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Who said: “Science without religion is lame; religion without science is blind.”
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Home > Category Index for Science Quotations > Category Index A > Category: Attain

Attain Quotes (125 quotes)


Man is the result of slow growth; that is why he occupies the position he does in animal life. What does a pup amount to that has gained its growth in a few days or weeks, beside a man who only attains it in as many years.
In Orison Swett Marden, 'Bell Telephone Talk: Hints on Success by Alexander G. Bell', How They Succeeded: Life Stories of Successful Men Told by Themselves (1901), 35.
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Ueber den Glauben lässt sich wissenschaftlich nicht rechten, denn die Wissenschaft und der Glaube schliessen sich aus. Nicht so, dass der eine die andere unmöglich machte oder umgekehrt, sondern so, dass, soweit die Wissenschaft reicht, kein Glaube existirt und der Glaube erst da anfangen darf, wo die Wissenschaft aufhört. Es lässt „sich nicht läugnen, dass, wenn diese Grenze eingehalten wird, der Glaube wirklich reale Objekte haben kann. Die Aufgabe der Wissenschaft ist es daher nicht, die Gegenstände des Glaubens anzugreifen, sondern nur die Grenzen zu stecken, welche die Erkenntniss erreichen kann, und innerhalb derselben das einheitliche Selbstbewusstsein zu begründen.
There is no scientific justification for faith, for science and faith are mutually exclusive. Not that one made the other impossible, or vice versa, but that, as far as science goes, there is no faith, and faith can only begin where science ends. It can not be denied that, if this limit is adhered to, faith can really have real objects. The task of science, therefore, is not to attack the objects of faith, but merely to set the limits which knowledge can attain and to establish within it the unified self-esteem.
Original German from 'Der Mensch' (1849), collected in Gesammelte abhandlungen zur wissenschaftlichen medicin (1856), 6. Webmaster used Google translate for the English version. This longer quote unites the shorter quotes from within it shown separately on the Rudolf Virchow quotations page, with alternative translations, which begin: “There can be no scientific dispute…”, “Belief has no place…”, and “The task of science…”.
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A man does not attain the status of Galileo merely because he is persecuted; he must also be right.
In essay 'Velikovsky in Collision', Natural History (Mar 1975), collected in Ever Since Darwin: Reflections in Natural History (1977, 1992), 154.
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A mathematician who can only generalise is like a monkey who can only climb UP a tree. ... And a mathematician who can only specialise is like a monkey who can only climb DOWN a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise. ... There is, I think, a moral for the teacher. A teacher of traditional mathematics is in danger of becoming a down monkey, and a teacher of modern mathematics an up monkey. The down teacher dishing out one routine problem after another may never get off the ground, never attain any general idea. and the up teacher dishing out one definition after the other may never climb down from his verbiage, may never get down to solid ground, to something of tangible interest for his pupils.
From 'A Story With A Moral', Mathematical Gazette (Jun 1973), 57, No. 400, 86-87
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A modern branch of mathematics, having achieved the art of dealing with the infinitely small, can now yield solutions in other more complex problems of motion, which used to appear insoluble. This modern branch of mathematics, unknown to the ancients, when dealing with problems of motion, admits the conception of the infinitely small, and so conforms to the chief condition of motion (absolute continuity) and thereby corrects the inevitable error which the human mind cannot avoid when dealing with separate elements of motion instead of examining continuous motion. In seeking the laws of historical movement just the same thing happens. The movement of humanity, arising as it does from innumerable human wills, is continuous. To understand the laws of this continuous movement is the aim of history. … Only by taking an infinitesimally small unit for observation (the differential of history, that is, the individual tendencies of man) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.
War and Peace (1869), Book 11, Chap. 1.
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A patient pursuit of facts, and cautious combination and comparison of them, is the drudgery to which man is subjected by his Maker, if he wishes to attain sure knowledge.
In 'Productions Mineral, Vegetable and Animal', Notes on the State of Virginia (1787), 112.
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All knowledge attains its ethical value and its human significance only by the human sense with which it is employed. Only a good man can be a great physician.
Inaugural address (1882), quoted in Johann Hermann Baas, Henry Ebenezer Handerson (trans.), Outlines of the History of Medicine and the Medical Profession (1889), 966.
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An inventor is an opportunist, one who takes occasion by the hand; who, having seen where some want exists, successfully applies the right means to attain the desired end. The means may be largely, or even wholly, something already known, or there may be a certain originality or discovery in the means employed. But in every case the inventor uses the work of others. If I may use a metaphor, I should liken him to the man who essays the conquest of some virgin alp. At the outset he uses the beaten track, and, as he progresses in the ascent, he uses the steps made by those who have preceded him, whenever they lead in the right direction; and it is only after the last footprints have died out that he takes ice-axe in hand and cuts the remaining steps, few or many, that lift him to the crowning height which is his goal.
In Kenneth Raydon Swan, Sir Joseph Swan (1946), 44.
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And as to the faculties of the mind, setting aside the arts grounded upon words, and especially that skill of proceeding upon generall, and infallible rules, called Science; which very few have, and but in few things; as being not a native faculty, born within us; nor attained, (as Prudence,) while we look after somewhat else.
Leviathan (1651), ed. C. B. Macpherson (1968), Part 1, Chapter 13, 183.
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Architects who have aimed at acquiring manual skill without scholarship have never been able to reach a position of authority to correspond to their pains, while those who relied only upon theories and scholarship were obviously hunting the shadow, not the substance. But those who have a thorough knowledge of both, like men armed at all points, have the sooner attained their object and carried authority with them.
Vitruvius
In De Architectura, Book 1, Chap 1, Sec. 2. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 3.
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As regards religion, on the other hand, one is generally agreed that it deals with goals and evaluations and, in general, with the emotional foundation of human thinking and acting, as far as these are not predetermined by the inalterable hereditary disposition of the human species. Religion is concerned with man’s attitude toward nature at large, with the establishing of ideals for the individual and communal life, and with mutual human relationship. These ideals religion attempts to attain by exerting an educational influence on tradition and through the development and promulgation of certain easily accessible thoughts and narratives (epics and myths) which are apt to influence evaluation and action along the lines of the accepted ideals.
…...
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As the first monogamian family has improved greatly since the commencement of civilization, and very sensibly in our times, it is at least supposable that it is capable of still further improvement until the equality of the sexes is attained.
As quoted in Charles H. Seaholm, The Kelts and the Vikings (1974), 48.
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Ask a follower of Bacon what [science] the new philosophy, as it was called in the time of Charles the Second, has effected for mankind, and his answer is ready; “It has lengthened life; it has mitigated pain; it has extinguished diseases; it has increased the fertility of the soil; it has given new securities to the mariner; it has furnished new arms to the warrior; it has spanned great rivers and estuaries with bridges of form unknown to our fathers; it has guided the thunderbolt innocuously from heaven to earth; it has lighted up the night with the splendour of the day; it has extended the range of the human vision; it has multiplied the power of the human muscles; it has accelerated motion; it has annihilated distance; it has facilitated intercourse, correspondence, all friendly offices, all dispatch of business; it has enabled man to descend to the depths of the sea, to soar into the air, to penetrate securely into the noxious recesses of the earth, to traverse the land in cars which whirl along without horses, to cross the ocean in ships which run ten knots an hour against the wind. These are but a part of its fruits, and of its first-fruits; for it is a philosophy which never rests, which has never attained, which is never perfect. Its law is progress. A point which yesterday was invisible is its goal to-day, and will be its starting-point to-morrow.”
From essay (Jul 1837) on 'Francis Bacon' in Edinburgh Review. In Baron Thomas Babington Macaulay and Lady Trevelyan (ed.) The Works of Lord Macaulay Complete (1871), Vol. 6, 222.
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But I do not feel obliged to believe that that same God who has endowed us with senses, reason, and intellect has intended to forgo their use and by some other means to give us knowledge which we can attain by them.
Letter to Madame Christina of Lorraine, Grand Duchess of Tuscany: (1615). In Discoveries and Opinions of Galileo, trans. Stillman Drake (1957), 183.
