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

Today in Science History - Quickie Quiz
Who said: “I was going to record talking... the foil was put on; I then shouted 'Mary had a little lamb',... and the machine reproduced it perfectly.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index I > Category: Invariant

Invariant Quotes (10 quotes)

Attaching significance to invariants is an effort to recognize what, because of its form or colour or meaning or otherwise, is important or significant in what is only trivial or ephemeral. A simple instance of failing in this is provided by the poll-man at Cambridge, who learned perfectly how to factorize a²-b² but was floored because the examiner unkindly asked for the factors of p²–q².
In 'Recent Developments in Invariant Theory', The Mathematical Gazette (Dec 1926), 13, No. 185, 217. [Note: A poll-man is a student who takes the ordinary university degree, without honours. -Webmaster]
Science quotes on:  |  Ask (411)  |  Color (137)  |  Effort (227)  |  Ephemeral (4)  |  Examiner (5)  |  Factor (46)  |  Fail (185)  |  Form (959)  |  Important (209)  |  Instance (33)  |  Learn (629)  |  Learned (235)  |  Man (2251)  |  Meaning (233)  |  Provide (69)  |  Recognize (125)  |  Significance (113)  |  Significant (74)  |  Simple (406)  |  Student (300)  |  Trivial (57)

For mathematics, in a wilderness of tragedy and change, is a creature of the mind, born to the cry of humanity in search of an invariant reality, immutable in substance, unalterable with time.
In The American Mathematical Monthly (1949), 56, 19. Excerpted in John Ewing (ed,), A Century of Mathematics: Through the Eyes of the Monthly (1996), 186.
Science quotes on:  |  Bear (159)  |  Change (593)  |  Creature (233)  |  Cry (29)  |  Humanity (169)  |  Immutable (22)  |  Mathematics (1328)  |  Mind (1338)  |  Reality (261)  |  Search (162)  |  Substance (248)  |  Time (1877)  |  Tragedy (29)  |  Unalterable (7)  |  Wilderness (45)

Historical science is not worse, more restricted, or less capable of achieving firm conclusions because experiment, prediction, and subsumption under invariant laws of nature do not represent its usual working methods. The sciences of history use a different mode of explanation, rooted in the comparative and observational richness in our data. We cannot see a past event directly, but science is usually based on inference, not unvarnished observation (you don’t see electrons, gravity, or black holes either).
…...
Science quotes on:  |  Achieve (66)  |  Badly (32)  |  Base (117)  |  Black Hole (17)  |  Black Holes (4)  |  Capable (168)  |  Comparative (13)  |  Conclusion (254)  |  Data (156)  |  Different (577)  |  Directly (22)  |  Do (1908)  |  Electron (93)  |  Event (216)  |  Experiment (695)  |  Explanation (234)  |  Firm (47)  |  Gravity (132)  |  Historical (70)  |  History (673)  |  Inference (45)  |  Law (894)  |  Less (103)  |  Method (505)  |  Methods (204)  |  Mode (41)  |  More (2559)  |  Nature (1926)  |  Observation (555)  |  Observational (15)  |  Past (337)  |  Prediction (82)  |  Represent (155)  |  Restrict (12)  |  Richness (14)  |  Root (120)  |  Science (3879)  |  See (1081)  |  Subsumption (3)  |  Unvarnished (2)  |  Use (766)  |  Usually (176)  |  Work (1351)

Historically [chemistry] arose from a constellation of interests: the empirically based technologies of early metallurgists, brewers, dyers, tanners, calciners and pharmacists; the speculative Greek philosphers' concern whether brute matter was invariant or transformable; the alchemists' real or symbolic attempts to achieve the transmutation of base metals into gold; and the iatrochemists' interst in the chemistry and pathology of animal and human functions. Partly because of the sheer complexity of chemical phenomena, the absence of criteria and standards of purity, and uncertainty over the definition of elements ... but above all because of the lack of a concept of the gaseous state of matter, chemistry remained a rambling, puzzling and chaotic area of natural philosophy until the middle of the eighteenth century.
The Chemical Tree: A History of Chemistry (2000), xxii.
Science quotes on:  |  Alchemist (22)  |  All (4108)  |  Animal (617)  |  Attempt (251)  |  Base (117)  |  Brute (28)  |  Century (310)  |  Chemical (292)  |  Chemistry (353)  |  Complexity (111)  |  Concept (221)  |  Concern (228)  |  Constellation (17)  |  Definition (221)  |  Early (185)  |  Element (310)  |  Function (228)  |  Gold (97)  |  Greek (107)  |  Human (1468)  |  Interest (386)  |  Lack (119)  |  Matter (798)  |  Metal (84)  |  Metallurgist (2)  |  Natural (796)  |  Natural Philosophy (52)  |  Pathology (18)  |  Pharmacist (2)  |  Philosophy (380)  |  Puzzling (8)  |  Remain (349)  |  State (491)  |  Transmutation (22)  |  Uncertainty (56)

