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Who said: “The conservation of natural resources is the fundamental problem. Unless we solve that problem it will avail us little to solve all others.”
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Aid Quotes (97 quotes)

A l’aide de ces sciences expérimentales actives, l’homme devient un inventeur de phénomènes, un véritable contremaître de la création; et l'on ne saurait, sous ce rapport, assigner de limites à la puissance qu’il peut acquérir sur la nature, par les progrès futurs des sciences expérimentales
With the aid of these active experimental sciences man becomes an inventor of phenomena, a real foreman of creation; and under this head we cannot set limits to the power that he may gain over nature through future progress of the experimental sciences.
Original French text in Introduction à l'Étude de la Médecine Expérimentale (1898), 32. English version from An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 18.
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Hie locus est ubi mars gaudet succurere vitae.
This place is where death rejoices to come to the aid of life.
Anonymous
In the anatomical dissection theatre of the University of Bologna.
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Omnes scientiae sunt connexae et fovent auxiliis sicut partes ejusdem totius, quarum quaelibet opus suum peragit non propter se sed pro aliis.
All sciences are connected; they lend each other material aid as parts of one great whole, each doing its own work, not for itself alone, but for the other parts; as the eye guides the body and the foot sustains it and leads it from place to place.
Opus Tertium [1266- 1268], chapter 4, Latin text quoted in J. B. Bury, The Idea of Progress (1920), 355 (footnote to page 25). In J. S. Brewer (ed.), Fr. Rogeri Bacon Opera ... inedita (1859), 18.
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[About Sir Roderick Impey Murchison:] The enjoyments of elegant life you early chose to abandon, preferring to wander for many successive years over the rudest portions of Europe and Asia—regions new to Science—in the hope, happily realized, of winning new truths.
By a rare union of favourable circumstances, and of personal qualifications equally rare, you have thus been enabled to become the recognized Interpreter and Historian (not without illustrious aid) of the Silurian Period.
Dedication page in Thesaurus Siluricus: The Flora and Fauna of the Silurian Period (1868), iv.
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A little science is something that they must have. I should like my nephews to know what air is, and water; why we breathe, and why wood burns; the nutritive elements essential to plant life, and the constituents of the soil. And it is no vague and imperfect knowledge from hearsay I would have them gain of these fundamental truths, on which depend agriculture and the industrial arts and our health itself; I would have them know these things thoroughly from their own observation and experience. Books here are insufficient, and can serve merely as aids to scientific experiment.
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All palaetiological sciences, all speculations which attempt to ascend from the present to the remote past, by the chain of causation, do also, by an inevitable consequence, urge us to look for the beginning of the state of things which we thus contemplate; but in none of these cases have men been able, by the aid of science, to arrive at a beginning which is homogeneous with the known course of events. The first origin of language, of civilization, of law and government, cannot be clearly made out by reasoning and research; and just as little, we may expect, will a knowledge of the origin of the existing and extinct species of plants and animals, be the result of physiological and geological investigation.
In History of the Inductive Sciences (1837), Vol. 3, 581.
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An example of such emergent phenomena is the origin of life from non-living chemical compounds in the oldest, lifeless oceans of the earth. Here, aided by the radiation energy received from the sun, countless chemical materials were synthesized and accumulated in such a way that they constituted, as it were, a primeval “soup.” In this primeval soup, by infinite variations of lifeless growth and decay of substances during some billions of years, the way of life was ultimately reached, with its metabolism characterized by selective assimilation and dissimilation as end stations of a sluiced and canalized flow of free chemical energy.
In 'The Scientific Character of Geology', The Journal of Geology (Jul 1961), 69, No. 4, 458.
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Art and science work in quite different ways: agreed. But, bad as it may sound, I have to admit that I cannot get along as an artist without the use of one or two sciences. ... In my view, the great and complicated things that go on in the world cannot be adequately recognized by people who do not use every possible aid to understanding.
Bertolt Brecht, John Willett (trans.), Brecht on Theatre (1964), 73.
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As he [Clifford] spoke he appeared not to be working out a question, but simply telling what he saw. Without any diagram or symbolic aid he described the geometrical conditions on which the solution depended, and they seemed to stand out visibly in space. There were no longer consequences to be deduced, but real and evident facts which only required to be seen. … So whole and complete was his vision that for the time the only strange thing was that anybody should fail to see it in the same way. When one endeavored to call it up again, and not till then, it became clear that the magic of genius had been at work, and that the common sight had been raised to that higher perception by the power that makes and transforms ideas, the conquering and masterful quality of the human mind which Goethe called in one word das Dämonische.
In Leslie Stephen and Frederick Pollock (eds.), Lectures and Essays by William Kingdon Clifford(1879), Vol. 1, Introduction, 4-5.
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Astronomers and physicists, dealing habitually with objects and quantities far beyond the reach of the senses, even with the aid of the most powerful aids that ingenuity has been able to devise, tend almost inevitably to fall into the ways of thinking of men dealing with objects and quantities that do not exist at all, e.g., theologians and metaphysicians. Thus their speculations tend almost inevitably to depart from the field of true science, which is that of precise observation, and to become mere soaring in the empyrean. The process works backward, too. That is to say, their reports of what they pretend actually to see are often very unreliable. It is thus no wonder that, of all men of science, they are the most given to flirting with theology. Nor is it remarkable that, in the popular belief, most astronomers end by losing their minds.
Minority Report: H. L. Mencken’s Notebooks (1956), Sample 74, 60.
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AZT stood up and said, 'Stop your pessimism. Stop your sense of futility. Go back to the lab. Go back to development. Go back to clinical trials. Things will work.'
[On the impact of AZT emerging as the long-sought first significant AIDS drug.]
As quoted in Emily Langer, 'Researcher Jerome P. Horwitz, 93, created AZT, the first approved treatment for HIV/AIDS' Washington Post (19 Sep 2012). The article was excerpted on blogs, sometimes referring to this quote by saying "AZT was more a cure for fatalism than for AIDS."
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Babylon,
Learned and wise, hath perished utterly,
Nor leaves her speech one word to aid the sigh
That would lament her.
From poem, 'Missions And Travels', collected in The Poetical Works of William Wordsworth: Complete in One Volume (1828), 176.
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Careful and correct use of language is a powerful aid to straight thinking, for putting into words precisely what we mean necessitates getting our own minds quite clear on what we mean.
In The Art of Scientific Investigation (1950,1957), 91.
