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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Retain Quotes (57 quotes)

...a man estimable for his learning, amiable for his life, and venerable for his piety. Arbuthnot was a man of great comprehension, skilful in his profession, versed in the sciences, acquainted with ancient literature, and able to animate his mass of knowledge by a bright and active imagination; a scholar with great brilliance of wit; a wit who, in the crowd of life, retained and discovered a noble ardour of religious zeal.
The Lives of the English Poets (1826), vol. 2, 257.
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A huge net is being dragged across the sea floor, destroying everything in its path. Ahead of it bloom undersea forests and their hundreds and thousands of living creatures, both plant and animal; behind it is a desert. The net is pulled to the surface and most of the dead and dying life forms in it are thrown out. A few marketable species are retained. [Trawling] is like taking a front-end loader and scraping up your entire front garden and shredding it, keeping a few pebbles, and dumping the rest of it down the drain.
In Payback: Debt and the Shadow Side of Wealth (2008), 191.
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Academies have been instituted to guard the avenues of their languages, to retain fugitives, and repulse intruders; but their vigilance and activity have hitherto been vain; sounds are too volatile and subtile for legal restraints; to enchain syllables, and to lash the wind, are equally the undertakings of pride, unwilling to measure its desires by its strength.
From Dictionary of the English Language (1818), Vol. 1, Preface, xxiii. Note: Subtile means subtle.
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All children are curious and I wonder by what process this trait becomes developed in some and suppressed in others. I suspect again that schools and colleges help in the suppression insofar as they meet curiosity by giving the answers, rather than by some method that leads from narrower questions to broader questions. It is hard to satisfy the curiosity of a child, and even harder to satisfy the curiosity of a scientist, and methods that meet curiosity with satisfaction are thus not apt to foster the development of the child into the scientist. I don't advocate turning all children into professional scientists, although I think there would be advantages if all adults retained something of the questioning attitude, if their curiosity were less easily satisfied by dogma, of whatever variety.
The Nature of Natural History (1950, 1990), 256-257.
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All good intellects have repeated, since Bacon’s time, that there can be no real knowledge but that which is based on observed facts. This is incontestable, in our present advanced stage; but, if we look back to the primitive stage of human knowledge, we shall see that it must have been otherwise then. If it is true that every theory must be based upon observed facts, it is equally true that facts cannot be observed without the guidance of some theory. Without such guidance, our facts would be desultory and fruitless; we could not retain them: for the most part we could not even perceive them.
The Positive Philosophy, trans. Harriet Martineau (1853), Vol. 1, 3-4.
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An old writer says that there are four sorts of readers: “Sponges which attract all without distinguishing; Howre-glasses which receive and powre out as fast; Bagges which only retain the dregges of the spices and let the wine escape, and Sives which retaine the best onely.” A man wastes a great many years before he reaches the ‘sive’ stage.
Address for the Dedication of the New Building of the Boston Medical Library (12 Jan 1901). Printed as 'Books and Men', The Boston Medical and Surgical Journal (17 Jan 1901), 144, No. 3, 60. [Presumably “Howre-glasses” refers to Hour-glasses. -Webmaster]
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As he sat alone in a garden, he [Isaac Newton in 1666, age 24] fell into a speculation on the power of gravity; that as this power is not found sensibly diminished at the remotest distance from the centre of the earth to which we can rise, neither at the tops of the loftiest buildings, nor even on the summits of the highest mountains, it appeared to him reasonable to conclude that this power must extend much further than was usually thought: why not as high as the moon? said he to himself; and if so, her motion must be influenced by it; perhaps she is retained in her orbit thereby.
View of Newton's Philosophy (1728), preface. In William Whewell, History of the Inductive Sciences (1847), Vol. 2, 166. Pemberton's narrative is based on firsthand conversations with Newton himself.
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As soon … as it was observed that the stars retained their relative places, that the times of their rising and setting varied with the seasons, that sun, moon, and planets moved among them in a plane, … then a new order of things began.… Science had begun, and the first triumph of it was the power of foretelling the future; eclipses were perceived to recur in cycles of nineteen years, and philosophers were able to say when an eclipse was to be looked for. The periods of the planets were determined. Theories were invented to account for their eccentricities; and, false as those theories might be, the position of the planets could be calculated with moderate certainty by them.
