Difference in Quantity Becomes Quality

Deleuze begins his chapter on "Action and Reaction" with one of his favorite quotes from Spinoza: "We do not even know what a body can do".  Here's the full quote from the Elwes translation.

"I have just pointed out that the objectors cannot fix the limits of the body's power, or say what can be concluded from a consideration of its sole nature, whereas they have experience of many things being accomplished solely by the laws of nature, which they would never have believed possible except under the direction of mind" (Spinoza's Ethics, Part 3, Proposition 2, Note)

While this may at first suggest a reduction of mind to body that anticipates modern neuroscience by 300 years, that's not how Spinoza saw the situation.  For Spinoza, mind and body are strictly parallel.  Anything that we think the mind is capable of, the body is likewise capable of in its own terms.  What he's objecting to is our habit of inserting a mysterious and a-causal mental interiority into the natural world to account for any part of it we don't understand.  We already saw that this was precisely what Nietzsche objected to in the Christian ideas of divine grace and free will -- our inability to see a meaning within existence leads us to posit a transcendental meaning outside of it.  

Spinoza's parallelism between mind and body has always struck me as a somewhat odd doctrine because of its obvious redundancy.  Nevertheless, this redundancy does at least serve to dethrone the mind from the privileged position it has occupied since the inception of philosophy.  For Spinoza, the mind is at least no more important than the body.  Nietzsche and Deleuze, however, take this same logic a step further and assert that the (conscious) mind is in fact the distinctly less powerful and less important of the two.  Once the parallelism has been broken this way, we do find that there is a sort of reductionism involved in asking what the body can do.  But the reductionism at work here is not based on our typical idea of reducing an immaterial mind to a merely material body.  Instead, by pursuing Spinoza's question, Deleuze will end up dethroning the entire duality between spirit and matter, and reducing both of them to asymmetric expressions of a third term -- the will to power.  

To eventually understand this subtle reductionism, we need to first examine how Deleuze defines the body and uncover what role the conscious mind plays in this definition.  A body is defined as simply any relation of forces.  We saw from the outset of the book that 'force' makes a peculiar fundamental metaphysical unit because it never exists by itself, but only in relation to other forces.  

Every force is related to others and it either obeys or commands. What defines a body is this relation between dominant and dominated forces. Every relationship of forces constitutes a body - whether it is chemical, biological, social or political. Any two forces, being unequal, constitute a body as soon as they enter into a relationship. (NP, 40)

A body, then, is what holds forces in relation, or perhaps more accurately, it simply is a relationship of forces.  Since forces have no inherent or a priori relation, the body is a product of the chance collision of various forces.  This makes the fact that it forms at all "astonishing" (in Nietzsche's words).  In other words, the identity of a body can never taken for granted but is always constructed by forces that have come into contact.  While for the sake of simplicity we will often speak of a body as composed of just two forces -- active and reactive, dominant and subservient -- it's clear that any actual body is composed of the many forces and their various relationships that give the body a hierarchy.  Finally, it's important to note that this definition of a body has nothing to do with its materiality.  As Deleuze says explicitly, a body may be physical, chemical, biological, social or political depending on the forces involved.  It's not clear to me whether this means that the forces themselves belong to these domains, or, more likely, that forces have no inherent domain but that the hierarchy of their relations defines various domains.  So here we can already see a break with the material-immaterial dualism I mentioned before.  A body is neither of these two sides, or both simultaneously.  

What happens when two different forces come into relation?  One of them is stronger, more active, more powerful than the other.  Each force has a quantity of power, and, for reasons we'll see in a minute, these quantities are never equal.  As a result, one force overpowers another and dominates it, while the second submits to it as an emissary  submits to its master or a tool to the designs of its user.  In the case of humans, the more powerful force constitutes the body, while the less powerful force is what we think of as 'us' -- our consciousness.  Our consciousness is actually a tool of the body, its 'subject', emissary, or slave.  

To remind consciousness of its necessary modesty is to take it for what it is: a symptom; nothing but the symptom of a deeper transformation and of the activities of entirely non-spiritual forces. (NP, 39)

The body is thus higher than consciousness in the hierarchy of forces that constitute our organism.  The body commands and consciousness obeys.  The body is active, and consciousness reactive.  

[Attentive readers may notice that we seem to be using the term body ambiguously to refer to both the stronger term in a relation of forces, as well as to the relation as a whole (which necessarily comprises both a stronger and weaker term).  This turns out to be a strategic ambiguity on the part of Deleuze.  The higher term in a relation of forces is always unconscious.  As a result, we aren't able to identify it as easily as we can the lower, conscious, level of a relation, and end up inferring it by seeing this lower level as a symptom.  Since we aren't directly conscious of the stronger term (the body), our access to it is only through seeing the weaker term (consciousness) as a weaker term.  Thus, in practice, we discover the unconscious body only as a relation that must include consciousness as one of its parts] 

The notion that our consciousness is a slave to the body is a total inversion of our normal way of seeing things.  Nevertheless, there are a few ways to make this idea more approachable.  Consider that on an evolutionary time scale, consciousness seems to be an extremely rare and late-breaking phenomenon.  How could it not be a tool of the body, something that would adaptively serves the ends of the body, under those circumstances?  Consider as well that we actually already conceive of our consciousness as determined or dominated by a larger force, though we don't often think of the relationship in quite those terms.  We usually call this force 'reality', or the 'external world'.  And we call the relation of consciousness to this superior force 'representation'.  In fact, we call a consciousness not dominated by reality in this way 'deranged', even though such a consciousness would at first glance appear to have more freedom of action.  If a properly functioning mind is merely the mirror of nature, it must also be the servant of nature.  This is what Deleuze is alluding to in comparing the Freudian to the Nietzschean conception of consciousness.

Like Freud, Nietzsche thinks that consciousness is the region of the ego affected by the external world (VP II 253/WP 524, GS 357). However, consciousness is defined less in relation to exteriority (in terms of the real) than in relation to superiority (in terms of values). This distinction is essential to a general conception of consciousness and the unconscious. In Nietzsche consciousness is always the consciousness of an inferior in relation to a superior to which he is subordinated or into which he is "incorporated". (NP, 39)

So while it may seem counterintuitive to think of consciousness as inferior, Nietzsche is, in a sense, merely being more explicit about the fact that our consciousness is only a small part of a larger whole.  Instead of taking the reality of the exterior world for granted, Nietzsche begins with the more fundamental relations of power that are implicit in our conception of this world.  At its core, reality is what commands us, what we can't change, what we're forced to accept.  We rightly ascribe this power of command to something external to our ego, but we err in hypostatizing this larger force.  We don't really know what's out there because it is, by definition, outside of and more powerful than our consciousness.  

In Nietzsche consciousness is always the consciousness of an inferior in relation to a superior to which he is subordinated or into which he is "incorporated". Consciousness is never self-consciousness, but the consciousness of an ego in relation to a self which is not itself conscious. It is not the master's consciousness but the slave's consciousness in relation to a master who is not himself conscious. (NP, 39)

If we want to replace the concept of reality with the concept of the body, we need to be careful not to slip into thinking of the the body as my body.  My body belongs to my conscious ego.  The body is the superior force that constructs precisely this ego as its tool or servant.  Consciousness is not the possessor of the body, but on the contrary is possessed by it.  This means that there's a certain deliberate vagueness in the way Deleuze is using the term body.  He doesn't mean to deny that consciousness is to some extent a tool of the biological body of an individual organism.  But he also doesn't want to limit the concept in this way and foreclose on other, more abstract bodies that also dominate consciousness.  

"Consciousness usually only appears when a whole wants to subordinate itself to a superior whole . . . Conscious- ness is born in relation to a being of which we could be a function" (VP II227). This is the servility of consciousness; it merely testifies to the "formation of a superior body". (NP, 39)

If we ask ourself what "superior body" "incorporates" our human consciousness, I think the most obvious answer is not our individual biological bodies, or even our personal energy bodies, but the social body.  I wouldn't care to argue that this is the only superior body our consciousness is but a part of, but it seems clear to me that a significant fraction of our ego's reactions are programmed by fairly general societal forces.  Of course these forces are as diverse as they are contradictory, so maybe it would make more sense to say that our conscious ego is the inferior term constructed at the nexus of many bodies.  So while the point of this first subsection (2.1) is to put consciousness in its place as an inferior and reactive force, the superior and active force to which it corresponds is largely left open.