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Children are told that an apple fell on Isaac Newton’s head and he was led to state the law of gravity. This, of course, is pure foolishness. What Newton discovered was that any two particles in the universe attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This is not learned from a falling apple, but by observing quantities of data and developing a mathematical theory that can be verified by additional data. Data gathered by Galileo on falling bodies and by Johannes Kepler on motions of the planets were invaluable aids to Newton. Unfortunately, such false impressions about science are not universally outgrown like the Santa Claus myth, and some people who don’t study much science go to their graves thinking that the human race took until the mid-seventeenth century to notice that objects fall.
In How to Tell the Liars from the Statisticians (1983), 127.
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Electronic aids, particularly domestic computers, will help the inner migration, the opting out of reality. Reality is no longer going to be the stuff out there, but the stuff inside your head. It's going to be commercial and nasty at the same time, like 'Rite of Spring' in Disney's Fantasia ... our internal devils may destroy and renew us through the technological overload we've invoked.
Interview in Heavy Metal (Apr 1971). Reprinted in Re/Search, No. 8/9 (1984).
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Examples ... show how difficult it often is for an experimenter to interpret his results without the aid of mathematics.
Quoted in E. T. Bell, Men of Mathematics, xvi.
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Food may be defined as material which, when taken into the body, serves to either form tissue or yield energy, or both. This definition includes all the ordinary food materials, since they both build tissue and yield energy. It includes sugar and starch, because they yield energy and form fatty tissue. It includes alcohol, because the latter is burned to yield energy, though it does not build tissue. It excludes creatin, creatininin, and other so-called nitrogeneous extractives of meat, and likewise thein or caffein of tea and coffee, because they neither build tissue nor yield energy, although they may, at times, be useful aids to nutrition.
Methods and Results of Investigations on the Chemistry and Economy of Food, Bulletin 21, US Department of Agriculture (1895). Quoted in Ira Wolinsky, Nutrition in Exercise and Sport (1998), 36.
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For many parts of Nature can neither be invented with sufficient subtlety, nor demonstrated with sufficient perspicuity, nor accommodated to use with sufficient dexterity, without the aid and intervention of Mathematic: of which sort are Perspective, Music, Astronomy, cosmography, Architecture, Machinery, and some others.
In De Augmentis, Bk. 3; The Advancement of Learning (1605), Book 3. As translated in Francis Bacon, ‎James Spedding and ‎Robert Leslie Ellis, 'Of the great Appendix of Natural Philosophy, both Speculative and Operative, namely Mathematic; and that it ought rather to be placed among Appendices than among Substantive Sciences. Division of Mathematic into Pure and Mixed', The Works of Francis Bacon (1858), Vol. 4, Chap. 6, 371.
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Four hundred thousand South Africans are dying of AIDS every year. This makes the war on Iraq look like a birthday party.
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Gold is found in our own part of the world; not to mention the gold extracted from the earth in India by the ants, and in Scythia by the Griffins. Among us it is procured in three different ways; the first of which is in the shape of dust, found in running streams. … A second mode of obtaining gold is by sinking shafts or seeking among the debris of mountains …. The third method of obtaining gold surpasses the labors of the giants even: by the aid of galleries driven to a long distance, mountains are excavated by the light of torches, the duration of which forms the set times for work, the workmen never seeing the light of day for many months together.
In Pliny and John Bostock (trans.), The Natural History of Pliny (1857), Vol. 6, 99-101.
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He that borrows the aid of an equal understanding, doubles his own; he that uses that of a superior elevates his own to the stature of that he contemplates.
Collected, without citation, in Edge-tools of Speech (1886), 406. Also quoted, without citation, Ralph Waldo Emerson, 'Quotation and Originality', in Letters and Social Aims (1875, 1917), 178. Webmaster has not yet identified a primary source.
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He was an admirable marksman, an expert swimmer, a clever rider, possessed of great activity [and] prodigious strength, and was notable for the elegance of his figure and the beauty of his features, and he aided nature by a careful attendance to his dress. Besides other accomplishments he was musical, a good fencer, danced well, and had some acquaintance with legerdemain tricks, worked in hair, and could plait willow baskets.
In Richard Rhodes, John James Audubon: The Making of an American (2004), 36.
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Hence, even in the domain of natural science the aid of the experimental method becomes indispensable whenever the problem set is the analysis of transient and impermanent phenomena, and not merely the observation of persistent and relatively constant objects.
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However, if we consider that all the characteristics which have been cited are only differences in degree of structure, may we not suppose that this special condition of organization of man has been gradually acquired at the close of a long period of time, with the aid of circumstances which have proved favorable? What a subject for reflection for those who have the courage to enter into it!
In Recherches sur l'Organization des corps vivans (1802), as translated in Alpheus Spring Packard, Lamarck, the Founder of Evolution: His Life and Work (1901), 363. Packard's italics.
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I am a strong advocate for free thought on all subjects, yet it appears to me (whether rightly or wrongly) that direct arguments against christianity & theism produce hardly any effect on the public; & freedom of thought is best promoted by the gradual illumination of men's minds, which follow[s] from the advance of science. It has, therefore, been always my object to avoid writing on religion, & I have confined myself to science. I may, however, have been unduly biassed by the pain which it would give some members of my family, if I aided in any way direct attacks on religion.
Letter to E.B. Aveling (13 Oct 1880).
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I begin my work at about nine or ten o'clock in the evening and continue until four or five in the morning. Night is a more quiet time to work. It aids thought.
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), 31.
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I had made up my mind to find that for which I was searching even if it required the remainder of my life. After innumerable failures I finally uncovered the principle for which I was searching, and I was astounded at its simplicity. I was still more astounded to discover the principle I had revealed not only beneficial in the construction of a mechanical hearing aid but it served as well as means of sending the sound of the voice over a wire. Another discovery which came out of my investigation was the fact that when a man gives his order to produce a definite result and stands by that order it seems to have the effect of giving him what might be termed a second sight which enables him to see right through ordinary problems. What this power is I cannot say; all I know is that it exists and it becomes available only when a man is in that state of mind in which he knows exactly what he wants and is fully determined not to quit until he finds it.
As quoted, without citation, in Mack R. Douglas, Making a Habit of Success: How to Make a Habit of Succeeding, How to Win With High Self-Esteem (1966, 1994), 38. Note: Webmaster is dubious of a quote which seems to appear in only one source, without a citation, decades after Bell’s death. If you know a primary source, please contact Webmaster.
