Some Easy Spinoza

Spinoza is a difficult thinker, not so much to understand, but to tolerate.

That is, there is something so tutorial about his main work the Ethics, it sometimes takes a great deal of effort, or merely exposure, to realize that he has quite benign intentions and realizations, and that there is something even more than a cold wind that blows through the architecture of all those propositions, proofs and scholia. But the work somehow always even upon embrace sits uncomfortably in the mind. It seems to be at the same time obviously false (or intellectually presumptuous), but also evocatively true in ambition and even somehow in reference.

I had a bit of a light-weight epiphany the other day when spending the afternoon down by the creek. The sun was radiating down, the water rushing in that relentless and still pleasurable way, and I lifted my head and stared at the huge boulders that filled the very small valley. In their very size, and the luminosity of the sun upon them they possessed a kind temporality what was in distinct contrast to the ephemera of the day, and of course of myself.

It was in those rocks that something about Spinoza occurred to me, that the kind of things that Spinoza is arguing for in all his elaborate ways are really pretty simple. They are listable.

1. There is one world, which means that when you and I are talking about it, or reacting to it, we are talking about and reacting to the same thing.

2. Things may change in that world, but it is still the same world.

3. We are part of that world, and being part of it is what allows us to communicate and be.

4. Through imagination we helpfully separate out one part of that world from the rest.

5. Through rationality we connect the separated out parts, which are not really separate.

6. Intuition is the flash of this connection. We all experience it.

7. We have very little control over ourselves (much less than we think), and the control we do have comes from thinking clearly.

9. Blaming (and overly praising) things external to us is largely a mistake.

10. Our salvation – in the grand sense, and the daily sense – depends on the salvation of things/persons external to us.

11. No soul can be freed without the body.

12. At any moment you can achieve greater freedom by changing the way that you think.

13. Any thorough embrace of “I” in the most selfish sense, undermines the sense of what an “I” is.

14. Understanding how something works is key to freedom.

15. We are our machines and techniques.

16. Nothing is completely unreal.

17. Everything outside of us has an explanation (causes), but an explanation which we can never be completely clear about.

18. Eternity is just the term for something that is not bounded, but is merely and entirely expressive.

19. The more we become like eternity, even in the most pragmatic situations, the freer and more powerful we are.

20. Gaining control involves separating out yourself from that which is outside of you, then reconnecting yourself by realizing that you were always connected but not in the way that you thought.

21. Things could not have been different than they have been, a thought that makes things very different in the future.

22. Everything thinks, however dimly. Which is another way of saying that things are all to some degree organizing, and not merely passively organized.

23. Thinking involves starting from the widest and working in.

24. I necessarily feel and see the world through others.

25. When we’re wrong, we’re only partially wrong.

This certainly is not exhaustive of Spinoza truths, and some of them may simply be inaccurate. They are a kind of intutional snap shot of much of my reading and thinking on Spinoza recently, and are worth putting down.

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.

Looking at the Limb-loosener: Between Image and Word

Roxana Ghita over at the floating bridge of dreams posts a gorgeous photographic expression of the “limb-loosener”, drawing in part on my own thoughts of Sappho’s erotic figure. She seems to specialize in the transposition of photography and poetry, and the site is haunting,  and the poem there by Amy Lowell called to mind another Sappho fragment, number 2, of which I include a lexically highly experimental translation.

…there, water cold-soul’d was ringing through braids

of apple-wool, as with roses, the whole child-place

had cast shadows, and from the shimmering of leaves

a coma was pouring down.

What is elegant about her image (and it is set askew by my cropping) is that the overt sensuality of the gaze, the hair, is captured by its frame. Not the border of the photograph, its frame. This is the marvelous thing about the internet. A single strain of thought encounters an image at a cross-section, and the duplication produces a marking, indulable transverse change of direction, beyond the imagination of each. This, not to mention, that 2,500 years lives suddeny compressed into a relative instant.

I want to say, do peer as well (…the way my eyes squint when I look at some of these condensations), into her the beautiful fullishness of things. And the visually fragile however fallible. Something quakes.

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.

