“We can no more have exact religious thinking without theology, than exact mensuration and astronomy without mathematics, or exact iron-making without chemistry”

— John Hall

Source: Dictionary of Burning Words of Brilliant Writers (1895), P. 580.

Adopted from Wikiquote. Last update June 3, 2021. History

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John Hall 20

Presbyterian pastor from Northern Ireland in New York, died… 1829–1898

Cyrus H. Gordon (1908–2001) American linguist

Introduction
Adventures in the Nearest East (1957)

“Cats can work out mathematically the exact place to sit that will cause most inconvenience.”

Pam Brown (1948) Australian poet

“Mathematical Reasoning is not only exact; it has its own criteria of reality”

Paul Karl Feyerabend book Science in a Free Society

pg 52.
Science in a Free Society (1978)

“The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.”

John Von Neumann (1903–1957) Hungarian-American mathematician and polymath

As quoted in Bigeometric Calculus: A System with a Scale-Free Derivative (1983) by Michael Grossman, and in Single Variable Calculus (1994) by James Stewart.

“We are… bound to attach the greatest importance to the preliminary step taken by Lavoisier, who is even more justly called the father of modern chemistry than Kepler is called the father of modern astronomy. The exact claims of Lavoisier to this important place in the history of chemistry have been variously stated: …since his time, and greatly through his labours, the quantitative method has been established as the ultimate test of chemical facts; the principle of this method being the rule that in all changes of combination and reaction, the total weight of the various ingredients—be they elementary bodies or compounds—remains unchanged. The science of chemistry was thus established upon an exact, a mathematical basis. By means of this method Lavoisier, utilising and analysing the results gained by himself and others before him, notably those of Priestley, Cavendish, and Black, succeeded in destroying the older theory of combustion, the so-called phlogistic theory.”

Antoine Lavoisier (1743–1794) French chemist

John Theodore Merz, A History of European Thought in the Nineteenth Century Vol.1 http://books.google.com/books?id=xqwQAAAAYAAJ (1903)

“The gratification of one desire only makes way for another still more exacting.”

Timothy Shay Arthur (1809–1885) Novelist, short story writer, publisher

Advice to Young Men on Their Duties and Conduct in Life (1848), p. 31

“If one cannot get along without a mirror, even in shaving oneself, how can one reconstruct oneself or one's life, without seeing oneself in the "mirror" of literature? Of course no one speaks about an exact mirror. No one even thinks of asking the new literature to have mirror-like impassivity. The deeper literature is, and the more it is imbued with the desire to shape life, the more significantly and dynamically it will be able to "picture" life.”

Leon Trotsky book Literature and Revolution

Literature and Revolution (1924), edited by William Keach (2005), Ch. 4 : Futurism, p. 120
Variants:
Art is not a mirror to hold up to society, but a hammer with which to shape it.
Remarks apparently derived from Trotsky's observations, or those he implies preceded his own, this is attributed to Bertolt Brecht in Paulo Freire : A Critical Encounter (1993) by Peter McLaren and Peter Leonard, p. 80, and to Vladimir Mayakovsky in The Political Psyche (1993) by Andrew Samuels, p. 9
Art is not a mirror held up to society, but a hammer with which to shape it.
Context: Art, it is said, is not a mirror, but a hammer: it does not reflect, it shapes. But at present even the handling of a hammer is taught with the help of a mirror, a sensitive film that records all the movements. Photography and motion-picture photography, owing to their passive accuracy of depiction, are becoming important educational instruments in the field of labor. If one cannot get along without a mirror, even in shaving oneself, how can one reconstruct oneself or one's life, without seeing oneself in the "mirror" of literature? Of course no one speaks about an exact mirror. No one even thinks of asking the new literature to have mirror-like impassivity. The deeper literature is, and the more it is imbued with the desire to shape life, the more significantly and dynamically it will be able to "picture" life.

“Every one knows that the fine phrase "God geometrizes" is attributed to Plato, but few know where this famous passage is found, or the exact words in which it was first expressed. Those who, like the author, have spent hours and even days in the search of the exact statements, or the exact references, of similar famous passages, will not question the timeliness and usefulness of a book whose distinct purpose it is to bring together into a single volume exact quotations, with their exact references, bearing on one of the most time-honored, and even today the most active and most fruitful of all the sciences, the queen-mother of all the sciences, that is, mathematics.”

Robert Edouard Moritz (1868–1940) German mathematician

Robert Edouard Moritz. On Mathematics and Mathematicians https://archive.org/details/onmathematicsmat00mori, 1914, 1942, 1958; p. v; Preface, lead sentence

“The objection made to the numerical method, to wit, the difficulty or impossibility of forming classes of similar facts, is alike applicable to all the methods that might be substituted; that it is impossible to appreciate each case with mathematical exactness, and it is precisely on this account that enumeration becomes necessary; by so doing, the errors, (which are inevitable,) being the same in two groups of patients subjected to different treatment, mutually compensate each other, and they may be disregarded without sensibly affecting the exactness of the results.”

Pierre Charles Alexandre Louis (1787–1872) French physician

p, 125
Researches on the effects of bloodletting... (1836)

“"One sees, from this Essay, that the theory of probabilities is basically just common sense reduced to calculus; it makes one appreciate with exactness that which accurate minds feel with a sort of instinct, often without being able to account for it."”

Pierre-Simon Laplace (1749–1827) French mathematician and astronomer

"On voit, par cet Essai, que la théorie des probabilités n'est, au fond, que le bon sens réduit au calcul; elle fait apprécier avec exactitude ce que les esprits justes sentent par une sorte d'instinct, sans qu'ils puissent souvent s'en rendre compte."
From the Introduction to Théorie Analytique des Probabilités http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-88764, second and later editions; also published separately as Essai philosophique sur les Probabilités (1814). Œuvres complètes de Laplace, tome VII, p. cliii, Paris: Gauthier-Villars, 1878-1912.
Also reported as: "The theory of probabilities is at bottom nothing but common sense reduced to calculus; it enables us to appreciate with exactness that which accurate minds feel with a sort of instinct for which ofttimes they are unable to account."
Or as: "Probability theory is nothing but common sense reduced to calculation."

“We can no more have exact religious thinking without theology, than exact mensuration and astronomy without mathematics, or exact iron-making without chemistry”

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John Hall 20

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