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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Home > Category Index for Science Quotations > Category Index S > Category: Shadow

Shadow Quotes (52 quotes)


Combien de gens se font abstraits pour paraître profonds! La plupart des termes abstraits sont des ombres qui cachent des vides.
How many people become abstract in order to appear profound! Most abstract terms are shadows that conceal a void.
Quoted in M. Paul De Raynal, Pensées de J. Joubert (1862), 456.
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Etiam capillus unus habet umbram suam.
The smallest hair casts a shadow.
In 'Ornamenta Rationalia, or, Elegant Sentences' (1625). As given in Essays, Moral, Economical, and Political: A New Edition, With the Latin Quotations Translated (1813), No. 10, 362.
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A fox looked at his shadow at sunrise and said, “I will have a camel for lunch today.” And all morning he went about looking for camels. But at noon he saw his shadow again - and he said, “A mouse will do.”
In Kahlil Gibran: The Collected Works (207), 18.
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An institution is the lengthened shadow of one man.
From 'Self-Reliance', collected in The Complete Works of Ralph Waldo Emerson (1903), 61.
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Architects who have aimed at acquiring manual skill without scholarship have never been able to reach a position of authority to correspond to their pains, while those who relied only upon theories and scholarship were obviously hunting the shadow, not the substance. But those who have a thorough knowledge of both, like men armed at all points, have the sooner attained their object and carried authority with them.
Vitruvius
In De Architectura, Book 1, Chap 1, Sec. 2. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 3.
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As science has supplanted its predecessors, so it may hereafter be superseded by some more perfect hypothesis, perhaps by some totally different way of looking at the phenomena—of registering the shadows on the screen—of which we in this generation can form no idea. The advance of knowledge is an infinite progression towards a goal that for ever recedes.
In The Golden Bough: A Study in Magic and Religion (1890, 1900), Vol. 3, 460.
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Astrology is a disease, not a science... It is a tree under the shadow of which all sorts of superstitions thrive. ... Only fools and charlatans lend value to it.
Letter to Marseilles, 1195. Responsa, ii. 25b. In Philip Birnbaum (ed.), Mishneh Torah: Maimonides' Code of Law and Ethics (1974), 35.
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But however secure and well-regulated civilized life may become, bacteria, Protozoa, viruses, infected fleas, lice, ticks, mosquitoes, and bedbugs will always lurk in the shadows ready to pounce when neglect, poverty, famine, or war lets down the defenses.
Rats, Lice and History (1934), 13-4.
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But why, it has been asked, did you go there [the Antarctic]? Of what use to civilization can this lifeless continent be? ... [Earlier] expeditions contributed something to the accumulating knowledge of the Antarctic ... that helps us thrust back further the physical and spiritual shadows enfolding our terrestrial existence. Is it not true that one of the strongest and most continuously sustained impulses working in civilization is that which leads to discovery? As long as any part of the world remains obscure, the curiosity of man must draw him there, as the lodestone draws the mariner's needle, until he comprehends its secret.
In 'Hoover Presents Special Medal to Byrd...', New York Times (21 Jun 1930), 1.
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Eratosthenes of Cyrene, employing mathematical theories and geometrical methods, discovered from the course of the sun, the shadows cast by an equinoctial gnomon, and the inclination of the heaven that the circumference of the earth is two hundred and fifty-two thousand stadia, that is, thirty-one million five hundred thousand paces.
Vitruvius
In De Architectura, Book 1, Chap 6, Sec. 9. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 27-28.
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Even now, the imprisoned winds which the earliest poet made the Grecian warrior bear for the protection of his fragile bark; or those which, in more modern times, the Lapland wizards sold to the deluded sailors;—these, the unreal creations of fancy or of fraud, called, at the command of science, from their shadowy existence, obey a holier spell: and the unruly masters of the poet and the seer become the obedient slaves of civilized man.
In 'Future Prospects', On the Economy of Machinery and Manufactures (1st ed., 1832), chap. 32, 280.
