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Feb 14, 2011

Geometry and infinity

Post @ 13:33:06 | thoughts

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Consider a triangle motif with a few local copies, called translates. As soon as those translates are distinct, it is obviously impossible to cover them with one translated copy of the motif. Now, relax triangles to cones (by fixing one apex, and letting the other two triangle vertices go far away while keeping their edge direction). It is always possible to cover those cone translates with one copy of the cone. The science of infinity is puzzling as clearly no eye sees "it", but only our mind imagines it. There is not a single infinity. Cantor had great difficulties conveying those notions, and sadly suffered of depression. Godel's incompleteness theorem also kicks in the Continuum Hypothesis that can neither be proven true nor false...

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