TODAY IN SCIENCE HISTORY ®  •  TODAYINSCI ®
Celebrating 24 Years on the Web
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “Science without religion is lame; religion without science is blind.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index T > Category: Tangent

Tangent Quotes (6 quotes)

Curves that have no tangents are the rule. … Those who hear of curves without tangents, or of functions without derivatives, often think at first that Nature presents no such complications. … The contrary however is true. … Consider, for instance, one of the white flakes that are obtained by salting a solution of soap. At a distance its contour may appear sharply defined, but as we draw nearer its sharpness disappears. The eye can no longer draw a tangent at any point. … The use of a magnifying glass or microscope leaves us just as uncertain, for fresh irregularities appear every time we increase the magnification. … An essential characteristic of our flake … is that we suspect … that any scale involves details that absolutely prohibit the fixing of a tangent.
(1906). As quoted “in free translation” in Benoit B. Mandelbrot, The Fractal Geometry of Nature (1977, 1983), 7.
Science quotes on:  |  Absolutely (41)  |  Appear (122)  |  Characteristic (154)  |  Complication (30)  |  Consider (428)  |  Contour (3)  |  Contrary (143)  |  Curve (49)  |  Defined (4)  |  Derivative (6)  |  Detail (150)  |  Disappear (84)  |  Distance (171)  |  Draw (140)  |  Essential (210)  |  Eye (440)  |  First (1302)  |  Fixing (2)  |  Flake (7)  |  Fresh (69)  |  Function (235)  |  Glass (94)  |  Hear (144)  |  Increase (225)  |  Involve (93)  |  Irregularity (12)  |  Magnification (10)  |  Magnifying Glass (3)  |  Microscope (85)  |  Nature (2017)  |  Nearer (45)  |  Obtain (164)  |  Point (584)  |  Present (630)  |  Prohibit (3)  |  Rule (307)  |  Scale (122)  |  Sharply (4)  |  Sharpness (9)  |  Soap (11)  |  Solution (282)  |  Suspect (18)  |  Think (1122)  |  Time (1911)  |  Uncertain (45)  |  Use (771)  |  White (132)

If, for example, I had some idea, which, as it turned out would, say, be quite wrong, was going off of the tangent, Watson would tell me in no uncertain terms this was nonsense, and vice-versa. If he had some idea I didn’t like and I would say so and this would shake his thinking about it and draw him back again. And in fact, it’s one of the requirements for collaboration of this sort that you must be perfectly candid, one might almost say rude, to the person you are working with. It’s useless, working with somebody who’s either much too junior than yourself, or much too senior, because then politeness creeps in. And this is the end of all real collaboration in science.
As quoted in Robert Olby, The Path to the Double Helix: The Discovery of the Double Helix, (1974, 1994), 316, citing Transcript of BBC TV program, The Prizewinners (1962).
Science quotes on:  |  Back (395)  |  Candid (3)  |  Collaboration (16)  |  Creep (15)  |  Draw (140)  |  End (603)  |  Fact (1257)  |  Idea (881)  |  Junior (6)  |  Must (1525)  |  Nonsense (48)  |  Person (366)  |  Politeness (4)  |  Real (159)  |  Requirement (66)  |  Rude (6)  |  Say (989)  |  Senior (7)  |  Shake (43)  |  Tell (344)  |  Term (357)  |  Terms (184)  |  Thinking (425)  |  Turn (454)  |  Uncertain (45)  |  Useless (38)  |  Vice (42)  |  James Watson (33)  |  Working (23)  |  Wrong (246)

In the beginning of the year 1665 I found the Method of approximating series & the Rule for reducing any dignity of any Bionomial into such a series. The same year in May I found the method of Tangents of Gregory & Slusius, & in November had the direct method of fluxions & the next year in January had the Theory of Colours & in May following I had entrance into ye inverse method of fluxions. And the same year I began to think of gravity extending to ye orb of the Moon & (having found out how to estimate the force with wch [a] globe revolving within a sphere presses the surface of the sphere) from Keplers rule of the periodic times of the Planets being in sesquialterate proportion of their distances from the center of their Orbs, I deduced that the forces wch keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about wch they revolve: & thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, & found them answer pretty nearly. All this was in the two plague years of 1665-1666. For in those days I was in the prime of my age for invention & minded Mathematicks & Philosophy more then than at any time since.
Quoted in Richard Westfall, Never at Rest: A Biography of Isaac Newton (1980), 143.
Science quotes on:  |  Age (509)  |  Answer (389)  |  Beginning (312)  |  Being (1276)  |  Binomial (6)  |  Calculus (65)  |  Color (155)  |  Differentiation (28)  |  Dignity (44)  |  Direct (228)  |  Distance (171)  |  Earth (1076)  |  Entrance (16)  |  Estimate (59)  |  Fluxion (7)  |  Force (497)  |  Gravity (140)  |  Invention (400)  |  Inverse Square Law (5)  |  Johannes Kepler (95)  |  Law Of Gravity (16)  |  Method (531)  |  Mind (1377)  |  Moon (252)  |  More (2558)  |  Must (1525)  |  Nearly (137)  |  Next (238)  |  Orb (20)  |  Orbit (85)  |  Philosophy (409)  |  Plague (42)  |  Planet (402)  |  Prime (11)  |  Proportion (140)  |  Revolve (26)  |  Rule (307)  |  Series (153)  |  Sphere (118)  |  Square (73)  |  Surface (223)  |  Surface Of The Earth (36)  |  Theory (1015)  |  Think (1122)  |  Time (1911)  |  Two (936)  |  Year (963)

