Frames /sing


Tag Archives: Maturana

10 Greatest Philosophers (sigh): Desert Island Question

Tool Kit

Jon Cogburn’s list in the comments section over at Perverse Egalitarianism  it seems has forced/spurred me onto my own list, as absurd as it may be, (but processes of organization are creative). It is a conflation of “greatest influence,”  upon me, but also as I read it, “greatest influence” upon the best solution for the pressing questions of our historical moment, a solution which must resonate down to the root/earth of the Western Philosophical tree. In a sense the list represents the authors from whom — if I was on a desert island and had to compose a philosophical theoretical perspective for our Age, and could be given the entire oeuvre of each — I would compose my island library; where there are two, I get two for the price of one. I include a small note on what seems the most germane contribution, though effects are radial.

1. Spinoza (parallel postulate under a register of power)

2. Plato (formulating the Orphic)

3. Augustine (Immanent Semiotics of truth)

4. Plotinus (Degree of Being transformation of Plato)

5. Davidson (Triangulation and Objectivity)

6. Guattari and Deleuze (Ontology of Affects)

7. Wittgenstein (Language Game)

8. Nietzsche (Ascent of Metaphor)

9. Sophocles (The Surpass of Tragedy)

10. Maturana and Varela (Operational Closure)

A large measure of this ranking can be seen as an after-image of an entire branch of thinking stemming from Descartes’ Central Clarity Consciousness  conception, which had its reverberations and mal-interpretations running through both the Continental and Analytic sides, a branch that is best left behind for now.

The actual numbers are only as they came to me without very much juggling. Tons of beautiful philosophers left off, some of my most favorite ones with whom I agree much more, and more inspire me, than some on the list…but that is the beauty of lists they force a composition, a constellation. Of course I would love to hear any of your own lists under something of the same criteria (or whatever).

(On another para-frivolous note, I would love to do a NCAA like bracket “playoff” of the 64 greatest philosophers, a competition/comparison which could have serious conceptual implications about truth and correction.)

Here a BBC Greatest Philosopher List


Conjoined Semiosis: A “Nerve Language” of Bodies

The Polyvalent and Cross-tongued

Chang and Eng Bunker

Chang and Eng Bunker

At times with an idea it is best to come up to a phenomena and embrace it as exemplary, a way of showing to others the heart of what you mean, and something of this comes through in the example of Conjoined Twins. I was discussing with my wife the nature of what I have been trying to put forth, which at the time had come down to the search for a term. A term was needed to crystallize just what sort of ontological distinction I was attempting to make when speaking of the polyvalence of semiotic elements that help form a body. As I explained to her, the very helpful notion of polyvalence lacked something. Yes, semiotic elements indeed could turn in every direction, but this poly-directionality was not fully what I meant. There was a constitutive sharing, a priority of investment and incarnation, a fleshed interweave that was not captured in the idea of a “polyvalent semiotics”. It is much more like Siamese Twins what share an organ, or body parts, aspects of the physical coherence of one body are already functioning as aspects of coherence for another (or really multiple, or illimitable) body/ies. There is a semiotic tugging, or in many cases tearing of bodies. In terms of history, they are not just layered upon each other like cells that lay with cells, composing organs, and with organs, composing bodies. Rather, bodies are already cross-semiotic to each other, their cognitive bodies woven into. We tried words like “inter-phenomenal” or “contra-phenomenal” (in answer to the ever popular “epiphenomenal”), but somehow the image of a shared body kept returning. It was that the semiotic order of a single body was enfleshed with other bodies. Finally my wife offered, expertly as always, How about just “‘conjoined”? So the term was born, Conjoined Semiosis. There is the difficulty that the example of Siamese Twins would override the concept, for what really is meant here is a great abstraction, albeit as concrete as possible, from the condition of such Twins. The questions of personal identity, autonomy, emotional coherence (for instance those so powerfully displayed in the story of Chang and Eng Bunker) are more peripheral to the term Conjoined Semiosis. I say peripheral here, though Conjoined Semiosis has profound effects on descriptions of normativity upon consciousness and questions of personal coherence. It is mostly the way that functioning differences in compositional elements necessarily are shared between bodies, across the cognitive boundary that they would from one coherent perspective form. This is analogous to (though perhaps still exemplified by) conjoined twins.

