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— Henri Poincare"So is not mathematical analysis then not just a vain game of the mind? To the physicist it can only give a convenient language; but isn't that a mediocre service, which after all we could have done without; and, it is not even to be feared that this artificial language be a veil, interposed between reality and the physicist's eye? Far from that, without this language most of the initimate analogies of things would forever have remained unknown to us; and we would never have had knowledge of the internal harmony of the world, which is, as we shall see, the only true objective reality."
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We thought of life by analogy with a journey, a pilgrimage, which had a serious purpose at the end, and the thing was to get to that end, success or whatever it is, maybe heaven after you’re dead. But we missed the point the whole way along. It was a musical thing and you were supposed to sing or to dance while the music was being played.
— Alan Watts
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Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don't look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding.
— Gian-Carlo Rota
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