The Virtual and the Intensive in the Actual

Continuing on from my last post on individuation, I look here at the ontological system outlined by Deleuze in terms of the actual, the intensive, and the virtual. This is likely somewhat repetitive for people have been studying Deleuze for a while (Massthink has their own version up, which was helpful in organizing my own thoughts), but I figure others might find it useful. These past few posts have all been towards my larger thesis project, so any external comments are welcome. That also means that you’ll find references throughout this post to other sections of my paper, and lots of academically satisfying footnotes. Anyways, on to the good stuff!

UPDATE: Larval Subjects has a new post that resonates with a lot of the work I've been developing here. Whereas I've been timidly working around how to translate this ontology into concrete social terms, Sinthome jumps right into it, giving an excellent post on what it might entail.

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With the importance of individuation and the basic approach outlined, we are now in a position to examine in more detail the ontological system. As already mentioned, this model of reality can be abstractly analyzed into three realms: (1) the actual which consists of the stable, identifiable systems and individuals which tend to cover over (2) the intensive process of individuation that produced them, consisting of far-from-equilibrium processes that are ‘metastable’ and that embody (3) the virtual structure of potentialities that are immanent to a situation. It is important to remember that these three areas are, strictly speaking, not separate or based on a hierarchy. While we can break them apart for convenience, each is real and always in a concrete mixture with the others.

The actual is perhaps the simplest and most straightforward aspect of Deleuze’s ontological system. In his early, philosophical work, the actual consisted of the individuated phenomenon of a present experience (i.e. the basis of empiricism). In his later, more explicitly political work with Guattari and Parnet, the actual found new expressions as the stabilized systems of power and desire, whether of individuals, communities, classes or states. The link between these various examples of the actual is their reliance upon identity – the point at which ‘something’ coalesces into an individuated object or subject. This individuated product can usefully be explained in terms of complexity theory,[1] a recent scientific paradigm which many commentators have found to resonate with Deleuze’s work.[2] Put briefly, the constructed individual acts as a system[3] in a state of equilibrium or stasis.[4] More precisely, since an individual is never ontologically independent of its milieu, the individual acts as an ‘open system’ through which various material flows pass. Given this openness, the stabilization of the individual relies upon the existence of certain endogenously generated equilibrium points,[5] called ‘attractors’ or ‘singularities’. These attractors are the products of the interactions of the various trajectories which define a particular system. When the path of a system comes within a certain distance of an attractor (the ‘basin of attraction’), it inexorably converges towards it. Since it is open, however, the system never actually reaches the attractor; instead it asymptotically approaches it, subject to constant, generally minute, fluctuations resulting from various perturbations. The attractor itself is “real without being actual, ideal without being abstract”.[6] Having converged upon an attractor, however, the individual-system takes on a stability which lends it a sense of solidity, and permits theorists to draw out its ‘essential’ properties, without which the system would become something different. The constructed essence is then retroactively used to explain why the individual is the way it is; e.g. “it is a nation-state because it has the properties of x, y, and z”. In other words, the essence becomes a transcendent entity that is posited to explain the empirical world. As we saw with Aristotle, however, this form of thinking overlooks precisely the real, systemic processes which led the individual to converge upon a particular singularity in the first place. Similar to our earlier criticisms of focusing on the individuated product, focusing solely on the stable systems which permit a certain traditional mode of theorizing (susceptible to classification, linear causality where A affects B without B affecting A, etc.) neglects the ways in which the actual effaces its intensive genesis. It is to these key intensive processes that we turn now.

As noted earlier, the intensive level is an aspect of Deleuze’s ontology that has been relatively neglected. This is unfortunate, because the reduction of his ontology to the virtual and the actual means that there is no account of how the intensive ‘spatiotemporal dynamisms’ “immediately incarnate the differential relations, the singularities and the progressivities immanent in the [virtual] Idea."[7] In other words, without recognition of the intensive level, Deleuze is susceptible to the criticisms of people like Alain Badiou who wish to radically separate the actual and the virtual, and present the virtual as a modern day version of Platonic Ideas.[8] Against this tendency, we must insist upon the intensive level which “incarnates” the virtual and produces the actual, while also being itself reciprocally determined by the actual situation. In this regard, complexity theory is again a useful means to explain how these three moments can still be conceived as monistic. Whereas the actual consists of the stable, equilibrium states of systems, the intensive field is populated by systems far-from-equilibrium. These are systems which, unlike the actual, have been pushed outside the basin of an attractor. Instead, they are systems in becoming, subject to the constraints of the various elements and forces which constitute them. These multiple forces, pulling in different directions, compel the system to waver on the edge of a variety of attractors. This makes them extremely sensitive to their environment and to their initial conditions, as the slightest inclination can send them off in a particular direction.[9],[10],[11] Intensive systems are further characterized by a number of other properties that John Protevi and Mark Bonta outline:

“Processes exhibiting intensive properties are those that (1) cannot be changed beyond critical thresholds (the ‘line of flight’) in control parameters without a change of kind (a ‘becoming’), and that (2) show the capacity for meshing into ‘consistencies’, that is, networks of bodies that preserve the heterogeneity of the members even while enabling systematic emergent behaviour."[12]

It is these ‘preindividual’ processes which both produce stable, identifiable individuals, and which are retained alongside the constituted individual, thereby leaving it open for further “individualization”.[13] What is particularly unique about the intensive level is the fact that it is a realm of inclusive disjunction, where heterogeneity is retained and each virtual singularity really exists despite the fact that they cannot all be actualized at once. It is in the process of individuation, therefore, that the inclusive disjunction (and…and…) becomes transformed into an exclusive disjunction (or…or…).[14]

This idea of inclusive disjunction also reveals the in-between nature of the intensive. While embodying the multiple, incompatible potentials of virtual (through a superposition of their attractors), they are also drawn towards individuating themselves into actual systems; they are between the virtual and the actual.[15] In order for this to be possible though, they must embody a particular type of relation. This is significant because our emphasis on individuation means that the ontological status of relations must take on a new shape. They can no longer be thought of as between pre-constituted substances, since this would presuppose what has been put into question. Neither can we simply posit that relations take precedence over terms, since that would entail identifying relations and thus returning to a form of constituted individuals. Neither, however, can relations simply be internal to some larger unity, such as society or Being. It is here that the concept of multiplicity plays a central role. With multiplicity, the heterogeneous multiple itself becomes a substantive, rather than some form of overarching unity (the One), or some collection of basic units (the Multiple).[16] There is no external principle (such as economic determinism) which would determine the nature or progression of the multiplicity; there is only the immanent measure reciprocally determined by the intensive differences between its elements.[17] These intensive multiplicities are distinguished from virtual multiplicities by the nature of this intensive difference.[18] As DeLanda argues, “the key concept in the definition of the intensive is productive difference."[19] Intensive difference is productive because the tension at the heart of its difference is capable of spontaneously generating the movement of a system towards a nearby attractor. In other words, it is capable of producing order from chaos, without any mediation by an external authority (such as concepts, social movement leaders or the state). An intensive assemblage, therefore, is ‘metastable’ meaning that “’prior’ to individuality, being is affected by inconsistency, populated by divergent tensions, and pregnant with incompatible potentials."[20]

How then, do the various dimensions of an intensive system combine heterogeneous aspects to produce a functioning system? Since a multiplicity consists of neither atomistic individuals, nor a totality in which all relations would be internal, the solution is to insist upon the externality of relations.[21] This system relies, therefore, upon a distinction between the ‘properties’ of a term and its ‘capacities’.[22] Properties, simply enough, are the extensive and qualitative characteristics that we can attribute to a term at a present moment. They are intrinsic to and determined by the nature of the individual (an individual which is itself subject to an analysis of individuation). Thus, for example, a communication network has certain properties such as the number of input and output points, and the speed and strength of the connections. In a fully actualized system, it is only properties like these that are available for empirical study. Capacities, on the other hand, are not limited by the actualized system. Like singularities, they are real without necessarily being actual; that is to say, they are virtual. They are the potential ways that an individual can both affect and be affected by the external relations it enters into. An individual, in this case, is never completely defined by its properties, but also by its unexercised capacities. Using our earlier example, the communication network could enter into a novel assemblage with a group of disillusioned individuals, who then exert the capacity of the communications infrastructure to mobilize and organize a terrorist network. This capacity is not intrinsic to the communications since it relies upon an external, heterogeneous element. Since there is no a priori way to determine the possible ways in which a term can exert its capacities, it is always a matter of empirical study, and therefore always open-ended.[23] Intensive systems, as a result, are networks in which a number of different capacities for terms are simultaneously capable of being actualized. Individuated systems, by contrast, are those in which only a single set of capacities have been actualized into definite properties and relations. Again, the actual covers over the intensive potentials – both the tendencies towards attractors, and the capacity to enter into new relations.[24]