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But if anyone, well seen in the knowledge, not onely of Sacred and exotick History, but of Astronomical Calculation, and the old Hebrew Kalendar, shall apply himself to these studies, I judge it indeed difficult, but not impossible for such a one to attain, not onely the number of years, but even, of dayes from the Creation of the World.
In 'Epistle to the Reader', The Annals of the World (1658). As excerpted in Wallen Yep, Man Before Adam: A Correction to Doctrinal Theology, "The Missing Link Found" (2002), 18.
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But it is precisely mathematics, and the pure science generally, from which the general educated public and independent students have been debarred, and into which they have only rarely attained more than a very meagre insight. The reason of this is twofold. In the first place, the ascendant and consecutive character of mathematical knowledge renders its results absolutely insusceptible of presentation to persons who are unacquainted with what has gone before, and so necessitates on the part of its devotees a thorough and patient exploration of the field from the very beginning, as distinguished from those sciences which may, so to speak, be begun at the end, and which are consequently cultivated with the greatest zeal. The second reason is that, partly through the exigencies of academic instruction, but mainly through the martinet traditions of antiquity and the influence of mediaeval logic-mongers, the great bulk of the elementary text-books of mathematics have unconsciously assumed a very repellant form,—something similar to what is termed in the theory of protective mimicry in biology “the terrifying form.” And it is mainly to this formidableness and touch-me-not character of exterior, concealing withal a harmless body, that the undue neglect of typical mathematical studies is to be attributed.
In Editor’s Preface to Augustus De Morgan and Thomas J. McCormack (ed.), Elementary Illustrations of the Differential and Integral Calculus (1899), v.
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Criticism, though dignified from the earliest ages by the labours of men eminent for knowledge and sagacity, has not yet attained the certainty and stability of science.
In Samuel Austin Allibone, Prose Quotations from Socrates to Macaulay (1880), 151.
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Dance … is life, or becomes it, in a way that other arts cannot attain. It is not in stone, or words or tones, but in our muscles. It is a formulation of their movements.
In Art Is Action: A Discussion of Nine Arts in a Modern World (1939), 56.
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Does it not seem as if Algebra had attained to the dignity of a fine art, in which the workman has a free hand to develop his conceptions, as in a musical theme or a subject for a painting? It has reached a point where every properly developed algebraical composition, like a skillful landscape, is expected to suggest the notion of an infinite distance lying beyond the limits of the canvas.
In 'Lectures on the Theory of Reciprocants', Lecture XXI, American Journal of Mathematics (Jul 1886), 9, No. 3, 136.
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Even as a coin attains its full value when it is spent, so life attains its supreme value when one knows how to forfeit it with grace when the time comes.
In The Crystal Arrow: Essays on Literature, Travel, Art, Love, and the History of Medicine (1964), 436.
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For it is the duty of an astronomer to compose the history of the celestial motions or hypotheses about them. Since he cannot in any certain way attain to the true causes, he will adopt whatever suppositions enable the motions to be computed correctly from the principles of geometry for the future as well as for the past.
From unauthorized preface Osiander anonymously added when he was entrusted with arranging the printing of the original work by Copernicus. As translated in Nicolaus Copernicus and Jerzy Dobrzycki (ed.), Nicholas Copernicus on the Revolutions (1978), xvi.
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Happy the men who made the first essay,
And to celestial regions found the way!
No earthly vices clogg’d their purer souls,
That they could soar so high as touch the poles:
Sublime their thoughts and from pollution clear,
Bacchus and Venus held no revels there;
From vain ambition free; no love of war
Possess’d their minds, nor wranglings at the bar;
No glaring grandeur captivates their eyes,
For such see greater glory in the skies:
Thus these to heaven attain.
In Craufurd Tait Ramage (ed., trans.), Beautiful Thoughts From Latin Authors, with English Translations (1864),
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Hast thou ever raised thy mind to the consideration of existence, in and by itself, as the mere act of existing?
Hast thou ever said to thyself thoughtfully it is! heedless, in that moment, whether it were a man before thee, or a flower, or a grain of sand;—without reference, in short, to this or that particular mode or form of existence? If thou hast, indeed, attained to this, thou wilt have felt the presence of a mystery, which must have fixed thy spirit in awe and wonder.
In 'Essay IX', The Friend: A Series of Essays (1818), Vol. 3, 250.
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I attained a triumph so complete that it is now rare to meet an American with marks of small pox on his face... Benefits are valuable according to their duration and extent, like the showers from heaven, but the benign remedy Vaccination saves millions of lives every century, like the blessing of the sun, universal and everlasting.
(Remark made near the end of his life.)
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I believe as a matter of faith that the extension of space travel to the limits of the solar system will probably be accomplished in several decades, perhaps before the end of the century. Pluto is 4000 million miles from the sun. The required minimum launching velocity is about 10 miles per second and the transit time is 46 years. Thus we would have to make the velocity considerably higher to make the trip interesting to man. Travel to the stars is dependent on radically new discoveries in science and technology. The nearest star is 25 million million miles way and requires a travel time of more than four years at the speed of light. Prof. Dr. Ing. E. Sanger has speculated that velocities comparable with the speed of light might be attained in the next century, but such extrapolation of current technology is probably not very reliable.
In Popular Mechanics (Sep 1961), 262.
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I call this Spirit, unknown hitherto, by the new name of Gas, which can neither be constrained by Vessels, nor reduced into a visible body, unless the feed being first extinguished. But Bodies do contain this Spirit, and do sometimes wholly depart into such a Spirit, not indeed, because it is actually in those very bodies (for truly it could not be detained, yea the whole composed body should I lie away at once) but it is a Spirit grown together, coagulated after the manner of a body, and is stirred up by an attained ferment, as in Wine, the juyce of unripe Grapes, bread, hydromel or water and Honey.
Oriatrike: Or, Physick Refined, trans. John Chandler (1662), 106.
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I conclude that, while it is true that science cannot decide questions of value, that is because they cannot be intellectually decided at all, and lie outside the realm of truth and falsehood. Whatever knowledge is attainable, must be attained by scientific methods; and what science cannot discover, mankind cannot know.
Religion and Science (1935), 243.
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I would be the last to deny that the greatest scientific pioneers belonged to an aristocracy of the spirit and were exceptionally intelligent, something that we as modest investigators will never attain, no matter how much we exert ourselves. Nevertheless … I continue to believe that there is always room for anyone with average intelligence … to utilize his energy and … any man could, if he were so inclined, be the sculptor of his own brain, and that even the least gifted may, like the poorest land that has been well-cultivated and fertilized, produce an abundant harvest..
From Preface to the second edition, Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad. (1897), as translated by Neely and Larry W. Swanson, in Advice for a Young Investigator (1999), xv.
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If any human being earnestly desire to push on to new discoveries instead of just retaining and using the old; to win victories over Nature as a worker rather than over hostile critics as a disputant; to attain, in fact, clear and demonstrative knowlegde instead of attractive and probable theory; we invite him as a true son of Science to join our ranks.
Novum Organum (1620), 34, Preface.
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If our intention had been merely to bring back a handful of soil and rocks from the lunar gravel pit and then forget the whole thing, we would certainly be history's biggest fools. But that is not our intention now—it never will be. What we are seeking in tomorrow's [Apollo 11] trip is indeed that key to our future on earth. We are expanding the mind of man. We are extending this God-given brain and these God-given hands to their outermost limits and in so doing all mankind will benefit. All mankind will reap the harvest…. What we will have attained when Neil Armstrong steps down upon the moon is a completely new step in the evolution of man.
Banquet speech on the eve of the Apollo 11 launch, Royal Oaks Country Club, Titusville (15 Jul 1969). In "Of a Fire on the Moon", Life (29 Aug 1969), 67, No. 9, 34.
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If you have great talents, industry will improve them; if moderate abilities, industry will supply their deficiencies. Nothing is denied to well-directed labour; nothing is ever to be attained without it.
From 'A Discourse Delivered to the Students of the Royal Academy, on the Distribution of Prizes' (11 Dec 1769), in Seven Discourses Delivered in the Royal Academy (1778), 57.
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In anything at all, perfection is finally attained not when there is no longer anything to add, but when there is no longer anything to take away.
