Cellular Automata and Dynamic Emergence in Humphreys "Synchronic and Diachronic Emergence"

by Corry Shores
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Paul Humphreys

"Synchronic and Diachronic Emergence"

Mind and Machines Dec. 2008

Abstract

Humphreys will contrast diachronic and synchronic emergence. He then discusses the historical aspect of Bedau's weak emergence. He argues that weak emergence is about token states and not types. Humphreys concludes by evaluating the weakness of weak emergence and discussing the lack of a unifying account for diachronic and synchronic emergence.

Introduction

Diachronic emergence differs from synchronic.

Diachronic emphasizes a novel phenomena's emergence across duration.

Synchronic stresses the lower level properties' and objects' coexistence with novel higher level ones.

Humphreys will argue:

1) Maybe someday we will be able to conceptualize a general sense of emergence that encompasses both diachronic and synchronic emergences. However, right now the two types of emergence are conceptually distinct. So for example, we know that the idea of synchronic emergence does not comply with diachronic; for, we cannot even say that synchronic emergences actually produce an emergence, because a historical development is always needed to produce the conditions for a synchronic emergence. So we might have two identical states, with only one being emergent, because its diachronic development provided for it.

2) There is a sort of emergence that we may characterize as "weak." Bedau offers this definition,

Weak emergence is the view that a system’s macro properties can be explained by its micro properties but only in an especially complicated way. (2008)

Humphreys says that the weak emergence account can explain a lot about diachronically emergent computational forms. But it can explain more if we were to add some of his suggestions.

3) To explain 'pattern emergence,' we need a satisfactory account of conceptual emergence. Humphrey's will only here discuss the philosophical implications.

Pattern Emergence

Pattern emergence

involves the appearance in a system of novel structure that results from the temporal evolution of the system. Pattern emergence is a common phenomenon in computational models such as agent based simulations and cellular automata, and it is widely agreed within the complexity theory literature that these patterns count as examples of emergent phenomena.

Humphrey's will use examples of pattern emergence in his argument. They are cellular automata with a spatial structure. He uses models rather than real world phenomena, because models are simpler to handle. These examples will also help us deal with the sociological notion of methodological individualism. Emergences from patters begin from the bottom up. So we are not concerned with a centralized 'top down' set of laws or rules that govern individuals' behavior.

Cellular Automata

Humphrey's illustrates weak emergence with a cellular automaton (CA). His example is two dimensional, so I will begin with an simpler one dimensional version. Cellular automata are little living abstract machines. They appear as patterns of squares that change according to a finite set of rules. Their space is a grid. In our one-dimensional version, it is a row of squares.

We apply transformation rules to the squares in that row, and place the changes in a new row below it.

So let's begin with this row, with just one darkened square in it.

We see that the black square has two neighbors: a white square on either side.

The other white squares have white neighbors.

We will go through each square, and depending on the contents of the neighborhood, we will transform the center block in the following row according to these rules. [Click to enlarge]

So we begin with the first neighborhood, and we see that we transform the white center block into another white block.

Now we have this for the next row so far:

And we do the same for the next neighborhood.

Now our second row is:

The next neighborhood has a black box on the one end, so we transform the center block to a dark one.

Now we have

Same for the original darkened box for the first row:

Which gives us

We continue this process for the rest of the row, and we obtain the full second row.

Now we repeat the procedure, this time only attending to the contents of the second row. We then obtain for the third row:

And then for the fourth row:

And next

Now notice the white "T" shape in the lower right side in the image below. This will appear as a triangle, and many more such triangles of various sizes will show as we continue the process.

Also, we presume from the beginning that the grid extends infinitely, so our picture above may continue expanding outward. The patterns that emerge from this automata are pseudo-random. Nonetheless, the character of its randomness emerges as the iterations proliferate. [Credits for the following images are given below. Click to enlarge. Thank you sources. Image 1]

[2]

[3]

[4], [This needs to be clicked to see what is going on, it's large.]

Humphrey has us consider a more complex two dimensional example. We are to imagine that

Over a wide range of initial states of the CA, appropriate updating rules can produce randomly distributed arrays of colored cells, stable patterns that persist across time, and dynamic patterns that evolve over time.

We are to suppose that the given transformation instructions will eventually produce the following form [5]:

To arrive at this form, we presumably had to carry-out the transformation operations many many times. What is important is that we cannot deduce that this form will come about merely by knowing the initial conditions. We always need to know the formation's preceding step, and its preceding step, and so on until we arrive back at the starting situation. Astronomers, however, can predict the next solar eclipses without needing to know the sun's positions in between eclipses. Such predictions are computationally "compressible," where cellular automata are "incompressible."

