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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Home > Category Index for Science Quotations > Category Index S > Category: Spring

Spring Quotes (70 quotes)

... we might say that the earth has a spirit of growth; that its flesh is the soil, its bones the arrangement and connection of the rocks of which the mountains are composed, its cartilage the tufa, and its blood the springs of water.
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A little Learning is a dang’rous Thing;
Drink deep, or taste not the Pierian Spring:
There shallow Draughts intoxicate the Brain,
And drinking largely sobers us again.
In An Essay on Criticism (Written 1709, published 1711), 14. (Written in 1709). Misquoted in The Monthly Miscellany; or Gentleman and Lady’s Complete Magazine (1774), as “Mr. Pope says, very truly, ‘A little knowledge is a dangerous thing.’” This latter version of the quote has, in modern times, been misattributed to Albert Einstein.
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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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Abstruse mathematical researches … are … often abused for having no obvious physical application. The fact is that the most useful parts of science have been investigated for the sake of truth, and not for their usefulness. A new branch of mathematics, which has sprung up in the last twenty years, was denounced by the Astronomer Royal before the University of Cambridge as doomed to be forgotten, on account of its uselessness. Now it turns out that the reason why we cannot go further in our investigations of molecular action is that we do not know enough of this branch of mathematics.
In 'Conditions of Mental Development', Lectures and Essays (1901), Vol. 1, 115.
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Copious springs are found where there are mines of gold, silver, iron, copper, lead, and the like, but they are very harmful.
Vitruvius
In De Architectura, Book 7, Chap 3, Sec. 5. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 234.
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Could Hamlet have been written by a committee, or the “Mona Lisa” painted by a club? Could the New Testament have been composed as a conference report? Creative ideas do not spring from groups. They spring from individuals. The divine spark leaps from the finger of God to the finger of Adam, whether it takes ultimate shape in a law of physics or a law of the land, a poem or a policy, a sonata or a mechanical computer.
Baccalaureate address (9 Jun 1957), Yale University. In In the University Tradition (1957), 156.
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Early Greek astronomers, derived their first knowledge from the Egyptians, and these from the Chaldeans, among whom the science was studied, at a very early period. Their knowledge of astronomy, which gave their learned men the name of Magi, wise men, afterwards degenerated into astrology, or the art of consulting the position of the stars to foretel events—and hence sprung the silly occupation of sooth saying, for which the Chaldeans were noted to a proverb, in later ages.
In Elements of Useful Knowledge (1806), Vol. 1, 8-9. Note “foretel” is as printed in this text.
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Even bees, the little alms-men of spring bowers,
Know there is richest juice in poison-flowers.
From poem, 'Isabella', collected in The Poetical Works of John Keats (1885), 186.
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Every great scientist becomes a great scientist because of the inner self-abnegation with which he stands before truth, saying: “Not my will, but thine, be done.” What, then, does a man mean by saying, Science displaces religion, when in this deep sense science itself springs from religion?
In 'The Real Point of Conflict between Science and Religion', collected in Living Under Tension: Sermons On Christianity Today (1941), 148.
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For the time of making Observations none can ever be amiss; there being no season, nor indeed hardly any place where in some Natural Thing or other does not present it self worthy of Remark: yea there are some things that require Observation all the Year round, as Springs, Rivers, &c. Nor is there any Season amiss for the gathering Natural Things. Bodies of one kind or other presenting themselves at all times, and in Winter as well as Summer.
In Brief Instructions for Making Observations in all Parts of the World (1696), 10-11.
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From Avarice thus, from Luxury and War
Sprang heavenly Science;
and from Science Freedom.
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Geology ... offers always some material for observation. ... [When] spring and summer come round, how easily may the hammer be buckled round the waist, and the student emerge from the dust of town into the joyous air of the country, for a few delightful hours among the rocks.
In The Story of a Boulder: or, Gleanings from the Note-book of a Field Geologist (1858), viii.
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Happy is he who bears a god within himself, an ideal of beauty, and obeys him: an ideal of art, an ideal of the virtues of the Gospel. These are the living springs of great thoughts and great actions. All are illuminated by reflections of the sublime.
Speech (27 Apr 1882) on his reception into the Académie Française, as translated in Maurice Benjamin Strauss, Familiar Medical Quotations (1968), 490.
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High technology has done us one great service: It has retaught us the delight of performing simple and primordial tasks—chopping wood, building a fire, drawing water from a spring.
