“Too often, this concern for the big picture is simply obscurantist and is put forward by people who prefer vagueness and mystery to (partial) answers. Vagueness is at times necessary and mystery is never in short supply, but I don’t think they’re anything to worship. Genuine science and mathematical precision are more intriguing than are the “facts” published in supermarket tabloids or a romantic innumeracy which fosters credulity, stunts skepticism, and dulls one to real imponderables.”

— John Allen Paulos

Source: Innumeracy: Mathematical Illiteracy and its Consequences (1988), Chapter 4, “Whence Innumeracy?” (pp. 126-127)

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John Allen Paulos 48

American mathematician 1945

John Tukey (1915–2000) American mathematician

The future of data analysis. Annals of Mathematical Statistics 33 (1), (1962), page 13.
Variant: "An approximate answer to the right question is worth a great deal more than a precise answer to the wrong question." "as the renowned statistician John Tukey once reportedly said," according to Super Freakonomics page 224.

“You must not know too much or be too precise or scientific about birds and trees and flowers and watercraft; a certain free-margin, or even vagueness - ignorance, credulity - helps your enjoyment of these things.”

Walt Whitman (1819–1892) American poet, essayist and journalist

“Poetry is a sort of inspired mathematics, which gives us equations, not for abstract figures, triangles, squares, and the like, but for the human emotions. If one has a mind which inclines to magic rather than science, one will prefer to speak of these equations as spells or incantations; it sounds more arcane, mysterious, recondite.”

Ezra Pound book The Spirit of Romance

The Spirit of Romance (1910), p. 5

“Progress in science is often built on wrong theories that are later corrected. It is better to be wrong than to be vague.”

Freeman Dyson (1923) theoretical physicist and mathematician

The Scientist As Rebel (2006)

“I don’t really distinguish between Linux and things that are more or less direct descendants of Unix. I think they’re all the same at some level. Often, people ask me, "Do you feel jealous about Linux being the big thing." And the answer is no, for the same reason. I think they’re the same.”

Dennis M. Ritchie (1941–2011) American computer scientist

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On Unix, Linux, and open-source (2001)

“Those who worship God for the hope of gaining, they’re not real worshippers, they’re merchants. Those who worship God out of fear (of punishment), they’re slaves. And those who worship God to be grateful towards their creator, they are the free people, and their worship is a real one.”

Husayn ibn Ali (626–680) The grandson of Muhammad and the son of Ali ibn Abi Talib

Majlisi, Bihārul Anwār, vol.78, p. 117
Religious-based Quotes

“You will perceive that economy, scientifically speaking, is a very contracted science; it is in fact a sort of vague mathematics which calculates the causes and effects of man's industry, and shows how it may be best applied.”

William Stanley Jevons (1835–1882) English economist and logician

Letter to Henrietta Jevons (28 February 1858), published in Letters and Journal of W. Stanley Jevons (1886), edited by Harriet A. Jevons, his wife, p. 101.
Context: You will perceive that economy, scientifically speaking, is a very contracted science; it is in fact a sort of vague mathematics which calculates the causes and effects of man's industry, and shows how it may be best applied. There are a multitude of allied branches of knowledge connected with mans condition; the relation of these to political economy is analogous to the connexion of mechanics, astronomy, optics, sound, heat, and every other branch more or less of physical science, with pure mathematics.

“People often complain that music is too ambiguous, that what they should think when they hear it is so unclear, whereas everyone understands words. With me, it is exactly the opposite, and not only with regard to an entire speech but also with individual words. These, too, seem to me so ambiguous, so vague, so easily misunderstood in comparison to genuine music, which fills the soul with a thousand things better than words. The thoughts which are expressed to me by music that I love are not too indefinite to be put into words, but on the contrary, too definite.”

Felix Mendelssohn (1809–1847) German composer, pianist and conductor

Die Leute beklagen sich gewöhnlich, die Musik sei so vieldeutig; es sei so zweifelhaft, was sie sich dabei zu denken hätten, und die Worte verstände doch ein Jeder. Mir geht es aber gerade umgekehrt. Und nicht blos mit ganzen Reden, auch mit einzelnen Worten, auch die scheinen mir so vieldeutig, so unbestimmt, so mißverständlich im Vergleich zu einer rechten Musik, die einem die Seele erfüllt mit tausend besseren Dingen als Worten. Das, was mir eine Musik ausspricht, die ich liebe, sind mir nicht zu unbestimmte Gedanken, um sie in Worte zu fassen, sondern zu bestimmte.
Letter to Marc-André Souchay, October 15, 1842, cited from Briefe aus den Jahren 1830 bis 1847 (Leipzig: Hermann Mendelssohn, 1878) p. 221; translation from Felix Mendelssohn (ed. Gisella Selden-Goth) Letters (New York: Pantheon, 1945) pp. 313-14.

“Between the one who counts the facts, grouped according to their resemblance, in order to know what to believe regarding the value of therapeutic agents and him who does not count but always says "more or less frequent," there is the difference between truth and error, between something that is clear and truly scientific and something that is vague and without value—for what place is there in Science for that which is vague?”

Pierre Charles Alexandre Louis (1787–1872) French physician

Recherches sur les effets de la saignée dans quelques maladies inflammatoires, et sur l'action de l'émétique et des vésicatoires dans la pneumonie (1835) as quoted by William Coleman, Death is a Social Disease: Public Health and Political Economy in Early Industrial France (1982)

“We speak of people "taking refuge" in vagueness — the more precise you are, in general the more likely you are to be wrong, whereas you stand a good chance of not being wrong if you make it vague enough.”

J. L. Austin (1911–1960) English philosopher

Sense and Sensibilia (1962), p. 125

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John Allen Paulos 48

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