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Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority.
In the old days when people invented a new function they had something useful in mind.
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.
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.
If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the different parts of physics, it is impossible not to be struck by the analogies existing.
Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.
Hypotheses are what we lack the least.
How is an error possible in mathematics?
Geometry is not true, it is advantageous.
Facts do not speak.
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.
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.
A small error in the former will produce an enormous error in the latter.
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