Autopoietic Closure

In explaining the idea to my wife I realized that if I am to make this clear I am going to have to begin at base concept, that is how semiotic differences can be seen to found the composition of an object. To get my point across we may have to begin in the middle, not with rocks or even chairs, but with the simplest of living structures, the single celled organism. It is biologists Maturana and Varela’s theory of Autopoiesis (much appreciated by latter Guattari we might say), that gives us a firm conceptual foothold here. Principle to their theory that living things can be described as Autopoietic Machines is the notion of Organizational Closure. That is, a living thing can be defined as an organizationally closed system of parts whose process it is to make the parts of which it is composed. It’s a machine that makes itself. Events at its boundary work as perturbations of a recursively defined set of relations within its boundary, such that no recourse to external facts are needed to explain the processes of differences that define its behavior. So, an autopoietic machine possess a kind of semiotic autonomy, the differences that make up the order of its internal actions are organizationally closed. The presence of a predator or a food source beyond the boundary of the organism is only a perturbation of its surface. The cascade of effects within need not be definable with reference to either “predator” or “food source”, but rather are in reference to a kind of homeostatic but living recursion. Maturana and Varela illustrate their idea of Organizational Closure with a know well-known example of the submarine pilot. We as observers may watch a submarine carefully navigate a series of reefs and dangers, and thrilled with the display would radio the pilot. “Congratulations on doing such a good job avoiding those reefs and powerful currents!” He is to reply something like, “I have no idea what you mean by ‘reefs’ or ‘currents’. I only moved some levers this way and that, put this factor in balance of that factor” utterly cut-off from the external meaning of his actions. Autopoietic theory is quite detailed, and I present only a bare aspect of it here, enough to point out what semiotic closure would mean. Simply, the differences that make a difference to the coherence of a body, are cognitively closed to the boundary of that body such that the boundary makes a domain. This is the “Recursive View”.

Maturana and Varela get out of this solipsism of organizational closure in several ways. For one, not to be gone into depth here, every autopoiestic systems, although it is organizationally closed, is structurally open. That is external parts of the world enter into boundary and can replace parts within that boundary, without changing its organizational closure, much as like nearly ever human cell you have today in your body is not one you had 10 years ago. This can lead to subtle shifts in organizational closure, as replacement parts can have slightly different properties. But the more systematic way that recursively closed autopoietic systems link up with the world is through what they call “structural coupling”. That is, if each cell is a kind of black box to an observer, experiencing “inputs,” and behavorially expressing “outputs” the internal organizations of one cell can be adapted to the regularities of those outputs (their relations to its own perturbations) such that the two organizationally closed systems become structurally linked. Hence, cells link with cells, cells produce organs, organs produce organisms, etc.  In this way, the regularities of surrounding cells are regularities of environment.

This becomes rather neat hand and glove, boundary to boundary nestling, wherein the semiotic closures of one system produce expressions which in their regularity and coherence serve to stabilize and inform the semiotic closures of another system. The two systems co-depend in this way, or one might say assemble, the differences in the one producing linked differences in the other, despite their own organizational closure. There is much that can be made profound in this kind of nesting, the kind of which which reflects what we see in the biological world, the remarkable way that organisms co-operate in parts, and it is for this reason that the biological body has been effectively used as a metaphor for, and an example of, coherence in both the history of Philosophy and Theology. The powers of communication amid apparent closure, and despite constant change, is a powerful testament. [If we were to make a premature theoretical leap] we could say that the closed organizations with which we combine are “black boxes” of the Latourian or Graham Harman sort, but boxes which are not so much “black” as transparent to the world, and not so much boxes, but spheres. That is, the regularities of expression of other semiotic closures by which we more powerfully act in the world, are the very same regularities that allow us to inhabit, and live through, in a kind of mutual organism of expression, making the world appear clear to us, mutually so.

Conjoined Semiosis

But I would like to go in another direction, a direction in particular counter to the hand and glove, boundary to boundary matching up. The necessity of “conjoined semiosis”. If we return to the base picture of the semiotically closed boundary, we must see that each of the differences which make up this boundary function as specific semiotic units. The ability of the closure to cognitively read the world depends upon the internal coherence of its closed relations.

The horizon of this “thing” is determined by the coherence of its differences, that is, the role of the differences help constitute its being. If any one portion of these constitutive elements cease to perform coherently, in a simplistic sense the system seeks to repair itself of its error, or dies. This is the meaning of the illustration I provided in my last post.

