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Who said: “A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.”
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Bare Quotes (33 quotes)

By the 18th century science had been so successful in laying bare the laws of nature that many thought there was nothing left to discover. Immutable laws prescribed the motion of every particle in the universe, exactly and forever: the task of the scientist was to elucidate the implications of those laws for any particular phenomenon of interest. Chaos gave way to a clockwork world. But the world moved on ...Today even our clocks are not made of clockwork. ... With the advent of quantum mechanics, the clockwork world has become a lottery. Fundamental events, such as the decay of a radioactive atom, are held to be determined by chance, not law.
Does God Play Dice?: The New Mathematics of Chaos (2002). xi.
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Copernicus, the most learned man whom we are able to name other than Atlas and Ptolemy, even though he taught in a most learned manner the demonstrations and causes of motion based on observation, nevertheless fled from the job of constructing tables, so that if anyone computes from his tables, the computation is not even in agreement with his observations on which the foundation of the work rests. Therefore first I have compared the observations of Copernicus with those of Ptolemy and others as to which are the most accurate, but besides the bare observations, I have taken from Copernicus nothing other than traces of demonstrations. As for the tables of mean motion, and of prosthaphaereses and all the rest, I have constructed these anew, following absolutely no other reasoning than that which I have judged to be of maximum harmony.
Dedication to the Duke of Prussia, Prutenicae Tabulae (1551), 1585 edition, as quoted in Owen Gingerich, The Eye of Heaven: Ptolemy, Copernicus, Kepler (1993), 227.
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During this [book preparation] time attacks have not been wanting—we must always be prepared for them. If they grow out of a scientific soil, they cannot but be useful, by laying bare weak points and stimulating to their correction; but if they proceed from that soil, from which the lilies of innocence and the palms of conciliation should spring up, where, however, nothing but the marsh-trefoil of credulity and the poisonous water-hemlock of calumniation grow, they deserve no attention.
Carl Vogt
From Carl Vogt and James Hunt (ed.), Lectures on Man: His Place in Creation, and in the History of the Earth (1861), Author's Preface, 2-3.
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Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.
Poem, 'Euclid Alone Has Looked on Beauty Bare", collected in Wallace Warner Douglas and Hallett Darius Smith (eds.), The Critical Reader: Poems, Stories, Essays (1949), 110.
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Euclid alone
Has looked on Beauty bare.
He turned away at once;
Far too polite to stare.
Parody after Edna St. Vincent Millay. In The Mathematical Intelligencer (Fall 1994), 16, No. 4, 20.
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For the holy Bible and the phenomena of nature proceed alike from the divine Word, the former as the dictate of the Holy Ghost and the latter as the observant executrix of God's commands. It is necessary for the Bible, in order to be accommodated to the understanding of every man, to speak many things which appear to differ from the absolute truth so far as the bare meaning of the words is concerned. But Nature, on the other hand, is inexorable and immutable; she never transgresses the laws imposed upon her, or cares a whit whether her abstruse reasons and methods of operation are understandable to men. For that reason it appears that nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called in question (much less condemned) upon the testimony of biblical passages which may have some different meaning beneath their words.
Letter to Madame Christina of Lorraine, Grand Duchess of Tuscany: Concerning the Use of Biblical Quotations in Matters of Science (1615), trans. Stillman Drake, Discoveries and Opinions of Galileo (1957), 182-3.
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I am the daughter of earth and water, And the nursling of the sky;
I pass through the pores of the ocean and shores;
I change, but I cannot die.
For after the rain when with never a stain,
The pavilion of Heaven is bare,
And the winds and sunbeams with their convex gleams,
Build up the blue dome of air,
I silently laugh at my own cenotaph, And out of the caverns of rain,
Like a child from the womb, like a ghost from the tomb,
I arise and unbuild it again.
The Cloud (1820). In K. Raine (ed.), Shelley (1974), 289.