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Eventually, we reach … the utmost limits of our telescopes. There, we measure shadows, and we search among ghostly errors of measurement for landmarks that are scarcely more substantial.
In Realm of the Nebulae: The Silliman Memorial Lectures Series (1936), 201-202. The lecture series was delivered at Yale University in Fall 1935. Part of a longer quote on this page that begins: “The explorations of space…”.
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Exper. I. I made a small hole in a window-shutter, and covered it with a piece of thick paper, which I perforated with a fine needle. For greater convenience of observation I placed a small looking-glass without the window-shutter, in such a position as to reflect the sun's light, in a direction nearly horizontal, upon the opposite wall, and to cause the cone of diverging light to pass over a table on which were several little screens of card-paper. I brought into the sunbeam a slip of card, about one-thirtieth of an inch in breadth, and observed its shadow, either on the wall or on other cards held at different distances. Besides the fringes of colour on each side of the shadow, the shadow itself was divided by similar parallel fringes, of smaller dimensions, differing in number, according to the distance at which the shadow was observed, but leaving the middle of the shadow always white. Now these fringes were the joint effects of the portions of light passing on each side of the slip of card and inflected, or rather diffracted, into the shadow. For, a little screen being placed a few inches from the card, so as to receive either edge of the shadow on its margin, all the fringes which had before been observed in the shadow on the wall, immediately disappeared, although the light inflected on the other side was allowed to retain its course, and although this light must have undergone any modification that the proximity of the other edge of the slip of card might have been capable of occasioning... Nor was it for want of a sufficient intensity of light that one of the two portions was incapable of producing the fringes alone; for when they were both uninterrupted, the lines appeared, even if the intensity was reduced to one-tenth or one-twentieth.
'Experiments and Calculations Relative to Physical Optics' (read in 1803), Philosophical Transactions (1804), 94, 2-3.
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For terrestrial vertebrates, the climate in the usual meteorological sense of the term would appear to be a reasonable approximation of the conditions of temperature, humidity, radiation, and air movement in which terrestrial vertebrates live. But, in fact, it would be difficult to find any other lay assumption about ecology and natural history which has less general validity. … Most vertebrates are much smaller than man and his domestic animals, and the universe of these small creatures is one of cracks and crevices, holes in logs, dense underbrush, tunnels, and nests—a world where distances are measured in yards rather than miles and where the difference between sunshine and shadow may be the difference between life and death. Actually, climate in the usual sense of the term is little more than a crude index to the physical conditions in which most terrestrial animals live.
From 'Interaction of physiology and behavior under natural conditions', collected in R.I. Bowman (ed.), The Galapagos (1966), 40.
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From this fountain (the free will of God) it is those laws, which we call the laws of nature, have flowed, in which there appear many traces of the most wise contrivance, but not the least shadow of necessity. These therefore we must not seek from uncertain conjectures, but learn them from observations and experimental. He who is presumptuous enough to think that he can find the true principles of physics and the laws of natural things by the force alone of his own mind, and the internal light of his reason, must either suppose the world exists by necessity, and by the same necessity follows the law proposed; or if the order of Nature was established by the will of God, the [man] himself, a miserable reptile, can tell what was fittest to be done.
…...
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I am always humbled by the infinite ingenuity of the lord, who can make a red barn cast a blue shadow.
In 'A Winter Diary', (Jan 1941), collected in One Man’s Meat (1942, 1982), 170.
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I fear that the character of my knowledge is from year to year becoming more distinct and scientific; that, in exchange for vistas wide as heaven’s scope, I am being narrowed down to the field of the microscope. I see details, not wholes nor the shadow of the whole. I count some parts, and say, “I know.”
(19 Aug 1851). In Henry David Thoreau and Bradford Torrey (ed.), The Writings of Henry Thoreau: Journal: II: 1850-September 15, 1851 (1906), 406.
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I have heard articulate speech produced by sunlight I have heard a ray of the sun laugh and cough and sing! … I have been able to hear a shadow, and I have even perceived by ear the passage of a cloud across the sun's disk.