I shall examine weak emergence in detail in a moment, but the essence of the idea is that a state of a system is weakly emergent just in case that state can be produced only through a step-by-step simulation of the system. In other words, the process that leads up to the state is computationally incompressible. In yet other words, unlike the prediction of future solar eclipses for which the computational difficulty of prediction is almost independent of how far into the future the eclipse will take place, predictions of future states of computationally incompressible systems must run through each of the intermediate time steps between the initial state and the predicted state. Letting the computational model work out its own development is thus the only effective way to discover how the system’s states evolve. The philosophical motivation for accepting this criterion as capturing a certain kind of emergence draws on the philosophical tradition that emphasizes the essential unpredictability of emergent phenomena. (emphasis mine)

Properties of Pattern Emergence

For there to be emergence, something must emerge from something else. The bow-tie pattern above emerged from the pattern of its rule-based re-iterations. If instead we made a stamp with that image, and stamped it on paper, we would not say that the formation emerged on the paper.

It is another token of the same pattern, but that token is not emergent because it is generated instantaneously.

This example tells us three things:

1) Pattern emergence is largely a "historical" phenomenon: "whether an instance of a pattern is emergent or not depends essentially upon the process that generated it." Thus we cannot look at the synchronic elements of some formation and determine whether or not it is emergent.

2) It cannot be synchronic, because that means we can look at a formation and determine the emergence. It also means that two of the same formations would bring about the same emergence. But we see that both the stamp and the automata have the same formation, but the stamp did not result from a pattern emergence.

3) If we looked at the two identical bow-tie patterns, one from automata, the other from an ink-stamp, and if we say there is the same formation, we are dealing with a type of formation. But we saw that in the one instance there was pattern emergence, but in the other instance there was not. Hence, "pattern emergence is about tokens or instances of patterns, not about types."

Weak Emergence

So we see with the automata that there are lower level circumstances and higher level properties. We call the lower level circumstances micro-facts and the higher level we call the macro-level. On the micro-level of cellular automata, there are only squares. So the property of being "bow-tie shaped" can only occur on the macro-level. We call such a property that can only appear on the higher level a nominally emergent property. We obtained it only by running the simulation that re-iterated the transformation rules. And we may characterize the individual square on the micro-level only in terms of its location and such intrinsic traits as it being black or white. The macro-level entity then is the aggregate of all the micro-constitutent states taken together along with their spatial relations. Because the whole of the macro-level structure can be reduced to the conglomeration of the micro-level states and locations, we call such a system a "locally reducible system."

Humphreys then defines weak emergence as (citing Bedau):

Assume that P is a nominally emergent property possessed by some locally reducible system S. Then P is weakly emergent if and only if P is derivable from all of S’s micro facts but only by simulation.’

We need to run the simulation, because the pattern must be computationally incompressible. Hence the bow-tie structure exemplifies weak emergence.

For the most part, this definition captures the sorts of emergences found in dynamical systems theory and in complexity theory. However, to fully apply, we need to supplement it in two ways.

1) We need to distinguish end states that are non-random from those which have "predicates picking out genuine macro-level properties."

1a) If the pattern begins random and ends random, that does not qualify as a novel emergence. For, even though each random pattern on its own is unique, all random patterns are of the type "random." So nothing is new when random transitions to random.

1b) If the pattern begins structured and ends ordered, then here also there would not be an emergence. For, we consider emergences to result from self-organization. But a turn to chaos is a self-disorganization. One thing that makes emergences so interesting is that they defy the Second Law of Thermodynamics (entropy). So we will not consider a random outcome from an ordered beginning to be emergent. It must have structure to be emergent. But there is a continuum between order and chaos, structure and random, so there is no clear way to make this distinction.

2) Maintaining the automata in a perpetually random state is not difficult to achieve. So we should not devalue the concept of weak emergence by including such cases.

Hence Humphreys offers this revised definition for weak emergence:

P is a non-random property of the system S that is distinct from any property possessed by the initial state of S.

Micro-stable and Micro-dynamic Patterns

Humphreys says that synchronic features are neither sufficient nor necessary conditions for pattern emergence.

Broadly speaking, there are two types of pattern emergences.

1) Micro-stable patterns.

Micro-stable patterns emerge when the computational process no longer develops because it has reached a stable non-random pattern which the transformation principles no longer alter. Our bow-tie pattern is such a case where there was a terminal form that maintained its exact shape.

2) Micro-dynamic patterns.

Micro-dynamic patterns emerge when a non-random pattern emerges, and that pattern itself cycles invariantly, on account of the transformation substitutions falling into a consistent pattern. To view a micro-dynamic pattern, scroll to the bottom of this page, and run the simulator.

We may distinguish three sub-types of micro-dynamic patterns.

2a) Recirculating autonomy

The micro-dynamic pattern exhibits recirculating autonomy if its same consistent parts cycle around in a constant pattern. We see this for example when we heat a fluid between two hot plates. Inter-locking columns of circulating fluid cycle in their cellular regions. These are calledBénard convection cells. [6]

[7]

[8]

[9]

Animation can be found here.

Another example of recirculating autonomy is Couette flow. This comes-about when we place a fluid between two concentric rotating cylinders that are moving at different speeds. "Vortex rolls form when the velocity gradient exceeds a critical value."

[10]

[11], [12]

[13]

In recirculating stability, a structure emerges that consists of a fixed collection of entities, and this structure remains constant while the micro-level entities undergo dynamic cycling across duration.

