29 January 2026

On Measures (-1849)

"Numbers prime to one another are those which are measured by a unit alone as a common measure." (Euclid, "The Elements", Book VII)

"Measure, time and number are nothing but modes of thought or rather of imagination." (Baruch Spinoza, [Letter to Ludvicus Meyer] 1663)

"To measure motion, space is as necessary to be considered as time. [... They] are made use of to denote the position of finite: real beings, in respect one to another, in those infinite uniform oceans of duration and space." (John Locke, "An Essay Concerning Human Understanding", 1689)

"Most of our philosophical instruments are measures of effects. The progress made in natural philosophy increases every day by the number of these measures; by these it still continues to be improved." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

"Mathematical analysis is as extensive as nature itself; it defines all perceptible relations, measures times, spaces, forces, temperatures; this difficult science is formed slowly, but it preserves every principle which it has once acquired; it grows and strengthens itself incessantly in the midst of the many variations and errors of the human mind. It's chief attribute is clearness; it has no marks to express confused notations. It brings together phenomena the most diverse, and discovers the hidden analogies which unite them." (J B Joseph Fourier, "The Analytical Theory of Heat", 1822)

"The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible, or all of which have the same chance." (Siméon-Denis Poisson, "Recherches sur la Probabilités des Jugemens" ["An Investigation of the Laws of Thought"], 1837)

"Yet time and space are but inverse measures of the force of the soul. The spirit sports with time." (Ralph W Emerson, "Essays", 1841)

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On Measures (-1849)

"Numbers prime to one another are those which are measured by a unit alone as a common measure." (Euclid, "The Elements"...