The Virtual, the Actual, and the Intensive

[Background emissions in space (1992) as proof of the Big Bang; Image from the New York Times]

[Based on the lectures of John Protevi, who also has a blog. The majority of the quotes come from Mark Bonta and John Protevi’s Deleuze and Geophilosophy, supplemented by Manuel De Landa’s Intensive Science and Virtual Philosophy and James Williams’s guide to Gilles Deleuze’s Difference and Repetition.]

De Landa explains in Intensive Science and Virtual Philosophy that “Deleuze is not a realist about essences, or any other transcendent entity” (5). Nonetheless, he is a realist. “A non-realist can simply declare essences mental entities, or reduce them to social conventions” (6). Not Deleuze. Deleuze “does not get rid of essences until [he] replaces them with something else,” something else to “explain what gives objects their identity and what preserves this identity through time” (6, 5). This something else consists (using the terminology of Difference and Repetition) in the virtual, the actual, and the intensive.

Draw a diagram/schema. Above (or below; there’s no hierarchy), sketch a series of xs that shade off into one another. That’s the virtual (an egg, or an embryo). It has also been called structure, spatium, depth, the plane of consistency, the earth, the body without organs (laid out by the quasi-causal operator, or abstract machines, i.e. the xs). It is the realm of Ideas, transcendental (but not transcendent), universal (but not general), that lay out the many ways that a thing can exist (26). Or it is the realm of problems (like a question: How can I draw a schema of the virtual, the actual, and the intensive? Or: How can I play football? Well, there is no one way). More technically speaking, Bonta and Protevi describe it as “the modal status of the set of possible states of the system, along with the probabilities of attaining a particular subset of those states” (17).

The virtual is differentiated to begin with, with the things in there, the Ideas, the abstract machines, distinct from each other. Yet, they are perplicated, shading off into one another (like the xs you drew), with no fixed boundaries between them, no sharp distinctions. This is how “the structure of the virtual [. . . is] a meshed continuum of heterogeneous multiplicities defined by zones of indiscernability or ‘lines of flight’” (16). In other words, the Ideas are distinct but obscure. The xs are not different (actual) characteristics, but rather (virtual) conditions that are differentiated yet perplicated, like different regions (such as the region of games, within that the region of ball games, within that the region of football games . . .). Or think of the xs as patterns of change “contain[ing both] the patterns and thresholds of behavior of the material systems in their intensive and actual conditions” (16). While undetermined, the virtual is not indeterminate. Deleuze prefers to describe it as differentiated.

Ideas are n-dimensional multiplicities composed of differential elements (elements, members, or components that have no properties on their own but have meaning only when in a differential position in a network), differential relations (the rates of change of these elements that are linked to each other), and singularities (thresholds, special points in the relations, in which the multiplicity changes character, bifurcation happens, and choices are made; when such a bifurcation is triggered, an event happens). They “make up regions of intensity [. . .,] are in continuous variation [. . . and] have borders linking them to other Ideas” (26).

Differentiation (or the divine game or the unfolding of the plane of consistency) refers to the “internal structure of Ideas, or, better, the self-differentiating process by which Ideas spread throughout the virtual as the possible ways of being of different formations become more complex” (26). Described in another way, Williams refers to it as the process “when intensities bring about shifts within individuals beyond their actual identities as their sensations express the intensities that accompany a shift in the clarity and obscurity of Ideas” (164). Differentiation, in other words, simply points to the fact of the virtual being (already) differentiated. It—everything—is, to begin with, different in itself. It is, however, as Williams is quick to point out, “not chaotic with respect to that which has a propensity to be expressed in actual things. The virtual is not an undifferentiated mass of becomings but a changing mass of relations: [I]deas are structures of pure becomings” (14).

Below, way below (or above, way above; there’s no hierarchy, remember?), draw a number of squares (or rectangles, or circles, or whatever shape you want, or different shapes even, or not shapes at all, so long as you draw delimited entities) next to but separated from each other. That’s the actual (a chick, or an infant, a person, or a person at a particular moment in his/her life), the strata. You can also call them products, substances, organisms, or the different names that you presume to give to actual things in the world (e.g. football, soccer, rugby, etc.).

