This doesn’t seem to be hugely known, but de Freitas and Sinclair refer to it. The preface to the book mentions that Chatelet did not live to see this work in print. This book is gorgeous, costs a bomb and has to be requested from the bloody British Library. But, thank the lord, I found this.
The intro talks about reconciling technique with humanism via results eg. butterfly effect. Relationship to Kant’s sublime? Gesture is seen as cutting out, he talks in a very exciting and baffling way about a new physico-mathematics.
Chatelet begins by pointing to the mathematics / physicality split effected by Aristotle, and his reversible abstraction-prosthesis process.
But can one extract a part from a whole without leaving scars? Can one solder determinations back on at will?
Mathematical beings appear above all as impoverished physical beings…
the principle of cutting out mathematical beings by thought, which allows them to be sheltered from the mobility of the world.p.18
can one conceive of physico-mathematical beings that are not irremediably enslaved to the appetites of the world, without turning them into abstract figures reduced to existence by proxy? p. 19
Still talking about Aristotle, he talks about motion and potentialities, and Leibniz taking up the idea of virtuality to reconcile multiplicity and magnitude and other stuff. Avicenna: the quantitas virtualis is therefore linked to the susceptibility of the matter to acquire extension and to become graspable in three dimensions, and is what gives it its character as a corporeal form. There’s a bunch of stuff about Leibniz, Aristotle, plasticity of mass.
In Leibniz, a new type of mathematical being, the differential, escapes being trapped between identity and absolute otherness; its emergence is completely contemporaneous with the idea of the live force element, which allows the conatus (acceleration) to be grasped prior to any impetuous actualisation.
Leibniz’s spatium of monads (metaphysical points, thunderbolts from the gods) does not come from the abstraction of that which does have parts, but from an a priori relation between non-extended things. p. 25
3. The principle of Virtual Velocities (Lagrange). There’s a whole lot of lovely stuff about bodies and forces. Then 4. Cauchy and Poisson’s Virtual Cutouts – hopping about in the complex plane to avoid bumping into a point…
Cauchy and Poisson revolutionised the coarse conception of the point as a simple position established through designation. p. 33
We’re into cutting out cavities in a domain – reference to the theory of residues wrt a curve?
In giving a point thickness, I thereby cause it to reverberate through the whole plane: this is the miracle of holomorphy. The designated, ‘purely geometric’ point opposed itself coarsely to the plane as a whole; in detecting a more subtle duality between the whole and the part, the point, as a virtual cavity, introduces the geometer into a new landscape, almost against his will: the hole invites a number of turns and this number of turns aticulates a point and families of loops. p. 36
II begins with a Leibniz quote:
we should have to postulate that there is a screen in this dark room to receive the species, and that it is not uniform but is diversified by folds representing items of innate knowledge; and, what is more, that this screen or membrane, being under tension, has a kind of elasticity or active force, and indeed that it acts (or reacts) in ways which are adapted both to past folds and to new ones coming from impressions from the species. This action would consist in certain vibrations or oscillations, like those we see when a cord under tension is plucked and gives off something of a musical sound. For not only do we receive images and traces in the brain, but we form new ones from them when we bring complex ideas to mind; and so the screen which represents the brain must be active and elastic. This analogy would explain reasonably well what goes on in the brain.” from New Essays on the Human Understanding, II, 12, 1
and goes on to Oresme’s clarification of the relation L = VT, which is, y’know, fine. Then there’s RESTRAINED RELATIVITY AS PERSPECTIVE PROJECTION OF ORESME’S DIAGRAMS and here we have the stuff about the hinge in the picture plane, a beautiful idea.
The infinite, degrees of removal in a line of poplars, the hinge… this is all on p. 50 and is all very interesting.
With the horizon, the infinite at last finds a coupling place with the finite… Finitiude fetishises iteration
Perspectival drawing, infinity and limits have some interesting links. These thoughts about the horizon line, too, could be useful for talking about graphs. p. 53-56.
Then there’s a lot of stuff about Einstein and light, then in IIII Dialectical Balances and points of contact of curves. Argand write about real/imaginary and impossible/absurd.
IV is Grassman’s Capture of the Extension: Dialectical Geometry. This reminds me of that Laws of Form book. V: Electrogeometric Space mentions knot theory.
This book is basically pretty out there, and written in a really surprising style. It’s kind of great and kind of impenetrable. I feel like bits of it could be very good to think about but it would take an awfully long time to grasp the real substance of what he’s talking about, which I don’t currently have. He might make another appearance though.
Briefly, from wikipedia:
In 1993 Éditions du Seuil published his book Les Enjeux du mobile, (Translated into English as Figuring Space) which was a study of mathematics, physics and philosophy. In this book, Châtelet tries to reflect on the perception of movement in philosophy, mathematics and physics by way of using concepts of virtuality and intensive quantities borrowed from Nicole Oresme and Gottfried Wilhelm Leibniz, He presents his conception of the deafening but complicated relationship between mathematics, physics and philosophy through a comparison between intuition and discourse, sense and speech.