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If, then, there must be something eternal, let us see what sort of Being it must be. And to that it is very obvious to Reason, that it must necessarily be a cogitative Being. For it is as impossible to conceive that ever bare incogitative Matter should produce a thinking intelligent Being, as that nothing should of itself produce Matter...
In Essay Concerning Human Understanding (1690, 1801), Book 4, Chap. 10, Sec. 10, 114.
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In our search after the Knowledge of Substances, our want of Ideas, that are suitable to such a way of proceeding, obliges us to a quite different method. We advance not here, as in the other (where our abstract Ideas are real as well as nominal Essences) by contemplating our Ideas, and considering their Relations and Correspondencies; that helps us very little, for the Reasons, and in another place we have at large set down. By which, I think it is evident, that Substances afford Matter of very little general Knowledge; and the bare Contemplation of their abstract Ideas, will carry us but a very little way in the search of Truth and Certainty. What then are we to do for the improvement of our Knowledge in Substantial beings? Here we are to take a quite contrary Course, the want of Ideas of their real essences sends us from our own Thoughts, to the Things themselves, as they exist.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 4, Chapter 12, Section 9, 644.
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It is only at the beginning of the age of the dinosaurs that the deep sea, hitherto bare of organisms, was finally invaded by life.
(1965). In Isaac Asimov’s Book of Science and Nature Quotations (1988), 136.
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It so happens that the work which is likely to be our most durable monument, and to convey some knowledge of us to the most remote posterity, is a work of bare utility; not a shrine, not a fortress, not a palace, but a bridge.
Writing upon the opening of the Brooklyn Bridge, New York.
'The Bridge as a Monument', Harper's Weekly (26 May 1883), 27, 326. In David P. Billington, The Tower and the Bridge: The New Art of Structural Engineering (1983), 17.
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Mathematics is not only one of the most valuable inventions—or discoveries—of the human mind, but can have an aesthetic appeal equal to that of anything in art. Perhaps even more so, according to the poetess who proclaimed, “Euclid alone hath looked at beauty bare.”
From 'The Joy of Maths'. Collected in Arthur C. Clarke, Greetings, Carbon-Based Bipeds!: Collected Essays, 1934-1998, 460.
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Most of these Mountains and Inland places whereon these kind of Petrify’d Bodies and Shells are found at present, or have been heretofore, were formerly under the Water, and that either by the descending of the Waters to another part of the Earth by the alteration of the Centre of Gravity of the whole bulk, or rather by the Eruption of some kind of Subterraneous Fires or Earthquakes, great quantities of Earth have been deserted by the Water and laid bare and dry.
Lectures and Discourses of Earthquakes (1668). In The Posthumous Works of Robert Hooke, containing his Cutlerian Lectures and other Discourses read at the Meetings of the Illustrious Royal Society (1705), 320-1.
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Nothing is more humbling than to look with a strong magnifying glass at an insect so tiny that the naked eye sees only the barest speck and to discover that nevertheless it is sculpted and articulated and striped with the same care and imagination as a zebra. Apparently it does not occur to nature whether or not a creature is within our range of vision, and the suspicion arises that even the zebra was not designed for our benefit.
…...
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Now length of Fame (our second life) is lost,
And bare threescore is all ev’n that can boast;
Our sons their fathers’ failing language see.
In An Essay on Criticism (1749), 64. Note: first published anonymously in 1711 when Pope was 22 years old.
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On laying bare the roots of the spinal nerves, I found that I could cut across the posterior fasciculus of nerves, which took its origin from the posterior portion of the spinal marrow without convulsing the muscles of the back; but that on touching the anterior fasciculus with the point of a knife, the muscles of the back were immediately convulsed.
Idea of a New Anatomy of the Brain (1811, 22.
