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By Gilles Châtelet

In Figuring Space Gilles Châtelet seeks to trap the matter of instinct of mobility in philosophy, arithmetic and physics. This he does via virtuality and extensive amounts (Oresme, Leibniz), wave-particle duality and point of view diagrams, philosophy of nature and Argand's and Grassman's geometric discoveries and, eventually, Faraday's, Maxwell's and Hamilton's electrophilosophy.
This tumultuous dating among arithmetic, physics and philosophy is gifted by way of a comparability among intuitivepractices and Discursive practices. the subsequent techniques are handled intimately: the idea that of virtuality; inspiration experiments; diagrams; specified relativity; German Naturphilosophie and `Romantic' technological know-how.
Readership: The booklet doesn't require any significant mathematical heritage, however it does insist that the reader give up the typical instrumental notion of language. it is going to curiosity expert philosophers, mathematicians, physicists, or even more youthful scientists desirous to comprehend the `unreasonable effectiveness of mathematics'.

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Additional resources for Figuring Space: Philosophy, Mathematics and Physics

Sample text

The shift becomes inevitable. Mathematical beings appear above aB as impoverished physical beings, and the latter remain prisoners of the order of final causes: a moving body is moved according to the form that it should have and according to the place where it ought to remain. These shortcomings at least have the merit of drawing attention to two crucial points: - the principle of cutting out mathematical beings by thought, which aBows them to be sheltered from the mobility of the world. Later we will show the creative force of this principle at work in the thought experiments of modern physics (chapters II and III);6 - the characterization of the physical as sensible matter, a strong mixture of friskiness 7 and submission to the order of final causes.

It is from this point of view that we should assess the efforts of Jauge's Theory. What is at stake in the latter is not so much the discovery of the formula that will 'finally' condense the equivalence of natural forces, but the 'physical' understanding of geometry, in other words the opening up of the effort of construction of worlds in general to pure mobility, an effort derived from the vacillation of the categories of the 'purely geometrical' and the 'purely physical'. It is true, however, that there is always something scandalous about revealing the physical existence of this or that concept that was previously grasped as 'purely mathematical'.

The task of choosing is therefore far from simple. It is not easy to weigh in a single balance a 'real' existence, which is independent of us, but mobile and corruptible, and an intelligible matter, which exists only by proxy through the wit of the geometer. 3 We know how Aristotle reconciles the two rivals: by subordinating them to metaphysics - the first philosophy - whose objective is the theory of immobile and real being, immutable substance. But Aristotle does not content himself with the tutelage of metaphysics; his theory of abstraction also takes care to make a more concrete passage between the two natures, whose opposition he had so strongly underlined.

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