Essay for a cosmology of inversion





Abstract

Around two-thousand years ago, someone compiled a book with texts by a few of the philosophers of Greek antiquity. It contained an aphorism stating that «God is the Infinite Sphere whose Center is Everywhere and Circumference Nowhere.» Over the course of the centuries, this image of an impossible sphere was adapted to no longer describe God, but to imagine the shape of the Universe.

Using the dream-like quality of this impossible geometry as an argument, and a text by Jorge Luis Borges as a guide, the author follows a philosophical chain of associations that lead from one fundamental to another, from geometry to music to language to intelligence to paradoxa to zero to inversions to infinity. This tour d’horizon inspires the proposal of a novel geometric shape    the ‹spherene›    which may suffice the conditions called for in the aphorism, while possibly being globally hyperbolic. Maybe one day, we will learn that the Greek philosophers were right all along.

The argumentative structure of the text assumes the form of a lemniscate, supporting the conclusion that fundamentals build on other fundamentals, organized in infinite loops. Notes provide alternate readings, supplemental information and sometimes little escapes.

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