2) Transient autonomy

In transient autonomy, the macro-structure emerges and persists. But unlike recirculating autonomy where the micro-entities remained the same while changing location, in transient autonomy the micro-constituents are continually substituted by the same type of entity. We may see this in river flows, for example, where the ripples repeat, but always with new water molecules. [14]

3) Equivalent class autonomy

Equivalent class autonomy occurs when the macro-level pattern is sustained by the cycling of lower level entities that are of the same general type. for example, if our river ripples came to be replaced by wine, beer, broth, etc.

Hence there are two roles for micro-process dynamics in pattern formation and perpetuation.

A) Bringing about the initial formation of the structured pattern. This role is important when considering pure diachronic emergence.

B) The persistence of the pattern while the micro-dynamics continue. This role draws upon both diachronic and synchronic emergence, because the stability of the cycling dynamics suggests a trans-temporal 'synchronic' form that manifests dynamically.

For these cycling patterns, again, see the animation at the bottom of this page. Humphreys offers an example where we begin with a random distribution of values [15]

and after 500 iterations, a spiral pattern emerges [16]

Humphreys then wonders if we can characterize this formation as "spiral" as though there were something about it to make it different from any other spatial pattern of cells.

Pattern Emergence and Supervenience

Consider if the bow-tie were a different color. Would it be the same pattern? It's not clear what our criteria will be for distinguishing patterns.

If I am correct about the role that this kind of pattern persistence plays in diachronic emergence, then whether the criteria for pattern identity turn out to be objective, subjective, pragmatic, or based on some other ground, that feature will automatically carry over to computational diachronic emergence itself.

Humphreys, Paul. "Synchronic and Diachronic Emergence." Minds and Machines. Vol.18, Number 4, December, 2008, pp.431-442.

More information and online text available at:

http://www.springerlink.com/content/d442431150343t17/?p=f1cef51a00d346b582d2c3ad1386c814π=1

Image credits:

[1], [3]

http://mathworld.wolfram.com/Rule30.html

[2]

http://www.jeffcook.com/skimboard/index.html

(The Author writes: Wolfram's "A New Kind of Science." ... The first 50 iterations of Rule 30 are shown on page 25 of Wolfram's book.)

[4]

http://commons.wikimedia.org/wiki/File:Rule_30_2000Generations.gif

[5], [15], [16]

Humphreys, Paul. "Synchronic and Diachronic Emergence." Minds and Machines. Vol.18, Number 4, December, 2008, pp.431-442.

http://www.springerlink.com/content/d442431150343t17/fulltext.html

[6]

http://hnsttl.blogspot.com/2008/10/downward-causation-in-fluids.html

[7]

http://web.phys.tue.nl/nl/de_faculteit/capaciteitsgroepen/transportfysica/fluid_dynamics_lab/turbulence_vortex_dynamics/rotating_rayleigh_benard_convection/

Schematic drawing of a Rayleigh-B\'enard cell. The red-shaded areas of the cell show regions of hot fluid, while the blue areas indicate cold fluid. Adapted from L. Kadanoff, Physics Today 54, 34 (2001).

[8]

http://www.etl.noaa.gov/about/eo/science/convection/RBCells.html

[9]

http://www.catea.gatech.edu/grade/mecheng/mod8/mod8.html

[10]

http://serve.me.nus.edu.sg/limtt/TCF_0.8.JPG

[11], [12]

http://www.mech.northwestern.edu/fac/lueptow/TC_Rich_new.html

[13]

http://www.vacet.org/gallery/images_video/flux_400.png

[14]

http://riverweaver.net/

The Abstract Machine of Love's Diagrammatic Functioning in Mille Plateaux / Thousand Plateaus §170

by Corry Shores
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Gilles Deleuze & Félix Guattari

Capitalism et schizophrénie 2: Mille plateaux

A Thousand Plateaus

Ch. 5

587 av. J.-C.-70 ap. - Sur quelques régimes de signes

587 B.C. — A.D 70: On Several Regimes of Signs

Paragraph 170

[The one beginning with the following line.]

Les principales strates qui ligotent l'homme, ce sont l'organisme, mais aussi la signifiance et l'interprétation, la subjectivation et l'assujettissement. (167bc)

The principal strata binding human beings are the organism, signifiance and interpretation, and subjectification and subjection. (148bc)

Organization orders. It binds. If we belong to such an organization as a football team, we will be given a certain role. Everyone takes a different position and function. But because the team works organically, each member is limited to the scope of her functionality. One player is only supposed to perform certain functions, and the other team members perform the rest. This holds as well for our own bodies. When our whole body works organically, the mouth does its job, the arms and legs do their jobs. But what if the mouth were free to dance, to contribute to the dancing of the body? Such a body would no longer work organically. The mouth would not be the mouth-organ. It will be a dance organ for the moment it dances, but after it will incorporate again into the whole body whose zones and regions are not functionally divided like a football team. [See the end of the third video where Iggy Pop's mouth becomes a dance organ.] If we consider ourselves some certain functional organ in the larger social body, we will not be free to become into a self that is not yet known to us.