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I have never had any student or pupil under me to aid me with assistance; but have always prepared and made my experiments with my own hands, working & thinking at the same time. I do not think I could work in company, or think aloud, or explain my thoughts at the time. Sometimes I and my assistant have been in the Laboratory for hours & days together, he preparing some lecture apparatus or cleaning up, & scarcely a word has passed between us; — all this being a consequence of the solitary & isolated system of investigation; in contradistinction to that pursued by a Professor with his aids & pupils as in your Universities.
Letter to C. Ransteed, 16 Dec 1857. In L. Pearce Williams (ed.), The Selected Correspondence of Michael Faraday (1971), Vol. 2, 888.
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I should rejoice to see … Euclid honourably shelved or buried “deeper than did ever plummet sound” out of the schoolboys’ reach; morphology introduced into the elements of algebra; projection, correlation, and motion accepted as aids to geometry; the mind of the student quickened and elevated and his faith awakened by early initiation into the ruling ideas of polarity, continuity, infinity, and familiarization with the doctrines of the imaginary and inconceivable.
From Presidential Address (1869) to the British Association, Exeter, Section A, collected in Collected Mathematical Papers of Lames Joseph Sylvester (1908), Vol. 2, 657. Also in George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 93. [Note: “plummet sound” refers to ocean depth measurement (sound) from a ship using a line dropped with a weight (plummet). —Webmaster]
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I trust ... I have succeeded in convincing you that modern chemistry is not, as it has so long appeared, an ever-growing accumulation of isolated facts, as impossible for a single intellect to co-ordinate as for a single memory to grasp.
The intricate formulae that hang upon these walls, and the boundless variety of phenomena they illustrate, are beginning to be for us as a labyrinth once impassable, but to which we have at length discovered the clue. A sense of mastery and power succeeds in our minds to the sort of weary despair with which we at first contemplated their formidable array. For now, by the aid of a few general principles, we find ourselves able to unravel the complexities of these formulae, to marshal the compounds which they represent in orderly series; nay, even to multiply their numbers at our will, and in a great measure to forecast their nature ere we have called them into existence. It is the great movement of modern chemistry that we have thus, for an hour, seen passing before us. It is a movement as of light spreading itself over a waste of obscurity, as of law diffusing order throughout a wilderness of confusion, and there is surely in its contemplation something of the pleasure which attends the spectacle of a beautiful daybreak, something of the grandeur belonging to the conception of a world created out of chaos.
Concluding remark for paper presented at the Friday Discourse of the the Royal Institution (7 Apr 1865). 'On the Combining Power of Atoms', Proceedings of the Royal Institution (1865), 4, No. 42, 416.
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I would not have it inferred ... that I am, as yet, an advocate for the hypothesis of chemical life. The doctrine of the vitality of the blood, stands in no need of aid from that speculative source. If it did, I would certainly abandon it. For, notwithstanding the fashionableness of the hypothesis in Europe, and the ascendancy it has gained over some minds in this country [USA], it will require stubborn facts to convince me that man with all his corporeal and intellectual attributes is nothing but hydro-phosphorated oxyde of azote ... When the chemist declares, that the same laws which direct the crystallization of spars, nitre and Glauber's salts, direct also the crystallization of man, he must pardon me if I neither understand him, nor believe him.
Medical Theses (1805), 391-2, footnote.
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If it were always necessary to reduce everything to intuitive knowledge, demonstration would often be insufferably prolix. This is why mathematicians have had the cleverness to divide the difficulties and to demonstrate separately the intervening propositions. And there is art also in this; for as the mediate truths (which are called lemmas, since they appear to be a digression) may be assigned in many ways, it is well, in order to aid the understanding and memory, to choose of them those which greatly shorten the process, and appear memorable and worthy in themselves of being demonstrated. But there is another obstacle, viz.: that it is not easy to demonstrate all the axioms, and to reduce demonstrations wholly to intuitive knowledge. And if we had chosen to wait for that, perhaps we should not yet have the science of geometry.
In Gottfried Wilhelm Leibnitz and Alfred Gideon Langley (trans.), New Essays Concerning Human Understanding (1896), 413-414.
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If the historical development of science has indeed sometimes pricked our vanity, it has not plunged us into an abyss of immorality ... it has liberated us from misconceptions, and thereby aided us in our moral progress.
…...
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In 1735 the solving of an astronomical problem, proposed by the Academy, for which several eminent mathematicians had demanded several months’ time, was achieved in three days by Euler with aid of improved methods of his own. … With still superior methods this same problem was solved by the illustrious Gauss in one hour.
In History of Mathematics (1897), 248.
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In general the position as regards all such new calculi is this That one cannot accomplish by them anything that could not be accomplished without them. However, the advantage is, that, provided such a calculus corresponds to the inmost nature of frequent needs, anyone who masters it thoroughly is able—without the unconscious inspiration of genius which no one can command—to solve the respective problems, yea, to solve them mechanically in complicated cases in which, without such aid, even genius becomes powerless. Such is the case with the invention of general algebra, with the differential calculus, and in a more limited region with Lagrange’s calculus of variations, with my calculus of congruences, and with Möbius’s calculus. Such conceptions unite, as it were, into an organic whole countless problems which otherwise would remain isolated and require for their separate solution more or less application of inventive genius.
Letter (15 May 1843) to Schumacher, collected in Carl Friedrich Gauss Werke (1866), Vol. 8, 298, as translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 197-198. From the original German, “Überhaupt verhält es sich mit allen solchen neuen Calculs so, dass man durch sie nichts leisten kann, was nicht auch ohne sie zu leisten wäre; der Vortheil ist aber der, dass, wenn ein solcher Calcul dem innersten Wesen vielfach vorkommender Bedürfnisse correspondirt, jeder, der sich ihn ganz angeeignet hat, auch ohne die gleichsam unbewussten Inspirationen des Genies, die niemand erzwingen kann, die dahin gehörigen Aufgaben lösen, ja selbst in so verwickelten Fällen gleichsam mechanisch lösen kann, wo ohne eine solche Hülfe auch das Genie ohnmächtig wird. So ist es mit der Erfindung der Buchstabenrechnung überhaupt; so mit der Differentialrechnung gewesen; so ist es auch (wenn auch in partielleren Sphären) mit Lagranges Variationsrechnung, mit meiner Congruenzenrechnung und mit Möbius' Calcul. Es werden durch solche Conceptionen unzählige Aufgaben, die sonst vereinzelt stehen, und jedesmal neue Efforts (kleinere oder grössere) des Erfindungsgeistes erfordern, gleichsam zu einem organischen Reiche.”