In 'Science and Technology', A Voice Crying in the Wilderness (Vox Clamantis in Deserto) (1989), 91.
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I can see him [Sylvester] now, with his white beard and few locks of gray hair, his forehead wrinkled o’er with thoughts, writing rapidly his figures and formulae on the board, sometimes explaining as he wrote, while we, his listeners, caught the reflected sounds from the board. But stop, something is not right, he pauses, his hand goes to his forehead to help his thought, he goes over the work again, emphasizes the leading points, and finally discovers his difficulty. Perhaps it is some error in his figures, perhaps an oversight in the reasoning. Sometimes, however, the difficulty is not elucidated, and then there is not much to the rest of the lecture. But at the next lecture we would hear of some new discovery that was the outcome of that difficulty, and of some article for the Journal, which he had begun. If a text-book had been taken up at the beginning, with the intention of following it, that text-book was most likely doomed to oblivion for the rest of the term, or until the class had been made listeners to every new thought and principle that had sprung from the laboratory of his mind, in consequence of that first difficulty. Other difficulties would soon appear, so that no text-book could last more than half of the term. In this way his class listened to almost all of the work that subsequently appeared in the Journal. It seemed to be the quality of his mind that he must adhere to one subject. He would think about it, talk about it to his class, and finally write about it for the Journal. The merest accident might start him, but once started, every moment, every thought was given to it, and, as much as possible, he read what others had done in the same direction; but this last seemed to be his real point; he could not read without finding difficulties in the way of understanding the author. Thus, often his own work reproduced what had been done by others, and he did not find it out until too late.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 266-267.
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I hate science. It denies a man’s responsibility for his own deeds, abolishes the brotherhood that springs from God’s fatherhood. It is a hectoring, dictating expertise, which makes the least lovable of the Church Fathers seem liberal by contrast. It is far easier for a Hitler or a Stalin to find a mock-scientific excuse for persecution than it was for Dominic to find a mock-Christian one.
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If in our withered leaves you see
Hint of your own mortality:—
Think how, when they have turned to earth,
New loveliness from their rich worth
Shall spring to greet the light; then see
Death as the keeper of eternity,
And dying Life’s perpetual re-birth !
Anonymous
Poem attributed with initials W.L., epigraph for chapter on 'The Nitrogen Cycle', in Arthur E. Shipley, Life: A Book for Elementary Students (1925, 2013), 37.
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In scientific investigations it is grievously wrong to pander to the public’s impatience for results, or to let them think that for discovery it is necessary only to set up a great manufactory and a system of mass production. If in treatment team work is effective, in research it is the individual who counts first and above all. No great thought has ever sprung from anything but a single mind, suddenly conceiving. Throughout the whole world there has been too violent a forcing of the growth of ideas; too feverish a rush to perform experiments and publish conclusions. A year of vacation for calm detachment with all the individual workers thinking it all over in a desert should be proclaimed.
In Viewless Winds: Being the Recollections and Digressions of an Australian Surgeon (1939), 286.
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INVENTOR, n. A person who makes an ingenious arrangement of wheels, levers and springs, and believes it civilization.
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary,  173-174.
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It has often been said that power corrupts. But it is perhaps equally important to realize that weakness, too, corrupts. Power corrupts the few, while weakness corrupts the many. Hatred, malice, rudeness, intolerance, and suspicion are the faults of weakness. The resentment of the weak does not spring from any injustice done to them but from the sense of inadequacy and impotence. We cannot win the weak by sharing our wealth with them. They feel our generosity as oppression. St. Vincent De Paul cautioned his disciples to deport themselves so that the poor “will forgive them the bread you give them.”
In 'The Awakening of Asia', The Ordeal of Change (1963), 12.
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It is a happy world after all. The air, the earth, the water teem with delighted existence. In a spring noon, or a summer evening, on whichever side I turn my eyes, myriads of happy beings crowd upon my view. “The insect youth are on the wing.” Swarms of new-born flies are trying their pinions in the air. Their sportive motions, their wanton mazes, their gratuitous activity testify their joy and the exultation they feel in their lately discovered faculties … The whole winged insect tribe, it is probable, are equally intent upon their proper employments, and under every variety of constitution, gratified, and perhaps equally gratified, by the offices which the author of their nature has assigned to them.
Natural Theology: or, Evidences of the Existence and Attributes of The Deity, Collected from the Appearances of Nature (1802), 490-1.
