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Means Quotes (167 quotes)

[Defining Organism] That in which every part is at once means and end.
Kritik der Urtheilskraft in Werke, IV, 260). In George Henry Lewes, Aristotle (1864), 229.
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A general course in mathematics should be required of all officers for its practical value, but no less for its educational value in training the mind to logical forms of thought, in developing the sense of absolute truthfulness, together with a confidence in the accomplishment of definite results by definite means.
In 'Mathematics at West Point and Annapolis', United States Bureau of Education, Bulletin 1912, No. 2, 11.
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A conflict arises when a religious community insists on the absolute truthfulness of all statements recorded in the Bible. This means an intervention on the part of religion into the sphere of science; this is where the struggle of the Church against the doctrines of Galileo and Darwin belongs. On the other hand, representatives of science have often made an attempt to arrive at fundamental judgments with respect to values and ends on the basis of scientific method, and in this way have set themselves in opposition to religion. These conflicts have all sprung from fatal errors.
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A first step in the study of civilization is to dissect it into details, and to classify these in their proper groups. Thus, in examining weapons, they are to be classed under spear, club, sling, bow and arrow, and so forth; among textile arts are to be ranged matting, netting, and several grades of making and weaving threads; myths are divided under such headings as myths of sunrise and sunset, eclipse-myths, earthquake-myths, local myths which account for the names of places by some fanciful tale, eponymic myths which account for the parentage of a tribe by turning its name into the name of an imaginary ancestor; under rites and ceremonies occur such practices as the various kinds of sacrifice to the ghosts of the dead and to other spiritual beings, the turning to the east in worship, the purification of ceremonial or moral uncleanness by means of water or fire. Such are a few miscellaneous examples from a list of hundreds … To the ethnographer, the bow and arrow is the species, the habit of flattening children’s skulls is a species, the practice of reckoning numbers by tens is a species. The geographical distribution of these things, and their transmission from region to region, have to be studied as the naturalist studies the geography of his botanical and zoological species.
In Primitive Culture (1871), Vol. 1, 7.
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A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.
From Preface to the first printing, reprinted in How to Solve It: A New Aspect of Mathematical Method (2004), v.
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A Law of Nature, (Lex Naturalis) is a Precept, or general Rule, found out by Reason, by which a man is forbidden to do, that, which is destructive of his life, or taketh away the means of preserving the same; and to omit, that, by which he thinketh it may be best preserved
Leviathan, ch. 14 (1651).
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A man has a very insecure tenure of a property which another can carry away with his eyes. A few months reduced me to the cruel necessity either of destroying my machine, or of giving it to the public. To destroy it, I could not think of; to give up that for which I had laboured so long, was cruel. I had no patent, nor the means of purchasing one. In preference to destroying, I gave it to the public.
[On his inability to keep for himself a profitable income from his invention of the Spinning Mule.]
As quoted in James Mason, The Great Triumphs of Great Men (1875), 579.
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A State without the means of some change is without the means of its conservation.
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A teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a taste for, and some means of, independent thinking.
In How to Solve It (1948), Preface.
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A time will come when science will transform [our bodies] by means which we cannot conjecture... And then, the earth being small, mankind will migrate into space, and will cross the airless Saharas which separate planet from planet, and sun from sun. The earth will become a Holy Land which will be visited by pilgrims from all quarters of the universe.
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All progress is based upon a universal innate desire of every organism to live beyond its means.
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America has never been united by blood or birth or soil. We are bound by ideals that move us beyond our backgrounds, lift us above our interests and teach us what it means to be citizens. Every child must be taught these principles. Every citizen must uphold them. And every immigrant, by embracing these ideals, makes our country more, not less, American.
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An infinity of these tiny animals defoliate our plants, our trees, our fruits... they attack our houses, our fabrics, our furniture, our clothing, our furs ... He who in studying all the different species of insects that are injurious to us, would seek means of preventing them from harming us, would seek to cause them to perish, proposes for his goal important tasks indeed.
In J. B. Gough, 'Rene-Antoine Ferchault de Réaumur', in Charles Gillispie (ed.), Dictionary of Scientific Biography (1975), Vol. 11, 332.
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An inventor is one who can see the applicability of means to supply demand five years before it is obvious to those skilled in the art.
Aphorism listed Frederick Seitz, The Cosmic Inventor: Reginald Aubrey Fessenden (1866-1932) (1999), 54, being Transactions of the American Philosophical Society, Held at Philadelphia For Promoting Useful Knowledge, Vol. 86, Pt. 6.
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An unelectrified atom is so elusive that unless more than a million million are present we have no means sufficiently sensitive to detect them, or, to put it another way, unless we had a better test for a man than for an unelectrified molecule, we should be unable to find out that the earth was inhabited. … A billion unelectrified atoms may escape our observation, whereas a dozen or so electrified ones are detected without difficulty.
From the Romanes Lecture (10 Jun 1914) delivered in the Sheldonian Theatre, published as The Atomic Theory (1914), 9.
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Analysis and natural philosophy owe their most important discoveries to this fruitful means, which is called induction. Newton was indebted to it for his theorem of the binomial and the principle of universal gravity.
In Frederick Wilson Truscott (trans.) and Frederick Lincoln Emory (trans.), A Philosophical Essay on Probabilities (1902), 176.
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Any conception which is definitely and completely determined by means of a finite number of specifications, say by assigning a finite number of elements, is a mathematical conception. Mathematics has for its function to develop the consequences involved in the definition of a group of mathematical conceptions. Interdependence and mutual logical consistency among the members of the group are postulated, otherwise the group would either have to be treated as several distinct groups, or would lie beyond the sphere of mathematics.
In 'Mathematics', Encyclopedia Britannica (9th ed.).
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Archimedes possessed so high a spirit, so profound a soul, and such treasures of highly scientific knowledge, that though these inventions [used to defend Syracuse against the Romans] had now obtained him the renown of more than human sagacity, he yet would not deign to leave behind him any commentary or writing on such subjects; but, repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit, he placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life; studies, the superiority of which to all others is unquestioned, and in which the only doubt can be whether the beauty and grandeur of the subjects examined, or the precision and cogency of the methods and means of proof, most deserve our admiration.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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Art and Religion are, then, two roads by which men escape from circumstance to ecstasy. Between aesthetic and religious rapture there is a family alliance. Art and Religion are means to similar states of mind.
In Art (1913), 92.
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At the present time there exist problems beyond our ability to solve, not because of theoretical difficulties, but because of insufficient means of mechanical computation.
In 'Proposed Automatic Calculating Machine' (1937). As quoted in I. Bernard Cohen, Gregory W. Welch (eds.), Makin' Numbers: Howard Aiken and the Computer (1999), 13.
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Behavioral avoidance, not physiological adaptations, is an organism’s primary response to an environmental challenge. This point is elementary, but it is by no means trivial.
From 'Interspecific comparison as a tool for ecological physiologists', collected in M.E. Feder, A.F. Bennett, W.W. Burggren, and R.B. Huey, (eds.), New Directions in Ecological Physiology (1987), 18.
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Biology is the only science in which multiplication means the same thing as division.
Anonymous
[Note: which is what cells do.]