A symbol is fixed to what it refers to. The crucifix we affix to Christ. In fact, whole systems of symbols, like a language, fix a body of referents, their relations, and the values attached to them. In a Christian system of symbols, "daily bread" might not merely refer to what sustains us each day. It also carries with it the highest value, the flesh of God. But such a meaning would not hold for other religions. So each system imposes a certain order. Hence signification is another thing that constrains us.

Also such systems as Christianity will characterize what humans are. We are embodied souls. We carry the original sin. We are subjected-to these views that tell us who and what we are, in a very general sense. They make us certain sorts of subjects. So subjection and subjectification also limit our freedom to become something we would never expect.

The ways we come to give meaning and value to things and symbols is based on our manner of interpretation. We might for example see the body as the cause of our misbehaviors, and our souls as the guardians responsible for controlling our impulses. Or perhaps we instead interpret our base actions as being the victory of the unconscious id over our superegos. Even some of the simplest most mundane interpretations carry with them values and beliefs that bind us. So even to see the table as a material object is already to posit a materiality that is fundamental to reality. This might imply that we too as individuals are somehow bound-up with materiality, which could influence how we see ourselves. Hence even the way we interpret such things as tables also can hinder us from becoming new things.

Deleuze & Guattari call such factors "les principales strates qui ligotent l'homme": "the principal strata binding human beings."

Now consider differences. See the cup not as a cup. Regard it as being a category all its own. It might be next to another cup. But do not consider them as both cups. Each one is an individual, a thing all its own. Appreciate its difference. It is not "one of these things." It is "this thing." It is a haecceity. Notice its internal variations. The continuous curve of its rim. The shading of light and color that is nowhere uniform. It is internally heterogeneous. It is made up of differences. Each variation is just a degree of difference from its neighboring variation. As one variation moves to the next, it is tending toward that change, even before it gets there, but it is also tending towards many other ways it can be expressed. Its curves are being push-and-pulled so many ways, even just at one point. But these tendencies of variation do not extend. They are there at points. The are tendencies tending inward. They are intensities.

Previously we spoke of the "strata" that organize, homogenize, and constrain individuals. But this heterogeneous dimension is sort of a layer in a way too. The differences consist together. Along the bend of the cup's curve are infinitely many points of variation. But they all fall along the same line. Each is individual and different. But they all consist together. We call such a continuum of consisting individuals the plane of consistency. [We will later see that more variation and heterogeneity than is found in a cup is needed for the plane of consistency. But the consisting parts in the more radical case still hold together as consistently as the variations of the cup.]

We will also later speak of the pure creative functions of matter. Such functions do not have concrete form. So we will call them abstract. And they are production engines. So we call them machines. They are abstract machines. The Turing Machine is considered an abstract machine in the strict sense of its terms. But its functions are formalized through its programming. So it is not an abstract machine in the Deleuzean & Guattarian sense. The abstract machine is a computer without programs, a machine without mechanisms. The hazard of the dice, in the hands of Cage, is such an abstract machine, that produces a "Cage" composition. This composition itself influences the minds of its listeners in a way that creates and actualizes certain tendencies they did not know they had. Their own productions will be shaped by listening to a "Cage." Hence the "Cage" itself is an abstract machine. And John Cage's body is made-up of matter. It's functioning created new abstract machines in new ways. So Cage himself was an abstract machine.

The binding strata hold us away from individualizing and changing. They block us from participating in the heterogeneous dimension of the plane of consistency. The strata also give us form and instructions on how to function. So they as well prevent us from becoming abstract machines.

We say that the symbolic systems impose forms and values that are coded into the signs we use to identify ourselves and other things. It's a "regime of signs." However, if we could operate out of junction with the regime, we could be free from the constraints it places on our abilities to change and become new things. So in the heterogeneous dimension of abstract machinery, there is no such symbolic order constraining the way we operate.

A system such a Christianity has staked its claim. It has drawn boundaries around our bodies, and cordoned them off from our spiritual forces. These boundaries have given us defined bodily and spiritual forms. In this way, human bodies have become territorialized by the sign system. The sign for "body" marks a region. Now the system has made our bodies a part of its territory.

Now suppose we suffer a head injury. We loose much of our brain. Family and friends notice marked changes in our behavior and personality. We no longer act and decide the way we used-to. But our soul is still intact, right? But it's not us any more. People can change "spiritually" or psychologically just with the loss of their limbs. So in fact it is not so easy to keep the territorial boundaries fixed. It is said that our bodies replenish their cells, and by a certain point in our lives, we have none of the cells we were born with. Our nerve and brain cells might be the same, but the materials that make them up have been replenished, so even they are materially different then the ones you were born with. So we lose everything that made-up our bodies without losing our spiritual or psychological selves.

