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Who said: “Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed.”
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Die Gewohnheit einer Meinung erzeugt oft völlige Ueberzeugung von ihrer Richtigkeit, sie verbirgt die schwächeren Theile davon, und macht uns unfähig, die Beweise dagegen anzunehmen.
The habit of an opinion often leads to the complete conviction of its truth, it hides the weaker parts of it, and makes us incapable of accepting the proofs against it.
(1827). German text in Ira Freund, The Study of Chemical Composition (1904), 31. Translated form in Carl Schorlemmer, The Rise and Development of Organic Chemistry (1894), 49.
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Dieu, c'est le voile mystérieux sous lequel nous cachons notre ignorance de la cause première.
God is the mysterious veil under which we hide our ignorance of the cause.
In Recueil d'Œuvres de Léo Errera: Botanique Générale (1908), 193. Google translation by Webmaster.
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phusis kruptesthai philei
Nature loves to hide.
Sentence Fragment 123. Themistius, Orations 5.69b . As translated in Presocratic Reflexivity: The Construction of Philosophical Discourse (1996), 234.
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A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.
In Mathematical Problems', Bulletin American Mathematical Society, 8, 438.
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John Ray quote: A multitude of words doth rather obscure than illustrate, they being a burden to the memory, and the first apt t
A multitude of words doth rather obscure than illustrate, they being a burden to the memory, and the first apt to be forgotten, before we come to the last. So that he that uses many words for the explaining of any subject, doth, like the cuttle-fish, hide himself, for the most part, in his own ink.
John Ray
The Wisdom of God Manifested in the Works of the Creation (1691).
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All things are hidden, obscure and debatable if the cause of the phenomena is unknown, but everything is clear if its cause be known.
In Louis Pasteur and Harold Clarence Ernst (trans), The Germ Theory and Its Application to Medicine and Surgery, Chap. 2. Reprinted in Charles W. Eliot (ed.), The Harvard Classics: Scientific Papers: Physiology, Medicine, Surgery, Geology (1897, 1910), Vol. 38, 384. Cited as read before French Academy of Science (20 Apr 1878), published in Comptes Rendus de l’Académie des Sciences, 84, 1037-43.
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Any fool can destroy trees. They cannot run away; and if they could, they would still be destroyed,—chased and hunted down as long as fun or a dollar could be got out of their bark hides, branching horns, or magnificent bole backbones. Few that fell trees plant them; nor would planting avail much towards getting back anything like the noble primeval forests. During a man’s life only saplings can be grown, in the place of the old trees—tens of centuries old—that have been destroyed.
John Muir
In 'The American Forests', Atlantic Monthly (Aug 1897), Vol. 80, 157.
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But for the persistence of a student of this university in urging upon me his desire to study with me the modern algebra I should never have been led into this investigation; and the new facts and principles which I have discovered in regard to it (important facts, I believe), would, so far as I am concerned, have remained still hidden in the womb of time. In vain I represented to this inquisitive student that he would do better to take up some other subject lying less off the beaten track of study, such as the higher parts of the calculus or elliptic functions, or the theory of substitutions, or I wot not what besides. He stuck with perfect respectfulness, but with invincible pertinacity, to his point. He would have the new algebra (Heaven knows where he had heard about it, for it is almost unknown in this continent), that or nothing. I was obliged to yield, and what was the consequence? In trying to throw light upon an obscure explanation in our text-book, my brain took fire, I plunged with re-quickened zeal into a subject which I had for years abandoned, and found food for thoughts which have engaged my attention for a considerable time past, and will probably occupy all my powers of contemplation advantageously for several months to come.
In Johns Hopkins Commemoration Day Address, Collected Mathematical Papers, Vol. 3, 76.
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Civilized people can talk about anything. For them no subject is taboo…. In civilized societies there will be no intellectual bogeys at sight of which great grown-up babies are expected to hide their eyes
In Civilization: An Essay (1928), 138.
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Even on the most solemn occasions I got away without wearing socks and hid that lack of civilisation in high boots.
…...
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Exits sun; enters moon.
This moon is never alone.
Stars are seen all around.
These twinklers do not make a sound.
The tiny ones shine from their place.
Mother moon watches with a smiling face.
Its light is soothing to the eyes.
Night’s darkness hides its face.
Cool and calm is its light.
Heat and sweat are never felt.
Some days, moon is not seen.
Makes kids wonder, where had it been?
Partial eclipse shades the moon.
In summers it does not arrive soon.
Beautiful is this milky ball.
It is the love of one and all.
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Genius knows where the questions are hidden
City Aphorisms, Fourth Selection (1987).
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Hide not your talents, they for use were made. What’s a sundial in the shade?
