Celebrating 18 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “Dangerous... to take shelter under a tree, during a thunder-gust. It has been fatal to many, both men and beasts.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index S > Category: Sharpen

Sharpen Quotes (15 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.
…...
Science quotes on:  |  Axe (15)  |  Blunt (5)  |  Equally (25)  |  Impossible (108)  |  Instead (19)  |  Language (217)  |  Pencil (17)  |  Try (141)  |  Vain (29)

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.
…...
Science quotes on:  |  Anew (8)  |  Astonished (8)  |  Beauty (239)  |  Become (172)  |  Begin (106)  |  Characteristic (94)  |  Color (99)  |  Completely (32)  |  Different (178)  |  Differentiate (12)  |  Discover (196)  |  Elude (3)  |  Fine (33)  |  First (313)  |  Flight (63)  |  Gradually (21)  |  Half (56)  |  Homogeneous (5)  |  Indescribable (2)  |  Learn (281)  |  Month (31)  |  Nuance (4)  |  Ocean (148)  |  Part (220)  |  Perception (61)  |  Planet (262)  |  Rich (61)  |  Sea (187)  |  See (369)  |  Seem (143)  |  Shade (22)  |  Spread (33)  |  Surface (101)  |  Various (46)  |  Vision (94)

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.
Science quotes on:  |  Auxiliary (6)  |  Desire (140)  |  Disembodied (6)  |  Disinterest (6)  |  Knowledge (1293)  |  Life (1124)  |  Science And Art (181)

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.
Science quotes on:  |  Abstract (79)  |  Accomplishment (79)  |  Accumulate (26)  |  Addition (29)  |  Application (166)  |  Attention (115)  |  Author (61)  |  Base (71)  |  Basis (89)  |  Begin (106)  |  Bring (90)  |  Case (98)  |  Completely (32)  |  Conclusion (157)  |  Conviction (71)  |  Correct (83)  |  Course (83)  |  Danger (78)  |  Decade (32)  |  Development (276)  |  Difficult (116)  |  End (195)  |  Essential (115)  |  Exclusive (16)  |  Extent (49)  |  Extreme (54)  |  Follow (123)  |  Former (25)  |  Formerly (5)  |  Formulation (25)  |  Framework (20)  |  Gradual (26)  |  Grammar (13)  |  Harness (19)  |  High School (11)  |  Hold (92)  |  Implant (3)  |  Important (202)  |  Inclined (12)  |  Indispensable (27)  |  Inquire (9)  |  Instruction (72)  |  Interest (235)  |  Introduction (34)  |  Kernel (4)  |  Language (217)  |  Leave (127)  |  Logic (247)  |  Lose (93)  |  Majority (42)  |  Mastery (27)  |  Mathematics (1149)  |  Matter (340)  |  Middle (15)  |  Modern (159)  |  Need (283)  |  Outer (13)  |  Pendulum (15)  |  Permit (30)  |  Point (122)  |  Possible (155)  |  Premise (25)  |  Proper (36)  |  Psychological (12)  |  Purpose (193)  |  Pursue (21)  |  Quicken (7)  |  Reason (454)  |  Receive (59)  |  Recommend (7)  |  Rigid (12)  |  Secure (20)  |  Sense (315)  |  Set Aside (4)  |  Share (49)  |  Side (51)  |  Solid (50)  |  Starting Point (13)  |  Student (201)  |  Stunt (3)  |  Subject (235)  |  Success (248)  |  Swing (10)  |  Teach (179)  |  Teaching of Mathematics (31)  |  Tendency (54)  |  Think (341)  |  Transition (18)  |  True (201)  |  Understand (326)  |  Want (175)  |  Whole (189)  |  Wise (60)  |  World (892)  |  Young (98)

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.
Science quotes on:  |  Beak (4)  |  Bird (119)  |  Eternity (49)  |  Hundred (64)  |  Infinity (72)  |  Mile (39)  |  Mountain (145)  |  Pass (91)  |  Single (119)  |  Thousand (152)  |  Worn (5)  |  Year (299)

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.
Science quotes on:  |  Abstract (79)  |  Accomplishment (79)  |  Activity (128)  |  Aim (88)  |  Application (166)  |  Arouse (11)  |  Awaken (15)  |  Beauty (239)  |  Call (127)  |  Clear (97)  |  Command (27)  |  Complete (84)  |  Contend (6)  |  Decide (40)  |  Deep (121)  |  Doubt (159)  |  Edifice (15)  |  Equal (77)  |  Esthetic (3)  |  Ethical (13)  |  Feel (165)  |  Finally (26)  |  First (313)  |  High School (11)  |  Impulse (33)  |  Insight (69)  |  Instruction (72)  |  Interest (235)  |  Life (1124)  |  Mathematics (1149)  |  Neglect (33)  |  Opinion (176)  |  Penetration (18)  |  Philosophical (23)  |  Practical (129)  |  Provide (68)  |  Reference (33)  |  Scientific (232)  |  Structure (221)  |  Subject (235)  |  System (191)  |  Teaching of Mathematics (31)  |  Theory (690)  |  Together (77)  |  Toward (45)  |  Understand (326)  |  Value (240)