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The point of seeing consciousness as the inferior force in a relation is not to somehow deny the reality of consciousness and condemn it as an illusion.  The existence of the master does not negate the slave.  The point is not to say that inferior forces have no power.   Rather, the point is to see these as forces.  Inferior or reactive forces are a type of force.  They possess the type of force that belongs to a tool or agent which is made to serve a master.  But we can only understand the forces of this type if we see that they do not exist on their own, but always as the inferior terms in a relation.  

Inferior forces do not, by obeying, cease to be forces distinct from those which command. Obeying is a quality of force as such and relates to power just as much as commanding does: "individual power is by no means surrendered. In the same way, there is in commanding an admission that the absolute power of the opponent has not been vanquished, incorporated, disintegrated. 'Obedience' and 'commanding' are forms of struggle." (VP II 91/WP 642) Inferior forces are defined as reactive; they lose nothing of their force, of their quantity of force, they exercise it by securing mechanical means and final ends, by fulfilling the conditions of life and the functions and tasks of conversation, adaptation and utility. (NP, 40)

We've seen that consciousness is one of these reactive forces.  But it is only one example of a general class.  It turns out that much of our modern scientific worldview is unwittingly constructed from reactive forces that have been divorced from the body to which they belong.  Consider the basic concept (though perhaps not the actual practice) of science.  Science only deals with things that follow laws.  The whole point is to find out what is fully determined to happen, what must happen, according to the laws of nature.  The domain that it investigates, and the manner in which it pursues the investigation are specifically designed to strip the subject matter of any activity of its own.  In physics, matter is inert.  It merely obeys laws which are not themselves material.  Even in biology, we interpret organisms as nothing more than machines for duplicating themselves, and lionize the evolutionary law that relegates the forces that create and modify these organisms to chance.  In other words, we always conceive the subject matter of science as entirely reactive, and pack all the true activity of nature into a separate world of general laws.   These laws project the dominant and determining forces into another world, a world which, conveniently, our reactive consciousness is uniquely equipped to understand.

It is inevitable that consciousness sees the organism from its own point of view and understands it in its own way; that is to say, reactively. What happens is that science follows the paths of consciousness, relying entirely on other reactive forces; the organism is always seen from the petty side, from the side of its reactions. The problem of the organism, according to Nietzsche, is not an issue between mechanism and vitalism. What is the value of vitalism as long as it claims to discover the specificity of life in the same reactive forces that mechanism interprets in another way? The real problem is the discovery of active forces without which the reactions themselves would not be forces. (NP, 41)

Part of the goal in discussing reactive forces is to restore these to their rightful place as forces.  They have a power of obeying or executing which properly belongs to them, even if this power is always steered by and in service of an active force.  But of course, part of the goal is also to bring the active forces back into this world and reverse the mysterious separation of the two sides of force.  Active forces are harder to characterize because they always escape consciousness.  These unconscious forces don't operate according to the principle of identity and following the rules of law that consciousness understands.  Instead, these are the forces that give rise to identity, that create forms and that represent an immanent law unto themselves.  Seeing the world through the lens and categories of consciousness makes active forces nearly invisible, which is why science ends up describing a cold and mechanistic world.  Restoring activity to the natural world means putting the creative and self-organizing force back into matter in exactly the manner popularized by Manuel de Landa.

Perhaps the easiest place to notice the conspicuous absence of actives forces in our habitual view is in the case of biology.  Just where we would expect to find some creative action, some life, we are told there is only a tendency to establish and reestablish the identity of the organism.  Our actions as living organisms are all purported to serve the self-evident goal of maintaining us within a viable equilibrium that itself serves only as a means for producing an identical copy of this equilibrium tending machine.  But where are the forces that create this identity and equilibrium to begin with?  What forces within life produce this machine for reproducing a reproduction (of equilibrium state), and what forces allow it to adapt when a new equilibrium is called for?  This is why Deleuze mentions the failure of vitalism.  If we understand vitalism as the principle that there is some inner life force or will to survive leading an organism to preserve and duplicate itself, then vitalism merely describes the same equilibrium seeking behavior as mechanism.  In either case, where is the force that would explain why just this equilibrium, or why there's any equilibrium at all?  Within Darwinism, the answer is clear -- chance is the only force that can initially give rise to an organism and chance is the only force that can modify it.  Yet chance is explicitly outside the theory of natural selection and outside the domain of life as such.  Which leads us back to a question that our esteemed colleague over at the Capitalist Axiomatic posed more than a decade ago: What is evolution a theory of?  Do we think that nature is only capable of following laws and reproducing forms and never creates new ones?  This question lies under Nietzsche's critique of Darwinian evolution. 

"What is active? - reaching out for power" (VP II 43/WP 657). Appropriating, possessing, subjugating, dominating - these are the characteristics of active force. To appropriate means to impose forms, to create forms by exploiting circumstances (BGE 259 and VP II 63/WP 647). Nietzsche criticizes Darwin for interpreting evolution and chance within evolution in an entirely reactive way. He admires Lamarck because Lamarck foretold the existence of a truly active plastic force, primary in relation to adaptations: a force of metamorphosis. (NP, 42)

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Section 2.3 begins to address a tricky question left hanging by our definition of a body as a relation of active and reactive forces.  If what makes a force active is simply its greater quantity of power relative to its reactive partner, then why are we introducing a qualitative difference between the two types of forces?  Why can't we just reduce the strength of a force to a single number?  The answer is basically that there is no single, global scale for quantifying force that would apply to all forces at once.  The fact that there is no single real force capable of dominating 'existence as a whole' means that no absolute scale can be imposed on force.  It's like a good friend once told me in defense of his decision to drink Budweiser: "there ain't no king of wines".  Instead, all we can find in the absence of a global coordinate system are local relations of power.  Power is a manifold.  As a result, we discover that while a force is characterized by a quantity of power, differences in this quantity cannot be reduced to a simple quantity of difference, but actually give rise to different qualities.  

... differences in quantity cannot be reduced to equality. Quality is distinct from quantity but only because it is that aspect of quantity that cannot be equalised, that cannot be equalised out in the difference between quantities. Difference in quantity is therefore, in one sense, the irreducible element of quantity and in another sense the element which is irreducible to quantity itself. Quality is nothing but difference in quantity and corresponds to it each time forces enter into relation. (NP, 43)

The subtext here is that Nietzsche's previous critique of the tendency of science to see matter (and the body) as homogenous, inert, stuff, is not made in the name of a romantic appeal to some irreducible spiritual quality.  On the contrary, there is nothing but quantity.  It's just that quantity is more complex than we usually give it credit for.  Echoing Spinoza, we might say that we don't even know what quantity can do.

This same line of thinking casts a new light on the idea of affirming chance.  When we sought to affirm all of chance at once, in a single throw of the dice, we stumbled over the fact that no existing force was capable of appropriating all the others.  There is no largest force.  So the affirmation of chance had to proceed from affirming the Return of a single moment, a single fragment of chance.  When completely affirmed though, it turned out that this fragment was ultimately connected to and dispersed in a larger totality that had the power to bring it back again (and launch it out again, endlessly).  We do not affirm chance globally and as a totality, but locally and piece by piece.  This appears to conflict with the idea of affirming chance all at once, but that is the paradox of ER.  When we affirm the power of a force -- whether it is active or reactive -- we find it connected to other forces, which are in turn connected to yet other forces, in a series of local patchworks that extend indefinitely.  Since everything is connected to everything, but not in any order, Deleuze can introduce a contrast between chance and a continuum.  Like power, chance is a manifold, a holey-space that cannot be defined in its entirety from a single perspective.

By affirming chance we affirm the relation of all forces. And, of course, we affirm all of chance all at once in the thought of the eternal return. But all forces do not enter into relations all at once on their own account. Their respective power is, in fact, fulfilled by relating to a small number of forces. Chance is the opposite of a continuum (on the continuum cf. VP II 356). The encounters of forces of various quantities are therefore the concrete parts of chance, the affirmative parts of chance and, as such, alien to every law; the limbs of Dionysus. (NP, 44)

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Section 2.4 continues the theme of Nietzsche's relation to science and culminates in a comparison between two types of scientific cosmology and the cosmology of Eternal Return.  The basic idea is the same one we've already seen.  Science proceeds by equalizing difference.  Whether it's particles that obey the laws of physics or organisms that obey the laws of evolution, the 'subjects' of a science are all equivalent when it comes to these laws.  The goal is to see the world as an inert and undifferentiated material; it's all the same stuff, just with different numbers attached to it.  We've seen that Nietzsche is opposed to this type of reductionism.   

