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Who said: “Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.”
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Home > Category Index for Science Quotations > Category Index S > Category: Small

Small Quotes (163 quotes)

...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.
I Want to be a Mathematician: an Automathography in Three Parts (1985), 324.
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A stands for atom; it is so small No one has ever seen it at all.
B stands for bomb; the bombs are much bigger,
So, brother, do not be too fast on the trigger.
H has become a most ominous letter.
It means something bigger if not something better.
As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 74.
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Quand on demande à nos philosophes à quoi sert ce nombre prodigieux d’étoiles fixes, dont une partie suffirait pour faire ce qu’elles font toutes, ils vous répondent froidement qu’elles servent à leur réjouir la vue.
When our philosophers are asked what is the use of these countless myriads of fixed stars, of which a small part would be sufficient to do what they all do, they coolly tell us that they are made to give delight to their eyes.
In 'Premier Soir', Entretiens Sur La Pluralité Des Mondes (1686, 1863), 29. French and translation in Craufurd Tait Ramage, Beautiful Thoughts from French and Italian Authors (1866), 117.
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A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator the smaller the fraction.
Quoted, without citation, in Howard Whitley Eves, Return to Mathematical Circles (1988), 81.
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A mathematician of the first rank, Laplace quickly revealed himself as only a mediocre administrator; from his first work we saw that we had been deceived. Laplace saw no question from its true point of view; he sought subtleties everywhere; had only doubtful ideas, and finally carried the spirit of the infinitely small into administration.
As quoted in E.T. Bell, Men of Mathematics (1937, 1965), 182. Without citation, except, “As it is often quoted as … Napoleon’s famous estimate of Laplace, of which he is reported to have delivered himself while he was a prisoner at St. Helena.” Laplace had a six-week tenure in the Ministry of the Interior.
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A modern branch of mathematics, having achieved the art of dealing with the infinitely small, can now yield solutions in other more complex problems of motion, which used to appear insoluble. This modern branch of mathematics, unknown to the ancients, when dealing with problems of motion, admits the conception of the infinitely small, and so conforms to the chief condition of motion (absolute continuity) and thereby corrects the inevitable error which the human mind cannot avoid when dealing with separate elements of motion instead of examining continuous motion. In seeking the laws of historical movement just the same thing happens. The movement of humanity, arising as it does from innumerable human wills, is continuous. To understand the laws of this continuous movement is the aim of history. … Only by taking an infinitesimally small unit for observation (the differential of history, that is, the individual tendencies of man) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.
War and Peace (1869), Book 11, Chap. 1.
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A scientist is in a sense a learned small boy. There is something of the scientist in every small boy. Others must outgrow it. Scientists can stay that way all their lives.
Nobel banquet speech (10 Dec 1967). In Ragnar Granit (ed.), Les Prix Nobel en 1967 (1968).
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A small cabin stands in the Glacier Peak Wilderness, about a hundred yards off a trail that crosses the Cascade Range. In midsummer, the cabin looked strange in the forest. It was only twelve feet square, but it rose fully two stories and then had a high and steeply peaked roof. From the ridge of the roof, moreover, a ten-foot pole stuck straight up. Tied to the top of the pole was a shovel. To hikers shedding their backpacks at the door of the cabin on a cold summer evening—as the five of us did—it was somewhat unnerving to look up and think of people walking around in snow perhaps thirty-five feet above, hunting for that shovel, then digging their way down to the threshold.
In Encounters with the Archdruid (1971), 3.
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A strong feeling of adventure is animating those who are working on bacterial viruses, a feeling that they have a small part in the great drive towards a fundamental problem in biology.
From 'Experiments with Bacterial Viruses (Bacteriophages)', Harvey Lecture (1946), 41, 187. As cited in Robert Olby, The Path of the Double Helix: The Discovery of DNA (1974, 1994), 238.
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A time will come when science will transform [our bodies] by means which we cannot conjecture... And then, the earth being small, mankind will migrate into space, and will cross the airless Saharas which separate planet from planet, and sun from sun. The earth will become a Holy Land which will be visited by pilgrims from all quarters of the universe.
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A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment.
In 'Chance', Science et Méthode (1908). Quoted in Richard Kautz, Chaos: The Science of Predictable Random Motion (2011), 167 as translated in Science and Method by F. Maitland (1918).
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Alexander the king of the Macedonians, began like a wretch to learn geometry, that he might know how little the earth was, whereof he had possessed very little. Thus, I say, like a wretch for this, because he was to understand that he did bear a false surname. For who can be great in so small a thing? Those things that were delivered were subtile, and to be learned by diligent attention: not which that mad man could perceive, who sent his thoughts beyond the ocean sea. Teach me, saith he, easy things. To whom his master said: These things be the same, and alike difficult unto all. Think thou that the nature of things saith this. These things whereof thou complainest, they are the same unto all: more easy things can be given unto none; but whosoever will, shall make those things more easy unto himself. How? With uprightness of mind.
In Thomas Lodge (trans.), 'Epistle 91', The Workes of Lucius Annaeus Seneca: Both Morrall and Naturall (1614), 383. Also in Robert Édouard Moritz, Memorabilia Mathematica (1914), 135.
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All of us who are concerned for peace and triumph of reason and justice must be keenly aware how small an influence reason and honest good will exert upon events in the political field.
…...
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All over the world there lingers on the memory of a giant tree, the primal tree, rising up from the centre of the Earth to the heavens and ordering the universe around it. It united the three worlds: its roots plunged down into subterranean abysses, Its loftiest branches touched the empyrean. Thanks to the Tree, it became possible to breathe the air; to all the creatures that then appeared on Earth it dispensed its fruit, ripened by the sun and nourished by the water which it drew from the soil. From the sky it attracted the lightning from which man made fire and, beckoning skyward, where clouds gathered around its fall. The Tree was the source of all life, and of all regeneration. Small wonder then that tree-worship was so prevalent in ancient times.
From 'L'Arbre Sacre' ('The Sacred Tree'), UNESCO Courier (Jan 1989), 4. Epigraph to Chap 1, in Kenton Miller and Laura Tangley, Trees of Life: Saving Tropical Forests and Their Biological Wealt (1991), 1.
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All rivers, small or large, agree in one character; they like to lean a little on one side; they cannot bear to have their channels deepest in the middle, but will always, if they can, have one bank to sun themselves upon, and another to get cool under.
In 'Water', The True and the Beautiful in Nature, Art, Morals, and Religion (1872), 62.
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And, in this case, science could learn an important lesson from the literati–who love contingency for the same basic reason that scientists tend to regard the theme with suspicion. Because, in contingency lies the power of each person, to make a difference in an unconstrained world bristling with possibilities, and nudgeable by the smallest of unpredictable inputs into markedly different channels spelling either vast improvement or potential disaster.
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Anyone who doesn’t take truth seriously in small matters cannot be trusted in large ones either.
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Archimedes … had stated that given the force, any given weight might be moved, and even boasted, we are told, relying on the strength of demonstration, that if there were another earth, by going into it he could remove this. Hiero being struck with amazement at this, and entreating him to make good this problem by actual experiment, and show some great weight moved by a small engine, he fixed accordingly upon a ship of burden out of the king’s arsenal, which could not be drawn out of the dock without great labor and many men; and, loading her with many passengers and a full freight, sitting himself the while far off with no great endeavor, but only holding the head of the pulley in his hand and drawing the cords by degrees, he drew the ship in a straight line, as smoothly and evenly, as if she had been in the sea. The king, astonished at this, and convinced of the power of the art, prevailed upon Archimedes to make him engines accommodated to all the purposes, offensive and defensive, of a siege. … the apparatus was, in most opportune time, ready at hand for the Syracusans, and with it also the engineer himself.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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As for the search for truth, I know from my own painful searching, with its many blind alleys, how hard it is to take a reliable step, be it ever so small, towards the understanding of that which is truly significant.
Letter to an interested layman (13 Feb 1934). In Helen Dukas and Banesh Hoffman, Albert Einstein: The Human Side: New Glipses From His Archives (1981), 18.
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As man advances in civilisation, and small tribes are united into larger communities, the simplest reason would tell each individual that he ought to extend his social instincts and sympathies to all the members of the same nation, though personally unknown to him. This point being once reached, there is only an artificial barrier to prevent his sympathies extending to the men of all nations and races.
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Ask why God made the GEM so small,
And why so huge the granite?