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One-story intellects, two-story intellects, three-story intellects with skylights. All fact-collectors, who have no aim beyond their facts, are one-story men. Two-story men compare, reason, generalize, using the labors of the fact-collectors as well as their own. Three-story men idealize, imagine, predict; their best illumination comes from above, through the skylight. There are minds with large ground-floors, that can store an infinite amount of knowledge; some librarians, for instance, who know enough of books to help other people, without being able to make much other use of their knowledge, have intellects of this class. Your great working lawyer has two spacious stories; his mind is clear, because his mental floors are large, and he has room to arrange his thoughts so that lie can get at them,—facts below, principles above, and all in ordered series; poets are often narrow below, incapable of clear statement, and with small power of consecutive reasoning, but full of light, if sometimes rather bare of furniture, in the attics.
The Poet at the Breakfast Table (1883), 50.
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Our school curricula, by stripping mathematics of its cultural content and leaving a bare skeleton of technicalities, have repelled many a fine mind.
In Number, the Language of Science: A Critical Survey Written for the Cultured Non-mathematician (1930), vii.
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Science is the tool of the Western mind and with it more doors can be opened than with bare hands. It is part and parcel of our knowledge and obscures our insight only when it holds that the understanding given by it is the only kind there is.
Carl Jung
In Jung’s 'Commentary' as translated for the English edition of Richard Wilhelm, The Secret Of The Golden Flower: A Chinese Book of Life (1999, 2013), 82.
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The average English author [of mathematical texts] leaves one under the impression that he has made a bargain with his reader to put before him the truth, the greater part of the truth, and nothing but the truth; and that if he has put the facts of his subject into his book, however difficult it may be to unearth them, he has fulfilled his contract with his reader. This is a very much mistaken view, because effective teaching requires a great deal more than a bare recitation of facts, even if these are duly set forth in logical order—as in English books they often are not. The probable difficulties which will occur to the student, the objections which the intelligent student will naturally and necessarily raise to some statement of fact or theory—these things our authors seldom or never notice, and yet a recognition and anticipation of them by the author would be often of priceless value to the student. Again, a touch of humour (strange as the contention may seem) in mathematical works is not only possible with perfect propriety, but very helpful; and I could give instances of this even from the pure mathematics of Salmon and the physics of Clerk Maxwell.
In Perry, Teaching of Mathematics (1902), 59-61.
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The bird which is drawn to the water by its need of finding there the prey on which it lives, separates the digits of its feet in trying to strike the water and move about on the surface. The skin which unites these digits at their base acquires the habit of being stretched by these continually repeated separations of the digits; thus in course of time there are formed large webs which unite the digits of ducks, geese, etc., as we actually find them. In the same way efforts to swim, that is to push against the water so as to move about in it, have stretched the membranes between the digits of frogs, sea-tortoises, the otter, beaver, etc.
On the other hand, a bird which is accustomed to perch on trees and which springs from individuals all of whom had acquired this habit, necessarily has longer digits on its feet and differently shaped from those of the aquatic animals that I have just named. Its claws in time become lengthened, sharpened and curved into hooks, to clasp the branches on which the animal so often rests.
We find in the same way that the bird of the water-side which does not like swimming and yet is in need of going to the water's edge to secure its prey, is continually liable to sink into the mud. Now this bird tries to act in such a way that its body should not be immersed in the liquid, and hence makes its best efforts to stretch and lengthen its legs. The long-established habit acquired by this bird and all its race of continually stretching and lengthening its legs, results in the individuals of this race becoming raised as though on stilts, and gradually obtaining long, bare legs, denuded of feathers up to the thighs and often higher still.
Philosophie Zoologique (1809), Vol. 1, 249-50, trans. Hugh Elliot (1914), 119-20.
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The day dawned grey and dreary
The sky made of silver
While the first snowflakes
Began to fall.
A lone bird chirped
In a tree bare of its leaves.
Standing on a lonely road
I stood watching as the world
Started changing.
And I embraced the winter
With memories of summer’s warmth
Still in my heart.
And soon the snowflakes
Began to dance about me
And I twirled around and around
As everything
Turned into a winter wonderland.
…...
