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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.”
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Home > Category Index for Science Quotations > Category Index D > Category: Division

Division Quotes (19 quotes)

“The Universe repeats itself, with the possible exception of history.” Of all earthly studies history is the only one that does not repeat itself. ... Astronomy repeats itself; botany repeats itself; trigonometry repeats itself; mechanics repeats itself; compound long division repeats itself. Every sum if worked out in the same way at any time will bring out the same answer. ... A great many moderns say that history is a science; if so it occupies a solitary and splendid elevation among the sciences; it is the only science the conclusions of which are always wrong.
In 'A Much Repeated Repetition', Daily News (26 Mar 1904). Collected in G. K. Chesterton and Dale Ahlquist (ed.), In Defense of Sanity: The Best Essays of G.K. Chesterton (2011), 82.
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Ode to The Amoeba
Recall from Time's abysmal chasm
That piece of primal protoplasm
The First Amoeba, strangely splendid,
From whom we're all of us descended.
That First Amoeba, weirdly clever,
Exists today and shall forever,
Because he reproduced by fission;
He split himself, and each division
And subdivision deemed it fitting
To keep on splitting, splitting, splitting;
So, whatsoe'er their billions be,
All, all amoebas still are he.
Zoologists discern his features
In every sort of breathing creatures,
Since all of every living species,
No matter how their breed increases
Or how their ranks have been recruited,
From him alone were evoluted.
King Solomon, the Queen of Sheba
And Hoover sprang from that amoeba;
Columbus, Shakespeare, Darwin, Shelley
Derived from that same bit of jelly.
So famed is he and well-connected,
His statue ought to be erected,
For you and I and William Beebe
Are undeniably amoebae!
(1922). Collected in Gaily the Troubadour (1936), 18.
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Dass die bis jetzt unzerlegten chemischen Elemente absolut unzerlegbare Stoffe seien, ist gegenwärtig mindestens sehr unwahrscheinlich. Vielmehr scheint es, dass die Atome der Elemente nicht die letzten, sondern nur die näheren Bestandtheile der Molekeln sowohl der Elemente wie der Verbindungen bilden, die Molekeln oder Molecule als Massentheile erster, die Atome als solche zweiter Ordnung anzusehen sind, die ihrerseits wiederum aus Massentheilchen einer dritten höheren Ordnung bestehen werden.
That the as yet undivided chemical elements are absolutely irreducible substances, is currently at least very unlikely. Rather it seems, that the atoms of elements are not the final, but only the immediate constituents of the molecules of both the elements and the compounds—the Molekeln or molecule as foremost division of matter, the atoms being considered as second order, in turn consisting of matter particles of a third higher order.
[Speculating in 1870, on the existence of subatomic particles, in opening remark of the paper by which he became established as co-discoverer of the Periodic Law.]
'Die Natur der chemischen Elemente als Function ihrer Atomgewichte' ('The Nature of the Chemical Elements as a Function of their Atomic Weight'), Annalen der Chemie (1870), supp. b, 354. Original German paper reprinted in Lothar Meyer and Dmitry Ivanovich Mendeleyev, Das natürliche System der chemischen Elemente: Abhandlungen (1895), 9. Translation by Webmaster, with punctuation faithful to the original, except a comma was changed to a dash to improve readability.
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Every creature has its own food, and an appropriate alchemist with the task of dividing it ... The alchemist takes the food and changes it into a tincture which he sends through the body to become blood and flesh. This alchemist dwells in the stomach where he cooks and works. The man eats a piece of meat, in which is both bad and good. When the meat reaches the stomach, there is the alchemist who divides it. What does not belong to health he casts away to a special place, and sends the good wherever it is needed. That is the Creator's decree... That is the virtue and power of the alchemist in man.
Volumen Medicinae Paramirum (c. 1520), in Paracelsus: Essential Readings, edited by Nicholas Goodrick-Clarke (1990), 50-1.
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Every utterance from government - from justifying 90-day detention to invading other countries [and] to curtailing civil liberties - is about the dangers of religious division and fundamentalism. Yet New Labour is approving new faith schools hand over fist. We have had the grotesque spectacle of a British prime minister, on the floor of the House of Commons, defending - like some medieval crusader - the teaching of creationism in the science curriculum at a sponsor-run school whose running costs are wholly met from the public purse.
In The Guardian (10 Apr 2006).
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I may finally call attention to the probability that the association of paternal and maternal chromosomes in pairs and their subsequent separation during the reducing division as indicated above may constitute the physical basis of the Mendelian law of heredity.
'On the Morphology of the Chromosome Group in Brachystola Magna', Biological Bulletin (1902), 4, 39.
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It is known that there is an infinite number of worlds, but that not every one is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so if every planet in the Universe has a populations of zero then the entire population of the Universe must also be zero, and any people you may actually meet from time to time are merely the products of a deranged imagination.
'Fit the Fifth', The Original Hitchhiker Radio Script, 102. In Alma E. Cavazos-Gaither, Mathematically Speaking (1998), 58.
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Mathematics—a wonderful science, but it hasn't yet come up with a way to divide one tricycle between three small boys.