Because God meant, mankind should set
That higher value on it.
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Astronomy is perhaps the science whose discoveries owe least to chance, in which human understanding appears in its whole magnitude, and through which man can best learn how small he is.
Aphorism 23 in Notebook C (1772-1773), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 35.
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Astrophysicists have the formidable privilege of having the largest view of the Universe; particle detectors and large telescopes are today used to study distant stars, and throughout space and time, from the infinitely large to the infinitely small, the Universe never ceases to surprise us by revealing its structures little by little.
In Black Holes (1992), xv.
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Before I flew I was already aware of how small and vulnerable our planet is; but only when I saw it from space, in all its ineffable beauty and fragility, did I realize that humankind’s most urgent task is to cherish and preserve it for future generations.
In Jack Hassard and Julie Weisberg , Environmental Science on the Net: The Global Thinking Project (1999), 40.
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Building goes on briskly at the therapeutic Tower of Babel; what one recommends another condemns; what one gives in large doses another scarce dares to prescribe in small doses; and what one vaunts as a novelty another thinks not worth rescuing from merited oblivion. All is confusion, contradiction, inconceivable chaos. Every country, every place, almost every doctor, have their own pet remedies, without which they imagine their patients can not be cured; and all this changes every year, aye every mouth.
Weekly Medical Gazette, of Vienna
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But, as we consider the totality of similarly broad and fundamental aspects of life, we cannot defend division by two as a natural principle of objective order. Indeed, the ‘stuff’ of the universe often strikes our senses as complex and shaded continua, admittedly with faster and slower moments, and bigger and smaller steps, along the way. Nature does not dictate dualities, trinities, quarterings, or any ‘objective’ basis for human taxonomies; most of our chosen schemes, and our designated numbers of categories, record human choices from a cornucopia of possibilities offered by natural variation from place to place, and permitted by the flexibility of our mental capacities. How many seasons (if we wish to divide by seasons at all) does a year contain? How many stages shall we recognize in a human life?
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Civilisations as yet have only been created and directed by a small intellectual aristocracy, never by crowds. Crowds are only powerful for destruction.
From original French, “Les civilisations n’ont été créées et guidées jusqu’ici que par une petite aristocratie intellectuelle, jamais par les foules. Les foules n’ont de puissance que pour détruire,” in Psychologie des Foules (1895), Preface, 6. English text in The Crowd: A Study of the Popular Mind (1897), Introduction, xviii. Also seen translated as, “All the civilizations we know have been created and directed by small intellectual aristocracies, never by people in the mass. The power of crowds is only to destroy.”
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Does it mean, if you don’t understand something, and the community of physicists don’t understand it, that means God did it? Is that how you want to play this game? Because if it is, here’s a list of the things in the past that the physicists—at the time—didn’t understand … [but now we do understand.] If that’s how you want to invoke your evidence for God, then God is an ever-receding pocket of scientific ignorance, that’s getting smaller and smaller and smaller, as time moves on. So just be ready for that to happen, if that’s how you want to come at the problem. That’s simply the “God of the Gaps” argument that’s been around for ever.
From interview, The Science Studio video series of The Science Network website, episode 'The Moon, the Tides and why Neil DeGrasse Tyson is Colbert’s God' (20 Jan 2011), time 26:58-27:55.
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Each of the major sciences has contributed an essential ingredient in our long retreat from an initial belief in our own cosmic importance. Astronomy defined our home as a small planet tucked away in one corner of an average galaxy among millions; biology took away our status as paragons created in the image of God; geology gave us the immensity of time and taught us how little of it our own species has occupied.
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Earthworms, though in appearance a small and despicable link in the chain of nature, yet, if lost, would make a lamentable chasm … worms seem to be the great promoters of vegetation, which would proceed but lamely without them.
[Showing an early awareness in ecology.]
Letter XXXV, to Daines Barrington, (20 May 1777) in The Natural History of Selborne (1789), 216 and (1899), 174.
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Everyone makes for himself a clear idea of the motion of a point, that is to say, of the motion of a corpuscle which one supposes to be infinitely small, and which one reduces by thought in some way to a mathematical point.
Théorie Nouvelle de la Rotation des Corps (1834). As translated by Charles Thomas Whitley in Outlines of a New Theory of Rotatory Motion (1834), 1.
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Everything about microscopic life is terribly upsetting. How can things so small be so important?
Epigraph in Isaac Asimov’s Book of Science and Nature Quotations (1988), 156.
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Fear of something is at the root of hate for others and hate within will eventually destroy the hater. Keep your thoughts free from hate, and you will have no fear from those who hate you. ...
David, though small, was filled with truth, right thinking and good will for others. Goliath represents one who let fear into his heart, and it stayed there long enough to grow into hate for others.
In Alvin D. Smith, George Washington Carver: Man of God (1954), 43. Cited in Linda O. McMurry, George Washington Carver, Scientist and Symbol (1982), 107. Smith's book is about his recollections of G.W. Carver's Sunday School classes at Tuskegee, some 40 years earlier. Webmaster, who has not yet been able to see the original book, cautions this quote may be the gist of Carver's words, rather than a verbatim quote.
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For a stone, when it is examined, will be found a mountain in miniature. The fineness of Nature’s work is so great, that, into a single block, a foot or two in diameter, she can compress as many changes of form and structure, on a small scale, as she needs for her mountains on a large one; and, taking moss for forests, and grains of crystal for crags, the surface of a stone, in by far the plurality of instances, is more interesting than the surface of an ordinary hill; more fantastic in form and incomparably richer in colour—the last quality being, in fact, so noble in most stones of good birth (that is to say, fallen from the crystalline mountain ranges).
Modern Painters, 4, Containing part 5 of Mountain Beauty (1860), 311.
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For many planet hunters, though, the ultimate goal is still greater (or actually, smaller) prey: terrestrial planets, like Earth, circling a star like the Sun. Astronomers already know that three such planets orbit at least one pulsar. But planet hunters will not rest until they are in sight of a small blue world, warm and wet, in whose azure skies and upon whose wind-whipped oceans shines a bright yellow star like our own.
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For small creatures such as we the vastness is bearable only through love.
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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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Four circles to the kissing come,
The smaller are the benter.
The bend is just the inverse of
The distance from the centre.
Though their intrigue left Euclid dumb
There’s now no need for rule of thumb.
Since zero bend’s a dead straight line
And concave bends have minus sign,
The sum of squares of all four bends
Is half the square of their sum.
In poem, 'The Kiss Precise', Nature (20 Jun 1936), 137, 1021, as quoted, cited, explained and illustrated in Martin Gardner, The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems (2001), 139-141.
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From the infinitely great down to the infinitely small, all things are subject to [the laws of nature]. The sun and the planets follow the laws discovered by Newton and Laplace, just as the atoms in their combinations follow the laws of chemistry, as living creatures follow the laws of biology. It is only the imperfections of the human mind which multiply the divisions of the sciences, separating astronomy from physics or chemistry, the natural sciences from the social sciences. In essence, science is one. It is none other than the truth.
In Cours d’Economie Politique (1896-97).
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Guid gear gangs intae sma bouk. (Good equipment goes into small bulk.)
As quoted in Alan L. Mackay, A Dictionary of Scientific Quotations (1991), 219.
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Histology is an exotic meal, but can be as repulsive as a dose of medicine for students who are obliged to study it, and little loved by doctors who have finished their study of it all too hastily. Taken compulsorily in large doses it is impossible to digest, but after repeated tastings in small draughts it becomes completely agreeable and even addictive. Whoever possesses a refined sensitivity for artistic manifestations will appreciate that, in the science of histology, there exists an inherent focus of aesthetic emotions.
Opening remarks of paper, 'Art and Artifice in the Science of Histology' (1933), reprinted in Histopathology (1993), 22, 515-525. Quoted in Ross, Pawlina and Barnash, Atlas of Descriptive Histology (2009).
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How vast those Orbs must be, and how inconsiderable this Earth, the Theatre upon which all our mighty Designs, all our Navigations, and all our Wars are transacted, is when compared to them. A very fit consideration, and matter of Reflection, for those Kings and Princes who sacrifice the Lives of so many People, only to flatter their Ambition in being Masters of some pitiful corner of this small Spot.
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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 do not understand modern physics at all, but my colleagues who know a lot about the physics of very small things, like the particles in atoms, or very large things, like the universe, seem to be running into one queerness after another, from puzzle to puzzle.