Rightly or wrongly Nietzsche believes that science, in the way it handles quantities always tends to equalize them, to make up for inequalities. Nietzsche, as critic of science, never invokes the rights of quality against quantity; he invokes the rights of difference in quantity against equality, of inequality against equalization of quantities. (NP, 45)

[ Note that the first words of this quote allude to a question Deleuze chooses to skip over.  Is Nietzsche right about science, or is he critiquing a straw man?  After a long discussion of this we would inevitably conclude that the answer is yes.  Surely Nietzsche's hypostatization of 'Science' results in something of a caricature.  At the same time, I think we can recognize a large majority of scientist's worldviews and a huge chunk of scientific activity in this caricature.  It's simply not all that science could be.]

The essence of quality does not lie in some supplementary spiritual dimension.  It escapes our conscious scientific concepts to become the hard problem of qualia not because it is mysteriously added to the material world, but because it is the irreducible element of differentiation within the world.  It stems from the fact that two interacting forces cannot be made perfectly equal and interchangeable.  

This is why his whole critique operates on three levels; against logical identity, against mathematical equality and against physical equilibrium. Against the three forms of the undifferentiated. (NP, 45)

The fact that the world cannot exist in an undifferentiated state is really a corollary of the metaphysics of force we have been describing.  It's another way of saying that existence is necessarily linked to diversity and multiplicity.  Or that it is empty of intrinsic nature and always dependent on a way of seeing that simultaneously fabricates an active and a reactive force.   

While it's not immediately obvious, the Eternal Return encapsulates this idea of the always differentiated.  It affirms the world as an unlimited becoming that can never be grasped as a total identity, never fall into a cycle which repeats the same state as equal, and never come to rest in an equilibrium.  In other words, it is designed to reject all three forms of the undifferentiated.  

It's probably obvious from the name how ER rejects the idea of a single straight line of existence that begins with the The Word and ends with Eschaton.  The universe has no transcendent goal or meaning and is not ruled by a divine plan.  Existence is not a single identity that can be totalized in this way.  Nor, however, is it the meaningless increase in entropy that inevitably ends in the equilibrium of heat death.  Nietzsche argues that if it were possible to reach an equilibrium, the universe would already have done so (we'll investigate this idea more in the next section).  The difference between forces can never be canceled out in equilibrium.  Nietzsche opposes the Return to both of these interpretations of existence.  It produces neither identity nor equilibrium, but an endless circulation where everything comes back again and again.  

Probably less obvious is the way the Return also rejects the repetition of the same.  The touchstone is always: what returns is not the same thing but everything.  This distinguishes the return from a cyclical cosmology, where the universe (perhaps due to ergodicity?) eventually returns to the same state where it 'started'.  Once a state is duplicated at the 'end' though, the laws of physics insist that the system as a whole will endlessly repeat the exact same cycle.  Here again, we see science associated with a form of the undifferentiated.  Start and end must be exactly equal states, with no difference between them.  In addition, this point on the circle we've labeled start/end is entirely arbitrary, and not fundamentally different from any of the other states, all of which are endlessly duplicated.  The irreducible difference in quantity (quality) becomes mere quantity of difference through the trajectory of the cycle, and is finally zeroed completely as the circle closes.  Just like it rejected an endpoint for existence, ER rejects the limit on becoming that this cosmology necessitates.  What returns is not the same state.  After all, how could exactly the same state ever repeat?  It wouldn't be a return if it was identical to the first time.  How would we ever know it was the second go-round?  Either we need some force outside existence to count the number of repetitions of this state, or, if we make this counting force part of existence, then there was no repetition after all.  Nietzsche's Return is not the repetition of the identical but the synthesis of the difference between the first and second (and Nth) times.  

According to Nietzsche the eternal return is in no sense a thought of the identical but rather a thought of synthesis, a thought of the absolutely different which calls for a new principle outside science. This principle is that of the reproduction of diversity as such, of the repetition of difference; the opposite of "adiaphoria". (NP, 46)

It is not the 'same' or the 'one' which comes back in the eternal return but return is itself the one which ought to belong to diversity and to that which differs (NP, 46)

The eternal return affirms the unequalizability of any two moments, but it does so precisely by putting them into a relation.  I assume Deleuze will later explore how this is related to the definition of force.  

 

Nietzschean Not-Self (Chapter 2)

Klossowski's second chapter appears to be a completely separate essay that does not build on the first one.  This means we have to start again from scratch with another difficult and slippery text.  The main goal seems to be to elaborate a Nietzschean theory of not-self (anattā) that would apply successively at various levels of abstraction ranging from the personal, to the psychic, and all the way down to the organic. 

Klossowski begins at the personal level, with a discussion of the relation between Nietzsche's writing and the fluctuations in his health.  The letters he quotes demonstrate that while Nietzsche's famous migraines often kept him from writing and even thinking, these same sufferings seem to have been brought on by Nietzsche's own overactive brain.  So Klossowski's first point is that this cycle -- a thinking that rises to a fever pitch which blots out thinking, resulting in a forced rest that restores thought but resets the mechanism -- got Nietzsche thinking about the relationship between a thinking brain and suffering body.

The act of thinking became identical with suffering, and suffering with thinking. From this fact, Nietzsche posited the coincidence of thought with suffering, and asked what a thought would be that was deprived of suffering. Thinking suffering, reflecting on past suffering - as the impossibility of thinking - then came to be experienced by Nietzsche as the highest joy. But does thought really have the power to actualize itself without itself suffering, without reconstituting its own suffering? Does thought itself suffer from its own inability to actualize itself? What then is doing the suffering or enjoying? The brain? Can the cerebral organ enjoy the suffering of the body of which it is a function? Can the body rejoice in the suffering of its supreme organ? (NVC, 23)

While the questions that conclude this passage are at this point rhetorical, they introduce the main idea of the essay -- the material and the spiritual are not always on the same page, and perhaps are even directly at odds with one another.  In itself, this idea would be neither novel nor surprising.  Almost every religion, and particularly Christianity, has long claimed that the gross materiality of the body is an impediment to spiritual development.  The thinking soul has a moral obligation to transcend the suffering of the body; salvation lies in precisely this transcendence.  The interesting thing about Nietzsche is that he runs this same logic backwards.  In his case, it's actually the thinking soul, and the brain itself, that is the cause of suffering.  It's only when the attempt to identify with and carry out this thinking is released that the episode passes and Nietzsche begins his convalescence.  In other words, Nietzsche experiences his own brain as a sort of parasite (perhaps the sort of "metaphysical virus" mentioned on pg. 6) attacking his body, which the body in turn fights back against.  Obviously, it becomes difficult to know who's who here.

The agonizing migraines, which Nietzsche experienced periodically as an aggression that suspended his thought, were not an external aggression; the root of the evil was in himself, in his own organism: his own physical self was attacking in order to defend itself against a dissolution. But what was being threat­ened with dissolution? Nietzsche's own brain. Whenever his migraines subsided, Nietzsche would put his state of respite in the service of this dissolution. For the dissolution was judged to be such only by the brain, for whom the physical self and the moral self apparently coincide. But the body provided Nietzsche with a completely different perspective, namely, the perspective of active forces which (as organic and therefore subordinate functions) expressed a will to break with this servitude. But they could do so only if this will passed through the brain. The brain, on the other hand, could experience this only as its own subordination to these dissolving forces: it was threatened with the impossibility of thinking. (NVC, 24)

This passage is complicated not simply because it tries to express the circular aggression of body attacking brain because brain attacked 'first', but also because it alludes to the way these two sides are not symmetrical.  Nietzsche does not merely invert the Christian moral relationship between between body and soul, but distinguishes them in kind in a new way.  'The body' is composed of a multitude of forces or drives that have no pre-established unity amongst them.  By contrast, the brain takes for granted its own unity as well as the unity of its moral self with a physical self (that it also presumes to be a unity).  As a result, it's only on the side of the brain that there can be anything like a fear of dissolution, because it's only on that side that some unity has been posited.  'The body', as we'll see more clearly in a moment, is a chaotic interaction of various impulses that have been imperfectly and temporarily captured by an organism.  Unlike a Christian's identification with their immortal soul, the identification of 'Nietzsche' with 'his body' cannot help but be a paradoxical affair once the founding principle of a unit of identity has come into question.

Nietzsche experienced this dissolving confrontation be­tween somatic and spiritual forces for a long time, and he observed it passionately. The more he listened to his body, the more he came to distrust the person the body supports. (NCV, 24)

Here we see the beginning of the transition to Klossowski's next level of analysis.  Instead of the the brain, he will begin to talk about the conscious self or the person that we often identify with the brain.  But how does this conscious self that we always imagine is 'us' actually get produced by the body?  