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It is a lovely and terrible wilderness, such as wilderness as Christ and the prophets went out into; harshly and beautifully colored, broken and worn until its bones are exposed, its great sky without a smudge of taint from Technocracy, and in hidden corners and pockets under its cliffs the sudden poetry of springs.
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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Keep your faith in all beautiful things; in the Sun when it is hidden, in the Spring when it is gone.
…...
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Law springs from experiment, but not immediately. Experiment is individual, the law deduced from it is general; experiment is only approximate, the law is precise, or at least pretends to be. Experiment is made under conditions always complex, the enunciation of the law eliminates these complications. This is what is called ‘correcting the systematic errors’.
From La Valeur de la Science (1904), 142, as translated by George Bruce Halsted (trans.), in The Value of Science (1907), 77. From the French, “La loi sort de l’expérience, mais elle n’en sort pas immédiatement. L’expérience est individuelle, la loi qu’on en tire est générale, l’expérience n’est qu’approchée, la loi est précise ou du moins prétend l’élre. L’expérience se fait dans des conditions toujours complexes, l’énoncé de la loi élimine ces complications. C’est ce qu’on appelle ‘corriger les erreurs systématiques’.”
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Let Nature do your bottling and your pickling and preserving. For all Nature is doing her best each moment to make us well. She exists for no other end. Do not resist her. With the least inclination to be well, we should not be sick. Men have discovered—or think they have discovered—the salutariness of a few wild things only, and not of all nature. Why, “nature” is but another name for health, and the seasons are but different states of health. Some men think that they are not well in spring, or summer, or autumn, or winter; it is only because they are not well in them.
(23 Aug 1853). In Henry David Thoreau and Bradford Torrey (ed.), The Writings of Henry Thoreau: Journal: V: March 5-November 30, 1853 (1906), 395.
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Let us award a just, a brilliant homage to those rare men whom nature has endowed with the precious privilege of arranging a thousand isolated facts, of making seductive theories spring from them; but let us not forget to state, that the scythe of the reaper had cut the stalks before one had thought of uniting them into sheaves!
In François Arago, trans. by William Henry Smyth, Baden Powell and Robert Grant, 'Fourier', Biographies of Distinguished Scientific Men (1859), Vol. 1, 409.
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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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Life has found ways to flourish in boiling hot springs and on icy mountain tops, to fly, glow in the dark, put forth leaves in a rainless desert, or plumb the ocean, reproducing and adapting, reincarnating itself in new forms in defiance of time and death.
…...
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Looking back across the long cycles of change through which the land has been shaped into its present form, let us realise that these geographical revolutions are not events wholly of the dim past, but that they are still in progress. So slow and measured has been their march, that even from the earliest times of human history they seem hardly to have advanced at all. But none the less are they surely and steadily transpiring around us. In the fall of rain and the flow of rivers, in the bubble of springs and the silence of frost, in the quiet creep of glaciers and the tumultuous rush of ocean waves, in the tremor of the earthquake and the outburst of the volcano, we may recognise the same play of terrestrial forces by which the framework of the continents has been step by step evolved.
Lecture at the Evening Meeting, Royal Geographical Society (24 Mar 1879), 'Discussion on Geographical Evolution', in Proceedings of the Royal Geographical Society and Monthly Record (1879), New Monthly Series, 1, 443.
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Many a genius has been slow of growth. Oaks that flourish for a thousand years do not spring up into beauty like a reed.
In The Spanish Drama: Lope de Vega and Calderon (1846), 60.
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Maple-trees are the cows of trees (spring-milked).
In Proverbs from Plymouth Pulpit (1887), 10. Presumably referring to maple syrup production.
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Mathematics, while giving no quick remuneration, like the art of stenography or the craft of bricklaying, does furnish the power for deliberate thought and accurate statement, and to speak the truth is one of the most social qualities a person can possess. Gossip, flattery, slander, deceit, all spring from a slovenly mind that has not been trained in the power of truthful statement, which is one of the highest utilities.
In Social Phases of Education in the School and the Home (1900), 30.
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Men have called me mad; but the question is not yet settled, whether madness is or is not the loftiest intelligence—whether much that is glorious—whether all that is profound—does not spring from disease of thought—from moods of mind exalted at the expense of the general intellect.
In Eleonora (1850). Collected on The Works of the Late Edgar Allan Poe (1859), Vol. 1, 446.