In 'On Science and Certainty', Discover Magazine (Oct 1980).
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I don't grow up. In me is the small child of my early days.
As quoted on the website mcescher.com, without citation.
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I forget whether you take in the Times; for the chance of your not doing so, I send the enclosed rich letter. It is, I am sure, by Fitz-Roy. … It is a pity he did not add his theory of the extinction of Mastodon, etc., from the door of the Ark being made too small.
Letter (5 Dec 1859) to Charles Lyell. In Francis Darwin and Albert Charles Seward (eds.), More Letters of Charles Darwin: A Record of his Work in a Series of Hitherto Unpublished Letters (103), Vol. 1, 129. The referenced letters in the Times were on 1 Dec and 5 Dec 1859, signed under the pseudonym “Senex”, on the topic of “Works of Art in the Drift.”
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I have always found small mammals enough like ourselves to feel that I could understand what their lives would be like, and yet different enough to make it a sort of adventure and exploration to see what they were doing.
Echoes of Bats and Men (1959), 2.
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I have no doubt that it is possible to give a new direction to technological development, a direction that shall lead it back to the real needs of man, and that also means: to the actual size of man. Man is small, and, therefore, small is beautiful. To go
Small is Beautiful (1973).
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I have no doubt that many small strikes of a hammer will finally have as much effect as one very heavy blow: I say as much in quantity, although they may be different in mode, but in my opinion, everything happens in nature in a mathematical way, and there is no quantity that is not divisible into an infinity of parts; and Force, Movement, Impact etc. are types of quantities.
From the original French, “Ie ne doute point que plusieurs petits coups de Marteau ne fassent enfin autant d’effet qu’vn fort grand coup, ie dis autant en quantité, bien qu’ils puissent estre différents, in modo; mais apud me omnia fiunt Mathematicè in Natura, & il n’y a point de quantité qui ne soit divisible en une infinité de parties; Or la Force, le Mouuement, la Percussion, &c. sont des Especes de quantitez,” in letter (11 Mar 1640) to Père Marin Mersenne (AT III 36), collected in Lettres de Mr Descartes (1659), Vol. 2, 211-212. English version by Webmaster using online resources.
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I have said that mathematics is the oldest of the sciences; a glance at its more recent history will show that it has the energy of perpetual youth. The output of contributions to the advance of the science during the last century and more has been so enormous that it is difficult to say whether pride in the greatness of achievement in this subject, or despair at his inability to cope with the multiplicity of its detailed developments, should be the dominant feeling of the mathematician. Few people outside of the small circle of mathematical specialists have any idea of the vast growth of mathematical literature. The Royal Society Catalogue contains a list of nearly thirty- nine thousand papers on subjects of Pure Mathematics alone, which have appeared in seven hundred serials during the nineteenth century. This represents only a portion of the total output, the very large number of treatises, dissertations, and monographs published during the century being omitted.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 285.
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I now never make the preparations for penetrating into some small province of nature hitherto undiscovered without breathing a prayer to the Being who hides His secrets from me only to allure me graciously on to the unfolding of them.
As quoted in E.P. Whipple, 'Recollections of Agassiz', in Henry Mills Alden (ed.), Harper's New Monthly Magazine (June 1879), 59, 103.
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If a nonnegative quantity was so small that it is smaller than any given one, then it certainly could not be anything but zero. To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be. These supposed mysteries have rendered the calculus of the infinitely small quite suspect to many people. Those doubts that remain we shall thoroughly remove in the following pages, where we shall explain this calculus.
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If I choose to impose individual blame for all past social ills, there will be no one left to like in some of the most fascinating periods of our history. For example ... if I place every Victorian anti-Semite beyond the pale of my attention, my compass of available music and literature will be pitifully small. Though I hold no shred of sympathy for active persecution, I cannot excoriate individuals who acquiesced passively in a standard societal judgment. Rail instead against the judgment, and try to understand what motivates men of decent will.
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If there is a small rocket on top of a big one, and if the big one is jettisoned and the small one is ignited, then their speeds are added.
In 'My Contributions to Astronautics' (1967), collected in Smithsonian Annals of Flight (1971), 131.
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If we turn our backs on things as yet untried within our own small realm of reference, we’re guilty of a sin against ourselves: An unwillingness to experiment.
In 'Reactions to Man’s Landing on the Moon Show Broad Variations in Opinions', The New York Times (21 Jul 1969), 6.
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If we view mathematical speculations with reference to their use, it appears that they should be divided into two classes. To the first belong those which furnish some marked advantage either to common life or to some art, and the value of such is usually determined by the magnitude of this advantage. The other class embraces those speculations which, though offering no direct advantage, are nevertheless valuable in that they extend the boundaries of analysis and increase our resources and skill. Now since many investigations, from which great advantage may be expected, must be abandoned solely because of the imperfection of analysis, no small value should be assigned to those speculations which promise to enlarge the field of anaylsis.
In Novi Comm. Petr., Vol. 4, Preface.
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If you throw a stone in a pond... the waves which strike against the shores are thrown back towards the spot where the stone struck; and on meeting other waves they never intercept each other’s course... In a small pond one and the same stroke gives birth to many motions of advance and recoil.
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In a large proportion of cases treated by physicians the disease is cured by nature, not by them. In a lesser, but not a small proportion, the disease is cured by nature in spite of them.
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In Pure Mathematics, where all the various truths are necessarily connected with each other, (being all necessarily connected with those hypotheses which are the principles of the science), an arrangement is beautiful in proportion as the principles are few; and what we admire perhaps chiefly in the science, is the astonishing variety of consequences which may be demonstrably deduced from so small a number of premises.
In Elements of the Philosophy of the Human Mind (1827), Vol. 3, Chap. 1, Sec. 8, 186.
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In shades of black and blue the skies do bow as darkness falls the lights go out.
Nature softly immersed in glee as all mankind drifts off to sleep.
Water breathes a sigh of relief now aquatic creatures can do as they please.
Animals whether large or small regain the natural instincts that man has fought.
The moon shines bright he’s happy too people can’t over-ride his rules.
Midnight calms the wounds of the world the break of dawn disperses new hope...
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In space there are countless constellations, suns and planets; we see only the suns because they give light; the planets remain invisible, for they are small and dark. There are also numberless earths circling around their suns, no worse and no less than this globe of ours. For no reasonable mind can assume that heavenly bodies that may be far more magnificent than ours would not bear upon them creatures similar or even superior to those upon our human earth.
As quoted in Dave Goldberg, The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality (2013), 74.
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In summary, very large populations may differentiate rapidly, but their sustained evolution will be at moderate or slow rates and will be mainly adaptive. Populations of intermediate size provide the best conditions for sustained progressive and branching evolution, adaptive in its main lines, but accompanied by inadaptive fluctuations, especially in characters of little selective importance. Small populations will be virtually incapable of differentiation or branching and will often be dominated by random inadaptive trends and peculiarly liable to extinction, but will be capable of the most rapid evolution as long as this is not cut short by extinction.
Tempo and Mode in Evolution (1944), 70-1.
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In the final analysis, our most basic common link is that we all inhabit this small planet. We all breathe the same air. We all cherish our children's future. And we are all mortal.
Commencement Address at American University, Washington, D.C. (Jun 1963). In Steven Cohen, Understanding Environmental Policy (2006), Preface, xi. Also on web site of John F. Kennedy Presidential Library and Museum.
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In the universe great acts are made up of small deeds.
Lao Tzu
In Lao Tsu and Jane English (trans.), Tao Te Ching (1989), sec. 63, 66.
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It has always seemed to me extreme presumptuousness on the part of those who want to make human ability the measure of what nature can and knows how to do, since, when one comes down to it, there is not one effect in nature, no matter how small, that even the most speculative minds can fully understand.
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It is a great thing to start life with a small number of really good books which are your very own.
In Through the Magic Door (1908), Chap. 2, 24.
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It is no small comfort when I reflect that we should not so much marvel at the vast and almost infinite breadth of the most distant heavens but much more at the smallness of us manikins and the smallness of this our tiny ball of earth and also of all the planets.
From Letter to Johann Herwart (1598), as quoted in Murray Roston, Milton and the Baroque (1980), 17.
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It is one of the triumphs of human wit ... to conquer by humility and submissiveness ... to make oneself small in order to appear great ... such ... are often the expedients of the neurotic.