Lecture delivered to the Royal Institution (5 Feb 1864), 'On the Science of History'. Collected in Notices of the Proceedings at the Meetings of the Members of the Royal Institution of Great Britain with Abstracts of the Discourses (1866), Vol. 4, 187.
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Book-knowledge is a poor resource … In many cases, ignorance is a good thing: the mind retains its freedom of investigation and does not stray along roads that lead nowhither, suggested by one’s reading. … Ignorance can have its advantages; the new is found far from the beaten track.
In Jean-Henri Fabre and Alexander Teixeira de Mattos (trans.), The Life and Love of the Insect (1918), 243.
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By considering the embryological structure of man - the homologies which he presents with the lower animals - the rudiments which he retains - and the reversions to which he is liable, we can partly recall in imagination the former condition of our early progenitors; and we can approximately place them in their proper position in the zoological series. We thus learnt that man is descended from a hairy quadruped, furnished with a tail and pointed ears, probably arboreal in its habit, and an inhabitant of the Old World. This creature, if its whole structure had been examined by a naturalist, would have been classed among the Quadrumana, as surely as would be the common and still more ancient progenitor of the Old and New World monkeys.
The Descent of Man (1871), Vol. 2, 389.
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By the classification of any series of objects, is meant the actual or ideal arrangement together of those which are like and the separation of those which are unlike ; the purpose of this arrangement being to facilitate the operations of the mind in clearly conceiving and retaining in the memory the characters of the objects in question.‎
In 'Lecture I: On the Classification of Animals', Lectures on the Elements of Comparative Anatomy: On the ... - (1864), 1.
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Evolution is an integration of matter and concomitant dissipation of motion during which the matter passes from an indefinite incoherent homogeneity to a definite coherent heterogeneity, and during which the retained motion undergoes a parallel transformation.
First Principles of a New System of Philosophy (1864), 407.
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Exper. I. I made a small hole in a window-shutter, and covered it with a piece of thick paper, which I perforated with a fine needle. For greater convenience of observation I placed a small looking-glass without the window-shutter, in such a position as to reflect the sun's light, in a direction nearly horizontal, upon the opposite wall, and to cause the cone of diverging light to pass over a table on which were several little screens of card-paper. I brought into the sunbeam a slip of card, about one-thirtieth of an inch in breadth, and observed its shadow, either on the wall or on other cards held at different distances. Besides the fringes of colour on each side of the shadow, the shadow itself was divided by similar parallel fringes, of smaller dimensions, differing in number, according to the distance at which the shadow was observed, but leaving the middle of the shadow always white. Now these fringes were the joint effects of the portions of light passing on each side of the slip of card and inflected, or rather diffracted, into the shadow. For, a little screen being placed a few inches from the card, so as to receive either edge of the shadow on its margin, all the fringes which had before been observed in the shadow on the wall, immediately disappeared, although the light inflected on the other side was allowed to retain its course, and although this light must have undergone any modification that the proximity of the other edge of the slip of card might have been capable of occasioning... Nor was it for want of a sufficient intensity of light that one of the two portions was incapable of producing the fringes alone; for when they were both uninterrupted, the lines appeared, even if the intensity was reduced to one-tenth or one-twentieth.
'Experiments and Calculations Relative to Physical Optics' (read in 1803), Philosophical Transactions (1804), 94, 2-3.
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Governments and parliaments must find that astronomy is one of the sciences which cost most dear: the least instrument costs hundreds of thousands of dollars, the least observatory costs millions; each eclipse carries with it supplementary appropriations. And all that for stars which are so far away, which are complete strangers to our electoral contests, and in all probability will never take any part in them. It must be that our politicians have retained a remnant of idealism, a vague instinct for what is grand; truly, I think they have been calumniated; they should be encouraged and shown that this instinct does not deceive them, that they are not dupes of that idealism.
