„The physicist who states a law of nature with the aid of a mathematical formula is abstracting a real feature of a real material world, even if he has to speak of numbers, vectors, tensors, state-functions, or whatever to make the abstraction.“

—  Hilary Putnam, in What is Mathematics, in [Hilary Putnam, Mathematics, matter, and method, Cambridge University Press, 1979, 0521295505, 60]
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Hilary Putnam
1926 - 2016

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Nikolai Ivanovich Lobachevsky photo

„There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.“

—  Nikolai Ivanovich Lobachevsky Russian mathematician of Ukrainian origin 1792 - 1856
As quoted in George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane, Springer (1998 [1975]), p. 225; also in Stanley Gudder, A Mathematical Journey, McGraw-Hill (1976), p. 36.

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„It is really quite impossible to say anything with absolute precision, unless that thing is so abstracted from the real world as to not represent any real thing.“

—  Richard Feynman American theoretical physicist 1918 - 1988
Context: The real problem in speech is not precise language. The problem is clear language. The desire is to have the idea clearly communicated to the other person. It is only necessary to be precise when there is some doubt as to the meaning of a phrase, and then the precision should be put in the place where the doubt exists. It is really quite impossible to say anything with absolute precision, unless that thing is so abstracted from the real world as to not represent any real thing.Pure mathematics is just such an abstraction from the real world, and pure mathematics does have a special precise language for dealing with its own special and technical subjects. But this precise language is not precise in any sense if you deal with real objects of the world, and it is only pedantic and quite confusing to use it unless there are some special subtleties which have to be carefully distinguished. " New Textbooks for the "New" Mathematics http://calteches.library.caltech.edu/2362/1/feynman.pdf", Engineering and Science volume 28, number 6 (March 1965) p. 9-15 at p. 14 Paraphrased as "Precise language is not the problem. Clear language is the problem."

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Paul Klee photo

„[It].... is a real declaration of love toward art. Abstraction from this world more as a game, less as a failure of the earthly. Somewhere in between. The man in love no longer drinks and eats..“

—  Paul Klee German Swiss painter 1879 - 1940
1911 - 1914, Diary entry (1912), # 922; as quoted by Francesco Mazzaferro, in 'The Diaries of Paul Klee Part Four', : Klee as an Expressionist and Constructivist Painter http://letteraturaartistica.blogspot.nl/2015/05/paul-klee-ev27.html

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Ernest Flagg photo

„In the human form, as nature tries to make it, every feature is useful and every feature is beautiful. Each member is perfectly adapted to the function it has to perform; nothing is superfluous“

—  Ernest Flagg American architect 1857 - 1947
Small Houses: Their Economic Design and Construction (1922), Context: In the human form, as nature tries to make it, every feature is useful and every feature is beautiful. Each member is perfectly adapted to the function it has to perform; nothing is superfluous, yet the whole and every part is supremely decorative.<!-- Introduction

George Woodcock photo

„Proudhon goes on to suggest that the real laws by which society functions have nothing to do with authority; they are not imposed from above, but stem from the nature of society itself. He sees the free emergence of such laws as the goal of social endeavour.“

—  George Woodcock Canadian writer of political biography and history, an anarchist thinker, an essayist and literary critic 1912 - 1995
Anarchism : A History of Libertarian Ideas and Movements (1962), Context: Proudhon goes on to suggest that the real laws by which society functions have nothing to do with authority; they are not imposed from above, but stem from the nature of society itself. He sees the free emergence of such laws as the goal of social endeavour. … Proudhon conceiving a natural law of balance operating within society, rejects authority as an enemy and not a friend of order, and throws back at the authoritarians the accusations leveled at anarchists; in the process he adopts the title he hopes to have cleared of obloquy. Prologue

„Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam egestas wisi a erat. Morbi imperdiet, mauris ac auctor dictum.“

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