Die and Dance in Spinozist Terms

Corry Shores has done a beautiful rumination spurred by my last short post on Deaththat really for some reason stirs me. In serpentine fashion he takes us through the infinimicules of existences, early views in microscopy (citing my favorite, under-read Spinoza document, Kerckring’s testament of animalcules), Deleuze’s conception of bodies in variation and thoughts about Michael Jackson (of whom I have been a little media’d out, but here I enjoyed contemplating). I like very much the thought that we have to ask ourselves, What has our body done in this life? And I love the thought that in living longer we simply expose our bodies to greater variation of expression (and experience), no matter how hard we strain to maintain the border of the same. We should say, What are our bodies enfolding (in dance), what are they expressing? We do not own them. One thinks of as well Spinoza’s Spanish poet (E4p39s), who no longer could recognize his own poetry, and so was no longer “himself”. Reminding us that there are many kinds of death, and thus many kinds of openings.

Death, Bodies, Last

When a body dies, there is a change in the echo of external events. Perhaps that is all there is. And therefore a body does not truly die, which is not to say that there is no change, but that the very notion of change is negotiable, perceptual. A “change in the echo” is to say, it has been dulled, muted, mortified, but it has not ended. This perhaps is what Spinoza means by “God”. Past events continue in their echoeous life in other taken-to-be-living bodies, how Mozart lives across us, and our instruments, our material etchings; but the body itself, as it once was, opens itself up to other confabulation, other involvements. And we think of the first as “ghost” and the second as “decay”, when in fact this splitting is only a growing wide of, and a variant to, Donne’s Compass. Due to the former half, the persistence of the echo taken from its source, some people want to say that there is a fundamental alienation to these processes (poor Mozart can never get back to his “body”); and some people want to see in death a return to a wholeness from which conscious life poses some primary alienation. Instead of course, neither of these is correct. Death is not “lack” nor entropy, but best understood as an opening.

Spinoza and Mechanical Infinities

The Mechanically Bound Infinite

I want to respond to Corry Shores’ wonderful incorporation of my Spinoza Foci  research into his philosophical project (which has a declaimed Deleuzian/Bergsonian direction). It feels good to have one’s own ideas put in the service of another’s productive thoughts. You come to realize something more about what you were thinking. And to wade back through one’s arguments re-ordered is something like coming to your own house in a dream.

This being said, Corry’s reading of my material thrills, for he is, at least in evidentary fashion, one of the first persons to actually read it all closely. And the way that he fits it in with his own appreciation for Spinoza’s concepts of Infinity certainly opens up new possibility for the Spinoza-as-lens-grinder, Spinoza-as-microscope-maker, Spinoza-as-technician interpretations of his thinking.

There is much to take up here, but I would like to begin at least with the way in which certain parallels Corry draws that change the way that I see what Spinoza was saying (or more exactly, what Spinoza was thinking of, and perhaps associating on), when talking about infinities. Key, as always, is coming to understand just what Spinoza had in mind when drawing this Bound Infinities diagram:

Corry points out in his analysis/summation of Letter 12, grafting from Gueroult’s commentary, that in order to understand the epistemic point (the status of mathematical figures, and what they can describe), one has to see that what Spinoza as in mind in writing to Meyer is a very similar diagram found in his Principles of Cartesian Philosophy, of which Meyer was the active editor. There the diagram is not so Euclidean, but rather is mechanical, or, hydro-dynamical:

The diagram illustrates water moving at a constant rate (a “fixed ratio” one might say), but due to the nature of the tube it must be moving at point B, four time faster than at AC, and a full differential of speeds between. There you can see that any section of the intervening space between the two circles composed of “inequalities of distance”  in the Letter 12 diagram (AB/CD) is not really meant as an abstraction of lines and points as it would seem at first blush (the imaginary of mathematics), but rather real, mechanical differentials of speed and material change. The well-known passage

As, for instance, in the case of two circles, non-concentric, whereof one encloses the other, no number can express the inequalities of distance which exist between the two circles, nor all the variations which matter in motion in the intervening space may undergo. This conclusion is not based on the excessive size of the intervening space. However small a portion of it we take, the inequalities of this small portion will surpass all numerical expression. Nor, again, is the conclusion based on the fact, as in other cases, that we do not know the maximum and the minimum of the said space. It springs simply from the fact, that the nature of the space between two non-concentric circles cannot be expressed in number.