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New scientific ideas never spring from a communal body, however organized, but rather from the head of an individually inspired researcher who struggles with his problems in lonely thought and unites all his thought on one single point which is his whole world for the moment.
Address on the 25th anniversary of the Kaiser-Wilhelm Gesellschaft (Jan 1936). Quoted in Surviving the Swastika: Scientific Research in Nazi Germany (1993), 97.
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Nothing is so beautiful as spring—
When weeds in wheels, shoot long and lovely and lush;...
'Spring' (1877), reprinted in Gerard Manley Hopkins and Michael White (ed.) Some Poems of Gerard Manley Hopkins, (1945), 7.
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Our obligation to survive and flourish is owed not just to ourselves, but also to the cosmos, ancient and vast, from which we spring.
…...
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Philosophy, and science, and the springs
Of wonder, and th wisdom of the world,
I have essayed; and in my mind there is
A power to make these subject to itself...
From poem 'Manfred'.
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Poised for flight,
Wings spread bright,
Spring from night into the Sun.
Help on the Way
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Power corrupts the few, while weakness corrupts the many.… The resentment of the weak does not spring from any injustice done to them but from the sense of their inadequacy and impotence. They hate not wickedness but weakness. When it is in their power to do so, the weak destroy weakness wherever they see it.
In The Passionate State of Mind (1955), 28.
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Research in neurophysiology is much more like paddling a small canoe on a mountain river. The river which is fed by many distant springs carries you along all right though often in a peculiar direction. You have to paddle quite hard to keep afloat. And sooner or later some of your ideas are upset and are carried downstream like an upturned canoe.
From Speech (10 Dec 1963) at the Nobel Banquet in Stockholm, Sweden. Collected inGöran Liljestrand (ed.), Les Prix Nobel en 1963, (1964).
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The axe and saw are insanely busy, chips are flying thick as snowflakes, and every summer thousands of acres of priceless forests, with their underbrush, soil, springs, climate, scenery, and religion, are vanishing away in clouds of smoke, while, except in the national parks, not one forest guard is employed.
John Muir
From 'The American Forests', The Atlantic (Aug 1897), 80, No. 478, 157.
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The concept of number is the obvious distinction between the beast and man. Thanks to number, the cry becomes a song, noise acquires rhythm, the spring is transformed into a dance, force becomes dynamic, and outlines figures.
Epigraph, without citation, in Corrective and Social Psychiatry and Journal of Behavior Technology Methods and Therapy (1966), Vol. 12, 409.
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The earliest of my childhood recollections is being taken by my grandfather when he set out in the first warm days of early spring with a grubbing hoe (we called it a mattock) on his shoulder to seek the plants, the barks and roots from which the spring medicine for the household was prepared. If I could but remember all that went into that mysterious decoction and the exact method of preparation, and with judicious advertisement put the product upon the market, I would shortly be possessed of wealth which might be made to serve the useful purpose of increasing the salaries of all pathologists. … But, alas! I remember only that the basic ingredients were dogwood bark and sassafras root, and to these were added q.s. bloodroot, poke and yellow dock. That the medicine benefited my grandfather I have every reason to believe, for he was a hale, strong old man, firm in body and mind until the infection came against which even spring medicine was of no avail. That the medicine did me good I well know, for I can see before me even now the green on the south hillside of the old pasture, the sunlight in the strip of wood where the dogwood grew, the bright blossoms and the delicate pale green of the leaf of the sanguinaria, and the even lighter green of the tender buds of the sassafras in the hedgerow, and it is good to have such pictures deeply engraved in the memory.
From address, 'A Medical Retrospect'. Published in Yale Medical Journal (Oct 1910), 17, No. 2, 57. [Note: q.s. in an abbreviation for quantum sufficit meaning “as much as is sufficient,” when used as a quantity specification in medicine and pharmacology. -Webmaster]
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The extraordinary development of mathematics in the last century is quite unparalleled in the long history of this most ancient of sciences. Not only have those branches of mathematics which were taken over from the eighteenth century steadily grown, but entirely new ones have sprung up in almost bewildering profusion, and many of them have promptly assumed proportions of vast extent.
In The History of Mathematics in the Nineteenth Century', Congress of Arts and Sciences (1905), Vol. 1, 474. As cited and wuoted in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 110.
