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Dynamic systems theory: Deleuze and Guattari

Employing the neologisms of Capitalism and Schizophrenia, I will argue that identifiable unities and entities are no more and no less than dynamic systems themselves. This is another way of saying that existent objects are simultaneously stable and unstable, structured and unstructured, closed and open, complete and incomplete. Or again, as Deleuze and Guattari tend to call them, they are abstract machines, composed of unformed deterritorialized flows or the Body without Organs (BwO) that are drawn onto a surface or plane of consistency in which recognizable identities emerge. Determinate identities are inseparable from the lifeblood or intensive flow that creates and sustains them, but it is at the same time the very condition that contributes to their adaptation or collapse. In this sense dynamic systems are best thought of as strata at the “edge of chaos”, what Jeffrey Bell will describe as a fundamental both/and chaos-mos, simultaneously ordered and chaotic.

Difference or the BwO is presupposed as a requisite condition for dynamic systems to function at all. According to Deleuze and Guattari, every existent individuation or determination presupposes a dark precursor or an indeterminate substance as its necessary condition of possibility, an indeterminate reality of the virtual that can in turn be actualized through differing modes of itself. For this reason, concrete objects must maintain both stable strata as well as unstable deterritorializing flows in order to exist.

Although the creative chaos or BwO enables the plane of consistency to be actualized in a recognizable form, the success of the constitution of perceivable objects is not guaranteed, it can go one of three ways. The most obvious outcome is, of course, properly functioning dynamic systems. However, the abstract machine is also vulnerable to failure at actualizing such systems and “instead collapses into either the cancerous body of uncontrolled proliferation and chaos or the fascist body of smothering identity” (Bell, Philosophy at the Edge of Chaos, p. 5). That is, pure chaos or inert orderliness.

The essential point in the last resort is the connection between the two facets of the double bind, the process whereby the nomadic distributions come-into-being or become determinable and known. In effect, production can actualize dynamic or chaosmic systems by filtering and containing the purely unformed substance of the BwO, but it also runs the risk of producing destructive forces or lifeless objects when the two aspects of self-contained identities, chaos and order, are not properly balanced.

The double articulation through which the given is given, to be more precise, is much more nuanced as Deleuze presents it than expressed above. In the first articulation the body without organs becomes determinable as such. That is, the chaos is rendered into something that can be connected, linked and assembled. The second articulation, on the other hand, enables the given substance of the first articulation “to be actualized into identifiable, functioning states and systems” (Philosophy at the Edge of Chaos, p. 7). In other words, pre-given discrepant quasi-objects can then be unified and classified into meaningful systems or statements. In this precise sense the philosophy of Deleuze occasions a significant improvement on previous philosophies of difference which seem to lack an account of the production or genesis of difference in itself.

In the remainder of this section I will give scrupulous attention to the precise character of dynamic systems at the edge of chaos or, as Deleuze and Guattari call them, abstract machines. It will be argued that said identities are both self-contained and excessive, containing the intensive depth or fullness of difference that simultaneously preserves and transgresses itself. Ontology, for Guattari and Deleuze in particular, is an odd accord of nomadic singularities and, as such, the condition for the possibility of identifiable entities or systems to come into being. This is said to take place by an act of restraining and funneling the non-integrable forces or vectors of chaos into consistent and unified objects or partial-objects. Furthermore, given the univocity of being, we also know that the existent individuations of being are distributed points of difference itself, that is, mere nodes of intensive force that have been slowed down to a degree that is identifiable to recognition. All of this suggests that the filter of selection from which familiar unities emerge can never fully master the infinite speeds or non-integrable vectors of chaos. In short, we can never wholly totalize, identify or complete the integration of singular individuals. There always remains an excess of chaos that goes unfiltered, which implies the surmountable undermining of those very identities.

Given that being is restless and that actual determinations in the world are inseparable from this being, identifiable dynamic systems are equally anxious. As a result, identities are never assured of their permanence. Rather they are always already in jeopardy of becoming otherwise than they currently are. As already seen, stable strata are merely precarious equilibriums of cosmos and chaos.

Moreover, neither chaos nor cosmos are apprehended to the omission of the other. Given their reciprocal determination, both are necessary for the realization of either one. Indeed, dynamical systems operate best at this dangersome and delicate harmony: “A functioning system would collapse under either of the two possibilities – pure chaos would destroy just as readily as pure cosmos, for to function a system needs order and predictability (cosmos), but to be able to adapt to novel, unforeseen situations a system needs to experiment with untried, uncommon methods (chaos)” (Philosophy at the Edge of Chaos, p. 36). It suffices to show that the uncommon is immanent to the common or that chaos is in the cosmos. Therefore, no system is completely protected from transformation, variability or collapse. All identifiable meanings are subject to uncommon change and subversion.


Chaosmos: Does religious ritual have to preserve humanity from chaos and entropy?

Recently I came across a theological post that struck me with fascination but one that, I concluded, was ultimately erroneous (the original article can be found here). The argument purports that the practice of liturgy is necessary to preserve humanity from the onrush of chaos. More specifically, the author David Gelernter notes that the second law of thermodynamics “helps to write a commentary on religion”. He claims additionally, more boldly this time, given the Second Law, science must therefore sit “at the feet of religion”. Although this statement is obscurely unclear, he implies that religion must defy the “onrush of chaos”, the propensity of the universe to run down. Or again, the entropy of the universe naturally moves towards chaos, disorder, and “mixed-upness”. To be sanctified then, according to Gelernter, is to separate “the forward-tumbling chaos of ordinary time” from the rest of existence.

