Sulphur, or that of Salt, as by distilling or Resolving Vitriol by the fire."

"But I will not... trouble you with what I have largely discoursed in the Sceptical Chymist, to call in question the grounds on which Chymists assert, that all mixt bodies are compounded of Salt, Sulphur, and Mercury. For it may suffice me now to tell you that, whatsoever they may be able to obtain from other bodies, it does not appear by Experience, which is the grand, if not the onely, Argument they rely on, that all mixt bodies that have Qualities consist of their tria prima, since they have not been able, that we know, truly, and without new Compositions, to resolve into those three, either Gold, or Silver, or Crystal, or Venetian Talck, or some other bodies, that I elsewhere name; & yet these bodies are endowed with divers Qualities, as the two former with Fusibleness and Malleability, and all of them with Weight and Fixity; so that in these and the like bodies, whence Chymisats have not made it yet appear, that their Salt, Sulphur and Mercury, can be truly and adequately separated, 'twill scarce be other than precarious to derive the malleableness, colour, and other Qualities of such bodies from those Principles."

"The doctrine of the four elements seems to have continued undisputed till the time of the alchemists. These men, better acquainted than the ancient philosophers with the analysis of bodies, became convinced of the inadequacy of that doctrine to explain all the phenomena which were presented to their view. Hence they substituted in its stead a theory of their own; namely, that all bodies are composed of three elements, salt, sulphur, and mercury, which they distinguished by the appellation of the tria prima. To these principles, which were embraced by succeeding writers, Paracelsus added two more, phlegm and caput mortuum."

"The alchemists seem to have attached only a very indefinite meaning to the terms salt, sulphur, and mercury: since by salt they appear to have designated every thing which is fixed in the fire; all inflammable substances they denominated sulphur; and every substance which flies off without burning, mercury."

"In conformity with this theory they maintained, that all bodies may be decomposed by means of fire into these three principles; the salt remains behind fixed, the sulphur takes fire, and the mercury flies off in the form of smoke. The phlegm and caput mortuum of Paracelsus were the water and earth of the ancient philosophers."

"Boyle attacked this hypothesis in his Sceptical Chemist, and several of his other publications: proving that under each of the terms salt, sulphur, mercury, phlegm, and earth are comprehended substances of very different properties; that all bodies are not composed of these principles; and that the principles themselves are not elements, but compounds."

"From this epocha the hypothesis of the tria prima seems wholly to have been abandoned: whilst a very different doctrine was proposed by Beccher in his Physica Subterranea [1669], and to which we are perhaps indebted for the present advanced state of chemical science; since he was the first to point out chemical analysis as the only true method of ascertaining the elements of bodies. According to his doctrine, all terrestrial bodies are composed of water, air, and three earths; viz. the fusible, the inflammable or sulphureous, and the mercurial. The three earths, combined in nearly equal proportions, compose the metals: when the proportion of mercurial earth is very small, they compose stones; when the fusible predominates, the resulting compounds are the precious stones; when the sulphureous predominates, and the fusible is deficient, the compounds are the calorific earths: fusible earth and water compose an universal acid, very much resembling sulphuric acid, from which all other acids derive their acidity; water, fusible earth, and mercurial earth, constitute common salt; sulphureous earth and the universal acid form sulphur. Such was the theory of Beccher, which was afterward considerably modified by Stahl."

"The "Chemico-physical Doubts and Paradoxes" raised by Boyle "touching the experiments whereby vulgar Spagyrists are wont to endeavour to evince their Salt, Sulphur, and Mercury to be the true Principles of Things," eventually sealed the fate of the doctrine of the tria prima, and of the tenets of the school of Paracelsus."

"In this treatise Boyle sets out to prove that the number of the peripatetic elements or principles hitherto assumed by chemists is, to say the least, doubtful."

"The words "element" and "principle" are used by him as equivalent terms, and signify those primitive and simple bodies of which compounds may be said to be composed, and into which these compounds are ultimately resolvable."

"He concludes... that the Paracelsian elements—their "salt," "sulphur," and "mercury"—are not the first and most simple principles of bodies; but that these consist, at most, of concretions of corpuscles or particles more simple than they, and possessing the radical and universal properties of volume, shape, and motion."

"[Paracelsus] arranged the several parts of man, his own universal elements, and the Aristotelian elements in triplets, thus :—"

"[T]he writings and labours of the alchemists were both extensive and important. ...[T]heir studies, although misdirected, were not... haphazard. The alchemists had a definite, and... logical, system of philosophy... [T]hey recognised—(1) the unity of matter; (2) the three principles—philosophical mercury, sulphur, and salt; (3) the four elements—fire, air, water, and earth; and (4) the seven metals—gold, silver, mercury, copper, , tin, and ."

"The original matter, or ', was called by various names—universal substance, seed, chaos. Although matter changes its form, it cannot be destroyed. ...In its nature the ' was assumed to be a liquid, containing everything in posse, but nothing in esse."

"All metals and minerals consist of certain principles. These were at first called "mercury" and "sulphur," not the ordinary substances... but a philosophical mercury and a philosophical sulphur. ...At a later period the alchemists added a philosophical salt, or a philosophical arsenic, but they never ascribed to these the importance they attached to the other two principles."

"Traces of these ancient conceptions are still to be recognised in the word "quick-silver," that is living silver, a literal translation of argentum vivum. A term "quick-sulphur" (sulphur vivum) was also in use, but it has long since disappeared."

"The mercury of a metal... represented its lustre, volatility, fusibility, and malleability; the sulphur of the metal, its colour, combustibility, affinity, and hardness."

"The salt of the was merely a means of union between the mercury and the sulphur, just as the vital spirit in man unites soul and body. It was doubtless devised to impart a triple form to the idea, in conformity with the method of the theological schoolmen."

"Mercury, sulphur, and salt were not three matters, but one, derived from the '."

"[W]hen an alchemist converted a metal into its oxide, or, as they expressed it, "made a " of it, he thought he had volatilised its mercury and fixed its sulphur. When he distilled ordinary mercury and found a solid residue in the , he called it the "sulphur" of mercury; when he found a sublimed product in the receiver (mercury bichloride), he termed it the "mercury" of mercury or "corrosive sublimate.""

"The more logical mind of Artephius Longaevus introduced a modification of this theory. He distinguished two properties in a metal—the visible and the occult. The former, comprehending its colour, lustre, extension, and other properties visible to the eye, he called its "sulphur"; the latter, comprehending its fusibility, malleability, volatility, and other properties not visible until after... special treatment, he called its "mercury.""

"Practically... there was little difference in the application of these diverse theories regarding the three principles."

"At a still later date [post-16th century] it was argued that exact and natural sciences proceed by induction and deduction, and occult and spiritual sciences by analogy. Following out this line of thought the alchemists produced the following remarkable trilogy:—"

"Each of these was a trinity in unity, and a unity in trinity. In each world was a distinct design,—in the material, the perfection of the metals; in the human, the perfection of the soul; in the divine, the contemplation of the Deity in His splendour."

"These mystic alchemists interpreted the three principles in their own fashion. Mercury, the passive and female principle, was matter; sulphur, the active and male principle, was force; and salt, the middle term in the proposition, was movement, which applied force to matter. Or, expressed in another shape, mercury was the subject: sulphur, the cause; and salt, the effect. Symbolically, the theory was represented by an equilateral triangle, in one angle of which was the sign of sulphur or force; in the second, the sign of mercury or matter; and in the third, the sign of salt or movement."

"Aristotle had considered metals to be formed by the combination of moist and dry exhalations, and in the Jabirian works these... are... vapours of mercury and sulphur. The cause of the different metals was the... quality of the sulphur... The term sulphur ...as a component of metals probably referred to a volatile combustible material to which no... substance corresponded exactly. Likewise mercury... may... have been... an approximation to the other volatile liquid component of metals. ...The notion that metals contained a combustible principle persisted, and... provided the inspiration for the phlogiston theory."

"The Jabirian alchemists... believed that metals were ultimately composed of the four Aristotelian elements earth, water, air and fire... A base metal had to be treated with a medicine or elixir to adjust... qualities... with the proportions of gold. ...[Q]ualities of heat, cold, moisture and dryness could each be separated in pure form. ...First they subjected various organic materials to dry distillation... which often resulted in... a volatile combustible... (air), a liquid (water), a combustible tarry material (fire) and a dry residue (ash). [Each of] [t]hese elements were supposed... composed of two qualities, and... could be isolated by... purification. Thus water... could be converted into pure cold by repeated distillation... and further [distillations] in the presence of a drying agent. The resulting pure cold... a brilliant white solid."