In The Neurotic Constitution (1917), 81-82.
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It is probable that all organisms now alive are descended from one ancestor, for the following reason. Most of our structural molecules are asymmetrical, as shown by the fact that they rotate the plane of polarized light, and often form asymmetrical crystals. But of the two possible types of any such molecule, related to one another like a right and left boot, only one is found throughout living nature. The apparent exceptions to this rule are all small molecules which are not used in the building of the large structures which display the phenomena of life.
In 'The Origin of Life', The Inequality of Man: And Other Essays (1932), 157.
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It is said that the composing of the Lilavati was occasioned by the following circumstance. Lilavati was the name of the author’s daughter, concerning whom it appeared, from the qualities of the ascendant at her birth, that she was destined to pass her life unmarried, and to remain without children. The father ascertained a lucky hour for contracting her in marriage, that she might be firmly connected and have children. It is said that when that hour approached, he brought his daughter and his intended son near him. He left the hour cup on the vessel of water and kept in attendance a time-knowing astrologer, in order that when the cup should subside in the water, those two precious jewels should be united. But, as the intended arrangement was not according to destiny, it happened that the girl, from a curiosity natural to children, looked into the cup, to observe the water coming in at the hole, when by chance a pearl separated from her bridal dress, fell into the cup, and, rolling down to the hole, stopped the influx of water. So the astrologer waited in expectation of the promised hour. When the operation of the cup had thus been delayed beyond all moderate time, the father was in consternation, and examining, he found that a small pearl had stopped the course of the water, and that the long-expected hour was passed. In short, the father, thus disappointed, said to his unfortunate daughter, I will write a book of your name, which shall remain to the latest times—for a good name is a second life, and the ground-work of eternal existence.
In Preface to the Persian translation of the Lilavati by Faizi (1587), itself translated into English by Strachey and quoted in John Taylor (trans.) Lilawati, or, A Treatise on Arithmetic and Geometry by Bhascara Acharya (1816), Introduction, 3. [The Lilavati is the 12th century treatise on mathematics by Indian mathematician, Bhaskara Acharya, born 1114.]
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It is the middle of the night when a glittering theatre of light suddenly appears in front of the Dhaka. Where, moments before there was only darkness, suddenly there are hundreds of columns of light. The sound of helicopters and car horns carry across to the ship on the breeze. There is the scent of rain after it has evaporated from warm streets. This is unmistakably Singapore, the small city-state at the most southern point of the Asiatic mainland. Singapore was built as a centre for world trade by the British over 250 years ago, and today, Singapore has the largest container harbour in the world. This is where the axes of world trade cross paths: from the Far East to Europe, from the Far East to Southeast Asia/the East, and from the Far East to Australia. Everything runs like clockwork here. Within five hours the Dhaka has been unloaded.
Made on Earth
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It suddenly struck me that that tiny pea, pretty and blue, was the Earth. I put up my thumb and shut one eye, and my thumb blotted out the planet Earth. I didn’t feel like a giant. I felt very, very small.
…...
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It was his [Leibnitz’s] love of method and order, and the conviction that such order and harmony existed in the real world, and that our success in understanding it depended upon the degree and order which we could attain in our own thoughts, that originally was probably nothing more than a habit which by degrees grew into a formal rule. This habit was acquired by early occupation with legal and mathematical questions. We have seen how the theory of combinations and arrangements of elements had a special interest for him. We also saw how mathematical calculations served him as a type and model of clear and orderly reasoning, and how he tried to introduce method and system into logical discussions, by reducing to a small number of terms the multitude of compound notions he had to deal with. This tendency increased in strength, and even in those early years he elaborated the idea of a general arithmetic, with a universal language of symbols, or a characteristic which would be applicable to all reasoning processes, and reduce philosophical investigations to that simplicity and certainty which the use of algebraic symbols had introduced into mathematics.
A mental attitude such as this is always highly favorable for mathematical as well as for philosophical investigations. Wherever progress depends upon precision and clearness of thought, and wherever such can be gained by reducing a variety of investigations to a general method, by bringing a multitude of notions under a common term or symbol, it proves inestimable. It necessarily imports the special qualities of number—viz., their continuity, infinity and infinite divisibility—like mathematical quantities—and destroys the notion that irreconcilable contrasts exist in nature, or gaps which cannot be bridged over. Thus, in his letter to Arnaud, Leibnitz expresses it as his opinion that geometry, or the philosophy of space, forms a step to the philosophy of motion—i.e., of corporeal things—and the philosophy of motion a step to the philosophy of mind.
In Leibnitz (1884), 44-45. [The first sentence is reworded to better introduce the quotation. —Webmaster]
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Keep away from people who try to belittle your ambitions. Small people always do that, but the really great make you feel that you, too, can become great.
…...
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Laws are like Cobwebs, which may catch small Flies, but let Wasps and Hornets break through.
In 'A Tritical Essay Upon the Faculties of the Mind' (6 Aug 1707), collected in various volumes and editions, for example, The Works of J.S, D.D, D.S.P.D.: Volume 1: Miscellanies in Prose (1739), 173. An earlier, undated, fourth volume of Miscellanies gives the 6 Aug 1707 date the essay was written. The final Latin phrase can be translated as, “Can you help laughing, friends?” attributed to Horace.
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Man is a small thing, and the night is large and full of wonder.
In Plays of Gods and Men (1917), 102.
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Many billions of years will elapse before the smallest, youngest stars complete their nuclear burning and into white dwarfs. But with slow, agonizing finality perpetual night will surely fall.
In The Last Three Minutes: Conjectures About The Ultimate Fate Of The Universe (1994, 2008), 50.
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Many small make a great.
Quoting a proverb, in The Canterbury Tales (1860), 215.
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Many small strikes of a hammer will finally have as much effect as one very heavy blow.
From the original French, “Plusieurs petits coups de Marteau ne fassent enfin autant d’effet qu’vn fort grand coup,” in letter (11 Mar 1640) to Père Marin Mersenne (AT III 36), collected in Lettres de Mr Descartes (1659), Vol. 2, 211-212. English version by Webmaster using online resources. See context in longer quote that begins, “I have no doubt….” on the René Descartes Quotes page of this website.
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March 15th. Imperial Banquet for Welcoming the English Cruelty to Animals. MENU OF FOODS: VITAMIN A, Tin Sardines. VITAMIN B, Roasted Beef. VITAMIN C, Small Roasted Suckling Porks. VITAMIN D, Hot Sheep and Onions. VITAMIN E, Spiced Turkey. VITAMIN F, Sweet Puddings. VITAMIN G, Coffee. VITAMIN H, Jam.
In Black Mischief (1932), 1962 edn., 170.
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Mathematical discoveries, small or great … are never born of spontaneous generation. They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.
As given, without citation, in Eric Temple Bell, Men of Mathematics (1937), 548.
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Mr. Cayley, of whom it may be so truly said, whether the matter he takes in hand be great or small, "nihil tetigit quod non ornavit," …
In Philosophic Transactions of the Royal Society (1864), 17, 605. [“Nihil tetigit quod non ornavit” translates as “He touched nothing without embellishing it”. —Webmaster]
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My picture of the world is drawn in perspective and not like a model to scale. The foreground is occupied by human beings and the stars are all as small as three-penny bits. I don't really believe in astronomy, except as a complicated description of part of the course of human and possibly animal sensation. I apply my perspective not merely to space but also to time. In time the world will cool and everything will die; but that is a long time off still and its present value at compound discount is almost nothing.
From a paper read to the Apostles, a Cambridge discussion society (1925). In 'The Foundations of Mathematics' (1925), collected in Frank Plumpton Ramsey and D.H. Mellor (ed.), Philosophical Papers (1990), Epilogue, 249. Citation to the paper, in Nils-Eric Sahlin, The Philosophy of F.P. Ramsey (1990), 225.
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Myriad small ponds and streams would reflect the full glare of the sun for one or two seconds, then fade away as a new set of water surfaces came into the reflecting position. The effect was as if the land were covered with sparkling jewels.
…...
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Nature has but one plan of operation, invariably the same in the smallest things as well as in the largest, and so often do we see the smallest masses selected for use in Nature, that even enormous ones are built up solely by fitting these together. Indeed, all Nature’s efforts are devoted to uniting the smallest parts of our bodies in such a way that all things whatsoever, however diverse they may be, which coalesce in the structure of living things construct the parts by means of a sort of compendium.