In Henri Poincaré and George Bruce Halsted (trans.), The Value of Science: Essential Writings of Henri Poincare (1907), 84.
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I have long been interested in landscape history, and when younger and more robust I used to do much tramping of the English landscape in search of ancient field systems, drove roads, indications of prehistoric settlement. Towns and cities, too, which always retain the ghost of their earlier incarnations beneath today's concrete and glass.
From 'An Interview With Penelope Lively', in a Reading Guide to the book The Photograph on the publisher's Penguin website.
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I myself consider that gravity is merely a certain natural inclination with which parts are imbued by the architect of all things for gathering themselves together into a unity and completeness by assembling into the form of a globe. It is easy to believe that the Sun, Moon and other luminaries among the wandering stars have this tendency also, so that by its agency they retain the rounded shape in which they reveal themselves, but nevertheless go round their orbits in various ways. If then the Earth also performs other motions, as for example the one about the centre, they must necessarily be like those which are similarly apparent in many external bodies in which we find an annual orbit.
'Book One. Chapter IX. Whether several motions can be attributed to the Earth, and on the centre of the universe', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans. A. M. Duncan (1976), 46.
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I should like to draw attention to the inexhaustible variety of the problems and exercises which it [mathematics] furnishes; these may be graduated to precisely the amount of attainment which may be possessed, while yet retaining an interest and value. It seems to me that no other branch of study at all compares with mathematics in this. When we propose a deduction to a beginner we give him an exercise in many cases that would have been admired in the vigorous days of Greek geometry. Although grammatical exercises are well suited to insure the great benefits connected with the study of languages, yet these exercises seem to me stiff and artificial in comparison with the problems of mathematics. It is not absurd to maintain that Euclid and Apollonius would have regarded with interest many of the elegant deductions which are invented for the use of our students in geometry; but it seems scarcely conceivable that the great masters in any other line of study could condescend to give a moment’s attention to the elementary books of the beginner.
In Conflict of Studies (1873), 10-11.
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If this fire determined by the sun, be received on the blackest known bodies, its heat will be long retain'd therein; and hence such bodies are the soonest and the strongest heated by the flame fire, as also the quickest dried, after having been moisten'd with water; and it may be added, that they also burn by much the readiest: all which points are confirm'd by daily observations. Let a piece of cloth be hung in the air, open to the sun, one part of it dyed black, another part of a white colour, others of scarlet, and diverse other colours; the black part will always be found to heat the most, and the quickest of all; and the others will each be found to heat more slowly, by how much they reflect the rays more strongly to the eye; thus the white will warm the slowest of them all, and next to that the red, and so of the rest in proportion, as their colour is brighter or weaker.
A New Method of Chemistry, 2nd edition (1741), 262.
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In the year 1666 he retired again from Cambridge... to his mother in Lincolnshire & whilst he was musing in a garden it came into his thought that the power of gravity (wch brought an apple from the tree to the ground) was not limited to a certain distance from the earth but that this power must extend much farther than was usually thought. Why not as high as the moon said he to himself & if so that must influence her motion & perhaps retain her in her orbit, whereupon he fell a calculating what would be the effect of that supposition but being absent from books & taking the common estimate in use among Geographers & our seamen before Norwood had measured the earth, that 60 English miles were contained in one degree of latitude on the surface of the Earth his computation did not agree with his theory & inclined him then to entertain a notion that together with the force of gravity there might be a mixture of that force wch the moon would have if it was carried along in a vortex.
[The earliest account of Newton, gravity and an apple.]
Memorandum of a conversation with Newton in August 1726. Quoted in Richard Westfall, Never at Rest: A Biography of Isaac Newton (1980), 154.
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It has long been a complaint against mathematicians that they are hard to convince: but it is a far greater disqualification both for philosophy, and for the affairs of life, to be too easily convinced; to have too low a standard of proof. The only sound intellects are those which, in the first instance, set their standards of proof high. Practice in concrete affairs soon teaches them to make the necessary abatement: but they retain the consciousness, without which there is no sound practical reasoning, that in accepting inferior evidence because there is no better to be had, they do not by that acceptance raise it to completeness.