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I do hate sums. There is no greater mistake than to call arithmetic an exact science. There are permutations and aberrations discernible to minds entirely noble like mine; subtle variations which ordinary accountants fail to discover; hidden laws of number which it requires a mind like mine to perceive. For instance, if you add a sum from the bottom up, and then from the top down, the result is always different. Again if you multiply a number by another number before you have had your tea, and then again after, the product will be different. It is also remarkable that the Post-tea product is more likely to agree with other people’s calculations than the Pre-tea result.
Letter to Mrs Arthur Severn (Jul 1878), collected in The Letters of a Noble Woman (Mrs. La Touche of Harristown) (1908), 50. Also in 'Gleanings Far and Near', Mathematical Gazette (May 1924), 12, 95.
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I prefer the spagyric chemical physicians, for they do not consort with loafers or go about gorgeous in satins, silks and velvets, gold rings on their fingers, silver daggers hanging at their sides and white gloves on their hands, but they tend their work at the fire patiently day and night. They do not go promenading, but seek their recreation in the laboratory, wear plain learthern dress and aprons of hide upon which to wipe their hands, thrust their fingers amongst the coals, into dirt and rubbish and not into golden rings. They are sooty and dirty like the smiths and charcoal burners, and hence make little show, make not many words and gossip with their patients, do not highly praise their own remedies, for they well know that the work must praise the master, not the master praise his work. They well know that words and chatter do not help the sick nor cure them... Therefore they let such things alone and busy themselves with working with their fires and learning the steps of alchemy. These are distillation, solution, putrefaction, extraction, calcination, reverberation, sublimination, fixation, separation, reduction, coagulation, tinction, etc.
Quoted in R. Oesper, The Human Side of Scientists (1975), 150. [Spagyric is a form of herbalism based on alchemic procedures of preparation.]
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If in physics there’s something you don’t understand, you can always hide behind the uncharted depths of nature. You can always blame God. You didn’t make it so complex yourself. But if your program doesn’t work, there is no one to hide behind. You cannot hide behind an obstinate nature. If it doesn’t work, you’ve messed up.
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If the doctor cures, the sun sees it; but if he kills, the earth hides it.
In John Wade, Select Proverbs of all Nations (1824), 124.
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If they needed to, twenty-five furtive cells could hide under this period.
In The Center of Life: A Natural History of the Cell (1977, 1978), 8.
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In natural history, great discovery often requires a map to a hidden mine filled with gems then easily gathered by conventional tools, not a shiny new space-age machine for penetrating previously inaccessible worlds.
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In teaching man, experimental science results in lessening his pride more and more by proving to him every day that primary causes, like the objective reality of things, will be hidden from him forever and that he can only know relations.
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In the end, science as we know it has two basic types of practitioners. One is the educated man who still has a controlled sense of wonder before the universal mystery, whether it hides in a snail’s eye or within the light that impinges on that delicate organ. The second kind of observer is the extreme reductionist who is so busy stripping things apart that the tremendous mystery has been reduced to a trifle, to intangibles not worth troubling one’s head about.
In 'Science and the Sense of the Holy,' The Star Thrower (1978), 190.
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In this physical world there is no real chaos; all is in fact orderly; all is ordered by the physical principles. Chaos is but unperceived order- it is a word indicating the limitations of the human mind and the paucity of observational facts. The words “chaos,” “accidental,” “chance,” “unpredictable," are conveniences behind which we hide our ignorance.
From Of Stars and Men: The Human Response to an Expanding Universe (1958 Rev. Ed. 1964), Foreword.
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Is it in Time to hide Eternity?
And why not in an Atom on the Shore,
To cover Ocean? or a Mote, the Sun?
The Complaint: or, Night-Thoughts on Life, Death, and Immortality (1742, 1750), Night 6, 127. [A mote means a speck - Webmaster]
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It is hard to hide our genes completely. However devoted someone may be to the privacy of his genotype, others with enough curiosity and knowledge can draw conclusions from the phenotype he presents and from the traits of his relatives.
In The Lives to Come: the Genetic Revolution and Human Possibilities (1997), 127.