Now I suggest that it is not only the case that the regularities of structural coupling are enough to describe how boundaries relate to each other. Rather – and we leave here merely the examples of living, autopoietic bodies, moving onto the the greater category of any recursively organized cognitive boundary where in the differences that make up its interior serve to produce its horizon of inside and outside – these component differences that make a difference are already serving their purpose within other cognitive bodies. That is to say, the boundary of inside/outside which interprets the differences that make up the whole is insufficient to explain the coherence of behaviors within it. Events in the world that happen outside of it, necessarily happen across it, intersecting its boundary. Hence my second diagram:

The importance of this distinction of cross- or conjoined  semiosis is this. Parts within a cognitive body do not simply malfunction, or even out of their plenitude escape the regime of coherence established by the organism (top down), all this can be admitted. More, they possess what is experienced as a zombie-like property, and eruptive autonomy that cannot simply be chalked up to error. This autonomy of report can be both pernicious, leading to paranoiac self-purging, the attempt to cut out the semiotic “cancer” that is no longer “you”, or can be experienced ecstatically, with the sense that one is taken up into a power greater than oneself (itself a coin of paranoia).

The Worker Part

How to envision this. Taking up from a point made by Levi at Larval Subjects, it is important to see that the body of a factory (what he calls an Objec-tile), is made up of other bodies, for instance the persons that work the factory. In a certain sense, the allopoietic automobile factory (making things other than itself) is itself autopoietic, in that it has a recursivity of parts which make the parts that compose it (hire workers, make managerial rules, purchase materials, exact quotas, etc.). It seeks a homeostasis, or even a growth. Now, it is not enough to say that the body of the factory contains within it the bodies of persons. One has to also understand that the behaviors of those persons, as semiotic differences, not only inform the internal coherence of the factory, but also participate in the organization of other bodies, such as a Worker’s Union (or working class masculinity). So, when worker output slows during contract negotiations, the coherence of the factory, as far as it organizes itself upon its cognitive boundary: events outside in the world (like product demand, the social standing of the brand name, the price of oil, logical problems with delivery, the election of a new president) vs. inside the factory (like quota expectations, the means of expressing managerial authority, hiring practice profiles, worker hours), the cognitive answer may not reside in either an external cause or an internal one, but perhaps in a Conjoined Semiosis. That is, workers who are expressing the fitness of internal relations in the factory’s self-critique, and reflecting outside events, are also participating as semiotic units (differences that make differences) in the Worker’s Union. The behaviors of the factory workers – their slowing of productivity – is caused by something other than external factors, or internal coherence, but rather by a cross-semiotic relationship to another body. The “sense” of those behaviors is found in the coherence of a body whose semiotic parts intersect the factory. And the factory will have a sense that it is being pulled apart from within, that there is an autonomy of semiotic parts which is no longer coherently informing an inside/outside cognitive horizon, a zombie-like mutiny of parts. The Worker’s Union pervades within, and threatens from without. The same might be said if a woman is hired, and the behaviors of the male workers begins to exhibit the coherence of working-class masculinity.

So it is not enough just to say that the aggregate possesses a dynamic possibility of forming other bodies or objects. Rather, one has to understand that the aggregate is already cross-sectioned by semiotic polyvalence, its constituent parts are already communicating coherences to bodies other than itself. These are not objects rising up out of the aggregate, but rather pre-existing semiotic investments which interweave any coherent body or object. Even, or one might want to say especially, in instances where the factory is working quite well wherein the factory is transparent to its own internal coherence, only making minor corrections here and there (lobbying for new city council labor statutes, firing the unproductive worker), these cross-semiotic coherences are already operating. They simply are not making differences that make a direct – or threshold-passing – difference on the factory. This operation, the meshing of semiotic coherences across boundaries actually works to stabilize and produce resiliency within the cognitive horizon of the factory. The semiotic roles of objects within the factory are entrenched, become tied down across any number of vectors which inhabit it, all helping produce the transparency of operations. In this sense, the cross-boundary Conjoined Semiosis operates as a kind of field, yet a field always capable of cognitively tearing in any one direction (or multiple directions), upon perturbation, as itself is over-woven at its boundaries (the difference between field and body may be arbitrary to description, a question of focus, fields themselves constituting bodies). The question is one of report and horizon. The differences which make up a boundary are themselves already differences among other external differences, which make up other boundaries. It is the tugging from within towards events which seem external which often signals this trans-Subjectivity condition being simulated. It is not just that any person (or thing) possesses sub-elements within it that cannot be forced into line, that won’t restrict themselves to the overarching coherence, as if in some primordial anarchy of parts, a multitude ever in surpass of its expression. More, it is that “parts” are already parts of something else, not in hierarchical layers, from simple to complex wherein the complex just has to master and dominate the simple, but that the simple (the simple difference that makes a difference) is conjoined to other complexities which do not reflect the cognitive horizon of inside and outside itself. And it is only by being able to read these conjoined semiotic relations (which are so plenary and largely invisible as not to be read in great detail in advance), that a body can make sense of itself.