Letter to his father (26 Feb 1880), describing his photophone research. Transcript with Bell Papers, Library of Congress.
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I saw Eternity the other night,
Like a great Ring of pure and endless light,
All calm, as it was bright;
And round beneath it,
Time, in hours, days, years,
Driv’n by the spheres
Like a vast shadow mov’d; in which the world
And all her train were hurl’d.
In 'The World', in Silex Scintillans (1650), 91.
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I suppose that I tend to be optimistic about the future of physics. And nothing makes me more optimistic than the discovery of broken symmetries. In the seventh book of the Republic, Plato describes prisoners who are chained in a cave and can see only shadows that things outside cast on the cave wall. When released from the cave at first their eyes hurt, and for a while they think that the shadows they saw in the cave are more real than the objects they now see. But eventually their vision clears, and they can understand how beautiful the real world is. We are in such a cave, imprisoned by the limitations on the sorts of experiments we can do. In particular, we can study matter only at relatively low temperatures, where symmetries are likely to be spontaneously broken, so that nature does not appear very simple or unified. We have not been able to get out of this cave, but by looking long and hard at the shadows on the cave wall, we can at least make out the shapes of symmetries, which though broken, are exact principles governing all phenomena, expressions of the beauty of the world outside.
In Nobel Lecture (8 Dec 1989), 'Conceptual Foundations of the Unified Theory of Weak and Electromagnetic Interactions.' Nobel Lectures: Physics 1971-1980 (1992), 556.
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I used to measure the Heavens, now I measure the shadows of Earth. The mind belonged to Heaven, the body's shadow lies here.
Kepler's epitaph for himself.
Johannes Kepler Gesammelte Werke (1937- ), vol. 19, p. 393.
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Wilhelm Röntgen quote: If the hand be held between the discharge-tube and the screen, the darker shadow of the bones is seen wit
If the hand be held between the discharge-tube and the screen, the darker shadow of the bones is seen within the slightly dark shadow-image of the hand itself… For brevity’s sake I shall use the expression “rays”; and to distinguish them from others of this name I shall call them “X-rays”.
From 'On a New Kind of Rays' (1895). In Herbert S. Klickstein, Wilhelm Conrad Rontgen: On a New Kind of Rays, A Bibliographic Study (1966), 4.
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Imperceptibly a change had been wrought in me until I no longer felt alone in a strange, silent country. I had learned to hear the echoes of a time when every living thing upon this land and even the varied overshadowing skies had its voice, a voice that was attentively heard and devoutly heeded by the ancient people of America. Henceforth, to me the plants, the trees, the clouds and all things had become vocal with human hopes, fears and supplications.
From Preface, Indian Games and Dances with Native Songs (1915), v.
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In the world of physics we watch a shadowgraph performance of the drama of familiar life. The shadow of my elbow rests on the shadow table as the shadow ink flows over the shadow paper. It is all symbolic, and as a symbol the physicist leaves it. ... The frank realization that physical science is concerned with a world of shadows is one of the most significant of recent advances.
In The Nature of the Physical World (1928, 2005), xiv-xv.
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Keep your face to the sunshine and you cannot see the shadow.
…...
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M. Waldman … concluded with a panegyric upon modern chemistry…:— “The ancient teachers of this science” said he, “Promised impossibilities and performed nothing. The modern masters promise very little; they know that metals cannot be transmuted and that the elixir of life is a chimera. But these philosophers seem only made to dabble in dirt, and their eyes to pore over the microscope or crucible, have indeed performed miracles. They penetrate into the recesses of nature and show how she works in her hiding-places. They ascend into the heavens; they have discovered how the blood circulates, and the nature of the air we breathe. They can command the thunders of heaven, mimic the earthquake, and even mock the invisible world with its own shadows.”
