In Figuring Space Gilles Châtelet seeks to capture the problem of intuition of mobility in philosophy, mathematics and physics. This he does by means of virtuality and intensive quantities (Oresme, Leibniz), wave-particle duality and perspective diagrams, philosophy of nature and Argand''s and Grassman''s geometric discoveries and, finally, Faraday''s, Maxwell''s and Hamilton''s electrophilosophy. This tumultuous relationship between mathematics, physics and philosophy is presented in terms of a comparison between intuitive practices and Discursive practices. The following concepts are treated in detail: The concept of virtuality; thought experiments; diagrams; special relativity; German Naturphilosophie and Romantic'' science. Readership: The book does not require any considerable mathematical background, but it does insist that the reader quit the common instrumental conception of language. It will interest professional philosophers, mathematicians, physicists, and even younger scientists eager to understand the unreasonable effectiveness of mathematics''.

Introduction. One: The Enchantment of the Virtual. Two: The Screen, the Spectrum and the Pendulum. Three: The Force of Ambiguity: Dialectical Balances. Four: Grassmann''s Capture of the Extension Geometry and Dialectic. Five: Electrogeometric Space. Appendix I: Note on Quaternions. Appendix II: Note on Hamilton''s astronomical example. Appendix III: Hamilton''s operator.