“For although it is certainly true that quantitative measurements are of great importance, it is a grave error to suppose that the whole of experimental physics can be brought under this heading. We can start measuring only when we know what to measure: qualitative observation has to precede quantitative measurement, and by making experimental arrangements for quantitative measurements we may even eliminate the possibility of new phenomena appearing.”

—  Hendrik Casimir

in his memoirs, as quoted by [Jean Matricon, G. Waysand, Charles Glashausser, The cold wars: a history of superconductivity, Rutgers University Press, 2003, 0813532957, 18]

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Hendrik Casimir 1
Dutch physicist 1909–2000

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“Today we preach that science is not science unless it is quantitative. We substitute correlations for causal studies, and physical equations for organic reasoning. Measurements and equations are supposed to sharpen thinking, but, in my observation, they more often tend to make the thinking noncausal and fuzzy. They tend to become the object of scientific manipulation instead of auxiliary tests of crucial inferences.
Many - perhaps most - of the great issues of science are qualitative, not quantitative, even in physics and chemistry. Equations and measurements are useful when and only when they are related to proof; but proof or disproof comes first and is in fact strongest when it is absolutely convincing without any quantitative measurement.
Or to say it another way, you can catch phenomena in a logical box or in a mathematical box. The logical box is coarse but strong. The mathematical box is fine-grained but flimsy. The mathematical box is a beautiful way of wrapping up a problem, but it will not hold the phenomena unless they have been caught in a logical box to begin with.”

John R. Platt (1918–1992) American physicist

John R. Platt (1964) " Science, Strong Inference -- Proper Scientific Method (The New Baconians) http://256.com/gray/docs/strong_inference.html. In: Science Magazine 16 October 1964, Volume 146, Number 3642. Cited in: Gerald Weinberg (1975) Introduction to General Systems Thinking. p. 1, and in multiple other sources.

“As every bookie knows instinctively, a number such as reliability - a qualitative rather than a quantitative measure - is needed to make the valuation of information practically useful.”

Hans Christian von Baeyer (1938) American physicist

Source: Information, The New Language of Science (2003), Chapter 24, Bits, Bucks, Hits and Nuts, Information theory beyond Shannon, p. 221

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“The first step is to measure whatever can easily be measured. This is OK as far as it goes. The second step is to disregard that which can't be easily measured or to give it an arbitrary quantitative value. This is artificial and misleading. The third step is to presume that what can't be measured easily really isn't important. This is blindness. The fourth step is to say that what can't be easily measured really doesn't exist. This is suicide.”

Charles Handy (1932) Irish economist

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“Nevertheless, there remains still in the new kind of theory an objective reality, inasmuch as these theories deny any possibility for the observer to influence the result of a measurement, once the experimental arrangement is chosen.”

Wolfgang Pauli (1900–1958) Austrian physicist, Nobel prize winner

"Matter" in Man's Right to Knowledge, 2nd series (1954), p. 10; also in Writings on Physics and Philosophy‎ (1994) edited by Charles Paul P. Enz and Karl von Meyenn
Context: In the new pattern of thought we do not assume any longer the detached observer, occurring in the idealizations of this classical type of theory, but an observer who by his indeterminable effects creates a new situation, theoretically described as a new state of the observed system. In this way every observation is a singling out of a particular factual result, here and now, from the theoretical possibilities, therefore making obvious the discontinuous aspect of physical phenomena.
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“Heredity. Given any organ in a parent and the same or any other organ in its offspring, the mathematical measure of heredity is the correlation of these organs for pairs of parent and offspring... The word organ here must be taken to include any characteristic which can be quantitatively measured.”

Karl Pearson (1857–1936) English mathematician and biometrician

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“It is not easy to measure the ocean, but we can be measured by it, confront it, and be in it.”

Terence McKenna (1946–2000) American ethnobotanist

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“Dalton, the mathematical tutor, following up the lead of Newton, combined the whole of the results of quantitative measurement which had accumulated up to his time, in a comprehensive theory, based on the concept of the chemical atom.”

J. R. Partington (1886–1965) British chemist

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Higher Mathematics for Chemical Students (1911)

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“What has philosophy got to do with measuring anything? It's the mathematicians you have to trust, and they measure the skies like we measure a field.”

Galileo Galilei (1564–1642) Italian mathematician, physicist, philosopher and astronomer

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“The problem with trying to measure productivity is that it measures only how well people can do the wrong jobs. Any job that can be measured for productivity probably should be eliminated from the list of jobs that people do.”

Kevin Kelly (1952) American author and editor

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