"Paracelsus made an important contribution to chemical theory. He extended the sulphur-mercury theory of the Islamic chemists by adding a third principle... salt. Thus, when wood burned, the combustible component was identified with sulphur, the volatile component with mercury and the ashes... with salt. The composition of all substances could be expressed in terms of these three principles, or tria prima. As in previous theories... [these] were not... common materials... but rather... essential qualities."

"By 3000 BCE the Sumerians, perhaps while heating copper to make it more malleable, had discovered that more copper could be retrieved from the fire if the metal were heated with certain types of dirt and stones—that is, certain earths. These earths were the metal s, and the process they discovered, ', reduced metal salts to pure metal by the action of in the fire. The process of changing metal salts into pure metal is known as reduction because the metal without the accompanying oxygen, , or of the salt weighs less than the ore. Eventually metal workers learned to distinguish various metal-bearing ores by color, texture, weight, flame color, or smell when heated (such as garlic odor of ores) and they could produce a desired material on demand."

"Pliny recorded processes involving metals, salts, , glass, mortar, soot, ash, and a large variety of s, earths, and stones. He describes the manufacture of charcoal; the enrichment of the soil with lime, ashes, and manure; the production of wines and ; varieties of s; plants of medicinal or chemical interest; and types of , gems and precious stones. He discusses some simple chemical reactions... and a crude indicator paper... of strips soaked in an extract of oak galls that changed color when dipped in solutions of blue vitriol... contaminated with ."

"The Earths are white, inodorous, tasteless, and uninflammable substances—non-conductors of electricity, insoluble in water, but soluble in one or more of the acids. Sp. gr. compared to that of water, not exceeding five to one. They are six in number; viz. silica, alumine, , gluttine, augustine, ytria; the consideration of which falls under their alphabetical order."

"What made silica so interesting was that... it did not seem to follow the established rules of chemical combination. In Smithson's time, chemical combination was... an acid combining with an alkali to produce a stable, neutral... "." Acids did not combine chemically with each other, nor did alkalis... [A] substance... found to contain an alkali... must also contain an acid—and vice versa. Bergman's description of the compounds containing earths as... "natural compositions of acids" meant... the other component must be alkaline—which the earths all seemed to be, except for silica."

"Earth is one of the four simple substances called elements, or primitive principles; because they are indeed the most simple of all those which enter into the combination of compound bodies. We cannot doubt, in particular, that the greatest part of the compounds which we can analyse contain earth as one of their principles; for after art has exhausted all its efforts to decompose them, a fixed and solid matter always remains, upon which no change can be produced; and this is what is generally called earth. It has the solidity, weight, fixity, and other principal properties of the mass of solid matter which forms the globe we inhabit, called also the earth."

"These general considerations are sufficient to convince us, that in nature a substance exists whose properties are different from those of fire, air, water; and which is, like these other substances, one of the elements of compound bodies. But a vague assertion like this does not satisfy chemists. Besides the ascertaining of the exigence of the different substances submitted to their examination, they require to know the properties of these substances in their greatest degree of purity and simplicity; but they have found much difficulty and uncertainty in investigating the essential properties of the purest and simplest terrestrial element."

"Earth is not found so pure as the other elements, fire, air, and water, which, though not entirely free from mixture, are however so pure, that we may certainly and easily discover their fundamental properties. These properties of each of these pure elements are so well ascertained, and so evident, that nobody has yet attempted to distinguish different kinds of fire, air, or water, notwithstanding the differences which may arise from the heterogeneous substances with which they are almost always mixed."

"But we cannot say the same of earth; for a considerable number of substances are called earths, because they possess the principal properties of the terrestrial element: but these substances, when examined more particularly, are always found to differ from each other so much in other respects, and to be so difficultly purifiable from heterogeneous matter, that we have not ascertained whether only one simple and elementary earth, or several ones essentially different, although equally simple, exist."

"The most general and most probable opinion is, that as only one kind of fire, of air, and of water, so only one kind of simple elementary earth, exists. Alchemists chiefly have endeavoured to discover this primary earth, not with an intention to ascertain its properties, but because they imagined that as gold is the purest of metals, the earth of which it is partly composed must be also the most pure; they have, therefore, searched every where for this earth, which they call pure earth and virgin earth. They have endeavoured to obtain it from dew, rain, the air, ashes of vegetables, animals, and several minerals: but it was impossible to find it in compound bodies; for we shall see that when once this element makes part of a compound body, it cannot be disengaged from the substances with which it has united."

"Some of the best philosophical chemists have rather chose to admit different kinds of elementary earths, than to investigate the nature of the most simple and elementary of all. Becker admits three principles, which he calls earths, namely, the vitrifiable, the inflammable, and the mercurial earth..."

"Mr. Pott, examining the principal natural earths, divides them into four kinds, the vitrifiable, the , the argillaceous, and the gypseous earths. This able chemist shew the essential properties of these four kinds of earths, without affirming that they are all equally simple, and without even determining which of them he considered as most simple."

"As earth is an element... it deserves an accurate investigation to discover which is the most simple and elementary of all the substances to which the name earth has been applied. ...considering, first, what are the essential properties by which earthy substances differ from other elements, and then by determining that earth to be the most pure and simple, which possesses these properties most eminently and decisively; for ...the more eminently any substance possesses these characteristic properties... the nearer it approaches to this element..."

"[A]ll the substances which may reasonably be considered as earthy... possess much greater weight, hardness, fixity, and infusibility, than any other element; for these qualities are insensible, or do dot exist, in the element of fire; they are in an exceedingly small degree in the air, and are more sensible and considerable in water; but are infinitely less than in any thing which can be considered as earth. Hence... the qualities above-mentioned are the distinguishing and characteristic essential properties of the earthy element. But these qualities are not so eminently united in any of those [earthy] substances... as in... vitrifiable earth. ...[T]hen ...this earth is the heaviest, hardest, most fixed, and most infusible, and even the most apyrous of all earths, when it is very pure; and also... the most homogeneous, the most simple, and elementary earth, as we shall prove by a more particular examination of its properties, and by a companion of these with the properties of the other earthy substances."

"We call that vitrifiable earth, the integrant parts of which when united form masses of matter or stones, absolutely white and colorless, much more transparent and hard than any other natural substances, and which suffers no alteration, or even fusion, by the strongest fire which we can apply to it."

"Amongst the hard stones called vitrifiable... few... strictly possess all the qualities... mentioned; because in very few... the vitrifiable earth is pure. Most of these stones, as hard pebbles of all kinds, sand, free-stone, s, , rock-crystal, and the stones called precious, are deficient in some... qualities required to constitute the purest vitrifiable earth. Some... are opake, or only semitransparent; others... colored; some... fusible by a great heat; and, lastly, others, although much harder than any other kind of stones, want the last degree of hardness; all which prove that they are mixed with heterogeneous substances, chiefly phlogistic, metallic, or even earthy, of a different kind."

"The purest of all the vitrifiable stones is the diamond, which is perfectly white, free from all color or stain, and transparent. This stone is also known to be the hardest of all, is absolutely apyrous, that is, incapable of receiving any alteration by the most violent heat. We, therefore, consider the matter of this stone as the purest, simplest, and most elementary earth that is known. The properties, then, of this stone, and of the other vitrifiable stones which resemble it, may give us notions of the properties of primary, elementary, unchanged earth. In this our opinion is conformable to that of the illustrious Stahl, who indeed admits the three earths of Becker; but, at the same time, corrects the theory of this chemist, by declaring that he only considers the first earth of Becker, or vitrifiable earth, as the proper terrestrial or earthy element."

"[T]he name vitrifiable earth... may produce false notions of the nature of these stones."

"[T]he epithet, vitrifiable is given, first, because some stones of this kind are, by means of their heterogeneous matters, capable of fusion and conversion into glass, without addition, and merely by the action of a very violent heat; and secondly, because other stones... require for their perfect fusion and vitrification a less quantity of flux, and a less degree of heat."