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But we shall not satisfy ourselves simply with improving steam and explosive engines or inventing new batteries; we have something much better to work for, a greater task to fulfill. We have to evolve means for obtaining energy from stores which are forev
http://web.archive.org/web/20070109161311/http://www.knowprose.com/node/12961
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Chemistry is one of those branches of human knowledge which has built itself upon methods and instruments by which truth can presumably be determined. It has survived and grown because all its precepts and principles can be re-tested at any time and anywhere. So long as it remained the mysterious alchemy by which a few devotees, by devious and dubious means, presumed to change baser metals into gold, it did not flourish, but when it dealt with the fact that 56 g. of fine iron, when heated with 32 g. of flowers of sulfur, generated extra heat and gave exactly 88 g. of an entirely new substance, then additional steps could be taken by anyone. Scientific research in chemistry, since the birth of the balance and the thermometer, has been a steady growth of test and observation. It has disclosed a finite number of elementary reagents composing an infinite universe, and it is devoted to their inter-reaction for the benefit of mankind.
Address upon receiving the Perkin Medal Award, 'The Big Things in Chemistry', The Journal of Industrial and Engineering Chemistry (Feb 1921), 13, No. 2, 163.
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Chymistry. … An art whereby sensible bodies contained in vessels … are so changed, by means of certain instruments, and principally fire, that their several powers and virtues are thereby discovered, with a view to philosophy or medicine.
An antiquated definition, as quoted in Samuel Johnson, entry for 'Chymistry' in Dictionary of the English Language (1785). Also in The Quarterly Journal of Science, Literature, and the Arts (1821), 284, wherein a letter writer (only identified as “C”) points out that this definition still appeared in the, then, latest Rev. Mr. Todd’s Edition of Johnson’s Dictionary, and that it showed “very little improvement of scientific words.” The letter included examples of better definitions by Black and by Davy. (See their pages on this website.)
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Conservation means the wise use of the earth and its resources for the lasting good of men.
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Doctors in all ages have made fortunes by killing their patients by means of their cures. The difference in psychiatry is that is the death of the soul.
From Address (Jul 1967), 'The Obvious', to the Congress on the Dialectics of Liberation, London, collected in David Cooper, The Dialectics of Liberation (2015), 19.
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Does it mean, if you don’t understand something, and the community of physicists don’t understand it, that means God did it? Is that how you want to play this game? Because if it is, here’s a list of the things in the past that the physicists—at the time—didn’t understand … [but now we do understand.] If that’s how you want to invoke your evidence for God, then God is an ever-receding pocket of scientific ignorance, that’s getting smaller and smaller and smaller, as time moves on. So just be ready for that to happen, if that’s how you want to come at the problem. That’s simply the “God of the Gaps” argument that’s been around for ever.
From interview, The Science Studio video series of The Science Network website, episode 'The Moon, the Tides and why Neil DeGrasse Tyson is Colbert’s God' (20 Jan 2011), time 26:58-27:55.
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Engineering is the art of directing the great sources of power in nature for the use and the convenience of people. In its modern form engineering involves people, money, materials, machines, and energy. It is differentiated from science because it is primarily concerned with how to direct to useful and economical ends the natural phenomena which scientists discover and formulate into acceptable theories. Engineering therefore requires above all the creative imagination to innovate useful applications of natural phenomena. It seeks newer, cheaper, better means of using natural sources of energy and materials.
In McGraw Hill, Science and Technology Encyclopedia
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Engineering is the art or science of utilizing, directing or instructing others in the utilization of the principles, forces, properties and substance of nature in the production, manufacture, construction, operation and use of things ... or of means, methods, machines, devices and structures ...
(1920}
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Engineering is the practice of safe and economic application of the scientific laws governing the forces and materials of nature by means of organization, design and construction, for the general benefit of mankind.
1920
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Every rule has its limits, and every concept its ambiguities. Most of all is this true in the science of life, where nothing quite corresponds to our ideas; similar ends are reached by varied means, and no causes are simple.
In Internal Factors in Evolution (1965), 13.
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Everything that the greatest minds of all times have accomplished toward the comprehension of forms by means of concepts is gathered into one great science, mathematics.
In 'Pestalozzi's Idee eines A B C der Anschauung', Werke[Kehrbach] (1890), Bd.l, 163. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 5.
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Five centuries ago the printing press sparked a radical reshaping of the nature of education. By bringing a master’s words to those who could not hear a master’s voice, the technology of printing dissolved the notion that education must be reserved for those with the means to hire personal tutors. Today we are approaching a new technological revolution, one whose impact on education may be as far-reaching as that of the printing press: the emergence of powerful computers that are sufficiently inexpensive to be used by students for learning, play and exploration. It is our hope that these powerful but simple tools for creating and exploring richly interactive environments will dissolve the barriers to the production of knowledge as the printing press dissolved the barriers to its transmission.
As co-author with A.A. diSessa, from 'Preface', Turtle Geometry: The Computer as a Medium for Exploring Mathematics (1986), xiii.
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For a physicist mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created.
In 'Mathematics in the Physical Sciences', Scientific American (Sep 1964), 211, No. 3, 129.
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For just as musical instruments are brought to perfection of clearness in the sound of their strings by means of bronze plates or horn sounding boards, so the ancients devised methods of increasing the power of the voice in theaters through the application of the science of harmony.
Vitruvius
In Vitruvius Pollio and Morris Hicky Morgan (trans.), 'Book V: Chapter III', Vitruvius, the Ten Books on Architecture (1914), 139. From the original Latin, “Ergo veteres Architecti, naturae vestigia persecuti, indagationibus vocis scandentes theatrorum perfecerunt gradationes: & quaesiuerunt per canonicam mathematicorum,& musicam rationem, ut quaecunq; vox effet in scena, clarior & suauior ad spectatorum perueniret aures. Uti enim organa in aeneis laminis, aut corneis, diesi ad chordarum sonituum claritatem perficiuntur: sic theatrorum, per harmonicen ad augendam vocem, ratiocinationes ab antiquis sunt constitutae.” In De Architectura libri decem (1552), 175.
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For me, a rocket is only a means--only a method of reaching the depths of space—and not an end in itself… There’s no doubt that it’s very important to have rocket ships since they will help mankind to settle elsewhere in the universe. But what I’m working for is this resettling… The whole idea is to move away from the Earth to settlements in space.
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For the mind is so intimately dependent upon the condition and relation of the organs of the body, that if any means can ever be found to render men wiser and more ingenious than hitherto, I believe that it is in medicine they must be sought for. It is true that the science of medicine, as it now exists, contains few things whose utility is very remarkable.
In A Discourse on Method (1637) as translated by John Veitch, Everyman’s Library: Philosophy & Theology: A Discourse on Method, Etc. (1912, 1916), 49-50. A later translation of this quote begins “Even the mind…” on this web page.
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From a pragmatic point of view, the difference between living against a background of foreigness (an indifferent Universe) and one of intimacy (a benevolent Universe) means the difference between a general habit of wariness and one of trust.
…...
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From religion comes a man's purpose; from science, his power to achieve it. Sometimes people ask if religion and science are not opposed to one another. They are: in the sense that the thumb and fingers of my hands are opposed to one another. It is an opposition by means of which anything can be grasped.
In Sir Kerr Grant, The Life and Work of Sir William Bragg (1952), 43.
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He that desireth to acquire any art or science seeketh first those means by which that art or science is obtained.
In An Apology For the True Christian Divinity (1825), 15.
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I agree with your remark about loving your enemy as far as actions are concerned. But for me the cognitive basis is the trust in an unrestricted causality. ‘I cannot hate him, because he must do what he does.’ That means for me more Spinoza than the prophets.
…...
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I am a Christian which means that I believe in the deity of Christ, like Tycho de Brahe, Copernicus, Descartes, Newton, Leibnitz, Pascal ... like all great astronomers mathematicians of the past.
…...
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I can’t recall a single problem in my life, of any sort, that I ever started on that I didn't solve, or prove that I couldn’t solve it. I never let up, until I had done everything that I could think of, no matter how absurd it might seem as a means to the end I was after.
