Around two-thousand years ago, a book with texts by some of the philosophers of Greek antiquity was compiled. 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 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 spatial 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.
Christian Waldvogel