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I shall conclude that there is in all of us an intuitive notion of the continuum of any number of dimensions whatever because we possess the capacity… - Henri Poincaré
" "I shall conclude that there is in all of us an intuitive notion of the continuum of any number of dimensions whatever because we possess the capacity to construct a physical and mathematical continuum; and that this capacity exists in us before any experience, because, without it, experience properly speaking would be impossible and would be reduced to brute sensations. ... And yet this capacity could be used in different ways; it could enable us to construct a space of four just as well as a space of three dimensions.
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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
Are the laws of acceleration and composition of forces nothing but arbitrary conventions? Conventions, yes; arbitrary, no; they would seem arbitrary if we forgot the experiences which guided the founders of science to their adoption and which are, although imperfect, sufficient to justify them. Sometimes it is useful to turn our attention to the experimental origin of these conventions.
How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.
The notion of infinity had long since been introduced into mathematics, but this infinity was what philosophers call a becoming. Mathematical infinity was only a quantity susceptible of growing beyond all limit; it was a variable quantity of which it could not be said that it had passed, but only that it would pass, all limits.
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