As quoted in French Strother, 'The Modern Profession of Inventing', World's Work and Play (Jul 1905), 6, No. 32, 186.
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I have no doubt that it is possible to give a new direction to technological development, a direction that shall lead it back to the real needs of man, and that also means: to the actual size of man. Man is small, and, therefore, small is beautiful. To go
Small is Beautiful (1973).
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I should be the last to discard the law of organic heredity ... but the single word “heredity” cannot dispense science from the duty of making every possible inquiry into the mechanism of organic growth and of organic formation. To think that heredity will build organic beings without mechanical means is a piece of unscientific mysticism.
In 'On the Principles of Animal Morphology', Proceedings of the Royal Society of Edinburgh (1888), 15, 294-295. Original as Letter to Mr John Murray, communicated to the Society by Professor Sir William Turner. Page given as in collected volume published 1889.
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I should regard them [the Elves interested in technical devices] as no more wicked or foolish (but in much the same peril) as Catholics engaged in certain kinds of physical research (e.g. those producing, if only as by-products, poisonous gases and explosives): things not necessarily evil, but which, things being as they are, and the nature and motives of the economic masters who provide all the means for their work being as they are, are pretty certain to serve evil ends. For which they will not necessarily be to blame, even if aware of them.
From Letter draft to Peter Hastings (manager of a Catholic bookshop in Oxford, who wrote about his enthusiasm for Lord of the Rings) (Sep 1954). In Humphrey Carpenter (ed.) assisted by Christopher Tolkien, The Letters of J.R.R. Tolkien (1995, 2014), 190, Letter No. 153.
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If a lunatic scribbles a jumble of mathematical symbols it does not follow that the writing means anything merely because to the inexpert eye it is indistinguishable from higher mathematics.
In Men of Mathematics (1937), Vol. 2, 232. Also in J.R. Newman (ed.) The World of Mathematics (1956, 1960), Vol. 1, 308.
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If we compare a mathematical problem with an immense rock, whose interior we wish to penetrate, then the work of the Greek mathematicians appears to us like that of a robust stonecutter, who, with indefatigable perseverance, attempts to demolish the rock gradually from the outside by means of hammer and chisel; but the modern mathematician resembles an expert miner, who first constructs a few passages through the rock and then explodes it with a single blast, bringing to light its inner treasures.
In Die Entwickelung der Mathematik in den letzten Jahrhunderten (1869), 9. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 114. From the original German, “Vergleichen wir ein mathematisches Problem mit einem gewaltigen Felsen, in dessen Inneres wir eindringen wollen, so erscheint die Arbeit der griechischen Mathematiker uns als die eines rüstigen Steinhauers, der mit Hammer und Meissel in unermüdlicher Ausdauer den Felsen langsam von aussen her zu zerbröckeln beginnt; der moderne Mathematiker aber als ein trefflicher Minirer, der diesen Felsen zunächst mit wenigen Gängen durchzieht, von denen aus er dann den Felsblock mit einem gewaltigem Schlage zersprengt und die Schätze des Inneren zu Tage fördert.”
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If, unwarned by my example, any man shall undertake and shall succeed in really constructing an engine embodying in itself the whole of the executive department of mathematical analysis upon different principles or by simpler mechanical means, I have no fear of leaving my reputation in his charge, for he alone will be fully able to appreciate the nature of my efforts and the value of their results.
In Passages from the Life of a Philosopher (1864), 450.
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In the beginning (if there was such a thing), God created Newton’s laws of motion together with the necessary masses and forces. This is all; everything beyond this follows from the development of appropriate mathematical methods by means of deduction.
Autobiographical Notes (1946), 19. In Albert Einstein, Alice Calaprice, Freeman Dyson , The Ultimate Quotable Einstein (2011), 397.
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In the case of a Christian clergyman, the tragic-comical is found in this: that the Christian religion demands love from the faithful, even love for the enemy. This demand, because it is indeed superhuman, he is unable to fulfill. Thus intolerance and hatred ring through the oily words of the clergyman. The love, which on the Christian side is the basis for the conciliatory attempt towards Judaism is the same as the love of a child for a cake. That means that it contains the hope that the object of the love will be eaten up.
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In the hands of Science and indomitable energy, results the most gigantic and absorbing may be wrought out by skilful combinations of acknowledged data and the simplest means.
From Introduction to Lecture on the Pendulum-Experiments at Harton Pit (1855), iv. The quote comes from the printed Introduction in the published booklet, but was not part of the printed lecture itself. At the request of a “deputation of gentlemen of South Shields,” the printed version of the lecture was written “in extenso, from memory,” after the original talk was given on 24 Oct 1854 at South Shields, County Durham, England.
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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 a misfortune for a science to be born too late when the means of observation have become too perfect. That is what is happening at this moment with respect to physical chemistry; the founders are hampered in their general grasp by third and fourth decimal places.
Science and Hypothesis (1902), trans. W. J. G. and preface by J. Larmor (1905), 181.
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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 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 means you can try to answer questions you thought the universe was going to have to do without.
On supercomputers, NY Times 3 Jul 84
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It would be an unsound fancy and self-contradictory to expect that things which have never yet been done can be done except by means which have never yet been tried.
From Novum Organum (1620), Book 1, Aphorism 6. Translated as The New Organon: Aphorisms Concerning the Interpretation of Nature and the Kingdom of Man), collected in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1857), Vol. 4, 48.
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It would not be difficult to come to an agreement as to what we understand by science. Science is the century-old endeavor to bring together by means of systematic thought the perceptible phenomena of this world into as thoroughgoing an association as possible. To put it boldly, it is the attempt at the posterior reconstruction of existence by the process of conceptualization. But when asking myself what religion is I cannot think of the answer so easily. And even after finding an answer which may satisfy me at this particular moment, I still remain convinced that I can never under any circumstances bring together, even to a slight extent, the thoughts of all those who have given this question serious consideration.
…...
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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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Its [mathematical analysis] chief attribute is clearness; it has no means for expressing confused ideas. It compares the most diverse phenomena and discovers the secret analogies which unite them. If matter escapes us, as that of air and light because of its extreme tenuity, if bodies are placed far from us in the immensity of space, if man wishes to know the aspect of the heavens at successive periods separated by many centuries, if gravity and heat act in the interior of the solid earth at depths which will forever be inaccessible, mathematical analysis is still able to trace the laws of these phenomena. It renders them present and measurable, and appears to be the faculty of the human mind destined to supplement the brevity of life and the imperfection of the senses, and what is even more remarkable, it follows the same course in the study of all phenomena; it explains them in the same language, as if in witness to the unity and simplicity of the plan of the universe, and to make more manifest the unchangeable order which presides over all natural causes.
From Théorie Analytique de la Chaleur (1822), Discours Préliminaire, xiv, (Theory of Heat, Introduction), as translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7.
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Let us now declare the means whereby our understanding can rise to knowledge without fear of error. There are two such means: intuition and deduction. By intuition I mean not the varying testimony of the senses, nor the deductive judgment of imagination naturally extravagant, but the conception of an attentive mind so distinct and so clear that no doubt remains to it with regard to that which it comprehends; or, what amounts to the same thing, the self-evidencing conception of a sound and attentive mind, a conception which springs from the light of reason alone, and is more certain, because more simple, than deduction itself. …
It may perhaps be asked why to intuition we add this other mode of knowing, by deduction, that is to say, the process which, from something of which we have certain knowledge, draws consequences which necessarily follow therefrom. But we are obliged to admit this second step; for there are a great many things which, without being evident of themselves, nevertheless bear the marks of certainty if only they are deduced from true and incontestable principles by a continuous and uninterrupted movement of thought, with distinct intuition of each thing; just as we know that the last link of a long chain holds to the first, although we can not take in with one glance of the eye the intermediate links, provided that, after having run over them in succession, we can recall them all, each as being joined to its fellows, from the first up to the last. Thus we distinguish intuition from deduction, inasmuch as in the latter case there is conceived a certain progress or succession, while it is not so in the former; … whence it follows that primary propositions, derived immediately from principles, may be said to be known, according to the way we view them, now by intuition, now by deduction; although the principles themselves can be known only by intuition, the remote consequences only by deduction.