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The stories of Whitney’s love for experimenting are legion. At one time he received a letter asking if insects could live in a vacuum. Whitney took the letter to one of the members of his staff and asked the man if he cared to run an experiment on the subject. The man replied that there was no point in it, since it was well established that life could not exist without a supply of oxygen. Whitney, who was an inveterate student of wild life, replied that on his farm he had seen turtles bury themselves in mud each fall, and, although the mud was covered with ice and snow for months, emerge again in the spring. The man exclaimed, “Oh, you mean hibernation!” Whitney answered, “I don't know what I mean, but I want to know if bugs can live in a vacuum.”
He proceeded down the hall and broached the subject to another member of the staff. Faced with the same lack of enthusiasm for pursuing the matter further, Whitney tried another illustration. “I've been told that you can freeze a goldfish solidly in a cake of ice, where he certainly can't get much oxygen, and can keep him there for a month or two. But if you thaw him out carefully he seems none the worse for his experience.” The second scientist replied, “Oh, you mean suspended animation.” Whitney once again explained that his interest was not in the terms but in finding an answer to the question.
Finally Whitney returned to his own laboratory and set to work. He placed a fly and a cockroach in a bell jar and removed the air. The two insects promptly keeled over. After approximately two hours, however, when he gradually admitted air again, the cockroach waved its feelers and staggered to its feet. Before long, both the cockroach and the fly were back in action.
'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 357-358.
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There are various causes for the generation of force: a tensed spring, an air current, a falling mass of water, fire burning under a boiler, a metal that dissolves in an acid—one and the same effect can be produced by means of all these various causes. But in the animal body we recognise only one cause as the ultimate cause of all generation of force, and that is the reciprocal interaction exerted on one another by the constituents of the food and the oxygen of the air. The only known and ultimate cause of the vital activity in the animal as well as in the plant is a chemical process.
'Der Lebensprocess im Thiere und die Atmosphare', Annalen der Chemie und Pharmacie (1841), 41, 215-7. Trans. Kenneth L. Caneva, Robert Mo.yer and the Conservation of Energy (1993), 78.
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There is no science which does not spring from pre-existing knowledge, and no certain and definite idea which has not derived its origin from the senses.
In Willis (trans.) and Alex Bowie (trans.), 'The First Anatomical Disquisition on the Circulation of the Blood, Addressed to Jo. Riolan', On the Motion of the Heart and Blood in Animals (1889), 93.
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There is symbolic as well as actual beauty in the migration of the birds, the ebb and flow of the tides, the folded bud ready for the spring. There is something infinitely healing in the repeated refrains of nature—the assurance that dawn comes after night, and spring after the winter.
In The Sense of Wonder (1956, 1965), 88-89.
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There will one day spring from the brain of science a machine or force so fearful in its potentialities, so absolutely terrifying, that even man, the fighter, who will dare torture and death in order to inflict torture and death, will be appalled, and so abandon war forever.
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There will still be things that machines cannot do. They will not produce great art or great literature or great philosophy; they will not be able to discover the secret springs of happiness in the human heart; they will know nothing of love and friendship.
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Through the magic of motion pictures, someone who’s never left Peoria knows the softness of a Paris spring, the color of a Nile sunset, the sorts of vegetation one will find along the upper Amazon and that Big Ben has not yet gone digital.
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Water at command, by turning a tap and paying a tax, is more convenient than carrying it from a free spring.
In Sinner Sermons: A Selection of the Best Paragraphs of E. W. Howe (1926), 49.
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We all know, from what we experience with and within ourselves, that our conscious acts spring from our desires and our fears. Intuition tells us that that is true also of our fellows and of the higher animals. We all try to escape pain and death, while we seek what is pleasant. We are all ruled in what we do by impulses; and these impulses are so organized that our actions in general serve for our self preservation and that of the race. Hunger, love, pain, fear are some of those inner forces which rule the individual’s instinct for self preservation. At the same time, as social beings, we are moved in the relations with our fellow beings by such feelings as sympathy, pride, hate, need for power, pity, and so on. All these primary impulses, not easily described in words, are the springs of man’s actions. All such action would cease if those powerful elemental forces were to cease stirring within us. Though our conduct seems so very different from that of the higher animals, the primary instincts are much alike in them and in us. The most evident difference springs from the important part which is played in man by a relatively strong power of imagination and by the capacity to think, aided as it is by language and other symbolical devices. Thought is the organizing factor in man, intersected between the causal primary instincts and the resulting actions. In that way imagination and intelligence enter into our existence in the part of servants of the primary instincts. But their intervention makes our acts to serve ever less merely the immediate claims of our instincts.