"In the second place, as all the earths and stones called vitrifiable have, notwithstanding their impurity, more hardness and transparency than others, and are fitter to communicate these good qualities to glass, they are employed preferably to any other earths in the composition, of glass, or artificial crystal. These are the only reasons why this kind of earth has been called vitrifiable. But we ought not from thence to conclude, that the earthy substance [i.e., the earth element or principle] which almost entirely composes them is more fusible and more vitrifiable than other earths: on the contrary... vitrifiable earth, when very pure, is of all earths the least fusible, and the least vitrifiable."

"I was present at a fine experiment made relatively to this subject. Some diamond powder was mixed with a sufficient quantity of fixed alkali to vitrify another earthy matter, and the mixture exposed to a heat sufficient for the most difficult vitrifications. After the operation, no glass was found in the crucible; but part of the alkali had been dissipated by the violence of the heat, and the diamond powder did not shew any signs of a beginning fusion. Thus we may confider it as an established truth, that the earths and stones called vitrifiable are not essentially and really so; that the fusibility of some of these, by which property they are rendered the fittest earths for vitrification, proceeds from heterogeneous matter with which they are mixed: and that, in general, the whitest, clearest, most transparent and hardest of these stones are also the most refractory and unfusible."

"[T]he purest and simplest of all earths ought to be also the heaviest; and accordingly... pure vitrifiable earth is... heavier than calcareous, argillaceous, gypseous, or other earths. ...[N]evertheless ...metals, metallic earths, and several kinds of spars, both calcareous and selenitic, are much heavier than the most compact vitrifiable stones ... [P]arts may be so arranged that void spaces may be left betwixt them, sometimes larger, and sometimes less, therefore a body composed of parts essentially lighter, may yet have a greater specific gravity than another body whose parts are essentially heavier; and this happens in all metals and metallic matters. ...Thus the gravity of metals and of metallic earths and stones ought not to prevent our considering the pure and elementary earthy principle as the heaviest of all natural substances."

"[W]e may consider the properties of elementary earth in the purest vitrifiable stones, and... compare them with the properties of the other elements. Since of these elements water is the most capable of our examination, we shall compare it with the purest vitrifiable earth; observing always, that we consider these elements in their state of aggregation; for we have no method by which their primary integrant parts can be known and considered separately."

"I do not believe that a pure verifiable earth, as a diamond, can be fused even in the focus of the best burning speculums: but supposing that a sufficient heat might be produced... it would then melt, and would even be reduced to vapors, if the heat were sufficiently violent; and when this heat should cease, it would, when it cooled, fix again, and become such a substance as it was before. The same would happen to vitrifiable earth in these circumstances, which does happen to water rendered fluid, and reduced to vapor by a certain heat, and which is again frozen into solid ice when that heat is removed. The differences, therefore, betwixt these two substances are only... in the degrees; but also these differences are very considerable."

"[A]n inference seems deducible, that the elements or the simplest substances which we know are essentially only one and the same matter, and only differ from each other in the quantity and in the form of their primary integrant molecules, which... have a greater or less tendency to unite together..."

"[W]e cannot doubt but that earth chiefly differs from the other elements by the powerful tendency which its parts have to each other, and by the force of their cohesion. For its hardness, fusibility, fixity, and even its gravity, are evidently the necessary consequences of this... the cause of the consistence of all solid bodies."

"Lastly, as without fire the whole world would be one mass of solid and immoveable matter, so without earth it would be a confused heap of fogs, vapors, a chaos of incoherent atoms, destitute of that harmony and equilibrium which sustain it."

"[T]he general tendency of the parts of matter to each other is the grand spring of the universe; that by this power, all combinations, solutions, and, in a word, all the movements and operations of nature are performed: and as... the earthy element possesses this tendency in the greatest degree, we ought to consider earth as being in this sense the most active and powerful of all elements. ...[T]he force with which they adhere together, and which renders them incapable of forming other unions, the extreme hardness, and the insolubility of a mass of pure earth, ought to demonstrate to a true philosopher, that if we suppose the parts of earth so separated ...that they cannot unite ...they must then possess all their force of tendency ...in a state of violent effort, and consequently must tend with extreme force to unite with any parts of matter ...within their reach ...[W]e know compounds in which the primitive integrant parts of the earthy element are only combined with the parts of water, which are incapable of satisfying all their tendency to union. These are the most simple saline substances, such as s and alkalis; and we may judge by the force and vehemence of the action of these solvents, how violent the action of the parts of earth would be, which should be capable of exerting all the attractive force which belongs to them."

"Although the entire mass of our globe be probably formed by an immense heap of elementary, vitrifiable, and even actually vitrified earth, as the illustrious Buffon believes, we do not find upon its surface but a very small quantity of this earth, unaltered, and in its primary state. Perhaps even none of it exists in that state: for, as we have observed, the common vitrifiable stones, which are chiefly formed of it, are very far from the degree of purity of primary elementary earth; and even perfect diamonds, which seem of all these stones to approach the nearest to this purity, seem to have been elaborated by the waters, if we can judge from their regularly crystallized form."

"We shall not be surprized at the scarcity of pure earthy element, if we consider that the surface of the earth... has been from the beginning of the world exposed to the constant action of the other elements; and that by uninterrupted operations, nature, assisted by fire, air, and water, has gradually disunited the integrant parts of elementary earth, and by combining them in manners and proportions infinitely various with parts of the other elements, has formed the numberless compound bodies, which occupy a certain thickness near the circumference of the globe, probably very small in comparison of the diameter of the earth, but very large with regard to us, whose greatest efforts only extend to a few hundred feet below its surface."

"[T]he earth which makes [shells and scales] of the crustaceous animals... takes the character of that earth which is called calcareous, and which is capable of conversion into quicklime by the action of fire. The earth which has entered into the composition of plants, and even of the bodies of animals, after having been deprived... of... principles of these compounds to which it was united, forms all the argillaceous earths. Some... partake both of the calcareous and of the argillaceous properties, and are called es. Marles have not yet been sufficiently well examined by chemists. They are either a mixture of clay and calcareous earth, or they have been so elaborated by nature as to be transformed into a particular earth, partly calcareous, and partly argillaceous, such as the earth of animal bones seems to be."

"As the earth which forms sands and the common impure vitrifiable stones retains more than the rest the essential properties of elementary earth, notwithstanding the heterogeneous, phlogistic, and other parts with which it is mixed; we cannot easily know whether it has once made a part of some very compound bodies, from the principles of which it has been more perfectly separated than the argillaceous and calcareous earths; or whether it be the primitive earth, which, without having made part of any intimate combination, has only been divided and conveyed by waters, and the parts of which have afterwards reunited, having only contracted a slight union with some phlogistic, metallic, and other matters, with which it is found mixed. This latter supposition appears to me to be the most probable. But very extensive researches in natural history and in chemistry are requisite to determined this question."

"[E]xcepting the purest vitrifiable earth, all the others are mixed with heterogeneous matter. By these remaining heterogeneous matters are the different kinds of earth specified and characterised: and as they all preserve and retain their peculiar character, we ought to conclude from thence, that these extraneous matters are very intimately united. To purify and simplify these mixed earths, so that they shall be assimilated to the purest vitrifiable earth, would be a fine problem. But, probably, this problem is beyond the power of our art. For... the perfect separation of two substances, united together, is exceedingly difficult, this difficulty must greatly increase, when one of the... substances... has a very strong attractive power, as earth has. This is the... reason why we find so small a portion of pure earth amongst the bodies within our reach; and that on the contrary, the globe is covered with so great a quantity of earthy substances differing from each other so much, that we might be inclined to believe them to be bodies essentially different."