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.
Science quotes on:  |  Body (243)  |  Cure (96)  |  Defect (15)  |  Dull (31)  |  Eye (218)  |  Faculty (65)  |  Intellectual (120)  |  Posture (6)  |  Pure Mathematics (63)  |  Quick (13)  |  Remedy (54)  |  Tennis (7)  |  Value Of Mathematics (55)  |  Wit (35)

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.
Science quotes on:  |  Axiom (52)  |  Consequence (110)  |  Definition (191)  |  Deny (41)  |  Exact (64)  |  Excellent (26)  |  Geometry (215)  |  Habit (107)  |  Logic (247)  |  Methodical (7)  |  Mind (743)  |  Postulate (31)  |  Reasoning (95)  |  Refuse (23)  |  Strengthen (20)  |  Truth (914)  |  Value Of Mathematics (55)

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.
Science quotes on:  |  Ambition (34)  |  Danger (78)  |  Exalt (2)  |  Hatred (19)  |  Imagination (268)  |  Love (222)  |  Memory (105)  |  Powerful (66)  |  Spur (4)  |  Stimulant (3)  |  Wine (28)  |  Wit (35)

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.”)
Science quotes on:  |  Applicable (11)  |  Approximate (10)  |  Become (172)  |  Best (172)  |  Complete (84)  |  Expression (104)  |  Form (308)  |  Germany (12)  |  God (535)  |  Great (524)  |  Inorganic (12)  |  Knowledge (1293)  |  Language (217)  |  Mathematics (1149)  |  Matter (340)  |  Mediate (4)  |  Mind (743)  |  Nature (1211)  |  Need (283)  |  Organic (54)  |  Process (261)  |  Real (148)  |  School (117)  |  Simplify (11)  |  Speech (46)  |  Thought (536)  |  World (892)

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.
Science quotes on:  |  Book (257)  |  Disagree (11)  |  Good (345)  |  Wit (35)

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).
Science quotes on:  |  Ailment (6)  |  Apply (76)  |  Blade (9)  |  Book (257)  |  Business (84)  |  Calorie (2)  |  Clear (97)  |  Crank (13)  |  Cure (96)  |  Cut (39)  |  Decision (72)  |  Down (86)  |  Egypt (22)  |  Electronic (12)  |  Extrasensory Perception (2)  |  Foot (60)  |  Genuine (26)  |  Horoscope (4)  |  Indignation (4)  |  Lose (93)  |  Loud (9)  |  Media (9)  |  Model (80)  |  Moral (123)  |  Pet (8)  |  Plant (199)  |  Razor (4)  |  Right (196)  |  Rub (4)  |  Scientist (519)  |  Talk (99)  |  Thank (12)  |  Voice (50)  |  Weight (75)

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?
Science quotes on:  |  Data (120)  |  Fit (48)  |  Model (80)  |  Purpose (193)  |  Question (404)

There is no such whetstone, to sharpen a good wit and encourage a will to learning, as is praise.
The Schoolmaster (1570)
Science quotes on:  |  Encourage (24)  |  Good (345)  |  Learn (281)  |  Praise (25)  |  Whetstone (2)  |  Wit (35)

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.
Science quotes on:  |  Anchor (10)  |  Ballast (2)  |  Beauty (239)  |  Contemplation (51)  |  Credulous (3)  |  Difficulty (144)  |  Diligence (16)  |  Discipline (53)  |  Fortify (3)  |  Idea (577)  |  Investigate (65)  |  Knowledge (1293)  |  Labyrinth (9)  |  Lamp (16)  |  Maze (10)  |  Meditation (12)  |  Mind (743)  |  Nature (1211)  |  Philosophy (257)  |  Pleasure (130)  |  Prejudice (66)  |  Presumption (13)  |  Reason (454)  |  Scepticism (8)  |  Simplicity (146)  |  Spur (4)  |  Study (461)  |  Suffrage (4)  |  Truth (914)  |  Value Of Mathematics (55)  |  Vanity (19)  |  Whetstone (2)  |  Wit (35)


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
Quotations by:Albert EinsteinIsaac NewtonLord KelvinCharles DarwinSrinivasa RamanujanCarl SaganFlorence NightingaleThomas EdisonAristotleMarie CurieBenjamin FranklinWinston ChurchillGalileo GalileiSigmund FreudRobert BunsenLouis PasteurTheodore RooseveltAbraham LincolnRonald ReaganLeonardo DaVinciMichio KakuKarl PopperJohann GoetheRobert OppenheimerCharles Kettering  ... (more people)

Quotations about:Atomic  BombBiologyChemistryDeforestationEngineeringAnatomyAstronomyBacteriaBiochemistryBotanyConservationDinosaurEnvironmentFractalGeneticsGeologyHistory of ScienceInventionJupiterKnowledgeLoveMathematicsMeasurementMedicineNatural ResourceOrganic ChemistryPhysicsPhysicianQuantum TheoryResearchScience and ArtTeacherTechnologyUniverseVolcanoVirusWind PowerWomen ScientistsX-RaysYouthZoology  ... (more topics)
Sitewide search within all Today In Science History pages:
Visit our Science and Scientist Quotations index for more Science Quotes from archaeologists, biologists, chemists, geologists, inventors and inventions, mathematicians, physicists, pioneers in medicine, science events and technology.

Names index: | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

Categories index: | 1 | 2 | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



who invites your feedback
Thank you for sharing.
Today in Science History
Sign up for Newsletter
with quiz, quotes and more.