From the French, “Il semble que la perfection soit atteinte non quand il n'y a plus rien à ajouter, mais quand il n'y a plus rien à retrancher,” in Terre des Hommes (1939). As translated by Lewis Galantière, in Wind, Sand, and Stars (1939), 66.
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In Man the brain presents an ascensive step in development, higher and more strongly marked than that by which the preceding subclass was distinguished from the one below it. Not only do the cerebral hemispheres overlap the olfactory lobes and cerebellum, but they extend in advance of the one, and further back than the other. Their posterior development is so marked, that anatomists have assigned to that part the character of a third lobe; it is peculiar to the genus Homo, and equally peculiar is the 'posterior horn of the lateral ventricle,' and the 'hippocampus minor,' which characterize the hind lobe of each hemisphere. The superficial grey matter of the cerebrum, through the number and depth of the convolutions, attains its maximum of extent in Man. Peculiar mental powers are associated with this highest form of brain, and their consequences wonderfully illustrate the value of the cerebral character; according to my estimate of which, I am led to regard the genus Homo, as not merely a representative of a distinct order, but of a distinct subclass of the Mammalia, for which I propose a name of 'ARCHENCEPHALA.'
'On the Characters, Principles of Division, and Primary Groups of the Class MAMMALIA' (1857), Journal of the Proceedings of the Linnean Society of London (1858), 2, 19-20.
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In science it is a service of the highest merit to seek out those fragmentary truths attained by the ancients, and to develop them further.
In The Maxims and Reflections of Goethe (1906), 198.
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In the animal world we have seen that the vast majority of species live in societies, and that they find in association the best arms for the struggle for life: understood, of course, in its wide Darwinian sense—not as a struggle for the sheer means of existence, but as a struggle against all natural conditions unfavourable to the species. The animal species, in which individual struggle has been reduced to its narrowest limits, and the practice of mutual aid has attained the greatest development, are invariably the most numerous, the most prosperous, and the most open to further progress. The mutual protection which is obtained in this case, the possibility of attaining old age and of accumulating experience, the higher intellectual development, and the further growth of sociable habits, secure the maintenance of the species, its extension, and its further progressive evolution. The unsociable species, on the contrary, are doomed to decay.
Mutual Aid: A Factor of Evolution (1902), 293.
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In the light of knowledge attained, the happy achievement seems almost a matter of course, and any intelligent student can grasp it without too much trouble. But the years of anxious searching in the dark, with their intense longing, their alternations of confidence and exhaustion, and the final emergence into the light—only those who have experienced it can understand that.
Quoted in Banesh Hoffmann and Helen Dukas, Albert Einstein: Creator and Rebel (1972), 124.
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In this country all a man need to do is to attain a little eminence and immediately he begins to talk. Usually his eminence is financial, and the greater this eminence the more he talks and the further his voice reaches. I don't blame the rich people for talking; many of them don’t know what else to do with themselves. The fault is with these who listen. If no one would listen no harm would he done. But the American people are willing to listen to any one who has attained prominence. The main fact is that we've heard a man's name a great many times; that makes us ready to accept whatever he says. … We listen to the one who talks the most and loudest.
As quoted in 'Electricity Will Keep The World From Freezing Up', New York Times (12 Nov 1911), SM4.
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Inspiration plays no less a role in science than it does in the realm of art. It is a childish notion to think that a mathematician attains any scientifically valuable results by sitting at his desk with a ruler, calculating machines or other mechanical means. The mathematical imagination of a Weierstrass is naturally quite differently oriented in meaning and result than is the imagination of an artist, and differs basically in quality. But the psychological processes do not differ. Both are frenzy (in the sense of Plato’s “mania”) and “inspiration.”
Max Weber
From a Speech (1918) presented at Munich University, published in 1919, and collected in 'Wissenschaft als Beruf', Gessammelte Aufsätze zur Wissenschaftslehre (1922), 524-525. As given in H.H. Gerth and C. Wright-Mills (translators and eds.), 'Science as a Vocation', Max Weber: Essays in Sociology (1946), 136.
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It is admitted by all that a finished or even a competent reasoner is not the work of nature alone; the experience of every day makes it evident that education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history, may be chosen for this purpose. Now of all these, it is desirable to choose the one which admits of the reasoning being verified, that is, in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not. When the guiding property of the loadstone was first ascertained, and it was necessary to learn how to use this new discovery, and to find out how far it might be relied on, it would have been thought advisable to make many passages between ports that were well known before attempting a voyage of discovery. So it is with our reasoning faculties: it is desirable that their powers should be exerted upon objects of such a nature, that we can tell by other means whether the results which we obtain are true or false, and this before it is safe to trust entirely to reason. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is obtained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if, as was said before, reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. Between the meaning of terms there is no distinction, except a total distinction, and all adjectives and adverbs expressing difference of degrees are avoided.
In On the Study and Difficulties of Mathematics (1898), chap. 1.
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It is an irony of fate that I myself have been the recipient of excessive admiration and reverence from my fellow-beings, through no fault, and no merit, of my own. The cause of this may well be the desire, unattainable for many, to understand the few ideas to which I have with my feeble powers attained through ceaseless struggle. I am quite aware that for any organisation to reach its goals, one man must do the thinking and directing and generally bear the responsibility. But the led must not be coerced, they must be able to choose their leader.
In 'What I Believe', Forum and Century (1930), 84, 193-194.
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It is good to recall that three centuries ago, around the year 1660, two of the greatest monuments of modern history were erected, one in the West and one in the East; St. Paul’s Cathedral in London and the Taj Mahal in Agra. Between them, the two symbolize, perhaps better than words can describe, the comparative level of architectural technology, the comparative level of craftsmanship and the comparative level of affluence and sophistication the two cultures had attained at that epoch of history. But about the same time there was also created—and this time only in the West—a third monument, a monument still greater in its eventual import for humanity. This was Newton’s Principia, published in 1687. Newton's work had no counterpart in the India of the Mughuls.
'Ideals and Realities' (1975). Reprinted in Ideals and Realities (1984), 48.
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It is interesting to observe the result of habit in the peculiar shape and size of the giraffe (Camelo-pardalis): this animal, the largest of the mammals, is known to live in the interior of Africa in places where the soil is nearly always arid and barren, so that it is obliged to browse on the leaves on the trees and to make constant efforts to reach them. From this habit long maintained in all its race, it has resulted that the animal's fore-legs have become longer than its hind legs, and that its neck is lengthened to such a degree that the giraffe, without standing up on its hind legs, attains a height of six metres (nearly 20 feet).
Philosophie Zoologique (1809), Vol. 1, 256, trans. Hugh Elliot (1914), 122.
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It is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.
…...
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It is no crime to accumulate wealth, provided it was attained by honest and proper means, but it is a crime to devote it to an improper use.
As quoted in Edward J. Wheeler (ed.), 'The Demeanor of John D. Rockefeller, Jr., Under Fire,' Current Opinion (Jul 1914), 57, No. 1, 21. This quote was one out of a collation in the article, “from his many talks to the Bible Class he formerly conducted and from various interviews.”
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It is not possible to find in all geometry more difficult and more intricate questions or more simple and lucid explanations [than those given by Archimedes]. Some ascribe this to his natural genius; while others think that incredible effort and toil produced these, to all appearance, easy and unlaboured results. No amount of investigation of yours would succeed in attaining the proof, and yet, once seen, you immediately believe you would have discovered it; by so smooth and so rapid a path he leads you to the conclusion required.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
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It is only in mathematics, and to some extent in poetry, that originality may be attained at an early age, but even then it is very rare (Newton and Keats are examples), and it is not notable until adolescence is completed.
In A Study of British Genius (1904), 142
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It is perhaps a law of nature that when a species (or group) fits itself to a place not previously occupied, and in which it is subject to no opposition from beings of its own class, or where it attains so great a perfection as to be able easily to overcome all opposition, the character eventually loses its original plasticity, or tendency to vary, since improvement in such a case would be superfluous, and becomes, so to speak, crystallized in that form which continues thereafter unaltered. … [Such as] the humming-bird.
In The Naturalist in La Plata (1895), 40.