"Earth (Animal) is the earth of shells of animals; or that which is obtained by , or putrefaction of animal substances. 1. The earths of the shells of Sea Fishes have the general properties of calcareous earths. It is said to differ from the mineral calcareous earths in being more difficultly soluble by vitriolic acid, and in being less disposed to vitrify along with salts and metallic glasses. The shells of eggs are also calcareous, but are somewhat fusible by fire. 2. The earths of calcined bones and horns are soluble by nitrous, marine, and vegetable acids, and with difficulty by vitriolic acid; but are not capable of being converted into quicklime by . They are said to be unfusible, even when mixed with salt, metallic glasses, and other fusible mixtures. They are therefore used in the composition of enamels and opake white glasses. Nevertheless, Wallerius affirms, that the earth of calcined bones, by intense heat, was changed, without addition, to a green glass. The same author says, that the earth of the whites and yolks of eggs was easily fusible, and that in general the fusibility of animal earths is in proportion to the softness of the parts from which they were obtained. 3. The earth of blood, flesh and skins of animals, is soluble by all acids, and is fusible by fire; that of blood and of other animal fluids being most fusible. This earth, like that of burnt bones and horns, is not calcareous; but both these kinds of earth are said to be rendered calcareous by being dissolved in acids, precipitated by fixed alkali from those acids, and afterwards calcined. They probably contain some mucilaginous substance, from which they cannot be entirely divested by fire without a previous solution in acids."

"The class of bodies called earths by chemists are nine in number; their names are Lime, Magnesia, Barytes, Strontites, Alumine or Argil, Silex, Yttria, Glucine and Zircone. The three last are recently discovered and scarce."

"The earths constitute the bases of the fossil kingdom. Though they have frequently been suspected to be compound bodies, and several attempts have been made to decompose them, it does not yet appear but that they are simple or elementary substances. Some of the earths possess alkaline properties; others are without such... but they all partake of the following characters: 1. They are incombustible, or do not unite with oxygen; 2. they are inferior to the metals in lustre and opacity; 3. they are sparingly soluble in water; 4. they are difficultly fusible, or resist great heat with out alteration; 5. they combine with acids; 6. they combine with each other, and with metallic oxides; and, 7. their specific gravities are from 1 to 5."

"The latest attempt to decompose the earths is that of Mr. Davy; he seems to have shewn, that some of the earths are analogous to the fixed alkalies, in respect to their properties of forming metals; but these metals, like those of the alkalies, are most probably compounds of hydrogen and the respective earths."

"Twenty years ago few substances seemed more likely to retain a permanent place in chemical arrangements, than the solid and refractory earths which compose the crust of the globe."

"Analysis has shewn, that the various stony or pulverulent masses which form our mountains, valleys, and plains, might be considered as resulting from combination or intermixture, in various numbers and proportions, of nine primitive earths, to which the following names were given:— 1. Baryta. 2. Strontia. 3. Lime. 4. Magnesia. 5. Alumina, or . 6. Silica. 7. Glucina. 8. Zirconia. 9. Yttria."

"Alkalis, s, metallic s, and s, were supposed to be of an entirely dissimilar constitution."

"The brilliant discovery by Sir H. Davy in 1808, of the metallic bases of , soda, strontia, and lime, subverted the ancient ideas regarding the earths, and taught us to regard them as all belonging, by most probable analogies, to the metallic class. According to an ingenious suggestion of Mr Smithson silica, however, ought to be ranked acids, since it has the power, in native mineral compounds, of neutralizing the alkaline earths, as well as the common metallic oxides. But as this property is also possessed by many metallic oxides, it can afford no evidence against the metallic nature of the siliceous basis. Alumina, by the experiments of Ehrman, may be made to saturate lime, producing a glass; and the triple compounds of magnesia, alumina, and lime, are perfectly neutral in . We might therefore refer alumina, as well as silica, to the same class with the oxides of , , , columbium, , , and . Alumina, however, bears to silica the same relation that oxide of antimony does to that of arsenic; the antecedent pair acting the part of bases, while the consequent pair act only as acids. The compound of the fluoric principle with silica is... mysterious... The almost universal function which silica enjoys, of saturating the alkaline oxides in the native earthy minerals, is exhibited in a very striking manner in Mr Allan's valuable Synoptic Tables. From his fifth to his fifteenth table of analyses, the column of silica is always complete, whatever deficiency or variation may occur in the columns of the earthy bases. At least, only a very few exceptions need be made for the oriental gems, which consist of strongly aggregated alumina."

"Whatever may be the revolutions of chemical nomenclature, mankind will never cease to consider as Earths those solid bodies, composing the mineral strata, which are incombustible, colourless, not convertible into metals by all the ordinary methods of reduction, or, when reduced by scientific refinements, possessing but an evanescent metallic existence, and which either alone, or at least when combined with , are insipid and insoluble in water."

"Substances which resembled salts in general appearance, but were insoluble in water, and very fixed in the fire, were called "earths"; and, as was generally done in those days, the existence of a primordial earth was assumed, more or less of which was supposed to be present in actual earths. This recognition of the possibility of more or less of the primordial earth being present in actually occurring earths, of course necessitated the existence of various kinds of earth. The earths were gradually distinguished from each other; lime was recognized as a substance distinct from baryta, baryta as distinct from alumina, etc."

"Stahl taught that one essential property of an earth was by fire, with production of a substance more or less like glass. This property was possessed in a remarkable degree by quartz or silica. Hence silica was regarded as the typical earth, until Berzelius, in 1815, proved it to be an acid. But the earths resembled alkalis, inasmuch as they too combined with, and so neutralized, ."

"There is an alkali hidden in every earth, said some chemists. An alkali is an earth refined by the presence of acid and combustible matter, said others."

"Earths thus came to be included in the term "alkali," when that term was used in its widest acceptation. But a little later it was found that some of the earths were thrown down in the solid form from their solutions in s by the addition of alkalis; this led to a threefold division... The distinction at first drawn between "earth" and "alkali" was too absolute; the intermediate group of "alkaline earths" served to bridge over the gap between the extreme groups."

"At this stage of advance, then, an earth is regarded as differing from an alkali in being insoluble, or nearly insoluble in water; in not being soapy to the touch, and not turning vegetable reds to blue: but as resembling an alkali, in that it combines with and neutralizes an acid; and the product of this neutralization, whether accomplished by an alkali or by an earth, is called a salt."

"To the earth or alkali, as being the foundation on which the salt is built, by the addition of acid, the name of base was given by Rouelle in 1744."

"But running through every conception which was formed of these substances-acid, alkali, earth, salt-We find a tendency, sometimes forcibly marked, sometimes feebly indicated, but always present, to consider salt as a term of much wider acceptation... An acid and an alkali, or an acid and an earth, combine to form a salt; but the salt could not have been thus produced unless the acid, the alkali and the earth had contained in themselves some properties which, when combined, form the properties of the salt."

"The acid, the alkali, the earth, each is, in a sense, a salt. The perfect salt is produced by the coalescence of the saltness of the acid with the saltness of the alkali. This conception finds full utterance in the names, once in common use, of sal acidum for acid, sal alkali for alkali, and sal salsum or sal neutrum for salt. All are salts; at one extreme comes that salt which is marked by properties called acid properties, at the other extreme comes the salt distinguished by alkaline properties, and between these, and formed by the union of these, comes the middle or neutral salt."

"It is thus that the nomenclature of chemistry marks the advances made in the science. "What's in a name?" To the historical student of science, almost everything."

"The administration and faculty at Massachusetts Institute of Technology (MIT) performed the first and most famous in-depth study on the status of women faculty within a particular institution. A group of senior women on the faculty had gathered preliminary evidence that they had less laboratory space, less access to research funding, and lower salaries than their male counterparts. In addition, they were infrequently represented on committees that made decisions about hiring and research funding. MIT's administration responded by researching the charges, finding that they were accurate, and taking steps to correct the inequities. The abstract to their report is an excellent description of the issues that still confront women scientists and analysis of why they went unrecognized by administration as well as by the women themselves."

"I think most importantly, men tend to get the top jobs, with which they get a bully pulpit for publication and speaking or exerting authority. I think women can be much more appreciated in science than they are."

"... although close to nothing was known, until recently, of the history of women in American science, women have been an integral part of the scientific community for well over a century. I can still recall my astonishment when I discovered in 1972 some women's entries in the old directories, and when I read biographies of several scientists in the then-new '. Here were people who had been present at many of the familiar places and events, but who were totally unknown even to those of us well versed in the history of American science. I felt like a modern Alice who had fallen down a rabbit hole into a wonderland of the history of science that was familiar in some respects but distorted and alien in many others. Learning more about these women and bringing their stories into closer connection with the rest of the history of this period became a compelling and absorbing intellectual task."

"... As early as 1982, 's superbly researched first volume on women scientists in America startled its readers with its meticulously drawn picture of the double bind women scientists fell into from the late nineteenth into the early twentieth century. Caught between 'two almost mutually exclusive stereotypes' they were 'atypical' as both women and scientists. Thus, even as higher education opened up to them, they found it easier to be educated in science than to be successfully employed in it: an impasse which proved to be long-lasting."