To put it one way, when one is experiencing an eruptive, counter insurgence of autonomous effects in an otherwise coherent experience (be they psychoanalytic drives, population protests, a resistance to project), it is best to look not only within, but also across to the points of intersection, the way in which elements which formerly read as coherent, producing transparency of the world, are involved in other coherences, other transparencies, other horizons, in which you already have a concrete, body-sharing investment. One is Siamese to other parts of the world such that your boundaries do not match up. Perhaps this works for the social world, as long as we are talking about persons (subjectivities) or factories, classes of human beings, all the way down to the biotic. But what of the inanimate. Are these bodies, objects, shot through with Conjoined semiosis?

Nail in the Coffin of Objects

Let us take up an intermediary inanimate, a hammer. It has no obvious cognition of its own, and has a socially constructed role in expectant future actions. Yet we can grant to the hammer the abstract informational distinction that it, like a living cell, is composed of differences that make a difference. If wood did not have the resilient (but still vibrational) quality that it does, it would not be what it is, a hammer. At least it would not be that hammer. So there is a certain internal coherence to its differences that make a difference. These differences are in my view semiotic to the object, that is, they indicate to each other parts of an organization which allow the object to be so constituted (whether we take it’s objecthood as a hammer to be a product of the mind or not, we grant that there is just such an organization of real differences, and that these differences indicate to each other). Now, the question is, do these differences also compose differences cojoined semiotically to other bodies. We have to say, yes. To list a few, the metal head participates in the organizational body of the Earth’s magnetic field, its differences informing the coherence of that body. The wood handle participates in the combustibility of objects in the workshed such that for instance if a fire was started there would be differences that make a difference that could impinge upon whether a fire would go out, or further inflame. The split in its handle may be said to participate in the informing body of broken things in the shed, such that the shed itself becomes a symbol of lost craftsmanship to a poet who writes a prodigious poem on the matter, eventually to land the hammer in a museum.

None of these communitarian differences which cross-hatch the hammer to the rest of the world have a constitutive effect on the hammer itself, that is, it is not tidally tugged in a direction which confuses it, for it lacks an overt self-regularity, in some auto-critique of its own semiology. Though I am not sure how categorical one can get about this, for the composite of differences does cohere, and in a sense read itself. The disintegration of its handle in a shed-fire is a kind of tugging away from its horizon. But there is no agent to the hammer, other than its persistence. (To these differences we need only add the differences that make up the hammer that allow it to participate in the assemblages which make of it a tool and allow it to persist:  its rigidity, its center of gravity, the vibrational quality of its wood, its mass; all of these and an infinite variety of others allow it to participate in the mutuality of its use such that a human being can compose with it a new body, human body-hammer-nail perhaps, a body which contains its own recursive structure of communicated differences.) In this way, insofar as differences that make differences can be seen as semiotic, that is, as informing wholes, it is requisite not only that such horizoned wholes match up with the boundaries of other horizoned wholes, in a kind of dovetailing workmanship, but also, the informing differences of any object are necessarily conjoined semiotically to wholes that intersect it. In this way, the most ancient of Western Philosophical problems, the relation of the One to the Many, on the grandest of scales, mislead our eyes to an essential binary logic, one that obscures how the Many already historically, and determinatively are invested across any particular One, cross-linking it with another One, whose coherence can tidally rule it, experienced as both outside and inside its horizon. It is not a question merely of matching up two externalized “Ones”. Thus, the Self, and the Other serves as an oversimplification, as does the Self and the World, for it is not only a matter of creating a space where the Self and the Other can fruitfully live as seemingly opposed externalities to each other, but more a question of identifying the hidden, invisible semiotic cross-threads in the fabric of each, the way that trans-boundary bodies tidally pull on the objecthood of each, not into a subsuming whole (although this too can be possible), but into a cognitive direction. If there is anything I would want to emphasize it is the semiotic, and thus material, bodily, Siamese codependence that any coherences is built out of, the way that one’s own constituent parts necessarily act creating differences which inform not only of outside or inside, but of a bit of each. It is that the very groundwork of our own coherence, the substance of which it is composed, and the reserve upon which we draw, is disturbingly conjoined [with no inherent value judgment as to whether this is for the better or the worse]. The signals that we (and others, objects) receive within are necessarily cross-tongued, polyvalent, and tidally pulled. And our most rich transparencies are the products of Siamese, often inseparable boundaries.

