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What is “Passing through Infinities”?

Corry Shores has another beautiful, traveling meditation and analysis of some thoughts that I raised (I certainly enjoy seeing my thoughts reflected in that mirror, as I discover things that I must have been thinking however dimly, or should be thinking). Here he takes on the trope of “passing through infinities” that I found in von Kleist’s “On the Marionette Theatre”  and the appeal I made to Leibniz’s triangle. He does such an excellent job of explicating Kleist’s story, I recommend his post if only for this. There is a certain openness and journeying that marks Corry’s analysis of things, as he works his way forward, a real pleasure. And Corry does a wonderful job of bringing out the illustration of the concave mirror, and the reversal/vanishing of the image that occurs as the object approaches the focal point (passing onto Deleuze and Bergson). Again, Spinoza’s optics, his experiences with the building of telescopes (and perhaps likely use of mirrors and/or camera obscuras), is something no one has considered when weighing the meanings of Spinoza’s take on infinities. What Corry brings out, though not explicitly, is that Spinoza’s own position upon infinities was itself shaped by his work with lenses and mirrors.

Transverse Condensation

But I want to think to myself about what it means for us to “pass through an infinity” as Kleist claims that a conscious person must in order to attain grace. What I strongly suspect is that this is what Spinoza has in mind when he talks of the three tiers of knowledge, with emphasis on the latter two of these: the imaginary, the rational and the intuitional. Intuitional knowledge is that which is produced when rule-following, rational description is suddenly acceded, surpassed with a kind of accelerated leap of clarity, a clarity which is necessarily comprehensive and not apparitional: Spinoza uses the example of how we can do mathematics without having to move consciously through all our steps. As we journey down into the details of anything in the world, including ourselves, any rational ordering of “what is” not only employs imaginary separation of things from all else (their causes included), but there is a certain density that is achieved in any contemplation wherein one crosses through to the other side, having absorbed the orderings of our body. The confusions and conflations that mark out our imaginary engagements, bringing together under a certain mode of intensity, are first separated out into rational descriptions of causation, but then these delimitations are transcended. The world itself is not transcended. Only our imaginary/rational structurings of it are. And in this way Spinoza’s “intuition” bears a certain condensive similarity to “imagination” such that the two work to prepare and then exonerate the rational which lies inbetween.

I want to say that it is not enough to be analogical here, or more loosely, metaphorical. It is not that we cross through infinities like passing through the focal point of a curved mirror, or like a line crossing over another. Instead infinities are literally gathered up in bounded limitations, and pursued together along certain lines of traverse, and that then these infinities are passed through, onto the other side so to speak, unto a certain comprehensiveness, the kind of comprehensiveness that Spinoza (contrary to Decartes) urges us to start with.

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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.