In An Examination of Sir William Hamilton’s Philosophy (1878), 611.
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It is possible to state as a general principle that the mesodermic phagocytes, which originally (as in the sponges of our days) acted as digestive cells, retained their role to absorb the dead or weakened parts of the organism as much as different foreign intruders.
'Uber die Pathologische Bedeutung der Intracellularen Verduung', Fortschritte der Medizin (1884), 17, 558-569. Trans. Alfred I. Tauber and Leon Chernyak, Metchnikoff and the Origins of Immunology (1991), 141.
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It seems wonderful to everyone that sometimes stones are found that have figures of animals inside and outside. For outside they have an outline, and when they are broken open, the shapes of the internal organs are found inside. And Avicenna says that the cause of this is that animals, just as they are, are sometimes changed into stones, and especially [salty] stones. For he says that just as the Earth and Water are material for stones, so animals, too, are material for stones. And in places where a petrifying force is exhaling, they change into their elements and are attacked by the properties of the qualities [hot, cold, moist, dry] which are present in those places, and in the elements in the bodies of such animals are changed into the dominant element, namely Earth mixed with Water; and then the mineralizing power converts [the mixture] into stone, and the parts of the body retain their shape, inside and outside, just as they were before. There are also stones of this sort that are [salty] and frequently not hard; for it must be a strong power which thus transmutes the bodies of animals, and it slightly burns the Earth in the moisture, so it produces a taste of salt.
De Mineralibus (On Minerals) (c.1261-1263), Book I, tract 2, chapter 8, trans. Dorothy Wyckoff (1967), 52-53.
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It surely can be no offence to state, that the progress of science has led to new views, and that the consequences that can be deduced from the knowledge of a hundred facts may be very different from those deducible from five. It is also possible that the facts first known may be the exceptions to a rule and not the rule itself, and generalisations from these first-known facts, though useful at the time, may be highly mischievous, and impede the progress of the science if retained when it has made some advance.
Sections and Views Illustrative of Geological Phenomena (1830), viii.
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Just as eating contrary to the inclination is injurious to the health, so study without desire sports the memory, and it retains nothing that it takes in.
…...
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Man was made to try. Afterward he’s free to keep or throw away what pleasures or what promise that he’s found. What knowledge gained or stumbled on can be discarded or retained.
In 'Reactions to Man’s Landing on the Moon Show Broad Variations in Opinions', The New York Times (21 Jul 1969), 6.
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Many will, no doubt, prefer to retain old unsystematic names as far as possible, but it is easy to see that the desire to avoid change may carry us too far in this direction; it will undoubtedly be very inconvenient to the present generation of chemists to abandon familiar and cherished names, but nevertheless it may be a wise course to boldly face the difficulty, rather than inflict on coming generations a partially illogical and unsystematic nomenclature.
'International Conference on Chemical Nomenclature', Nature (19 May 1892), 46, 57.
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Modesty. Never think you know all. Though others may flatter you, retain the courage to say, “I am ignorant”.
Translation of a note, 'Bequest of Pavlov to the Academic Youth of his Country', written a few days before his death for a student magazine, The Generation of the Victors. As published in 'Pavlov and the Spirit of Science', Nature (4 Apr 1936), 137, 572.
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My earliest impressions of wildlife and its pursuit retain a vivid sharpness of form, color, and atmosphere that half a century of professional wildlife experience has failed to obliterate or improve on.
In 'Red Legs Kicking', A Sand County Almanac, and Sketches Here and There (1949, 1987), 120.
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Nevertheless, his [Dostoyevsky’s] personality retained sadistic traits in plenty, which show themselves in his irritability, his love of tormenting, and his intolerance even towards people he loved, and which appear also in the way in which, as an author, he treats his readers. Thus in little things he was a sadist towards others, and in bigger things a sadist towards himself, in fact a masochist—that is to say the mildest, kindliest, most helpful person possible.
