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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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Home > Category Index for Science Quotations > Category Index S > Category: Sharpen

Sharpen Quotes (22 quotes)

About the use of language: it is impossible to sharpen a pencil with a blunt axe. It is equally vain to try to do it with ten blunt axes instead.
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Although the ocean’s surface seems at first to be completely homogeneous, after half a month we began to differentiate various seas and even different parts of oceans by their characteristic shades. We were astonished to discover that, during an flight, you have to learn anew not only to look, but also to see. At first the finest nuances of color elude you, but gradually your vision sharpens and your color perception becomes richer, and the planet spreads out before you with all its indescribable beauty.
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Art includes everything that stimulates the desire to live; science, everything that sharpens the desire to know. Art, even the most disinterested, the most disembodied, is the auxiliary of life.
Rémy de Gourmont and Glenn Stephen Burne (ed.), Selected Writings (1966), 170.
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Bombs and pistols do not make a revolution. The sword of revolution is sharpened on the whetting-stone of ideas.
Quoted in India Today (Apr 2008), 33, No 16, as cited on webpage of Dhirubhai Ambani Institute of Information and Communication Technology.
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Each of us has read somewhere that in New Guinea pidgin the word for 'piano' is (I use English spelling) 'this fellow you hit teeth belonging to him he squeal all same pig'. I am inclined to doubt whether this expression is authentic; it looks just like the kind of thing a visitor to the Islands would facetiously invent. But I accept 'cut grass belong head belong me' for 'haircut' as genuine... Such phrases seem very funny to us, and make us feel very superior to the ignorant foreigners who use long winded expressions for simple matters. And then it is our turn to name quite a simple thing, a small uncomplicated molecule consisting of nothing more than a measly 11 carbons, seven hydrogens, one nitrogen and six oxygens. We sharpen our pencils, consult our rule books and at last come up with 3-[(1, 3- dihydro-1, 3-dioxo-2H-isoindol-2-yl) oxy]-3-oxopropanoic acid. A name like that could drive any self-respecting Papuan to piano-playing.
The Chemist's English (1990), 3rd Edition, 57.
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First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
In Ueber den Mathematischen Unterricht an den hoheren Schulen; Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 11, 131.
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High in the North in a land called Svithjod there is a mountain. It is a hundred miles long and a hundred miles high and once every thousand years a little bird comes to this mountain to sharpen its beak. When the mountain has thus been worn away a single day of eternity will have passed
In The Story of America (1921). As cited in David Blatner, Spectrums: Our Mind-boggling Universe from Infinitesimal to Infinity (2012), 24.
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I am of the decided opinion, that mathematical instruction must have for its first aim a deep penetration and complete command of abstract mathematical theory together with a clear insight into the structure of the system, and doubt not that the instruction which accomplishes this is valuable and interesting even if it neglects practical applications. If the instruction sharpens the understanding, if it arouses the scientific interest, whether mathematical or philosophical, if finally it calls into life an esthetic feeling for the beauty of a scientific edifice, the instruction will take on an ethical value as well, provided that with the interest it awakens also the impulse toward scientific activity. I contend, therefore, that even without reference to its applications mathematics in the high schools has a value equal to that of the other subjects of instruction.
In 'Ueber das Lehrziel im mathemalischen Unterricht der höheren Realanstalten', Jahresbericht der Deutschen Mathematiker Vereinigung, 2, 192. (The Annual Report of the German Mathematical Association. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 73.
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I took a good clear piece of Cork and with a Pen-knife sharpen'd as keen as a Razor, I cut a piece of it off, and thereby left the surface of it exceeding smooth, then examining it very diligently with a Microscope, me thought I could perceive it to appear a little porous; but I could not so plainly distinguish them, as to be sure that they were pores, much less what Figure they were of: But judging from the lightness and yielding quality of the Cork, that certainly the texture could not be so curious, but that possibly, if I could use some further diligence, I might find it to be discernable with a Microscope, I with the same sharp Penknife, cut off from the former smooth surface an exceeding thin piece of it with a deep plano-convex Glass, I could exceedingly plainly perceive it to be all perforated and porous, much like a Honey-comb, but that the pores of it were not regular; yet it was not unlike a Honey-comb in these particulars.
First, in that it had a very little solid substance, in comparison of the empty cavity that was contain'd between, ... for the Interstitia or walls (as I may so call them) or partitions of those pores were neer as thin in proportion to their pores as those thin films of Wax in a Honey-comb (which enclose and constitute the sexangular cells) are to theirs.
Next, in that these pores, or cells, were not very deep, but constituted of a great many little Boxes, separated out of one continued long pore, by certain Diaphragms...