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It is the destiny of the sciences, which must necessarily be in the hands of a few, that the utility of their progress should be invisible to the greater part of mankind, especially if those sciences are associated with unobtrusive pursuits. Let a greater facility in using our navigable waters and opening new lines of communication but once exist, simply because at present we know vastly better how to level the ground and construct locks and flood-gates—what does it amount to? The workmen have had their labors lightened, but they themselves have not the least idea of the skill of the geometer who directed them; they have been put in motion nearly as the body is by a soul of which it knows nothing; the rest of the world has even less perception of the genius which presided over the enterprise, and enjoys the success it has attained only with a species of ingratitude.
As quoted in Joseph Henry, 'Report of the Secretary', Annual Report of the Board of Regents of the Smithsonian Institution for 1859 (1860), 16-17. Webmaster has not yet been able to locate a primary source for this quote.
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It takes someone with a vision of the possibilities to attain new levels of experience. Someone with the courage to live his dreams.
Les Brown
…...
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It was his [Leibnitz’s] love of method and order, and the conviction that such order and harmony existed in the real world, and that our success in understanding it depended upon the degree and order which we could attain in our own thoughts, that originally was probably nothing more than a habit which by degrees grew into a formal rule. This habit was acquired by early occupation with legal and mathematical questions. We have seen how the theory of combinations and arrangements of elements had a special interest for him. We also saw how mathematical calculations served him as a type and model of clear and orderly reasoning, and how he tried to introduce method and system into logical discussions, by reducing to a small number of terms the multitude of compound notions he had to deal with. This tendency increased in strength, and even in those early years he elaborated the idea of a general arithmetic, with a universal language of symbols, or a characteristic which would be applicable to all reasoning processes, and reduce philosophical investigations to that simplicity and certainty which the use of algebraic symbols had introduced into mathematics.
A mental attitude such as this is always highly favorable for mathematical as well as for philosophical investigations. Wherever progress depends upon precision and clearness of thought, and wherever such can be gained by reducing a variety of investigations to a general method, by bringing a multitude of notions under a common term or symbol, it proves inestimable. It necessarily imports the special qualities of number—viz., their continuity, infinity and infinite divisibility—like mathematical quantities—and destroys the notion that irreconcilable contrasts exist in nature, or gaps which cannot be bridged over. Thus, in his letter to Arnaud, Leibnitz expresses it as his opinion that geometry, or the philosophy of space, forms a step to the philosophy of motion—i.e., of corporeal things—and the philosophy of motion a step to the philosophy of mind.
In Leibnitz (1884), 44-45. [The first sentence is reworded to better introduce the quotation. —Webmaster]
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It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained. … I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject.
In Presidential Address British Association for the Advancement of Science, Section A., (1890), Nature, 42, 466.
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Just as a physicist has to examine the telescope and galvanometer with which he is working; has to get a clear conception of what he can attain with them, and how they may deceive him; so, too, it seemed to me necessary to investigate likewise the capabilities of our power of thought.
'An Autobiographical Sketch' (1891). Trans. E. Atkinson, Popular Lectures on Scientific Subjects, Second Series, New Edition (1895), 284-5.
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Leaving aside genetic surgery applied humans, I foresee that the coming century will place in our hands two other forms of biological technology which are less dangerous but still revolutionary enough to transform the conditions of our existence. I count these new technologies as powerful allies in the attack on Bernal's three enemies. I give them the names “biological engineering” and “self-reproducing machinery.” Biological engineering means the artificial synthesis of living organisms designed to fulfil human purposes. Self-reproducing machinery means the imitation of the function and reproduction of a living organism with non-living materials, a computer-program imitating the function of DNA and a miniature factory imitating the functions of protein molecules. After we have attained a complete understanding of the principles of organization and development of a simple multicellular organism, both of these avenues of technological exploitation should be open to us.
From 3rd J.D. Bernal Lecture, Birkbeck College London (16 May 1972), The World, the Flesh and the Devil (1972), 6. Collected in The Scientist as Rebel (2006), 292. (The World, the Flesh & the Devil: An Enquiry into the Future of the Three Enemies of the Rational Soul is the title of a book by J. D Bernal, a scientist who pioneered X-ray crystallography.)
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Leibnitz’s discoveries lay in the direction in which all modern progress in science lies, in establishing order, symmetry, and harmony, i.e., comprehensiveness and perspicuity,—rather than in dealing with single problems, in the solution of which followers soon attained greater dexterity than himself.
In Leibnitz (1884), 112.
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Life is not easy for any of us, but what of that? We must have perseverance and above all confidence in ourselves. We must believe that we are gifted in something, and that this thing, at whatever cost, must be attained.
Letter to brother (1894). In Eve Curie, Madame Curie: a Biography by Eve Curie (1937, 2007), 158.
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Man is not a machine, ... although man most certainly processes information, he does not necessarily process it in the way computers do. Computers and men are not species of the same genus. .... No other organism, and certainly no computer, can be made to confront genuine human problems in human terms. ... However much intelligence computers may attain, now or in the future, theirs must always be an intelligence alien to genuine human problems and concerns.
Computer Power and Human Reason: From Judgment to Calculation, (1976) 203 and 223. Also excerpted in Ronald Chrisley (ed.), Artificial Intelligence: Critical Concepts (2000), Vol. 3, 313 and 321. Note that the second ellipsis spans 8 pages.
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Many psychologists ... thought by turning their attention to their own consciousness to be able to explain what happened when we were thnking. Or they sought to attain the same end by asking another person a question, by means of which certain processes of thought would be excited, and then by questioning the person about the introspection he had made. It is obvious ... that nothing can be discovered in such experiments.
An Introduction to Psychology (1912)
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Mathematics is an obscure field, an abstruse science, complicated and exact; yet so many have attained perfection in it that we might conclude almost anyone who seriously applied himself would achieve a measure of success.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 82.
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Natural ability without education has more often attained to glory and virtue than education without natural ability.
In M. P. Singh, Quote Unquote (2005), 1.
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Natural science is one of man’s weapons in his fight for freedom. For the purpose of attaining freedom in the world of nature, man must use natural science to understand, conquer, and change nature and thus attain freedom from nature.
In Speech (5 Feb 1940) to the Natural Science Research Society for the Border Regions, The Thoughts of Chairman Mao Tse-tung (1967) 127.
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No more impressive warning can be given to those who would confine knowledge and research to what is apparently useful, than the reflection that conic sections were studied for eighteen hundred years merely as an abstract science, without regard to any utility other than to satisfy the craving for knowledge on the part of mathematicians, and that then at the end of this long period of abstract study, they were found to be the necessary key with which to attain the knowledge of the most important laws of nature.
In Introduction to Mathematics (1911), 136-137.
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Note the saying of Protagoras that man is the measure of things. With the senses man measures perceptible things, with the intellect he measures intelligible things, and he attains unto supra-intelligible things transcendently
Dialog, 'De Beryllo' (1458). As translated in Jasper Hopkins, Complete Philosophical and Theological Treatises of Nicholas of Cusa: De visione Dei (2001), Vol. 2, 793.
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Only by following out the injunction of our great predecessor [William Harvey] to search out and study the secrets of Nature by way of experiment, can we hope to attain to a comprehension of 'the wisdom of the body and the understanding of the heart,' and thereby to the mastery of disease and pain, which will enable us to relieve the burden of mankind.
'The Wisdom of the Body', The Lancet (1923), 205, 870.
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Our children will attain to a far more fundamental insight into language, if we, when teaching them, connect the words more with the actual perception of the thing and the object. … Our language would then again become a true language of life, that is, born of life and producing life.
In Friedrich Fröbel and Josephine Jarvis (trans.), The Education of Man (1885), 145.
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Owing to his lack of knowledge, the ordinary man cannot attempt to resolve conflicting theories of conflicting advice into a single organized structure. He is likely to assume the information available to him is on the order of what we might think of as a few pieces of an enormous jigsaw puzzle. If a given piece fails to fit, it is not because it is fraudulent; more likely the contradictions and inconsistencies within his information are due to his lack of understanding and to the fact that he possesses only a few pieces of the puzzle. Differing statements about the nature of things, differing medical philosophies, different diagnoses and treatments—all of these are to be collected eagerly and be made a part of the individual's collection of puzzle pieces. Ultimately, after many lifetimes, the pieces will fit together and the individual will attain clear and certain knowledge.