In Frankenstein: Or, The Modern Prometheus (1823), Vol. 1, 73-74. Webmaster note: In the novel, when the fictional characters meet, M. Waldman, professor of chemistry, sparks Victor Frankenstein’s interest in science. Shelley was age 20 when the first edition of the novel was published anonymously (1818).
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Metaphysical ghosts cannot be killed, because they cannot be touched; but they may be dispelled by dispelling the twilight in which shadows and solidities are easily confounded. The Vital Principle is an entity of this ghostly kind; and although the daylight has dissipated it, and positive Biology is no longer vexed with its visitations, it nevertheless reappears in another shape in the shadowy region of mystery which surrounds biological and all other questions.
The History of Philosophy from Thales to Comte (1867), lxxxiv.
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Nature will be reported. Everything in nature is engaged in writing its own history; the planet and the pebble are attended by their shadows, the rolling rock leaves its furrows on the mountain-side, the river its channel in the soil; the animal, its bones in the stratum; the fern and leaf, their modest epitaph in the coal.
In The Prose Works of Ralph Waldo Emerson (1847, 1872), Vol. 2, 141.
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Nearly every subject has a shadow, or imitation. It would, I suppose, be quite possible to teach a deaf and dumb child to play the piano. When it played a wrong note, it would see the frown of its teacher, and try again. But it would obviously have no idea of what it was doing, or why anyone should devote hours to such an extraordinary exercise. It would have learnt an imitation of music. and it would fear the piano exactly as most students fear what is supposed to be mathematics.
In Mathematician's Delight (1943), 8.
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Never in its life has the sun seen shade,
Never in its life seen a shadow where it falls:
There, always there, in the sun-swept glade,
It lurks below the leaf; behind bodies, under walls,
Creeps, clings, hides. Be it millions, be it one—
The sun sees no shadow, and no shadow sees the sun.
Poem, as quoted in Arthur E. Shipley, Life: A Book for Elementary Students (1925, 2013), 31.
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Painting the desert, sun-setting the tone
Starving backstage, morning-stars are jaded
The moonshine murmur still shivers alone
Curved slice of sliver, shear breath shadows stone
Suspending twilight shiny and shaded
Painting the desert, sun-setting the tone
Carving solace into silver in June
On horizons’ glow from forgotten gold
The moonshine’s’ shilling delivers alone
Gleaming duels of knights, pierce deathly silence
Steel tines of starlight, clashing swords they hold
Painting the desert, sun-setting the tone
Dimples aware, sparkle sand on the dune
Winking at comets, after tails are told
The moon-sand whispers, sift rivers alone
Sharpness they hone, filing skills onto stone
Starlight dazzles, its own space created
Painting the desert, sun-setting the tone
From owls’ talon, moonlight shimmers alone
Earth Man
…...
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Poets need be in no degree jealous of the geologists. The stony science, with buried creations for its domains, and half an eternity charged with its annals, possesses its realms of dim and shadowy fields, in which troops of fancies already walk like disembodied ghosts in the old fields of Elysium, and which bid fair to be quite dark and uncertain enough for all the purposes of poesy for centuries to come.
Lecture Third, collected in Popular Geology: A Series of Lectures Read Before the Philosophical Institution of Edinburgh, with Descriptive Sketches from a Geologist's Portfolio (1859), 127.
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Science is a body of truths which offers clear and certain knowledge about the real world and is therefore superior to tradition philosophy religion dogma and superstition which offer shadowy knowledge about an ideal world.
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Sometime in my early teens, I started feeling an inner urgency, ups and downs of excitement and frustration, caused by such unlikely occupations as reading Granville’s course of calculus ... I found this book in the attic of a friend’s apartment. Among other standard stuff, it contained the notorious epsilon-delta definition of continuous functions. After struggling with this definition for some time (it was the hot Crimean summer, and I was sitting in the shadow of a dusty apple tree), I got so angry that I dug a shallow grave for the book between the roots, buried it there, and left in disdain. Rain started in an hour. I ran back to the tree and exhumed the poor thing. Thus, I discovered that I loved it, regardless.