What makes the body/soul distinction possible are two factors. Within us are arrangements of parts, which we would not need at first to consider either bodily or spiritual. Who we are is largely the dynamics of interrelated functions. The brain influences the rest of the body in certain unique ways for each person. These behaviors are more the psychological side to us. But it takes a secondary act to make a distinction between physical and non-physical. Really all we have are the dynamics of functioning materials. Pure functioning of matter. Nothing says the body must stay a body. In fact, they fall apart, and become worms, trees, soil. Our mouths at some times eat. Other times breath. Sometimes yell for help. Or contort to frighten others. Sometimes they speak poems. Or cry. When our hands are busy, our mouths might hold an envelope until our hands become free. They might kiss. In an act of surprise, they might whiten and stretch back with our cheeks, taking on their pallor. In that case the difference between mouth and cheek disappears.

What makes us creatures who can be assigned distinct parts that work together is the fact that there are regions of variation that assemble together. Lips and tongue might assemble to speak or kiss. But lips and cheek might assemble to gasp. So these are assemblages and reassemblages of operational groupings. On the one hand, the way we distinguish them is based on the regime of signs used to signify the parts, such as mind, brain, body, soul, heart, spirit, and so forth. But on the other hand, these assemblages reassemble in disjunction to the forms that the regimes impose on them. Their parts have the capacity to be grouped. But that same capacity allows them to group in other ways, in defiance of the symbolic order placed on them.

Ce sont toutes ces strates ensemble qui nous séparent du plan de consistance et de la machine abstraite, là où il n'y a plus de régime de signes, mais où la ligne de fuite effectue sa propre positivité potentielle, et la déterritorialisation sa puissance absolue. (167bc)

These strata together are what separates us from the plane of consistency and the abstract machine, where there is no longer any regime of signs, where the line of flight effectuates its own potential positivity and deterritorialization its absolute power. (148bc)

Deleuze & Guattari see the challenge to be finding ways to move the dynamics of the assembly from one constrained by the symbolic systems, to the dynamics of unpredictable reconfigurations and the new emergences they bring about. Such a reconfiguration in terms of our body would mean that it would take on new arrangements (based on the dynamics and functional relations of its operation and not the physical structure. So a new arrangement would not mean growing a leg on your head, but perhaps rather becoming a dancer, and having your mind and legs operate together in ways you never thought were possible). Because the normal organic relations would reassemble, we call such a indeterminate un-organic state being a "body without organs."

Or le problème à cet égard est bien de faire basculer l'agencement le plus favorable: le faire passer, de sa face tournée vers les strates, à l'autre face tournée vers le plan de consistance ou le corps sans organes. (167c)

The problem, from this standpoint, is to tip the most favorable assemblage from its side facing the strata to its side facing the plane of consistency or the body without organs. (148bc)

When we are told we have a soul that must control our bodies, then our desires are properly directed toward moral behavior rather than sensuous pleasure. Or perhaps we are instead under the impression that we need to negotiate with our ids to allow our drives to find proper expression. No matter the subjectivity we are subjected to having, our desires are defined and expressed according to systems and values that determine their source, nature, and proper outlets.

Because our desires are not free to express themselves in unfettered and unpredictable ways, they build-up in the confinement of their bounded territories. Consider a person with incredible spiritual fervor. She thinks she has a soul distinct from her body. And she believes one day her soul will unite with God. That desire to be one with God builds and builds, because it must be kept a spiritual desire. She cannot express it as lust for God. That is far out of the territory's bounds. The word "soul" does not signify something that can have lust. So her confined desire builds rather than expresses itself in new unpredictable creative ways in other dimensions of expression.

Deleuze & Guattari say two things can happen from such a subjectified and confined desire. For, it will build up to such an excessive state that something will have to stop it from becoming dangerous. One possibility is that it self-destructs. Her spiritual desire for God becomes so strong and dissatisfied that it gives up. She resigns to the mundanity of life. The immediate world which was already undervalued, now becomes a source of her resentment. She cannot let her spiritual desire run too rampant, because this filthy world stands between her and God. The other possibility is that the desire changes planes.

La subjectivation porte le désire à un tel point d'excès et de décollement qu'il doit ou bien s'abolir dans un trou noir, ou bien changer de plan. (167c)

Subjectification carries desire to such a point of excess and unloosening that it must either annihilate itself in a black hole or change planes.

Consider for example the story of the ecstasy of St. Teresa of Avila. [Click on images for enlargement. Image credits are at the end. Thank you, sources. Image 1.]

An angel appears to her. He was

most beautiful — his face burning, as if he were one of the highest angels, who seem to be all of fire. I saw in his hand a long spear of gold, and at the iron's point there seemed to be a little fire. He appeared to me to be thrusting it at times into my heart, and to pierce my very entrails; when he drew it out, he seemed to draw them out also, and to leave me all on fire with a great love of God. The pain was so great, that it made me moan; and yet so surpassing was the sweetness of this excessive pain, that I could not wish to be rid of it. The soul is satisfied now with nothing less than God. The pain is not bodily, but spiritual; though the body has its share in it, even a large one. It is a caressing of love so sweet which now takes place between the soul and God, that I pray God of His goodness to make him experience it who may think that I am lying. (The Life of St. Teresa of Jesus.)