These are the material things (but not just physical things; could also be a manner of doing something, such as a way of playing football, e.g. what the rest of the world calls football) you recognize in your daily life, what Bonta and Protevi describe as substances in equilibrium, steady state, or stable systems, singular things with determined, recognizable properties (that thus makes you think of types, of essences, which you then project to the virtual, as the virtual (well, technically, as the form, the possible), which is imprecise), extensities we can separate from each other without the thing losing its character, without it changing its quality (hence it was important that you drew delimited entities, that you separated the squares from each other) (14). As such, they “lend themselves [by means of a striated space] to linear models that [. . .] strive to isolate a law-like relation of independent [i.e. cause] and dependent variables [i.e. effect]” (14).

These substances are the conditioned, conditioned by the structure (the virtual) and the process (the intensive) that they have gone through to become actual things, i.e. to have “extensive properties [. . .] and definite qualities” (14). Through what Williams calls a “reciprocal determination” of the virtual and the actual, “individuals are syntheses of virtual ideas and intensities,” i.e. “the virtual syntheses in [I]deas drive actual syntheses in habit, memory, or creation” (14).

Actual things already surround a particular attractor or trajectory (a region of state space), existing in that attractor’s basin of attraction, i.e. they already manifest a certain pattern of behavior (in contrast to the virtual that consists in the patterns of behavior and change themselves) (Bonta and Protevi 20). They are solutions to particular problems (a particular region of the virtual), but which do not exhaust the problem (There is no one way of solving a problem. Even if it is “already” solved, the problem persists. There are other ways of solving the problem. There are other ways of going about the same goal. The problem is never gone. There is always the virtual, which is differentiated, not essential.)

Actual things are differenciated from each other: they are different from each other, you can separate them; but then there is no more process, the process is over, we already have the products. Moreover, the process is driven by difference. Hence, the actualizations are divergent, i.e. “the same virtual multiplicity can provide the structure for intensive processes that yield [actual] products with vastly different extensive properties” (16). But we forget this. So we look into the properties, what’s similar about them, then we classify them, derive/project essences. But this is the nature of the process: to conceal itself (Do you think about the process when you’re looking at / using the product?), which is but the same thing that Marx referred to as commodity fetishism. We forget about difference. Difference is suicidal. Difference cancels itself, self-cancels. Difference is subordinated by the same.

Between the virtual and the actual (or the actual and the virtual; there’s no hierarchy, right?), draw lines (no, they do not have to be straight; perhaps better if not straight) that diverge from each other. Some of them start out as one line, but then in an instant (at that point of the dark precursor), all of a sudden they divide into two, three, four, or a hundred lines simultaneously, a thousand plateaus. That’s the intensive. Or the realm of intensity, constituted by far-from-equilibrium processes, characterized by intensive properties of the processes that cannot be divided without qualitative change (e.g. temperature, pressure, density), without the multiplicity changing in character (15). Hence the intensive cannot be sufficiently analyzed by linear models. It calls for the nonlinear models used in complexity theory, what Bonta and Protevi describe as “the study of the self-organizing capacities of ‘open’ systems (those through which matter and energy flow),” in order to account for “feedback loops that produce a multidirectional causality” (18, 16-7, 19).

The intensive has also been called spatio-temporal dynamism, the process of actualization, differenciation (as opposed to the differentiated and the differenciated; differenciation to point out that the process is driven by difference, that the actualizations are divergent), or, simply, production. As Bonta and Protevi explain, “actualization or differenciation is the construction of exclusive disjunctions, the selection of a series of singularities whose actualization precludes the simultaneous actualization of others, which would then have the modal status of the (virtual) ‘road not taken’” (27). Put in yet other words, Williams describes differenciation happening “when changes in the relations of intensities accompany a shift in the clarity and obscurity of Ideas as the intensities are expressed in actual individuals through their sensations” (164). The intensive, of course, as De Landa points out, is also where individuation takes place.

Equally important, it is in the intensive where consistencies, assemblages, rhizomes, or war machines emerge. That is, intensities “show the capacity for meshing into ‘consistencies,’ that is, networks of bodies that preserve the heterogeneity of [its] members even while enabling systematic emergent behavior” (15). Immensely (intensely!) different individuals can thus hook up with each other, form an assemblage, in such an intensity that each does not lose its uniqueness at the same time that each sufficiently connects with each other (not a half-hearted, but an “I love you” full of meaning, full of potential) thereby constituting a rhizomatic network that generates more than would have been produced had the components remained alone, isolated, by themselves.

