Celebrating 19 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index S > Category: Shortest

Shortest Quotes (16 quotes)

A closer look at the course followed by developing theory reveals for a start that it is by no means as continuous as one might expect, but full of breaks and at least apparently not along the shortest logical path. Certain methods often afforded the most handsome results only the other day, and many might well have thought that the development of science to infinity would consist in no more than their constant application. Instead, on the contrary, they suddenly reveal themselves as exhausted and the attempt is made to find other quite disparate methods. In that event there may develop a struggle between the followers of the old methods and those of the newer ones. The former's point of view will be termed by their opponents as out-dated and outworn, while its holders in turn belittle the innovators as corrupters of true classical science.
In 'On the Development of the Methods of Theoretical Physics in Recent Times', Populäre Schriften, Essay 14. Address (22 Sep 1899) to the Meeting of Natural Scientists at Munich. Collected in Brian McGuinness (ed.), Ludwig Boltzmann: Theoretical Physics and Philosophical Problems, Selected Writings (1974), 79.
Science quotes on:  |   (2863)  |  Application (242)  |  Attempt (251)  |  Break (99)  |  Certain (550)  |  Classical (45)  |  Closer (43)  |  Consist (223)  |  Constant (144)  |  Continuous (82)  |  Contrary (141)  |  Course (409)  |  Develop (268)  |  Development (422)  |  Event (216)  |  Expect (200)  |  Find (998)  |  Follow (378)  |  Former (137)  |  Handsome (4)  |  Infinity (90)  |  Look (582)  |  Mean (809)  |  Means (579)  |  Men Of Science (143)  |  Method (505)  |  Methods (204)  |  More (2559)  |  Most (1731)  |  Old (481)  |  Opponent (19)  |  Other (2236)  |  Path (144)  |  Point (580)  |  Point Of View (80)  |  Result (677)  |  Reveal (148)  |  Science (3879)  |  Start (221)  |  Struggle (105)  |  Suddenly (88)  |  Term (349)  |  Themselves (433)  |  Theory (970)  |  Thought (953)  |  Turn (447)  |  View (488)  |  Will (2355)

A million years is a short time—the shortest worth messing with for most problems. You begin tuning your mind to a time scale that is the planet’s time scale. For me, it is almost unconscious now and is a kind of companionship with the earth.
In Basin and Range (1981), 134.
Science quotes on:  |   (2863)  |  Begin (260)  |  Companionship (4)  |  Earth (996)  |  Kind (557)  |  Mess (13)  |  Million (114)  |  Mind (1338)  |  Most (1731)  |  Planet (356)  |  Problem (676)  |  Scale (121)  |  Short (197)  |  Time (1877)  |  Tune (19)  |  Unconscious (22)  |  Worth (169)  |  Year (933)

Between two truths of the real domain, the easiest and shortest path quite often passes through the complex domain.
From the French, “…entre deux vérités du domaine réel, le chemin le plus facile et le plus court passe bien souvent par le domaine complexe,” in Notice sur les Travaux Scientifiques (1900), 2. Widely seen incorrectly attributed to Hadamard, who quoted it himself as from an unnamed source, and paraphrased thus, “It has been written that the shortest path between two truths in the real domain passes through the complex domain,” in Jacques Hadamard, An Essay on the Psychology of Invention in the Mathematical Field (1945), 123. Now often seen misattributed to Hadamard in a shorter paraphrase, for example as, “The shortest path between two truths in the real domain passes through the complex domain,” in Craig Smorynski, 'The Need for Abstraction', The College Mathematics Journal (Jan 1985), 16, No. 1, 11. For a longer discussion of the Painlevé source, see homepage.math.uiowa.edu/~jorgen/hadamardquotesource.html, which is the source for the English translation in the subject quote.
Science quotes on:  |  Complex (188)  |  Domain (69)  |  Easy (204)  |  Often (106)  |  Pass (238)  |  Path (144)  |  Real (149)  |  Short (197)  |  Through (849)  |  Truth (1057)  |  Two (937)