Letter 12

The Lathe Buried Under the Euclidean Figure

But, and this is where Corry Shores alerted me to something I did not formerly see, the relationship between the two diagrams is even further brought forth when we consider Spinoza’s daily preoccupation with lens-grinding and instrument making. It has been my intuition, in particular, that Spinoza’s work at the grinding lathe which required hours of patient and attentive toil, MUST have had a causal effect upon his conceptualizations; and the internal dynamics of the lathe (which fundamentally involve the frictioned interactions of two spherical forms under pressure – not to mention the knowing human eye and hand), must have been expressed by (or at least served as an experiential confirmation of) his resultant philosophy. If there was this heretofore under-evaluated structuring of his thought, it would seem that it would make itself most known in his Natural Philosophy areas of concern, that is to say, where he most particularly engaged Descartes’s mechanics (and most explicitly where he refused aspects of his optics, in letters 39 and 40). And as we understand from Spinoza’s philosophy, Natural Philosophy and metaphysics necessarily coincide.

What Shores shows me is that Spinoza’s Bound infinities diagram (letter 12), his very conception of the circle, is intimately and “genetically”  linked to the kinds of motions that produce them. It is with great likelihood that Spinoza is thinking of his off-center circles, not only in terms of the hydrodynamics that circulate around them, but also in terms of Descartes’ tangents of Centrifugal force.

There is a tendency in Spinoza to conflate diagrams, and I cannot tell if this is unconscious (and thus a flaw in his reasoning process) or if he in his consummate philosophy feels that all of these circular diagrams are describing the very same thing simply on different orders of description. But the connection between a tangential tendency to motion conception of the circle (which Corry makes beautifully explicit in terms of optics) and Spinoza’s consideration of bound Infinities in the letter 12 (which remains implicit in Corry’s organization of thoughts), unfolds the very picture of what Spinoza has in mind when he imagines two circles off-center to each other. Spinoza is thinking of is lens-grinding blank, and the spinning grinding form.

One can see the fundamental dynamic of the lathe from Van Gutschoven’s 1663 letter to Christiaan Huygens, illustrating techniques for grinding and polishing small lenses,

And it is my presumption that Spinoza worked at a Springpole lathe, much like one used by Hevelius, Spinoza’s Grinding Lathe: An Extended Hypothesis, the dynamics of which are shown here:

In any case, when one considers Spinoza’s Bound Infinity diagram, under the auspices of tangential motion tendencies, and the hydrodynamic model of concentric motions, I believe one cannot help but also see that the inner circle BC which is off-center from the first, is representationally the lens-blank, and the larger circle AD, is potentially the grinding form. And the reason why Spinoza is so interested in the differenitals of speed (and inequalities of distance) between two, is that daily, in his hand he felt the lived, craftsman consequence of these off-center disequilibria. To put it one way sympathetic to Corry’s thinking, one could feel them analogically, with the hand, though one could not know them digitally, with math. The human body’s material (extensional) engagements with those differentials (that ratio, to those ratios), is what produced the near perfectly spherical lens; and the Intellect intuitionally – and not mathematically – understands the relationship, in a clear and distinct fashion, a fashion aided by mathematics and figure illustration, which are products of the imagination.

What is compelling about this view is that what at first stands as a cold, abstract figure of simply Euclidean relationships, suddenly takes on a certain flesh when considering Spinoza’s own physical experiences at lens-grinding. Coming to the fore in such a juxtaposition is not only a richer understanding of the associations that helped produce it, but also the very nature of Spinoza’s objection to the sufficiency of mathematical knowledge itself. For him the magnitudes of size, speed and intensity that are buried between any two limits are not just abstract divisions of line and figure, or number to number. They are felt  differentials of real material force and powers of interaction, in which, of which, the body itself necessarily participates. The infinities within (and determinatively outside of) any bound limits, are mechanical, analogical, felt and rational.

Corry raises some very interesting relationship question between the Spinoza Bound Infinities Diagram and the Diagram of the Ideal Eye from letter 39. They are things I might have to think on. The image of the ideal eye is most interesting because it represents (as it did for Descartes) a difficult body/world shore that duplicates itself in the experiential/mathematical dichotomy. Much as our reading of the duplicity of the Bound Infinity Diagram which shows mathematical knowledge to be a product of the imaginary, the diagram of the ideal eye, also exposes a vital nexus point between maths, world and experience.

