Plea for Euclid*
Bernard Cache
www.objectile.net
Of course, we cannot affirm that space exists as such, nor can we affirm anything of its substance. Some would even deny that things exist, and maintain that perceptions are just mental events. Nevertheless, we know that there are differences in our perception. A diversity of things are thought before we even think of ourselves as the subject of that thinking. The Leibnizian cogitata comes prior to the Cartesian cogito. And, following Kant, space is the form according to which we organize variations in what occurs to us simultaneously, just as time is the form according to which we organize variations in what occurs to us in succession. Kant thought that Euclidean geometry was the ultimate organization of this form of intuition we call space. But some twenty years after Kant died in 1804, several mathematicians working independently, including: Gauss, Bolyai and Lobachevsky - discovered that we can think of other geometries. These non-euclidean geometries were based on counter-intuitive assumptions and at first were thought of as nothing but a mathematician's game. But less than a hundred years later, Einstein found that in his theory of general relativity, space was better described by using a complex variant of Lobachevsky's geometry. And as this theory of relativity was given very precise experimental validation, non-euclidean geometry proved its relevance and could no longer appear as an exotic logic...
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["Plea for Euclid" is published both by Arch'it and ANY Review. The italian translation is by Marco Brizzi. By Bernard Cache, MIT Press published "Earth Moves", available at Amazon.com]
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