First, In showing in how to avoid attempting impossibilities. Second, In securing us from important mistakes in attempting what is, in itself possible, by means either inadequate or actually opposed to the end in view. Thirdly, In enabling us to accomplish our ends in the easiest, shortest, most economical, and most effectual manner. Fourth, In inducing us to attempt, and enabling us to accomplish, object which, but for such knowledge, we should never have thought of understanding.
On the ways that a knowledge of the order of nature can be of use.
Quoted in Robert Routledge, Discoveries and Inventions of the 19th Century (1890), 665.
Science quotes on:  |  Attempt (251)  |  Avoid (116)  |  End (590)  |  First (1283)  |  Inadequate (19)  |  Knowledge (1529)  |  Mean (809)  |  Means (579)  |  Mistake (169)  |  Most (1731)  |  Nature (1926)  |  Never (1087)  |  Object (422)  |  Order (632)  |  Possible (552)  |  Thought (953)  |  Understanding (513)  |  Use (766)  |  View (488)  |  Way (1217)

For if as scientists we seek simplicity, then obviously we try the simplest surviving theory first, and retreat from it only when it proves false. Not this course, but any other, requires explanation. If you want to go somewhere quickly, and several alternate routes are equally likely to be open, no one asks why you take the shortest. The simplest theory is to be chosen not because it is the most likely to be true but because it is scientifically the most rewarding among equally likely alternatives. We aim at simplicity and hope for truth.
Problems and Projects (1972), 352.
Science quotes on:  |  Aim (165)  |  Ask (411)  |  Chosen (48)  |  Course (409)  |  Equally (130)  |  Explanation (234)  |  First (1283)  |  Hope (299)  |  Most (1731)  |  Open (274)  |  Other (2236)  |  Prove (250)  |  Require (219)  |  Scientific Method (175)  |  Scientist (820)  |  Seek (213)  |  Simplicity (167)  |  Theory (970)  |  Truth (1057)  |  Try (283)  |  Want (497)  |  Why (491)

I am paid by the word, so I always write the shortest words possible.
…...
Science quotes on:  |  Pay (43)  |  Possible (552)  |  Short (197)  |  Word (619)  |  Write (230)

In geologists’ own lives, the least effect of time is that they think in two languages, function on two different scales. … “A million years is a short time—the shortest worth messing with for most problems.”
In Basin and Range (1981), 134.
Science quotes on:  |  Different (577)  |  Effect (393)  |  Function (228)  |  Geologist (75)  |  Language (293)  |  Life (1795)  |  Live (628)  |  Million (114)  |  Most (1731)  |  Problem (676)  |  Scale (121)  |  Short (197)  |  Think (1086)  |  Time (1877)  |  Two (937)  |  Worth (169)  |  Year (933)

In my opinion instruction is very purposeless for such individuals who do no want merely to collect a mass of knowledge, but are mainly interested in exercising (training) their own powers. One doesn't need to grasp such a one by the hand and lead him to the goal, but only from time to time give him suggestions, in order that he may reach it himself in the shortest way.
Letter to Heinrich Schumacher (2 Oct 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.
Science quotes on:  |  Achievement (179)  |  Do (1908)  |  Education (378)  |  Goal (145)  |  Himself (461)  |  Individual (404)  |  Instruction (91)  |  Interest (386)  |  Knowledge (1529)  |  Lead (384)  |  Mass (157)  |  Merely (316)  |  Opinion (281)  |  Order (632)  |  Power (746)  |  Reach (281)  |  Suggestion (46)  |  Time (1877)  |  Training (80)  |  Want (497)  |  Way (1217)

Mathematical language is not only the simplest and most easily understood of any, but the shortest also.
In Works of Henry, Lord Brougham: Vol. 7: Rhetorical and literary Dissertions and Addresses (1856), 317, footnote.
Science quotes on:  |  Easy (204)  |  Language (293)  |  Mathematics (1328)  |  Mathematics As A Language (20)  |  Most (1731)  |  Short (197)  |  Simple (406)  |  Understand (606)  |  Understood (156)