In our century the conceptions substitution and substitution group, transformation and transformation group, operation and operation group, invariant, differential invariant and differential parameter, appear more and more clearly as the most important conceptions of mathematics.
In Lapziger Berichte, No. 47 (1896), 261.
Science quotes on:  |  Appear (118)  |  Century (310)  |  Clearly (41)  |  Conception (154)  |  Differential (7)  |  Group (78)  |  Important (209)  |  Mathematics (1328)  |  Modern Mathematics (50)  |  More (2559)  |  Most (1731)  |  Operation (213)  |  Parameter (4)  |  Substitution (13)  |  Transformation (69)

In science there is and will remain a Platonic element which could not be taken away without ruining it. Among the infinite diversity of singular phenomena science can only look for invariants.
In Jacques Monod and Austryn Wainhouse (trans.), Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology (1971), 101.
Science quotes on:  |  Diversity (73)  |  Element (310)  |  Infinite (231)  |  Look (582)  |  Phenomenon (318)  |  Platonic (3)  |  Remain (349)  |  Ruin (42)  |  Science (3879)  |  Singular (23)  |  Will (2355)

It [mathematics] is in the inner world of pure thought, where all entia dwell, where is every type of order and manner of correlation and variety of relationship, it is in this infinite ensemble of eternal verities whence, if there be one cosmos or many of them, each derives its character and mode of being,—it is there that the spirit of mathesis has its home and its life.
Is it a restricted home, a narrow life, static and cold and grey with logic, without artistic interest, devoid of emotion and mood and sentiment? That world, it is true, is not a world of solar light, not clad in the colours that liven and glorify the things of sense, but it is an illuminated world, and over it all and everywhere throughout are hues and tints transcending sense, painted there by radiant pencils of psychic light, the light in which it lies. It is a silent world, and, nevertheless, in respect to the highest principle of art—the interpenetration of content and form, the perfect fusion of mode and meaning—it even surpasses music. In a sense, it is a static world, but so, too, are the worlds of the sculptor and the architect. The figures, however, which reason constructs and the mathematic vision beholds, transcend the temple and the statue, alike in simplicity and in intricacy, in delicacy and in grace, in symmetry and in poise. Not only are this home and this life thus rich in aesthetic interests, really controlled and sustained by motives of a sublimed and supersensuous art, but the religious aspiration, too, finds there, especially in the beautiful doctrine of invariants, the most perfect symbols of what it seeks—the changeless in the midst of change, abiding things hi a world of flux, configurations that remain the same despite the swirl and stress of countless hosts of curious transformations.
In 'The Universe and Beyond', Hibbert Journal (1904-1906), 3, 314.
Science quotes on:  |  Abide (12)  |  Aesthetic (46)  |  Alike (60)  |  All (4108)  |  Architect (29)  |  Art (657)  |  Artistic (23)  |  Aspiration (32)  |  Beautiful (258)  |  Behold (18)  |  Being (1278)  |  Change (593)  |  Character (243)  |  Cold (112)  |  Color (137)  |  Configuration (7)  |  Construct (124)  |  Content (69)  |  Control (167)  |  Correlation (18)  |  Cosmos (63)  |  Countless (36)  |  Curious (91)  |  Delicacy (8)  |  Derive (65)  |  Despite (7)  |  Devoid (11)  |  Doctrine (75)  |  Dwell (15)  |  Emotion (100)  |  Ensemble (7)  |  Especially (31)  |  Eternal (110)  |  Everywhere (94)  |  Figure (160)  |  Find (998)  |  Flux (21)  |  Form (959)  |  Fusion (16)  |  Glorify (6)  |  Grace (31)  |  Grey (10)  |  High (362)  |  Home (170)  |  Host (16)  |  Hue (3)  |  Illuminate (24)  |  Infinite (231)  |  Inner (71)  |  Interest (386)  |  Intricacy (8)  |  Lie (364)  |  Life (1795)  |  Light (607)  |  Logic (287)  |  Manner (58)  |  Mathematics (1328)  |  Mean (809)  |  Meaning (233)  |  Midst (7)  |  Mode (41)  |  Mood (13)  |  Most (1731)  |  Motive (59)  |  Music (129)  |  Narrow (84)  |  Nature Of Mathematics (80)  |  Nevertheless (90)  |  Order (632)  |  Paint (22)  |  Pencil (20)  |  Penetration (18)  |  Perfect (216)  |  Poise (4)  |  Principle (507)  |  Psychic (13)  |  Pure (291)  |  Radiant (15)  |  Really (78)  |  Reason (744)  |  Relationship (104)  |  Religious (126)  |  Remain (349)  |  Respect (207)  |  Restrict (12)  |  Rich (62)  |  Same (157)  |  Sculptor (9)  |  Seek (213)  |  Sense (770)  |  Sensuous (5)  |  Sentiment (14)  |  Silent (29)  |  Simplicity (167)  |  Solar (8)  |  Spirit (265)  |  Static (8)  |  Statue (16)  |  Stress (22)  |  Sublime (46)  |  Surpass (32)  |  Sustain (46)  |  Swirl (10)  |  Symbol (93)  |  Symmetry (43)  |  Temple (42)  |  Thing (1915)  |  Thought (953)  |  Throughout (98)  |  Tint (2)  |  Transcend (26)  |  Transformation (69)  |  True (212)  |  Type (167)  |  Variety (132)  |  Verity (5)  |  Vision (123)  |  World (1774)

