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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.


The “Glassy Essence” and a Rorty Reflection

Richard Rorty, in his very influential Philosophy and the Mirror of Nature, argues that since the time of the Greeks, Western philosophy has been dominated by one over-riding metaphor, that the mind forms a mirror which reflects with more or less accuracy that which Real. This is a superb critique of philosophy, partly because it subsumes many otherwise diverse arguments and positions within a much wider scope, allowing us to see their own relations to each other. The Picture of Reality notion of truth is a significant one, one that pervades some of the most sophisticated of theories of the Mind and Knowing, and I am in favor of much that follows from Rorty’s critique.

But I was at the lake today, sitting with my wife, staring across that water plane, and I was thinking heartily, if absently, about the nature of reflection. The sun was showing itself on the dark, muddy green surface, in patches. There would be halos of it, which my wife pointed out, where the water seemed to ripple out, as if for no reason. And the rest would remain dark. I said, that must be where the lake has grown shallow, and the breeze stirs it up, just so to catch the light. I think she agreed. So the lake as bespotted with light lay there, shimmer in this kind of expressive way.

We sat for a while, eating our sandwiches, watching the light show, and suddenly the breeze kicked up. Across this perfect skin spread a wave of glittering light, just near the shore, spreading out in an incredible patten, like a harp stroke. At the same time one could read the “shape of the wind” and also the hidden topography of the unseen bottom of the lake. The two unvisibles meet in an ephemeral sheen.

Now it occurred to me that if indeed the metaphor of reflection has dominated philosophical thinking for more than two thousand years, it is not just the kind of reflection we think of with the perfectly clean mirrors of our machined age (and our “mirrors” are very good now). It had also to be the reflection of natural phenomena, in particular the kind of which we saw today.


Different from the now long abhorred “transcendental” aims of using the mirror to see beyond itself, the mirror trope tells us things about our relation to things other than some conceived Real (or Divine). When the breeze passed over the lake, I was as much fascinated with what was revealed “below” as the print of the wind itself. And the sun’s reflection was not the point. What was revealed was much more local, much more contingent and unexpectant. I came in contact with the lake’s bottom and the breeze, through this reflection.

We see this trope of reflection all the time, as we watch the world being reflected across the faces (and bodies, and we could even say words), of those we interact with. I say “reflected” (but not necessarily represented). For just like the sheen of a passing gust on the surface of a lake, so too an effect, perhaps a cry-out in a room, passes across the surface of others. Through this we come to learn and coordinate ourselves to what others are experiencing, and we can “see” the invisibles of breeze. There is nothing transcendental about this, but there is something revealing.

It is this substantial knowing of what is hidden and effects otherwise unseen that is captured in the notion of reflection. Reflection is something that we in a kind of mother’s milk understand and experience as causal and triangulating, bringing our world into coherence. So a forest of downed trees reflects the storm that passed.

If we see the world through others, it is not because those that are very still and seemingly clear have transcended our contingent place, but rather because our community with them, as a materiality, is experienced as being connected to both us and it. Even the most cloudy of us concretize the reality of what is near, and carnate our most dense human affective possibilities. If we are mirrors, we are affective mirrors, and it is the material sheen of our felt textures (even our thoughts have textures and speeds) which communicate our states to each other, such that “image” and “representation” is no longer a sufficient trope.

But man, proud man,
Drest in a little brief authority,
Most ignorant of what he ‘s most assured,
His glassy essence, like an angry ape,
Plays such fantastic tricks before high heaven
As make the angels weep.


Spinoza: The Body of Ideas as Lens



Something that has always tugged on me in the effort to understand Spinoza. No commentator I know of has made much of the ideas implicit in Spinoza’s means of survival. In fact it strikes me as dramatically under studied. He was a lens grinder (in fact it is assumed that he died an early death from the glass inhalations of that work). If one thinks about what lens grinding is, it is the shaping of a material thing, glass, according very precise mathematical ideas (calculations), the result of which is the change in the idea (representations) that are produced by that lens. In a sense, the lens holds the analogy whereby the material expresses an idea, whose product is a representation. The better the math, the clearer (literally), the image. Spinoza lived at the rise of the use of the camera obscura (Hockney), and it was the master painter Rembrandt who lived down the street in his childhood neighborhood.In the age of representation, that is just after Descartes, when ideas will be thought of clear and unclear representations of reality, Spinoza had a priviledged position. He actually was a grinder of a mechanism of representation, so he understood both the ideational and the material aspects of what makes representations happen. In this way, he is not interested so much in the Cartesian theatre, that is what he calls “fictions we feign from the illusion of free will”:

Spinoza wrote:

We must investigate, I say, whether there is any other affirmation or negation in the Mind except that which the idea involves, insofar as it is an idea…so that our thought does not fall into pictures. For by ideas I understand, not the images that are formed at the back of the eye (and if you like, at the middle of the brain), but concepts of Thought [or the objective Being of a thing, insofar as it exists only in Thought]

Ethics, 2p48s.


The pictures made, the imaginary images that supposedly occur to us in our Cartesian theatre, are really of less interest to Spinoza. And perhaps this is because he was a lens grinder. What he imagines is that if we get more adequate ideas, not our pictures will become sharper, but the lens itself will become more capable of acting, more Joyful, more expressive. In a sense perhaps, as a lens grinder, Spinoza was a first primative computer programmer, to return to your illustration, in that he took a program (a mathematical formula) and programmed a piece of material (glass), so as to produce some capacity of informing action. He imagined though, that the ideas that were important were not those that were supposedly projected at the back of the head (in a Cartesian world), to be viewed by an abstract will, but were the very ideas which constituted the material organization of the body, in a kind of mobius loop. That is, like a program, the ideas we hold shape, and express our very construct, and end up producing our very affective experience of ourselves and the world. While we spend much time looking the the Cartesian movie show, and thinking about just what is going on there, what it means, I think Spinoza wants us to spend more time thinking about what it means to be, and what it feels like being, a lens. An interesting turn on Plontus’ analogy of the Mirror and light. The very least, I think that being a lens grinder convinced him of the absolutely material, and parallel manifestation of any idea.