In James Strachey (ed.), 'Dostoyevsky and Parricide', The Standard Edition of the Complete Psychological Works of Sigmund Freud (1953-74), Vol. 21, 178-179. Reprinted in Writings on Art and Literature (1997), 236
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No one must think that Newton’s great creation can be overthrown in any real sense by this [Theory of Relativity] or by any other theory. His clear and wide ideas will for ever retain their significance as the foundation on which our modern conceptions of physics have been built.
In 'Time, Space, and Gravitation', The Times (28 Nov 1919). Excerpted in David E. Rowe and Robert J. Schulmann, Einstein on Politics: His Private Thoughts and Public Stands on Nationalism, Zionism, War, Peace, and the Bomb (2007), 104.
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Not only such Actions as were at first Indifferent to us, but even such as were Painful, will by Custom and Practice become Pleasant. Sir Francis Bacon observes in his Natural Philosophy, that our Taste is never pleased better, than with those things which at first created a Disgust in it. He gives particular Instances of Claret, Coffee, and other Liquors, which the Palate seldom approves upon the first Taste; but when it has once got a Relish of them, generally retains it for Life.
In The Spectator (2 Aug 1712), No. 447, collected in The Spectator (9th ed., 1728), Vol. 6, 225-226.
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Nothing retains less of desire in art, in science, than this will to industry, booty, possession.
Mad Love (1937) translated by Mary Ann Caws (1988), 25.
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Now if Light be reflected, not by impinging on the solid parts of Bodies, but by some other principle; it's probable that as many of its Rays as impinge on the solid parts of Bodies are not reflected but stifled and lost in the Bodies. For otherwise we must allow two sorts of Reflexions. Should all the Rays be reflected which impinge on the internal parts of clear Water or Crystal, those Substances would rather have a cloudy Colour than a clear Transparency. To make Bodies look black, it's necessary that many Rays be stopp'd, retained, and lost in them; and it seems not probable that any Rays can be stopp'd and stifled in them which do not impinge on their parts.
Opticks (1704), Book 2, Part 3, Prop. VIII, 69.
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Our most distinguished “man of science” was the then veteran John Dalton. He was rarely absent from his seat in a warm corner of the room during the meetings of the Literary and Philosophical Society. Though a sober-minded Quaker, he was not devoid of some sense of fun; and there was a tradition amongst us, not only that he had once been a poet, but that, although a bachelor, two manuscript copies were still extant of his verses on the subject of matrimonial felicity; and it is my belief there was foundation for the tradition. The old man was sensitive on the subject of his age. Dining one day ... he was placed between two ladies ... [who] resolved to extract from him some admission on the tender point, but in vain. Though never other than courteous, Dalton foiled all their feminine arts and retained his secret. ... Dalton's quaint and diminutive figure was a strongly individualized one.
In Reminiscences of a Yorkshire Naturalist (1896), 73-74.
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Owing to the imperfection of language the offspring is termed a new animal, but it is in truth a branch or elongation of the parent; since a part of the embryon-animal is, or was, a part of the parent; and therefore in strict language it cannot be said to be entirely new at the time of its production; and therefore it may retain some of the habits of the parent-system. (1794)
Zoonomia, Or, The Laws of Organic Life, in three parts (1803), Vol. 1, 395.
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Physicians still retain something of their priestly origin; they would gladly do what they forbid.
Quoted in Frank Heynick, Jews and Medicine: An Epic Saga (2002), 293.
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Ploughing deep, your recipe for killing weeds, is also the recipe for almost every good thing in farming. … We now plough horizontally following the curvatures of the hills and hollows, on the dead level, however crooked the lines may be. Every furrow thus acts as a reservoir to receive and retain the waters, all of which go to the benefit of the growing plant, instead of running off into streams … In point of beauty nothing can exceed that of the waving lines and rows winding along the face of the hills and vallies.
In letter (17 Apr 1813) from Jefferson at Monticello to Charles Willson Peale. Collected in The Jefferson Papers: 1770-1826 (1900), 178-180.
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Progress, far from consisting in change, depends on retentiveness. When change is absolute there remains no being to improve and no direction is set for possible improvement: and when experience is not retained, as among savages, infancy is perpetual. Those who cannot remember the past are condemned to repeat it.
