Henri Poincaré, Why space with three dimensions – Continuum and cuts

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But what is a continuum with n dimensions; how does it differ from a continuum whose number of dimensions is larger or smaller? First, let us recall some results recently obtained by the students of Cantor. It is possible to … Read More

Henri Poincaré, Why space with three dimensions – Analysis Situs (Topology)

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Geometers usually distinguish two kinds of geometries, which they call the first of metric and the second of projective; metric geometry is based on the notion of distance; two figures are regarded as equivalent when they are “equal” in the … Read More

Henri Poincaré, Space and time (2) – Physical and psychological relativity

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The psychological time, the Bergsonian duration, from which the scientist’s time has come out, serves to classify the phenomena that occur in the same consciousness; it is powerless to classify two psychological phenomena which have for their theater two different … Read More

Henri Poincaré, Space and time (1)

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One of the reasons that led me to return to one of the questions I have most often dealt with, is the recent revolution in our ideas on mechanics. Will the principle of relativity, as conceived by Lorentz, not impose … Read More

Henri Poincaré, The evolution of laws (8)

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I suppose a world whose various parts possess a heat conductivity so perfect that they are constantly in equilibrium of temperature. The inhabitants of this world would have no idea of ​​what we call temperature difference; in their treatises on … Read More

Henri Poincaré, The evolution of laws (7)

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Let us now turn to another point of view. The laws that direct observation gives us are never more than results. Take for example the law of Mariotte. For most physicists, this is only a consequence of the kinetic theory … Read More

Henri Poincaré, The evolution of laws (6)

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And if humanity were to last longer than we have supposed, long enough to see the laws evolve before its eyes? Or even if it came to acquire instruments delicate enough that this variation, slow as it is, becomes sensitive … Read More

Henri Poincaré, The evolution of laws (5)

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I raised this question incidentally only; it deserves to be thought about; but I do not want to be dragged too far from my subject. Is it possible that the contradictions of geologists never lead scientists to conclude the evolution … Read More

Henri Poincaré, The evolution of laws (4)

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Let me digress here. We have just seen that the geologist possesses an instrument which the mathematician misses and which enables him to conclude from the present to the past. Why does the same instrument not allow us to conclude … Read More

Henri Poincaré, The evolution of laws (3)

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At this point, we can oppose an argument of fact. “You say that in seeking to ascend, thanks to the knowledge of the laws, from the present to the past, one will never meet with a contradiction, and yet the … Read More

Henri Poincaré, The evolution of laws (2)

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But, it will be said, could it not be that the application of the preceding process would lead to a contradiction, or, if one wishes, that our differential equations admit no solution? Since the hypothesis of the immutability of laws, … Read More

Henri Poincaré: The evolution of laws (1)

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Mr. Boutroux, in his work on the contingency of the laws of nature, wondered if natural laws are not likely to change, if while the world is changing continuously, the laws themselves, that is to say to say the rules … Read More

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