Although the argument is provocative, if not at least interesting, there is plenty of scientific evidence and theoretical speculation that is pointing in a divergent direction. The claim presented here, as follows, argues that order or cosmos presupposes chaos, what we can describe as chaosmology, to use a Joycean phrase. A brief theological interpretation is attempted here in response to the aforementioned post, but the present argument will go much further in elaborating the distinct contribution of systems theory and the idea that systems, structures or existent entities in general require some degree of unsystematic, unstructured or unrepresentable substance as their necessary condition of possibility. (For what I consider a more persuasive account of theological ‘becoming’ see Catherine Keller, Face of the Deep, or related posts here and here).

A central axiom of dynamic systems theory is the notion that order emerges from and even presupposes chaos. In fact, even once constituted, chaos continues to circulate within identifiable and ordered entities as a vital force to the continuation of those very identities. Indeed, it is the very lifeblood or life-force of existent individuals. To be desiccated of these ‘crowned anarchies’ or ‘nomadic distributions’, to employ the terminology of Deleuze, identifiable entities would in effect – metaphorically – bleed out and die, or as Deleuze puts it, collapse into the immobile fascist body.

To use an example of Deleuze’s, the becoming of sedimentary rock is a process that involves the transformation of heterogeneous sedimentary particles through a filtering process into consistent, homogeneous layers. In other words, the identifiable entity of sedimentary rock is recognized through a process of differentiation and differenciation in which the ‘unstructured’ flows of sediment are strained and condensed to form a critical density mass. Indeed, the formalized and structured entity of sedimentary rock presupposes as its own condition of possibility the fluid and chaotic-like substance of sedimentary particles.

This process can again be reversed, as Deleuze notes in the opening of Difference and Repetition: “The constants of one law are in turn variables of a more general law, just as the hardest rocks become soft and fluid matter on the geological scale of millions of years. So at each level, it is in relation to large, permanent natural objects that the subject of a law experiences its own powerlessness…” (p. 2). Although the case cannot be seen as readily in rocks as in living organisms, “a dynamic system involves stability, slowness, and stratified elements, while also requiring the flexibility to adapt, transform, and destabilize these very elements” (Philosophy at the Edge of Chaos, p. 221). Put simply, the synthesis and cementation of heterogeneous elements into a homogeneous, self-consistent strata can always in turn collapse back into its disparate parts.

The point is, for Deleuze and Guattari, as follows: the differentiation of unstructured, indeterminate ‘anarchic’ flows is the necessary facilitation for the possibility of various new stable and consistent forms to emerge in the cosmos. Of course, this process does not guarantee success, but no new states or determinate substances can emerge without this condition. Or to repeat Nietzsche’s claim, one must have chaos in one’s self to give birth to a dancing star.

This peculiar tendency of stable objects emerging from ostensible chaos is lucidly described in detail in Philosophy at the Edge of Chaos, a passage worth quoting at considerable length:

A guiding question of recent work in dynamic systems is how order – that is, the sophisticated, stable patters which are readily apparent – are able to emerge despite the second law of thermodynamics, which states that order tends to move to chaos, or that systems in disequilibrium tend to move to equilibrium.[…] To take a frequently cited example, oil, when heated, will suddenly exhibit convection rolls and vortices as it is heated and before it boils. Before the oil is heated, the oil is in an equilibrium state in which entropy is at a maximum; in other words, the oil molecules are randomly scattered throughout the container such that no order or consistency is present. One section of the container would be indistinguishable from another. We thus have chaos, or a random set of points with no identifiable order, what is called ‘equilibrium thermal chaos.’ When heated, however, the oil moves away from equilibrium, and it is under these conditions that the convection rolls and vortices appear. Once the oil is in a full boil, chaos reappears, or ‘non-equilibrium thermal chaos,’ and subsequently one section of the boiling oil is indistinguishable from any other. Dynamic systems and chaos theorists will pay particular attention to far-from-equilibrium conditions, and more precisely to the order which emerges at the critical threshold between equilibrium and non-equilibrium chaos.

The far-from-equilibrium conditions which give rise to spontaneous order most often occur during what is called phase transition. A phase transition is a transition between two steady and stable equilibrium states, such as liquid and gas, or liquid and solid. As these systems approach a phase transition, they enter a far-from-equilibrium state wherein self-organized patterns tend to emerge, and at a critical point (e.g., of temperature), there is a discontinuous jump to the new phase. Related to these phase transitions, and also occurring in far-from-equilibrium conditions, is the phenomenon of bifurcations. As Ilya Priogogine and Isabelle Stengers discuss bifurcations in their well-known book Order out of Chaos, a bifurcation point arises at a critical point where a system is poised to transition and when not just one stable state but, rather, ‘two new stable solutions emerge.’ For example, at the critical point where the stable solution of a convection roll appears in the heated oil the rolling motion may assume either a clockwise or counterclockwise direction – both solutions are possible. Which solution, or which branch of the bifurcation the system will ‘choose,’ is impossible to predict: ‘How will the system choose between left and right? There is an irreducible random element; the macroscopic equation cannot predict the path the system will take … We are faced with the chance events very similar to the fall of dice.’ As the oil is heated, further bifurcations appear, rolls within rolls, in what is called a process of ‘cascading bifurcations,’ which then leads to turbulent chaos. A bifurcation diagram of such a process between ‘equilibrium thermal chaos’ and ‘non-equilibrium thermal chaos’ is surprisingly ordered, or ‘order or coherence is sandwiched between thermal chaos and non-equilibrium turbulent chaos’ (Jeffrey Bell, Philosophy at the Edge of Chaos, pp. 200-201)