From Mechanics to Optics (to Perception)

It should be worthy to note that Spinoza’s take on the impossibility of maths to distinguish any of the bound infinities (aside from imposing the bounds themselves), bears some homology to Spinoza’s pragmatic dismissal of the problem of spherical aberration which drove Descartes to champion the hyperbolic lens. When one considers Spinoza’s ideal eye and sees the focusing of pencils of light upon the back at the retina (focusingswhich as drawn do not include the spherical aberration which Spinoza was well-aware of), one understands Spinoza’s appreciation of the approximate nature of perceptual and even mathematical knowledge. This is to say, as these rays gather in soft focus near the back of the eye (an effect over-stated, as Spinoza found it to be via Hudde’s Specilla circularia), we encounter once again that infinite grade of differential relations, something to be traced mathematically, but resultantlyexperienced under the pragmatic effects of the body itself. “The eye is not so perfectly constructed” Spinoza says, knowing as well that even if it were a perfect sphere there as yet would be gradations of focus from the continumof rays of light so refracted by the circular lens. What Spinoza has in mind, one strongly suspects, and that I have argued at length, is that the Intellect, with its comprehensive rational in-struction from the whole, ultimately Substance/God, in intuitional and almost anagogic fashion, is the very best instrument for grasping and acting through the nature of Nature, something that neither bodily perception, or mathematical analysis may grasp. Indeed, as Corry Shores suggests in his piece, it is the very continuum of expressional variability of Substance (real infinities within infinities) which defies the sufficiency of mathematical description, but it is the holistic, rational cohesion of expression which defies experiential clusterings of the imagination: the two, mathematics and imaginary perception, forming a related pair.

In the end I suspect that there is much more to mine from the interelationship between Spinoza’s various circular diagrams, in particular these three: that of the relationship of the modes to Substance (EIIps), that of the the hydrodynamics of circulating water (PCP, implicit in the Letter 12 diagram of Bound Infinites), and the Ideal eye (letter 39), each of these to be seen in the light of the fundamental dynamics of the lens-grinding lathe to which Spinoza applied himself for so many years, and at which he achieved European renown expertise.

The Infinities Beneath the Microscope

I would like to leave, if only for Corry Shores’ consideration, one more element to this story about Real Infinities (and I have mentioned it in passing before on my blog). There is an extraordinary historical invocation of something very much like Spinoza’s Bound Infinities in the annals of anatomical debates that were occurring in last decade of Spinoza’s life. I would like to treat this in a separate post and analysis, but it is enough to say that with the coming of the microscope what was revealed about the nature of the human body actually produced more confusion than understandings in what it revealed, at least for several decades. Only recently was even the basic fact of the circulation of blood in the body, something we take for granted, grasped. And in the 1670s the overall structure or system of human anatomy was quite contested, contradictory evidence from the microscope being called in support one theory or another. Among these debators was Theodore Kerckring, who was weighing in against the theory that the human body was primarily a system of “glands” (and not ducts). Kerckring’s  connection to Spinoza is most interesting, much of it brought to light in Wim Klever’s inferential and quite compelling treatment of the relationship of Van den Enden  and Spinoza. In any case Kerckring  is in possession of a microscope made by Spinoza (the only record of its kind), and by virtue of its powers of clarity he is exploring the structure of ducts and lymph nodes. Yet he has skepticism for what is found in the still oft-clouded microscope glass leads him to muse about the very nature of perception and magnification, after he tells of the swarming of tiny animals he has seen covering the viscera of the cadaver, (what might be the first human sighting of bacteria). He writes of the way in which even if we see things clearly, unless we understand all the relationships between things, from the greatest breadth to the smallest, we simply cannot fully know what is happening, if it is destruction or preservation:

On this account by my wondrous instrument’s clear power I detected something seen that is even more wondrous: the intestines plainly, the liver, and other organs of the viscera to swarm with infinitely minute animalcules, which whether by their perpetual motion they corrupt or preserve one would be in doubt, for something is considered to flourish and shine as a home while it is lived in, just the same, a habitation is exhausted by continuous cultivation. 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