'On the Developmental Process', in H. B. Adelmann (ed.), Marcello Malpighi and the Evolution of Embryology (1966), Vol. 2, 843.
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Nature, … in order to carry out the marvelous operations [that occur] in animals and plants has been pleased to construct their organized bodies with a very large number of machines, which are of necessity made up of extremely minute parts so shaped and situated as to form a marvelous organ, the structure and composition of which are usually invisible to the naked eye without the aid of a microscope. … Just as Nature deserves praise and admiration for making machines so small, so too the physician who observes them to the best of his ability is worthy of praise, not blame, for he must also correct and repair these machines as well as he can every time they get out of order.
'Reply to Doctor Sbaraglia' in Opera Posthuma (1697), in H. B. Adelmann (ed.), Marcello Malpighi and the Evolution of Embryology (1966), Vol. 1, 568.
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Neutrinos, they are very small
They have no charge and have no mass
And do not interact at all.
The earth is just a silly ball
To them, through which they simply pass,
Like dustmaids down a drafty hall
Or photons through a sheet of glass.
They snub the most exquisite gas,
Ignore the most substantial wall,
Cold-shoulder steel and sounding brass,
Insult the stallion in his stall,
And, scorning barriers of class,
Infiltrate you and me! Like tall
And painless guillotines, they fall
Down through our heads into the grass.
At night, they enter at Nepal
And pierce the lover and his lass
From underneath the bed—you call
It wonderful; I call it crass.
In poem 'Cosmic Gall', The New Yorker (17 Dec 1960). Collected in Telephone Poles and Other Poems (1964), 5. Note: In fact, about 1014 neutrinos from the Sun and 103 neutrinos in cosmic rays pass through our bodies each second. Neutrinos are now known to have a very small amount of mass, and they do interact (through the weak force).
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Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it is the only thing that ever has.
Although this quote is frequently seen, “the quotation does not appear in any of Mead’s published work, and may have first appeared in one of her public speeches, perhaps, some say, in her speech at the Earth Day celebration in 1970.” As stated by Nancy Lutkehaus, 'Margaret Mead: Public Anthropologist', Anthropology Now (Apr 2009), 1, No. 1, 34.
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Nothing is really small; whoever is open to the deep penetration of nature knows this.
Victor Hugo and Charles E. Wilbour (trans.), Les Misérables (1862), 41.
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Now when naturalists observe a close agreement in numerous small details of habits, tastes, and dispositions between two or more domestic races, or between nearly-allied natural forms, they use this fact as an argument that they are descended from a common progenitor who was thus endowed; and consequently that all should be classed under the same species. The same argument may be applied with much force to the races of man.
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One has a feeling that one has a kind of home in this timeless community of human beings that strive for truth ... I have always believed that Jesus meant by the Kingdom of God the small group scattered all through time of intellectually and ethically valuable people.
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One of the most curious and interesting reptiles which I met with in Borneo was a large tree-frog, which was brought me by one of the Chinese workmen. He assured me that he had seen it come down in a slanting direction from a high tree, as if it flew. On examining it, I found the toes very long and fully webbed to their very extremity, so that when expanded they offered a surface much larger than the body. The forelegs were also bordered by a membrane, and the body was capable of considerable inflation. The back and limbs were of a very deep shining green colour, the undersurface and the inner toes yellow, while the webs were black, rayed with yellow. The body was about four inches long, while the webs of each hind foot, when fully expanded, covered a surface of four square inches, and the webs of all the feet together about twelve square inches. As the extremities of the toes have dilated discs for adhesion, showing the creature to be a true tree frog, it is difficult to imagine that this immense membrane of the toes can be for the purpose of swimming only, and the account of the Chinaman, that it flew down from the tree, becomes more credible. This is, I believe, the first instance known of a “flying frog,” and it is very interesting to Darwinians as showing that the variability of the toes which have been already modified for purposes of swimming and adhesive climbing, have been taken advantage of to enable an allied species to pass through the air like the flying lizard. It would appear to be a new species of the genus Rhacophorus, which consists of several frogs of a much smaller size than this, and having the webs of the toes less developed.
Malay Archipelago
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Perseus and St. George. These dragon-slayers did not take lessons in dragon-slaying, nor do leaders of forlorn hopes generally rehearse their parts beforehand. Small things may be rehearsed, but the greatest are always do-or-die, neck-or-nothing matters.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 222.
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Quantum theory thus reveals a basic oneness of the universe. It shows that we cannot decompose the world into independently existing smallest units. As we penetrate into matter, nature does not show us any isolated “building blocks,” but rather appears as a complicated web of relations between the various parts of the whole. These relations always include the observer in an essential way. The human observer constitute the final link in the chain of observational processes, and the properties of any atomic object can be understood only in terms of the object’s interaction with the observer.
In The Tao of Physics (1975), 68.
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Quietly, like a night bird, floating, soaring, wingless.
We glide from shore to shore, curving and falling
but not quite touching;
Earth: a distant memory seen in an instant of repose,
crescent shaped, ethereal, beautiful,
I wonder which part is home, but I know it doesn’t matter . . .
the bond is there in my mind and memory;
Earth: a small, bubbly balloon hanging delicately
in the nothingness of space.
…...
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Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics. … The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible. … I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s Algebra published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.
In Presidential Address British Association for the Advancement of Science, Section A (1890), Nature, 42, 466.
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Researchers, with science as their authority, will be able to cut [animals] up, alive, into small pieces, drop them from a great height to see if they are shattered by the fall, or deprive them of sleep for sixteen days and nights continuously for the purposes of an iniquitous monograph... Animal trust, undeserved faith, when at last will you turn away from us? Shall we never tire of deceiving, betraying, tormenting animals before they cease to trust us?
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Returning now to the Malay Archipelago, we find that all the wide expanse of sea which divides Java, Sumatra, and Borneo from each other, and from Malacca and Siam, is so shallow that ships can anchor in any part of it, since it rarely exceeds forty fathoms in depth; and if we go as far as the line of a hundred fathoms, we shall include the Philippine Islands and Bali, east of Java. If, therefore, these islands have been separated from each other and the continent by subsidence of the intervening tracts of land, we should conclude that the separation has been comparatively recent, since the depth to which the land has subsided is so small. It is also to be remarked that the great chain of active volcanoes in Sumatra and Java furnishes us with a sufficient cause for such subsidence, since the enormous masses of matter they have thrown out would take away the foundations of the surrounding district; and this may be the true explanation of the often-noticed fact that volcanoes and volcanic chains are always near the sea. The subsidence they produce around them will, in time, make a sea, if one does not already exist.
Malay Archipelago
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Science is often regarded as the most objective and truth-directed of human enterprises, and since direct observation is supposed to be the favored route to factuality, many people equate respectable science with visual scrutiny–just the facts ma’am, and palpably before my eyes. But science is a battery of observational and inferential methods, all directed to the testing of propositions that can, in principle, be definitely proven false ... At all scales, from smallest to largest, quickest to slowest, many well-documented conclusions of science lie beyond the strictly limited domain of direct observation. No one has ever seen an electron or a black hole, the events of a picosecond or a geological eon.
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Scientific inquiry would thus he conceived of as analogous to terrestrial exploration, whose product—geography—yields results of continually smaller significance which fill in ever more minute gaps in our information. In such a view, later investigations yield findings of ever smaller importance, with each successive accretion making a relatively smaller contribution to what has already come to hand. The advance of science leads, step by diminished step, toward a fixed and final view of things.
In The Limits Of Science (1984, Rev. 1999), 67.
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Scientists like myself merely use their gifts to show up that which already exists, and we look small compared to the artists who create works of beauty out of themselves. If a good fairy came and offered me back my youth, asking me which gifts I would rather have, those to make visible a thing which exists but which no man has ever seen before, or the genius needed to create, in a style of architecture never imagined before, the great Town Hall in which we are dining tonight, I might be tempted to choose the latter.
Nobel Banquet Speech (10 Dec 1962).
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Since [World War I] we have seen the atomic age, the computer age, the space age, and the bio-engineering age, each as epochal as the Bronze Age, the Iron Age, the Renaissance and the Industrial Revolution. And all these have occurred in one generation. Man has stood on the moon and looked back on the earth, that small planet now reduced to a neighbourhood. But our material achievements have exceeded the managerial capacities of our human minds and institutions.