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In modern Europe, the Middle Ages were called the Dark Ages. Who dares to call them so now? … Their Dante and Alfred and Wickliffe and Abelard and Bacon; their Magna Charta, decimal numbers, mariner’s compass, gunpowder, glass, paper, and clocks; chemistry, algebra, astronomy; their Gothic architecture, their painting,—are the delight and tuition of ours. Six hundred years ago Roger Bacon explained the precession of the equinoxes, and the necessity of reform in the calendar; looking over how many horizons as far as into Liverpool and New York, he announced that machines can be constructed to drive ships more rapidly than a whole galley of rowers could do, nor would they need anything but a pilot to steer; carriages, to move with incredible speed, without aid of animals; and machines to fly into the air like birds.
In 'Progress of Culture', an address read to the Phi Beta Kappa Society at Cambridge, 18 July 1867. Collected in Works of Ralph Waldo Emerson (1883), 475.
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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 discovery of lemmas the best aid is a mental aptitude for it. For we may see many who are quick at solutions and yet do not work by method ; thus Cratistus in our time was able to obtain the required result from first principles, and those the fewest possible, but it was his natural gift which helped him to the discovery.
Proclus
As given in Euclid, The Thirteen Books of Euclid's Elements, translated from the text of Johan Ludvig Heiberg by Sir Thomas Little Heath, Vol. 1, Introduction and Books 1,2 (1908), 133. The passage also states that Proclus gives the definition of the term lemma as a proposition not proved beforehand. Glenn Raymond Morrow in A Commentary on the First Book of Euclid's Elements (1992), 165, states nothing more seems to be known of Cratistus.
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It certainly strikes the beholder with astonishment, to perceive what vast difficulties can be overcome by the pigmy arms of little mortal man, aided by science and directed by superior skill.
About his visit to Lockport on the Erie Canal, in Letter IX, to a friend in England from Lockport, New York (25 Jul 1831), collected in Narrative of a Tour in North America (1834), Vol. 1, 233-234,
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It is by the aid of iron that we construct houses, cleave rocks, and perform so many other useful offices of life. But it is with iron also that wars, murders, and robberies are effected, and this, not only hand to hand, but from a distance even, by the aid of missiles and winged weapons, now launched from engines, now hurled by the human arm, and now furnished with feathery wings. This last I regard as the most criminal artifice that has been devised by the human mind; for, as if to bring death upon man with still greater rapidity, we have given wings to iron and taught it to fly. ... Nature, in conformity with her usual benevolence, has limited the power of iron, by inflicting upon it the punishment of rust; and has thus displayed her usual foresight in rendering nothing in existence more perishable, than the substance which brings the greatest dangers upon perishable mortality.
Natural History of Pliny, translation (1857, 1898) by John Bostock and H. T. Riley, 205-6.
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It is in this mutual dependence of the functions and the aid which they reciprocally lend one another that are founded the laws which determine the relations of their organs and which possess a necessity equal to that of metaphysical or mathematical laws, since it is evident that the seemly harmony between organs which interact is a necessary condition of existence of the creature to which they belong and that if one of these functions were modified in a manner incompatible with the modifications of the others the creature could no longer continue to exist.
Leçons d' anatomie comparée, Vol. I, 47. Trans. William Coleman, Georges Cuvier Zoologist: A Study in the History of Evolution Theory (1964), 67-8.
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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 science alone that can solve the problems of hunger and poverty, of insanitation and illiteracy, of superstition and deadening custom and tradition, of vast resources running to waste, of a rich country inhabited by starving people… Who indeed could afford to ignore science today? At every turn we have to seek its aid … the future belongs to science and those who make friends with science.
From address to the Indian Science Congress (26 Dec 1937). As cited in M.J. Vinod and Meena Deshpande, Contemporary Political Theory (2013), 507. An earlier, longer version of the quote is in Atma Ram, 'The Making of Optical Glass in India: Its Lessons for Industrial Development', Proceedings of the National Institute of Sciences of India (1961), 27, 564-5.
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Learning is wealth to the poor, an honor to the rich, an aid to the young, and a support and comfort to the aged.
As cited in Abram N. Coleman (ed.), Proverbial Wisdom: Proverbs, Maxims and Ethical Sentences (1903), 130. Often-seen attribution to John C. Lavater is probably erroneous. Several quote collections of the same era give the quote without citation. In Tryon Edwards, Dictionary of Thoughts (1908), 294, this quote is given without citation, followed by a blank line separator, and then an unrelated quote by Lavater. This juxtaposition is likely the source of confusion in attribution.
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Life is order, death is disorder. A fundamental law of Nature states that spontaneous chemical changes in the universe tend toward chaos. But life has, during milliards of years of evolution, seemingly contradicted this law. With the aid of energy derived from the sun it has built up the most complicated systems to be found in the universe—living organisms. Living matter is characterized by a high degree of chemical organisation on all levels, from the organs of large organisms to the smallest constituents of the cell. The beauty we experience when we enjoy the exquisite form of a flower or a bird is a reflection of a microscopic beauty in the architecture of molecules.
The Nobel Prize for Chemistry: Introductory Address'. Nobel Lectures: Chemistry 1981-1990 (1992), 69.
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Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation, but, we venture to say, they will find themselves very much enlightened during the process, and will even be doubtful whether the ideas as expressed in symbols had ever quite found their way out of the equations into their minds.
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Mathematics … belongs to every inquiry, moral as well as physical. Even the rules of logic, by which it is rigidly bound, could not be deduced without its aid. The laws of argument admit of simple statement, but they must be curiously transposed before they can be applied to the living speech and verified by observation. In its pure and simple form the syllogism cannot be directly compared with all experience, or it would not have required an Aristotle to discover it. It must be transmuted into all the possible shapes in which reasoning loves to clothe itself. The transmutation is the mathematical process in the establishment of the law.
From Memoir (1870) read before the National Academy of Sciences, Washington, printed in 'Linear Associative Algebra', American Journal of Mathematics (1881), 4, 97-98.
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Mathematics, among all school subjects, is especially adapted to further clearness, definite brevity and precision in expression, although it offers no exercise in flights of rhetoric. This is due in the first place to the logical rigour with which it develops thought, avoiding every departure from the shortest, most direct way, never allowing empty phrases to enter. Other subjects excel in the development of expression in other respects: translation from foreign languages into the mother tongue gives exercise in finding the proper word for the given foreign word and gives knowledge of laws of syntax, the study of poetry and prose furnish fit patterns for connected presentation and elegant form of expression, composition is to exercise the pupil in a like presentation of his own or borrowed thoughtsand their development, the natural sciences teach description of natural objects, apparatus and processes, as well as the statement of laws on the grounds of immediate sense-perception. But all these aids for exercise in the use of the mother tongue, each in its way valuable and indispensable, do not guarantee, in the same manner as mathematical training, the exclusion of words whose concepts, if not entirely wanting, are not sufficiently clear. They do not furnish in the same measure that which the mathematician demands particularly as regards precision of expression.