I no sooner discerned these (which were indeed the first microscopical pores I ever saw, and perhaps, that were ever seen, for I had not met with any Writer or Person, that had made any mention of them before this) but me thought I had with the discovery of them, presently hinted to me the true and intelligible reason of all the Phænomena of Cork.
Micrographia, or some Physiological Descriptions of Minute Bodies made by Magnifying Glasses with Observations and Inquiries thereupon (1665), 112-6.
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In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it. So that as tennis is a game of no use in itself, but of great use in respect it maketh a quick eye and a body ready to put itself into all postures; so in the mathematics, that use which is collateral and intervenient is no less worthy than that which is principal and intended.
As translated in John Fauvel and Jeremy Gray (eds.) A History of Mathematics: A Reader (1987), 290-291. From De Augmentis, Book 3, The Advancement of Learning (1605), Book 2. Reprinted in The Two Books of Francis Bacon: Of the Proficience and Advancement of Learning, Divine and Human (2009), 97.
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It has been my misfortune never to have had any neighbours whose studies have led them towards the pursuit of natural knowledge; so that, for want of a companion to quicken my industry and sharpen my attention, I have made but slender progress in a kind of information to which I have been attached from my childhood.
In Letter to Thomas Pennant (4 Aug 1767), in The Natural History and Antiquities of Selborne (1789), 27.
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It hath been an old remark, that Geometry is an excellent Logic. And it must be owned that when the definitions are clear; when the postulata cannot be refused, nor the axioms denied; when from the distinct contemplation and comparison of figures, their properties are derived, by a perpetual well-connected chain of consequences, the objects being still kept in view, and the attention ever fixed upon them; there is acquired a habit of reasoning, close and exact and methodical; which habit strengthens and sharpens the mind, and being transferred to other subjects is of general use in the inquiry after truth.
In 'The Analyst', in The Works of George Berkeley (1898), Vol. 3, 10.
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Love is of all stimulants the most powerful. It sharpens the wits like danger, and the memory like hatred; it spurs the will like ambition; it exalts the imagination like hashish; it intoxicates like wine.
In novel, Debenham’s Vow (1870, publ. Hurst and Blackett), Vol. 1, 137. In later collections of quotations, the phrase about “imagination” is omitted, for example, in Maturin M. Ballou (ed.), Edge-Tools of Speech (1886), 284.
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Mathematics is the language of languages, the best school for sharpening thought and expression, is applicable to all processes in nature; and Germany needs mathematical gymnasia. Mathematics is God’s form of speech, and simplifies all things organic and inorganic. As knowledge becomes real, complete and great it approximates mathematical forms. It mediates between the worlds of mind and of matter.
Summarizing the ideas presented by Christian Heinrich Dillmann in Die Mathematik die Fackelträgerin einer neuen Zeit (1889). From book review, 'Recent Literature on Arithmetic and Arithmetical Teaching', in Granville Stanley Hall (ed.), The Pedagogical Seminary (1892), 2, 168. Dillmann’s book title translates as “Mathematics the Torchbearer of a New Era”. (However, Conant concluded that it was a “loosely-written, vague and incoherent book, which belies every anticipation awakened by its attractive title.”)
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Science is a game—but a game with reality, a game with sharpened knives … If a man cuts a picture carefully into 1000 pieces, you solve the puzzle when you reassemble the pieces into a picture; in the success or failure, both your intelligences compete. In the presentation of a scientific problem, the other player is the good Lord. He has not only set the problem but also has devised the rules of the game—but they are not completely known, half of them are left for you to discover or to deduce. The experiment is the tempered blade which you wield with success against the spirits of darkness—or which defeats you shamefully. The uncertainty is how many of the rules God himself has permanently ordained, and how many apparently are caused by your own mental inertia, while the solution generally becomes possible only through freedom from its limitations.
Quoted in Walter Moore, Schrödinger: Life and Thought (1989), 348.
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Some books are like grindstones, good to sharpen your wits on just because you disagree from them.
Concluding remark in book review, no author credit, 'Dubois’s “Influence of Mind on Body”', The American Journal of Clinical Medicine (Jan 1907), 14, No. 1, 115. Also as filler on p.150 of the Feb 1907 issue, credited to E. M. Epstein.
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Thanks to the freedom of our press and the electronic media, the voices of cranks are often louder and clearer than the voices of genuine scientists. Crank books—on how to lose weight without cutting down on calories, on how to talk to plants, on how to cure your ailments by rubbing your feet, on how to apply horoscopes to your pets, on how to use ESP in making business decisions, on how to sharpen razor blades by putting them under little models of the great Pyramid of Egypt—far outsell many books… I reserve the right of moral indignation.
As quoted, without citation, in obituary by Morton Schatzman, 'Martin Gardner: Scientific and Philosophical Writer Celebrated for his Ingenious Mathematical Puzzles and Games', Independent (28 May 2010).