As quoted in Colin Bingham (ed.), Wit and Wisdom: A Public Affairs Miscellany (1982), 227.
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So far as modern science is concerned, we have to abandon completely the idea that by going into the realm of the small we shall reach the ultimate foundations of the universe. I believe we can abandon this idea without any regret. The universe is infinite in all directions, not only above us in the large but also below us in the small. If we start from our human scale of existence and explore the content of the universe further and further, we finally arrive, both in the large and in the small, at misty distances where first our senses and then even our concepts fail us.
To the German Society of Scientists and Physicists, Braunschweig, Germany (Sep 1896). As quoted in Anton Z. Capri, Quips, Quotes, and Quanta: An Anecdotal History of Physics (2011), 20. Wiechert was reporting his measurement of the mass of the moving particles in a cathode ray beam (electrons).
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Speaking of libraries: A big open-stack academic or public library is no small pleasure to work in. You’re, say, trying to do a piece on something in Nevada, and you go down to C Floor, deep in the earth, and out to what a miner would call a remote working face. You find 10995.497S just where the card catalog and the online computer thought it would be, but that is only the initial nick. The book you knew about has led you to others you did not know about. To the ceiling the shelves are loaded with books about Nevada. You pull them down, one at a time, and sit on the floor and look them over until you are sitting on a pile five feet high, at which point you are late home for dinner and you get up and walk away. It’s an incomparable boon to research, all that; but it is also a reason why there are almost no large open-stack libraries left in the world.
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Spontaneous generation, to put the matter simply, takes place in smaller plants, especially in those that are annuals and herbaceous. But still it occasionally occurs too in larger plants whenever there is rainy weather or some peculiar condition of air or soil; for thus it is said that the silphium sprang up in Libya when a murky and heavy sort of wet weather condition occurred, and that the timber growth which is now there has come from some similar reason or other; for it was not there in former times.
De Causis Plantarum 1.5.1, in Robert Ewing Dengler (trans.) Theophrastus: De Causis Plantarum Book One: Text, Critical Apparatus, Translation, and Commentary, (1927), 31.
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Statistical analysis in cases involving small numbers can be particularly helpful because on many occasions intuition can be highly misleading.
In essay 'Statistical Proof of Employment Discrimination', collected in Judith M. Tanur et al. (eds.), Statistics, a Guide to the Unknown (3rd ed., 1989), 83.
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Suddenly, from behind the rim of the moon, in long, slow-motion moments of immense majesty, there emerges a sparkling blue and white jewel, a light, delicate sky-blue sphere laced with slowly swirling veils of white, rising gradually like a small pearl in a thick sea of black mystery. It takes more than a moment to fully realize this is Earth . . . home.
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Suppose physics soon succeeds, as Stephen Hawking and a few other physicists hope and believe, in reducing physics to a single equation or a small set of equations that will “explain” all of nature’s fundamental laws. We can then ask the unanswerable question, "Why this set of equations?”
In Introduction, The Night Is Large: Collected Essays 1938-1995 (1996), xvii.
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Suppose then I want to give myself a little training in the art of reasoning; suppose I want to get out of the region of conjecture and probability, free myself from the difficult task of weighing evidence, and putting instances together to arrive at general propositions, and simply desire to know how to deal with my general propositions when I get them, and how to deduce right inferences from them; it is clear that I shall obtain this sort of discipline best in those departments of thought in which the first principles are unquestionably true. For in all our thinking, if we come to erroneous conclusions, we come to them either by accepting false premises to start with—in which case our reasoning, however good, will not save us from error; or by reasoning badly, in which case the data we start from may be perfectly sound, and yet our conclusions may be false. But in the mathematical or pure sciences,—geometry, arithmetic, algebra, trigonometry, the calculus of variations or of curves,— we know at least that there is not, and cannot be, error in our first principles, and we may therefore fasten our whole attention upon the processes. As mere exercises in logic, therefore, these sciences, based as they all are on primary truths relating to space and number, have always been supposed to furnish the most exact discipline. When Plato wrote over the portal of his school. “Let no one ignorant of geometry enter here,” he did not mean that questions relating to lines and surfaces would be discussed by his disciples. On the contrary, the topics to which he directed their attention were some of the deepest problems,— social, political, moral,—on which the mind could exercise itself. Plato and his followers tried to think out together conclusions respecting the being, the duty, and the destiny of man, and the relation in which he stood to the gods and to the unseen world. What had geometry to do with these things? Simply this: That a man whose mind has not undergone a rigorous training in systematic thinking, and in the art of drawing legitimate inferences from premises, was unfitted to enter on the discussion of these high topics; and that the sort of logical discipline which he needed was most likely to be obtained from geometry—the only mathematical science which in Plato’s time had been formulated and reduced to a system. And we in this country [England] have long acted on the same principle. Our future lawyers, clergy, and statesmen are expected at the University to learn a good deal about curves, and angles, and numbers and proportions; not because these subjects have the smallest relation to the needs of their lives, but because in the very act of learning them they are likely to acquire that habit of steadfast and accurate thinking, which is indispensable to success in all the pursuits of life.
In Lectures on Teaching (1906), 891-92.
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Taking … the mathematical faculty, probably fewer than one in a hundred really possess it, the great bulk of the population having no natural ability for the study, or feeling the slightest interest in it*. And if we attempt to measure the amount of variation in the faculty itself between a first-class mathematician and the ordinary run of people who find any kind of calculation confusing and altogether devoid of interest, it is probable that the former could not be estimated at less than a hundred times the latter, and perhaps a thousand times would more nearly measure the difference between them.
[* This is the estimate furnished me by two mathematical masters in one of our great public schools of the proportion of boys who have any special taste or capacity for mathematical studies. Many more, of course, can be drilled into a fair knowledge of elementary mathematics, but only this small proportion possess the natural faculty which renders it possible for them ever to rank high as mathematicians, to take any pleasure in it, or to do any original mathematical work.]
In Darwinism, chap. 15.
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The belief is growing on me that the disease is communicated by the bite of the mosquito. … She always injects a small quantity of fluid with her bite—what if the parasites get into the system in this manner.
Letter (27 May 1896) to Patrick Manson. In The Great Malaria Problem and Its Solution: From the Memoirs of Ronald Ross (1988), 72. Ross asked for Manson’s opinion; the ellipsis above, in full is: “What do you think?” As quoted in William Derek Foster, A History of Parasitology (1965), 173. (It was for this insight that Ross was awarded a Nobel Prize.)
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The Builder of this Universe was wise,
He plann’d all souls, all systems, planets, particles:
The Plan He shap'd all Worlds and Æons by,
Was—Heavens!—was thy small Nine-and-thirty Articles!
In 'Practical-Devotional', Past and Present, Book 2, Chap 15, collected in On Heroes, Hero-Worship and the Heroic in History (1840), 101. Note: “Nine-and-thirty Articles” of the Church of England.
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The condensed air becomes attached to [the metallic calx], and adheres little by little to the smallest of its particles: thus its weight increases from the beginning to the end: but when all is saturated, it can take up no more.
Jean Rey
The Increase in Weight of Tin and Lead on Calcination (1630), Alembic Club Reprint (1895), 52.
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The conscious life of the mind is of small importance in comparison with its unconscious life.
From original French, “La vie consciente de l’esprit ne représente qu’une bien faible part auprès de sa vie inconsciente,” in Psychologie des Foules (1895), 16. English text in The Crowd: A Study of the Popular Mind (1897), Book 1, Chap. 1, 7. [A closer translation could be: “The conscious life of the mind represents only a very small part of of his unconscious life.” —Webmaster]
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The created world is but a small parenthesis in eternity.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 7
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The dodo never had a chance. He seems to have been invented for the sole purpose of becoming extinct and that was all he was good for. … I’m not blaming the Dodo but he was a mess. He had an ugly face with a large hooked beak, a tail in the wrong place, wings too small … and a very prominent stomach.
In 'The Dodo', How to Become Extinct (1941), 163.
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The Earth is a very small stage in a vast cosmic arena. Think of the rivers of blood spilled by all those generals and emperors, so that, in glory and triumph, they could become the momentary masters of a fraction of a dot. Think of the endless cruelties visited by the inhabitants of one corner of this pixel on the scarcely distinguishable inhabitants of some other corner, how frequent their misunderstandings, how eager they are to kill one another, how fervent their hatreds.