Bernini renders the event in stone like this. [2], [3], [4], [5]

One possible interpretation is that her spiritual desire became so profound that it spilled-over into her body. Another interpretation could be that her erotic bodily desires were confined and could not express themselves in their proper physiological zones. Hence these bodily lusts spilled-over into the spiritual plane. [Of course probably neither is the case, but the example just serves illustration here.]

When desire leaps to a different level, there can be something spasmodic about the motion. Imagine we are shaking dice in our hands. At this part of the ritual, we are calling together fate and chance. When we cast, it is at some arbitrary point in the shaking. Yet, our release seems not to be deliberate. Rather it is as though something out of our control opens our hands. It is a sort of spasm. The forces of chance and fate struggle in the cups of our hands. The intensity of their strife becomes so great that it spills out of its indeterminate state, and lands on the ground in determinate form, all in one dramatic spasm. Painter Francis Bacon, an avid gambler, would cast paint onto his partially painted canvass. This was like rolling the dice. It scrambled the painting. The smears pushed and pulled the painting's development in different directions. Bacon read the distorting splatters as though they were a "diagram" indicating the different divergent dimensions he could develop the imagery. But also, his throwing the paint was not an aimed and deliberate throw. He really intended to inject chaos into the work. His own inner intensities built-up and spasmed-out at an arbitrary point, just like when casting the dice.

Now consider self consciousness. We reflect on ourselves. Our consciousness doubles in a way. We stand before the mirror. What do we see? What we see, and what is seeing, are locked into each other. We cannot change past ourselves if we are self-conscious. We become a broken record whose melody cannot escape its little segment of repetition. But desire cannot be confined like this. Love cannot involve subjectification. If we are fixed to ourselves, we cannot love.

This is Henry Miller's lesson that Deleuze & Guattari cite. Miller first explains that the one who is enslaved by the other lover in a sense can have more power, for these reasons:

1) The slave creates a fragile dependence relationship. The master always fears that the enslaved lover will decrease her dependence just enough to steal the master's power away.

The man who must conquer the woman, subjugate her, bend her to his will, form her according to his desires — is he not the slave of his slave? How easy it is, in this relationship, for the woman to upset the balance of power! The mere threat of self-dependence, on the woman's part, and the gallant despot is seized with vertigo. (289b)

2) By openly confessing our weaknesses, we are already very close to overcoming them. So when a lover overtly professes his weakness to a woman in the fullest way, he enslaves her.

The man who admits to himself that he is a coward has made a step towards conquering his fear; but the man who frankly admits it to every one, who asks that you recognize it in him and make allowance for it in dealing with him, is on the way to becoming a hero. Such a man is often surprised, when the crucial test comes, to find that he knows no fear. Having lost the fear of regarding himself as a coward he is one no longer: only the demonstration is needed to prove the metamorphosis. It is the same in love. The man who admits not only to himself but to his fellowmen, and even to the woman he adores, that he can be twisted around a woman's finger, that he is helpless where the other sex is concerned, usually discovers that he is the more powerful of the two. Nothing breaks a woman down more quickly than complete surrender. A woman is prepared to resist, to be laid siege to: she has been trained to behave that way. When she meets no resistance she falls headlong into the trap. (289b-d)

3) But there is something more important than power. By surrendering our selfhood, we are no longer confined within the bounded territories we draw around ourselves and that semiotic systems draw around us. Who we are is not the person in the mirror. Our true selves are like Bacon's portraits. Dice throws push-and-pull our selfhoods in many directions at once. These are the intensities of the proto-forming, larval self. But when we submit fully to our lover, we affirm chance. We throw the paint at our own proto-formed image. When we are self-conscious, we double our consciousness. And if we are egotistical towards a lover, we make our passion just another false reflection of ourselves that we present to our lovers. This does neither them nor ourselves any good. Better is when both lovers take this opportunity to diagram themselves, and actualize their implicit tendencies for modulating into new modes of selfhood.

Déstratifier, s'ouvrir sur une nouvelle fonction, diagrammatique. Que la conscience cesse d'être son propre double, et la passion le double de l'un pour l'autre. (167cd)

Destratify, open up to a new function, a diagrammatic function. Let consciousness cease to be its own double, and passion the double of one person for another. (148c)

Miller writes:

To be able to give oneself wholly and completely is the greatest luxury that life affords. Real love only begins at this point of dissolution. The personal life is altogether based on dependence, mutual dependence. Society is the aggregate of persons all interdependent. There is another richer life beyond the pale of society, beyond the personal, but there is no knowing it, no attainment possible, without first traversing the heights and depths of the personal jungle. To become the great lover, the magnetiser and catalyzer, the blinding focus and inspiration of the world, one has to first experience the profound wisdom of being an utter fool. The man whose greatness of heart leads him to folly and ruin is to a woman irresistible. To the woman who loves, that is to say. As to those who ask merely to be loved, who seek only their own reflection in the mirror, no love however great, will ever satisfy them. In a world so hungry for love it is no wonder that men and women are blinded by the glamour and glitter of their own reflected egos. No wonder that the revolver shot is the last summons. No wonder that the grinding wheels of the subway express, though they cut the body to pieces, fail to precipitate the elixir of love. In the egocentric prism the helpless victim is walled in by the very light which he refracts. The ego dies in its own glass cage. (290a-c)

