The Bear with the Rapier: Kleist on Leibniz and Microscopic Infinities

Dancing Bears Passing Through Infinities

More on Corry Shore’s “Deleuze and Dance…” post. In the comments section of my last post an exchange lead me to recall von Kleist’s wonderful “On the Marionette Theatre”.  – There is some debate as to how much irony is in the story, if there is a kind of Kierkegaardian reverse or distance, but I suspect that given the power of the von Kleist oeuvre and the place that he gives to the power of the sudden and the supernatural communication, any irony is subsumed by a certain belief, or trust – but what struck me was the kind of (unconscious) parallel between a point Corry was making in calling up Leibniz’s triangle of differentials, appealed to by Deleuze, and Kleist’s own striking analogy of passing through infinities.

First though, Kleist presents the figure of a bear that is able to fence with extraordinary deftness, such that man cannot even approach:

They urged me to attack. “See if you can hit him!” they shouted. As I had now recovered somewhat from my astonishment I fell on him with my rapier. The bear made a slight movement with his paw and parried my thrust. I feinted, to deceive him. The bear did not move. I attacked again, this time with all the skill I could muster. I know I would certainly have thrust my way through to a human breast, but the bear made a slight movement with his paw and parried my thrust. By now I was almost in the same state as the elder brother had been: the bear’s utter seriousness robbed me of my composure. Thrusts and feints followed thick and fast, the sweat poured off me, but in vain. It wasn’t merely that he parried my thrusts like the finest fencer in the world; when I feinted to deceive him he made no move at all. No human fencer could equal his perception in this respect. He stood upright, his paw raised ready for battle, his eye fixed on mine as if he could read my soul there, and when my thrusts were not meant seriously he did not move…

The Microscopy Beneath Human Sagacity

We are returned to Spinoza’s “we do not even know what a body can do”, the sense in which there are powers within our body which cannot be completely absorbed, understood or even anticipated. (Corry makes use of this to speak of the kind of apparitional capacties of Michael Jackson, for instance his introduction of the moonwalk.) We are like fantastic sleepwalkers…

However, no one has hitherto laid down the limits to the powers of the body, that is, no one has as yet been taught by experience what the body can accomplish solely by the laws of nature, in so far as she is regarded as extension. No one hitherto has gained such an accurate knowledge of the bodily mechanism, that he can explain all its functions; nor need I call attention to the fact that many actions are observed in the lower animals, which far transcend human sagacity, and that somnambulists do many things in their sleep, which they would not venture to do when awake: these instances are enough to show, that the body can by the sole laws of its nature do many things which the mind wonders at. (E3p2s).

But I want to return to Corry’s Deleuzian citation of the Leibnizian triangle of differentials, and the sense that Spinoza has in mind a kind of bound infinity of parts that grow infinitely smaller within any one delimitation, almost combustable (at least combustable to knowledge) bodies within bodies, growing infinitely minute:

Deleuze characterizes these smallest bodies as being inextensive; they are like calculus limits, or Newton’s “vanishing” (“évanouissants“) quantities. So these infinitely small bodies are not themselves “things” but are more like the differential relations of calculus. (Deleuze, Cours Vincennes: 10/03/1981)

 To better grasp what Deleuze will say about these differential relations, we should take his advice(Cours Vincennes – 22/04/1980) and briefly examine Leibniz’ simple triangle explanation of the differential ratios. [Click on images to enlarge].

The image is of an infinitely diminishing triangle as the intersection of lines near an vertex descrease:

Kleist has something of the very same kind of thought, he may even have Leibniz in mind, but he complicates it, implicates it, as to the very process of coming through or passing through those miniscule infinities.

..We see that in the organic world, as thought grows dimmer and weaker, grace emerges more brilliantly and decisively. But just as a section drawn through two lines suddenly reappears on the other side after passing through infinity, or as the image in a concave mirror turns up again right in front of us after dwindling into the distance, so grace itself returns when knowledge has as it were gone through an infinity. Grace appears most purely in that human form which either has no consciousness or an infinite consciousness. That is, in the puppet or in the god.

The human being passes through the infinitely small point, entering into the “looking glass” so to speak, but it is not a reversal in the Hegelian sense of reflective consciousness, or a transcedence, so much as an actual process of engagment, something I think Spinoza also might have in mind.

Corry does well to cite the possible Spinozist Theodore Kerckring’s thoughts that were induced by the looking through human anatomy by virtue of the powers of the an early microscope made by Spinoza. The human being as it swims down into the smaller and smaller bodies has a literal encounter with the limits of the mechanical infinite:

Marvelous is nature in her arts, and more marvelous still is Nature’s Lord, how as he brought forth bodies, thus to the infinite itself one after another by magnitude they having withdrawn so that no intellect is able to follow whether it is, which it is, or where is the end of their magnitude; thus if in diminishments you would descend, never will you discover where you would be able to stand.

Spicilegium Anatomicum 1670

[Discussed also here: Spinoza and Mechanical Infinities ]

Much as Kleist speak of the passing through concavity, of knowledge passing through an infinity, Kerckring finds that microscopy will only induct us to an infinity that resists us, or at least our eyes. There is a certain regard in which the delimiting mind must release its apprehension to a kind of apogogic comprehension, letting itself be comprehended, so to speak, with a sewn-in result that it is ever and always the body through which powers are channeled and therefore expressed.

Whence Salvation?

Somewhere between the first photo of an imprisonment of powers (the bear chained to perform out of its reservoir of powers), and Leibniz’s evocative minuscule infinities of abstract mathematical division is located Spinoza point about what Infinities are, and perhaps just as importantly how they are to be unlocked, or tapped into. Freedoms are and must be material engagements, combinations, things of which our own bodies are composed, and must be achieved through the soterial collection of that which appears not to think (feel, and act) as much as it can.