"Both ancient and medieval observers had noted that in many respects nature appeared to be governed by the principle of simplicity, and they had recorded the substance of their observations to this effect in the form of proverbial s which had become currently accepted bits of man's conception of the world. That falling bodies moved perpendicularly towards the earth, that light travelled in straight lines, that projectiles did not vary from the direction in which they were impelled, and countless other familiar facts of experience, had given rise to such common proverbs as: 'Natura semper agit per vias brevissimas'; 'natura nihil facit frustra'; 'natura neque redundat in superfluis neque deficit in necessariis' [Nature always acts by the shortest path; nature does nothing in vain; nature never overflows into the unnecessary, nor is she deficient in what is necessary]. This notion, that nature performs her duties in the most commodious fashion, without extra labour, would have tended to decrease somewhat the repulsion which most minds must have felt at Copernicus; the cumbrous epicycles had been decreased in number, various irregularities in the Ptolemaic scheme were eliminated... That such a tremendous shift in the point of reference could be legitimate was a suggestion quite beyond the grasp of people trained for centuries to think in terms of a homocentric philosophy and a geocentric physics. ...Copernicus could take the step because... he had definitely placed himself in... [the] dissenting Platonic movement. ...It was no accident that he became familiar with the remains of the early Pythagoreans, who almost alone among the ancients had ventured to suggest a non-geocentric astronomy."

"Ptolemy... against the champions of this or that cosmology of the heavens... had dared to claim that it is legitimate to interpret the facts of astronomy by the simplest geometrical scheme which will 'save the phenomena,' no matter whose metaphysics might be upset. His conception of the physical structure of the earth, however, prevented him from carrying through in earnest this principle of relativity, as his objections to the hypothesis that the earth moves amply show."

"Galileo had the experience of beholding the heavens as they actually are for perhaps the first time, and wherever he looked he found evidence to support the Copernican system against the Ptolemaic, or at least weaken the authority of the ancients. This shattering experience—of observing the depths of the universe, of being the first mortal to know what the heavens are actually like—made so deep an impression... that it is only by considering the events of 1609... that one can understand the subsequent direction of his life."

"The Greek philosopher, Plato, in the fourth century B.C. asked his students if they could devise a theory or explanation to explain this erratic planetary motion using some form of circular motion. Being keen observers, the Greeks came up with the most logical and obvious conclusions; namely, that the earth was the center about which the sun, the moon, planets, and the stars rotated. This model of the universe is called a geocentric or earth-centered model. It satisfactorily explained the daily motion of the stars and sun by assuming that they were attached to invisible crystalline spheres that rotated about the earth. The axis of the sphere of the sun was tilted with respect to that of the stars to account for the variation of the sun's height at with the various seasons. Since the sun appears to move through the stars and was brighter, it was assumed to be nearer to the earth than the stars. The spheres of the Moon, Mercury, and Venus were placed within the sphere of the sun while those of Mars, Jupiter, and Saturn were placed outside the sphere of the sun but within the sphere of the stars."

"The fundamental core of contemporary Darwinism, the theory of DNA-based reproduction and evolution, is now beyond dispute among scientists. It demonstrates its power every day, contributing crucially to the explanation of planet-sized facts of geology and meteorology, through middle-sized facts of ecology and agronomy, down to the latest microscopic facts of genetic engineering. It unifies all of biology and the history of our planet into a single grand story. Like Gulliver tied down in Lilliput, it is unbudgable, not because of some one or two huge chains of argument that might — hope against hope — have weak links in them, but because it is securely tied by thousands of threads of evidence anchoring it to virtually every other area of human knowledge. New discoveries may conceivably lead to dramatic, even "revolutionary" shifts in the Darwinian theory, but the hope that it will be "refuted" by some shattering breakthrough is about as reasonable as the hope that we will return to a geocentric vision and discard Copernicus."

"The present revolution of scientific thought follows in natural sequence on the great revolutions at earlier epochs in the history of science. Einstein's special theory of relativity, which explains the indeterminateness of the frame of space and time, crowns the work of Copernicus who first led us to give up our insistence on a geocentric outlook on nature; Einstein's general theory of relativity, which reveals the curvature or non-Euclidean geometry of space and time, carries forward the rudimentary thought of those earlier astronomers who first contemplated the possibility that their existence lay on something which was not flat. These earlier revolutions are still a source of perplexity in childhood, which we soon outgrow; and a time will come when Einstein's amazing revelations have likewise sunk into the commonplaces of educated thought."

"Fundamental changes in science have always been accompanied by deeper digging toward the philosophical foundations. Changes like the transition from the Ptolemaic to the Copernican system, from Euclidean to non-Euclidean geometry, from Newtonian to relativistic mechanics... have brought about a radical change in our common-sense explanation of the world. From all these considerations everyone who is to get a satisfactory understanding of twentieth century science will have to absorb a good deal of philosophical thought. But he will soon feel the same thing holds for a thorough understanding of the science which originated in any period of history."

"Persisting in their original resolve to destroy me and everything mine by any means they can think of, these men are aware of my views in astronomy and philosophy. They know that as to the arrangement of the parts of the universe, I hold the sun to be situated motionless in the center of the revolution of the celestial orbs while the earth revolves about the sun. They know also that I support this position not only by refuting the arguments of Ptolemy and Aristotle, but by producing many counter-arguments; in particular, some which relate to physical effects whose causes can perhaps be assigned in no other way. In addition there are astronomical arguments derived from many things in my new celestial discoveries that plainly confute the Ptolemaic system while admirably agreeing with and confirming the contrary hypothesis."

"It may be true that and (not science and evolution) are among the causes of atheism and materialism. It is at least equally true that biblical literalism, from its earlier flat-earth and geocentric forms to its recent young-earth and flood-geology forms, is one of the major causes of atheism and materialism. Many scientists and intellectuals have simply taken the literalists at their word and rejected biblical materials as being superseded or contradicted by modern science. Without having in hand a clear and persuasive alternative, they have concluded that it is nobler to be damned by the literalists than to dismiss the best testimony of research and reason. Intellectual honesty and integrity demand it."

"The odd thing about this story is that the heliocentric view was known in Europe long before Copernicus but, for various reasons, was totally ignored by the "established" dogma... All this time all kinds of absurdities were written about the heavens, the celestial spheres, the Empyrean and so on, which constituted the “established” view. And all the time the real knowledge was there and all those schoolmen, could, with some practical observation and sensible application of Mathematics, have found out that the Ptolemaic system was not true. But they did not: they preferred to argue about such weighty matters as how many angles could sit on the point of a pin. And when the proofs were presented to them in black and white, hard and irrefutable mathematical demonstrations, they still rejected them preferring the comforts of the ‘‘established” dogma. Theology (and Church interests) decided what was acceptable, not Mathematics."

"I shall try to sum up the main obstacles which arrested the progress of science for such an immeasurable time. The first was the splitting of the world into two spheres, and the mental split which resulted from it. The second was the geocentric dogma, the blind eye turned on the promising line of thought which had started with the Pythagoreans and stopped abruptly with Aristarchus of Samos. The third was the dogma of uniform motion in perfect circles. The fourth was the divorcement of science from mathematics. The fifth was the inability to realize that a body at rest tended to stay at rest, a body in motion tended to stay in motion. The main achievement of the first part of the scientific revolution was the removal of these five cardinal obstacles. This was done chiefly by three men: Copernicus, Kepler and Galileo. After that, the road was open to the Newtonian synthesis; from there on the journey led with rapidly gaining speed to the atomic age."

"Joseph Ratzinger has stood still because as a Bavarian Catholic in the Hellenistic tradition, interpreted in Roman terms, he wanted to stand still. To this degree he represented and represents a different basic model of theology and church, as different from mine as in astronomy Ptolemy's geocentric picture of the world is different from Copernicus' heliocentric picture."