In Rules for the Direction of the Mind, Philosophy of Descartes. [Torrey] (1892), 64-65.
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Let us tenderly and kindly cherish, therefore, the means of knowledge. Let us dare to read, think, speak, and write.
Dissertation on the Canon and Feudal Law (as it was later known), originally published untitled and with no author credited in the Boston Gazette (Aug 1765). Collected in John Adams and Charles Francis Adams (ed.), The Works of John Adams (1851), Vol. 3, 462.
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Mathematicians pretend to count by means of a system supposed to satisfy the so-called Peano axioms. In fact, the piano has only 88 keys; hence, anyone counting with these axioms is soon played out.
In Mathematics Made Difficult (1971). As quoted in Michael Stueben and Diane Sandford, Twenty Years Before the Blackboard (1998), 131.
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Mathematics accomplishes really nothing outside of the realm of magnitude; marvellous, however, is the skill with which it masters magnitude wherever it finds it. We recall at once the network of lines which it has spun about heavens and earth; the system of lines to which azimuth and altitude, declination and right ascension, longitude and latitude are referred; those abscissas and ordinates, tangents and normals, circles of curvature and evolutes; those trigonometric and logarithmic functions which have been prepared in advance and await application. A look at this apparatus is sufficient to show that mathematicians are not magicians, but that everything is accomplished by natural means; one is rather impressed by the multitude of skilful machines, numerous witnesses of a manifold and intensely active industry, admirably fitted for the acquisition of true and lasting treasures.
In Werke [Kehrbach] (1890), Bd. 5, 101. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 13.
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Mathematics has beauties of its own—a symmetry and proportion in its results, a lack of superfluity, an exact adaptation of means to ends, which is exceedingly remarkable and to be found only in the works of the greatest beauty. … When this subject is properly and concretely presented, the mental emotion should be that of enjoyment of beauty, not that of repulsion from the ugly and the unpleasant.
In The Teaching of Mathematics in the Elementary and the Secondary School (1906), 44-45.
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Mathematics, as much as music or any other art, is one of the means by which we rise to a complete self-consciousness. The significance of mathematics resides precisely in the fact that it is an art; by informing us of the nature of our own minds it informs us of much that depends on our minds.
In Aspects of Science: Second Series (1926), 94.
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Mathematics, the science of the ideal, becomes the means of investigating, understanding and making known the world of the real. The complex is expressed in terms of the simple. From one point of view mathematics may be defined as the science of successive substitutions of simpler concepts for more complex.
In A Scrap-book of Elementary Mathematics (1908), 215.
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Money. It has such an inherent power to run itself clear of taint that human ingenuity cannot devise the means of making it work permanent mischief, any more than means can be found of torturing people beyond what they can bear. Even if a man founds a College of Technical Instruction, the chances are ten to one that no one will be taught anything and that it will have been practically left to a number of excellent professors who will know very well what to do with it.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 221.
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Nature clasps all her creatures in a universal embrace; there is not one of them which she has not plainly furnished with all means necessary to the conservation of its being.
The Essays of Michel de Montaigne, Book 2, Chapter 12, 'Apology for Raymond Sebond', trans. M. A. Screech (1991), 509.
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Nature hides her secret because of her essential loftiness, but not by means of ruse.
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Nature is disordered, powerful and chaotic, and through fear of the chaos we impose system on it. We abhor complexity, and seek to simplify things whenever we can by whatever means we have at hand. We need to have an overall explanation of what the universe is and how it functions. In order to achieve this overall view we develop explanatory theories which will give structure to natural phenomena: we classify nature into a coherent system which appears to do what we say it does.
In Day the Universe Changed (1985), 11.
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Nature never makes excellent things, for mean or no uses: and it is hardly to be conceived, that our infinitely wise Creator, should make so admirable a Faculty, as the power of Thinking, that Faculty which comes nearest the Excellency of his own incomprehensible Being, to be so idlely and uselesly employ’d, at least 1/4 part of its time here, as to think constantly, without remembering any of those Thoughts, without doing any good to it self or others, or being anyway useful to any other part of Creation.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 2, Chapter 1, Section 15, 113.
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No disease that can be treated by diet should be treated by any other means.
As quoted in Robert Taylor, White Coat Tales: Medicine's Heroes, Heritage, and Misadventures (2010), 124.
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Nothing in the entire universe ever perishes, believe me, but things vary, and adopt a new form. The phrase “being born” is used for beginning to be something different from what one was before, while “dying” means ceasing to be the same. Though this thing may pass into that, and that into this, yet the sums of things remains unchanged.
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Of course we have no means of staying back for any length of Time, any more than a savage or an animal has of staying six feet above the ground. But a civilized man is better off than the savage in this respect. He can go up against gravitation in a balloon, and why should he not hope that ultimately he may be able to stop or accelerate his drift along the Time-Dimension, or even turn about and travel the other way?
In The Time Machine (1898), 13.
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On principle, there is nothing new in the postulate that in the end exact science should aim at nothing more than the description of what can really be observed. The question is only whether from now on we shall have to refrain from tying description to a clear hypothesis about the real nature of the world. There are many who wish to pronounce such abdication even today. But I believe that this means making things a little too easy for oneself.
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Organization is simply the means by which the acts of ordinary men can be made to add up to extraordinary results. To this idea of progress that does not wait on some lucky break, some chance discovery, or some rare stroke of genius, but instead is achieved through systematic, cumulative effort, the engineer has contributed brilliantly.
In A Professional Guide for Young Engineers (1949, 1967), 36.
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Our immediate interests are after all of but small moment. It is what we do for the future, what we add to the sum of man's knowledge, that counts most. As someone has said, 'The individual withers and the world is more and more.' Man dies at 70, 80, or 90, or at some earlier age, but through his power of physical reproduction, and with the means that he has to transmit the results of effort to those who come after him, he may be said to be immortal.
'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 360.
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Our inventions are wont to be pretty toys, which distract our attention from serious things. They are but improved means to an unimproved end.
In Walden (1854, 1906), 57.
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Our mind, by virtue of a certain finite, limited capability, is by no means capable of putting a question to Nature that permits a continuous series of answers. The observations, the individual results of measurements, are the answers of Nature to our discontinuous questioning.
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People in the computer industry use the term ‘user,’ which to them means ‘idiot.’.
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Perfection of means and confusion of ends seems to characterize our age.
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Plants, generally speaking, meet the impact of the terrestrial environment head on, although of course they in turn modify the physical environment by adventitious group activity. The individual plant cannot select its habitat; its location is largely determined by the vagaries of the dispersal of seeds or spores and is thus profoundly affected by chance. Because of their mobility and their capacity for acceptance or rejection terrestrial animals, in contrast, can and do actively seek out and utilize the facets of the environment that allow their physiological capacities to function adequately. This means that an animal by its behavior can fit the environment to its physiology by selecting situations in which its physiological capacities can cope with physical conditions. If one accepts this idea, it follows that there is no such thing as The Environment, for there exist as many different terrestrial environments as there are species of animals.
