Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “Genius is two percent inspiration, ninety-eight percent perspiration.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index S > Category: Series

Series Quotes (18 quotes)

Derrière la série de Fourier, d'autres séries analogues sont entrées dans la domaine de l'analyse; elles y sont entrees par la même porte; elles ont été imaginées en vue des applications.
After the Fourier series, other series have entered the domain of anylsis; they entered by the same door; they have been imagined in view of applications.
La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 74.
Science quotes on:  |  Baron Jean-Baptiste-Joseph Fourier (5)

La théorie des séries infinies en général est justqu’à présent très mal fondée. On applique aux séries infinies toutes les opérations, come si elles aient finies; mais cela est-il bien permis? Je crois que non. Où est-il démonstré qu/on ontient la différentielle dune série infinie en prenant la différentiaella de chaque terme. Rien n’est plus facile que de donner des exemples où cela n’est pas juste.
Until now the theory of infinite series in general has been very badly grounded. One applies all the operations to infinite series as if they were finite; but is that permissible? I think not. Where is it demonstrated that one obtains the differential of an infinite series by taking the differential of each term? Nothing is easier than to give instances where this is not so.
Quoted in Reinhold Remmert and Robert B. Burckel, Theory of Complex Functions: Readings in Mathematics (1991), 125.
Science quotes on:  |  Finite (13)  |  Infinite (37)  |  Operation (54)  |  Term (34)  |  Theory (346)

Embryonic stem cell research is at the leading edge of a series of moral hazards.
'Address to the Nation on Stem Cell Research', (9 Aug 2001) in Public Papers Of The Presidents Of The United States, George W. Bush, 2001 (2004), Book 2, 955.
Science quotes on:  |  Embryonic (2)  |  Hazard (6)  |  Moral (38)  |  Research (358)  |  Stem Cell (8)

Entropy theory, on the other hand, is not concerned with the probability of succession in a series of items but with the overall distribution of kinds of items in a given arrangement.
In Entropy and Art: An Essay on Disorder and Order (1974), 19.
Science quotes on:  |  Arrangement (26)  |  Concern (30)  |  Distribution (15)  |  Entropy (25)  |  Given (2)  |  Kind (26)  |  Other Hand (2)  |  Probability (54)  |  Succession (29)  |  Theory (346)

I'd like the [Cosmos] series to be so visually stimulating that somebody who isn't even interested in the concepts will just watch for the effects. And I'd like people who are prepared to do some thinking to be really stimulated.
Quoted by Dennis Meredith, in 'Carl Sagan's Cosmic Connection and Extraterrestrial Life-Wish', Science Digest (Jun 1979), 85, 38. Reproduced in Carl Sagan and Tom Head, Conversations With Sagan (2006), 55.
Science quotes on:  |  Concept (36)  |  Cosmos (21)  |  Effect (70)  |  Interest (75)  |  Person (32)  |  Stimulation (7)  |  Thinking (163)  |  Visualize (2)

