"The n equal parts that can be thought of as composing a total magnitude of course have the same magnitude as the n equal parts into which the total magnitude can be thought to be decomposable. All physical measurement is based on this principle. All mental measurement will also have to be based on it. ... In general, mental measurement is not particularly relevant to practical life. But it has enormous scientific importance and far-reaching implications. First, because of the common subordination of both the mental and the physical realms to the principle of mathematical determination; and second, because of the lawful relation between mental and physical magnitudes which automatically obtains when a mental measure is found." (p. 213)
Fechner, Gustav Theodor (1887, 1987) My own viewpoint on mental measurement. Trans. E. Scheerer. Psychological Research, 49, 213-219.
"I often say that when you can measure what you are speaking about and express it in numbers you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be."
Lord Kelvin, Electrical Units of Measurement, 1883.
A mathematical idea develops best when it faces hard concrete problems which are not in the "domain of attraction" of existing proof techniques. An area develops worst along the "lines of least resistance" in which existing results are slightly generalized or abstracted. I ... discourage theoreticians from the pursuit of minor variations of the known and the formalization of the ... obvious, and encourage instead the pursuit of the unknown and the unobvious.
D. Aldous (1989) Probability Approximations via the Poisson Clumping Heuristic. New York: Spring Verlag. p. 252.
"The fundamental problem of scientific progress, and a fundamental one of everyday life, is that of learning from experience."
H. Jeffreys (1961) Theory of Probability. 3rd Edition. Oxford: Clarendon Press. p.1
Fechner, G.; Lord Kelvin; Aldous, D.; Jeffreys, H.; Rasch, G. Quotations. Rasch Measurement Transactions, 2000, 14:3 p.757, 761, 765
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