This is the sense in which Daniel Schreber’s paranoic “Nerve-Language,” written about his sadly and beautifully powerful Memoirs of My Mental Illness, describes insightfully the subcutaneous semiotic ordering that occurs at a distance. A bit of it:

Apart from normal human language there is also a kind of nerve-language of which, as a rule, the healthy human being is not aware. In my opinion this is best understood when one thinks of the processes by which a person tries to imprint certain words in his memory in a definite order, for instance a child learning a poem by heart which is going to recite at school, or a priest a sermon he is going to deliver in Church. The words are repeated silently [as if in a silent prayer to which the congregation is called from the pulpit], that is to say a human being causes his nerves to vibrate in the way which corresponds to the use of the words concerned, but the real organs of speech (lips, tongue, teeth, etc.) are either not set in motion at all or only coincidentally. Naturally under normal (in consonance with the Order of the World) conditions, use of this nerve-language depends only on the will of the person whose nerves are concerned; no human being as such can force another to use this nerve-language. In my case, however, since my nervous illness took the above mentioned critical turn, my nerves have been set in motion from without incessantly and without any respite.

Apart from the power structure of control which reads as a fantasy product of the invasion of coherence, it is precisely this conjoined semiotic quality and determination which inhabits each body, maintaining and testing its coherence. This conjoined semiosis is something long missed when the primary dyads of subject/object, or object/object, ever attempted to be resolved in growing hierarchies of control and abstraction, predominate philosophical questions. Indeed there is room for subsuming abstractions, negotiations of agreement, the calling together of more coherent wholes, but these projects of affective communication, joining the edges of boundaries to the edges of other boundaries, are advised to be made with as close a view as possible to the fabric of conjoined cross-weave which both supports and tears across every object-body. It is not enough to attribute these capacities merely to the dynamics of aggregates, or even of assemblages.  It is in the nature of the materially coherent to be materially conjoined at a valence of coherence which pulls at the differences that make differences.

The “Corporeal Equation” of 1:3: What Makes A Body for Spinoza?

If a Body Catch a Body Comin’ Through the Rye

I have always been fascinated by Spinoza’s defintion of a body as found in the Second Part of the Ethics. Not because it reflected some proto-physics, but because it allowed a radical revisioning of what defined boundaries between persons, and between persons and things. What seems implicit in such a definition is that something of a cybernetic recusivity surrounds and defines any isolated “part” of the Universe, yet, a recursivity that only comes clear by taking a perspective. One understands that really for Spinoza the entire Universe composes a single such body.

Here is Spinoza’s famous Ethics  defintion, and an even more elementary and bold one from his much earlier Short Treatise on God, Man and His Well-Being (KV)

Ethics: When a number of bodies of the same or different magnitude form close contact with one another through the pressure of other bodies upon them, or if they are moving at the same or different rates of speed so as to preserve an unvarying relation of movement among themselves, these bodies are said to be united with one another and all together to form one body or individual thing, which is distinguished from other things through this union of bodies (E2p13a2d)

KV: Every particular corporeal thing [lichaamelijk ding] is nothing other than a certain ratio [zeekere proportie] of motion and rest.

Yet, such a vision for Spinoza is more than an instructive imaginary relation, it indeed is a proto-physics, a concrete real which must be accepted as such. There is a certain sense in which Spinoza’s conception of a body must be reconciled with the “facts” of contempory physics if we are to geta stronger impression of the truth of his metaphysics and psychology. As Spinoza wrote to Blyenbergh, “Ethics, … as everyone knows, ought to be based on metaphysics and physics” (Ep 38). At a general level, in Spinoza’s own terms, if his physics is radically wrong this may pose serious doubts as to his Ethics (an entirely rationalist reading of his philosophy notwithstanding). And concordantly, one might assume, new information in physics could have a rippling effect across his philosophy and Ethics.

It is not my aim here to explore these wider meta-questions, but rather to for a moment pause upon a change in my own thinking. I had always taken Spinoza’s above defintions just as I explained, fantastic frameworks for revisioning the world as it common-sensically and historically has come down to us, intellectual opportunities for instance to see the connections between bodies in a Batesonian or an Autopoietic sense. This still remains. But I came to realize that when Spinoza is thinking about a “certain ratio” (as Shirley translates) or a “fixed manner” (Curley), he is thinking of something quite quantifiable, something numeric. I had of course loosely thought that this was the case, but until recently I had never strictly thought about it.

