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 (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 (11)
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So 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 … Read More

Henri Poincaré, The evolution of laws (10)
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Thus there is not a single law that we can state with the certainty that it has always been true in the past with the same approximation as today, I will say more, with the certainty that we will never … Read More

Henri Poincaré, The evolution of laws (9)
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Let us return to our imaginary world and ask ourselves if its inhabitants could not, without renewing the history of the sleepers of Ephesus, perceive this evolution. No doubt, no matter how perfect the heat conductivity on their planet, it … 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

Philosophy of physics
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(The wave-particle duality, in which we can see how the same phenomenon can be perceived in two different ways, was one of the philosophical problems posed by quantum mechanics.) The philosophy of physics refers to the set of philosophical reflections … 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

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