In its earliest development knowledge is self-sown. Impressions force themselves upon men’s senses whether they will or not, and often against their will. The amount of interest in which these impressions awaken is determined by the coarser pains and pleasures which they carry in their train or by mere curiosity; and reason deals with the materials supplied to it as far as that interest carries it, and no further. Such common knowledge is rather brought than sought; and such ratiocination is little more than the working of a blind intellectual instinct. It is only when the mind passes beyond this condition that it begins to evolve science. When simple curiosity passes into the love of knowledge as such, and the gratification of the æsthetic sense of the beauty of completeness and accuracy seems more desirable that the easy indolence of ignorance; when the finding out of the causes of things becomes a source of joy, and he is accounted happy who is successful in the search, common knowledge passes into what our forefathers called natural history, whence there is but a step to that which used to be termed natural philosophy, and now passes by the name of physical science.
In this final state of knowledge the phenomena of nature are regarded as one continuous series of causes and effects; and the ultimate object of science is to trace out that series, from the term which is nearest to us, to that which is at the farthest limit accessible to our means of investigation.
The course of nature as it is, as it has been, and as it will be, is the object of scientific inquiry; whatever lies beyond, above, or below this is outside science. But the philosopher need not despair at the limitation on his field of labor; in relation to the human mind Nature is boundless; and, though nowhere inaccessible, she is everywhere unfathomable.
The Crayfish: an Introduction to the Study of Zoölogy (1880), 2-3. Excerpted in Popular Science (Apr 1880), 16, 789-790.
Science quotes on:  |  Accuracy (33)  |  Aesthetic (10)  |  Beauty (83)  |  Boundless (6)  |  Cause (116)  |  Cause And Effect (4)  |  Completeness (9)  |  Continuity (17)  |  Curiosity (49)  |  Determination (32)  |  Development (117)  |  Evolution (332)  |  Finding (18)  |  Forefather (2)  |  Gratification (7)  |  Happiness (56)  |  Human Mind (21)  |  Ignorance (110)  |  Impression (29)  |  Indolence (5)  |  Inquiry (12)  |  Instinct (25)  |  Intellect (95)  |  Interest (75)  |  Investigation (81)  |  Joy (25)  |  Knowledge (662)  |  Labour (26)  |  Limitation (8)  |  Mind (266)  |  Natural History (23)  |  Nature (524)  |  Pain (48)  |  Phenomenon (113)  |  Philosophy (128)  |  Physical Science (31)  |  Pleasure (51)  |  Ratiocination (2)  |  Reason (172)  |  Sense (100)  |  Term (34)  |  Tracing (2)  |  Will (21)

Laplace would have found it child's-play to fix a ratio of progression in mathematical science between Descartes, Leibnitz, Newton and himself
The Education of Henry Adams: An Autobiography? (1918), 491.
Science quotes on:  |  René Descartes (32)  |  Pierre-Simon Laplace (45)  |  Gottfried Wilhelm Leibniz (24)  |  Mathematics (355)  |  Sir Isaac Newton (174)  |  Progress (198)

My experiments with single traits all lead to the same result: that from the seeds of hybrids, plants are obtained half of which in turn carry the hybrid trait (Aa), the other half, however, receive the parental traits A and a in equal amounts. Thus, on the average, among four plants two have the hybrid trait Aa, one the parental trait A, and the other the parental trait a. Therefore, 2Aa+ A +a or A + 2Aa + a is the empirical simple series for two differing traits.
Letter to Carl Nägeli, 31 Dec 1866. In Curt Stern and Eva R. Sherwood (eds.), The Origin of Genetics: A Mendel Source Book (1966), 63.
Science quotes on:  |  Difference (129)  |  Empiricism (13)  |  Equal (21)  |  Experiment (367)  |  Genetics (78)  |  Hybrid (7)  |  Parent (23)  |  Plant (93)  |  Simple (24)  |  Trait (9)