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The Earth Speaks, clearly, distinctly, and, in many of the realms of Nature, loudly, to William Jennings Bryan, but he fails to hear a single sound. The earth speaks from the remotest periods in its wonderful life history in the Archaeozoic Age, when it reveals only a few tissues of its primitive plants. Fifty million years ago it begins to speak as “the waters bring forth abundantly the moving creatures that hath life.” In successive eons of time the various kinds of animals leave their remains in the rocks which compose the deeper layers of the earth, and when the rocks are laid bare by wind, frost, and storm we find wondrous lines of ascent invariably following the principles of creative evolution, whereby the simpler and more lowly forms always precede the higher and more specialized forms.
The earth speaks not of a succession of distinct creations but of a continuous ascent, in which, as the millions of years roll by, increasing perfection of structure and beauty of form are found; out of the water-breathing fish arises the air-breathing amphibian; out of the land-living amphibian arises the land-living, air-breathing reptile, these two kinds of creeping things resembling each other closely. The earth speaks loudly and clearly of the ascent of the bird from one kind of reptile and of the mammal from another kind of reptile.
This is not perhaps the way Bryan would have made the animals, but this is the way God made them!
The Earth Speaks to Bryan (1925), 5-6. Osborn wrote this book in response to the Scopes Monkey Trial, where William Jennings Bryan spoke against the theory of evolution. They had previously been engaged in the controversy about the theory for several years. The title refers to a Biblical verse from the Book of Job (12:8), “Speak to the earth and it shall teach thee.”
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The instinctive tendency of the scientific man is toward the existential substrate that appears when use and purpose—cosmic significance, artistic value, social utility, personal preference—have been removed. He responds positively to the bare “what” of things; he responds negatively to any further demand for interest or appreciation.
In Systemic Psychology: Prolegomena (1929), 32-33.
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The understanding must not however be allowed to jump and fly from particulars to axioms remote and of almost the highest generality (such as the first principles, as they are called, of arts and things), and taking stand upon them as truths that cannot be shaken, proceed to prove and frame the middle axioms by reference to them; which has been the practice hitherto, the understanding being not only carried that way by a natural impulse, but also by the use of syllogistic demonstration trained and inured to it. But then, and then only, may we hope well of the sciences when in a just scale of ascent, and by successive steps not interrupted or broken, we rise from particulars to lesser axioms; and then to middle axioms, one above the other; and last of all to the most general. For the lowest axioms differ but slightly from bare experience, while the highest and most general (which we now have) are notional and abstract and without solidity. But the middle are the true and solid and living axioms, on which depend the affairs and fortunes of men; and above them again, last of all, those which are indeed the most general; such, I mean, as are not abstract, but of which those intermediate axioms are really limitations.
The understanding must not therefore be supplied with wings, but rather hung with weights, to keep it from leaping and flying. Now this has never yet been done; when it is done, we may entertain better hopes of science.
From Novum Organum (1620), Book 1, Aphorism 104. 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, 97.
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The university imparts information, but it imparts it imaginatively. At least, this is the function which it should perform for society. A university which fails in this respect has no reason for existence. This atmosphere of excitement, arising from imaginative consideration, transforms knowledge. A fact is no longer a bare fact: it is invested with all its possibilities. It is no longer a bur. den on the memory: it is energising as the poet of our dreams, and as the architect of our purposes.
In 'Universities and Their Function', The Aims of Education: & Other Essays (1917), 139.
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This is the element that distinguishes applied science from basic. Surprise is what makes the difference. When you are organized to apply knowledge, set up targets, produce a usable product, you require a high degree of certainty from the outset. All the facts on which you base protocols must be reasonably hard facts with unambiguous meaning. The challenge is to plan the work and organize the workers so that it will come out precisely as predicted. For this, you need centralized authority, elaborately detailed time schedules, and some sort of reward system based on speed and perfection. But most of all you need the intelligible basic facts to begin with, and these must come from basic research. There is no other source. In basic research, everything is just the opposite. What you need at the outset is a high degree of uncertainty; otherwise it isn’t likely to be an important problem. You start with an incomplete roster of facts, characterized by their ambiguity; often the problem consists of discovering the connections between unrelated pieces of information. You must plan experiments on the basis of probability, even bare possibility, rather than certainty.