Klowssowki here gives us an intriguing, but in my mind not completely satisfying, explanation of how the brain forms consciousness in response to bodily pain.  The idea seems to be that the body sets up the brain as a specialized organ for combatting a painful excitation that appears to invade from the outside.  However, this system for avoiding pain or pursuing pleasure can only work if the brain codes the excitations coming from the body according to whether approaching or retreating from them has resulted in other painful or pleasant excitations in the past.  Since the excitations coming from the body are so manifold, the brain has to reduce them to a simple code of valence, and the key to this code is nothing more than whether it is self-reinforcing -- does classifying an excitation as painful lead to actions that avoid other excitations that would be classified as painful?  Klossowski's idea seems to be that this valence code is almost completely self-referential and independent of what the excitation might actually mean for 'the body'.  As a multiplicity, the body doesn't have a single point of view on what is pleasurable or painful.  The brain, however, as possessor of a unified code, does have a single point of view, though this viewpoint is only constructed from what habitually appears pleasant or painful for the brain.  This unified self-reinforcing viewpoint is what we call consciousness.  

   The body wants to make itself understood through the intermediary of a language of signs that is fallaciously deci­phered by consciousness. Consciousness itself constitutes this code of signs that inverts, falsifies and filters what is expressed through the body.
   Consciousness is itself nothing other than a deciphering of the messages transmitted by the impulses. The deciphering is in itself an inversion of the message, which is now attributed to the individual. Since everything leads to the 'head' (the upright position), the message is deciphered in a way that will maintain this 'vertical' position; there would be no message as such if this position were not habitual and specific. Meaning is formed in the upright position, and in accordance with its own criteria: high, low, before, after. (NVC, 26)

From a biological perspective, this explanation isn't quite satisfying because it seems that my body comes with any number of pre-programmed interpretations or reflexes that don't depend much on my consciousness of their valence.  I drop hot things, orient on noises from nearby foliage while hiking, and duck when people swing a cleaver at my head.  So it seems that my organism probably has some sort of unity, some sort of 'mind of its own', independently of my consciousness.  However, I'm willing to investigate whether the unity of my body may perhaps be an illusion, and whether these reflexes can perhaps be de-conditioned.  And it's clear that moving the unity back to the level of the organism doesn't solve the philosophical problem of how it arises to begin with, so perhaps the objection is not so important.  At any rate, Klowssowski seems to be adopting the hypothesis that the body has no unity of its own.  It's unity is fictitiously imposed by the consciousness installed on top of it, which seeks to keep itself upright simply because that's what it has always done.  

Nietzsche did not speak on behalf of a 'hygiene' of the body, established by reason. He spoke on behalf of corporeal states as the authentic data that consciousness must conjure away in order to be an individual. This viewpoint far surpasses a purely 'physiological' conception of life.  The body is a product of chance; it is nothing but the locus where the group of individuated impulses confront each other so as to produce this interval that constitutes a human life, impulses whose sole ambition is to de-individuate themselves. (NVC, 26)

 

At the end of this passage we see the idea I mentioned earlier -- the body is a chaos.  This chaos is structured by a clash of impulses that seek to "de-individuate" themselves, which I think is another way of talking about the will to power.  In truth, the impulses don't want anything at all, even power.  Goals and intentions are fictions posited at the level of consciousness.  Instead what the impulses 'want' is simply to act, to dominate, to "draw their ultimate consequence at every moment" (NVC, 45) -- in other words, to make themselves universal.  It's as if each impulse wants to swallow everything and is only prevented from doing so by the all the other like-minded impulses it encounters.  We can imagine shifting constellations of warring Leibnizian monads, red in tooth and claw, without a pre-established harmony between them.      

From each of our fundamental impulses comes a perspectival appreciation of every event and of every lived experience. Each of these impulses is hindered or favoured or flattered by every other impulse, each with its own formative law (its risings and fallings its own rhythm, etc.) - and one impulse dies when another one arises. (NVC, 44)

The fortuitous and chaotic body does nothing to preserve itself because it has no sense of self at all.  The conscious brain built on top of it, on the other hand, seeks to preserve the body within a set of states compatible with its own cerebral existence, almost as if the whole point of having a body was merely to produce a conscious brain.  The root of the principle of identity that we see developing here always goes back the brain's desire to code the flux of the body in a simple, consistent, and upright way.  But the branches of that principle have profound ramifications.  Once some identity has been installed in the organism, the chaotic body becomes my body.  All the forces or impulses felt in this body must be assimilated to the code that constitutes the unity of the conscious brain.  These are the initial steps in forming a person or self that maintains a continuous identity over time despite the fluctuations of the body.  This person is actually a product of the body, but the way it takes possession of the mechanism that created it leads us to reverse the cause and effect.  

   The body, insofar as it is grasped by consciousness, dissoci­ates itself from the impulses that flow through it, and which, having come together fortuitously, continue to sustain the body in an equally fortuitous manner. The organ that these impulses have developed at the 'highest' extremity of the body considers this fortuitous yet obvious sustenance to be necessary for its conservation. Its 'cerebral' activity therefore selects only those forces that preserve this activity, or, rather, those that can be assimilated to it.  And the body adopts only those reflexes that allow it to maintain itself for this cerebral activity, just as the latter henceforth adopts the body as its own product. 

   To understand Nietzsche, it is important to see this reversal brought about by the organism: the most fragile organ it has developed comes to dominate the body, one might say, because of its very fragility.  (NVC, 27)

This is one of Klossowski's main points, so it pays to belabor it.  We have magicked up a self-referential identity that rests on nothing but its own continuity, yet which appears to be not only a solid thing in itself, but to be the 'head' and owner of a body as well as the cause of its actions.   The body possessed in this way is the impulsive body enslaved (to choose the most dramatic term) by our self.  The tail has come to wag the dog.  The epiphenomenon has become the phenomenon.  The 'means' has come to posit itself as end, with the quotes here indicating that the very distinction between means and ends cannot exist at the level of the fortuitous and impulsive body.  The notion of an aim or endpoint only comes into existence alongside the principle of self-identity.  

So how can we combat this cerebral takeover that imprisons the impulsive body within a fictitious self?  Can we set a conscious intention to overcome the tendency to construct of a conscious state that constantly classifies and assimilates anything new to its unconscious and habitual patterns?  Won't that just enmesh us more deeply in the same problem?  It seems like our only option for liberating the body would be to go back to being 'unconscious', to do away with our own brain and self entirely.  But what could this even mean?  In fact, the distinction between conscious and unconscious meets with the same fate as the distinction between means and ends.  It is only from the perspective of and by contrast with consciousness that there is anything that could be called the unconscious.  Consciousness is really nothing more than the new application of an old and often repeated code -- which Klossowski increasingly calls, "the code of everyday signs", ie. words.  The 'unconscious' and habitual world would seem to be structured in the same way and by the same codes as the conscious one.  From the perspective of the liberated impulsive body, both sides of this code's assimilation are equivalent fixations and falsifications of its ceaseless and manifold flux.  Indeed, the only difference seems to be that one side speaks in the present while the other side remains silently implied by the past.  

Moreover, let us try to understand how. given his notion that conscious life is subordinated to fluctuations of intensities, he explains what we call an intention and a goal at the level of consciousness, and what this latter term signifies in relation to the term unconsciousness. What do these these refer to in Nietzsche? Are they different from the term conscious and unconscious, in Freud's sense of the 'iceberg'? For it would seem that neither consciousness nor unconsciousness - nor willing or non-willing - have ever existed. Within a system of designating fluctuations, there is only a discontinuity between silence and declarations in the agent. (NVC, 37)

What we need to find instead of this code of everyday signs is something like 'the unconscious of the body' rather than a cerebral or individual unconscious.  But this would seem to be some sort of impossibly complex representation of the constantly shifting battle of the impulses, created by means of those very impulses. If we do away with the level of the conscious code that only pretends to float free of the impulsive body, we would be left with the infinitely subtle 'language' of this body alone.  This 'language' wouldn't be any sort of fixed and continuous code though, but something closer to a music that can swing rapidly and discontinuously from one affective state to another.