Several things are going on here (and in the surrounding context), but what seems most striking given our topic, we once again get a glimpse into the material, and indeed historical matterings of what bound, mechanical infinities might be. (As a point of reference, at the time of Kerckring’s  publishing Spinoza had just moved to the Hague and published his Theological-Political Treatise, having taken a respite from his Ethics approximately half done, and he will have died seven years later.) Kerckring  in a remarkable sense of historical conflation looks on real retreating infinities with Spinoza’s own microscope, and exacts much of the same ultimate skepticism toward human scientific knowledge, as per these infinities, as Spinoza  does in his letter to Meyer. This does not mean that we cannot know things through observation, or that imaginary products are not of use to us, but only that there is ultimately for Spinoza and Kerckring  a higher, rational power of interpretation, the comprehensiveness of what abounds. Neither measurement or calculation is disqualified, in fact Spinoza in his letters and experiments and instrument making showed himself to be quite attentive to each. It is rather that the very nature of human engagement requires both attention to the bodily interaction with devices and the measured thing, and also a sensitivity to anagogic, rational clarity, something found in the very unbroken nature of Substance’s Infinity. What Kerckring’s description does is perform the very consequence of conception in scientific observation itself, almost in Spinoza’s stead (expressing very simililar  sentiments as Spinoza does in Letter 32 to Oldenburg on lymph and blood, and the figure of the worm in blood,

Let us imagine, with your permission, a little worm, living in the blood¹, able to distinguish by sight the particles of blood, lymph, &c., and to reflect on the manner in which each particle, on meeting with another particle, either is repulsed, or communicates a portion of its own motion. This little worm would live in the blood, in the same way as we live in a part of the universe, and would consider each particle of blood, not as a part, but as a whole. He would be unable to determine, how all the parts are modified by the general nature of blood, and are compelled by it to adapt themselves, so as to stand in a fixed relation to one another.

There is great conceptual proximity in these two descriptions, suggesting I imagine that Spinoza used his microscopes as well, for observation, not to mention that Kerckring and Spinoza come from a kind of school of thought on scientific observation of human anatomy, perhaps inspired by or orchestrated by Van den Enden, as argued by Klever. Just the same, at the very least, Kerckring  presents greater context of just what kinds of retreating infinities Spinoza  had in mind in his letter 12 diagram, not simply a differential of motions, but also a differential of microscopic magnitudes, each of which were an expression of an ultimate destruction/preservation analysis, something that falls to the very nature of what is body is. Spinoza not only ground lenses, but also made both telescopes and microscopes, gazing through each at the world, this at a time when the microcosmic and macrocosmic, nested infinities were just presenting themselves to human beings. And as such his critique of scientific observation and mathematical calculation preserves a valuable potentiality for our (postish) modern distancings and embrace of the sciences.

Spinoza and Optics and Pirates

I see now that Corry Shores has put up a reading, and mutual expression of some of my work on Spionza and Optics, “Spinoza’s Foci for Deleuze’s Attraction”. I have to say that I have not read it yet (for sometimes I savor/reserve the first reading of a text for a generous moment, for when you first enter into a thought-space associations and inference trails occur that are highly valuable, and may not occur again), but by all cursory scans, it is the very first close reading of my research, and I can’t wait to see what he says. Read it before I do.

}∅{ The Full Set

The Full-ness of a Body

This is not what I intend to write on the Subject of Infinity, but it is a projective chain of thoughts. It is a tracing of a yet un-consolidated line of interpretation.

Fido the Yak presents a symbol/concept which – and I’m not sure of its origin or complete meaning – is quite intriguing in the light of my recent readings on Spinoza, the Infinite and mathematics. What I would like to call the Full Set. This is how Fido describes his imagination of it

}∅{ is like an in-cept, yet it emerges discursively as a response to the arche. How does it originate? Autopoietically? Or do we acknowledge that it is a con-cept with the arche? (Like its withness with the empty set.) I talk about }∅{ extemporaneously because the extemporaneous describes it. If you can be in a state of consciousness that includes nothing while excluding nothing then }∅{ can describe such a state of consciousness, or a goal of thinking, a guideline, better. Maybe you’d want it to represent an empty concept, I don’t know. I say now the }∅{ expresses the acknowledgment that the explanation never exceeds its explained, which is a way of saying it never accomplishes what it sets out to do, and that “foundation” is a metaphor—you may see why I call it “the breach.”

We are running in similar directions, but I prefer in my own thinking to not think of it as a breach, so much as a whole plenitude, close to Deleuze’s Full Body, the Body without Organs. (Here my thoughts proceed from his in-spiration, in perhaps an appropriation.) It is closely related to Spinoza’s notion of the Infinite as something that cannot be broken. So, in my hands, it would describe the infinite proximity between any two limits.