From 'The role of physiology in the distribution of terrestrial vertebrates', collected in C.L. Hubbs (ed.), Zoogeography: Publ. 51 (1958), 84.
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Pure reasoning as a means of arriving at truth is like the spider who spins a web out of himself. The web is orderly and elaborate, but it is only a trap.
In Reconstruction in Philosophy (1920), 32.
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Quality means doing it right when no one is looking.
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Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics. … The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible. … I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s Algebra published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.
In Presidential Address British Association for the Advancement of Science, Section A (1890), Nature, 42, 466.
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Reflexion is careful and laborious thought, and watchful attention directed to the agreeable effect of one’s plan. Invention, on the other hand, is the solving of intricate problems and the discovery of new principles by means of brilliancy and versatility.
Vitruvius
In De Architectura, Book 1, Chap 2, Sec. 2. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 14.
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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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Science gives us the grounds of premises from which religious truths are to be inferred; but it does not set about inferring them, much less does it reach the inference; that is not its province. It brings before us phenomena, and it leaves us, if we will, to call them works of design, wisdom, or benevolence; and further still, if we will, to proceed to confess an Intelligent Creator. We have to take its facts, and to give them a meaning, and to draw our own conclusions from them. First comes Knowledge, then a view, then reasoning, then belief. This is why Science has so little of a religious tendency; deductions have no power of persuasion. The heart is commonly reached, not through the reason, but through the imagination, by means of direct impressions, by the testimony of facts and events, by history, by description. Persons influence us, voices melt us, looks subdue us, deeds inflame us. Many a man will live and die upon a dogma; no man will be a martyr for a conclusion.
Letter collected in Tamworth Reading Room: Letters on an Address Delivered by Sir Robert Peel, Bart., M.P. on the Establishment of a Reading Room at Tamworth (1841), 32. Excerpted in John Henry Newman, An Essay in Aid of a Grammar of Assent (1870), 89 & 94 footnote.
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Science has gone a long way toward helping man to free himself from the burden of hard labor; yet, science itself is not a liberator. It creates means, not goals. It is up to men to utilize those means to achieve reasonable goals.
In 'I Am an American' (22 Jun 1940), Einstein Archives 29-092. Excerpted in David E. Rowe and Robert J. Schulmann, Einstein on Politics: His Private Thoughts and Public Stands on Nationalism, Zionism, War, Peace, and the Bomb (2007), 470. The British Library Sound Archive holds a recording of this statement by Einstein. It was during a radio broadcast for the Immigration and Naturalization Service, interviewed by a State Department Official. Einstein spoke following an examination on his application for American citizenship in Trenton, New Jersey. The attack on Pearl Harbor and America’s declaration of war on Japan was still over a year in the future.
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Science has thus, most unexpectedly, placed in our hands a new power of great but unknown energy. It does not wake the winds from their caverns; nor give wings to water by the urgency of heat; nor drive to exhaustion the muscular power of animals; nor operate by complicated mechanism; nor summon any other form of gravitating force, but, by the simplest means—the mere contact of metallic surfaces of small extent, with feeble chemical agents, a power everywhere diffused through nature, but generally concealed from our senses, is mysteriously evolved, and by circulation in insulated wires, it is still more mysteriously augmented, a thousand and a thousand fold, until it breaks forth with incredible energy.
Comment upon 'The Notice of the Electro-Magnetic Machine of Mr. Thomas Davenport, of Brandon, near Rutland, Vermont, U.S.', The Annals of Electricity, Magnetism, & Chemistry; and Guardian of Experimental Science (1838), 2, 263.
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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, in the immediate, produces knowledge and, indirectly, means of action. It leads to methodical action if definite goals are set up in advance. For the function of setting up goals and passing statements of value transcends its domain. While it is true that science, to the extent of its grasp of causative connections, may reach important conclusions as to the compatibility and incompatibility of goals and evaluations, the independent and fundamental definitions regarding goals and values remain beyond science’s reach.
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Science, unguided by a higher abstract principle, freely hands over its secrets to a vastly developed and commercially inspired technology, and the latter, even less restrained by a supreme culture saving principle, with the means of science creates all the instruments of power demanded from it by the organization of Might.
In the Shadow of Tomorrow, ch. 9 (1936).
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Scientists and particularly the professional students of evolution are often accused of a bias toward mechanism or materialism, even though believers in vitalism and in finalism are not lacking among them. Such bias as may exist is inherent in the method of science. The most successful scientific investigation has generally involved treating phenomena as if they were purely materialistic, rejecting any metaphysical hypothesis as long as a physical hypothesis seems possible. The method works. The restriction is necessary because science is confined to physical means of investigation and so it would stultify its own efforts to postulate that its subject is not physical and so not susceptible to its methods.
The Meaning of Evolution: A Study of the History of Life and of its Significance for Man (1949), 127.
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Setting an example is not the main means of influencing another, it is the only means.
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Since men are really interested in nothing but their own opinions, every one who puts forward an opinion looks about him right and left for means of strengthening himself and others in it.
In The Maxims and Reflections of Goethe (1906), 193.
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Skeptical scrutiny is the means, in both science and religion, by which deep insights can be winnowed from deep nonsense.
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Stem cells are probably going to be extremely useful. But it isn’t a given, and even if it were, I don’t think the end justifies the means. I am not against stem cells, I think it’s great. Blanket objection is not very reasonable to me—any effort to control scientific advances is doomed to fail. You cannot stop the human mind from working.
From Cornelia Dean, 'A Conversation with Joseph E. Murray', New York Times (25 Sep 2001), F5.
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Technological progress has merely provided us with more efficient means for going backwards.
In Ends and Means: An Inquiry Into the Nature of Ideals and Into Methods (1937), 9.
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Technology means the systematic application of scientific or other organized knowledge to practical tasks.
In 'The Imperatives of Technology', The New Industrial State (1967), Chap. 2, 12.
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That which, to the anatomist, is the end,—is, to the sculptor, the means. The former desires details, for their own sake; the latter, that by means of them, he may kindle his work with life, and stamp it with beauty.
In 'Sculpture', The True and the Beautiful in Nature, Art, Morals, and Religion (1872), 205.
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The advancement of agriculture, commerce and manufactures, by all proper means, will not, I trust, need recommendation. But I cannot forbear intimating to you the expediency of giving effectual encouragement as well to the introduction of new and useful inventions from abroad, as to the exertions of skill and genius in producing them at home.
Early suggestion for awarding patent protection. In First Annual Message to Congress on the State of the Union (8 Jan 1790).
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The American, by nature, is optimistic. He is experimental, an inventor and a builder who builds best when called upon to build greatly. Arouse his will to believe in himself, give him a great goal to believe in, and he will create the means to reach it.
Given with date 1 Jan 1960 in Brian M. Thomsen, The Dream That Will Not Die: Inspiring Words of John, Robert, and Edward Kennedy (2010), 79. Webmaster has not seen a primary document for this quote. Although it is widely circulated, the origin is usually never cited. If you know the primary source, please contact Webmaster.
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The art of research [is] the art of making difficult problems soluble by devising means of getting at them.
Pluto's Republic (1982), 2.
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The business of concrete mathematics is to discover the equations which express the mathematical laws of the phenomenon under consideration; and these equations are the starting-point of the calculus, which must obtain from them certain quantities by means of others.
In Positive Philosophy, Bk. 1, chap. 2.