To use conscious categories as a means to attain an end outside consciousness is still to remain subordinate to the false perspective of consciousness. A consciousness that would be conscious of being an instrument of Chaos would no longer be capable of obeying the 'aim' of a chaos that would not even ask it to pursue such an aim. Chaos in term would then be 'conscious' -- and would no longer be Chaos. The terms conscious and unconscious are therefore applicable to nothing that is real. If Nietzsche made use of them, it was only as a 'psychological' convention, but he nonetheless let us hear what he did not say: namely, that the act of thinking corresponds to a passivity, and that this passivity is grounded in the fixity of the signs of language whose combinations simulate gestures and movements that reduce language to silence. (NVC, 43)

Klossowski's essay ends with an exploration of how such a 'language of affects' (analogous to a "culture of the affects") might differ from the code of everyday language, and how this everyday code could have been built on top of the impulsive body.  Because the new 'language' we are looking for would operate below the level of our everyday language, Klossowki begins all the way back at the beginning with a discussion of what separates the organic from the inorganic.  Nevertheless, this way of presenting things leads to a bit of confusion in my mind.  We've been talking all along about various levels of duality -- a thinking mind and a suffering body, a brain that habitually codes for valence and an impulsive body, a continuous conscious self, and a discontinuous chaotic body.  Some form of 'the body' is always the term employed for the multiple, flowing, side of the duality, for Becoming as opposed to Being.  Yet now, in trying to answer the question of how codes get formed, Klossowski employs the same dualism in a way that seems to put the impulsive body on the side of the inorganic.

   'Every movement should be conceived as a gesture, a kind of language in which (impulsive) forces make themselves heard. In the inorganic world there is no misunderstanding, communication seems to be perfect. Error begins in the organic world.'
   In the inorganic world, communication seems perfect. Nietzsche means: there is no possible disagreement between what is strong and what is weak. 'Every power draws its ultimate consequence at every moment'. he says elsewhere. Persuasion is immediate.
  In the organic world, by contrast, where exchange and assimilation are necessary, misunderstanding becomes poss­ible, since exchange and assimilation take place only through interpretation: from trial and error to certainty - the certainty of the conditions of existence. The latter can be obtained only after a long experimentation with the similar and the dissimilar, and thus with identity. Only then can points of reference, repetition and comparison appear - and finally, comparable signs.
  Now in a universe dominated by the inorganic, organic life is itself a fortuitous case - hence a possible 'error' in the cosmic economy. It is within this economy that interpretation, grounded in the fear of error, becomes susceptible to error.  Even if the origin of organic life lies in purely random combinations, it can no longer behave randomly once it comes into existence. It must believe in its necessity, and therefore it must maintain the conditions of its existence, and to do so it must avoid chance and not commit any errors. Hence the double aspect of error in Nietzsche: life depends on an illusion (its 'necessity') - whence the verdict: 'Truth is the kind of error without which a certain species of life could not live.' (NVC, 45)

Viewed from the perspective of the energetic fluctuations of the inorganic, organic life is nothing more than a temporarily self-reinforcing feedback loop. From the organic perspective though, this same feedback loop appears to be selective, to have a goal and a will (its own self-preservation).  It's the same dualism we saw before, but now the organic (the body) is on the side of an illusory principle of unity, namely the unified organism (which appears to contradict the earlier idea that the body has no unity of its own but borrows it entirely from the self, thus pulling itself up by its own bootstraps, as it were).  

This curious inversion seems intended to situate the impulses somewhere between the level of the inorganic and the level of a fully signifying conscious self.  Perhaps this is why Klossowski earlier introduced the idea of the brain as a level of analysis or intermediary step between the body and the person?  It's not clear to me if I'm missing something important here, or whether Klossowski is not being completely sober and consistent in his terminology.  At any rate, the idea now seems to be that there are 3 levels.

1) The inorganic has no need of the concept of valence and the unified perspective of interpretation this implies -- at this level things just happen, there is perfect communication and no need of signs.  This is what we were earlier calling the "impulsive body", which we saw the brain fighting against with its "code".  

2) Once an organism has been formed though, the various excitations it receives are interpreted according to a "code of signs" that classify them as attracting or repelling the organism.  Klossowski will now refer to this level as the level of impulses and "signs" (ie. not quite a "code" properly speaking).  Impulses in this sense do appear to refer to the unity of an organism (as I argued before that they should).    These impulses are not just a raw energy or dimensionless number, but are a sort of vector defined on one end by the unity of the organism, and on the other end by what the impulses 'seek' or 'avoid'.  The quotes here indicate that even at this level, an impulse in itself has no goal or aim, and in fact is not even individuated.  It's only the constellation of impulses, and their interrelationship in service of maintaining an organism, that individuates them and produces the appearance of what we might term an "attractor" (to distinguish it from a goal), or what Klossowski calls a "phantasm".  Thus a phantasms seems to be the motive force for an organism, whose movements and "gestures" are the signs of the impulsive forces reaching a fragile and moment to moment arrangement consistent with the existence of the organism.  

3) Finally, a conscious signifying level is installed on top of the organic level.  This is the level of a "code", or what Klossowski will call (following Nietzsche) the "abbreviation of signs".  At this level the phantasm that momentarily bound and ordered the impulsive organic level and attracted the organism is retroactively posited as the original goal.  We already explored the logic of this inversion of cause and effect earlier.  Klossowski again finds its root in the way a fixed code must necessarily compress or abbreviate the rich language of organic signs in a way that keeps the battle of impulses within the narrow range of states compatible with its own (the code's) continued existence.  This compression is lossy however, and the signs are always overflowing the code scheme in the same way music defies our ability to talk about it.

This at least is my interpretation of the complicated section on pages 45-48.  For the most part it seems to reflect the idea of capture and over-coding we've discussed.  Except that there appears to be a duplication of that same logic in moving from levels 1 to 2 and levels 2 to 3. The upshot is that the abbreviation of signs in level 3 quiets the tumult of the impulses by fixing them in a rigid conscious code.

'The contradiction is not between the "true" and the "false" but between "abbreviations of signs" and the "signs " themselves.'  What this means is that the impulses - which confront and interpret each other through their fluctuations of intensity and, at the level of organized beings, through gestures - create forms out of these movements and gestures, and cannot be distinguished from this invention of signs, which stabilizes them through abbreviation. For in abbreviating them, these signs reduce the impulses, apparently suspending their fluctuation once and for all. But in the intervals of the (fixed) signs of language, the intensity of the impulses can only be designated in an intermittent and arbitrary manner, in comparison with these abbreviations. Their movement is constituted as a meaning only if they take this designating abbreviation as their aim, and reach it through a combination of unities. The latter then form a declaration which sanctions the fall of the intensity, once and for all. (NVC, 48)

Given this story of the genesis of signs and abbreviations of signs, the final question is how we could make our way back towards the language of signs, thus liberating ourselves from the constrictive, compressing, code of consciousness.  Klossowski's interpretation of Nietzsche answer to this question is fascinating, but also, I suspect, preliminary; we will almost certainly understand it better as the book progresses.  The basic idea is clear though.  We can't, nor would we want to, go backwards into 'unconsciousness'.  What we can do, however, is to use our conscious "abbreviations of signs" (ie. words) to simulate the forces underlying those abbreviations.  It's kind of like: (simulating your own computer's hardware (simulating your own computer's hardware (...) ) ).  Obviously, to do this, you have to treat your self as an impulsive automaton that operates according the the levels and logic we've described.

First, one must admit everything that is purely 'auto­matic': to dismantle an automaton is not to reconstruct a 'subject'. Since perspectivism is the characteristic illusion of this automaton, to provide it with the knowledge of this illusory perspective, the 'consciousness' of this 'unconscious', is to create the conditions of a new freedom, a creative freedom. The 'consciousness' of the 'unconscious' can consist only in a simulation of forces. It is not a matter of destroying what Nietzsche calls the abbreviation (of signs) by signs themselves - the encoding of movements - but of retranslating the 'conscious' semiotic into the semiotic of the impulses. The 'conscious categories' that avoid, repudiate and betray these movements - and thus remain ignorant of the perpetual combat of forces - sustain the automatism under the apparent spontaneity of thought. To recover an authentic spontaneity, the producer of these 'categories', the intellectual organ, must in tum be treated as a simple automaton, a pure tool. By consequence. as a spectator of itself, the automaton finds its freedom only in the spectacle that moves from intensity to intention, and from the latter to intensity. (NVC, 50)

The idea of a conscious simulation of the unconscious gives new meaning to the Eternal Return.  If we believe that we necessarily repeat what has come before, we turn ourselves into a sort of automaton.  Here we can see ER as the perfect symbol of the emptiness of the do-er.  The impulsive action has occurred before, without any need for the conscious aim we imagined was its purpose and cause.  Of course, we might legitimately wonder whether it's safe to let our automaton cross the street (again?).  Does consciousness and intention have some crucial evolutionary role in keeping us alive?  Are the errors it produces, the falsifications and abbreviations, completely avoidable, or are they truths: errors necessary for life?  Or do we lose nothing if we imply let these errors come and go while we live the unconscious forces that produced them to begin with?  What kind of life would this be that persists through the emptiness of consciousness?  Klossowski leaves the essay with these questions.