"Let us... examine the point on which Newton, apparently with sound reasons, rests his distinction of absolute and relative motion. If the earth is affected with an absolute rotation about its axis, centrifugal forces are set up in the earth: it assumes an oblate form, the acceleration of gravity is diminished at the equator, the plane of Foucault's pendulum rotates, and so on. All these phenomena disappear if the earth is at rest and the other heavenly bodies are affected with absolute motion round it, such that the same relative rotation is produced. This is, indeed, the case, if we start ab initio from the idea of absolute space. But if we take our stand on the basis of facts, we shall find we have knowledge only of relative spaces and motions. Relatively, not considering the unknown and neglected medium of space, the motions of the universe are the same whether we adopt the Ptolemaic or the Copernican mode of view. Both views are, indeed, equally correct; only the latter is more simple and more practical. The universe is not twice given, with an earth at rest and an earth in motion; but only once, with its relative motions, alone determinable. It is, accordingly, not permitted us to say how things would be if the earth did not rotate. We may interpret the one case that is given us, in different ways. If, however, we so interpret it that we come into conflict with experience, our interpretation is simply wrong. The principles of mechanics can, indeed, be so conceived, that even for relative rotations centrifugal forces arise."

"Talk of the sublime, the exalted, the eternal, the passionate, of glory, challenge, or majesty fills some of us with bewilderment, discomfort, and embarrassment; others with sour resentment or scornful disbelief. To reinstate such values seems to us like trying to reinstate Ptolemaic astronomy—equally misguided, incomprehensible, and inimical to our perceived interests."

"It became clear that our Galaxy is only one system among many, and that the universe is far vaster than the particular stellar system to which the Sun and planets belong. Since then developments have been more rapid than at any time since the days of Copernicus, Digges and Bruno when the geocentric hypothesis of the cosmos received its death-blow."

"These seven bodies were the Sun, the Moon, Mercury, Venus, Mars, Jupiter, and Saturn, all of which were documented by the Babylonians over three thousand years ago. Until the sixteenth century, the most commonly held view was that the Earth was at the centre of the Universe and that the seven bodies revolved around the Earth."

"The affinities of all the beings of the same class have sometimes been represented by a great tree. I believe this simile largely speaks the truth. … As buds give rise by growth to fresh buds, and these, if vigorous, branch out and overtop on all sides many a feebler branch, so by generation I believe it has been with the great Tree of Life, which fills with its dead and broken branches the crust of the earth, and covers the surface with its ever branching and beautiful ramifications."

"For evolutionary biologists there is something very special about the classification of living organisms, something that is not true of any other kind of taxonomy. It follows from the idea of evolution that there is one uniquely correct branching family tree of all living things, and we can base our taxonomy upon it."

"Here Pharnaces... broke in... you are not going to draw me on... to answer your charges against the Stoics, unless we first get an account of your conduct in turning the universe upside." Lucius smiled : "Yes, my friend," he said, "only do not threaten us with... heresy, such as used to think that the Greeks should have had served upon Aristarchus of Samos, for shifting the hearth of the Universe, because that great man attempted 'to save phenomena' with his hypothesis that the heavens are stationary, while our earth moves round in an oblique orbit, at the same time whirling about her own axis. ...[W]hy are those who assume that the moon is an earth turning things upside down, any more than you who fix the earth where she is, suspended in mid air, a body considerably larger than the moon? At least mathematicians tell us so, calculating the magnitude of the obscuring body from... eclipses, and from the passages of the moon through the shadow. For the shadow of the earth is less as it extends, because the illuminating body is greater, and its upper extremity is fine and narrow, as even Homer... did not fail to notice. He called night 'pointed' because of the sharpness of the shadow. Such... is the body by which the moon is caught in her eclipses, and yet she barely gets clear by a passage equal to three of her own diameters. Just consider how many moons go to make an earth, if the earth cast a shadow as broad at its shortest as three moons. Yet you have fears for the moon lest she should tumble, while as for our earth, Aeschylus has perhaps satisfied you that Atlas'Stands, and the pillar which parts Heaven and Earth His shoulders prop, no load for arms t' embrace!'Then you think that under the moon there runs light air, quite inadequate to support a solid mass, while the earth, in Pindar's words, 'is compassed by pillars set on adamant.' And this is why Pharnaces has no fear... of the earth's falling, but pities those who lie under the orbit of the moon... Yet the moon has that which helps her against falling, in her very speed and the swing of her passage round, as objects placed in slings are hindered from falling by the whirl of the rotation. For everything is borne on in its own natural direction unless this is changed by some other force. Therefore the moon is not drawn down by her weight, since that tendency is counteracted by her circular movement. ...[B]ut the earth, being destitute of any other movement, might naturally be moved by its own weight; being heavier than the moon not merely in proportion to its greater bulk, but because the moon has been rendered lighter by heat and conflagration. It would actually seem that the moon, if she is a fire, needs earth all the more, a solid substance whereon she moves and to which she clings, so feeding and keeping up the force of her flame. For it is impossible to conceive fire as maintained without fuel. But you Stoics say that our earth stands firm without foundation or root." "Of course," said Pharnaces, "it keeps its proper and natural place, as being the essential middle point, that place around which all weights press and bear, converging towards it from all sides. But all the upper region, even if it receive any earth-like body thrown up with force, immediately thrusts it out hitherward, or rather lets it go, to be borne down by its own momentum.""

"Reason may be employed in two ways to establish a point: firstly, for the purpose of furnishing sufficient proof of some principle... Reason is employed in another way, not as furnishing a sufficient proof... but... confirming an already established principle, by showing the congruity of its results, as in astronomy the theory of eccentrics and epicycles is considered as established, because thereby the sensible appearances of the heavenly movements can be explained [saved] (possunt salvari apparentia sensibilia); not, however, as if this proof were sufficient, forasmuch as some other theory might explain them."

"[I]t does not follow that because heaven moves in a circle that the earth or something else rests at its center... because circular movement... does not require... any body at rest at the center... [I]t is possible to imagine that the earth moves with heaven in its daily movement... [A]ssuming that the earth moves with or contrariwise to heaven, it does not follow... that celestial movement would stop; so... this circular movement of heaven does not require that the earth should remain motionless at the center of the world. ...[I]t is not impossible that the whole earth moves, with a different movement or in another way... For otherwise the parts near the center would never reach the place where they are destroyed and would be perpetual... Against this objection and against the principal argument is the manifest evidence of heaven itself, for to save appearances and from our observations of celestial movements... there are spherical bodies called epicycles in heaven, and that each epicycle has its own proper circular movement about its center... different from the... heavenly sphere... [I]t is impossible... that any body should be at rest in the center of this epicycle."

"The first book contains the general description of the universe and the foundations by which he undertakes to save the appearances and the observations of all ages. He adds as much of the doctrine of sines and plane and spherical triangles as he deemed necessary to the work."

"For it is now clear to me that there are no solid spheres in the heavens... But there really are not any spheres in the heavens.... and those which have been devised by the authors to save the appearances exist only in the imagination, for the purpose of permitting the mind to conceive the motion which the heavenly bodies trace in their course and, by the aid of geometry, to determine the motion numerically through the use of arithmetic... Of course, almost the whole of antiquity and also very many recent philosophers consider as certain and unquestionable the view that the heavens are made of a hard and impenetrable substance, that it is divided into various spheres, and that the heavenly bodies, attached to some of these spheres, revolve on account of the motion of these spheres. But this opinion does not correspond to the truth of the matter..."