The Life of Reason, or the Phases of Human Progress (1954), 82.
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Scientists have one thing in common with children: curiosity. To be a good scientist you must have kept this trait of childhood, and perhaps it is not easy to retain just one trait. A scientist has to be curious like a child; perhaps one can understand that there are other childish features he hasn't grown out of.
What Little I Remember (1979), 86.
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Sylvester was incapable of reading mathematics in a purely receptive way. Apparently a subject either fired in his brain a train of active and restless thought, or it would not retain his attention at all. To a man of such a temperament, it would have been peculiarly helpful to live in an atmosphere in which his human associations would have supplied the stimulus which he could not find in mere reading. The great modern work in the theory of functions and in allied disciplines, he never became acquainted with …
What would have been the effect if, in the prime of his powers, he had been surrounded by the influences which prevail in Berlin or in Gottingen? It may be confidently taken for granted that he would have done splendid work in those domains of analysis, which have furnished the laurels of the great mathematicians of Germany and France in the second half of the present century.
In Address delivered at a memorial meeting at the Johns Hopkins University (2 May 1897), published in Bulletin of the American Mathematical Society (Jun 1897), 303. Also in Johns Hopkins University Circulars, 16 (1897), 54.
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Thales thought that water was the primordial substance of all things. Heraclitus of Ephesus… thought that it was fire. Democritus and his follower Epicurus thought that it was the atoms, termed by our writers “bodies that cannot be cut up” or, by some “indivisibles.” The school of the Pythagoreans added air and the earthy to the water and fire. Hence, although Democritus did not in a strict sense name them, but spoke only of indivisible bodies, yet he seems to have meant these same elements, because when taken by themselves they cannot be harmed, nor are they susceptible of dissolution, nor can they be cut up into parts, but throughout time eternal they forever retain an infinite solidity.
Vitruvius
In De Architectura, Book 2, Chap 2, Sec. 1. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 42.
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The Big Idea that had been developed in the seventeenth century ... is now known as the scientific method. It says that the way to proceed when investigating how the world works is to first carry out experiments and/or make observations of the natural world. Then, develop hypotheses to explain these observations, and (crucially) use the hypothesis to make predictions about the future outcome of future experiments and/or observations. After comparing the results of those new observations with the predictions of the hypotheses, discard those hypotheses which make false predictions, and retain (at least, for the time being) any hypothesis that makes accurate predictions, elevating it to the status of a theory. Note that a theory can never be proved right. The best that can be said is that it has passed all the tests applied so far.
In The Fellowship: the Story of a Revolution (2005), 275.
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The bones of Descartes were returned to France (all except those of the right hand, which were retained by the French Treasurer-General as a souvenir for his skill in engineering the transaction) and were re-entombed in what is now the Pantheon. There was to have been a public oration, but this was hastily forbidden by order of the crown, as the doctrines of Descartes were deemed to be still too hot for handling before the people.
In Men of Mathematics (1937), 51-52. The remains of Descartes were returned to his native France, seventeen years after he died in Stockholm, Sweden.
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The comparatively small progress toward universal acceptance made by the metric system seems to be due not altogether to aversion to a change of units, but also to a sort of irrepressible conflict between the decimal and binary systems of subdivision.
[Remarking in 1892 (!) that although decimal fractions were introduced about 1585, America retains measurements in halves, quarters, eights and sixteenths in various applications such as fractions of an inch, the compass or used by brokers.]
'Octonary Numeration', Bulletin of the New York Mathematical Society (1892),1, 1.
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The general knowledge of our author [Leonhard Euler] was more extensive than could well be expected, in one who had pursued, with such unremitting ardor, mathematics and astronomy as his favorite studies. He had made a very considerable progress in medical, botanical, and chemical science. What was still more extraordinary, he was an excellent scholar, and possessed in a high degree what is generally called erudition. He had attentively read the most eminent writers of ancient Rome; the civil and literary history of all ages and all nations was familiar to him; and foreigners, who were only acquainted with his works, were astonished to find in the conversation of a man, whose long life seemed solely occupied in mathematical and physical researches and discoveries, such an extensive acquaintance with the most interesting branches of literature. In this respect, no doubt, he was much indebted to an uncommon memory, which seemed to retain every idea that was conveyed to it, either from reading or from meditation.