   On the one hand, forgetfulness and unconsciousness are necessary to life; on the other hand, there is a 'will to unconsciousness' which, precisely because it is willed, implies the consciousness of our conditioned state: an irresoluble antinomy.
   Now 'life itself created this grave thought [of the Etemal Return]; life wants to overcome its supreme obstacle'. (NVC, 54)

The Depths of the Surface

Last time we finally reached Deleuze's articulation of the full fold.  The soul is folded and matter is folded and the two sides are folded together into a single world which the soul in-folds and matter un-folds.  The concept of "resemblance" served as a hinge that carried us from one side to the other because.  The folds of matter are completely separate from the folds of the soul, and yet they resemble one another because of their pre-established harmony.  Consider again the fractal curve that illustrates the fold -- each in-curve of one side is perfectly matched by an out-curve of the other in smaller and smaller details to infinity.  While the distinction between the two sides is completely real, it is nevertheless a consequence of the fact that they are two sides of a single curve.  Recall that resemblance is really nothing more than the differential relations of the folding itself.  Thus the fold is non-dual -- distinction and inseparability go hand in hand.  Matter and the soul are two sides of a single and same world that matter realizes and the soul actualizes.  These operations are distinct, but the bear on the same world.  This explains why Deleuze insists (F, 149) that the sides are two floors of a single house, and not two separate worlds.  The screen or wall or membrane or curve which divides the two floors is contiguous with the rooftop and foundation which holds the whole structure together.  This feature is part of the architecture of the Baroque Fold.  In going to infinity (and in both directions) it brings the sides into such intimate contact that we can hardly tell where one ends and the other begins.  At the limit, they converge to the same world, which can frame both of them only via a "torsion" or topological twist that fuses interior and exterior, and makes the curve cover everything.

I've stated this initial summary in architectural terms because Deleuze begins chapter 8 by returning to a reference he made to Bernard Cache back in chapter 2.  Bear with me though, as this connection is rather winding.

The difference between the two floors is like the difference between a curve of infinite inflection defined immanently (what would be called a mani-fold in two dimensions), and the same curve embedded in an exterior coordinate system.  As we recall from our discussion of Cache, points of inflection are primitive or intrinsic or immanent singularities of a curve.  These do not depend on the orientation of the curve for their definition.  By contrast, the singularities of minimum and maximum of a curve do depend on this embedding -- or framing--  of a curve within a two dimensional coordinate system.  The same curve can be looked at from the inside or the outside.

And yet it is indeed a question of two halves, as we have seen in the case of the infinitesmial calculus. In effect, if we assimilate the object—that is to say, the world—to the primitive equation of a curve with an infinite inflection, we obtain the position or the respective point of view of monads as primitive forces, through a simple rule of tangents (vectors of concavity); from the equation, we can extract differential relations between the minute perceptions that are present in every monad, in such a manner that every monad expresses the entire curve from its point of view. This is thus a first part, a first moment, of the object—the object as perceived, or the world as the expressed. But there still remains the question of knowing what the other part is, which now corresponds to the initial equation: these are no longer pure relations, perception—that is, which concern matter and the bodies that perception resembles. This is the second moment of the object—no longer expression, but content. These are no longer decrees, but the maxims or empirical laws of second Nature. They are no longer singularities of inflection, but singularities of extremum, because the curve is now—and only now—related to coordinates that allow us to determine minima or maxima. (F, 128)

Here Deleuze delivers on the promise he made back on pg. 117 to articulate a fourth type of singularity. 1) Inflection 2) Center of curvature or point of view 3) The 'remarkable' differential relations between micro-perceptions that fill this point of view with various macro-perceptions and 4) Singularities of extrema.  

It's interesting to compare these four singularities to the four classes of beings Deleuze arrived at Back in chapter 4.  I don't think that these should map one-to-one, but there's still some clear parallels.  Back then, it seemed obvious that the monad corresponded to the fourth class of beings -- individuals.  These were closely related to the third class of beings -- things -- because both things and monads were defined by the convergence of an infinite series of differential relations.  In the case of things, this convergence was analogous to the converge of dy/dx to the derivative at a point.  We saw, in that case, that the limit was effectively 'folded into' the point; even though the terms of the series vanished, their relation at a particular point on the curve remained determinate (F, 21).  Later though, we saw Deleuze use a very similar analogy to explain the relation of minute perceptions and conscious perceptions in the monad (F, 113).  In that case, the conscious perceptions that constitute the clear zone inside the monad arise when a set of differentials of consciousness (micro-perceptions) enter into a relation that defines a "remarkable" point or singularity.  These descriptions of the type of convergence of a thing and of a monad's perception are not exactly the same, but they seem to resemble one another.  Especially in the context of the quote above, they're enough to make us wonder whether the third type of singularity -- the "thing" -- is meant to refer to both real objects and objects as actually perceived.  These are the two "moments" of the object or thing.  Are thoughts things?  This in turn suggests that all of the first three singularities could be paired with the first three classes of being and thought of as belonging entirely on the side of the soul or monad, the inside of the curve.  After all, these fall into what Deleuze called the "domain of essences" (F, 73)   Inflections are the primitive or simple singularities which 'condense' into a monad (F, 87), providing it with a point of view that includes not only these particular singularities of inflection but the entire curve (I imagine a Taylor series approximation to a complete function that involves only higher order derivatives at a single point), and within this point of view arise perceptions that select and relate certain differentials that define a singular clear zone.  These internal building blocks of the monad seem to correspond reasonably well to the first three singularities.

Whatever we think of this parallel between things and perceptions, what interests me most here is the the way they both contrast to the type of convergence necessary to define the full monad or fourth class of "unitarily simple" being.  The difference is that the limit which defines the monad itself (as distinct from its perceptions) is exterior to the monad and not localizable within it.  Essentially this limit is the world that all the monads converge to -- the best world.  While we don't want to confuse the two, this is a moment when the monad effectively 'becomes' the whole world, its moment of closure.  In this case, perhaps, the fourth class of beings is as much the world as it is the monad -- or rather it is the completion of the monad through the world, and of the world through the monad.  In a way, these two both lie 'outside' of one another and serve as the convergent limit of one another.  Does this suggest that the world itself is also an example of the fourth type of singularity -- a singularity of extremum? 

It's only at this point that we can come back to our initial idea of framing.  Cache pointed out that it is only the frame which establishes the coordinates for a curve and allows for minima and maxima to be calculated.  The process is like coupling a weightless curve to the force of gravity that operates in a particular direction.  In fact, this seems to be exactly how the monad and the world relate.  The world is the closure of the monad, its exterior limit, and is precisely what allows it to coordinate or harmonize with the other monads.  In short, the world is a frame that the monad passes through to become a complete individual. And this frame is an example of the fourth type of singularity -- the world is singularity of extremum because it is the best possible world. 

