Figuring Space: Philosophy, Mathematics and Physics

by Gilles Châtelet

French

Genres: Philosophy, Mathematics, Physics, Theory, Metaphysics

199 pages, Hardcover

First published January 1, 1993

About the author

Gilles Châtelet was a French philosopher and mathemetician.

Reviews

[Erik · Rating 3 out of 5]

The text is unreadable, probably deliberately, in the style of contemporary French philosophy. The math and the diagrams contain all the content. Chatalet's idea of constructing extension involves starting with an intensive magnitude without extension and a virtual or potential process for separating the parts of an intensive magnitude across virtual moments of time or space. He claims that this processes manifests across physics, in equations like W=Integral of Fdq. and geometry and in fact constitutes the link between the two. I thought work was a scalar and that F dq was a dot product however, not an area. This and other issues, for example Grassmann's exterior product of two vectors is not a parallelogram produced by one vector sliding over another but can have any shape. The tracing process of a given area is not unique. Also in more than 2 dimensions the extensions are not purely the result of exterior products of basis vectors. These and other subtleties were ignored. Nevertheless the philosophical view is interesting.

[Evan Chethik · Rating 5 out of 5]

Some may think a good book has been written, but they have not in fact read this

[isaac smith · Rating 3 out of 5]

Has brain fog ever got you from hours of trying to imagine the meaning of wiki pages about math topics beyond your level of study? Well, gilles chatalet provided this experience circa '93 with "Figuring spaces" plus the added benefit of slight misconstruals in the text itself...
But, chatalet shows how math's experimental aspect extends beyond electronic technology like computers & emerges in historical diagrams (& metaphors). Beyond isolated diagrams: the register they make up shows the evolution of geometric space into a space for thought...
The intersections of contemplation and operational formulas (which art & science already occupy) is a space where metaphor undergoes a transformative process, evolving into operation...
(as pointed out by Erik Banks: work is a dot product & thus a scalar & not an area. & exterior products are not strictly parallelograms, etc) but boy chatalet is romantic & did better than I could've, so "Enchantment of the virtual" forthcoming 2/13/24 is on the calendar