'Strategies of Resort to Curers in South India', contributed in Charles M. Leslie (ed.), Asian Medical Systems: A Comparative Study (1976), 185.
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Peace cannot be achieved through violence, it can only be attained through understanding.
…...
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Perfect concordance among reformers is not to be expected; and men who are honestly struggling towards the light cannot hope to attain at one bound to the complete truth. There is always a danger lest the fascination of a new discovery should lead us too far. Men of science, being human, are apt, like lovers, to exaggerate the perfections and be a little blind to the faults of the object of their choice.
'The Anniversary Address of the President', Quarterly Journal of the Geological Society of London, 1885, 41, 55.
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Physio-philosophy has to show how, and in accordance indeed with what laws, the Material took its origin; and, therefore, how something derived its existence from nothing. It has to portray the first periods of the world's development from nothing; how the elements and heavenly bodies originated; in what method by self-evolution into higher and manifold forms, they separated into minerals, became finally organic, and in Man attained self-consciousness.
In Lorenz Oken, trans. by Alfred Tulk, Elements of Physiophilosophy (1847), 1.
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Rulers and generals muster their troops. Magnates muster the sums of money which give them power. The fascist dictators muster the irrational human reactions which make it possible for them to attain and maintain their power over the masses. The scientists muster knowledge and means of research. But, thus far, no organization fighting for freedom has ever mustered the biological arsenal where the weapons are to be found for the establishment and the maintenance of human freedom. All precision of our social existence notwithstanding, there is as yet no definition of the word freedom which would be in keeping with natural science. No word is more misused and misunderstood. To define freedom is the same as to define sexual health. But nobody will openly admit this. The advocacy of personal and social freedom is connected with anxiety and guilt feelings. As if to be free were a sin or at least not quite as it should be. Sex-economy makes this guilt feeling comprehensible: freedom without sexual self-determination is in itself a contradiction. But to be sexual means—according to the prevailing human structure—to be sinful or guilty. There are very few people who experience sexual love without guilt feeling. “Free love” has acquired a degrading meaning: it lost the meaning given it by the old fighters for freedom. In films and in books, to be genital and to be criminal are presented as the same thing.
…...
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Saying that each of two atoms can attain closed electron shells by sharing a pair of electrons is equivalent to saying that husband and wife, by having a total of two dollars in a joint account and each having six dollars in individual bank accounts, have eight dollars apiece!
Quoted in Reynold E. Holmen, 'Kasimir Fajans (1887-1975): The Man and His Work', Bulletin for the History of Chemistry, 1990, 6, 7-8.
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Science asks no questions about the ontological pedigree or a priori character of a theory, but is content to judge it by its performance; and it is thus that a knowledge of nature, having all the certainty which the senses are competent to inspire, has been attained—a knowledge which maintains a strict neutrality toward all philosophical systems and concerns itself not with the genesis or a priori grounds of ideas.
Originally published in North American Review (1865). 'The Philosophy of Herbert Spencer,' repr. In Philosophical Writings of Chauncey Wright (1963), p. 8.
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Science, regarded as the pursuit of truth, which can only be attained by patient and unprejudiced investigation, wherein nothing is to be attempted, nothing so minute as to be justly disregarded, must ever afford occupation of consummate interest, and subject of elevated meditation.
On the Connexion of the Physical Sciences (1858), 2-3.
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Sometimes truth frightens us. And in fact we know that it is sometimes deceptive, that it is a phantom never showing itself for a moment except to ceaselessly flee, that it must be pursued further and ever further without ever being attained. … Yet truth should not be feared, for it alone is beautiful.
As translated by George Bruce Halsted, in 'The Value of Science', Popular Science Monthly (Sep 1906), 69 193.
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The advancement of science is slow; it is effected only by virtue of hard work and perseverance. And when a result is attained, should we not in recognition connect it with the efforts of those who have preceded us, who have struggled and suffered in advance? Is it not truly a duty to recall the difficulties which they vanquished, the thoughts which guided them; and how men of different nations, ideas, positions, and characters, moved solely by the love of science, have bequeathed to us the unsolved problem? Should not the last comer recall the researches of his predecessors while adding in his turn his contribution of intelligence and of labor? Here is an intellectual collaboration consecrated entirely to the search for truth, and which continues from century to century.
[Respecting how the work of prior researchers had enabled his isolation of fluorine.]
Proceedings of the Royal Institution (1897). In Annual Report of the Board of Regents of the Smithsonian Institution to July 1897 (1898), 262.
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The belief that mathematics, because it is abstract, because it is static and cold and gray, is detached from life, is a mistaken belief. Mathematics, even in its purest and most abstract estate, is not detached from life. It is just the ideal handling of the problems of life, as sculpture may idealize a human figure or as poetry or painting may idealize a figure or a scene. Mathematics is precisely the ideal handling of the problems of life, and the central ideas of the science, the great concepts about which its stately doctrines have been built up, are precisely the chief ideas with which life must always deal and which, as it tumbles and rolls about them through time and space, give it its interests and problems, and its order and rationality. That such is the case a few indications will suffice to show. The mathematical concepts of constant and variable are represented familiarly in life by the notions of fixedness and change. The concept of equation or that of an equational system, imposing restriction upon variability, is matched in life by the concept of natural and spiritual law, giving order to what were else chaotic change and providing partial freedom in lieu of none at all. What is known in mathematics under the name of limit is everywhere present in life in the guise of some ideal, some excellence high-dwelling among the rocks, an “ever flying perfect” as Emerson calls it, unto which we may approximate nearer and nearer, but which we can never quite attain, save in aspiration. The supreme concept of functionality finds its correlate in life in the all-pervasive sense of interdependence and mutual determination among the elements of the world. What is known in mathematics as transformation—that is, lawful transfer of attention, serving to match in orderly fashion the things of one system with those of another—is conceived in life as a process of transmutation by which, in the flux of the world, the content of the present has come out of the past and in its turn, in ceasing to be, gives birth to its successor, as the boy is father to the man and as things, in general, become what they are not. The mathematical concept of invariance and that of infinitude, especially the imposing doctrines that explain their meanings and bear their names—What are they but mathematicizations of that which has ever been the chief of life’s hopes and dreams, of that which has ever been the object of its deepest passion and of its dominant enterprise, I mean the finding of the worth that abides, the finding of permanence in the midst of change, and the discovery of a presence, in what has seemed to be a finite world, of being that is infinite? It is needless further to multiply examples of a correlation that is so abounding and complete as indeed to suggest a doubt whether it be juster to view mathematics as the abstract idealization of life than to regard life as the concrete realization of mathematics.
In 'The Humanization of Teaching of Mathematics', Science, New Series, 35, 645-46.
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The Chinese, who aspire to be thought an enlightened nation, to this day are ignorant of the circulation of the blood; and even in England the man who made that noble discovery lost all his practice in the consequence of his ingenuity; and Hume informs us that no physician in the United Kingdom who had attained the age of forty ever submitted to become a convert to Harvey’s theory, but went on preferring numpsimus to sumpsimus to the day of his death.
Reflection 352, in Lacon: or Many things in Few Words; Addressed to Those Who Think (1820), 164-165.
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The conception that antibodies, which should protect against disease, are also responsible for the disease, sounds at first absurd. This has as its basis the fact that we are accustomed to see in disease only the harm done to the organism and to see in the antibodies solely antitoxic [protective] substances. One forgets too easily that the disease represents only a stage in the development of immunity, and that the organism often attains the advantage of immunity only by means of disease. ... Serum sickness represents, so to speak, an unnatural (artificial) form of disease.