Science has hitherto been proceeding without the guidance of any rational theory of logic, and has certainly made good progress. It is like a computer who is pursuing some method of arithmetical approximation. Even if he occasionally makes mistakes in his ciphering, yet if the process is a good one they will rectify themselves. But then he would approximate much more rapidly if he did not commit these errors; and in my opinion, the time has come when science ought to be provided with a logic. My theory satisfies me; I can see no flaw in it. According to that theory universality, necessity, exactitude, in the absolute sense of these words, are unattainable by us, and do not exist in nature. There is an ideal law to which nature approximates; but to express it would require an endless series of modifications, like the decimals expressing surd. Only when you have asked a question in so crude a shape that continuity is not involved, is a perfectly true answer attainable.
Letter to G. F. Becker, 11 June 1893. Merrill Collection, Library of Congress. Quoted in Nathan Reingold, Science in Nineteenth-Century America: A Documentary History (1966), 231-2.
Science quotes on:  |  Absolute (32)  |  Answer (91)  |  Approximation (9)  |  Approximation (9)  |  Arithmetic (33)  |  Attainment (21)  |  Commitment (8)  |  Computer (51)  |  Crudity (2)  |  Decimal (8)  |  Endless (12)  |  Error (150)  |  Exactitude (3)  |  Existence (145)  |  Flaw (5)  |  Good (77)  |  Guidance (7)  |  Guidance (7)  |  Hitherto (2)  |  Ideal (26)  |  Logic (131)  |  Method (73)  |  Modification (21)  |  Nature (524)  |  Necessity (78)  |  Opinion (81)  |  Perfection (41)  |  Proceeding (10)  |  Progress (198)  |  Provision (10)  |  Pursuit (33)  |  Question (152)  |  Rapidity (14)  |  Rationality (4)  |  Satisfaction (29)  |  Science (850)  |  Sense (100)  |  Theory (346)  |  Theory (346)  |  Time (160)  |  Truth (440)  |  Universality (9)  |  Word (96)

The digestive canal is in its task a complete chemical factory. The raw material passes through a long series of institutions in which it is subjected to certain mechanical and, mainly, chemical processing, and then, through innumerable side-streets, it is brought into the depot of the body. Aside from this basic series of institutions, along which the raw material moves, there is a series of lateral chemical manufactories, which prepare certain reagents for the appropriate processing of the raw material.
Speech to the Society of Russian Physicians (Dec 1874). as translated in Daniel P. Todes, Pavlov's Physiology Factory: Experiment, Interpretation, Laboratory Enterprise (2002), 155.
Science quotes on:  |  Appropriateness (5)  |  Body (88)  |  Canal (3)  |  Certain (12)  |  Chemical (36)  |  Completeness (9)  |  Digestion (15)  |  Factory (6)  |  Innumerable (10)  |  Institution (14)  |  Lateral (2)  |  Material (54)  |  Mechanical (11)  |  Pass (18)  |  Preparation (21)  |  Process (97)  |  Raw (2)  |  Reagent (3)  |  Subject (48)

The divergent series are the invention of the devil, and it is a shame to base on them any demonstration whatsoever. By using them, one may draw any conclusion he pleases and that is why these series have produced so many fallacies and so many paradoxes.
From letter (Jan 1828) to his former teacher Berndt Holmböe. In Morris Kline, Mathematics: The Loss of Certainty (1982), 170.
Science quotes on:  |  Demonstration (27)  |  Devil (9)  |  General (23)  |  Invention (167)  |  Paradox (22)  |  Special (24)

The primitive history of the species is all the more fully retained in its germ-history in proportion as the series of embryonic forms traversed is longer; and it is more accurately retained the less the mode of life of the recent forms differs from that of the earlier, and the less the peculiarities of the several embryonic states must be regarded as transferred from a later to an earlier period of life, or as acquired independently. (1864)
As translated and quoted in Ernst Haeckel and E. Ray Lankester (trans.) as epigraph for Chap. 13, The History of Creation (1886), Vol. 1, 406.
Science quotes on:  |  Acquire (7)  |  Difference (129)  |  Earlier (7)  |  Embryonic (2)  |  Form (65)  |  History (151)  |  Later (4)  |  Life (439)  |  Peculiarity (11)  |  Period (22)  |  Primitive (13)  |  Proportion (23)  |  Recent (13)  |  Species (91)  |  Transfer (3)  |  Traverse (3)

The whole aim of practical politics is to keep the populace alarmed (and hence clamorous to be led to safety) by menacing it with an endless series of hobgoblins, all of them imaginary.
Essay, 'The Smart Set' (Dec 1921), 29. As cited in A Mencken Chrestomathy (1949, 2012), p. 29 (1949).
Science quotes on:  |  Aim (20)  |  Alarm (2)  |  Clamor (2)  |  Endless (12)  |  Imaginary (5)  |  Keep (9)  |  Lead (33)  |  Politics (50)  |  Populace (2)  |  Practical (30)  |  Safety (21)