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It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
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It is now necessary to indicate more definitely the reason why mathematics not only carries conviction in itself, but also transmits conviction to the objects to which it is applied. The reason is found, first of all, in the perfect precision with which the elementary mathematical concepts are determined; in this respect each science must look to its own salvation .... But this is not all. As soon as human thought attempts long chains of conclusions, or difficult matters generally, there arises not only the danger of error but also the suspicion of error, because since all details cannot be surveyed with clearness at the same instant one must in the end be satisfied with a belief that nothing has been overlooked from the beginning. Every one knows how much this is the case even in arithmetic, the most elementary use of mathematics. No one would imagine that the higher parts of mathematics fare better in this respect; on the contrary, in more complicated conclusions the uncertainty and suspicion of hidden errors increases in rapid progression. How does mathematics manage to rid itself of this inconvenience which attaches to it in the highest degree? By making proofs more rigorous? By giving new rules according to which the old rules shall be applied? Not in the least. A very great uncertainty continues to attach to the result of each single computation. But there are checks. In the realm of mathematics each point may be reached by a hundred different ways; and if each of a hundred ways leads to the same point, one may be sure that the right point has been reached. A calculation without a check is as good as none. Just so it is with every isolated proof in any speculative science whatever; the proof may be ever so ingenious, and ever so perfectly true and correct, it will still fail to convince permanently. He will therefore be much deceived, who, in metaphysics, or in psychology which depends on metaphysics, hopes to see his greatest care in the precise determination of the concepts and in the logical conclusions rewarded by conviction, much less by success in transmitting conviction to others. Not only must the conclusions support each other, without coercion or suspicion of subreption, but in all matters originating in experience, or judging concerning experience, the results of speculation must be verified by experience, not only superficially, but in countless special cases.
In Werke [Kehrbach] (1890), Bd. 5, 105. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 19.
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It may well be doubted whether, in all the range of Science, there is any field so fascinating to the explorer—so rich in hidden treasures—so fruitful in delightful surprises—as that of Pure Mathematics. The charm lies chiefly, I think, in the absolute certainty of its results: for that is what, beyond all mental treasures, the human intellect craves for. Let us only be sure of something! More light, more light … “And if our fate be death, give light and let us die” This is the cry that, through all the ages, is going up from perplexed Humanity, and Science has little else to offer, that will really meet the demands of its votaries, than the conclusions of Pure Mathematics.
Opening of 'Introduction', A New Theory of Parallels (1890), xv. As a non-fiction work, the author’s name on the title page of this book was Charles Lutwidge Dodgson. Being better known for his works of fiction as Lewis Carroll, all quotes relating to this one person, published under either name, are gathered on this single web page under his pen name.
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Keep your faith in all beautiful things; in the Sun when it is hidden, in the Spring when it is gone.
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Let truth be a banner big enough to hide the man who holds it up.
From chapter 'Jottings from a Note-Book', in Canadian Stories (1918), 169.
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Life is not a chain of events but an area—something spreading out from a hidden centre and welling at once toward all points of the compass.
The Gentle Art of Tramping (1926), 193.
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Nature hides her secret because of her essential loftiness, but not by means of ruse.
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Nature loves to hide.
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Never in its life has the sun seen shade,
Never in its life seen a shadow where it falls:
There, always there, in the sun-swept glade,
It lurks below the leaf; behind bodies, under walls,
Creeps, clings, hides. Be it millions, be it one—
The sun sees no shadow, and no shadow sees the sun.
Poem, as quoted in Arthur E. Shipley, Life: A Book for Elementary Students (1925, 2013), 31.
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Ode to Newton: Come celebrate with me in song the name Of Newton, to the Muses dear, for the Unlocked the hidden treasures of truth ... Nearer the gods no mortal may approach.
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Oh, how much is today hidden by science! Oh, how much it is expected to hide!
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One feature which will probably most impress the mathematician accustomed to the rapidity and directness secured by the generality of modern methods is the deliberation with which Archimedes approaches the solution of any one of his main problems. Yet this very characteristic, with its incidental effects, is calculated to excite the more admiration because the method suggests the tactics of some great strategist who foresees everything, eliminates everything not immediately conducive to the execution of his plan, masters every position in its order, and then suddenly (when the very elaboration of the scheme has almost obscured, in the mind of the spectator, its ultimate object) strikes the final blow. Thus we read in Archimedes proposition after proposition the bearing of which is not immediately obvious but which we find infallibly used later on; and we are led by such easy stages that the difficulties of the original problem, as presented at the outset, are scarcely appreciated. As Plutarch says: “It is not possible to find in geometry more difficult and troublesome questions, or more simple and lucid explanations.” But it is decidedly a rhetorical exaggeration when Plutarch goes on to say that we are deceived by the easiness of the successive steps into the belief that anyone could have discovered them for himself. On the contrary, the studied simplicity and the perfect finish of the treatises involve at the same time an element of mystery. Though each step depends on the preceding ones, we are left in the dark as to how they were suggested to Archimedes. There is, in fact, much truth in a remark by Wallis to the effect that he seems “as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results.” Wallis adds with equal reason that not only Archimedes but nearly all the ancients so hid away from posterity their method of Analysis (though it is certain that they had one) that more modern mathematicians found it easier to invent a new Analysis than to seek out the old.
In The Works of Archimedes (1897), Preface, vi.
