Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “I seem to have been only like a boy playing on the seashore, ... finding a smoother pebble or a prettier shell ... whilst the great ocean of truth lay all undiscovered before me.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index D > Category: Differentiation

Differentiation Quotes (11 quotes)

Common integration is only the memory of differentiation...
Science quotes on:  |  Integration (11)  |  Mathematics (367)

How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.
The Tragicomical History of Thermodynamics, 1822-1854 (1980), 51.
Science quotes on:  |  Biot_Jean (2)  |  Conduction (3)  |  Derive (4)  |  Equation (46)  |  Pierre-Simon Laplace (45)  |  Mathematician (110)  |  Mortal (6)  |  Ordinary (19)  |  Research (360)  |  Sink (6)  |  Superiority (6)  |  Swim (3)  |  Thermodynamics (17)

In summary, very large populations may differentiate rapidly, but their sustained evolution will be at moderate or slow rates and will be mainly adaptive. Populations of intermediate size provide the best conditions for sustained progressive and branching evolution, adaptive in its main lines, but accompanied by inadaptive fluctuations, especially in characters of little selective importance. Small populations will be virtually incapable of differentiation or branching and will often be dominated by random inadaptive trends and peculiarly liable to extinction, but will be capable of the most rapid evolution as long as this is not cut short by extinction.
Tempo and Mode in Evolution (1944), 70-1.
Science quotes on:  |  Accompany (3)  |  Adaptation (23)  |  Branch (23)  |  Capability (27)  |  Character (39)  |  Condition (68)  |  Cut (14)  |  Domination (8)  |  Evolution (342)  |  Extinction (38)  |  Fluctuation (4)  |  Importance (106)  |  Incapable (4)  |  Intermediate (10)  |  Large (22)  |  Liability (3)  |  Peculiarity (11)  |  Population (41)  |  Progressive (5)  |  Provision (10)  |  Random (11)  |  Rapidity (14)  |  Selection (20)  |  Size (21)  |  Small (35)  |  Summary (2)  |  Sustain (4)  |  Trend (8)

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:  |  Binomial (2)  |  Calculus (14)  |  Colour (32)  |  Fluxion (3)  |  Gravity (59)  |  Inverse Square Law (4)  |  Johannes Kepler (43)  |  Law Of Gravity (3)  |  Orbit (36)  |  Plague (30)  |  Prime (4)

It must be admitted that science has its castes. The man whose chief apparatus is the differential equation looks down upon one who uses a galvanometer, and he in turn upon those who putter about with sticky and smelly things in test tubes. But all of these, and most biologists too, join together in their contempt for the pariah who, not through a glass darkly, but with keen unaided vision, observes the massing of a thundercloud on the horizon, the petal as it unfolds, or the swarming of a hive of bees. And yet sometimes I think that our laboratories are but little earthworks which men build about themselves, and whose puny tops too often conceal from view the Olympian heights; that we who work in these laboratories are but skilled artisans compared with the man who is able to observe, and to draw accurate deductions from the world about him.
The Anatomy of Science (1926), 170- 1.
Science quotes on:  |  Bee (13)  |  Cloud (22)  |  Deduction (39)  |  Equation (46)  |  Flower (24)  |  Galvanometer (4)  |  Laboratory (75)  |  Observation (264)  |  Science (875)  |  Test Tube (7)  |  Thunder (3)  |  World (231)

My thesis is that what we call 'science' is differentiated from the older myths not by being something distinct from a myth, but by being accompanied by a second-order tradition—that of critically discussing the myth. … In a certain sense, science is myth-making just as religion is.
Conjectures and Refutations: the Growth of Scientific Knowledge (2002), 170-171.
Science quotes on:  |  Criticism (34)  |  Myth (24)  |  Science And Religion (159)  |  Thesis (4)

No branches of historical inquiry have suffered more from fanciful speculation than those which relate to the origin and attributes of the races of mankind. The differentiation of these races began in prehistoric darkness, and the more obscure a subject is, so much the more fascinating. Hypotheses are tempting, because though it may be impossible to verify them, it is, in the paucity of data, almost equally impossible to refute them.
Creighton Lecture delivered before the University of London on 22 Feb 1915. Race Sentiment as a Factor in History (1915), 3.
Science quotes on:  |  Data (59)  |  History (156)  |  Hypothesis (150)  |  Origin Of Man (7)  |  Race (36)  |  Speculation (44)

Now, we propose in the first place to show, that this law of organic progress is the law of all progress. Whether it be in the development of the Earth, in the development in Life upon its surface, in the development of Society, of Government, of Manufactures, of Commerce, of Language, Literature, Science, Art, this same evolution of the simple into the complex, through a process of continuous differentiation, holds throughout. From the earliest traceable cosmical changes down to the latest results of civilization, we shall find that the transformation of the homogeneous into the heterogeneous is that in which Progress essentially consists.
'Progress: Its Law and Cause', Westminster Review (1857), 67, 446-7.
Science quotes on:  |  Art (80)  |  Change (133)  |  Civilization (90)  |  Commerce (9)  |  Complexity (51)  |  Continuous (7)  |  Cosmos (23)  |  Development (122)  |  Earth (250)  |  Government (50)  |  Heterogeneity (3)  |  Homogeneity (3)  |  Language (71)  |  Law (273)  |  Life (460)  |  Literature (33)  |  Manufacturing (16)  |  Organic (19)  |  Progress (200)  |  Proposition (28)  |  Science (875)  |  Simplicity (92)  |  Society (84)  |  Surface (37)  |  Trace (10)  |  Transformation (27)