There is more danger of numerical sequences continued indefinitely than of trees growing up to heaven. Each will some time reach its greatest height.
Grundgesetz der Arithmetik(1893), Vol. 2, Section 60, In P. Greach and M. Black (eds., Translations from the Philosophical Writings of Gottlob Frege (1952), 204.
Science quotes on:  |  Number (88)

To trace the series of these revolutions, to explain their causes, and thus to connect together all the indications of change that are found in the mineral kingdom, is the proper object of a THEORY OF THE EARTH.
Illustrations of the Huttonian Theory of the Earth (1802), 2.
Science quotes on:  |  Cause (116)  |  Change (129)  |  Connection (39)  |  Earth (238)  |  Explanation (84)  |  Finding (18)  |  Indication (15)  |  Kingdom (17)  |  Mineral (24)  |  Object (44)  |  Properness (2)  |  Revolution (33)  |  Theory (346)  |  Trace (10)

Why it is that animals, instead of developing in a simple and straightforward way, undergo in the course of their growth a series of complicated changes, during which they often acquire organs which have no function, and which, after remaining visible for a short time, disappear without leaving a trace ... To the Darwinian, the explanation of such facts is obvious. The stage when the tadpole breathes by gills is a repetition of the stage when the ancestors of the frog had not advanced in the scale of development beyond a fish.
In The Works of Francis Maitland Balfour (1885), Vol. 1, 702.
Science quotes on:  |  Acquisition (21)  |  Advance (49)  |  Ancestor (17)  |  Animal (138)  |  Breathe (9)  |  Change (129)  |  Complication (15)  |  Charles Darwin (211)  |  Development (117)  |  Disappearance (14)  |  Explanation (84)  |  Fact (311)  |  Fish (31)  |  Frog (22)  |  Function (41)  |  Growth (65)  |  Leaving (4)  |  Obvious (24)  |  Organ (39)  |  Remain (18)  |  Repetition (18)  |  Simplicity (92)  |  Stage (15)  |  Trace (10)  |  Undergo (4)  |  Visibility (6)

With the exception of the geometrical series, there does not exist in all of mathematics a single infinite series the sum of which has been rigorously determined. In other words, the things which are the most important in mathematics are also those which have the least foundation.
From letter (Jan 1828) to his former teacher Berndt Holmböe. In Morris Kline, Mathematics: The Loss of Certainty (1982), 170.
Science quotes on:  |  Mathematics (355)

[It] may be laid down as a general rule that, if the result of a long series of precise observations approximates a simple relation so closely that the remaining difference is undetectable by observation and may be attributed to the errors to which they are liable, then this relation is probably that of nature.
'Mémoire sur les Inégalites Séculaires des Planètes et des Satellites' (I 785, published 1787). In Oeuvres completes de Laplace, 14 Vols. (1843-1912), Vol. 11, 57, trans. Charles Coulston Gillispie, Pierre-Simon Laplace 1749-1827: A Life in Exact Science (1997), 130.
Science quotes on:  |  Approximation (9)  |  Attribute (12)  |  Difference (129)  |  Error (150)  |  Nature (524)  |  Observation (256)  |  Precision (19)  |  Relation (33)  |  Result (127)  |  Rule (50)  |  Simplicity (92)  |  Undetectable (2)


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:
Custom Quotations Search - custom search within only our quotations 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 |
Author Icon
who invites your feedback

Today in Science History

Most Popular

Thank you for sharing.
Today in Science History
Sign up for Newsletter
with quiz, quotes and more.
- 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

New Book


The Simpsons and their Mathematical Secrets,
by Simon Singh

Cleverly embedded in many Simpsons plots are subtle references to mathematics, because the show's brilliant comedy writers with advanced degrees in math or science. Singh offers an entirely new insight into the most successful show in television history.