It is as if the equation of the world had to be written twice in the form of the two calculi—a first time in the minds that conceive it more or less distinctly, and a second time in a Nature that effectuates it. And no doubt the two calculi implicate and continue each other; they are complementary and must be homogeneized. This is why Leibniz can present the choice between the world and the monads as already operating through a calculus of maximum and minimum. Yet the difference between the two halves subsists, since in one case it is differential relations that determine a maximum of the quantity of being, while in the other case it is the maximum (or minimum) that determines the relations in the equation. We have seen the diversity of singular points in Leibniz: the properties of the extremum indeed governs the constitution of the world chosen in Nature, but the choice itself refers first of all to other properties (of inflection) that bring into play the form of the whole [l'ensemble], at a higher level, as the property of being the limit of a convergent series [suite]. The world, as the great equation, thus has two levels, two moments, or two halves: in the first, it is enveloped or folded in the monads; in the second, it is inserted or refolded into matter. If we confuse the two, the whole system collapses, mathematically no less than metaphysically. On the upper floor, we have a line of variable curvature, without coordinates, a curve with an infinite inflection, whose internal vectors of concavity mark, for each branch, the position of individual monads without mass [en apesanteur]. But it is only in the lower level that we have coordinates that determine the extrema—extrema that define the stability of figures, figures that organize masses, and masses that follow an extrinsic vector of gravity [pesanteur] or the greatest incline. Such is the ogive, [the Gothic arch], which puts symmetry into the inflection, and realizes the figure capable of encountering the minimum of resistance in a fluid. Such is the organization of the Baroque house, with its division into two floors—one made up of weightless individuals, the other of heavy masses [l'un tout en apesanteur individuelle, l'autre en pesanteur de masse]—and the tension between the two, when the first rises or falls (spiritual elevation and physical gravity). (F, 129)

My reading of all these correspondences still feels somewhat speculative to me, but I'm pretty sure about equating Deleuze's World and Cache's Frame, since that is precisely what we need to make sense of this complicated passage.  Because the interesting thing about Cache's frame is that it doesn't close off a space, without opening it up to new possibilities.  It's a strange type of limit that doesn't provide a stopping point without relaunching us.  Deleuze has already argued that this is how Leibniz's best possible world works as well.  Fundamentally, it is not about calculating the maximum of a particular variable, but about maximizing the diversity and continuity of the world as a whole.  Rather than the full curve being given in advance, the world is composed by joining up the singularities in the 'best' way.  This is the odd type of extremum that Deleuze is trying to capture when he insists that there are two types of calculus.  There is indeed a calculus of souls, a 'computation' of the best possible world composed by prolonging a singularity through the series of differential relations associated with it till it converges with the neighborhood of another singularity.  But this is not the same calculus as a calculus of matter, which takes the curve of the world as given, as completely specified and provided with coordinates, and seeks to determine the extremes of certain variables by setting the differential relations equal to zero.  The footnote to the passage above sheds more light on this question.

Insofar as the properties that make the selection possible are the properties of maximum or minimum, they confer on the obtained being an advantage of simplicity and, as it were, an appearance of finality, but this appearance disappears once we realize that what assures the passage to existence is not the fact that the properties in question are extremal properties, but that the selection they determine is implicated in the totality of the structure in question … The exceptional property that distinguishes it is no longer a property of extremum, but the property of being the limit of a convergent series. (F, 129)

So if the best world is a type of extreme, it is a moral extreme that opens the question of what should be optimized, instead of closing this question off by deciding in advance what the important variables are.  The world and the frame can't close the monad, without opening its continuity with other monads.  And, more importantly in this chapter, the world as a singularity of extremum doesn't close the monad without opening matter.  The world is the infinitely nested curve that allows us to pass from the side of the soul to the side of matter.  In fact, as we'll see, it's actually the matter of the world that allows us to pass from monad to monad in its composition.  The real subject of this chapter is this passage from one side of the curve to the other, "a to-and-fro [un va-et-vient]" (F, 150) or what Cache called an oscillation (and related to Simondon's scheme of crystalline individuation).

Before discussing this oscillation though, Deleuze spends some more time sharpening the distinction between the two sides by invoking Ruyer's opposition between "true forms" and "mere aggregates".  The soul knows itself directly and all-at-once, in a state of "self-survey" without distance, as if it were able to achieve a bird's eye view of itself as an absolute domain, one that does not require embedding in a higher dimensional space to be seen as a whole.  It has a trans-spatial and trans-temporal unity, a co-presence to all the parts of itself that Deleuze calls the "distributive" unity of an "every".  The monad is the world in a grain of sand, and every part or moment of the monad is a grain within it that includes the whole monad.  By contrast, matter operates step-by-step, within space and time, and can only be grasped as a whole by some sort of integrating force that stands apart from it or hidden within it.  Which is to say that matter is always an aggregation of separate units or "ones". 

What must be radically distinguished are the folds [replis] of matter, which always consist in hiding something from the relative surface that they affect, and the folds of the form, which on the contrary reveal to itself the detail of an absolute surface, co-present to all its affections. (F, 132)

The ultimate question, however, is how these two radically distinct sides can be related.  We saw part of the story last chapter.  Since the monad contains both clear and obscure regions, it must have a spiritual body constituted by the condensation of obscure perceptions into clear perceptions. In effect, this amounts to a restatement of the fact that soul contains an infinity of folds within it that come together to form one overall fold.  But then, because the structure of perception resembles something (= x), a fact guaranteed by Leibniz's pre-established harmony, we are surprised to discover that the structure internal to the monad must be matched by an external structure that fills it.  The spiritual body of step one therefore has a real counterpart.

The world is a virtuality that is actualized in monads or souls, but it is also a possibility that must be realized in matter or bodies. It is curious, one might object, that the question of reality is posed with respect to bodies which, even if they are not appearances, are simple phenomena. Yet what is a phenomenon, properly speaking, is what is perceived in the monad. When we ask, by virtue of the resemblance of the perceived to something = x, if bodies do not act on each other in such a way that our inner perceptions correspond to them, we are thereby asking the question of a realization of the phenomenon or, better, of a "realizing" of the perceived, that is, of the transformation of the actually perceived world into an objectively real world, an objective Nature. It is not the body that realizes, but it is in the body that something is realized, through which the body itself becomes real or substantial. (F, 133)

So far, so good.  The monad has a body.  And we even know that this body must be organic, in the sense that it is "infinitely machined" (F, 6) with parts that are themselves organisms.  This is the only way for a body to resemble the folds of a soul.  The trouble begins with the fact that this resemblance between the folds of the soul and the folds of matter seems so perfect that it threatens to undermine the radical qualitative distinction between the two sides.  The clear zone of the soul may be a condensation of certain folds, but the monad must nevertheless include the entire world.  It's all at once unity is distributive and trans-spatio-temporal.  So there's not really a sharp dividing line between the stuff inside the monad and the rest of the world; it's all down there somewhere.  But this is not how matter works.  It consists of limited and separated forms that are assembled piece by piece.  There seems to be some tension here between resemblance and belonging.

But what allows us to speak of "the body of a monad" or "its body," since the monad is always an Each, an Every, while the body, always a body, is a One? What grounds the appurtenance of a body to each monad, despite the real distinction and the difference of floors or regimes? It is necessary that a One, without ceasing to be a One, must belong to each Every. (F, 134)

How can a spiritual whole resemble just a material part?  Perhaps we can imagine a pre-established resemblance between the monad and all of matter taken as a whole (see my interpolation in the quote below).  And this seems to be exactly what we need to fill the infinite obscure folds of the soul with "a" body = x.  But this does not sound like a body that belongs to a monad in the sense we normally use this term.  In fact, it would seem that every monad should have the same body in this case; the only body would be the world as a whole.  What then would make this body mine?  This is a question that goes beyond pre-established harmony and asks about the union of body and soul, or the incarnation of a particular soul. 

In brief, the pre-established harmony is distinguished from Malebranche's occasionalism or Spinoza's parallelism not only in itself, but also by its consequences: far from replacing the problem of the union of soul and body, of the incarnation or the "immediate presence," it makes it all the more necessary, even if it is because it allows us to move from the first aspect to the second. In effect, harmony explains the correspondence between each [and every] soul and the [whole] material universe, but when it invokes the correspondence between the soul and its body, it cannot explain it through any relation in the body, because such a relation presupposes a prior belonging or "ownness" [appurtenance] (F, 134)

What follow from this question is a very complicated theory of belonging that centers on an interpretation of one of Leibniz's last and least clear concepts -- the vinculum or substantial link.  I'm not sure how useful the details are here, so I will try to go just deep enough to appreciate the main point -- the curve of the world doesn't allow us to pass from the side of the soul to that of matter without carrying us back and forth across this boundary an infinite number of times.  The more we zoom into the fractal curve, the more complexity we see, and the more rapidly we shuttle back and forth between increasingly tiny crenulations of body and soul.  But something strange happens at this infinite limit, some sort of twist or torsion results in the smallest variations exploding to the size of the whole universe.  We think we are plunging down, but somehow we end up rising all the way back to the surface of the world, just as if the center were nowhere and the periphery everywhere.  Thus this question of belonging, of possessing, which at first seems rather arcane, turns out to be central to the deepest understanding of the fold.  Belonging goes beyond the harmony of two separate floors and takes us to their inseparable union in a single house.

How can a body belong to me?  How can I have a body?  It becomes a strange question if you consider how it inverts the question "who am I?"  For something to belong to me, it can't be me.  Anything that I need to possess can't be essentially mine.  So, while we know I must have a body, I am not identical to that body, and this is why I must posses it.  In short, anything we can lose, we will.  Deleuze includes a brilliant quote from Gabriel Tarde that illustrates this.