Mathematics, among all school subjects, is especially adapted to further clearness, definite brevity and precision in expression, although it offers no exercise in flights of rhetoric. This is due in the first place to the logical rigour with which it develops thought, avoiding every departure from the shortest, most direct way, never allowing empty phrases to enter. Other subjects excel in the development of expression in other respects: translation from foreign languages into the mother tongue gives exercise in finding the proper word for the given foreign word and gives knowledge of laws of syntax, the study of poetry and prose furnish fit patterns for connected presentation and elegant form of expression, composition is to exercise the pupil in a like presentation of his own or borrowed thoughtsand their development, the natural sciences teach description of natural objects, apparatus and processes, as well as the statement of laws on the grounds of immediate sense-perception. But all these aids for exercise in the use of the mother tongue, each in its way valuable and indispensable, do not guarantee, in the same manner as mathematical training, the exclusion of words whose concepts, if not entirely wanting, are not sufficiently clear. They do not furnish in the same measure that which the mathematician demands particularly as regards precision of expression.
In Anleitung zum mathematischen Unterricht in höheren Schulen (1906), 17.
Science quotes on:  |  Adapt (66)  |  Aid (97)  |  All (4108)  |  Allow (45)  |  Apparatus (68)  |  Avoid (116)  |  Borrow (30)  |  Brevity (8)  |  Clarity (47)  |  Clear (100)  |  Composition (84)  |  Concept (221)  |  Connect (125)  |  Definite (110)  |  Demand (123)  |  Departure (9)  |  Description (84)  |  Develop (268)  |  Development (422)  |  Direct (225)  |  Do (1908)  |  Due (141)  |  Elegant (36)  |  Empty (80)  |  Enter (141)  |  Entirely (34)  |  Excel (4)  |  Exclusion (16)  |  Exercise (110)  |  Expression (175)  |  Find (998)  |  First (1283)  |  Fit (134)  |  Flight (98)  |  Foreign (45)  |  Form (959)  |  Furnish (96)  |  Give (202)  |  Ground (217)  |  Guarantee (30)  |  Immediate (95)  |  Indispensable (28)  |  Knowledge (1529)  |  Language (293)  |  Law (894)  |  Logical (55)  |  Manner (58)  |  Mathematician (387)  |  Mathematics (1328)  |  Measure (232)  |  Most (1731)  |  Mother (114)  |  Mother Tongue (3)  |  Natural (796)  |  Natural Science (128)  |  Never (1087)  |  Object (422)  |  Offer (141)  |  Other (2236)  |  Particularly (21)  |  Pattern (110)  |  Perception (97)  |  Phrase (61)  |  Place (177)  |  Poetry (143)  |  Precision (68)  |  Presentation (23)  |  Process (423)  |  Proper (144)  |  Prose (11)  |  Pupil (61)  |  Regard (305)  |  Respect (207)  |  Rhetoric (12)  |  Rigour (21)  |  Same (157)  |  School (219)  |  Science (3879)  |  Sense (770)  |  Short (197)  |  Statement (142)  |  Study (653)  |  Subject (521)  |  Sufficiently (9)  |  Syntax (2)  |  Teach (277)  |  Thought (953)  |  Tongue (43)  |  Training (80)  |  Translation (21)  |  Use (766)  |  Value (365)  |  Value Of Mathematics (60)  |  Want (497)  |  Way (1217)  |  Word (619)

The shortest and surest way of arriving at real knowledge is to unlearn the lessons we have been taught, to remount to first principles, and take no body’s word about them.
In Letters, on the Spirit of Patriotism: On the Idea of a Patriot King (1749), 78.
Science quotes on:  |   (2863)  |  Accept (191)  |  Arriving (2)  |  Body (537)  |  First (1283)  |  Knowledge (1529)  |  Lesson (57)  |  Mount (42)  |  Nobody (104)  |  Principle (507)  |  Real (149)  |  Surest (5)  |  Taught (4)  |  Unlearn (11)  |  Way (1217)  |  Word (619)

There may be some interest in one of my own discoveries in physics, entitled, “A Method of Approximating the Importance of a Given Physicist.” Briefly stated, after elimination of all differentials, the importance of a physicist can be measured by observation in the lobby of a building where the American Physical Society is in session. The importance of a given physicist varies inversely with his mean free path as he moves from the door of the meeting-room toward the street. His progress, of course, is marked by a series of scattering collisions with other physicists, during which he remains successively in the orbit of other individuals for a finite length of time. A good physicist has a mean free path of 3.6 ± 0.3 meters. The shortest m.f.p. measured in a series of observations between 1445 and 1947 was that of Oppenheimer (New York, 1946), the figure being 2.7 centimeters. I know. I was waiting for him on the street.
In 'A Newsman Looks at Physicists', Physics Today (May 1948), 1, No. 1, 33.
Science quotes on:  |  All (4108)  |  Being (1278)  |  Building (156)  |  Collision (15)  |  Course (409)  |  Discovery (780)  |  Door (93)  |  Elimination (25)  |  Figure (160)  |  Finite (59)  |  Free (232)  |  Good (889)  |  Importance (286)  |  Individual (404)  |  Interest (386)  |  Know (1518)  |  Lobby (2)  |  Marked (55)  |  Mean (809)  |  Measurement (174)  |  Meeting (20)  |  Method (505)  |  Move (216)  |  New (1216)  |  Observation (555)  |  J. Robert Oppenheimer (39)  |  Orbit (81)  |  Other (2236)  |  Path (144)  |  Physic (517)  |  Physical (508)  |  Physicist (259)  |  Physics (533)  |  Progress (465)  |  Remain (349)  |  Scattering (4)  |  Series (149)  |  Session (3)  |  Society (326)  |  Time (1877)  |  Waiting (43)

