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Henri Poincaré, The evolution of laws (11)

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Henri PoincaréSo far we have not seemed to worry about whether laws actually vary, but only if men can believe them to be variable. Are laws considered to exist outside the mind that creates or observes them immutable in themselves? Not only is the question insoluble, but it makes no sense. What is the use of wondering if in the world of things in itself the laws may vary with time, whereas in such a world the word of time may be meaningless? From what this world is, we can say nothing, or think nothing, but only from what it appears or could appear to intelligences that do not differ too much from ours.

The question thus posed has a solution. If we consider two spirits similar to ours, observing the universe on two different dates, separated for example by millions of years, each of these minds will build a science, which will be a system of laws deduced from the observed facts. It is likely that these sciences will be very different and in this sense one could say that the laws have evolved. But however great the gap may be, we shall always be able to conceive an intelligence of the same nature as ours, but of far greater significance, or called to a longer life, which will be able to synthesize and unite in a a unique, perfectly coherent formula, the two fragmentary and approximate formulas to which the two ephemeral researchers had arrived in the short time at their disposal. For him, the laws will not have changed, the science will be immutable, it will be only the scientists who have been imperfectly informed.

To take a geometric comparison, suppose that we can represent the variations of the world by an analytic curve. Each of us can see only a very small arc of this curve; if he knew him exactly, that would be enough for him to establish the equation of the curve, and to be able to prolong it indefinitely. But he has only an imperfect knowledge of this arc and he can be mistaken about this equation: if he tries to prolong the curve, the line he will draw will deviate from the real curve, especially since the known arc will be less extensive, and we will wish to extend the prolongation of this arc. Another observer will only know another bow and will know it also imperfectly only.
If the two workers are far from each other, these two extensions which they will trace will not be connected; but this does not prove that an observer with a longer view, who would directly perceive a greater length of curve, so as to embrace both these arches, would not be able to write a more exact equation and reconcile their divergent formulas; and even, however capricious the real curve may be, there will always be an analytic curve, which, for as long as one wants, will deviate as little as one likes.

No doubt many readers will be shocked to see that at any moment I seem to be replacing the world with a system of simple symbols. It’s not just a professional mathematician’s habit; the nature of my subject absolutely imposed this attitude on me. The Bergsonian world has no laws; what can be of it is simply the more or less distorted image that the scientists have of it. When we say that nature is governed by laws, we hear that this portrait is still rather resembling. It is therefore only on him and on him that we must reason, on pain of seeing the very idea of ​​law which was the object of our study vanish. But this image is removable; we can dissect it into elements, distinguish external moments from each other, independent parts. That if I have sometimes oversimplified and reduced these elements to too few, this is only a matter of degree: it did not change the nature of my reasoning and their scope; the exhibition simply became shorter.

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