It emerges from Spinoza’s diagram of bound infinities, which proclaims that within any bounds there are an infinity of magnitudes which are themselves divisible:

It is important to see that for Spinoza these are magnitudes(and not simply points on an imaginary line, which are at best ab-stractions). As magnitudes, they are FULL. Now, if we are to play with symbols, the requisite symbol for Spinoza’s point about bound infinities would be something like }∞{, which is to say, between any imposed limits, there are an infinity of magnitudes buried. Also importantly, and somewhat divergent from Badiou’s concept of Count-as-one, the symbol should not be {∞}, because for Spinoza any (abstract) internal bounds already, already refers to, or references to some degree a determination that lies outside of it, as in his Letter 12 diagram…

The sub-section between AB and CD {}, already includes comprehension of the circle circumstance itself, }{. Or, the internal count-as-one (set), really is composed, determined by the bordering edges of something beyond it, as a mode of comprehension, consciousness itself.

Playing With Symbols

So, while Spinoza in Letter 12 seems to be presenting something of a }∞{ determination, what would be the intuition of the full set }∅{, which is our subject here mean? It is not that between any two abstract limits there is some sort of nothing, or emptiness (for Spinoza denies the ontological consistency of the void). It is rather that the act of distinction and limitation itself drives itself toward the impossibility of separation: as we enter into the infinity of magnitudes (let us start with Badiou’s count-as-one teeming/erupting with multiplicities) {∞}, we are pre-positedly forced both outward…}∞{…but also inward to the full set itself…}∅{…the way in which what lies between simply cannot be divided at all and remains unbroken. It is not the sheer multiplicity that lies between any borders (inside, or outside), but rather the implicition that there is no “gap”, the very fullness of Being, from which mathematics, figure drawing and set-making composes only an abstraction, an imaginary class. It is for this reason that for Spinoza rational thought leads ultimately to an Intuition of immanent wholes and a speed of thought. 

Or, if put another way, any conception of emptiness, or lack, or nothing {∅} (whether it be mere psychological wanting, or mathematical 0), diverges upon the fullness of being, showing itself to be a figment.

Spinoza on the Infinite, the Unbound: Part I

Preliminary

Key to understanding Spinoza’s approach to the Infinite is appreciating that for him, primarily and speaking generally, The Infinite is Unbroken. And following this, modifications of the Infinite (how Spinoza defines the modes) do not break that unbroken state. For Spinoza, any treatment of Substance must follow from this understanding.

What makes this compelling, and ultimately germane to any assessment of the status of rational knowledge as it is found in logically related descriptions, and at the seeming apex of such, mathematical descriptions, is that insofar as numerical designation indicate a limitation, a bound, a break in The Infinite, this is an imaginary product and is not adequate knowledge. Perhaps, penultimately: mathematical, scientific knowledge stands at a skeptical remove from the true nature of Nature. Which is not to say that mathematical relations, and the various fields of mathematical description, do not play a significant role the human being coming into some form of absolute knowledge of God/Substance/Nature. At most, the internal coherence and powerful indications of mathematical forms act as Augustine’s finger, pointing to Substance’s moon.

One can see this in Meyer’s preface to Spinoza’s early career more geometrico treatment of Descartes’ philosophy, The Principles of Cartesian Philosophy. Meyer explicitly sets out Spinoza’s distance from Descartes’ matho-scientific treatment of Nature:

This [work] must not be regarded as expressing our Author’s own view. All such things, he holds, and many others even more sublime and subtle, can not only be conceived by use clearly and distinctly but can also be explained quite satisfactorily, provided that the human intellect can be guided to the search for truth and the knowledge of things along a path different from that which was opened up and leveled by Descartes. And so he holds that the foundations of the sciences laid by Descartes and the superstructure that he built thereon do not suffice to elucidate, and resolve all the most difficult problems that arise in metaphysics. Other foundations are required if we seek to raise our intellect to that pinnacle of knowledge.

I had to get this basic beginning out so that I can move on. Hopefully to follow soon: Spinoza’s hyper-proximity to Badiou (and Badiou’s intention misreading), Cantor’s attempt to in-concretize Spinoza’s Infinite (as transfinite), and, the Place of Mathematics within Spinoza’s theory of the Intellect and Knowledge, the weight of Letter 12  (or something of these sorts).