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The computational formalism of mathematics is a thought process that is externalised to such a degree that for a time it becomes alien and is turned into a technological process. A mathematical concept is formed when this thought process, temporarily removed from its human vessel, is transplanted back into a human mold. To think ... means to calculate with critical awareness.
Mathematics and Physics (1981), Foreward. Reprinted in Mathematics as Metaphor: Selected Essays of Yuri I. Manin (2007), 90.
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The eye, the window of the soul, is the chief means whereby the understanding can most fully and abundantly appreciate the infinite works of Nature; and the ear is second.
As quoted in Daniel J. Boorstin, The Discoverers (1983), 350.
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The first question which you will ask and which I must try to answer is this, “What is the use of climbing Mount Everest ?” and my answer must at once be, “It is no use.” There is not the slightest prospect of any gain whatsoever. Oh, we may learn a little about the behavior of the human body at high altitudes, and possibly medical men may turn our observation to some account for the purposes of aviation. But otherwise nothing will come of it. We shall not bring back a single bit of gold or silver, not a gem, nor any coal or iron. We shall not find a single foot of earth that can be planted with crops to raise food. It’s no use. So, if you cannot understand that there is something in man which responds to the challenge of this mountain and goes out to meet it, that the struggle is the struggle of life itself upward and forever upward, then you won’t see why we go. What we get from this adventure is just sheer joy. And joy is, after all, the end of life. We do not live to eat and make money. We eat and make money to be able to enjoy life. That is what life means and what life is for.
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The great difference between science and technology is a difference of initial attitude. The scientific man follows his method whithersoever it may take him. He seeks acquaintance with his subject­matter, and he does not at all care about what he shall find, what shall be the content of his knowledge when acquaintance-with is transformed into knowledge-about. The technologist moves in another universe; he seeks the attainment of some determinate end, which is his sole and obsessing care; and he therefore takes no heed of anything that he cannot put to use as means toward that end.
Systematic Psychology: Prolegomena (1929), 66.
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The great thing [about Kant’s philosophy] was to form the idea that this one thing—mind or world—may well be capable of other forms of appearance that we cannot grasp and that do not imply the notions of space and time. This means an imposing liberation from our inveterate prejudice.
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The Greeks in the first vigour of their pursuit of mathematical truth, at the time of Plato and soon after, had by no means confined themselves to those propositions which had a visible bearing on the phenomena of nature; but had followed out many beautiful trains of research concerning various kinds of figures, for the sake of their beauty alone; as for instance in their doctrine of Conic Sections, of which curves they had discovered all the principal properties. But it is curious to remark, that these investigations, thus pursued at first as mere matters of curiosity and intellectual gratification, were destined, two thousand years later, to play a very important part in establishing that system of celestial motions which succeeded the Platonic scheme of cycles and epicycles. If the properties of conic sections had not been demonstrated by the Greeks and thus rendered familiar to the mathematicians of succeeding ages, Kepler would probably not have been able to discover those laws respecting the orbits and motions of planets which were the occasion of the greatest revolution that ever happened in the history of science.
In History of Scientific Ideas, Bk. 9, chap. 14, sect. 3.
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The ideal of mathematics should be to erect a calculus to facilitate reasoning in connection with every province of thought, or of external experience, in which the succession of thoughts, or of events can be definitely ascertained and precisely stated. So that all serious thought which is not philosophy, or inductive reasoning, or imaginative literature, shall be mathematics developed by means of a calculus.
In Universal Algebra (1898), Preface.
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The ignorance of science means the enforced ignorance of mankind.
In The Grammar of Science (1892), 25.
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The method of definition is the method of discovering what the thing under consideration is by means of the definition of that thing in so far as it makes it known. This method involves two procedures, one being by composition and the other by resolution.
As quoted in Alistair Cameron Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100-1700 (1971), 63.
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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 native intellectual powers of men in different times, are not so much the causes of the different success of their labours, as the peculiar nature of the means and artificial resources in their possession‎. Independent of vessels of glass, there could have been no accurate manipulations in common chemistry: the air pump was necessary for live investigation of the properties of gaseous matter; and without the Voltaic apparatus, there was no possibility of examining the relations of electrical polarities to chemical attractions.
In Elements of Chemical Philosophy (1812), Vol. 1, Part 1, 28-29.
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The opinion appears to be gaining ground that this very general conception of functionality, born on mathematical ground, is destined to supersede the narrower notion of causation, traditional in connection with the natural sciences. As an abstract formulation of the idea of determination in its most general sense, the notion of functionality includes and transcends the more special notion of causation as a one-sided determination of future phenomena by means of present conditions; it can be used to express the fact of the subsumption under a general law of past, present, and future alike, in a sequence of phenomena. From this point of view the remark of Huxley that Mathematics “knows nothing of causation” could only be taken to express the whole truth, if by the term “causation” is understood “efficient causation.” The latter notion has, however, in recent times been to an increasing extent regarded as just as irrelevant in the natural sciences as it is in Mathematics; the idea of thorough-going determinancy, in accordance with formal law, being thought to be alone significant in either domain.
In Presidential Address British Association for the Advancement of Science (1910), Nature, 84, 290.
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The owner of the means of production is in a position to purchase the labor power of the worker. By using the means of production, the worker produces new goods which become the property of the capitalist. The essential point about this process is the relation between what the worker produces and what he is paid, both measured in terms of real value. In so far as the labor contract is free what the worker receives is determined not by the real value of the goods he produces, but by his minimum needs and by the capitalists’ requirements for labor power in relation to the number of workers competing for jobs. It is important to understand that even in theory the payment of the worker is not determined by the value of his product.
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The Patent-Office Commissioner knows that all machines in use have been invented and re-invented over and over; that the mariner’s compass, the boat, the pendulum, glass, movable types, the kaleidoscope, the railway, the power-loom, etc., have been many times found and lost, from Egypt, China and Pompeii down; and if we have arts which Rome wanted, so also Rome had arts which we have lost; that the invention of yesterday of making wood indestructible by means of vapor of coal-oil or paraffine was suggested by the Egyptian method which has preserved its mummy-cases four thousand years.
In Lecture, second in a series given at Freeman Place Chapel, Boston (Mar 1859), 'Quotation and Originality', Letters and Social Aims (1875, 1917), 178-179.
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The position in which we are now is a very strange one which in general political life never happened. Namely, the thing that I refer to is this: To have security against atomic bombs and against the other biological weapons, we have to prevent war, for if we cannot prevent war every nation will use every means that is at their disposal; and in spite of all promises they make, they will do it.
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The rapid growth of industry, the ever increasing population and the imperative need for more varied, wholesome and nourishing foodstuff makes it all the more necessary to exhaust every means at our command to fill the empty dinner pail, enrich our soils, bring greater wealth and influence to our beautiful South land, which is synonymous to a healthy, happy and contented people.
Letter to Marlin E. Penn (18 Jun 1927), Box 17, George Washington Carver Papers. Cited in Linda O. McMurry, George Washington Carver, Scientist and Symbol (1982), 264-5. Smith's book is about his recollections of G.W. Carver's Sunday School classes at Tuskegee, some 40 years earlier. Webmaster, who has not yet been able to see the original book, cautions this quote may be the gist of Carver's words, rather than an exact quote.
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The stream of thought flows on but most of its segments fall into the bottomless abyss of oblivion. Of some, no memory survives the instant of their passage. Of others, it is confined to a few moments, hours or days. Others, again, leave vestiges which are indestructible, and by means of which they may be recalled as long as life endures.
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The successful launching of the Sputnik was a demonstration of one of the highest scientific and technological achievements of man—a tantalizing invitation both to the militarist in search of ever more devastating means of destruction and to the astronomer searching for new means of carrying his instruments away from their earthbound environment.