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The bird which is drawn to the water by its need of finding there the prey on which it lives, separates the digits of its feet in trying to strike the water and move about on the surface. The skin which unites these digits at their base acquires the habit of being stretched by these continually repeated separations of the digits; thus in course of time there are formed large webs which unite the digits of ducks, geese, etc., as we actually find them. In the same way efforts to swim, that is to push against the water so as to move about in it, have stretched the membranes between the digits of frogs, sea-tortoises, the otter, beaver, etc.
On the other hand, a bird which is accustomed to perch on trees and which springs from individuals all of whom had acquired this habit, necessarily has longer digits on its feet and differently shaped from those of the aquatic animals that I have just named. Its claws in time become lengthened, sharpened and curved into hooks, to clasp the branches on which the animal so often rests.
We find in the same way that the bird of the water-side which does not like swimming and yet is in need of going to the water's edge to secure its prey, is continually liable to sink into the mud. Now this bird tries to act in such a way that its body should not be immersed in the liquid, and hence makes its best efforts to stretch and lengthen its legs. The long-established habit acquired by this bird and all its race of continually stretching and lengthening its legs, results in the individuals of this race becoming raised as though on stilts, and gradually obtaining long, bare legs, denuded of feathers up to the thighs and often higher still.
Philosophie Zoologique (1809), Vol. 1, 249-50, trans. Hugh Elliot (1914), 119-20.
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The purpose of models is not to fit the data but to sharpen the questions.
Quoted in several several sources as from “11th R.A. Fisher Memorial Lecture, to the Royal Society (20 April 1983)”. For example, see Alan L. Mackay, A Dictionary of Scientific Quotations (1991), 138. However, Webmaster has read, and searched, but cannot find such words in the printed record in 'The Eleventh R. A. Fisher Memorial Lecture: Kin Selection and Altruism', in S. Karlin and C. Matessi, Proceedings of the Royal Society of London. Series B, Biological Sciences (22 Oct 1983), 219, No. 1216, Mathematical Genetics, 327-353. So, as yet, although the article does discuss various models relevant to the titled subject, Webmaster cannot document a verification of this quote. Perhaps it was a verbal comment spoken from the podium, but not included in the printed prepared lecture? Perplexing. Can you help?
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The solution of fallacies, which give rise to absurdities, should be to him who is not a first beginner in mathematics an excellent means of testing for a proper intelligible insight into mathematical truth, of sharpening the wit, and of confining the judgment and reason within strictly orderly limits
In 'Vorwort', Mathematische Sophismen (1864), 3. As translated and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-Book (1914), 89. From the original German, “Das Aufsuchen der Trugschlüsse, durch welche Ungereimtheiten entstellen, dürfte nun für den nicht ganz ersten Anfänger in der Mathematik ein vorzügliches Mittel sein, eine richtige begriffliche Einsicht in die mathematischen Wahrheiten zu erproben, den Verstand zu schärfen und das Urtheilen und Schliessen in streng geregelte Grenzen zu dämmen.”
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There is no such whetstone, to sharpen a good wit and encourage a will to learning, as is praise.
The Schoolmaster (1570)
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These Disciplines [mathematics] serve to inure and corroborate the Mind to a constant Diligence in Study; to undergo the Trouble of an attentive Meditation, and cheerfully contend with such Difficulties as lie in the Way. They wholly deliver us from a credulous Simplicity, most strongly fortify us against the Vanity of Scepticism, effectually restrain from a rash Presumption, most easily incline us to a due Assent, perfectly subject us to the Government of right Reason, and inspire us with Resolution to wrestle against the unjust Tyranny of false Prejudices. If the Fancy be unstable and fluctuating, it is to be poized by this Ballast, and steadied by this Anchor, if the Wit be blunt it is sharpened upon this Whetstone; if luxuriant it is pared by this Knife; if headstrong it is restrained by this Bridle; and if dull it is rouzed by this Spur. The Steps are guided by no Lamp more clearly through the dark Mazes of Nature, by no Thread more surely through the intricate Labyrinths of Philosophy, nor lastly is the Bottom of Truth sounded more happily by any other Line. I will not mention how plentiful a Stock of Knowledge the Mind is furnished from these, with what wholesome Food it is nourished, and what sincere Pleasure it enjoys. But if I speak farther, I shall neither be the only Person, nor the first, who affirms it; that while the Mind is abstracted and elevated from sensible Matter, distinctly views pure Forms, conceives the Beauty of Ideas, and investigates the Harmony of Proportions; the Manners themselves are sensibly corrected and improved, the Affections composed and rectified, the Fancy calmed and settled, and the Understanding raised and excited to more divine Contemplations. All which I might defend by Authority, and confirm by the Suffrages of the greatest Philosophers.
Prefatory Oration in Mathematical Lectures (1734), xxxi.
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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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