Sunday, June 29, 2008

Jules-Henri Poincaré


1. ”Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence.... The two propositions: "The earth turns round" and "it is more convenient to suppose the earth turns round" have the same meaning; there is nothing more in the one than in the other.”
2. "A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of the same universe at a succeeding moment. But even if it were the case that the natural laws had nolonger any secret for us, we could still know the situation approximately. If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by the laws. But is not always so; it may happen that small differences in the initial conditions produce very great ones in the finalphenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible..."
3. " ...by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous."
4. "Facts do not speak."
5. "Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination."
6. “If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.”
7. "Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority. To invent is to discern, to choose."
8. “It is through science that we prove, but through intuition that we discover.”
9. ”Mathematicians are born, not made.”
10. “Science is built up of facts, as a house is with stone, but a collection of facts is no more of a science than a heap of stones is a house.”
11. “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. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living. Of course I do not here speak of that beauty that strikes the senses, the beauty of qualities and appearances; not that I undervalue such beauty, far from it, but it has nothing to do with science; I mean that profounder beauty which comes from the harmonious order of the parts, and which a pure intelligence can grasp.”
12. ”Thought is only a flash between two long nights, but this flash is everything.”
13. “To doubt everything or to believe everything are two equally convenient solutions; both dispense with the necessity of reflection.”
14. "What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details."