Metamorfosi del punto. Su Gilles Châtelet e Paul Klee

Abstract

This article examines the classical and inertial conception of the geometric point – defined as the smallest conceivable portion of space, a mere objective correlate of an act of designation (an “x, y, z”) – through the lens of the thoughts of Gilles Châtelet and Paul Klee. It demonstrates that these two major figures of the 20th century, although belonging to distinct fields (mathematics and philosophy for the former, painting and art theory for the latter), developed an intrinsically dynamic and metamorphic conception of the point. It is no longer a static entity but an agent, an operator characterized by its mobility and internal tension (Spannungs-wille). It is understood as a place of contraction and dilation, a germ of processes to come, a residue charged with virtualities. By making the point the seat of gestures other than simple pointing (gestures of tracing, propagation, rotation), Châtelet and Klee make it the heart of a “diagrammatic life” where the becoming-line and other plastic units originate. Through the analysis of three major conceptual parallels between the two authors, this article argues that their rehabilitation of the point opens a fruitful field of reflection for mathematics as thought experiments and for art as philosophical investigation.