C. von Pirquet and B. Schick, Die Serumkrankheit (1906), trans B. Schick, Serum Sickness (1951), 119-20.
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The Designe of the Royall Society being the Improvement of Naturall knowledge all ways and meanes that tend thereunto ought to be made use of in the prosecution thereof. Naturall knowledge then being the thing sought for, we are to consider by what meanes it may soonest easiest and most certainly attaind. These meanes we shall the sooner find if we consider where tis to be had to wit in three places. first in bookes, 2dly in men. 3ly in the things themselves. and these three point us out the search of books. the converse & correspondence with men the Experimenting and Examining the things themselves under each of these there is a multitude of businesse to be done but the first hath the Least [and is] the most easily attained, the 2d hath a great Deal and requires much en[deavour] and Industry; and the 3d is infinite and the difficultest of all.
'Proposals for advancement of the R[oyal] S[ociety]' (c.1700), quoted in Michael Hunter, Establishing the New Science: The Experience of the Early Royal Society (1989), 232.
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The domain of mathematics is the sole domain of certainty. There and there alone prevail the standards by which every hypothesis respecting the external universe and all observation and all experiment must be finally judged. It is the realm to which all speculation and thought must repair for chastening and sanitation, the court of last resort, I say it reverently, for all intellection whatsoever, whether of demon, or man, or deity. It is there that mind as mind attains its highest estate.
In 'The Universe and Beyond', Hibbert Journal (1904-1906), 3, 314.
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The elements of human nature are the learning rules, emotional reinforcers, and hormonal feedback loops that guide the development of social behaviour into certain channels as opposed to others. Human nature is not just the array of outcomes attained in existing societies. It is also the potential array that might be achieved through conscious design by future societies. By looking over the realized social systems of hundreds of animal species and deriving the principles by which these systems have evolved, we can be certain that all human choices represent only a tiny subset of those theoretically possible. Human nature is, moreover, a hodgepodge of special genetic adaptations to an environment largely vanished, the world of the Ice­Age hunter-gatherer.
In On Human Nature (1978), 196.
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The embryological record is almost always abbreviated in accordance with the tendency of nature (to be explained on the principle of survival of the fittest) to attain her needs by the easiest means.
A Treatise on Comparative Embryology (1880), Vol. I, 3-4.
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The ends to be attained [in Teaching of Mathematics in the secondary schools] are the knowledge of a body of geometrical truths, the power to draw correct inferences from given premises, the power to use algebraic processes as a means of finding results in practical problems, and the awakening of interest in the science of mathematics.
In 'Aim of the Mathematical Instruction', International Commission on Teaching of Mathematics, American Report: United States Bureau of Education: Bulletin 1912, No. 4, 7.
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The Engineer is one who, in the world of physics and applied sciences, begets new things, or adapts old things to new and better uses; above all, one who, in that field, attains new results in the best way and at lowest cost.
From Address on 'Industrial Engineering' at Purdue University (24 Feb 1905). Reprinted by Yale & Towne Mfg Co of New York and Stamford, Conn. for the use of students in its works.
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The extensive literature addressed to the definition or characterization of science is filled with inconsistent points of view and demonstrates that an adequate definition is not easy to attain. Part of the difficulty arises from the fact that the meaning of science is not fixed, but is dynamic. As science has evolved, so has its meaning. It takes on a new meaning and significance with successive ages.
Opening statement on 'The Meaning of “Science”', in Scientific Method: Optimizing Applied Research Decisions (1962), 1.
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The familiar idea of a god who is omniscient: someone who knows everything … does not immediately ring alarm bells in our brains; it is plausible that such a being could exist. Yet, when it is probed more closely one can show that omniscience of this sort creates a logical paradox and must, by the standards of human reason, therefore be judged impossible or be qualified in some way. To see this consider this test statement:
This statement is not known to be true by anyone.
Now consider the plight of our hypothetical Omniscient Being (“Big O”). Suppose first that this statement is true and Big O does not know it. Then Big O would not be omniscient. So, instead, suppose our statement is false. This means that someone must know the statement to be true; hence it must be true. So regardless of whether we assume at the outset that this statement is true or false, we are forced to conclude that it must be true! And therefore, since the statement is true, nobody (including Big O) can know that it is true. This shows that there must always be true statements that no being can know to be true. Hence there cannot be an Omniscient Being who knows all truths. Nor, by the same argument, could we or our future successors, ever attain such a state of omniscience. All that can be known is all that can be known, not all that is true.
In Impossibility: The Limits of Science and the Science of Limits (1999), 11.
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The first [quality] to be named must always be the power of attention, of giving one's whole mind to the patient without the interposition of anything of oneself. It sounds simple but only the very greatest doctors ever fully attain it. … The second thing to be striven for is intuition. This sounds an impossibility, for who can control that small quiet monitor? But intuition is only interference from experience stored and not actively recalled. … The last aptitude I shall mention that must be attained by the good physician is that of handling the sick man's mind.
In 'Art and Science in Medicine', The Collected Papers of Wilfred Trotter, FRS (1941), 98.
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The geometrical problems and theorems of the Greeks always refer to definite, oftentimes to rather complicated figures. Now frequently the points and lines of such a figure may assume very many different relative positions; each of these possible cases is then considered separately. On the contrary, present day mathematicians generate their figures one from another, and are accustomed to consider them subject to variation; in this manner they unite the various cases and combine them as much as possible by employing negative and imaginary magnitudes. For example, the problems which Apollonius treats in his two books De sectione rationis, are solved today by means of a single, universally applicable construction; Apollonius, on the contrary, separates it into more than eighty different cases varying only in position. Thus, as Hermann Hankel has fittingly remarked, the ancient geometry sacrifices to a seeming simplicity the true simplicity which consists in the unity of principles; it attained a trivial sensual presentability at the cost of the recognition of the relations of geometric forms in all their changes and in all the variations of their sensually presentable positions.
In 'Die Synthetische Geometrie im Altertum und in der Neuzeit', Jahresbericht der Deutschen Mathematiker Vereinigung (1902), 2, 346-347. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 112. The spelling of the first “Apollonius” has been corrected from “Appolonius” in the original English text. From the original German, “Die geometrischen Probleme und Sätze der Griechen beziehen sich allemal auf bestimmte, oft recht komplizierte Figuren. Nun können aber die Punkte und Linien einer solchen Figur häufig sehr verschiedene Lagen zu einander annehmen; jeder dieser möglichen Fälle wird alsdann für sich besonders erörtert. Dagegen lassen die heutigen Mathematiker ihre Figuren aus einander entstehen und sind gewohnt, sie als veränderlich zu betrachten; sie vereinigen so die speziellen Fälle und fassen sie möglichst zusammen unter Benutzung auch negativer und imaginärer Gröfsen. Das Problem z. B., welches Apollonius in seinen zwei Büchern de sectione rationis behandelt, löst man heutzutage durch eine einzige, allgemein anwendbare Konstruktion; Apollonius selber dagegen zerlegt es in mehr als 80 nur durch die Lage verschiedene Fälle. So opfert, wie Hermann Hankel treffend bemerkt, die antike Geometrie einer scheinbaren Einfachheit die wahre, in der Einheit der Prinzipien bestehende; sie erreicht eine triviale sinnliche Anschaulichkeit auf Kosten der Erkenntnis vom Zusammenhang geometrischer Gestalten in aller Wechsel und in aller Veränderlichkeit ihrer sinnlich vorstellbaren Lage.”
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The great testimony of history shows how often in fact the development of science has emerged in response to technological and even economic needs, and how in the economy of social effort, science, even of the most abstract and recondite kind, pays for itself again and again in providing the basis for radically new technological developments. In fact, most people—when they think of science as a good thing, when they think of it as worthy of encouragement, when they are willing to see their governments spend substance upon it, when they greatly do honor to men who in science have attained some eminence—have in mind that the conditions of their life have been altered just by such technology, of which they may be reluctant to be deprived.
In 'Contemporary World', Bulletin of the Atomic Scientists (Feb 1948), 4, 67.
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The investigation of the truth is in one way hard, in another easy. An indication of this is found in the fact that no one is able to attain the truth adequately, while, on the other hand, no one fails entirely, but every one says something true about the nature of things, and while individually they contribute little or nothing to the truth, by the union of all a considerable amount is amassed. Therefore, since the truth seems to be like the proverbial door, which no one can fail to hit, in this way it is easy, but the fact that we can have a whole truth and not the particular part we aim at shows the difficulty of it. Perhaps, as difficulties are of two kinds, the cause of the present difficulty is not in the facts but in us.