In Philosophical and Mathematical Dictionary (1815), 493-494.
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The primary rocks, … I regard as the deposits of a period in which the earth’s crust had sufficiently cooled down to permit the existence of a sea, with the necessary denuding agencies,—waves and currents,—and, in consequence, of deposition also; but in which the internal heat acted so near the surface, that whatever was deposited came, matter of course, to be metamorphosed into semi-plutonic forms, that retained only the stratification. I dare not speak of the scenery of the period. We may imagine, however, a dark atmosphere of steam and vapour, which for age after age conceals the face of the sun, and through which the light of moon or star never penetrates; oceans of thermal water heated in a thousand centres to the boiling point; low, half-molten islands, dim through the log, and scarce more fixed than the waves themselves, that heave and tremble under the impulsions of the igneous agencies; roaring geysers, that ever and anon throw up their intermittent jets of boiling fluid, vapour, and thick steam, from these tremulous lands; and, in the dim outskirts of the scene, the red gleam of fire, shot forth from yawning cracks and deep chasms, and that bears aloft fragments of molten rock and clouds of ashes. But should we continue to linger amid a scene so featureless and wild, or venture adown some yawning opening into the abyss beneath, where all is fiery and yet dark,—a solitary hell, without suffering or sin,—we would do well to commit ourselves to the guidance of a living poet of the true faculty,—Thomas Aird and see with his eyes.
Lecture Sixth, collected in Popular Geology: A Series of Lectures Read Before the Philosophical Institution of Edinburgh, with Descriptive Sketches from a Geologist's Portfolio (1859), 297-298.
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The primitive history of the species is all the more fully retained in its germ-history in proportion as the series of embryonic forms traversed is longer; and it is more accurately retained the less the mode of life of the recent forms differs from that of the earlier, and the less the peculiarities of the several embryonic states must be regarded as transferred from a later to an earlier period of life, or as acquired independently. (1864)
As translated and quoted in Ernst Haeckel and E. Ray Lankester (trans.) as epigraph for Chap. 13, The History of Creation (1886), Vol. 1, 406.
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The test of a first-rate intelligence is the ability to hold two opposed ideas in mind at the same time and still retain the ability to function.
The Crack-Up (1936, 1993), 69.
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There could not be a language more universal and more simple, more exempt from errors and obscurities, that is to say, more worthy of expressing the invariable relations of natural objects. Considered from this point of view, it is coextensive with nature itself; it defines all the sensible relations, measures the times, the spaces, the forces, the temperatures; this difficult science is formed slowly, but it retains all the principles it has once acquired. It grows and becomes more certain without limit in the midst of so many errors of the human mind.
From Théorie Analytique de la Chaleur, Discours Préliminaire (Theory of Heat, Introduction), quoted as translated in F.R. Moulton, 'The Influence of Astronomy on Mathematics', Science (10 Mar 1911), N.S. Vol. 33, No. 845, 359.
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There exists for every liquid a temperature at which no amount of pressure is sufficient to retain it in the liquid form.
[These words are NOT by Thomas Andrews. See below.]