In Bob Phillips, Phillips' Treasury of Humorous Quotations (2004), 171.
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Matter, though divisible in an extreme degree, is nevertheless not infinitely divisible. That is, there must be some point beyond which we cannot go in the division of matter. ... I have chosen the word “atom” to signify these ultimate particles.
Dalton's Manuscript Notes, Royal Institution Lecture 18 (30 Jan 1810). In Ida Freund, The Study of Chemical Composition: An Account of its Method and Historical Development (1910), 288.
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Not all living creatures die. An amoeba, for example, need never die; it need not even, like certain generals, fade away. It just divides and becomes two new amoebas.
In talk, 'Origin of Death' (1970).
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One has to divide one's time between politics and our equations. But our equations are much more important to me, because politics is for the present, while such an equation is for eternity.
Remark to his assistant, Ernst Straus,(late 1940s) while at Princeton University Institute of Advanced Study. As quoted in Albrecht Fösling and Ewald Osers (trans.), Albert Einstein: A Biography (1997), 725. At the time Einstein was one of the Emergency Committee of Atomic Scientists, concerned with informing the public on the atomic bomb and its effects. (He was its Chairman from May 1946.)
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Ordinarily logic is divided into the examination of ideas, judgments, arguments, and methods. The two latter are generally reduced to judgments, that is, arguments are reduced to apodictic judgments that such and such conclusions follow from such and such premises, and method is reduced to judgments that prescribe the procedure that should be followed in the search for truth.
Ampére expresses how arguments have a logical structure which he expected should be applied to relate scientific theories to experimental evidence. In James R. Hofmann, André-Marie Ampère (1996), 158. Cites Académie des Sciences Ampère Archives, École Normale lecture 15 notes, box 261.
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The divisions of science are not like different lines that meet in one angle, but rather like the branches of trees that join in one trunk.
The Works of Francis Bacon (1815), Vol. 6, 68.
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The extracellular genesis of cells in animals seemed to me, ever since the publication of the cell theory [of Schwann], just as unlikely as the spontaneous generation of organisms. These doubts produced my observations on the multiplication of blood cells by division in bird and mammalian embryos and on the division of muscle bundles in frog larvae. Since then I have continued these observations in frog larvae, where it is possible to follow the history of tissues back to segmentation.
'Ueber extracellulare Eutstehung thierischer Zelleu und üüber Vermehrung derselben durch Theilung', Archiv für Anatomie, Physiologie und Wissenschaftliche Medicin (1852), 1, 49-50. Quoted in Erwin H. Ackerknecht, Rudolf Virchow: Doctor Statesman Anthropologist (1953), 83-4.
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The nucleic acids, as constituents of living organisms, are comparable In importance to proteins. There is evidence that they are Involved In the processes of cell division and growth, that they participate In the transmission of hereditary characters, and that they are important constituents of viruses. An understanding of the molecular structure of the nucleic acids should be of value In the effort to understand the fundamental phenomena of life.
[Co-author with American chemist, B. Corey (1897-1971)]
'A Proposed Structure for the Nucleic Acids', Proceedings of the National Academy of Sciences (1953), 39, 84.
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The observer is not he who merely sees the thing which is before his eyes, but he who sees what parts the thing is composed of. To do this well is a rare talent. One person, from inattention, or attending only in the wrong place, overlooks half of what he sees; another sets down much more than he sees, confounding it with what he imagines, or with what he infers; another takes note of the kind of all the circumstances, but being inexpert in estimating their degree, leaves the quantity of each vague and uncertain; another sees indeed the whole, but makes such an awkward division of it into parts, throwing into one mass things which require to be separated, and separating others which might more conveniently be considered as one, that the result is much the same, sometimes even worse than if no analysis had been attempted at all.
In A System of Logic Ratiocinative and Inductive (1858), 216.
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This king [Sesostris] divided the land among all Egyptians so as to give each one a quadrangle of equal size and to draw from each his revenues, by imposing a tax to be levied yearly. But everyone from whose part the river tore anything away, had to go to him to notify what had happened; he then sent overseers who had to measure out how much the land had become smaller, in order that the owner might pay on what was left, in proportion to the entire tax imposed. In this way, it appears to me, geometry originated, which passed thence to Hellas.
Heroditus
(II. c. 109) As quoted in Florian Cajori, A History of Elementary Mathematics (1893), 10, footnoted to C.A. Bretschneider, Die Geometrie und die Geometer vor Eukides (1870). Note that the word geometry itself means “land measurement.”
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Words divide, pictures unite.
In Otto Neurath, Empiricism and Sociology (1973), 217.
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“She can’t do Subtraction.” said the White Queen. “Can you do Division? Divide a loaf by a knife—what's the answer to that?”
“I suppose-” Alice was beginning, but the Red Queen answered for her.
“Bread-and-butter, of course.”
Through the Looking Glass and What Alice Found There (1871, 1897), 189-190.
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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
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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
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Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
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Henry Adams
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John Dalton
- 40 -
Pierre Fermat
Edward Wilson
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JJ Thomson
Thomas Kuhn
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Archimedes
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- 30 -
Andreas Vesalius
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- 20 -
Carl Sagan
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- 10 -
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