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We see that experience plays an indispensable role in the genesis of geometry; but it would be an error thence to conclude that geometry is, even in … - Henri Poincaré
" "We see that experience plays an indispensable role in the genesis of geometry; but it would be an error thence to conclude that geometry is, even in part, an experimental science. If it were experimental it would be only approximative and provisional. And what rough approximation!
...The object of geometry is the study of a particular 'group'; but the general group concept pre-exists... in our minds. It is imposed on us, not as form of our sense, but as form of our understanding. Only, from among all the possible groups, that must be chosen... will be... the standard to which we shall refer natural phenomena.
Experience guides us in this choice without forcing it upon us; it tells us not which is the truest geometry, but which is the most convenient.
Notice that I have been able to describe the fantastic worlds... imagined without ceasing to employ the language of ordinary geometry.
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About Henri Poincaré
Jules Henri Poincaré (29 April 1854 – 17 July 1912), generally known as Henri Poincaré, was one of France's greatest mathematicians and theoretical physicists, and a philosopher of science.
Biography information from Wikiquote
Also Known As
Alternative Names:
Jules Henri Poincare
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Henri Poincare
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Poincare
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Jules Henri Poincaré
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Poincaré
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Additional quotes by Henri Poincaré
Le but principal de l'enseignement mathématique est de développer certaines facultés de l'esprit et parmi elles l'intuition n'est pas la moins précieuse. C'est par elle que le monde mathématique reste en contact avec le monde réel et quand les mathématiques pures pourraient s'en passer, il faudrait toujours y avoir recours pour combler l'abîme qui sépare le symbole de la réalité.
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We have selected the most convenient space, but experience has guided our choice; as this choice has been unconscious, we think it has been imposed upon us […] In this progressive education whose outcome has been the construction of space, it is very difcult to determine what is the terms of use, part of the individual, what the part of the race. How far could one of us, transported from birth to an entirely diferent world, where were dominant, for instance, bodies moving in conformity to the laws of motion of non-Euclidean solids, renounce the ancestral space to build a space completely new?
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