Châtelet Gilles. Figuring Space: Philosophy, Mathematics and Physics

Transl. by Robert Shore and Muriel Zagha. — Dordrecht: Springer-Science+Business Media, B.V., 2000. — 224 p. — ISBN 978-90-481-5287-2; ISBN 978-94-017-1554-6In 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'.Kenneth Knoespel / Diagrammatic writing and the configuration of space
Jean-Toussaint Desanti / The liberation of the gesture and the bias of the visibleThe enchantment of the virtualAbstraction and potential
Elastic and decisive virtuality
The principle of virtual velocities
Cauchy and Poisson’s virtual cutouts
NotesThe screen, the spectrum and the pendulum: horizons of acceleration and decelerationOresme’s diagrams
Spectra and horizons: restrained relativity as perspective projection of Oresme’s diagrams
Einstein and de Broglie: two symmetrical fans
Individuation by impact and individuation by election
NotesThe force of ambiguity: dialectical balancesIntroducing the great revolutions of the instability points
A question from Kant: what diagrams for the negative?
Argand and the attack of the lateral
Indifference centres and knots of ambiguity, fulcra of the balances of Being
Examples of production of ambiguity by a point-articulation 94 A The splitting in two of positive real numbers
NotesGrassmann’s capture of the extension: geometry and dialecticHow do you bring extended space back to life?
Articulate and generate: formal sciences and real sciences
Grassmann’s quadrilateral
The intensive/extensive dialectic
The additive generation of vectorial systems
Grassmann’s products
The stakes of the non-commutative
NotesElectrogeometric spaceLength and magnetism 150
The autonomy of the indifference centre: width and electricity
Electrical helices
The axial as subversion of the transitive
The electrogeometric experiment as square root
Towards the knot as secularization of the invisible
NotesAppendicesNote on quaternions
Note on Hamilton’s astronomical example
Hamilton’s operator V