The concept of the “virtual” is one of Gilles Deleuze’s most important concepts. It is perhaps best illustrated within the context of a discussion of non-linear dynamics. The “virtual” refers roughly to what in non-dynamical systems theory is referred to as a “phase space” and what in mathematics is known as a “manifold.” In the words of John Protevi, a phase space “is an imaginary space with as many dimensions as ‘interesting’ variables of a system; the choice of variables…depends on the interests of the modeller.” Likewise, themanifold as a phase space “represents the range of behaviour open to a system: ‘what a body can do'”.
But what does this mean, and how is virtuality distinct from potentiality? Levi Bryant suggests that Alfred North Whitehead, in his magnum opus “Process and Reality,” is anticipating the Deleuzian concept of the virtual. He distinguishes between “general” potentiality which merely refers to a bundle of possibilities vs. the “real” potentiality, which refers to that which “is conditioned by the data provided by the actual world.” Whitehead continues, “General potentiality is absolute, and real potentiality is relative to some actual entity, taken as a standpoint where the actual world is defined. It must be remembered that the phrase ‘actual world’ is like ‘yesterday’ and ‘tomorrow,’ in that it alters its meaning according to the standpoint. The actual world must always mean the community of all actual entities.”
Levi Bryant invites us to consider the example of an acorn. In the Aristotelian tradition, this is the classic example of potentiality. The acorn is an actual acorn but it is potentially an oak tree. The problem which this concept is that it refers merely to abstract potentiality. Instead of abstract, disembodied potentiality independent of concrete, spatiotemporal situations, that which is virtual refers to concrete, spatiotemporal coordinates of possibility. For example, an acorn cannot become an oak tree on the moon. Insofar as an acorn is on the moon, it is not a virtual oak tree. Instead, what we refer to as the “acorn” is a specific coordinate of converging forces, bodies and assemblages. The acorn may become an oak tree if it is the site of specific forces and bodily interactions (being in a suitable environment on earth). To speak of the virtual is to speak of a specific coordinate in a phase space insofar as it is capable of different actualizations depending upon what it affects or what affects it. Thus Protevi:
“The global condition of a system at any one point can be represented bya point in phase space with as many values as dimensions or ‘degrees of freedom’, to use complexity theory jargon. If you trac the system across time, you can see the point trace a trajectory through the manifold / phase space, a trajectory representing the behaviour of the system.”
The virtual is simply “what a body can do.” It refers to the sum total of the ways in which, or spatiotemporal points at which, a body or assemblage can affect other assemblages or be affected by them. Put simply, the virtual refers to real potential rather than abstract potential. To quote Whitehead again:
“Actual entities atomize the extensive continuum [the real potentials of the world]. This continuum is merely the potentiality for division; an actual entity effects this division. The objectification of the contemporary world merely expresses mutual perspectives which any such subdivision will bring into real effectiveness. These are the primary governing data for any actual entity; they express how all actual entities are in solidarity in one world. With the becoming of any actual entity what was previously potential in the space-time continuum is now the primary real phase in something actual. For each process of concrescence a regional standpoint in the world defining a limited potentiality for objectifications, has been adopted.”
The acorn does not possess the potential to become an oak tree on the moon. Nor does the acorn have the potential to become an oak tree in the Sahara desert. If these conditions are not met, then the acorn is not actualized and no processes of individuation take place. These latter conditions thus constitute real potentiality. This, incidentally, would be the problem with political theories such as we find in figures like Rawls. They only speak of general potentiality and therefore give no account of whether or not such egalitarian ideals have the potential to be realized in really existing situations. As such, they remain entirely abstract. We can ask the question of why such theories became thinkable at such and such a time and what potentialities of their own they produce, but there can be no honest question of these theories dealing with concrete situations. Such are the philosophies of the armchair. These potentials always have their somewhere and their somewhen. These potentials are, moreover, limited depending on the conditions governing the situation. As such, they function as the sufficient reason for the actualized occasion, or the reason for the actuality’s being.
Real potentiality would thus consist of the real potentials population a situation at a given point in time. It is for this reason that Whitehead is quick to emphasize that the term “actual world” is an indexical like yesterday or tomorrow. It is an indexical in the sense that its content perpetually changes. Similarly, relations among actual entities are perpetually changing, thus leading to transformations in the real potential of situations. With the actualization of virtual potentials, new potentials are produced that are, in turn, opportunities for further actualizations. All of this comes very close to what I’m trying to get at when speaking of “constellations“. A constellation refers to the real conditions encountered within a situation, and is committed to the thesis that thought must proceed from these conditions rather than from universalizing abstractions that ignore the actual world.
So also Deleuze:
“We opposed the virtual and the real: although it could not have been more precise before now, this terminology must be corrected. The virtual is opposed not to the real but to the actual. The virtual is fully real in so far as it is virtual. Exactly what Proust said of states of resonance must be said of the virtual: ‘Real without being actual, ideal without being abstract’; and symbolic without being fictional. Indeed, the virtual must be defined as strictly a part of the real object– as though the object had one part of itself in the virtual into which it plunged as though into an objective dimension… The reality of the virtual consists of the differential elements along with singular points which correspond to them. The reality of the virtual is structure. We must avoid giving the elements and relations which form a structure an actuality which they do not have, and withdrawing from them a reality which they have. We have seen that a double process of reciprocal determination and complete determination defined that reality: far from being undetermined, the virtual is completely determined. When it is claimed that works of art are immersed in a virtuality, what is being invoked is not some confused determination but the completely determined structure formed by its genetic differential elements, its ‘virtual’ or ’embryonic’ elements.”
The concept of a “line of flight” is a crucial component of Deleuze’s vocabulary. For Deleuze, a line of flight refers to a mutation that is actualized through the connection of bodies which had previously remained only implicit, or “virtual.” These connections enable new responses in these bodies that were previously unrealized. The line of flight is one of three kinds of lines, the other two being the molecular line and the molar line. The molar line constitutes a “binary, arborescent system of segments,” in the language of Tamsin Lorraine, whereas the molecular line is comparatively fluid.
The line of flight ruptures both. To be sure, the comparatively fluid molecular line deterritorializes continually. However, the series of repetitions in which it exists is quickly brought back into the capture which holds this series of repetitions captive. The line of flight, however, causes creative evolution in an assemblage and its surrounding bodies.
This concept fits crucially within Deleuze’s materialist philosophy. No ordinary materialism, Deleuze combines this metaphysics with his own distinctive vitalism and empiricism. It is highly informed, for example, by Gilbert Simondon’s rejection of the matter/form model. His aim is to challenge the hylomorphic model, according to which there is a distinct dichotomy btween matter and form.
Instead, Deleuze argues that matter exists in a state of constant variation. He emphasizes the flux-like nature of this matter when he refers to it as “mattermovement” or “matter-energy,” for example. In his work on Spinoza, he rejects the hierarchy of form and matter “by conceiving of an immanent ‘plane of consistency’ [body without organs, phase space, etc.] on which everything is laid out. The elements of this plane are distinguishable only in terms of movement and velocity. Deleuze and Guattari also talk of the plane being populated by infinite ‘bits’ of impalpable and anonymous matter that enter into varying connections,” as John Marks notes.
Deleuze wants to reject a mechanistic materialism. He rejects, for example, the atomistic idea that everything can be reduced to molecules or atoms. He enlists forms of art such as painting and cinema, appealing to them on the grounds that they can directly impact the brain and its neural pathways. Deleuze’s materialism is highly heterogeneous, and is an “expressive and intensive” materialism”, in the words of John Marks, rather than a reductive or an extensive materialism.