The Planning of Science, The Lives of a Cell: Notes of a Biology Watcher, (1974) .
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To err is to be as though truth did not exist. To lay bare the error to oneself and others is retrospective discovery.
In The Maxims and Reflections of Goethe (1906), 186.
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To the engineer falls the job of clothing the bare bones of science with life, comfort, and hope.
Reprint of his 1916 statement in 'Engineering as a Profession', Engineer’s Week (1954).
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We must also teach science not as the bare body of fact, but more as human endeavor in its historic context—in the context of the effects of scientific thought on every kind of thought. We must teach it as an intellectual pursuit rather than as a body of tricks.
In Kermit Lansner, Second-Rate Brains: A Factual, Perceptive Report by Top Scientists, Educators, Journalists, and Their Urgent Recommendations (1958), 31. Note: Dr. I.I. Rabi was chairman of President Eisenhower's Science Advisory Committee.
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We of an older generation can get along with what we have, though with growing hardship; but in your full manhood and womanhood you will want what nature once so bountifully supplied and man so thoughtlessly destroyed; and because of that want you will reproach us, not for what we have used, but for what we have wasted...So any nation which in its youth lives only for the day, reaps without sowing, and consumes without husbanding, must expect the penalty of the prodigal whose labor could with difficulty find him the bare means of life.
'Arbor Day: A Message to the School-Children of the United States', 15 Apr 1907. In Presidential Addresses and State Papers (1910), Vol. 11, 1207-8.
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What is peculiar and new to the [19th] century, differentiating it from all its predecessors, is its technology. It was not merely the introduction of some great isolated inventions. It is impossible not to feel that something more than that was involved. … The process of change was slow, unconscious, and unexpected. In the nineteeth century, the process became quick, conscious, and expected. … The whole change has arisen from the new scientific information. Science, conceived not so much in its principles as in its results, is an obvious storehouse of ideas for utilisation. … Also, it is a great mistake to think that the bare scientific idea is the required invention, so that it has only to be picked up and used. An intense period of imaginative design lies between. One element in the new method is just the discovery of how to set about bridging the gap between the scientific ideas, and the ultimate product. It is a process of disciplined attack upon one difficulty after another This discipline of knowledge applies beyond technology to pure science, and beyond science to general scholarship. It represents the change from amateurs to professionals. … But the full self-conscious realisation of the power of professionalism in knowledge in all its departments, and of the way to produce the professionals, and of the importance of knowledge to the advance of technology, and of the methods by which abstract knowledge can be connected with technology, and of the boundless possibilities of technological advance,—the realisation of all these things was first completely attained in the nineteeth century.
In Science and the Modern World (1925, 1997), 96.
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When I arrived in California to join the faculty of the New University which opened in October 1891, it was near the end of the dry season and probably no rain had fallen for three or four months. The bare cracked adobe fields surrounding the new buildings ... offered a decidedly unpromising outlook... A month or two later, however, there was a magical transformation. With the advent of the autumn rains the whole country quickly turned green, and a profusion of liverworts such as I had never seen before appeared on the open ground... I soon realized that right in my own backyard, so to speak, was a wealth of material such as I had never imagined would be my good fortune to encounter. ... Such an invitation to make a comprehensive study of the structure and development of the liverworts could not be resisted; and the next three years were largely devoted to this work which finally resulted in the publication of 'The Mosses and Ferns' in 1895.
In The Structure and Development of Mosses and Ferns (Archegoniatae) (1905, 3rd ed. 1918, rev. 1928). Cited in William C. Steere, Obituary, 'Douglas Houghton Campbell', American Bryological and Lichenological Society, The Bryologist (1953), 131.
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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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