'Mathematics as Profession and vocation', in V. Arnold et al. (eds.), Mathematics: Frontiers and Perspectives (2000), 153. Reprinted in Mathematics as Metaphor: Selected Essays of Yuri I. Manin (2007), 79.
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The explorations of space end on a note of uncertainty. And necessarily so. … We know our immediate neighborhood rather intimately. With increasing distance our knowledge fades, and fades rapidly. Eventually, we reach the dim boundary—the utmost limits of our telescopes. There, we measure shadows, and we search among ghostly errors of measurement for landmarks that are scarcely more substantial. The search will continue. Not until the empirical resources are exhausted, need we pass on to the dreamy realms of speculation.
From conclusion of The Silliman Memorial Lectures Series delivered at Yale University (Fall 1935). Collected in The Realm of the Nebulae: The Silliman Memorial Lectures Series (1936), 201-202.
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The external world of physics has … become a world of shadows. In removing our illusions we have removed the substance, for indeed we have seen that substance is one of the greatest of our illusions. Later perhaps we may inquire whether in our zeal to cut out all that is unreal we may not have used the knife too ruthlessly. Perhaps, indeed, reality is a child which cannot survive without its nurse illusion. But if so, that is of little concern to the scientist, who has good and sufficient reasons for pursuing his investigations in the world of shadows and is content to leave to the philosopher the determination of its exact status in regard to reality.
In Introduction to The Nature of the Physical World (1928), xiv.
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The Mathematics, I say, which effectually exercises, not vainly deludes or vexatiously torments studious Minds with obscure Subtilties, perplexed Difficulties, or contentious Disquisitions; which overcomes without Opposition, triumphs without Pomp, compels without Force, and rules absolutely without Loss of Liberty; which does not privately over-reach a weak Faith, but openly assaults an armed Reason, obtains a total Victory, and puts on inevitable Chains; whose Words are so many Oracles, and Works as many Miracles; which blabs out nothing rashly, nor designs anything from the Purpose, but plainly demonstrates and readily performs all Things within its Verge; which obtrudes no false Shadow of Science, but the very Science itself, the Mind firmly adhering to it, as soon as possessed of it, and can never after desert it of its own Accord, or be deprived of it by any Force of others: Lastly the Mathematics, which depends upon Principles clear to the Mind, and agreeable to Experience; which draws certain Conclusions, instructs by profitable Rules, unfolds pleasant Questions; and produces wonderful Effects; which is the fruitful Parent of, I had almost said all, Arts, the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human Affairs.
Address to the University of Cambridge upon being elected Lucasian Professor of Mathematics (14 Mar 1664). In Mathematical Lectures (1734), xxviii.
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The One remains, the many change and pass;
Heaven's light forever shines, Earth's shadows fly;
Life, like a dome of many-coloured glass,
Stains the white radiance of Eternity,
Until Death tramples it to fragments.
Adonais (1821), St. 52. In K. Raine (ed.), Shelley (1974), 209.
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The view of the moon that we’ve been having recently is really spectacular. It fills about three-quarters of the hatch window, and of course we can see the entire circumference even though part of it is in complete shadow and part of it is in earthshine. It’s a view worth the price of the trip.
…...
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There rolls the deep where grew the tree.
O earth, what changes hast thou seen!
There where the long street roars, hath been
The stillness of the central sea.
The hills are shadows, and they flow
From form to form, and nothing stands;
They melt like mist, the solid lands,
Like clouds they shape themselves and go.
In Memoriam A. H. H. (1850), canto 123. Collected in Alfred Tennyson and William James Rolfe (ed.) The Poetic and Dramatic works of Alfred, Lord Tennyson (1898), 194.
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Tonight, the moon came out, it was nearly full.
Way down here on earth, I could feel it’s pull.
The weight of gravity or just the lure of life,
Made me want to leave my only home tonight.
I’m just wondering how we know where we belong
Is it in the arc of the moon, leaving shadows on the lawn
In the path of fireflies and a single bird at dawn
Singing in between here and gone
…...