"The true opposite of the self is not the non-self, it is the mine; the true opposite of 'to be,' that is, having, is not non-being, but the had." Already in the monad, Leibniz had instituted "I am having diverse thoughts" as the correlate of "I am thinking": perceptions as included predicates, that is, as internal properties, came to replace the attributes. (F, 138)

Much of our discussion has covered things that are intrinsic to the monad -- there's no way it can lose its inflections or point of view or perceptions, ie. any of the first three singularities.  We can say it "possesses" these, but only as internal predicates or definitions, not the way an inert substance possesses attributes.  But the body is external to the monad, and only fills its folds by resemblance (F, 135).  And yet, Deleuze says that the body, while distinct from the monad and outside it, cannot be separated from it.  How do the two stay fixed together if they occupy qualitatively distinct sides that never touch?

We can gain an intuition for how this happens by once again considering the diagram of our curve.  Because it contains the whole world yet is nevertheless finite, the monad must necessarily have both obscure and clear regions within it.  The extent of these domains may grow or shrink, and in fact this is what defines the continuum of monads from rational to "naked", but every monad must contain some of both.  In fact, while the perceptions of the clear region may be consciously denumerable, the obscure region, by its very nature contains a non-denumerable infinity of hidden microperceptions.  No matter how much of the world is unfolded or exposed to our own internal point of view, there will always remain even more of it folded up invisibly inside of us.  In a sense, this is just a restatement of the fact that the fold is an infinite fractal as seen from the concave, or soul, side of the curve.  However, because of a pre-established harmony, the matter which fills this souls must then also be infinitely folded.  In a sense, this is a restatement of the fact that the matter which fills the soul must be 'organic', it must have an infinite nested hierarchy of layers to match the folds of the soul.  Each organism must be filled with and infinity of smaller organism, ad infinitum.  The two sides fit perfectly on an infinity of levels.  Even though they never quite touch, they share the common limit of the world as curve of variation.  

Now, try to imagine pulling these nested fractals two apart.  As soon as the curve of the world becomes a nested fractal, the two sides no longer simply match overall but become stuck to one another like velcro or puzzle pieces.  You can no longer just slide them apart from one another and instead need an extra dimension to disentangle them.  When the fold goes to infinity, we go from harmony, to inseparable union.

How can my monad have an extrinsic possession, outside of itself, on the lower floor? One of Leibniz's essential theses consists in positing both the real distinction and inseparability: it is not because two things are really distinct that they are separable. This is where Harmony and Union discover the principle of their distribution: the pre-established harmony of the soul and the body governs [régit] their real distinction, while union determines their inseparability. (F, 136)

When you fold a nested structure like our curve, you naturally produce a hidden substructure that tends to lock the fold in place, an interesting fact you can investigate with this origami pattern.

From the side of the soul, this nesting corresponds to my unconscious perceptions.  From the side of the body, the nesting corresponds to all of the organic parts and sub-parts -- the organs -- that compose the whole body of my organism.  That is, the details of my organs correspond to the unconscious microperceptions within my organism.  To fulfill the requirements though, these organs must themselves be organic -- they must contain an infinity of sub-organs ad infinitum.  Since we haven't reserved the term monad for human souls alone, each of these organic animal bodies has a corresponding monad of its own.  So the obscure folds inside of me turn out to be the shadows of the other monads needed to compose the world I include and which belong to the hidden organs within my organic body.  I contain multitudes, that is, crowds of other monads, not directly, but through the intermediary of my body.

Leibniz often insists on this point: God does not give the soul a body without furnishing this body with organs. Now what is it that makes a body organic, specific or generic? No doubt, it is made up of infinities of actual material parts, in conformity with infinite division, in conformity with the nature of masses or collections. But these infinities, in turn, would not compose organs if they were not inseparable from crowds of minute monads—monads of heart, liver, knee, eyes, hands (according to their privileged zone that corresponds to one infinity or another): animal monads that themselves belong to the material parts of "my" body, and which should not be confused with the monad to which my body belongs. These are only the requisites of my organic body, specific or generic; and there is no need to ask if matter thinks or perceives, but only whether or not it is separable from these minute souls capable of perception. (F, 136)

This is the process by which a very specific body gets 'stuck' to my monad.  There's now a nesting defined from a particular point of view and not only as a whole, and it's this nesting that makes it impossible to pull what is now my body apart from my soul.  The distributive unity of the soul requires parts that are hidden from it, and which operate like foreign agents embedded within it.  The soul 'possess' matter the way a spirit possess a shaman, but this operation requires another soul to be effective.

Defining "belonging" in this way turns out to have some very weird effects.  My body belongs to me, but its organs actually belong to other monads and not to my monad.  There's an inversion or double directionality of belonging here which forces us to admit that a body belongs to a monad, but every sub-monad belongs to a body.  The tight origami fit of the hierarchy of fractal folding makes us travel back and forth across the curve -- from my soul to its body, but then from the sub-bodies that compose it to their monads, and again from these sub-monads to their bodies, etc ... The direction of belonging flips with each iteration.

We can see, then, that Leibniz's theory of appurtenance brings about a fundamental inversion that will constantly be revived: monads that have a body, to which a body belongs, must be distinguishedfrom monads that are the specific requisites of this body, or which belong to parts of this body. And these second monads, these monads of bodies, themselves have a body that belongs to them, a body specifically other than the body whose requisites they are, and whose parts in turn possess crowds of tertiary monads. And these tertiary monads ...The soul and the body are always really distinct, but inseparability traces a coming-and-going between the  two floors: my unique monad has a body; the parts of this body have crowds of monads; each of these monads has a body…. (F, 136)

Belonging takes us further than harmony.  Its shuttling back and forth across the curve creates an inseparable union of the two sides, almost as if the curve of the world had gained a sort of "thickness" (F, 150) that led to their interpenetration and indiscernibility.  While this resolves the question of how it can be my body, and how I can be immediately present within it without necessarily completely controlling it, it also seems to create major headaches for Leibniz's system.  Because aren't the monads supposed to be completely separate from one another?  Even though they all express the same world, they are not supposed to interact directly, since each already contains everything.  And yet here, somehow, my body is filled with other monads, which are bound to me by what Leibniz calls a vinculum. Am I the only one around here who gives a shit about the rules?

But since no monad contains other monads, domination would remain a vague notion, having only a nominal definition, if Leibniz had not succeeded in defining it precisely by means of a "vinculum substantiale." It is a strange bond, a hook, a yoke, a knot, a complex relation that comprises variable terms and one constant term.
   The constant term will be the dominant monad, since the vincular relation belongs to it or is "fixed" in it. Apparently, we can be all the more astonished that this relation, having as its variable terms other monads (henceforth dominated), cannot be a predicate contained in its subject. That is why the relation will be said to be "substantial," not being a predicate. Since every relation has a subject, the dominant monad is indeed the subject of the vinculum, but it is a subject of "adhesion," not of inherence or inhesion.  This is an almost intolerable paradox in Leibnizianism ... (F, 139)

I don't want to delve into the details of the vinculum beyond what I've already said about the way it carries us back and forth across the curve.  What I find more interesting here is the way this "intolerable paradox" relates to the concept of "torsion" we discussed earlier.  Somehow the closure of the monad is the same as its opening to the continuity of the best world.  What seals it off from all the other monads is paradoxically the same thing that connects it to them as well.  Topologically speaking this paradox can only be resolved through a "twist" like that of a Möbius strip or a Klein bottle, which, unfortunately, makes it impossible to draw the resulting curve in two dimensions.  

... the "unilaterality" of the monad implies, as its condition of closure, a torsion of the world, an infinite fold, which can be unfolded in conformity with the condition only by restoring the other side, not as exterior to the monad, but as the exterior or the outside of its own interiority: a wall [paroi], a supple and adherent membrane, coextensive with the whole inside. Such is the vinculum, the primary and unlocalizable link that lines [borde] the absolute interior. (F, 140)

This is the deepest aspect of the Fold -- it confuses inside and outside and makes it impossible to see exactly what two things are being folded together (F, 150).  I think it also leads us back to the event of the world, "the expressible of all expressions, the realizible of all realizations, the Eventum tantum" (F, 133).  This is the simultaneous closing of all the monads, the completion that requires they pass through the bodies that belong to them and the monads that belong to the bodies' bodies, and ... in an infinitely renewed cycle.  We reach the world by plunging into the infinite series of folds between matter and soul, to the point where we reach a peculiar asymmetric indiscernibility where the curve fills all of space.