Aristotle
Metaphysics, 993a, 30-993b, 9. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. 2, 1569-70.
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The logic of the subject [algebra], which, both educationally and scientifically speaking, is the most important part of it, is wholly neglected. The whole training consists in example grinding. What should have been merely the help to attain the end has become the end itself. The result is that algebra, as we teach it, is neither an art nor a science, but an ill-digested farrago of rules, whose object is the solution of examination problems. … The result, so far as problems worked in examinations go, is, after all, very miserable, as the reiterated complaints of examiners show; the effect on the examinee is a well-known enervation of mind, an almost incurable superficiality, which might be called Problematic Paralysis—a disease which unfits a man to follow an argument extending beyond the length of a printed octavo page.
In Presidential Address British Association for the Advancement of Science (1885), Nature, 32, 447-448.
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The more a science advances, the more will it be possible to understand immediately results which formerly could be demonstrated only by means of lengthy intermediate considerations: a mathematical subject cannot be considered as finally completed until this end has been attained.
In Formensystem binärer Formen (1875), 2.
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The most successful men in the end are those whose success is the result of steady accretion. That intellectuality is more vigorous that has attained its strength gradually. It is the man who carefully advances step by step, with his mind becoming wider and wider—and progressively better able to grasp any theme or situation—persevering in what he knows to be practical, and concentrating his thought upon it, who is bound to succeed in the greatest degree.
In Orison Swett Marden, 'Bell Telephone Talk: Hints on Success by Alexander G. Bell', How They Succeeded: Life Stories of Successful Men Told by Themselves (1901), 35.
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The opening of a foreign trade, by making them acquainted with new objects, or tempting them by the easier acquisition of things which they had not previously thought attainable, sometimes works a sort of industrial revolution in a country whose resources were previously undeveloped for want of energy and ambition in the people; inducing those who were satisfied with scanty comforts and little work to work harder for the gratification of their new tastes, and even to save, and accumulate capital, for the still more complete satisfaction of those tastes at a future time.
In Principles of Political Economy, with Some of Their Applications to Social Philosophy Vol. 1 (1873), Vol. 1, 351.
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The reason it is so hard to attain to something good in any of the arts and sciences is that it involves attaining to a certain stipulated point; to do something badly according to a predetermined rule would be just as hard, if indeed it would then still deserve to be called bad.
Aphorism 53 in Notebook C (1772-1773), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 42.
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The study of … simple cases would, I think, often be of advantage even to students whose mathematical attainments are sufficient to enable them to follow the solution of the more general cases. For in these simple cases the absence of analytical difficulties allows attention to be more easily concentrated on the physical aspects of the question, and thus gives the student a more vivid idea and a more manageable grasp of the subject than he would be likely to attain if he merely regarded electrical phenomena through a cloud of analytical symbols.
Elements of the Mathematical Theory of Electricity and Magnetism (189S), v-vi.
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The true value of a human being is determined primarily by the measure and the sense in which he has attained to liberation from the self.
…...
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The whole philosophy of medicine consists in working out the histories of diseases, and applying the remedies which may dispel them; and Experience is the sole guide. This we attain by … the suggestions of common sense rather than of speculation.
In The Works of Thomas Sydenham, (1850), Vol. 2, 182.
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There are no inferior races; all are destined to attain freedom.
Webmaster cannot find a primary source for this as a brief quote. It is probably not verbatim, but does summarize the sentiment in the much longer quote (see this web page) which begins, “While we maintain the unity of the human species…”
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There are some men who are counted great because they represent the actuality of their own age, and mirror it as it is. Such an one was Voltaire, of whom it was epigrammatically said: “he expressed everybody's thoughts better than anyone.” But there are other men who attain greatness because they embody the potentiality of their own day and magically reflect the future. They express the thoughts which will be everybody's two or three centuries after them. Such as one was Descartes.
Quoted in James Roy Newman, The World of Mathematics (2000), Vol. 1, 239.
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There are still many unsolved problems about bird life, among which are the age that birds attain, the exact time at which some birds acquire their adult dress, and the changes which occur in this with years. Little, too, is known about the laws and routes of bird migration, and much less about the final disposition of the untold thousands which are annually produced.
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There is no art or science that is too difficult for industry to attain to; it is the gift of tongues, and makes a man understood and valued in all countries, and by all nations; it is the philosopher's stone, that turns all metals, and even stones, into gold, and suffers not want to break into its dwelling; it is the northwest passage, that brings the merchant's ships as soon to him as he can desire: in a word, it conquers all enemies, and makes fortune itself pay contribution.
'Essay on Industry' (1670). In Thomas Henry Lister, Life and Administration of Edward, first Earl of Clarendon (1838), Vol. 2, 566.
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There is probably no other science which presents such different appearances to one who cultivates it and to one who does not, as mathematics. To this person it is ancient, venerable, and complete; a body of dry, irrefutable, unambiguous reasoning. To the mathematician, on the other hand, his science is yet in the purple bloom of vigorous youth, everywhere stretching out after the “attainable but unattained” and full of the excitement of nascent thoughts; its logic is beset with ambiguities, and its analytic processes, like Bunyan’s road, have a quagmire on one side and a deep ditch on the other and branch off into innumerable by-paths that end in a wilderness.
In 'The Theory of Transformation Groups', (A review of Erster Abschnitt, Theorie der Transformationsgruppen (1888)), Bulletin New York Mathematical Society (1893), 2 (First series), 61.
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Through purely logical thinking we can attain no knowledge whatsoever of the empirical world.
In Francis Crick, The Astonishing Hypothesis: the Scientific Search for the Soul (1995), 215.
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To unfold the secret laws and relations of those high faculties of thought by which all beyond the merely perceptive knowledge of the world and of ourselves is attained or matured, is a object which does not stand in need of commendation to a rational mind.
An Investigation of the Laws of Thought (1854), 3.
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True poetry is truer than science, because it is synthetic, and seizes at once what the combination of all the sciences is able, at most, to attain as a final result.
Entry for 31 Oct 1852 in Amiel’s Journal: The Journal Intime of Henri-Frédéric Amiel, trans. Humphry Ward (1893), 30.
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Unless the structure of the nucleus has a surprise in store for us, the conclusion seems plain—there is nothing in the whole system if laws of physics that cannot be deduced unambiguously from epistemological considerations. An intelligence, unacquainted with our universe, but acquainted with the system of thought by which the human mind interprets to itself the contents of its sensory experience, and should be able to attain all the knowledge of physics that we have attained by experiment.
In Clive William Kilmister, Eddington's Search for a Fundamental Theory (1994), 202.
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Unless you expect the unexpected you will never find it, for it is hard to discover and hard to attain.
As quoted in Peter Pešic, Labyrinth: A Search for the Hidden Meaning of Science (2001), 2.
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We are as yet got little farther than to the surface of things: yet ought we not to be discouraged; though we can never hope to attain to the complete knowledge of the texture, or constituent frame and nature of bodies, yet may we reasonably expect by this method of experiments, to make farther and farther advances abundantly sufficient to reward our pains.
In 'Preface', Statical Essays: Containing Hæmastatics (1769), Vol. 2, ii.
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We had a clear, unmistakable, specific objective. Although at first there was considerable doubt whether we could attain this objective, there was never any doubt about what it was. Consequently the people in responsible positions were able to tailor their every action to its accomplishment.
In And Now It Can Be Told: The Story Of The Manhattan Project (1962), 414.
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We have seen that the cytoplasm of nerve has a fluid consistency. Hence its molecules are free to move. According to the thermodynamic principle known as the Gibbs-Thompson rule, any substance in the interior of a liquid which will reduce the free energy of the surface of the liquid, will be concentrated in the surface. The composition of the surface is, therefore, determined by the composition of the fluid from which it is formed; and as the rule is one having universal application, it must hold also for the cytoplasm of nerve. We must think of the surface membrane, then, as a structure which is in equilibrium with the interior of the axon, or at least as one which deviates from equilibrium only because, for dynamic reasons, equilibrium cannot be attained.
With Joseph Erlanger (1874-1965), American physiologist.