In BBC Reith Lecture (9 Nov 1958), 'Astronomy Breaks Free', published as The Individual and the Universe (1959, 1961), 72.
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The term ecology comes from the Greek word oikos, and means ‘the household.’ Ecological responsibility, then, begins at home and expands to fill the entire planet.
The Green Lifestyle Handbook
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The union of philosophical and mathematical productivity, which besides in Plato we find only in Pythagoras, Descartes and Leibnitz, has always yielded the choicest fruits to mathematics; To the first we owe scientific mathematics in general, Plato discovered the analytic method, by means of which mathematics was elevated above the view-point of the elements, Descartes created the analytical geometry, our own illustrious countryman discovered the infinitesimal calculus—and just these are the four greatest steps in the development of mathematics.
In Geschichte der Mathematik im Altertum und im Mittelalter (1874), 149-150. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 210. From the original German, “Die Verbindung philosophischer und mathematischer Productivität, wie wir sie ausser in Platon wohl nur noch in Pythagoras, Descartes, Leibnitz vorfinden, hat der Mathematik immer die schönsten Früchte gebracht: Ersterem verdanken wir die wissenschaftliche Mathematik überhaupt, Platon erfand die analytische Methode, durch welche sich die Mathematik über den Standpunct der Elemente erhob, Descartes schuf die analytische Geometrie, unser berühmter Landsmann den Infinitesimalcalcül—und eben daß sind die vier grössten Stufen in der Entwickelung der Mathematik.”
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There cannot be design without a designer; contrivance without a contriver; order without choice; arrangement, without any thing capable of arranging; subserviency and relation to a purpose; means suitable to an end, and executing their office in accomplishing that end, without the end ever having been contemplated, or the means accommodated to it. Arrangement, disposition of parts, subserviency of means to an end, relation of instruments to use, imply the preference of intelligence and mind.
Natural Theology: or, Evidences of the Existence and Attributes of The Deity, Collected from the Appearances of Nature (1802), 12.
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There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that... or: There is capitalism in so far as... The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills. [p.222]
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There isn’t one, not one, instance where it’s known what pattern of neural connectivity realizes a certain cognitive content, inate or learned, in either the infant’s nervous system or the adult’s. To be sure, our brains must somehow register the contents of our mental states. The trouble is: Nobody knows how—by what neurological means—they do so. Nobody can look at the patterns of connectivity (or of anything else) in a brain and figure out whether it belongs to somebody who knows algebra, or who speaks English, or who believes that Washington was the Father of his country.
In Critical Condition: Polemic Essays on Cognitive science and the Philosophy of the Mind (1988), 269-71. In Vinoth Ramachandra, Subverting Global Myths: Theology and the Public Issues Shaping our World (2008), 180.
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Therefore it is by no means an idle game if we become practiced in analysing long-held commonplace concepts and showing the circumstances on which their justification and usefulness depend, and how they have grown up, individually, out of the givens of experience. Thus their excessive authority will be broken.
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These are some of the things wilderness can do for us. That is the reason we need to put into effect, for its preservation, some other principle that the principles of exploitation or “usefulness” or even recreation. We simply need that wild country available to us, even if we never do more than drive to its edge and look in. For it can be a means of reassuring ourselves of our sanity as creatures, a part of the geography of hope.
Letter (3 Dec 1960) written to David E. Pesonen of the Outdoor Recreation Resources Review Commission. Collected in 'Coda: Wilderness Letter', The Sound of Mountain Water: The Changing American West (1969), 153.
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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 formula [for computing Bernoulli’s numbers] was first given by James Bernoulli…. He gave no general demonstration; but was quite aware of the importance of his theorem, for he boasts that by means of it he calculated intra semi-quadrantem horæ! the sum of the 10th powers of the first thousand integers, and found it to be
91,409,924,241,424,243,424,241,924,242,500.

In 'Bernoulli’s Expression for ΣNr', Algebra, Vol. 2 (1879, 1889), 209. The ellipsis is for the reference (Ars Conjectandi (1713), 97). [The Latin phrase, “intra semi-quadrantem horæ!” refers to within a fraction of an hour. —Webmaster]
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Those intervening ideas, which serve to show the agreement of any two others, are called proofs; and where the agreement or disagreement is by this means plainly and clearly perceived, it is called demonstration; it being shown to the understanding, and the mind made to see that it is so. A quickness in the mind to find out these intermediate ideas, (that shall discover the agreement or disagreement of any other) and to apply them right, is, I suppose, that which is called sagacity.
In An Essay concerning Human Understanding, Bk. 6, chaps. 2, 3.
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To believe in a God means to see that the facts of the world are not the end of the matter.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 41
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To believe that if we could have but this or that we would be happy is to suppress the realization that the cause of our unhappiness is in our inadequate and blemished selves. Excessive desire is thus a means of suppressing our sense of worthlessness.
In The Passionate State of Mind (1955), aph. 6.
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To furnish the means of acquiring knowledge is … the greatest benefit that can be conferred upon mankind. It prolongs life itself and enlarges the sphere of existence.
Report, as chairman of a committee, on the establishment of the Smithsonian Institution (Jan 1836). In Josiah Quincy, Memoir of the life of John Quincy Adams (1858), 265.
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To me, spirituality means “no matter what.” One stays on the path, one commits to love, one does one’s work; one follows one’s dream...no matter what.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 20
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To solve a problem means to reduce it to something simpler than itself.
In 'On Groups', Prelude to Mathematics (1955), 203.
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To some men knowledge of the universe has been an end possessing in itself a value that is absolute: to others it has seemed a means of useful applications.
In The Structure of Physical Chemistry (1951, 2005), 2.
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Today it is no longer questioned that the principles of the analysts are the more far-reaching. Indeed, the synthesists lack two things in order to engage in a general theory of algebraic configurations: these are on the one hand a definition of imaginary elements, on the other an interpretation of general algebraic concepts. Both of these have subsequently been developed in synthetic form, but to do this the essential principle of synthetic geometry had to be set aside. This principle which manifests itself so brilliantly in the theory of linear forms and the forms of the second degree, is the possibility of immediate proof by means of visualized constructions.
In Riemannsche Flächen (1906), Bd. 1, 234.
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Try and penetrate with our limited means the secrets of nature and you will find that, behind all the discernible concatenations, there remains something subtle, intangible and inexplicable. Veneration for this force beyond anything that we can comprehend is my religion. To that extent I am, in point of fact, religious.
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Vision, in my view, is the cause of the greatest benefit to us, inasmuch as none of the accounts now given concerning the Universe would ever have been given if men had not seen the stars or the sun or the heavens. But as it is, the vision of day and night and of months and circling years has created the art of number and has given us not only the notion of Time but also means of research into the nature of the Universe. From these we have procured Philosophy in all its range, than which no greater boon ever has come or will come, by divine bestowal, unto the race of mortals.
Plato
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We are living now, not in the delicious intoxication induced by the early successes of science, but in a rather grisly morning-after, when it has become apparent that what triumphant science has done hitherto is to improve the means for achieving unimproved or actually deteriorated ends.
Ends and Means: an Inquiry into the Nature of Ideals and into Methods Employed for their Realization (1937), 310.
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We are too ready to accept others and ourselves as we are and to assume that we are incapable of change. We forget the idea of growth, or we do not take it seriously. There is no good reason why we should not develop and change until the last day we live. Psychoanalysis is one of the most powerful means of helping us to realize this aim.
In 'Dedication', American Journal of Psychoanalysis (1942), 35, 99-100. As quoted and cited in Milton M. Berger, Women Beyond Freud: New Concepts Of Feminine Psychology (2013).