Weight is caused by one element being situated in another; and it moves by the shortest line towards its centre, not by its own choice, not because the centre draws it to itself, but because the other intervening element cannot withstand it.
…...
Science quotes on:  |  Being (1278)  |  Cause (541)  |  Centre (28)  |  Choice (110)  |  Draw (137)  |  Element (310)  |  Intervene (8)  |  Line (91)  |  Move (216)  |  Other (2236)  |  Short (197)  |  Situate (3)  |  Weight (134)  |  Withstand (3)

When I was eight, I played Little League. I was on first; I stole third; I went straight across. Earlier that week, I learned that the shortest distance between two points was a direct line. I took advantage of that knowledge.
In Comic Relief (1996).
Science quotes on:  |  Advantage (134)  |  Direct (225)  |  Distance (161)  |  First (1283)  |  Geometry (255)  |  Joke (83)  |  Knowledge (1529)  |  Learn (629)  |  Learned (235)  |  Little (707)  |  Point (580)  |  Shortest Distance (2)  |  Steal (13)  |  Straight (73)  |  Straight Line (30)  |  Two (937)  |  Week (70)

When the boy begins to understand that the visible point is preceded by an invisible point, that the shortest distance between two points is conceived as a straight line before it is ever drawn with the pencil on paper, he experiences a feeling of pride, of satisfaction. And justly so, for the fountain of all thought has been opened to him, the difference between the ideal and the real, potentia et actu, has become clear to him; henceforth the philosopher can reveal him nothing new, as a geometrician he has discovered the basis of all thought.
In Sprüche in Reimen. Sprüche in Prosa. Ethisches (1850), Vol. 3, 214. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 67. From the original German, “Wenn der knabe zu begreifen anfängt, daß einem sichtbaren Punkte ein unsichtbarer vorhergehen müsse, daß der nächste Weg zwischen zwei Punkten schon als Linie gedacht werde, ehe sie mit dem Bleistift aufs Papier gezogen wird, so fühlt er einen gewissen Stolz, ein Behagen. Und nicht mit Unrecht; denn ihm ist die Quelle alles Denkens aufgeschlossen, Idee und Verwirklichtes, potentia et actu, ist ihm klargeworden; der Philosoph entdeckt ihm nichts Neues; dem Geometer war von seiner Seite der Grund alles Denkens aufgegangen.” The Latin phrase, “potentia et actu” means “potentiality and actuality”.
Science quotes on:  |  All (4108)  |  Basis (173)  |  Become (815)  |  Begin (260)  |  Boy (94)  |  Clear (100)  |  Conceive (98)  |  Difference (337)  |  Discover (553)  |  Distance (161)  |  Draw (137)  |  Experience (467)  |  Feeling (250)  |  Fountain (16)  |  Geometer (24)  |  Ideal (99)  |  Invisible (63)  |  Justly (6)  |  New (1216)  |  Nothing (966)  |  Open (274)  |  Paper (182)  |  Pencil (20)  |  Philosopher (258)  |  Point (580)  |  Potentia (3)  |  Precede (23)  |  Pride (78)  |  Real (149)  |  Reveal (148)  |  Satisfaction (74)  |  Shortest Distance (2)  |  Straight (73)  |  Straight Line (30)  |  Thought (953)  |  Two (937)  |  Understand (606)  |  Visible (84)

~~[Misattributed]~~ The shortest path between two truths in the real domain passes through the complex domain.
In fact, this quote is a paraphras from Paul Painlevé.
Widely seen incorrectly attributed to Hadamard, and without primary source citation. However, Hadamard did not originate the quote, as shown by his own introductory phrase of, “It has been written that the shortest and best way between two truths of the real domain often passes through the imaginary one,” in An Essay on the Psychology of Invention in the Mathematical Field (1945), 123. The quote in fact originates from Paul Painlevé, Notice sur les travaux scientifiques (1900), 2. See the Paul Painlevé Quotes page on this website.
Science quotes on:  |  Complex (188)  |  Domain (69)  |  Fact (1210)  |  Misattributed (19)  |  Pass (238)  |  Path (144)  |  Quote (42)  |  Real (149)  |  Through (849)  |  Truth (1057)  |  Two (937)


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.