Joseph Erlanger and Herbert S. Gasser (eds.), Electrical Signs of Nervous Activity (1937), 136.
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We need another and a wiser and perhaps a more mystical concept of animals. Remote from universal nature, and living by complicated artifice, man in civilization surveys the creature through the glass of his knowledge and sees thereby a feather magnified and the whole image in distortion. We patronize them for their incompleteness, for their tragic fate of having taken form so far below ourselves. And therein we err, and greatly err. For the animal shall not be measured by man. In a world older and more complete than ours they move finished and complete, gifted with extensions of the senses we have lost or never attained, living by voices we shall never hear. They are not brethren, they are not underlings; they are other nations, caught with ourselves in the net of life and time, fellow prisoners of the splendour and travail of the earth.
The Outermost House (1928), 25.
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We stand by the river and admire the great body of water flowing so sweetly on; could you trace it back to its source, you might find a mere rivulet, but meandering on, joined by other streams and by secret springs, and fed by the rains and dews of heaven, it gathers volume and force, makes its way through the gorges of the mountains, plows, widens and deepens its channel through the provinces, and attains its present majesty.
From Address (1 Aug 1875), 'The Growth of Principles' at Saratoga. Collected in William L. Snyder (ed.), Great Speeches by Great Lawyers: A Collection of Arguments and Speeches (1901), 246.
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What is peculiar and new to the [19th] century, differentiating it from all its predecessors, is its technology. It was not merely the introduction of some great isolated inventions. It is impossible not to feel that something more than that was involved. … The process of change was slow, unconscious, and unexpected. In the nineteeth century, the process became quick, conscious, and expected. … The whole change has arisen from the new scientific information. Science, conceived not so much in its principles as in its results, is an obvious storehouse of ideas for utilisation. … Also, it is a great mistake to think that the bare scientific idea is the required invention, so that it has only to be picked up and used. An intense period of imaginative design lies between. One element in the new method is just the discovery of how to set about bridging the gap between the scientific ideas, and the ultimate product. It is a process of disciplined attack upon one difficulty after another This discipline of knowledge applies beyond technology to pure science, and beyond science to general scholarship. It represents the change from amateurs to professionals. … But the full self-conscious realisation of the power of professionalism in knowledge in all its departments, and of the way to produce the professionals, and of the importance of knowledge to the advance of technology, and of the methods by which abstract knowledge can be connected with technology, and of the boundless possibilities of technological advance,—the realisation of all these things was first completely attained in the nineteeth century.
In Science and the Modern World (1925, 1997), 96.
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When young Galileo, then a student at Pisa, noticed one day during divine service a chandelier swinging backwards and forwards, and convinced himself, by counting his pulse, that the duration of the oscillations was independent of the arc through which it moved, who could know that this discovery would eventually put it in our power, by means of the pendulum, to attain an accuracy in the measurement of time till then deemed impossible, and would enable the storm-tossed seaman in the most distant oceans to determine in what degree of longitude he was sailing?
Hermann von Helmholtz, Edmund Atkinson (trans.), Popular Lectures on Scientific Subjects: First Series (1883), 29.
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While it is true that scientific results are entirely independent from religious and moral considerations, those individuals to whom we owe the great creative achievements of science were all of them imbued with the truly religious conviction that this universe of ours is something perfect and susceptible to the rational striving for knowledge. If this conviction had not been a strongly emotional one and if those searching for knowledge had not been inspired by Spinoza's Amor Dei Intellectualis, they would hardly have been capable of that untiring devotion which alone enables man to attain his greatest achievements.
In response to a greeting sent by the Liberal Ministers’ Club of New York City, published in 'Religion and Science: Irreconcilable?' The Christian Register (Jun 1948). Collected in Ideas and Options (1954), 52.
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Why does a man want to be a scientist? There are many goals: fame, position, a thirst for understanding. The first two can be attained without intellectual integrity; the third cannot. … The thirst for knowledge, what Thomas Huxley called the ‘Divine dipsomania’, can only be satisfied by complete intellectual integrity. It seems to me the only one of the three goals that continues to reward the pursuer. He presses on, “knowing that Nature never did betray the heart that loved her”. Here is another kind of love, that has so many faces. Love is neither passion, nor pride, nor pity, nor blind adoration, but it can be any or all of these if they are transfigured by deep and unbiased understanding.
In Cecilia Payne-Gaposchkin: An Autobiography and Other Recollections (1996), 123.
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Without this language [mathematics] most of the intimate analogies of things would have remained forever unknown to us; and we should forever have been ignorant of the internal harmony of the world, which is the only true objective reality. …
This harmony … is the sole objective reality, the only truth we can attain; and when I add that the universal harmony of the world is the source of all beauty, it will be understood what price we should attach to the slow and difficult progress which little by little enables us to know it better.
From La Valeur de la Science, as translated by George Bruce Halsted, in 'The Value of Science', Popular Science Monthly (Sep 1906), 69 195-196.
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Words can sometimes, in moments of grace, attain the quality of deeds.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 239
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Young children were sooner allured by love, than driven by beating, to attain good learning.
The Scholemaster (1570), Book 1, Preface.
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[Euclid's Elements] has been for nearly twenty-two centuries the encouragement and guide of that scientific thought which is one thing with the progress of man from a worse to a better state. The encouragement; for it contained a body of knowledge that was really known and could be relied on, and that moreover was growing in extent and application. For even at the time this book was written—shortly after the foundation of the Alexandrian Museum—Mathematics was no longer the merely ideal science of the Platonic school, but had started on her career of conquest over the whole world of Phenomena. The guide; for the aim of every scientific student of every subject was to bring his knowledge of that subject into a form as perfect as that which geometry had attained. Far up on the great mountain of Truth, which all the sciences hope to scale, the foremost of that sacred sisterhood was seen, beckoning for the rest to follow her. And hence she was called, in the dialect of the Pythagoreans, ‘the purifier of the reasonable soul.’
From a lecture delivered at the Royal Institution (Mar 1873), collected postumously in W.K. Clifford, edited by Leslie Stephen and Frederick Pollock, Lectures and Essays, (1879), Vol. 1, 296.
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[Scientific research reveals] the majestic spectacle of the order of nature gradually unfolding itself to man’s consciousness and placing in his hands the implements of ever augmenting power to control his destinies and attain that ultimate comprehension of the universe which has in all ages constituted the supreme aspiration of man.
As quoted in book review by Ian Clunies Ross, "The Spirit of Research', The Australian Quarterly (Dec 1931), 3, No. 12, 126.
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[When nature appears complicated:] The moment we contemplate it as it is, and attain a position from which we can take a commanding view, though but of a small part of its plan, we never fail to recognize that sublime simplicity on which the mind rests satisfied that it has attained the truth.
Concluding remark in Dionysius Lardner (ed.), Cabinet Cyclopaedia, Vol 1, Preliminary Discourse on the Study of Natural Philosophy (1831), 361.
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… for it is very probable, that the motion of gravity worketh weakly, both far from the earth, and also within the earth: the former because the appetite of union of dense bodies with the earth, in respect of the distance, is more dull: the latter, because the body hath in part attained its nature when it is some depth in the earth.
[Foreshadowing Newton's Universal Law of Gravitation (1687)]
Sylva Sylvarum; or a Natural History in Ten Centuries (1627), Century 1, Experiment 33. Collected in The Works of Francis Bacon (1826), Vol 1, 255.
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… the three positive characteristics that distinguish mathematical knowledge from other knowledge … may be briefly expressed as follows: first, mathematical knowledge bears more distinctly the imprint of truth on all its results than any other kind of knowledge; secondly, it is always a sure preliminary step to the attainment of other correct knowledge; thirdly, it has no need of other knowledge.
In Mathematical Essays and Recreations (1898), 35.
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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 -
Antoine Lavoisier
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Euclid
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Andre Ampere
Winston Churchill
- 80 -
John Locke
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Bible
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- 70 -
Samuel Morse
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- 60 -
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Paul Dirac
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James Watson
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- 50 -
Stephen Hawking
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- 40 -
Pierre Fermat
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JJ Thomson
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Archimedes
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- 30 -
Andreas Vesalius
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- 20 -
Carl Sagan
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- 10 -
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