Mathematics accomplishes really nothing outside of the realm of magnitude; marvellous, however, is the skill with which it masters magnitude wherever it finds it. We recall at once the network of lines which it has spun about heavens and earth; the system of lines to which azimuth and altitude, declination and right ascension, longitude and latitude are referred; those abscissas and ordinates, tangents and normals, circles of curvature and evolutes; those trigonometric and logarithmic functions which have been prepared in advance and await application. A look at this apparatus is sufficient to show that mathematicians are not magicians, but that everything is accomplished by natural means; one is rather impressed by the multitude of skilful machines, numerous witnesses of a manifold and intensely active industry, admirably fitted for the acquisition of true and lasting treasures.
In Werke [Kehrbach] (1890), Bd. 5, 101. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 13.
Science quotes on:  |  Accomplishment (102)  |  Acquisition (46)  |  Active (80)  |  Admirably (3)  |  Advance (298)  |  Altitude (5)  |  Apparatus (70)  |  Application (257)  |  Ascension (4)  |  Await (6)  |  Circle (117)  |  Curvature (8)  |  Earth (1076)  |  Everything (489)  |  Evolute (2)  |  Find (1014)  |  Fit (139)  |  Function (235)  |  Heaven (266)  |  Heavens (125)  |  Impress (66)  |  Impressed (39)  |  Industry (159)  |  Intense (22)  |  Latitude (6)  |  Line (100)  |  Logarithmic (5)  |  Longitude (8)  |  Look (584)  |  Machine (271)  |  Magician (15)  |  Magnitude (88)  |  Manifold (23)  |  Marvellous (25)  |  Master (182)  |  Mathematician (407)  |  Mathematics (1395)  |  Mean (810)  |  Means (587)  |  Multitude (50)  |  Natural (810)  |  Nature Of Mathematics (80)  |  Network (21)  |  Normal (29)  |  Nothing (1000)  |  Numerous (70)  |  Outside (141)  |  Prepare (44)  |  Really (77)  |  Realm (87)  |  Recall (11)  |  Refer (14)  |  Right (473)  |  Show (353)  |  Skill (116)  |  Skillful (17)  |  Spin (26)  |  Sufficient (133)  |  System (545)  |  Treasure (59)  |  Trigonometry (7)  |  True (239)  |  Wherever (51)  |  Witness (57)

Stay your rude steps, or e’er your feet invade
The Muses’ haunts,ye sons of War and Trade!
Nor you, ye legion fiends of Church and Law,
Pollute these pages with unhallow’d paw!
Debased, corrupted, grovelling, and confin’d,
No definitions touch your senseless mind;
To you no Postulates prefer their claim,
No ardent Axioms your dull souls inflame;
For you no Tangents touch, no Angles meet,
No Circles join in osculation sweet!
From poem, with co-authors John Hookham Frere, George Canning and George Ellis, The Loves of the Triangles: A Mathematical and Philosophical Poem, Canto I, collected in Poetry of the Anti-Jacobin (1854), 124.
Science quotes on:  |  Angle (25)  |  Axiom (65)  |  Church (64)  |  Circle (117)  |  Claim (154)  |  Definition (238)  |  Dull (58)  |  Law (913)  |  Legion (4)  |  Mind (1377)  |  Muse (10)  |  Postulate (42)  |  Soul (235)  |  Step (234)  |  Sweet (40)  |  Touch (146)  |  War (233)

Too many heretics are simply witch-hunters off on an unaccustomed tangent.
…...
Science quotes on:  |  Heretic (8)  |  Hunter (28)  |  Simply (53)


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 |
Thank you for sharing.
- 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


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