In Anleitung zum mathematischen Unterricht in höheren Schulen (1906), 17.
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Nature, … in order to carry out the marvelous operations [that occur] in animals and plants has been pleased to construct their organized bodies with a very large number of machines, which are of necessity made up of extremely minute parts so shaped and situated as to form a marvelous organ, the structure and composition of which are usually invisible to the naked eye without the aid of a microscope. … Just as Nature deserves praise and admiration for making machines so small, so too the physician who observes them to the best of his ability is worthy of praise, not blame, for he must also correct and repair these machines as well as he can every time they get out of order.
'Reply to Doctor Sbaraglia' in Opera Posthuma (1697), in H. B. Adelmann (ed.), Marcello Malpighi and the Evolution of Embryology (1966), Vol. 1, 568.
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Nothing could have been worse for the development of my mind than Dr. Butler's school, as it was strictly classical, nothing else being taught, except a little ancient geography and history. The school as a means of education to me was simply a blank. During my whole life I have been singularly incapable of mastering any language. Especial attention was paid to versemaking, and this I could never do well. I had many friends, and got together a good collection of old verses, which by patching together, sometimes aided by other boys, I could work into any subject.
In Charles Darwin and Francis Darwin (ed.), Charles Darwin: His Life Told in an Autobiographical Chapter, and in a Selected Series of His Published Letters (1892), 8.
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O Logic: born gatekeeper to the Temple of Science, victim of capricious destiny: doomed hitherto to be the drudge of pedants: come to the aid of thy master, Legislation.
In John Browning (ed.), 'Extracts from Bentham’s Commonplace Book: Logic', The Works of Jeremy Bentham (1843), Vol. 10, 145.
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Only science, exact science about human nature itself, and the most sincere approach to it by the aid of the omnipotent scientific method, will deliver man from his present gloom and will purge him from his contemporary share in the sphere of interhuman relations.
In Ivan Pavlov and William Horsley Gantt (trans.), Lectures on Conditioned Reflexes (1928, 1941), Preface, 41.
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Physical investigation, more than anything besides, helps to teach us the actual value and right use of the Imagination—of that wondrous faculty, which, left to ramble uncontrolled, leads us astray into a wilderness of perplexities and errors, a land of mists and shadows; but which, properly controlled by experience and reflection, becomes the noblest attribute of man; the source of poetic genius, the instrument of discovery in Science, without the aid of which Newton would never have invented fluxions, nor Davy have decomposed the earths and alkalies, nor would Columbus have found another Continent.
Presidential Address to Anniversary meeting of the Royal Society (30 Nov 1859), Proceedings of the Royal Society of London (1860), 10, 165.
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Professor von Pirquet has come to this country exactly at the right time to aid us. He has shown us how to detect tuberculosis before it has become so developed as to be contagious and has so taken hold of the individual as to be recognized by any other means. In thousands of cases I for my part am unable to detect tuberculosis in infancy or early childhood without the aid of the tuberculin test which Prof. von Pirquet has shown to be the best. He has taught us how by tubercular skin tests, to detect it. ... What Dr. von Pirquet has done already will make his name go down to posterity as one of the great reformers in tuberculin tests and as one who has done an immense amount of good to humanity. The skin test in twenty-four hours will show you whether the case is tubercular.
Discussion on 'The Relation of Tuberculosis to Infant Mortality', read at the third mid-year meeting of the American Academy of Medicine, New Haven, Conn, (4 Nov 1909). In Bulletin of the American Academy of Medicine (1910), 11, 78.
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Science is but a feeble means for motivating life. It enlightens men, but fails to arouse them to deeds of self-sacrifice and devotion. … It dispels ignorance, but it never launched a crusade. It gives aid in the struggle with the hard surroundings of life, but it does not inform us to what end we struggle, or whether the struggle is worth while. … Intelligence can do little more than direct.
As quoted by M.G. Mellon in his retiring Presidential Address to the Winter Meeting of the Indiana Academy of Science at the University of Notre Dame (30 Oct 1942), 'Science, Scientists, and Society', printed in Proceedings of the Indiana Academy of Science (1943), 52, 15. No source citation given.
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Science is, and must be, culturally embedded; what else could the product of human passion be?... Culture is not the enemy of objectivity but a matrix that can either aid or retard advancing knowledge.
…...
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See skulking Truth to her old cavern fled,
Mountains of Casuistry heap’d o’er her head!
Philosophy, that lean’d on Heav’n before,
Shrinks to her second cause, and is no more.
Physic of Metaphysic begs defence,
And Metaphysic calls for aid on Sense!
See Mystery to Mathematics fly!
In The Dunciad, collected in The Poetical Works of Alexander Pope (1828), Vol. 3, 211.
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That mathematics “do not cultivate the power of generalization,”; … will be admitted by no person of competent knowledge, except in a very qualified sense. The generalizations of mathematics, are, no doubt, a different thing from the generalizations of physical science; but in the difficulty of seizing them, and the mental tension they require, they are no contemptible preparation for the most arduous efforts of the scientific mind. Even the fundamental notions of the higher mathematics, from those of the differential calculus upwards are products of a very high abstraction. … To perceive the mathematical laws common to the results of many mathematical operations, even in so simple a case as that of the binomial theorem, involves a vigorous exercise of the same faculty which gave us Kepler’s laws, and rose through those laws to the theory of universal gravitation. Every process of what has been called Universal Geometry—the great creation of Descartes and his successors, in which a single train of reasoning solves whole classes of problems at once, and others common to large groups of them—is a practical lesson in the management of wide generalizations, and abstraction of the points of agreement from those of difference among objects of great and confusing diversity, to which the purely inductive sciences cannot furnish many superior. Even so elementary an operation as that of abstracting from the particular configuration of the triangles or other figures, and the relative situation of the particular lines or points, in the diagram which aids the apprehension of a common geometrical demonstration, is a very useful, and far from being always an easy, exercise of the faculty of generalization so strangely imagined to have no place or part in the processes of mathematics.
In An Examination of Sir William Hamilton’s Philosophy (1878), 612-13.