Consciousness should not be a matter of freezing ourselves before the mirror. Every moment we should cast the dice, splatter paint on our faces, read the new chance-induced possibilities for change as though they were a 'diagram.' When deeply in love, we will do anything for our beloved. Never a poet? But so, when in love. We take extraordinary risks to express our love artistically, finding talents we never knew existed in us. In the mirror, we do not see the face of the poet. Cast dice! Splatter the beard of the bard on your chin. It takes only the slightest deformations of those frozen 'particles' of our self-image to send us off in unforeseen new directions of personal development. Out of our many parts or particles, our changing 'larval' selfhoods emerge. If we say, 'A poet cannot emerge from me, because none of my parts suggest such a modality,' then we have fixed a certain significance to our particles, which fixes their relation to each other. Hence nothing new can emerge from us. But when we cast the dice to disorganize the organization of our parts, then new arrangements of the particles (new molecules) can come about. Out of that, new modulations, such as being a poet, could emerge. We don't know. That's why we must cast the dice. Deleuze & Guattari write:

Faire de la conscience une expérimentation de vie, et de la passion un champ d'intensités continues, une émission de signes-particles. Faire le corps sans organes de la conscience et de l'amour. Se servir de l'amour et de la conscience pour abolir la subjectivation : « pour deviner le grand amant, le magnétiseur et le catalyseur, il faut d'abord vivre la sagesse de n'être que le dernier des idiots ». (167d)

Make consciousness an experimentation in life, and passion a field of continuous intensities, an emission of particles-signs. Make the body without organs of consciousness and love. Use love and consciousness to abolish subjectification: "To become the great lover, the magnetizer and catalyzer . . . one has to first experience the profound wisdom of being an utter fool." (148d)

We might think we have some sort of selfhood that stays the same despite our various experiences. We have a sort of self that says 'I think,' and that transcends all our modulations. Let it be wild! Don't let that sense of continuity freeze you. Instead, let that continuity be that at every moment you say, "all is wild. I roll the dice. I am not 'this person.' I am a metamorphosizing animal, a wild beast of prey on the open savanna." And according to Miller, when the man becomes slave to the woman by escaping his ego, he gives her power, but in return he is empowered to actualize his intensities. His 'becoming-woman' in the master/slave relationship frees him from the territorial bounds of his self-image.

Se servir du Je pense pour un devenir-animal, et de l'amour pour un devenir-femme de l'homme. Désubjectiver la conscience et la passion. (167-168)

Use the I think for a becoming-animal, and love for a becoming-woman of man. Desubjectify consciousness and passion. (148d)

If we keep our eyes in the mirror, our selfhoods become a broken record, stuck in the same groove, repeating the same notes, never permitting the melody to break free to move into new regions of development.

We noted before Bacon's diagramming function. He begins painting forms. Before they are finished, he spatters and smears paint over the formations. Then, he reads these distortions as thought they were a graph or diagram, telling him the dimensions that he can take the painting. He actualizes a multiplicity of those virtual dimensions, which creates a distorted image. But it is an intense image, because the figure is pushed-and-pulled into many directions of development at once. This pushes-and-pulls the viewer's faculties in many directions at once too. It disrupts the normal organic function of our body [see this entry for more on Bacon's technique]. We are no longer able to express ourselves using preformed significations. We rather express ourselves in a sort of 'schizophrenic' speech [see this entry for more on this sort of speech].

Deleuze has us consider now when language takes on a diagrammatic function. If Bacon diagrams by splattering paint, what does the writer do in order to diagram? He stutters. The intensity of the meanings pile-up on each other, causing the words to collide with each other. The speeds of articulation and expression of meaning change unpredictably. This creates tendencies for development. It makes the language intense. These new tendencies can then be actualized by the receiver of the expression, who takes the unactualized virtual tendencies of meaning-development into their own new directions. Deleuze gives the example of Gherasim Luca’s “Passionnément" in Le chant de la carpe. Certainly if you can, listen to it here. In particular, Deleuze & Guattari quote this passage:

« ne do ne domi ne passi ne dominez pas

ne dominez pas vos passions passives ne

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ne do dévorants ne do ne dominez pas

vos rats vos rations vos rats rations ne ne... »

do domi not passi do not dominate

do not dominate your passive passions not

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

do devouring not not dominate

your rats your rations your rats rations not not . . .