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Reach high, for stars lie hidden in your soul. Dream deep, for every dream precedes the goal.
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Scientific principles and laws do not lie on the surface of nature. They are hidden, and must be wrested from nature by an active and elaborate technique of inquiry.
In Reconstruction in Philosophy (1920), 32.
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The candor of science is the glory of the modern. It does not hide and repress; it confronts, turns on the light.
In Specimen Days & Collect (1882), 302.
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The science of optics, like every other physical science, has two different directions of progress, which have been called the ascending and the descending scale, the inductive and the deductive method, the way of analysis and of synthesis. In every physical science, we must ascend from facts to laws, by the way of induction and analysis; and we must descend from laws to consequences, by the deductive and synthetic way. We must gather and group appearances, until the scientific imagination discerns their hidden law, and unity arises from variety; and then from unity must reduce variety, and force the discovered law to utter its revelations of the future.
In On a General Method of Expressing the Paths of Light, & of the Planets, by the Coefficients of a Characteristic Function (1833), 7-8. [The spelling as “groupe” in the original text, has her been corrected to “group” to avoid an intrusive “sic”.]
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The secret to creativity is knowing how to hide your sources.
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There are hidden contradictions in the minds of people who “love Nature” while deploring the “artificialities” with which “Man has spoiled ‘Nature.’” The obvious contradiction lies in their choice of words, which imply that Man and his artifacts are not part of “Nature”—but beavers and their dams are.
In Time Enough for Love: The Lives of Lazarus Long (1973), 263.
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There is a road in the hearts of all of us, hidden and seldom traveled, which leads to an unknown, secret place.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 249
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There is inherent in nature a hidden harmony that reflects itself in our minds under the image of simple mathematical laws. That then is the reason why events in nature are predictable by a combination of observation and mathematical analysis. Again and again in the history of physics this conviction, or should I say this dream, of harmony in nature has found fulfillments beyond our expectations.
…...
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Thou, Chemistry, do penetrate
With vision keen the bowels of earth,
Reveal what treasure Russia hides there… .
As quoted, without citation, in Isaac Asimov and Jason A. Shulman (eds.), Isaac Asimov’s Book of Science and Nature Quotations (1988), 45.
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To use Newton’s words, our efforts up till this moment have but turned over a pebble or shell here and there on the beach, with only a forlorn hope that under one of them was the gem we were seeking. Now we have the sieve, the minds, the hands, the time, and, particularly, the dedication to find those gems—no matter in which favorite hiding place the children of distant worlds have placed them.
[Co-author with Dava Sobel.]
In Frank Drake and Dava Sobel, Is Anyone Out There? (1993), 236.
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Trust in dreams, for in them is the hidden gate to eternity.
…...
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Truths are immortal, my dear friend; they are immortal like God! What we call a falsity is like a fruit; it has a certain number of days; it is bound to decay. Whereas, what we call truth is like gold; days, months, even centuries can hide gold, can overlook it but they can never make it decay.
From the play Galileo Galilei (2001) .
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What strange wonder is this? Our prayer to thee was for water,
Earth! What is this that thou now send’st from thy womb in reply?
In the abyss is there life ? Or hidden under the lava
Dwelleth some race now unknown? Does what hath fled e’er return?
Greeks and Romans, oh come! Oh, see the ancient Pompeii
Here is discover’d again,—Hercules’ town is rebuilt!
Beginning lines of poem, 'Pompeii and Herculaneum', in Edgar A. Bowring (trans.), The Poems of Schiller (1875), 237.
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When I am silent, I have thunder hidden inside.
Rumi
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 189
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Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be toward which the leading mathematical spirits of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought will the new centuries disclose?
Opening of Lecture (1900), 'Mathematische Probleme' (Mathematical Problems), to the International Congress of Mathematicians, Paris. From the original German reprinted in David Hilbert: Gesammelte Abhandlungen (Collected Treatises, 1970), Vol. 3. For full citation, see the quote that begins, “This conviction of the solvability…”, on the David Hilbert Quotes page on this website.
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[Overfishing—] it’s not just that we’re taking too many out, it’s how we’re doing it. We are wiping out their nurseries, … [because some huge boats] … bottom trawl … [with] nets that 50 years ago you’d have to lift when you came to coral reefs or rocks or nooks and crannies. Now they’re so sophisticated and so heavy, the equipment, and the boat’s so powerful they can just drag right over the coral reefs and the rocks and the nooks and crannies, and turn them into a gravel pit. … The trouble is those are the nurseries. That’s where the little fish hide and get bigger and get big enough for us to eat.
From transcript of PBS TV interview by Tavis Smiley (28 Mar 2011).
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“What makes the desert beautiful,” said the little prince, “is that somewhere it hides a well …”
The Little Prince. Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 5
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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