Spinoza’s Objection

There is an interesting, rather provocative point in Spinoza’s letters to Oldenburg, as he is reporting back to this Secretary of the Royal Society on the progress of his brilliant neighbor Christiaan Huygens. It seems apparent from what Spinoza reports that he has had intermittent, but somewhat substantive discussions on not only optics and lens-grinding, but also on physics. Huygens, by what history tells, had corrected Descartes’ rules of motion, and done so through experiment. Huygens was quite interested in the rules of motion for he had invented the pendulum clock way back in 1656 (the same year he had discovered the rings and a moon of Saturn), and for a decade was focused on improving it. Spinoza reports back to Oldenburg Huygens’ disagreement with Descartes, but tantalizingly also speaks of his own disagreement, in particular, with the sixth rule of motion:

Spinoza: “It is quite a long time since he [Huygens] began to boast that his calculations had shown that the rules of motion and the laws of nature are very different from those given by Descartes, and that those of Descartes are almost all wrong…I know that about a year ago he told me that all his discoveries made by calculation regarding motion he had since found verified by experiment in England. This I can hardly believe, and I think that regarding the sixth rule of Motion in Descartes, both he and Descartes are quite in error.” (Letter 30A)

Oldenburg: “When you speak of Huygens’ Treatise on Motion, you imply that Descartes’ Rules of motion are nearly all wrong. I do not have to hand the little book which you published some time ago on ‘Descartes’ Principia demonstrated in geometrical fashion’. I cannot remember whether you there point out that error, or whether you followed Descartes closely to gratify others.” (Letter 31)

Spinoza: “As to what you say about my hinting that the Cartesian Rules of motion are nearly all wrong, if I remember correctly I said that Mr. Huygens thinks so, and I did not assert that any of the Rules were wrong accept the sixth, regarding which I said I thought that Mr. Huygens too was in error.” (Letter 32)

Many commentators have not been able to make much headway when interpreting Spinoza’s objection to Descartes sixth rule of motion, for at the very least, it seems woven to his other rules, and the objection should have spread far wider than this, as in the case with Huygens. Alan Gabbey (The Cambridge Companion ) for instance simply finds it nonsensical. And Lachterman in “The Physics of Spinoza’s Ethics”, really almost avoids the issue altogether. (Wim Klever has taken the question directly on in “Spinoza and Huyges: A Diversified Relationship Between Two Physicists”, tying it to a Cartesian difficulty in explaining cohension, while Rivaud finds what seems to be an untenable conceptual connection between speed and essence in his “La physique de Spinoza”.)

I certainly am not one here to solve the question, but it did get me thinking about how Spinoza conceived of a body, and what a “certain ratio” meant to him.

Descartes’ Sixth Rule of Motion and Spinoza’s Defintion of a Body in the Short Treatise

Below is the sixth rule of motion to which Spinoza found objection. It essentially describes what would ideally happen if two bodies of the same size, one in motion and one at rest, struck. Descartes suggests that if the moving body had four (4) degrees of speed before impact, after impact the ratio would be 1:3, with the body at rest taking on one (1) degree of speed, the bodies rebounding:

Descartes:51. Sixth rule.
Sixthly, if body C at rest were most accurately equal to body B moved toward it, it would be partly impelled by B and would partly repel it in the contrary direction. That is, if B were to approach C with four degrees of speed, it would communicate to C one degree and with the three remaining would be reflected in the opposite direction.

Huygens reportedly showed through experiments at the Royal Society that instead all the degrees of speed would be imparted to the body at rest, and the intially moving body would then be stopped, and it was to this, as well as to Descartes’ rule that Spinoza expressed an unspecified objection. But this is not the ultimate point here for me. I was rather struck by an early note on Spinoza’s defintion of a body found in the Short Treatise , which proposes the same ratio of 1:3 that Descartes used to illustrate his sixth rule, here below stated as the ratio of motion to rest, and not as “degrees of speed”:

Spinoza: Short Treatise, notes to the Preface to Part II:

12. As soon, then, as a body has and retains this proportion [a proportion of rest and motion which our body has], say e.g., of 1 to 3, then that soul and that body will be like ours now are, being indeed constantly subject to change, but none so great that it will exceed the limits of 1 to 3; though as much as it changes, so much does the soul always change….