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Tragically isolated, imprisoned in his own “self,” man has made a desperate effort to “leap beyond his shadow,” to embrace the external world. From this effort was born science….
In Einstein and the Universe; A Popular Exposition of the Famous Theory (1922), 239.
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True rigor is productive, being distinguished in this from another rigor which is purely formal and tiresome, casting a shadow over the problems it touches.
From address to the section of Algebra and Analysis, International Congress of Arts and Sciences, St. Louis (22 Sep 1904), 'On the Development of Mathematical Analysis and its Relation to Certain Other Sciences,' as translated by M.W. Haskell in Bulletin of the American Mathematical Society (May 1905), 11, 417.
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Very great charm of shadow and light is to be found in the faces of those who sit in the doors of dark houses. The eye of the spectator sees that part of the face which is in shadow lost in the darkness of the house, and that part of the face which is lit draws its brilliancy from the splendor of the sky. From this intensification of light and shade the face gains greatly in relief and beauty by showing the subtlest shadows in the light part and the subtlest lights in the dark part.
…...
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We are told that “Mathematics is that study which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation.” I think no statement could have been made more opposite to the facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas, and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activities of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world (to which the inner one in each individual man may, I think, be conceived to stand somewhat in the same relation of correspondence as a shadow to the object from which it is projected, or as the hollow palm of one hand to the closed fist which it grasps of the other), that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of the imagination and invention.
In Presidential Address to British Association, Exeter British Association Report (1869), pp. 1-9, in Collected Mathematical Papers, Vol. 2, 654.
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We entered into shadow. Contact with Moscow was gone. Japan floated by beneath us and I could clearly see its cities ablaze with lights. We left Japan behind to face the dark emptiness of the Pacific Ocean. No moon. Only stars, bright and far away. I gripped the handle like a man hanging onto a streetcar. Very slowly, agonizingly, half an hour passed, and with that, dawn on Earth. First, a slim greenish-blue line on the farthest horizon turning within a couple of minutes into a rainbow that hugged the Earth and in turn exploded into a golden sun. You’re out of your mind, I told myself, hanging onto a ship in space, and to your life, and getting ready to admire a sunrise.
…...
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What beauty. I saw clouds and their light shadows on the distant dear earth…. The water looked like darkish, slightly gleaming spots…. When I watched the horizon, I saw the abrupt, contrasting transition from the earth’s light-colored surface to the absolutely black sky. I enjoyed the rich color spectrum of the earth. It is surrounded by a light blue aureole that gradually darkens, becomes turquoise, dark blue, violet, and finally coal black.
Describing his view while making the first manned orbit of the earth (12 Apr 1961). As quoted in Don Knefel, Writing and Life: A Rhetoric for Nonfiction with Readings (1986), 93. Front Cover
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What is life? It is the flash of a firefly in the night. It is the breath of a buffalo in the wintertime. It is the little shadow which runs across the grass and loses itself in the sunset.
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When the sun is covered by clouds, objects are less conspicuous, because there is little difference between the light and shade of the trees and the buildings being illuminated by the brightness of the atmosphere which surrounds the objects in such a way that the shadows are few, and these few fade away so that their outline is lost in haze.
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You see but your shadow when you turn your back to the sun.
In Kahlil Gibran: The Collected Works (207), 188.
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You see layers as you look down. You see clouds towering up. You see their shadows on the sunlit plains, and you see a ship’s wake in the Indian Ocean and brush fires in Africa and a lightning storm walking its way across Australia. You see the reds and the pinks of the Australian desert, and it’s just like a stereoscopic view of all nature, except you’re a hundred ninety miles up.
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“I see no shadows,” saith the sun:
Yet he casts them every one.
Quoted without citation in George Iles, Canadian Stories (1918), 150. Webmaster has found no other source for this couplet, and wonders if it was coined by the author himself to ornament a chapter heading, or not. Please contact Webmaster if you know the primary source.
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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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