Wednesday, January 09, 2008

HENRI POINCARE : Mathematics and Science-Last Essays

Jules Henri Poincare (1854-1912)

The scientist does not study nature because it is useful. He studies it because he delights in it, and he delights in it because it is beautiful.

HENRI POINCARE Mathematics and Science:Last Essays

Since we are assuming at this juncture the point of view of the mathematician, we must give to this concept all the precision that it requires, even if it becomes necessary to use mathematical language. We should then say that the body of laws is equivalent to a system of differential equations which link the speed of variations of the different elements of the universe to the present values of these elements.

Such a system involves, as we know, an infinite number of solutions, But if we take the initial values of all the elements, that is,their values at the instant t =(which would correspond in ordinary language to the "present"), the solution is completely determined, so that we can calculate the values of all the elements at any period
whatever, whether we suppose />0, which corresponds to the "future," or whether we suppose t<0, which corresponds to the "past." What is important to remember is that the manner of inferring the past from the present does not differ from that of inferring the future from the present.

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