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We dissect nature along lines laid down by our native languages. The categories and types that we isolate from the world of phenomena we do not find there because they stare every observer in the face; on the contrary, the world is presented in a kaleidoscopic flux of impressions which has to be organized by our minds—and this means largely by the linguistic systems in our minds.
In Four Articles on Metalinguistics (1950), 5.
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We do not belong to this material world that science constructs for us. We are not in it; we are outside. We are only spectators. The reason why we believe that we are in it, that we belong to the picture, is that our bodies are in the picture. Our bodies belong to it. Not only my own body, but those of my friends, also of my dog and cat and horse, and of all the other people and animals. And this is my only means of communicating with them.
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We have no other means of recognising a work of art than our feeling for it.
In Art (1913), 8-9.
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We have now felled forest enough everywhere, in many districts far too much. Let us restore this one element of material life to its normal proportions, and devise means for maintaining the permanence of its relations to the fields, the meadows and the pastures, to the rain and the dews of heaven, to the springs and rivulets with which it waters down the earth.
From Man and Nature (1864), 328-329.
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We see, then, that the disappearance of the conscious personality, the predominance of the unconscious personality, the turning by means of suggestion and contagion of feelings and ideas in an identical direction, the tendency to immediately transform the suggested ideas into acts; these, we see, are the principal characteristics of the individual forming part of a crowd. He is no longer himself, but has become an automaton who has ceased to be guided by his will.
From Psychologie des Foules (1895), 20. English text in The Crowd: A Study of the Popular Mind (1897), Book 1, Chap. 1, 12. Original French text: “Donc, évanouissement de la personnalité consciente, prédominance de la personnalité inconsciente, orientation par voie de suggestion et de contagion des sentiments et des idées dans un même sens, tendance a transformer immédiatement en actes les idée suggérées, tels sont les principaux caractères de l’individu en foule. II n’est plus lui-même, il est devenu un automate que sa volonté ne guide plus.”
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We simply need that wild country available to us, even if we never do more than drive to its edge and look in. For it can be a means of reassuring ourselves of our sanity as creatures, a part of the geography of hope.
Conclusion of Letter (3 Dec 1960) written to David E. Pesonen of the Outdoor Recreation Resources Review Commission. Collected in 'Coda: Wilderness Letter', The Sound of Mountain Water: The Changing American West (1969), 153.
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Whatever answers faith gives.. .such answers always give an infinite meaning to the finite existence of man; a meaning that is not destroyed by suffering, deprivation or death. This means only in faith can we find the meaning and possibility of life.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 19
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When Da Vinci wanted an effect, he willed, he planned the means to make it happen: that was the purpose of his machines. But the machines of Newton … are means not for doing but for observing. He saw an effect, and he looked for its cause.
From The Common Sense of Science (1951), 25.
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When meditating over a disease, I never think of finding a remedy for it, but, instead, a means of preventing it.
From address (15 May 1884), to École Centrale des Arts et Manufactures, Paris. In Maurice Benjamin Strauss, Familiar Medical Quotations (1968), 451.
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When the Romans besieged the town [Sicily] (in 212 to 210 B.C.), he [Archimedes] is said to have burned their ships by concentrating on them, by means of mirrors, the sun’s rays. The story is highly improbable, but is good evidence of the reputation which he had gained among his contemporaries for his knowledge of optics.
In An Introduction to Mathematics (1911), 37.
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Whether science is seen as genie or devil, the attitude is wrong. We need to get some sort of perspective, so that people understand science is just one more intellectual tool, one more way of knowing enough things to give society a means of living on Earth.
From interview with Graham Chedd, 'The Lady Gets Her Way', New Scientist (5 Jul 1973), 59, No. 853, 16.
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While playing the part of the detective the investigator follows clues, but having captured his alleged fact, he turns judge and examines the case by means of logically arranged evidence. Both functions are equally essential but they are different.
In The Art of Scientific Investigation (1950, 1957), 92.
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Words were originally magic, and the word retains much of its old magical power even to-day, With words one man can make another blessed, or drive him to despair;… Words call forth effects and are the universal means of influencing human beings. Therefore let us not underestimate the use of words in psychotherapy.
From a series of 28 lectures for laymen, Part One, 'The Psychology of Errors'. Lecture 1, 'Introduction' collected in Sigmund Freud and G. Stanley Hall (trans.), A General Introduction to Psychoanalysis (1920), 3.
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You who are scientists may have been told that you are, in part, responsible for the debacle of today … but I assure you that it is not the scientists … who are responsible. … Surely it is time for our republics … to use every knowledge, every science that we possess. … You and I … will act together to protect and defend by every means … our science, our culture, our American freedom and our civilization.
Address (10 May 1940) to American Scientific Congress in Washington. This was the day the Nazis invaded the Low Countries. As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 64.
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[1155] Mechanics are the Paradise of mathematical science, because here we come to the fruits of mathematics.
Notebook E (1513), folio 8 back. In the original Italian: “La meccanica è il paradiso delle sciētie matematiche, perchè cō quella si viene al frutto matematico.” English and Italian in Jean Paul Richter (trans.), 'Philosophical Maxims: Of Mechanics', The Literary Works of Leonardo da Vinci (1883), Vol. 1, Part 2, 289, Aphorism 1155. [Note: da Vinci wrote ē=en, ō=on] Also translated as “Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics,” in Edward McCurdy, The Notebooks of Leonardo Da Vinci (1939, 1958), Vol. 1, 613.
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[On the first moon landing:] It means nothing to me. I have no opinion about it, and I don’t care.
In 'Reactions to Man’s Landing on the Moon Show Broad Variations in Opinions', The New York Times (21 Jul 1969), 6.
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[Philosopher Lao-tse] is not dogmatic, and he does not go in for big, universal ideas. For instance, I like what he says about failure and success, “Failure is the foundation of success and the means by which it is achieved. Success is the lurking place of failure; but who can tell when the turning point will come?”
As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 74.
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~~[Dubious]~~ I demonstrate by means of philosophy that the earth is round, and is inhabited on all sides; that it is insignificantly small, and is borne through the stars.
Included here to add a caution. As quoted in Paul Lyle, The Abyss of Time: A Study in Geological Time and Earth History (2015), 38, citing Astronomia Nova (1609). Webmaster has not yet been able to find in a primary source, so cannot vouch for this quote. Can you help?
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…so slow is moral progress. True, we have the bicycle, the motor-car, the dirigible airship and other marvellous means of breaking our bones; but our morality is not one rung the higher for it all. One would even say that, the farther we proceed in our conquest of matter, the more our morality recedes. The most advanced of our inventions consists in bringing men down with grapeshot and explosives with the swiftness of the reaper mowing the corn.
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“Wu Li” was more than poetic. It was the best definition of physics that the conference would produce. It caught that certain something, that living quality that we were seeking to express in a book, that thing without which physics becomes sterile. “Wu” can mean either “matter” or “energy.” “Li” is a richly poetic word. It means “universal order” or “universal law.” It also means “organic patterns.” The grain in a panel of wood is Li. The organic pattern on the surface of a leaf is also Li, and so is the texture of a rose petal. In short, Wu Li, the Chinese word for physics, means “patterns of organic energy” (“matter/ energy” [Wu] + “universal order/organic patterns” [Li]). This is remarkable since it reflects a world view which the founders of western science (Galileo and Newton) simply did not comprehend, but toward which virtually every physical theory of import in the twentieth century is pointing!
In The Dancing Wu Li Masters: An Overview of the New Physics (1979), 5.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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