In these stuttering repetitions, speeds unpredictably rise and fall as tendencies build and release. This is not the redundancy of the broken record. It is a diagrammatic redundancy, because it gives language a chance at every variation to go its own way. Each repetition is another cast of dice, another opportunity for the listener to take the meaning in a new direction. When there is a repetition, there is another underground shoot that is sent out, which can grow unto its own. If the repetition were just a broken record, it would not be like a growth shoot, it would just be like branches of a tree tangled together, unable to produce any new growth for the plant [see the end of this entry for a description of the rhizomatic structure]. And when we make language stutter, we are using our native tongue, but doing so in a way that makes it a new language all its own [see this entry and this entry for more on stuttering].

N'y a-t-il pas des redondances diagrammatiques qui ne se confondent ni avec les signifiantes, ni avec les subjectives? Des redondances qui ne seraient plus des noeuds d'arborescence, mais des reprises et des élancements dans un rhizome? Etre bègue du langage, étranger dans sa propre langue. (168a)

Are their not diagrammatic redundancies distinct from both signifying redundancies and subjective redundancies? Redundancies that would no longer be knots of arborescence but resumptions and upsurges in rhizome? Stammer language, be a foreigner in one's own tongue. (148d)

[The paragraph continues to say the following.

C'est comme s'il fallait distinguer trois types de déterritorialisation : les unes, relatives, propres aux strates, et qui culminent avec la signifiance ; les autres, absolues, mais encore négatives et stratiques, qui apparaissent dans la subjectivation (Ratio et Passio) ; enfin l'éventualité d'une déterritorialisation positive absolue sur le plan de consistance ou le corps sans organes. (168b)

It seems necessary to distinguish between three types of deterritorialization: the first type is relative, proper to the strata, and culimates in signifiance; the second is absolute, but still negative and stratic, and appears in subjectification (Ratio et Passio); finally, there is the possibility of a postive absolute deterritorialization on the plane of consistency or the body without organs. (149a)

Later, when I understand it, I will provide a better explanation. For now I will suggest this:

1) We said that the variations on the cup consisted together. Each point is different from the rest. However, all together, they make-up the "cup," which is something that can serve as a signified. But there is nonetheless continual variation, so this is the first kind of deterritorialization.

2) We might also consider a Pollock painting. [6]

Deleuze says that in such action paintings, the catastrophe fills the whole canvass. With the cup, each particle made sense because of its coherent relation to all the other particles. But here in this Pollock painting we see that there is no articulatable coherence between the points. If the painting were of a cup, we could say that the painter expressed something through the painting's content. But in Pollock, we cannot distinguish content from expression. That is because his technique is analog. What lands on the canvass, its content, is the imprint of his bodily expressions, his throwing the paint. But if there were a painted cup, we could say this part of the content is not that part, the cup is not the table. However, in Pollock's painting, we cannot make such discriminations. Nothing fits within a bounded territory like the cup's form. In fact, Deleuze writes that edges of the canvass are not limits of the painting, because the paint splatters off the canvass. And the whole painting is one field of catastrophe, so it is still a strata. Also, consider that part of what makes us the subjects we are is our unique passions. But such passions are of this second deterritorializing sort. So this form of deterritorializing is also found in subjectivation.

3) In the third type, like when we give ourselves up in love, this allows our tendencies for change to be free. There is not so much variation that we fall apart. Rather, there are changes in our speed of changing. This is the primary source of variation. Such speed changes create tendencies. When these tendencies are actualized, we leap to another level. So for example Teresa's spiritual love sped-up to a level where she was not expecting such an increase, and it spasmed out of her soul and leaped into another dimension, her physical body. Her love for God came to be expressed in bodily ecstasy. Thereby, she became an icon, a Saint, a statue and painting. There were tendencies for her to become in new directions. For them to be actualized, the tendencies needed to escape from the bounds of her selfhood's territory, and cross into a new domain. But doing so makes our organic parts take-on new functions or to malfunction. Hence this third sort of deterritorialization creates the body without organs. (see also Thousand Plateaus 101c-d / Mille Plateaux 116a for more on the first two distinctions.)]

Deleuze, Gilles & Félix Guattari. Capitalisme et Schizophrénie 2: Mille Plateaux. Paris: Les Éditions de Minuit, 1980.

Deleuze, Gilles & Félix Guattari. A Thousand Plateaus: Capitalism and Schizophrenia. Transl. Brian Massumi. London: Continuum, 1987.

St. Teresa of Avila. The Life of St. Teresa of Jesus.

Available online at:

http://www.ccel.org/ccel/teresa/life.html

Images obtained with deep gratitude from:

[1]

http://en.wikipedia.org/wiki/File:Teresa_of_Ávila.jpg

[2]

http://www.invokemagic.com/wp-content/uploads/2008/09/teresa_avila_bernini-216x299.jpg

[3]

http://pro.corbis.com/images/LX008625.jpg?size=67&uid={22DE431F-EC42-4173-80EB-A8122D61BB4B}

[4]

http://tesla.liketelevision.com/liketelevision/images/lowrez/bernini_st_teresa_face.jpg

[5]

http://www.all-art.org/history252-7.html

[6]

http://blog.cleveland.com/pdextra/2007/10/large_pollock8.jpg


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