"Now, so far as appearances go, it... the same thing whether the heavens, that is, all space with its contents, revolve round a spectator at rest in the earth's centre, or whether that spectator... turn round in the opposite direction in his place, and view them in succession. The aspect of the heavens, at every instant, as referred to his horizon (which must be supposed to turn with him), will be the same in both suppositions. And since... appearances are also, so far as the stars are concerned, the same to a spectator on the surface as to one at the centre, it follows that, whether we suppose the heavens to revolve without the earth, or the earth within the heavens, in the opposite direction, the diurnal phenomena, to all its inhabitants, will be no way different. The Copernican astronomy adopts the latter as the true explanation of these phenomena, avoiding... the necessity of otherwise resorting to the cumbrous mechanism of a solid but invisible sphere, to which the stars must be supposed attached, in order that they may be carried round the earth without derangement of their relative situations inter se [among themselves]. Such a contrivance would..., suffice to explain the diurnal revolution of the stars, so as to "save appearances;" but the movements of the sun and moon, as well as those of the planets, are incompatible with such a supposition... On the other hand, that a spherical mass of moderate dimensions (or, rather, when compared with the surrounding and visible universe, of evanescent magnitude), held by no tie, and free to move and to revolve, should do so, in conformity with those general laws which, so far as we know, regulate the motions of all material bodies, is so far from being a postulate difficult to be conceded, that the wonder would rather be should the fact prove otherwise. As a postulate, therefore, we shall henceforth regard it... The earth's rotation on its axis so admitted, explaining, as it evidently does, the apparent motion of the stars in a completely satisfactory manner, prepares us for... its motion, bodily, in space... to explain... the apparently complex and enigmatical motions of the sun, moon, and planets. The Copernican astronomy adopts this idea in its full extent, ascribing to the earth, in addition to its motion of rotation about an axis, also one of translation or transference through space, in such a course or orbit, and so regulated in direction and celerity, as, taken in conjunction with the motions of the other bodies of the universe, shall render a rational account of the appearances they successively present... [i.e.,] an account of which the several parts, postulates, propositions, deductions, intelligibly cohere, without contradicting... experience. In this view of the Copernican doctrine it is rather a geometrical conception than a physical theory, inasmuch it simply assumes the requisite motions, without attempting to explain their mechanical origin, or assign them any dependence on physical causes. The Newtonian theory of gravitation supplies this deficiency, and, by showing that all the motions required by the Copernican conception must, and that no others can, result from a single, intelligible, and very simple dynamical law, has given a degree of certainty to this conception, as a matter of fact, which attaches to no other creation of the human mind."

"The system of Anaxagoras, like that of Empedokles, aimed at reconciling the Eleatic doctrine that corporeal substance is unchangeable with... a world which... presents the appearance of coming into being and passing away. The conclusions of Parmenides are... accepted and restated. Nothing can be added to all things; for there cannot be more than all, and all is always equal... Nor can anything pass away. What men commonly call coming into being and passing away is... mixture and separation... This... reads almost like a prose paraphrase of Empedokles (fr. 9); and it is... probable... Anaxagoras derived his theory... from his younger contemporary, whose poem was most likely published before his own treatise. ...Empedokles sought to save the world of appearance by maintaining that the opposites—hot and cold, moist and dry—were things, each...real in the Parmenidean sense. Anaxagoras regarded this as inadequate. ...[T]hings of which the world is made are not "cut off with a hatchet" ...the true formula must be: There is a portion of everything in everything."

"The language... as to the Moon's movements and the Epicyclic Theory... settled later on by Ptolemy... deserve careful examination... Astronomy had... become... technical and mathematical, sharply distinguished from general physical enquiry. Even Hipparchus... "though he loved truth above everything," yet was not versed in "natural science," and was content to explain the motions of the heavenly bodies by an hypothesis mathematically consistent, without care for its physical truth... Take the case of the Moon. Ptolemy was content to "save the phenomena"... by a system which admirably accounted for her very complex movements, but which involved the consequence that her distance from us at the nearest must he half that at the farthest, and her angular diameter therefore double!"

"When Copernicus, instead of leaving the earth at rest in the center of the world, gave it not only two rotations on its own center, but... an annual revolution around the sun, astronomers were able to maintain that these hypotheses are not... realities, that it suffices for them to be fictions by which the phenomena are saved in a simpler... more exact manner than... Ptolemy's devices. But physicists did not willingly use this loophole; they not only saw in the system of Copernicus a model enabling them to construct new tables of celestial movements, they also imagined something... that claims to reveal a truth. They imagined that the earth is a planet of the same nature as Venus, Mars, or Jupiter. The problem... can each of the... wandering stars be a world similar to the world in which we are living, having at its center an earth covered by water, surrounded by air?"

"Rosen quotes various passages from De Revolutionibus in which Copernicus uses without distinction, the terms: principle, assumption and hypothesis, for fundamental s: "Furthermore astronomy, that divine rather than human science, which inquires into the loftiest things, is not free from difficulties. Especially with regard to its principles (principia) and assumptions (assumptiones), which the Greek call 'hypotheses' (hypotheses)..." These axioms, in order to be recognized as true, must satisfy two conditions: 1) apparentias salvare (save the appearances): "the results deduced from them must agree with the observed phenomena within satisfactory limits of error."..: 2) aequalitatem tueri [to protect equality]: "They must be consistent with certain preconceptions, called 'axioms of physics,' such as that every celestial motion is circular, every celestial motion is uniform, and so forth.""

"Let us define the job of the astronomer in the classical phrase as "saving the appearances" of the celestial movements. ...[A]n astronomical theory must "save" in the sense of "preserve"– ...[i.e.,] it must not deny any of the apparent celestial movements as appearances, and in this bare sense, it might merely comprise a record of observed positions... [I]n order to take into account all the apparent movements, it must... predict apparent movements in the future from those observed in the past. ...[T]o be able to look backwards and forwards beyond recorded positions of the planets, it must arrange the celestial movements in a pattern of orderly recurrence. ...[B]y setting up this pattern of order, it saves... in a second sense... [I]t gives them salvation... by making them intelligible and... explicating them in terms of a permanent order."

"When Newton wrote his Mathematical Principles of Natural Philosophy and System of the World, he distinguished the phenomena to be saved from the reality he postulated. He distinguished the "absolute magnitudes" that appear in his axioms from their "sensible measures" which are determined experimentally. He discussed carefully the ways in which, "the true motions of particular bodies [may be determined] from the apparent," via the assertion that "the apparent motions... are the differences of true motions.""

"Greek astronomers observed intricate motions of the sun, moon, and planets on the two-dimensional sky. They explained them—saved the appearances—by positing simple regular motions... in three dimensions. The success... [was] brought to a triumphant conclusion by Kepler..."

"In the 1590s... Kepler adopted the ideas of Copernicus. In the heliocentric model... the simultaneous motion of the earth around the sun and about its own axis explained the observed motion of the planets and stars. Kepler set out to prove that this... hypothesis... an attempt to "save the appearances", did... correspond with reality. In doing so, however, he noticed that the circular orbits... proposed by Copernicus were not in keeping with his... observations. ...Kepler wanted... to glorify God, who... was responsible for the harmonious arrangement of the universe... This aim is... in the... first lines of the preface to The Secret of the Cosmos: "It is my intention... to show... that the most great and good Creator, in the creation of this moving universe and the arrangement of the heavens, looked to these five regular solids... so celebrated from the time of Pythagoras and Plato... and that he fitted to the nature of those solids the number of the heavens, their proportions and the law of their motions.""

"The statement of Diogenes, that Herakleides attended the Pythagorean schools is of... importance... as it is... likely... their influence (which is also perceptible in his ideas about atoms, which he calls masses...), tended to convince him of the truth of the... simple explanation of the daily motion of the stars proposed by Hiketas and Ekphantus. ... He first alludes to Herakleides when discussing the chapter in which Aristotle considers the motion of the starry vault. Aristotle... remarks that, taking for granted that the earth is at rest, the starry sphere... and the planets might either both be at rest, or both be in motion, or one be at rest and the other in motion. And these cases he considers (says Simplicius) "on account of there being some, among whom were Herakleides of Pontus and Aristarchus, who believed they could save the phenomena (account for the observed facts) by making the heavens and the stars be immovable, but making the earth move round the poles of the equator... from the west, each day one revolution as near as possible; but 'as near as possible' is added on account of the [daily] motion of the sun of one part (degree); so that, if then the earth does not move, which presently he (Aristotle) is going to show, the hypothesis of both being at rest cannot possibly save the phenomena.""