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The aid which we feel impelled to give to the helpless is mainly an incidental result of the instinct of sympathy, which was originally acquired as part of the social instincts, but subsequently rendered, in the manner previously indicated, more tender and more widely diffused. Nor could we check our sympathy, even at the urging of hard reason, without deterioration in the noblest part of our nature.
…...
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The astronomer is, in some measure, independent of his fellow astronomer; he can wait in his observatory till the star he wishes to observe comes to his meridian; but the meteorologist has his observations bounded by a very limited horizon, and can do little without the aid of numerous observers furnishing him contemporaneous observations over a wide-extended area.
Second Report on Meteorology to the Secretary of the Navy (1849), US Senate Executive Document 39, 31st Congress, 1st session. Quoted in J. R. Fleming, Meteorology in America: 1800-1870 (1990), vii.
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The astronomer who studies the motion of the stars is surely like a blind man who, with only a staff [mathematics] to guide him, must make a great, endless, hazardous journey that winds through innumerable desolate places. What will be the result? Proceeding anxiously for a while and groping his way with his staff, he will at some time, leaning upon it, cry out in despair to Heaven, Earth and all the Gods to aid him in his misery.
In The Sleepwalkers by Arthur Koestler (1968).
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The attitude of the intellectual community toward America is shaped not by the creative few but by the many who for one reason or another cannot transmute their dissatisfaction into a creative impulse, and cannot acquire a sense of uniqueness and of growth by developing and expressing their capacities and talents. There is nothing in contemporary America that can cure or alleviate their chronic frustration. They want power, lordship, and opportunities for imposing action. Even if we should banish poverty from the land, lift up the Negro to true equality, withdraw from Vietnam, and give half of the national income as foreign aid, they will still see America as an air-conditioned nightmare unfit for them to live in.
In 'Some Thoughts on the Present', The Temper of Our Time (1967), 107.
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The calculus is the greatest aid we have to the appreciation of physical truth in the broadest sense of the word.
Conclusion of Presidential Address (27 Apr 1907) to the American Mathematical Society, 'The Calculus in Colleges and Technical Schools', published in Bulletin of the American Mathematical Society (Jun 1907), 13, 467.
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The contradictory experiments of chemists leave us at liberty to conclude what we please. My conclusion is, that art has not yet invented sufficient aids to enable such subtle bodies [air, light, &c.] to make a well-defined impression on organs as blunt as ours; that it is laudable to encourage investigation but to hold back conclusion.
Letter to Rev. James Madison (Paris, 19 Jul 1788). In Thomas Jefferson and John P. Foley (ed.), The Jeffersonian Cyclopedia (1900), 135. From H.A. Washington, The Writings of Thomas Jefferson (1853-54). Vol 2, 431.
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The glimpses of chemical industry's services to man afforded by this book could be presented only by utilizing innumerable chemical products. The first outline of its plan began to take shape on chemically produced notepaper with the aid of a chemically-treated graphite held in a synthetic resin pencil. Early corrections were made with erasers of chemically compounded rubber. In its ultimate haven on the shelves of your bookcase, it will rest on a coating of chemical varnish behind a pane of chemically produced glass. Nowhere has it been separated from that industry's products.
Man in a Chemical World (1937), L'Envoi, 284.
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The new chemistry indeed has given us a new principle of the generation of rain, by proving water to be a composition of different gases, and has aided our theory of meteoric lights.
Letter (5 Sep 1822) to George F. Hopkins. Collected in The Writings of Thomas Jefferson (1854), Vol. 7, 260.
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The next object which I have observed is the essence or substance of the Milky Way. By the aid of a telescope anyone may behold this in a manner which so distinctly appeals to the senses that all the disputes which have tormented philosophers through so many ages are exploded at once by the irrefragable evidence of our eyes, and we are freed from wordy disputes upon this subject, for the Galaxy is nothing else but a mass of innumerable stars planted together in clusters.
In pamphlet, The Sidereal Messenger (1610), reprinted in The Sidereal Messenger of Galileo Galilei: And a Part of the Preface to the Preface to Kepler's Dioptrics Containing the Original Account of Galileo's Astronomical Discoveries (1880), 42.
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The number of travellers by gigs, the outside of coaches, and on horseback, have, since the introduction of railways, been prodigiously diminished; and as, in addition, the members of the medical faculty having lent their aid to run down the use of water-proof (apparently having found it decided enemy against their best friends colds and catarrhs), the use of the article [the Macintosh] in the form of cloaks, etc., has of late become comparatively extinct.
A Biographical Memoir of the late Charles Macintosh Esq FRS (1847), 89.
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The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience.
In Immanuel Kant and F. Max Müller (trans.), 'Method of Transcendentalism', Critique of Pure Reason (1881), Vol. 2, 610.
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The study of mathematics is apt to commence in disappointment. The important applications of the science, the theoretical interest of its ideas, and the logical rigour of its methods all generate the expectation of a speedy introduction to processes of interest. We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.
Opening to An Introduction to Mathematics (1911), 7.
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The study of mathematics is apt to commence in disappointment. … We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this greatest science eludes the efforts of our mental weapons to grasp it.
Opening of Chap 1, in An Introduction to Mathematics (1911), 7.
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The true foundation of theology is to ascertain the character of God. It is by the aid of Statistics that law in the social sphere can be ascertained and codified, and certain aspects of the character of God thereby revealed. The study of statistics is thus a religious service.
As quoted by Florence Nightingale David in Games, Gods, and Gambling: A History of Probability and Statistical Ideas (1962, 1998), 103. David introduced the quote by saying “Florence Nightingale, after some lengthy calculations, wrote:”.
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The whole of Mathematics consists in the organization of a series of aids to the imagination in the process of reasoning.
In Universal Algebra (1898), 12.
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The [mechanical] bird I have described ought to be able by the help of the wind to rise to a great height, and this will prove to be its safety; since even if… revolutions [of the winds] were to befall it, it would still have time to regain a condition of equilibrium; provided that its various parts have a great power of resistance, so that they can safely withstand the fury and violence of the descent, by the aid of the defenses which I have mentioned; and its joints should be made of strong tanned hide, and sewn with cords of strong raw silk. And let no one encumber himself with iron bands, for these are very soon broken at the joints or else they become worn out, and consequently it is well not to encumber oneself with them.
'Of the Bird’s Movement' from Sul Voio degli Uccelli, 8 [7] r. in Leonardo da Vinci's Notebooks, trans. E. MacCurdy (1906), 153-4.