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The earth is simply too small and fragile a basket for the human race to keep all its eggs in.
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The Earth was small, light blue, and so touchingly alone, our home that must be defended like a holy relic. The Earth was absolutely round. I believe I never knew what the word round meant until I saw Earth from space.
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The end of the eighteenth and the beginning of the nineteenth century were remarkable for the small amount of scientific movement going on in this country, especially in its more exact departments. ... Mathematics were at the last gasp, and Astronomy nearly so—I mean in those members of its frame which depend upon precise measurement and systematic calculation. The chilling torpor of routine had begun to spread itself over all those branches of Science which wanted the excitement of experimental research.
Quoted in Sophia Elizabeth De Morgan, Memoir of Augustus De Morgan (1882), 41
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The future of humanity is uncertain, even in the most prosperous countries, and the quality of life deteriorates; and yet I believe that what is being discovered about the infinitely large and the infinitely small is sufficient to absolve this end of the century and millennium. What a very few are acquiring in knowledge of the physical world will perhaps cause this period not to be judged as a pure return to barbarism.
In 'News from the Sky', Other People’s Trades (1989), 23-24.
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The great artifice of regarding small deviations from the truth as being the truth itself is at the same time the foundation of wit, where the whole thing would often collapse if we were to regard these deviations in a spirit of philosophical rigor.
Aphorism from Georg Christoph Lichtenberg and R.J. Hollingdale (trans.) 'Notebook A: 1765-1770', The Waste Books (1990), 4. Also seen translated as, “The great trick of regarding small departures from the truth as the truth itself—on which is founded the entire integral calculus—is also the basis of our witty speculations, where the whole thing would often collapse if we considered the departures with philosophical rigour,” for example, as quoted in FractalVision: Put Fractals to Work For You (1992), 5, citing Aphorisms: 1764-1799.
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The horrors of Vivisection have supplanted the solemnity, the thrilling fascination, of the old unetherized operation upon the human sufferer. Their recorded phenomena, stored away by the physiological inquisitor on dusty shelves, are mostly of as little present use to man as the knowledge of a new comet or of a tungstate of zirconium … —contemptibly small compared with the price paid for it in agony and torture.
From address to the Massachusetts Medical Society (7 Jun 1871), 'Medical Education in America', collected in Surgical Anaesthesia: Addresses, and Other Papers (1894, 1900), 309.
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The human mind delights in finding pattern–so much so that we often mistake coincidence or forced analogy for profound meaning. No other habit of thought lies so deeply within the soul of a small creature trying to make sense of a complex world not constructed for it.
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The known is finite, the unknown infinite; spiritually we find ourselves on a tiny island in the middle of a boundless ocean of the inexplicable. It is our task, from generation to generation, to drain a small amount of additional land.
As given in Herbert and W. Roesky and Klaud Möckel, translated from the original German by T.N. Mitchell and W.E. Russey, Chemical Curiosities: Spectacular Experiments and Inspired Quotes (1996), 212. It is a restatement of an original quote from concluding remarks to a chapter by Thomas Huxley, 'On the Reception of the ‘Origin of Species’', the last chapter in Charles Darwin and Francis Darwin (ed.), The Life and Letters of Charles Darwin (1887), Vol. 1, 557. Webmaster suggests, the original Huxley quote was translated for the original German text, and when that was translated for the English edition, the quote morphed into into the form above.
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The mathematically formulated laws of quantum theory show clearly that our ordinary intuitive concepts cannot be unambiguously applied to the smallest particles. All the words or concepts we use to describe ordinary physical objects, such as position, velocity, color, size, and so on, become indefinite and problematic if we try to use them of elementary particles.
In Across the Frontiers (1974), 114.
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The modern airplane creates a new geographical dimension. A navigable ocean of air blankets the whole surface of the globe. There are no distant places any longer: the world is small and the world is one.
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The most remarkable feature about the magnitude scale was that it worked at all and that it could be extended on a worldwide basis. It was originally envisaged as a rather rough-and-ready procedure by which we could grade earthquakes. We would have been happy if we could have assigned just three categories, large, medium, and small; the point is, we wanted to avoid personal judgments. It actually turned out to be quite a finely tuned scale.
From interview with Henry Spall, as in an abridged version of Earthquake Information Bulletin (Jan-Feb 1980), 12, No. 1, that is on the USGS website.
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The next difficulty is in the economical production of small lights by electricity. This is what is commonly meant by the phrase, ‘dividing the electric light.’ Up to the present time, and including Mr. Edison’s latest experiments, it appears that this involves an immense loss of efficiency. Next comes the difficulty of distributing on any large scale the immense electric currents which would be needed.
In 'A Scientific View of It: Prof. Henry Morton Not Sanguine About Edison’s Success', New York Times (28 Dec 1879), 1.
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The operative definition of an expert … someone who doesn’t make small mistakes.
In Seeing Red: Redshifts, Cosmology and Academic Science (1998), 274.
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The question is not whether “big is ugly,” “small is beautiful,” or technology is “appropriate.” It is whether technologists will be ready for the demanding, often frustrating task of working with critical laypeople to develop what is needed or whether th
Technology Review (Feb 1980).
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The realization that our small planet is only one of many worlds gives mankind the perspective it needs to realize sooner that our own world belongs to all of its creatures, that the Moon landing marks the end of our childhood as a race and the beginning of a newer and better civilization.
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The result of teaching small parts of a large number of subjects is the passive reception of disconnected ideas, not illuminated with any spark of vitality. Let the main ideas which are introduced into a child’s education be few and important, and let them be thrown into every combination possible.
In The Organisation of Thought: Educational and Scientific (1917), 5.
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The theory here developed is that mega-evolution normally occurs among small populations that become preadaptive and evolve continuously (without saltation, but at exceptionally rapid rates) to radically different ecological positions. The typical pattern involved is probably this: A large population is fragmented into numerous small isolated lines of descent. Within these, inadaptive differentiation and random fixation of mutations occur. Among many such inadaptive lines one or a few are preadaptive, i.e., some of their characters tend to fit them for available ecological stations quite different from those occupied by their immediate ancestors. Such groups are subjected to strong selection pressure and evolve rapidly in the further direction of adaptation to the new status. The very few lines that successfully achieve this perfected adaptation then become abundant and expand widely, at the same time becoming differentiated and specialized on lower levels within the broad new ecological zone.
Tempo and Mode in Evolution (1944), 123.
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The view of the Earth from the Moon fascinated me - a small disk, 240,000 miles away… Raging nationalistic interests, famines, wars, pestilence don’t show from that distance.
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Theories rarely arise as patient inferences forced by accumulated facts. Theories are mental constructs potentiated by complex external prods (including, in idealized cases, a commanding push from empirical reality) . But the prods often in clude dreams, quirks, and errors–just as we may obtain crucial bursts of energy from foodstuffs or pharmaceuticals of no objective or enduring value. Great truth can emerge from small error. Evolution is thrilling, liberating, and correct. And Macrauchenia is a litoptern.
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There are no small problems. Problems that appear small are large problems that are not understood
From Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad. (1897), as translated by Neely and Larry W. Swanson, in Advice for a Young Investigator (1999), 17.
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There is no absolute scale of size in the Universe, for it is boundless towards the great and also boundless towards the small.
As restated by D'Arcy Wentworth Thompson, in On Growth and Form (1917, 1959), 24. Note that Thompson does not uses quotation marks when he gives this as what “Oliver Heaviside used to say.”
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There is no more reason to believe that man descended from some inferior animal than there is to believe that a stately mansion has descended from a small cottage.
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There is no need to worry about mere size. We do not necessarily respect a fat man more than a thin man. Sir Isaac Newton was very much smaller than a hippopotamus, but we do not on that account value him less.
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There is no smallest among the small and no largest among the large; but always something still smaller and something still larger.
Quoted in Eli Maor, To Infinity and Beyond (1991), 2.
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There is the immense sea of energy ... a multidimensional implicate order, ... the entire universe of matter as we generally observe it is to be treated as a comparatively small pattern of excitation. This excitation pattern is relatively autonomous and gives rise to approximately recurrent, stable separable projections into a three-dimensional explicate order of manifestation, which is more or less equivalent to that of space as we commonly experience it.
Wholeness and the Implicate Order? (1981), 192.