This is NOT a quote by Andrews. It is only included here to provide this caution, because at least one book attributes it incorrectly to Andrews, as in John Daintith, Biographical Encyclopedia of Scientists (3rd. ed., 2008), 19. Webmaster has determined that these words are those of William Allen Miller, in Elements of Chemistry (1855), Vol. 1, 257. In the article on Thomas Andrews in Charles Coulston Gillespie (ed.), Dictionary of Scientific Biography (1970), Vol. 1, 161, the later, third edition (1863) of Miller's textbook is named as the first printed account of Andrews' work. (Andrews had furnished his experimental results to Miller by letter.) After stating Miller's description of Andrews' results, the article in DSB refers ambiguously to “his” summary and gives the quote above. No quotation marks are present in Miller's book. Specifically, in fact, the words in the summary are by Miller. This is seen in the original textbook, because Miller prefaced the quote with “From these experiments it is obvious that...” and is summarizing the related work of several scientists, not just Andrews. Miller described the earlier experiments of those other researchers in the immediately preceding pages. It is clear that the quote does not come from Andrews when comparing Miller's first edition (1855), which had not yet included the work by Andrews. Thus, the same summary words (as quoted above) in the earliest edition refer to the experiments of only the other researchers, not including Andrews. Furthermore, the quote is not present in the Bakerian Lecture by Andrews on his work, later published in Philosophical Transactions of the Royal Society (1869). Webmaster speculates Daintith's book was written relying on a misreading of the ambiguous sentence in DSB.
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This science [experimental science] alone, therefore, knows how to test perfectly what can be done by nature, what by the effort of art, what by trickery, what the incantations, conjurations, invocations, deprecations, sacrifices that belong to magic mean and dream of, and what is in them, so that all falsity may be removed and the truth alone of art and nature may be retained. This science alone teaches us how to view the mad acts of magicians, that they may be not ratified but shunned, just as logic considers sophistical reasoning.
In Opus Majus (1267).
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Those who have taken upon them to lay down the law of nature as a thing already searched out and understood, whether they have spoken in simple assurance or professional affectation, have therein done philosophy and the sciences great injury. For as they have been successful in inducing belief, so they have been effective in quenching and stopping inquiry; and have done more harm by spoiling and putting an end to other men's efforts than good by their own. Those on the other hand who have taken a contrary course, and asserted that absolutely nothing can be known — whether it were from hatred of the ancient sophists, or from uncertainty and fluctuation of mind, or even from a kind of fullness of learning, that they fell upon this opinion — have certainly advanced reasons for it that are not to be despised; but yet they have neither started from true principles nor rested in the just conclusion, zeal and affectation having carried them much too far...
Now my method, though hard to practice, is easy to explain; and it is this. I propose to establish progressive stages of certainty. The evidence of the sense, helped and guarded by a certain process of correction, I retain. But the mental operation which follows the act of sense I for the most part reject; and instead of it I open and lay out a new and certain path for the mind to proceed in, starting directly from the simple sensuous perception.
Novum Organum (1620)
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To have heard without retaining does not make knowledge.
In 'Paradise', The Divine Comedy of Dante Alighieri (1308-1320), translated by Charles Eliot Norton (1902), Vol. 3, Canto 5, line 41-2, 36.
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What I have related is sufficient for establishing the main principle, namely, that the heat which disappears in the conversion of water into vapour, is not lost, but is retained in vapour, and indicated by its expansive form, although it does not affect the thermometer. This heat emerges again from this vapour when it becomes water, and recovers its former quality of affecting the thermometer; in short, it appears again as the cause of heat and expansion.
Lectures on the Elements of Chemistry, delivered in the University of Edinburgh (1803), Vol. I, 173.
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When you know a thing, to hold that you know it; and when you do not know a thing, to allow that you do not know it;—this is knowledge.
Confucius
In James Legge (trans.), 'The Confucian Analects', The Chinese Classics: Life and Teachings of Confucius (1861), Vol. 1, Book 2, Chap. 17, 15
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When you wish to instruct, be brief; that men's minds take in quickly what you say, learn its lesson, and retain it faithfully. Every word that is unnecessary only pours over the side of a brimming mind.
In Norbert Guterman, The Anchor Book of Latin Quotations (1990), 193.
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Words were originally magic, and the word retains much of its old magical power even to-day, With words one man can make another blessed, or drive him to despair;… Words call forth effects and are the universal means of influencing human beings. Therefore let us not underestimate the use of words in psychotherapy.
From a series of 28 lectures for laymen, Part One, 'The Psychology of Errors'. Lecture 1, 'Introduction' collected in Sigmund Freud and G. Stanley Hall (trans.), A General Introduction to Psychoanalysis (1920), 3.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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- 80 -
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- 70 -
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- 50 -
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- 40 -
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