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There really are not any spheres in the heavens ... Those which have been devised by the experts to save the appearances exist only in the imagination, for the purpose of enabling the mind to conceive the motion which the heavenly bodies trace in their course and, by the aid of geometry, to determine the motion numerically through the use of arithmetic.
J. L. E. Dreyer (ed.), Opera Omnia (1913-29), Vol. 4, 222. Trans. Edward Rosen, 'Nicholas Copernicus', in Charles C. Gillispie (ed.), Dictionary of Scientific Biography (1971), Vol. 3, 409.
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These machines [used in the defense of the Syracusans against the Romans under Marcellus] he [Archimedes] had designed and contrived, not as matters of any importance, but as mere amusements in geometry; in compliance with king Hiero’s desire and request, some time before, that he should reduce to practice some part of his admirable speculation in science, and by accommodating the theoretic truth to sensation and ordinary use, bring it more within the appreciation of people in general. Eudoxus and Archytas had been the first originators of this far-famed and highly-prized art of mechanics, which they employed as an elegant illustration of geometrical truths, and as means of sustaining experimentally, to the satisfaction of the senses, conclusions too intricate for proof by words and diagrams. As, for example, to solve the problem, so often required in constructing geometrical figures, given the two extremes, to find the two mean lines of a proportion, both these mathematicians had recourse to the aid of instruments, adapting to their purpose certain curves and sections of lines. But what with Plato’s indignation at it, and his invectives against it as the mere corruption and annihilation of the one good of geometry,—which was thus shamefully turning its back upon the unembodied objects of pure intelligence to recur to sensation, and to ask help (not to be obtained without base supervisions and depravation) from matter; so it was that mechanics came to be separated from geometry, and, repudiated and neglected by philosophers, took its place as a military art.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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This [the fact that the pursuit of mathematics brings into harmonious action all the faculties of the human mind] accounts for the extraordinary longevity of all the greatest masters of the Analytic art, the Dii Majores of the mathematical Pantheon. Leibnitz lived to the age of 70; Euler to 76; Lagrange to 77; Laplace to 78; Gauss to 78; Plato, the supposed inventor of the conic sections, who made mathematics his study and delight, who called them the handles or aids to philosophy, the medicine of the soul, and is said never to have let a day go by without inventing some new theorems, lived to 82; Newton, the crown and glory of his race, to 85; Archimedes, the nearest akin, probably, to Newton in genius, was 75, and might have lived on to be 100, for aught we can guess to the contrary, when he was slain by the impatient and ill mannered sergeant, sent to bring him before the Roman general, in the full vigour of his faculties, and in the very act of working out a problem; Pythagoras, in whose school, I believe, the word mathematician (used, however, in a somewhat wider than its present sense) originated, the second founder of geometry, the inventor of the matchless theorem which goes by his name, the pre-cognizer of the undoubtedly mis-called Copernican theory, the discoverer of the regular solids and the musical canon who stands at the very apex of this pyramid of fame, (if we may credit the tradition) after spending 22 years studying in Egypt, and 12 in Babylon, opened school when 56 or 57 years old in Magna Græcia, married a young wife when past 60, and died, carrying on his work with energy unspent to the last, at the age of 99. The mathematician lives long and lives young; the wings of his soul do not early drop off, nor do its pores become clogged with the earthy particles blown from the dusty highways of vulgar life.
In Presidential Address to the British Association, Collected Mathematical Papers, Vol. 2 (1908), 658.
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Through most of his existence man’s survival depended on his ability to cope with nature. If the mind evolved as an aid in human survival it was primarily as an instrument for the mastery of nature. The mind is still at its best when tinkering with the mathematics that rule nature.
In Before the Sabbath (1979), 26.
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Time will soon destroy the works of famous painters and sculptors, but the Indian arrowhead will balk his efforts and Eternity will have to come to his aid. They are not fossil bones, but, as it were, fossil thoughts, forever reminding me of the mind that shaped them… . Myriads of arrow-points lie sleeping in the skin of the revolving earth, while meteors revolve in space. The footprint, the mind-print of the oldest men.
(28 Mar 1859). In Henry David Thoreau and Bradford Torrey (ed.), The Writings of Henry Thoreau: Journal: XII: March, 2, 1859-November 30, 1859 (1906), 91.
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To render aid to the worthless is sheer waste. Rain does not freshen the Dead Sea, but only enables it to dissolve more salt.
From chapter 'Jottings from a Note-Book', in Canadian Stories (1918), 172.
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True science is distinctively the study of useless things. For the useful things will get studied without the aid of scientific men. To employ these rare minds on such work is like running a steam engine by burning diamonds.
From 'Lessons from the History of Science: The Scientific Attitude' (c.1896), in Collected Papers (1931), Vol. 1, 32.
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We all know, from what we experience with and within ourselves, that our conscious acts spring from our desires and our fears. Intuition tells us that that is true also of our fellows and of the higher animals. We all try to escape pain and death, while we seek what is pleasant. We are all ruled in what we do by impulses; and these impulses are so organized that our actions in general serve for our self preservation and that of the race. Hunger, love, pain, fear are some of those inner forces which rule the individual’s instinct for self preservation. At the same time, as social beings, we are moved in the relations with our fellow beings by such feelings as sympathy, pride, hate, need for power, pity, and so on. All these primary impulses, not easily described in words, are the springs of man’s actions. All such action would cease if those powerful elemental forces were to cease stirring within us. Though our conduct seems so very different from that of the higher animals, the primary instincts are much alike in them and in us. The most evident difference springs from the important part which is played in man by a relatively strong power of imagination and by the capacity to think, aided as it is by language and other symbolical devices. Thought is the organizing factor in man, intersected between the causal primary instincts and the resulting actions. In that way imagination and intelligence enter into our existence in the part of servants of the primary instincts. But their intervention makes our acts to serve ever less merely the immediate claims of our instincts.
…...
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We are told that “Mathematics is that study which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation.” I think no statement could have been made more opposite to the facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas, and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activities of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world (to which the inner one in each individual man may, I think, be conceived to stand somewhat in the same relation of correspondence as a shadow to the object from which it is projected, or as the hollow palm of one hand to the closed fist which it grasps of the other), that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of the imagination and invention.
In Presidential Address to British Association, Exeter British Association Report (1869), pp. 1-9, in Collected Mathematical Papers, Vol. 2, 654.
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We cannot hope to build a better world without improving the individual. Toward this end, each of us must work for his own highest development, accepting at the same time his share of responsibility in the general life of humanity—our particular duty being to aid those to whom we think we can be most useful.