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There may only be a small number of laws, which are self-consistent and which lead to complicated beings like ourselves. … And even if there is only one unique set of possible laws, it is only a set of equations. What is it that breathes fire into the equations and makes a universe for them to govern? Is the ultimate unified theory so compelling that it brings about its own existence?
Lecture (1987), 'The Origin of the Universe', collected in Black Holes And Baby Universes And Other Essays (1993), 99.
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Those individuals who give moral considerations a much greater weight than considerations of expediency represent a comparatively small minority, five percent of the people perhaps. But, In spite of their numerical inferiority, they play a major role in our society because theirs is the voice of the conscience of society.
In J. Robert Moskin, Morality in America (1966), 17. Otherwise unconfirmed in this form. Please contact webmaster if you know a primary print source.
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Throughout all of human history, we have taken, taken, taken, from the natural world. All creatures, however large or small, do this as a way of making a living. Humans, though, have gone way beyond what elephants have done to the planet or what birds or what any fish in the sea is capable of doing.
In interview with Pierce Nahigyan, 'Dr. Sylvia Earle: “We’re Literally Destroying The Systems That Keep Us Alive”', Huffington Post (6 Jan 2016).
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To pray without faith is to make a small fire while it is raining heavily.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 177
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To the east was our giant neighbor Makalu, unexplored and unclimbed, and even on top of Everest the mountaineering instinct was sufficient strong to cause me to spend some moments conjecturing as to whether a route up that mountain might not exist. Far away across the clouds the great bulk of Kangchenjunga loomed on the horizon. To the west, Cho Oyu, our old adversary from 1952, dominated the scene and we could see the great unexplored ranges of Nepal stretching off into the distance. The most important photograph, I felt, was a shot down the north ridge, showing the North Col and the old route that had been made famous by the struggles of those great climbers of the 1920s and 1930s. I had little hope of the results being particularly successful, as I had a lot of difficulty in holding the camera steady in my clumsy gloves, but I felt that they would at least serve as a record. After some ten minutes of this, I realized that I was becoming rather clumsy-fingered and slow-moving, so I quickly replaced my oxygen set and experience once more the stimulating effect of even a few liters of oxygen. Meanwhile, Tenzing had made a little hole in the snow and in it he placed small articles of food – a bar of chocolate, a packet of biscuits and a handful of lollies. Small offerings, indeed, but at least a token gifts to the gods that all devoted Buddhists believe have their home on this lofty summit. While we were together on the South Col two days before, Hunt had given me a small crucifix that he had asked me to take to the top. I, too, made a hole in the snow and placed the crucifix beside Tenzing’s gifts.
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University politics are vicious precisely because the stakes are so small.
Kissinger’s wording of an old academic saw. Variations of the same idea have been expressed by several other people. In Ralph Keyes, The Quote Verifier (2006), 1, Wallace Sayre is named as having been most prominent, with Sayre’s Law, “In any dispute the intensity of feeling is inversely proportional to the value of the stakes at issue—that is why academic politics are so bitter.”
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Walking home at night, I shine my flashlight up at the sky. I send billions of ... photons toward space. What is their destination? A tiny fraction will be absorbed by the air. An even smaller fraction will be intercepted by the surface of planets and stars. The vast majority ... will plod on forever. After some thousands of years they will leave our galaxy; after some millions of years they will leave our supercluster. They will wander through an even emptier, even colder realm. The universe is transparent in the direction of the future.
Atoms of Silence
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We all remember the fairy tales of science in our infancy, which played with the supposition that large animals could jump in the proportion of small ones. If an elephant were as strong as a grasshopper, he could (I suppose) spring clean out of the Zoological Gardens and alight trumpeting upon Primrose Hill. If a whale could leap from the water like a trout, perhaps men might look up and see one soaring above Yarmouth like the winged island of Laputa.
In Manalive (1912), 26.
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We are just beginning to understand how molecular reaction systems have found a way to “organize themselves”. We know that processes of this nature ultimately led to the life cycle, and that (for the time being?) Man with his central nervous system, i.e. his memory, his mind, and his soul, stands at the end of this development and feels compelled to understand this development. For this purpose he must penetrate into the smallest units of time and space, which also requires new ideas to make these familiar concepts from physics of service in understanding what has, right into our century, appeared to be beyond the confines of space and time.
Answering “Where Now?” as the conclusion of his Nobel Lecture (11 Dec 1967) on 'Immeasurably Fast Reactions', published in Nobel Lectures, Chemistry 1963-1970 (1972).
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What we do may be small, but it has a certain character of permanence and to have produced anything of the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men.
From Inaugural Lecture, Oxford (1920). Recalled in A Mathematician’s Apology (1940, 1967), 76.
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When the great truth accidentally revealed and experimentally confirmed is fully recognized, that this planet, with all its appalling immensity, is to electric currents virtually no more than a small metal ball and that by this fact many possibilities, ea
http://web.archive.org/web/20070109161311/http://www.knowprose.com/node/12961
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Who then understands the reciprocal flux and reflux of the infinitely great and the infinitely small, the echoing of causes in the abysses of being, and the avalanches of creation?
Victor Hugo and Charles E. Wilbour (trans.), Les Misérables (1862), 41.
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Who would believe that so small a space could contain the images of all the universe?
…...
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Whoopie! Man, that may have been a small one for Neil but that’s a long one for me.
(Commenting as the third man to step on the lunar surface, though of smaller stature, 5' 6", than Neil Armstrong.)
Spoken as Commander of the Apollo 12 lunar landing (1969). In British Broadcasting Corporation, The Listener (1969), 82, 729. On the previous Apollo 11 landing, Armstrong's famous remark had been "one small step for [a] man, one giant leap for mankind." At 5' 6", Conrad was six inches shorter than Armstrong.
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Why are atoms so small? ... Many examples have been devised to bring this fact home to an audience, none of them more impressive than the one used by Lord Kelvin: Suppose that you could mark the molecules in a glass of water, then pour the contents of the glass into the ocean and stir the latter thoroughly so as to distribute the marked molecules uniformly throughout the seven seas; if you then took a glass of water anywhere out of the ocean, you would find in it about a hundred of your marked molecules.
What is life?: the Physical Aspect of the Living Cell (1944). Collected in What is Life? with Mind And Matter & Autobiographical Sketches (1967, 1992), 6-7.
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You can’t see oxygen being generated by trees, carbon dioxide being taken up by trees, but we get that. We’re beginning to understand the importance of forests. But the ocean has its forests, too. They just happen to be very small. They’re very small in size but they’re very large in numbers.
In interview with Pierce Nahigyan, 'Dr. Sylvia Earle: “We’re Literally Destroying The Systems That Keep Us Alive”', Huffington Post (6 Jan 2016).
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[T]he small is great, the great is small; all is in equilibrium in necessity...
Victor Hugo and Charles E. Wilbour (trans.), Les Misérables (1862), 41.
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~~[Dubious]~~ I demonstrate by means of philosophy that the earth is round, and is inhabited on all sides; that it is insignificantly small, and is borne through the stars.
Included here to add a caution. As quoted in Paul Lyle, The Abyss of Time: A Study in Geological Time and Earth History (2015), 38, citing Astronomia Nova (1609). Webmaster has not yet been able to find in a primary source, so cannot vouch for this quote. Can you help?
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…forcing automakers to sell smaller cars to improve fuel economy [is like]… fighting the nation’s obesity problem by forcing clothing manufacturers to sell garments in only small sizes.
Bob Lutz
…...
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…small, yet they are extremely wise: Ants are creatures of little strength, yet they store up their food in the summer…
Bible
In Proverbs, 'Sayings of Agur', Ch. 30, v.24-25 in The Bible: New International Version (2001), 364.
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“True is it, my incorporate friends,” quoth he, “That I receive the general food at first, Which you do live upon; and fit it is, Because I am the storehouse and the shop Of the whole body. But, if you do remember, I send it through the rivers of your blood, Even to the court, the heart, to th’ seat o’ th’ brain; And, through the cranks and offices of man, The strongest nerves and small inferior veins From me receive that natural competency Whereby they live. And though that all at once”— You, good friends, this says the belly, mark me.
[Told as a fable, this is the belly’s answer to a complaint from the other members of the body that it received all the food but did no work.] In Coriolanus (1623), Act 1, Scene 1, line 130-141. Webmaster’s note: The Fable of the Belly has its roots in antiquity. William Harvey delivered a lecture in Apr 1616 on his discovery the circulation of blood in the body, but did not publish until 1628.
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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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