…14. But when other bodies act so violently upon ours that the proportion of motion [to rest] cannot remain 1 to 3, that means death, and the annihilation of the Soul, since this is only an Idea, Knowledge, etc., of this body having this proportion of motion and rest.

What is striking to me is that such an elementary numerical value for the definition of a body would occur to Spinoza in this context. Alan Gabbey wants us to point out that this ratio of 1:3 is found in editorial notes, and my not even be of Spinoza’s hand, though I am unsure if Spinoza would have allowed such a strong example to slip through if it was alien to his thinking. Provocative is that the context for this proposed illustration of a “corporeal equation” (as Matheron has named it), of 1 to 3, is that it is the human body that is being discussed and not abstract solids such as those Descartes discusses in his physics. Even if Spinoza does not imagine that the human body might actually retain such an elementary 1:3 ratio of motion to rest, somewhere in his conception of the human body there is an affinity to such an simple math. One for instance would not be describing a super computer whose mark would be its complexity, and turn to such a number. It would appear that at least figuratively Spinoza at the time of the Short Treatise  thought of the human body as elementarily composed such that its conatus expressed a homeostasis that was comprehesible and simple. The numerical value of 1 to 3 held perhaps a rhetorical attraction.

By the time of Spinoza’s geometrical treatment of Descartes’ philosophy, the proposed illustrative values that Descartes included in his rules for motion are no longer there. Spinoza generalizes them apart from any particular equation. One could see in this perhaps already a distancing from some of Descartes’ assertions, and Oldenburg tells Spinoza that he looked over Spinoza’s exposition of Descartes to see signs of his disagreement, finding none.

What the sixth rule Meant for Spinoza

For my part, if we take Descartes’ sixth rule at face value, and imagine the interaction between two bodies of the same size, one at rest, one in motion, we get a glimpse into the kind of change Spinoza thinks makes a body. For once the supposed transfer of a degree of speed occurs, the two bodies are now in communication. As long as they are not interacted with by other bodies their ratio will remain 1:3, and they would be considered an “individual”. And if one of those bodies interacted with another body so as to change its speed, immediately one realizes that if the idea of a single body is to be preserved the definition of parts needs to be expanded so that the ratio is to be expanded across a host of interactions. One sees how the definition of a body as a body is entirely contingent upon how you calculate.

Wim Klever finds in Spinoza’s 1665 objection to Descartes’ sixth rule (made almost 4 years after the writing of the Short Treatise ) a testament to Spinoza’s thorough-going commitment to a physics of immanence. This could be. But one could also imagine the case that Spinoza had been caught up in a conversation with Huygens at the Hofwijck estate and was entirely caught off guard by Huygens’ sweeping dismissal of Cartesian physics, which up to that point had been a touchstone for most scientific thinking in Europe. Spinoza’s objection to the sixth rule may have only been a reaction, one that prudently and instinctively placed himself between Descartes and Huygens, on a single point, a point he could not elaborate on.

But what was it about Huygens’ correction to Descartes which may have also given Spinoza pause, especially if Descartes’ rule for the transfer of motion between two equal bodies, one moving, one at rest helped frame Spinoza’s general notion of what makes a body? Would it not be that there was a complete tranfer of motion from one to the other, that one stopped and the other started? Because Spinoza envisioned bodies moving together in community, and integrated communication of impinging interactions that could be analyzed either in terms of their recursive cohensions (for instance how the human body can be studied solely in terms of its own internal events, as one might say, immanent to their essence), or in terms of extrinsic interactions which “through the pressure of other bodies” cause these internal events, the intuitional notion that a body in motion would deliver all of its motion to another body at rest, and not be rebounded simply defied the over all picture of what Spinoza imagined was happening.

I suggest that somewhere in the genealogy of Spinoza’s thought about what defines a body he found Descartes sixth rule quite suggestive. The idea that two bodies which do not seem to be in communication, one moving, one unmoving, (an essential perceptual differential which allows us to distinguish one thing from another in the world), suddenly can appear in communication from the change they bring about in each other in collision, now departing at a ratio of speeds, helped Spinoza psychologically and causally define the concrete yet contingent composition of an individual. The corporeal equation of 1 to 3 standing in for the possibility of mathematical determination which could conceptually unite any two parts in a single body, given the right analysis.