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We are told that “Mathematics is that study which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation.” I think no statement could have been made more opposite to the facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas, and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activities of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world (to which the inner one in each individual man may, I think, be conceived to stand somewhat in the same relation of correspondence as a shadow to the object from which it is projected, or as the hollow palm of one hand to the closed fist which it grasps of the other), that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of the imagination and invention.
In Presidential Address to British Association, Exeter British Association Report (1869), pp. 1-9, in Collected Mathematical Papers, Vol. 2, 654.
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We grow great by dreams. All big men are dreamers. They see things in the soft haze of a spring day or in the red fire of a long winter’s evening. Some of us let these great dreams die, but others nourish and protect them; nurse them through bad days till they bring them to the sunshine and light which comes always to those who sincerely hope that their dreams will come true.
Quoted, for example, in The American Exporter (1930), Vol. 106, 158. Webmaster has found this quote in numerous texts, but as yet has not identified the original. (Can you help?)
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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 stand by the river and admire the great body of water flowing so sweetly on; could you trace it back to its source, you might find a mere rivulet, but meandering on, joined by other streams and by secret springs, and fed by the rains and dews of heaven, it gathers volume and force, makes its way through the gorges of the mountains, plows, widens and deepens its channel through the provinces, and attains its present majesty.
From Address (1 Aug 1875), 'The Growth of Principles' at Saratoga. Collected in William L. Snyder (ed.), Great Speeches by Great Lawyers: A Collection of Arguments and Speeches (1901), 246.
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What I especially admire about you [Arnold Sommerfeld] is the way. at a stamp of your foot, a great number of talented young theorists spring up out of the ground.
As quoted in Paul Forman and Armin Hermann, 'Sommerfeld, Arnold (Johannes Wilhelm)', Biography in Dictionary of Scientific Biography (1975), Vol. 12, 529. Cited from Armin Herman (ed.), Albert Einstein/Arnold Sommerfeld. Briefwechsel: Sechzig Briefe aus dem goldenen Zeitalter der modernen Physik (1968, German), 98.
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Whatever may happen to the latest theory of Dr. Einstein, his treatise represents a mathematical effort of overwhelming proportions. It is the more remarkable since Einstein is primarily a physicist and only incidentally a mathematician. He came to mathematics rather of necessity than by predilection, and yet he has here developed mathematical formulae and calculations springing from a colossal knowledge.
In 'Marvels at Einstein For His Mathematics', New York Times (4 Feb 1929), 3.
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When air has been freshly and strongly tainted with putrefaction, so as to smell through the water, sprigs of mint have presently died, upon being put into it, their leaves turning black; but if they do not die presently, they thrive in a most surprizing manner. In no other circumstances have I ever seen vegetation so vigorous as in this kind of air, which is immediately fatal to animal life. Though these plants have been crouded in jars filled with this air, every leaf has been full of life; fresh shoots have branched out in various , and have grown much faster than other similiar plants, growing in the same exposure in common air.
This observation led me to conclude that plants, instead of affecting the air in the same manner with animal respiration, reverse the effects of breathing, and tend to keep the atmosphere sweet and wholesome, when it is become noxious, in consequence on animals living and breathing, or dying and putrefying in it.
In order to ascertain this, I took a quantity of air, made thoroughly noxious, by mice breathing and dying in it, and divided it into two parts; one of which I put into a phial immersed in water; and to the other (which was contained in a glass jar, standing in water) I put a sprig of mint. This was about the beginning of August 1771, and after eight or nine days, I found that a mouse lived perfectly well in that part of the air, in which the sprig of mint had grown, but died the moment it was put into the other part of the same original quantity of air; and which I had kept in the very same exposure, but without any plant growing in it.
'Observations on Different Kinds of Air', Philosophical Transactions (1772), 62, 193-4.
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When the time is ripe for certain things, these things appear in different places in the manner of violets coming to light in early spring.
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When you can dump a load of bricks on a corner lot, and let me watch them arrange themselves into a house — when you can empty a handful of springs and wheels and screws on my desk, and let me see them gather themselves together into a watch — it will be easier for me to believe that all these thousands of worlds could have been created, balanced, and set to moving in their separate orbits, all without any directing intelligence at all.
In 'If A Man Die, Shall He Live again?', More Power To You: Fifty Editorials From Every Week (1917), 218-219.