Finally, we reach what it is the most abstract portion of Deleuze’s ontology: the virtual. In part, the difficulty of understanding the virtual is that it eludes any empirical realization; it is the transcendental conditions of the empirical and, following upon our earlier arguments, it must therefore avoid placing an empirical instance as the transcendental principle. In other words, it must eschew any idea of founding itself upon an identity, whether it be an a priori principle, a universal law, or a self-identical being. Instead, the virtual is the realm of multiplicities. Our task, however, is made easier by the fact that we have already encountered a number of different aspects of the virtual (albeit in their embodied modalities) – namely, singularities and capacities. Both of these elements exist as unactualized potentials immanent to a particular situation. They exist, moreover, as a virtual structure: a multiplicity composed by (1) reciprocally determined differential relations[25] (each element is defined in relation to the others), and (2) the various attractors/singularities that emerge through the potential interactions of these relations, which mark off various stable points and thresholds beyond which a system bifurcates. This latter notion of bifurcation entails that virtual multiplicities are divergent in their incarnations; they can be actualized in an infinite number of ways. The image of the virtual we have developed here then is akin a diagram which would map out the immanent potentials hidden within a concrete social situation. The transition from this ontological potential to actual circumstances is carried out by the intensive processes, which embody a virtual differential relation and its variable elements and incarnate them in actual spatio-temporal relationships and variety of terms, respectively.[26]

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[1] It is significant to distinguish between two commonly confused theories: complexity and chaos theory. While both deal with dynamical, open systems (which make them especially suited to the social sciences), there are nevertheless some important distinctions. On the one hand, chaos theory remains basically positivist by attempting to explain the emergence of unpredictable behaviour from the interactions of a few basic mathematical equations (e.g. explaining how turbulence arises in currents of fluid). Complexity theory, on the other hand, seeks to explain how relatively simple structures (individuals) emerge from the enormous complexity of their parts (multiplicity). For further discussion on these differences, see: Protevi, John and Mark Bonta. Deleuze and Geophilosophy, 192n2, Mackenzie, Adrian. “The Problem of the Attractor.” and Kellert, Stephen. In the Wake of Chaos.

[2] The most important of these connections (but certainly not all of them) are to be found in Manuel DeLanda’s Intensive Science and Virtual Philosophy, Brian Massumi’s A User’s Guide to Capitalism and Schizophrenia, Miguel De Beistegui’s Truth & Genesis, and John Protevi and Mark Bonta’s Deleuze and Geophilosophy.

[3] The equating here of individuals with systems reinforces the notion that at the basis of ontology is not identity, but multiplicity.

[4] A common physical example of such a system is after the diffusion of a concentrated area of gas into another closed space. As the gas slowly diffuses, it eventually reaches a point at which it is evenly spread out over the entire space, thereby reaching equilibrium – a point of stasis or identity with itself. In a similar although much more complex way (to be analyzed in more detail later on), social systems also tend towards equilibrium points in which they take upon the normality of everyday life.

[5] While we will use the term ‘point’ for convenience, it is important to note that these attractors are not solely 0-dimensional points. There is a whole class of attractors which take on a variety of topological shapes, such as toruses or knots, and which reveal that equilibrium can also includes a number of periodic movements. Moreover, the use of the adjective ‘topological’ is not by accident since, as we will see, the singularities’ shapes can be deformed and altered radically through what are called ‘phase transitions’.

[6] Deleuze, Gilles. Difference & Repetition, 208. As we will see, this is also one of Deleuze’s favourite ways of characterizing the virtual.

[7] Ibid., 218. There is a parallel here, which Deleuze himself notes, between the spatiotemporal dynamisms and Kant’s schemata: each are taken to relate the transcendental conditions with the empirical actuality. The significant difference, however, is that Kant’s own theorization of the schemata leaves them external to what they purportedly unite. Deleuze’s intensive individuations, on the other hand, are immanent to the virtual multiplicities (they are structured by them), and they construct the actual by effacing itself in a sort of inversion (the intensive differences are inverted into everyday, extensive differences).

[8] Badiou makes explicit his avoidance of individuation in stating that for Deleuze “the nominal pair virtual/actual exhausts the deployment of univocal Being.” (Badiou, Alain. Deleuze: The Clamor of Being, 43)

[9] Moreover, this places fundamental limitations on prediction, since the degree of accuracy necessary for the initial conditions is far too sensitive to ever be accurately mapped.