But when Spinoza encountered Huygens’ thorough dispatch of Cartesian mechanics we can suspect that Spinoza came in contact with his own theoretical disatisfactions with Descartes. As we know, Spinoza was part of a small cadre of mathematicians and thinkers which found dissatisfaction with Descartes idealized optics, something that no doubt formed part of his discussions with fellow-lense grinding and instrument maker Christiaan Huygens. And too, Spinoza likely felt that though Descartes’ mechanics provided an excellent causal framework for rational explanations of the world, his determinations lacked experimental ground. It would seem to me that Spinoza’s objection to the sixth rule of motion poses something of a revelation into the indeterminancy of Spinoza’s physics. The sixth rule may have played a constructive role in his imagination of what a body must be, but in particular in view of Huygens’ confirmed rejection of the rule, it became simply insufficient. Spinoza’s physical conception of a body stands poised between a Cartesian rational framework of causal interaction and mechanism, which proves lacking in specifics, and the coming Newtonian mechanics of force. However, in such a fissure, one does have to place Spinoza’s notion of immanence.

Autopoiesis Comes?

Signficantly, and something which should not be missed, is that the definition from axiom 2 of proposition 13 of Part 2 above is not the only conclusive one that Spinoza provides in the Ethics. Lemma 4 under axiom 3 actually provides a view of the body which does not require that the parts themselves remain in a fixed ratio to each other. Rather, it is only the ratio itself that must be preserved:

If from a body, or an individual thing composed of a number of bodies, certain bodies are separated, and at the same time a like number of other bodies of the same nature take their place, the individual thing will retain its nature as before, without any change in its form [forma].

This allows us to see that by the time of his writing of the Ethics, Spinoza’s notion of ratio, the aim of his mechanics, is far from what Newton would develop. The causal histories traceable through interactions between bodies certainly were signficantly important for Spinoza, but it was the preservation of a mode of interaction which really concerned Spinoza’s focus. That all the bodies that compose and individual could conceivably be replaced, without that individual being considered as changed (as for instance we know of nearly every cell of the human body), is something that Newtonian physics would not enumerate. It is within this conception of preservation that I think Spinoza’s mechanical conceptions have to be framed, in the entirety of an effect between bodies, the cohesiveness of the modal expression.

One need only turn to something like Autopoietic theory (both those of life by Maturana and Varela, and suggestively of social forms by Luhmann) to see a lineage given from Spinoza’s Lemma 4 description:

The defintion of a living thing understood to be a self-producing machine:  “An autopoietic machine is a machine organized (defined as a unity) as a network of processes of production (transformation and destruction) of components which: (i) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produced them; and (ii) constitute it (the machine) as a concrete unity in space in which they (the components) exist by specifying the topological domain of its realization as such a network.” (Maturana, Varela, 1980, p. 78)

On the difference between “organization” and “structure”:  “…[I]n a toilet the organization of the system of water-level regulation consists in the relations between an apparatus capable of detecting the water level and another apparatus capable of stopping the inflow of water. The toilet unit embodies a mixed system of plastic and metal comprising a float and a bypass valve. This specific structure, however, could be modified by replacing the plastic with wood, without changing the fact that there would still be a toilet organization.”
(Maturana & Varela, 1987, p. 47)

Where Lies Spinoza’s Physics?

Spinoza’s immanent connection between physics and metaphysics in a turn toward a decisive ethics, is one in which any outright mechanics must be understood beyond simply A causes B, and the appropriately precise mathematical calculation of what results. If Spinoza’s physics (and even its relationship to Descartes who preceded him, and Newton who followed him) is to be understood, it is this recursive relationship between parts that has to be grasped, the way in which parts in communication can be analyzed in two ways, along a differential of events internal to a horizon, and events external to that horizon, interior and exterior, even with a view to the conceived totality. It seems that it is this replaceable nature of body-parts in composite that qualifies Spinoza’s physics as interpretively distinct, and what allows it to place within the domain of cause not only questions of material interaction, but also psychology and belief, and ultimately social values of good and bad. 

What it seems that Spinoza was most concerned with in his assessment of a physics is the kinds of concrete reactions which ground our selective ability to usefully distinguish one thing from another, a usefulness that ever trades on the community of rational explanations with share with others. The result of this physics is an ultimate ground upon which we can and do build our own mutual body of social wholes, our own physics of decisions and distinctions. Physics both ground and distinguish us for Spinoza, always suggesting an anatomy of joined, contiguous parts; it is an anatomy that guides the effortless butcher’s knife that ideally, knowingly, seldom would need sharpening.