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While religion prescribes brotherly love in the relations among the individuals and groups, the actual spectacle more resembles a battlefield than an orchestra. Everywhere, in economic as well as in political life, the guiding principle is one of ruthless striving for success at the expense of one’s fellow men. This competitive spirit prevails even in school and, destroying all feelings of human fraternity and cooperation, conceives of achievement not as derived from the love for productive and thoughtful work, but as springing from personal ambition and fear of rejection.
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You can prepare yourself for work. The paintings of the great masters, the compositions of great musicians, the sermons of great preachers, the policies of great statesmen, and the campaigns of great generals, do not spring full bloom from barren rock. … If you are a true student you will be more dissatisfied with yourself when you graduate than you are now.
From Cameron Prize Lecture (1928), delivered before the University of Edinburgh. As quoted in J.B. Collip 'Frederick Grant Banting, Discoverer of Insulin', The Scientific Monthly (May 1941), 52, No. 5, 473-474.
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[Animals] do not so much act as be put into action, and that objects make an impression on their senses such that it is necessary for them to follow it just as it is necessary for the wheels of a clock to follow the weights and the spring that pulls them.
[In his philosophy, he regarded animals to be merely automatons.].
'Traitez de la voix', Harmonie Universelle (1637), Vol. 1, prop. lii, 79. In Charles Coulston Gillespie (ed.), Dictionary of Scientific Biography (1974), Vol. 9, 318.
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[Bobby Clark:] What causes the water in a watermelon?
[Paul McCullough:] They plant the seeds in the spring.
From short movie Love and Hisses (1934). Writer, Ben Holmes (6 Nov 1890 - 2 Dec 1943). In Larry Langman and Paul Gold, Comedy Quotes from the Movies (2001), 241.
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[On the concept of group:] … what a wealth, what a grandeur of thought may spring from what slight beginnings.
From Address (1913) of the president to the Mathematical and Physical Science Section of the British Association for the Advancement of Science, Birmingham, 'The Place of Pure Mathematics', Science (12 Sep 1913), New Series,38, No. 976, 352. Excerpted in Florian Cajori, 'The Nineteenth and Twentieth Centuries: Introduction', A History of Mathematics (1919), 283
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[T]he history of science has proved that fundamental research is the lifeblood of individual progress and that the ideas that lead to spectacular advances spring from it.
In J. Edwin Holmström, Records and Research in Engineering and Industrial Science (1956), 7.
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~~[Misattributed ?]~~ Mathematical discoveries, like springtime violets in the woods, have their season which no human can hasten or retard.
Webmaster believes this quote is likely a misattributed paraphrase. The subject quote is as given in Israel Kleiner, 'Thinking the Unthinkable: The Story of Complex Numbers (with a Moral)', Mathematics Teacher (Oct 1988), 81, No. 7, 590. In Kleiner’s paper, alongside the quote is a citation, thus: “(Kline 1972)?” Notice the appended question mark. The reference at the end of the paper gives: Morris Kline, Mathematical Thought from Ancient to Modern Times (1972), but without page number. Webmaster checked a later edition, Vol. 3 (1990), 861, in which Kline has an epigraph, with different wording about violets, attributed - not to János - but to his father, “Wolfgang Bolyai” (who is also known as Farkas Bolyai). Translator Abe Shenitzer wrote an ambiguous passage in Herbert Meschkowski, NonEuclidean Geometry (1964), 33. In a discussion posted in the NCTM online Math Forum in 1998, Shenitzer clarified that the proper reading is that the “violet talk” is a simile used in advice given by the father to his son. Note that in the passage, János (Johann/John) reports about that advice in narrative form. Thus, one should also note that even in the original language, perhaps the father’s words are not verbatim. See Farkas Bolyai Quotes on another page of this website.
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“Bitzer,” said Thomas Gradgrind. “Your definition of a horse.”
“Quadruped. Graminivorous. Forty teeth; namely, twenty-four grinders, four eye-teeth, and twelve incisive. Sheds coat in the Spring; in marshy countries, sheds hoofs, too. Hoofs hard, but requiring to be shod with iron. Age known by marks in mouth.” Thus (and much more) Bitzer.
“Now girl number twenty,” said Mr. Gradgrind. “You know what a horse is.”
Spoken by fictional character Thomas Gringrind in his schoolroom with pupil Bitzer, Hard Times, published in Household Words (1 Apr 1854), Vol. 36, 3.
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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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