"In his commentary to the Physics of Aristotle, Simplicius gives us an interesting quotation from a commentary to the Meteorology of Posidonius, written by ... Dealing with the difference between physics and astronomy, Geminus says... to the former... belongs the examination of the nature, power, quality, birth, and decay of the heavens and the stars, but astronomy does not attempt... this, it makes known the arrangement of the heavenly bodies, it investigates the figure and size and distance of earth and sun and moon, the eclipses and conjunctions of stars and the quality and quantity of their motions... with help from arithmetic and geometry. But although the astronomer and the physicist often prosecute the same research... they do not proceed in the same manner, the latter seeking for causes and moving forces, while the astronomer finds certain methods, adopting which the observed phenomena can be accounted for. "For why do sun, moon, and planets appear to move unequally? Because, when we assume their circles to be excentric or the stars to move on an epicycle, the appearing anomaly can be accounted for.., and it is necessary to investigate in how many ways the phenomena can be represented, so that the theory of the wandering stars may be made to agree with the ... Therefore also... Herakleides of Pontus... said that also when the earth moved... and the sun stood still.., could the irregularity observed relatively to the sun be accounted for. ...[I]t is not the astronomer's business to see what by its nature is immovable and of what kind the moved things are, but framing hypotheses as to some things being in motion and others being fixed, he considers which hypotheses are in conformity with the phenomena in the heavens. He must accept as his principles from the physicist, that the motions of the stars are simple uniform, and regular, of which he shows that the revolutions are circular, some along parallels, some along oblique circles." This... distinguishes clearly between the physically true causes of observed phenomena and a mere mathematical hypothesis which (whether true or not) is able to "save the phenomena." This expression is ... a favourite... with Simplicius, who doubtless had it from the authors long anterior to himself, from whose works he derived his knowledge. It means that a certain hypothesis is able to account for the apparently irregular phenomena revealed by observation, which at first sight are puzzling and seem to defy all attempts to make them agree with the assumed regularity of all motions, both as to velocity and direction. In this passage Geminus points out that an astronomer's chief duty is to frame a theory which can represent the observed motions and make them subject to calculation, while it is for this purpose quite immaterial whether the theory is physically true or not."

"[I]n Plutarch's book On the face in the disc of the Moon...[o]ne of the persons in the dialogue, being called to account for turning the world upside down, says that he is quite content so long as he is not accused of impiety, "like as Kleanthes held that Aristarchus of Samos ought to be accused of impiety for moving the hearth of the world.., as the man in order to save the phenomena supposed... that the heavens stand still and the earth moves in an oblique circle at the same time as it turns round its axis.""

"[T]he principal reason why the heliocentric idea fell perfectly flat, was the rapid rise of practical astronomy, which had commenced from the time when the Alexandrian Museum became a centre of learning in the Hellenistic world. Aristarchus had no other phenomena to "save" except the stationary points and retrograde motions of the planets as well as their change of brilliancy; he may even have neglected the inequality of the sun's apparent motion originally discovered by Euktemon and recognized by Kalippus. But when similar and much more marked inequalities began to be perceived in the motions of the other planets, the hopelessness of trying to account for them by the beautifully simple idea of Aristarchus must have given the deathblow to his system, which thereby even among mathematicians lost its only claim to acceptance, that of being able to "save the phenomena." Most likely, as we have already said, these new inequalities had already more or less dimly commenced to make themselves felt in the days of Apollonius... and in that case we can understand why he did not feel disposed to simplify the system of movable excentrics by gathering the reins of all the unruly planetary steeds into one mighty hand, that of ."

"While knowledge of the dimensions of the universe had... advanced, philosophers found it... difficult to agree with regard to the physical constitution of... heavenly bodies, though all acknowledged that they were of a fiery nature, the Stoics in... supposing them... of... pure fire or ether, which pervaded... upper regions of space. ...[T]he peculiar appearance of the "face of the moon" pointed to its being... different... and... Anaxagoras and Demokritus... recognized... it was a solid mass having mountains and plains, while Plato held it to be chiefly... earthlike matter. ...[In] Plutarch "On the face in the disc of the moon"... opinion of the Stoics [that the moon is a mixture of air and gentle fire] is refuted, since the moon ought not... be invisible at new moon if it did not borrow all its light from the sun; and this... proves... it is not... a substance like glass or crystal, since s would... be impossible. The manner in which the sunlight is reflected... and... absence of a bright, reflected image of the sun and... earth, prove... the substance of the moon is not polished but is like... earth. ...Plutarch ...to combat the idea that the moon cannot be like the earth since it is not in the lowest place ...asserts ...it is not proved ...earth is in the centre of the universe, as space is infinite and therefore has no centre; ...if everything heavy and earthy were crowded together ...we should expect all ...fiery bodies ...likewise brought together."

"[T]he heliocentric idea of Aristarchus might just as well have sprung out of the epicyclic theory as from that of movable excentrics... But with regard to the curious dependence of each planet on the sun in the Ptolemaic system.., the zodiacal inequality of the planets showed that in any case a simple circular motion would not "save the phenomena"; while the discovery of a strongly marked inequality of the moon, depending on its position with regard to the sun, confirmed the notion that the sun was mixed up in the theories of all the celestial bodies alike. ...For more than fourteen hundred years it remained the Alpha and Omega of theoretical astronomy, and whatever views were held as to the constitution of the world, Ptolemy's system was almost universally accepted as the foundation of astronomical science."

"He gives the Greek text of the Placita Philosophorum... about Philolaus, Herakleides and Ekphantus, and continues: " Occasioned by this I also began to think of a motion of the earth, and although the idea seemed absurd, still, as others before me had been permitted to assume certain circles in order to explain the motions of the stars, I believed it would readily be permitted me to try whether on the assumption of some motion of the earth better explanations of the revolutions of the heavenly spheres might not be found. And thus I have, assuming the motions which I in the following work attribute to the earth, after long and careful investigation, finally found that when the motions of the other planets are referred to the circulation of the earth and are computed for the revolution of each star, not only do the phenomena necessarily follow therefrom, but the order and magnitude of the stars and all their orbs and the heaven itself are so connected that in no part can anything be transposed without confusion to the rest and to the whole universe." According to this statement, Copernicus first noticed how great was the difference of opinion among learned men as to the planetary motions; next he noticed that some had even attributed some motion to the earth, and finally he considered whether any assumption of that kind would help matters. ...It must then have struck him as a strange coincidence that the revolution of the sun round the and the revolution of the epicycle-centres of Mercury and Venus round the zodiac should take place in the same period, a year, while the period of the three outer planets in their epicycles was the synodic period, i.e. the time between two successive oppositions to the sun. This curious relationship between the sun and the planets must have struck scores of philosophers, but at last the problem was taken up by a man of a thoroughly unprejudiced mind and with a clear mathematical head. Probably it suddenly flashed on him that perhaps each of the deferents of the two inner planets and the epicycles of the three outer ones simply represented an orbit passed over by the earth in a year, and not by the sun! His emotion on finding that this assumption would really "save the phenomena," as the ancients had called it, that it would explain why Mercury and Venus always kept near the sun and why all the planets annually showed such strange irregularities in their motions, his emotion on finding this clear and beautifully simple solution of the ancient mystery must have been as great as that which long after overcame Newton when he discovered the law of universal gravitation. But Copernicus is silent on this point. This may have been the way followed by Copernicus, but we cannot be sure..."

"Korea’s science and technology are worth knowing and thinking about in connection with technology transfer for special reasons. Unlike China, Korea’s styles in thinking systematically and objectively about nature and in developing instruments and techniques of material culture were always defined in the shadow of a large sophisticated nearby civilization. The Korean experience differs from Japan’s in that its influences from China flowed in more freely and directly, across a shared land border or a short stretch of sea. It was from Korea in fact that new sciences and arts were carried into Japan during the early centuries until regular contact between Japan and China became possible. As recent Korean and Japanese scholarship begins to cohere, it is becoming plain that we have not yet adequately recognized what a great part immigrant Koreans played in the formative phases of Japanese civilization as men of learning, craftsmen, and indeed nobles. Korea thus presents for our reflection the case of a country seeking to maintain its identity against pressures too imminent to be shut out."

"(Jeon Sang-woon) is a Korean, and his pride in certain inventions and techniques is perceptibly greater than if he were a foreigner writing about Korean science. He knows that he is addressing a world-wide readership most of whom did not dream before they picked up his book that Korea is entitled to exert any claim upon the universal history of science. He knows that many educated people in Europe and the United States are just recovering from the shock of learning Joseph Needham’s lesson, that the Chinese tradition is as indispensable as that of the early West in determining the potentialities of science. This book opens up still another range of awareness by demonstrating that peripheral societies must be examined with equal seriousness if we are not to overlook real originality. The author also knows that this implication will be equally surprising to most of his fellow Koreans. In Korea today the power to exploit nature is seen as an importation, as foreign in its essence. Few people are aware that, say, Korea in 1400 may very well have had the most advanced astronomicalobservatories in the world. Is it possible that science is not fundamentally Caucasian and Judeo-Christian (and all sorts-of other things Koreans are not) after all?"