Geometry and the Making of Utopian Knowledge in Early Modern Europe

In his Della Pittura, Leon Battista Alberti initiated what I call a "utopian moment,"a philosophical and practical disposition fusing human ingenuity, geometry, and political harmony. This paper follows these notions as they evolved over the course of the sixteenth century and were embraced by the new science of Johannes Kepler and René Descartes, who reshaped these utopian dispositions with their new geometrical analyses of sight and light. In his Dioptrice, Kepler suggests a new science of refractions produced and manipulated artificially through lenses, their physical properties analyzed geometrically; in analyzing the rainbow, Descartes artificially reproduces it, initially through a glass flask filled with water, and then through a prism, thus giving a geometrical causal account of its colors. In both cases these analyses are entwined with subtle political metaphors, transforming the technical scientific issues into key features of a "utopian moment.".