“We have not a direct intuition of simultaneity, nor of the equality of two durations. If we think we have this intuition, this is an illusion. We replace it by the aid of certain rules which we apply almost always without taking count of them.
…We …choose these rules, not because they are true, but because they are the most convenient, and we may recapitulate them as follows: "The simultaneity of two events, or the order of their succession, the equality of two durations, are to be so defined that the enunciation of the natural laws may be as simple as possible. In other words, all these rules, all these definitions, are only the fruit of an unconscious opportunism."”
Source: The Value of Science (1905), Ch. 2: The Measure of Time
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Henri Poincaré 49
French mathematician, physicist, engineer, and philosopher … 1854–1912Related quotes
La plupart des évènements ont des causes aussi petites. Nous les ignorons, parce que la plupart des historiens les ont ignorées eux-mêmes, ou parce qu’ils n’ont pas eu d’yeux pour les appercevoir. Il est vrai qu’à cet égard l’esprit peut réparer leurs omissions : la connoissance de certains principes supplée facilement à la connoissance de certains faits.
Essay III, Chapter I
De l'esprit or, Essays on the Mind, and Its Several Faculties (1758)
"Systems of Logic Based on Ordinals," section 11: The purpose of ordinal logics (1938), published in Proceedings of the London Mathematical Society, series 2, vol. 45 (1939)
In a footnote to the first sentence, Turing added: "We are leaving out of account that most important faculty which distinguishes topics of interest from others; in fact, we are regarding the function of the mathematician as simply to determine the truth or falsity of propositions."
Context: Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning... The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.
Responding to the social theories of Benjamin Kidd, in "Kidd's 'Social Evolution'" in The North American Review (July 1895), p. 109
1890s
Context: A perfectly stupid race can never rise to a very high plane; the negro, for instance, has been kept down as much by lack of intellectual development as by anything else; but the prime factor in the preservation of a race is its power to attain a high degree of social efficiency. Love of order, ability to fight well and breed well, capacity to subordinate the interests of the individual to the interests of the community, these and similar rather humdrum qualities go to make up the sum of social efficiency. The race that has them is sure to overturn the race whose members have brilliant intellects, but who are cold and selfish and timid, who do not breed well or fight well, and who are not capable of disinterested love of the community. In other words, character is far more important than intellect to the race as to the individual. We need intellect, and there is no reason why we should not have it together with character; but if we must choose between the two we choose character without a moment's hesitation.
As quoted in A Dictionary of Scientific Quotations (1991) by Alan L. Mackay, p. 79
As quoted in Visions : How Science Will Revolutionize the Twenty-First Century (1999) by Michio Kaku, p. 295
2000s and attributed from posthumous publications
Foreword to the 1946 edition
Brave New World (1932)
Context: Unless we choose to decentralize and to use applied science, not as the end to which human beings are to be made the means, but as the means to producing a race of free individuals, we have only two alternatives to choose from: either a number of national, militarized totalitarianisms, having as their root the terror of the atomic bomb and as their consequence the destruction of civilization (or, if the warfare is limited, the perpetuation of militarism); or else one supra-national totalitarianism, called into existence by the social chaos resulting from rapid technological progress in general and the atomic revolution in particular, and developing, under the need for efficiency and stability, into the welfare-tyranny of Utopia. You pays your money and you takes your choice.