Quoted in Eve Curie Labouisse and Eve Curie, trans. by Vincent Sheean, Madame Curie (1937), 53.
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What appear to be the most valuable aspects of the theoretical physics we have are the mathematical descriptions which enable us to predict events. These equations are, we would argue, the only realities we can be certain of in physics; any other ways we have of thinking about the situation are visual aids or mnemonics which make it easier for beings with our sort of macroscopic experience to use and remember the equations.
In The Lost Cause: Causation and the Mind-body Problem (2003).
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When a machine begins to run without human aid, it is time to scrap it - whether it be a factory or a government.
In Rhoda Thomas Tripp, The International Thesaurus of Quotations (1970).
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When he can render no further aid, the physician alone can mourn as a man with his incurable patient. This is the physician's sad lot.
Attributed
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When the child outgrows the narrow circle of family life … then comes the period of the school, whose object is to initiate him into the technicalities of intercommunication with his fellow-men, and to familiarize him with the ideas that underlie his civilization, and which he must use as tools of thought if he would observe and understand the phases of human life around him; for these … are invisible to the human being who has not the aid of elementary ideas with which to see them.
In Psychologic Foundations of Education: An Attempt to Show the Genesis of the Higher Faculties of the Mind (1907), 265.
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While speaking, M. Bertrand is always in motion; now he seems in combat with some outside enemy, now he outlines with a gesture of the hand the figures he studies. Plainly he sees and he is eager to paint, this is why he calls gesture to his aid. With M. Hermite, it is just the opposite; his eyes seem to shun contact with the world; it is not without, it is within he seeks the vision of truth.
From La Valeur de la Science (1904), 14, as translated by George Bruce Halsted (trans.), in The Value of Science (1907), 16. From the French, “Tout en parlant, M. Bertrand est toujours en action; tantôt il semble aux prises avec quelque ennemi extérieur, tantôt il dessine d'un geste de la main les figures qu’il étudie. Évidemment, il voit et il cherche à peindre, c’est pour cela qu’il appelle le geste à son secours. Pour M. Hermite, c’est tout le contraire; ses yeux semblent fuir le contact du monde; ce n’est pas au dehors, c’est au dedans qu’il cherche la vision de la vérité.”
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Without doubt one of the most characteristic features of mathematics in the last century is the systematic and universal use of the complex variable. Most of its great theories received invaluable aid from it, and many owe their very existence to it.
In 'History of Mathematics in the Nineteenth Century', Congress of Arts and Sciences (1905), Vol. 1, 474. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 115.
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Workers must root out the idea that by keeping the results of their labors to themselves a fortune will be assured to them. Patent fees are so much wasted money. The flying machine of the future will not be born fully fledged and capable of a flight for 1,000 miles or so. Like everything else it must be evolved gradually. The first difficulty is to get a thing that will fly at all. When this is made, a full description should be published as an aid to others. Excellence of design and workmanship will always defy competition.
As quoted in Octave Chanute, Progress in Flying Machines (1894), 218.
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[All phenomena] are equally susceptible of being calculated, and all that is necessary, to reduce the whole of nature to laws similar to those which Newton discovered with the aid of the calculus, is to have a sufficient number of observations and a mathematics that is complex enough.
Unpublished Manuscript. Quoted In Frank Edward Manuel and Fritzie Prigohzy Manuel, Utopian Thought in the Western World (1979, 2009), 493.
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[Davy's] March of Glory, which he has run for the last six weeks—within which time by the aid and application of his own great discovery, of the identity of electricity and chemical attractions, he has placed all the elements and all their inanimate combinations in the power of man; having decomposed both the Alkalies, and three of the Earths, discovered as the base of the Alkalies a new metal... Davy supposes there is only one power in the world of the senses; which in particles acts as chemical attractions, in specific masses as electricity, & on matter in general, as planetary Gravitation... when this has been proved, it will then only remain to resolve this into some Law of vital Intellect—and all human knowledge will be Science and Metaphysics the only Science.
In November 1807 Davy gave his famous Second Bakerian Lecture at the Royal Society, in which he used Voltaic batteries to “decompose, isolate and name” several new chemical elements, notably sodium and potassium.
Letter to Dorothy Wordsworth, 24 November 1807. In Earl Leslie Griggs (ed.), The Collected Letters of Samuel Taylor Coleridge (1956), Vol. 3, 38.
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[Engineering] is a great profession. There is the fascination of watching a figment of the imagination emerge through the aid of science to a plan on paper. Then it moves to realization in stone or metal or energy. Then it brings homes to men or women. Then it elevates the standards of living and adds to the comforts of life. That is the engineer’s high privilege.
Reprint of his 1916 statement in 'Engineering as a Profession', Engineer’s Week (1954).
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[Modern science] passed through a long period of uncertainty and inconclusive experiment, but as the instrumental aids to research improved, and the results of observation accumulated, phantoms of the imagination were exorcised, idols of the cave were shattered, trustworthy materials were obtained for logical treatment, and hypotheses by long and careful trial were converted into theories.
In The Present Relations of Science and Religion (1913, 2004), 3
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[The body of law] has taxed the deliberative spirit of ages. The great minds of the earth have done it homage. It was the fruit of experience. Under it men prospered, all the arts flourished, and society stood firm. Every right and duty could be understood because the rules regulating each had their foundation in reason, in the nature and fitness of things; were adapted to the wants of our race, were addressed to the mind and to the heart; were like so many scraps of logic articulate with demonstration. Legislation, it is true occasionally lent its aid, but not in the pride of opinion, not by devising schemes inexpedient and untried, but in a deferential spirit, as a subordinate co-worker.
From biographical preface by T. Bigelow to Austin Abbott (ed.), Official Report of the Trial of Henry Ward Beecher (1875), Vol. 1, xii.
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“These changes in the body,” he wrote in the review paper he sent to the American Journal of Physiology late in 1913, “are, each one of them, directly serviceable in making the organism more efficient in the struggle which fear or rage or pain may involve; for fear and rage are organic preparations for action, and pain is the most powerful known stimulus to supreme exertion. The organism which with the aid of increased adrenal secretion can best muster its energies, can best call forth sugar to supply the labouring muscles, can best lessen fatigue, and can best send blood to the parts essential in the run or the fight for life, is most likely to survive. Such, according to the view here propounded, is the function of the adrenal medulla at times of great emergency.”
Quoted in S. Benison, A. C. Barger and E. L. Wolfe, Walter B Cannon: The Life and Times of a Young Scientist (1987), 311.
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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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