The advance from the simple to the complex, through a process of successive differentiations, is seen alike in the earliest changes of the Universe to which we can reason our way back, and in the earliest changes which we can inductively establish; it is seen in the geologic and climatic evolution of the Earth; it is seen in the unfolding of every single organism on its surface, and in the multiplication of kinds of organisms; it is seen in the evolution of Humanity, whether contemplated in the civilized individual, or in the aggregate of races; it is seen in the evolution of Society in respect alike of its political, its religious, and its economical organization; and it is seen in the evolution of all those endless concrete and abstract products of human activity which constitute the environment of our daily life. From the remotest past which Science can fathom, up to the novelties of yesterday, that in which Progress essentially consists, is the transformation of the homogeneous into the heterogeneous.
Progress: Its Law and Cause (1857), 35.
Science quotes on:  |  Abstract (19)  |  Activity (48)  |  Advancement (26)  |  Aggregation (4)  |  Change (133)  |  Civilization (90)  |  Climate (28)  |  Complexity (51)  |  Concrete (7)  |  Contemplation (17)  |  Daily Life (3)  |  Early (10)  |  Earth (250)  |  Economy (25)  |  Environment (75)  |  Establishment (19)  |  Evolution (342)  |  Fathom (3)  |  Geology (145)  |  Heterogeneity (3)  |  Homogeneity (3)  |  Humanity (46)  |  Individual (59)  |  Induction (22)  |  Kind (27)  |  Multiplication (11)  |  Novelty (9)  |  Organism (70)  |  Organization (51)  |  Past (42)  |  Politics (52)  |  Process (97)  |  Product (33)  |  Race (36)  |  Reason (173)  |  Religion (120)  |  Remoteness (4)  |  Simplicity (92)  |  Society (84)  |  Succession (30)  |  Surface (37)  |  Transformation (27)  |  Unfolding (5)  |  Universe (291)  |  Yesterday (3)

The proof given by Wright, that non-adaptive differentiation will occur in small populations owing to “drift,” or the chance fixation of some new mutation or recombination, is one of the most important results of mathematical analysis applied to the facts of neo-mendelism. It gives accident as well as adaptation a place in evolution, and at one stroke explains many facts which puzzled earlier selectionists, notably the much greater degree of divergence shown by island than mainland forms, by forms in isolated lakes than in continuous river-systems.
Evolution: The Modern Synthesis (1942), 199-200.
Science quotes on:  |  Accident (25)  |  Adaptation (23)  |  Analysis (82)  |  Chance (77)  |  Divergence (3)  |  Drift (2)  |  Evolution (342)  |  Island (8)  |  Lake (6)  |  Mathematics (367)  |  Mutation (12)  |  Population (41)  |  Proof (136)  |  River (34)

[The infinitely small] neither have nor can have theory; it is a dangerous instrument in the hands of beginners [ ... ] anticipating, for my part, the judgement of posterity, I would dare predict that this method will be accused one day, and rightly, of having retarded the progress of the mathematical sciences.
Annales des Mathematiques Pures et Appliquées (1814-5), 5, 148.
Science quotes on:  |  Accusation (4)  |  Anticipation (6)  |  Beginner (3)  |  Danger (32)  |  Infinity (44)  |  Instrument (40)  |  Judgment (39)  |  Mathematics (367)  |  Method (73)  |  Posterity (11)  |  Prediction (48)  |  Progress (200)  |  Retardation (4)  |  Theory (353)


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 Einstein • Isaac Newton • Lord Kelvin • Charles Darwin • Srinivasa Ramanujan • Carl Sagan • Florence Nightingale • Thomas Edison • Aristotle • Marie Curie • Benjamin Franklin • Winston Churchill • Galileo Galilei • Sigmund Freud • Robert Bunsen • Louis Pasteur • Theodore Roosevelt • Abraham Lincoln • Ronald Reagan • Leonardo DaVinci • Michio Kaku • Karl Popper • Johann Goethe • Robert Oppenheimer • Charles Kettering  ... (more people)

Quotations about: • Atomic  Bomb • Biology • Chemistry • Deforestation • Engineering • Anatomy • Astronomy • Bacteria • Biochemistry • Botany • Conservation • Dinosaur • Environment • Fractal • Genetics • Geology • History of Science • Invention • Jupiter • Knowledge • Love • Mathematics • Measurement • Medicine • Natural Resource • Organic Chemistry • Physics • Physician • Quantum Theory • Research • Science and Art • Teacher • Technology • Universe • Volcano • Virus • Wind Power • Women Scientists • X-Rays • Youth • Zoology  ... (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