The intensive is where the transcendental (or better: the virtual) becomes empirical (or better: the actual). This is where materials, potentials in the virtual, are processed to become something; puissance thus arises, measured in terms of intensity. The intensive is where intensity cancels itself, where a multiplicity becomes less intensive, more extensive, such that in differenciating (species into forms, parts into extensions), as the undetermined is progressively determined in this clear and confused process, when it is finally differenciated (when it reaches the actual) (i.e. when it is actualized divergently from other actual things), intensity cancels itself, i.e. intensity becomes hidden in the actual. Difference commits a suicide (and is now prone to being repressed by the same). However, as Bonta and Protevi point out, “this congealment is [but] a temporary fixing of an underlying flow that enables the emergence of functional structures; such structures are nonetheless always subject to the flight of particles from the grasp of the structure, even though the time scale of the structure is very long and the rate of flight is very low” (16). In other words, even in the actual, there are still (intensive) lines of flight.

The most striking feature of the intensive is that the “morphogenetic processes [therein] are characterized by linked rates of change such that any change in those internal relations past a threshold will trigger qualitative change in the assemblage” (15). The intensive, in other words, is constituted by the relations between the parts (of the egg or of the embryo) and their critical points (This is how it can be described! I.e. through the relations of the different parts/components, and their critical points or singularities). When critical points are reached, parts become singularly actualized, thereby becoming the (actual) parts of the body, and then the organism (the chick or the human being).

Now, the borders between the actual and (especially between) the virtual and the intensive are not definitively drawn. While Williams thus follows Deleuze in delineating his ontology as consisting merely of the actual and the virtual, De Landa, followed by Bonta and Protevi, are just as legitimate in (based on Deleuze) positing, to be more precise, the intensive.

If structures are the patterns of change and products are the results, the processes, the changes themselves, constitute genesis. In Bonta and Protevi’s summation, “The realm of the actual or the system of the strata is the realm of bodies produced by intensive morphogenetic processes (proceeding via the construction of assemblages) while the virtual (the plane of consistency) is the differential field of potential transformations that structures such intensive morphogenetic processes. In other words, the virtual is the ontological equivalent of the state space of a system, the set of patterns of processes and the thresholds at which it either adopts or changes those processes” (25).

Through all this, everything happens because of difference, i.e. because of the difference between at least two rates of change, i.e. through difference/s in intensity. Moreover, things are actualized divergently: different from other actual things (hence, rather than the virtual causing the actual, the actual manifests signs of the virtual) and different from the virtual patterns on which they are based. The whole ontology is thus based on difference. Difference first (later repressed, through representation, by the same, by identity)!

The signal-sign system, due to difference/s, flashes a sign, which then brings two series into communication. What flashes is the formation of a sphere that cancels out the difference/s, but it is a sign; thus we can work our way back and trace the phenomenon, the actual, to its intensive processes. Upon dealing with the actual, we can ask, What is it a sign of?

All sensations have intensity. Everything is related to intensity; hence it is always a relation to intensity = 0. There has to be intensity for there to be sensation. An intensive space, unlike a Cartesian striated metric space, is a smooth space; it looks at points not in relation to an outside grid, some external standard, but the points in relation to themselves. The elements, and how they relate to each other—i.e. the process—are intrinsically determined, and their actualizations are divergent. No form imposed on or copied by matter. Rather: a multiplicity.

The relationship, then, is between the virtual and the actual, not the possible and the real. The virtual is just as real as the actual. The actual—because it does not undergo a hylomorphic process wherein form is imposed on matter, or matter is made to conform to form—is different from the virtual (in fact, the process is driven by difference; remember the different linked rates of change?)—but again, both are equally real. Moreover, the virtual itself is composed of pure differences, of all sorts of becomings. What more (even more!), the relationship between the virtual and the actual involves complex perplications involving degrees of clarity and obscurity. As Williams says, “the whole of Ideas is only differentiated in terms of relations of clarity and obscurity and not existence and non-existence. Distant and very obscure Ideas have a real–rather than possible–role to play in the Ideas that are expressed with greatest clarity by an actual thing” (164).

The intensive thus witnesses the process not of realization (The virtual is just as real as the actual!), but of actualization. The virtual is actualized–through the intensive–due to difference. Difference thus rather than hylomorphism and identity. Rather than form and matter: virtual-intensive-actual.