FLOOD, CHAIN, BALL – NAUFRAGE
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We were together further than I expected. Orienting myself as best as I could, I returned straight to our beautiful anthill, when I met a deserted, mountainous, arid place, in which I had to run the greatest dangers. It was … Read More

Henri Poincaré, Why space with three dimensions – Analysis Situs and intuition
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I would like to add a remark which relates only indirectly to the foregoing; we have seen above the importance of the Analysis Situs and I explained that this is the real domain of geometric intuition. Does this intuition exist? … Read More

The adventures of a red ant: XVII. VITALITY OF ANOMMAS – THE HEN PASSES IN FRONT OF THE NOSE
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The adventures of a red ant: XVII. VITALITY OF ANOMMAS – THE HEN PASSES IN FRONT OF THE NOSE Before the end of the following week, I had eaten python like the others, we had surprised one in a swamp … Read More

Henri Poincaré, Why space with three dimensions – Space and Nature
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But the question can be asked from a completely different point of view. We have so far placed ourselves in a purely subjective, purely psychological or, if you will, physiological point of view; we have only considered the relations of … Read More

The adventures of a red ant: XVI. IN SENEGAL – N’DIEN – THE PYTHON
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I remained a few days in the orchard; but, by two or three adventures which nearly happened to me, I judged that the stay in the midst of those big oxen which blindly trampled all this campaign, was unhealthy for … Read More

Henri Poincaré, Why space with three dimensions – Space and movements
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It seems, therefore, that space cannot be constructed by considering sets of simultaneous sensations, which must be considered as sequences of sensations. Always go back to what I said before. Why do certain changes appear to us as changes of … Read More

The adventures of a red ant: XV. THE FAST – THE HARVESTERS
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“Enough Brazil! we would leave our skin … Let’s go … !!!“ Such was the resolution I took one fine morning, when the forces returned to me. I still had, I confess, a leg that worked with a little pain … Read More

Henri Poincaré, Why space with three dimensions – Space and senses
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The question seems resolved; we seem to have only to apply this rule, either to the physical continuum, which is the coarse image of space, or to the corresponding mathematical continuum which is its refined image and which is the … Read More

The adventures of a red ant: XIV. ANTEATER AND PUMA – DOUBLE-SPINE DEATH
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We both chatted, enjoying the delightful tranquility of the evening that was being made, and which, in these countries, is short, but delightful after the ardor of the day, when our attention was awakened by a slow, heavy step which … Read More

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

The adventures of a red ant: THE WALKING LEAVES – SOFT HEADS AND RUDE HEADS
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“I am very interested in you,” I said to my friend Double-Spine; ”the more I go, the more I understand and appreciate what I heard from an old queen from home: The world belongs to the ants! …” “Your old … 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

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