[10] This is also the reason why the actual tends to efface its own individuation process, since the set of attractors which determined it as an intensive system and the precise individuating factors which sent it towards an attractor are nowhere to be found in the actual. All that is visible is the sole attractor which determines the present actualized system.

[11] In political science, this concept of sensitivity to initial conditions has been picked up by path-dependency theorists. Undoubtedly, an excellent and productive analysis could be made of the relations between path-dependency theory, complexity theory and assemblage theory. Unfortunately, such a project must wait until time permits! For an exceptional work on path-dependency, see: Pierson, Paul. Politics in Time.

[12] Protevi, John, and Mark Bonta. Deleuze and Geophilosophy, 15.

[13] ‘Individualization’ is here a technical term, referring to “the ways in which the developing [individual] functions as a resource for its own further development” (Oyama, Susan, et al. (eds.) Cycles of Contingency, 5.) We will see later that this means development progresses by ‘recursive evolution’ or in a similar way to how Markov chains progress.

[14] The key political point here, which we will return to later in our discussion of social movements, is that the apparently exclusive possibilities posed by the actual world are in fact merely a small subset of the infinite potentials encompassed within intensive fields.

[15] Ultimately, they are indistinguishable in concrete situations, and this is in part what the concept of ‘assemblages’ will attempt to demonstrate. Assemblages are precisely both the intensive systems which incarnate virtual structures, and their temporary coagulations into actual identities.

[16] Politically speaking, this classical opposition between the One and the Multiple occurs between those who see the state as founded upon individual rights and those who see the state as subsuming citizens into a unified whole.

[17] These ‘elements’ are in fact dimensions of variability. As a result of the system being in a state of becoming, there are no definite identities to be found since each ‘element’ is continually, reciprocally determined by the changing relations it is entering into. An element, while retaining what we will call properties, are also determined by the various capacities they exert, and are therefore dependent upon the entire relational context that they are embedded within.

[18] Virtual multiplicities and intensive multiplicities share the same resistance to identity and homogeneity, but differ in the types of elements which compose them. For a brief analysis of virtual multiplicities, see the next paragraph.

[19] DeLanda, Manuel. Intensive Science and Virtual Philosophy, 71.

[20] Toscano, Alberto. The Theatre of Production, 138.

[21] “’Peter is smaller than Paul’, ‘The glass is on the table’: relation is neither internal to one of the terms which would consequently be subject, nor to two together. Moreover, a relation may change without the terms changing. One may object that the glass is perhaps altered when it is moved off the table, but that is not true. The ideas of the glass and the table, which are the true terms of the relation, are not altered. … Empiricists are not theoreticians, they are experimenters: they never interpret, they have no principles.” (Deleuze, Gilles, and Claire Parnet. Dialogues II, 55, emphasis added.)

[22] In some of the literature on Deleuze, capacities are also referred to as ‘affects’ – both the capacity to affect and the capacity to be affected.

[23] “We know nothing about a body until we know what it can do, in other words, what its affects are, how they can or cannot enter into composition with other affects, with the affects of another body, either to destroy that body or to be destroyed by it, either to exchange actions and passions with it or to join with it in composing a more powerful body.” (Deleuze, Gilles, and Felix Guattari. A Thousand Plateaus, 257.)

[24] Deleuze will refer to this ability of the actual to cover over the intensive as the ‘transcendental illusion’. It is easy to see that positivism is the position most blinded by this illusion.

[25] Mathematically, differential relations are symbolized by dy/dx, where each term equals the infinitesimal, instantaneous rate of change in a variable. As Deleuze notes, either term on its own (dy or dx) is strictly speaking nothing, since as infinitesimals they are posited to equal 0. In other words, they are ‘undetermined’. It is only in their reciprocal relation that they become ‘determinable’ through a process of ‘reciprocal determination’. The interesting mathematical (and metaphysical) point here is that their relation dy/dx equals 0/0, without however equaling 0. What subsists at the virtual level is therefore the pure potentiality of the differential relation, devoid of any substantial term. For a more in depth analysis of Deleuze’s use of calculus, see: Duffy, Simon. The Logic of Expression.

[26] “A multiple ideal connection, a differential relation, must be actualized in diverse spatio-temporal relationships, at the same time as its elements are actually incarnated in a variety of terms and forms.” (Deleuze, Gilles. Difference & Repetition, 183.)