Non-standard analysis frequently simplifies substantially the proofs, not only of elementary theorems, but also of deep results. This is true, e.g., also for the proof of the existence of invariant subspaces for compact operators, disregarding the improvement of the result; and it is true in an even higher degree in other cases. This state of affairs should prevent a rather common misinterpretation of non-standard analysis, namely the idea that it is some kind of extravagance or fad of mathematical logicians. Nothing could be farther from the truth. Rather, there are good reasons to believe that non-standard analysis, in some version or other, will be the analysis of the future.
In 'Remark on Non-standard Analysis' (1974), in S. Feferman (ed.), Kurt Gödel Collected Works: Publications 1938-1974 (1990), Vol. 2, 311.
Science quotes on:  |  Analysis (233)  |  Common (436)  |  Compact (13)  |  Deep (233)  |  Degree (276)  |  Elementary (96)  |  Existence (456)  |  Fad (10)  |  Farther (51)  |  Future (429)  |  Good (889)  |  Idea (843)  |  Improvement (108)  |  Kind (557)  |  Logician (17)  |  Mathematics (1328)  |  Nothing (966)  |  Other (2236)  |  Prevent (94)  |  Proof (287)  |  Reason (744)  |  Result (677)  |  State (491)  |  Theorem (112)  |  Truth (1057)  |  Will (2355)

One evening at a Joint Summer Research Congerence in the early 1990’s Nicholai Reshetikhin and I [David Yetter] button-holed Flato, and explained at length Shum’s coherence theorem and the role of categories in “quantum knot invariants”. Flato was persistently dismissive of categories as a “mere language”. I retired for the evening, leaving Reshetikhin and Flato to the discussion. At the next morning’s session, Flato tapped me on the shoulder, and, giving a thumbs-up sign, whispered, “Hey! Viva les categories! These new ones, the braided monoidal ones.”
In David N. Yetter, Functorial Knot Theory: Categories of Tangles, Coherence, Categorical Deformations, and Topological Invariants (2001), 8. Yetter writes this personal anecdote is given as a narrative in his own words. Presumable the phrases in quotation marks are based on recollection when written years later.
Science quotes on:  |   (2863)  |  Category (18)  |  Coherence (13)  |  David (6)  |  Discussion (72)  |  Early (185)  |  Explain (322)  |  Give (202)  |  Joint (31)  |  Knot (11)  |  Language (293)  |  Leave (130)  |  Length (23)  |  Mere (84)  |  Morning (94)  |  New (1216)  |  Next (236)  |  Quantum (117)  |  Research (664)  |  Retire (3)  |  Role (86)  |  Session (3)  |  Shoulder (33)  |  Sign (58)  |  Summer (54)  |  Tap (10)  |  Theorem (112)  |  Thumb (17)  |  Whisper (11)

[The] first postulate of the Principle of Uniformity, namely, that the laws of nature are invariant with time, is not peculiar to that principle or to geology, but is a common denominator of all science. In fact, instead of being an assumption or an ad hoc hypothesis, it is simply a succinct summation of the totality of all experimental and observational evidence.
'Critique of the Principle of Uniformity', in C. C. Albritton (ed.), Uniformity and Simplicity (1967), 29.
Science quotes on:  |  All (4108)  |  Assumption (92)  |  Being (1278)  |  Common (436)  |  Evidence (248)  |  Experimental (192)  |  Fact (1210)  |  First (1283)  |  Geology (220)  |  Hypothesis (296)  |  Law (894)  |  Nature (1926)  |  Observational (15)  |  Peculiar (113)  |  Postulate (38)  |  Principle (507)  |  Science (3879)  |  Summation (3)  |  Time (1877)  |  Totality (15)  |  Uniformity (37)


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.