Also, it’s the Year of the Horse! That’s my year. It doesn’t mean anything to me but I’ll own anything if I’m told that it’s mine.

This is Part 3 of 4, on “The Actualization of the Virtual in Time”. (The final chapter will be “Virtuality and the Laws of Physics”).

In Part 1 (based on “The Mathematics of the Virtual”) I outlined DeLanda’s translation of Deleuze’s ontology, introducing the framework and the vocabulary.

In Part 2 (based on “The Actualization of the Virtual in Space”), I expanded on how virtual and actual things relate to each other, and how multiplicities relate to each other (ex. assemblages).


The Nature of Extensive Time

Classical Newtonian physics presents a static, picture-frame universe “a universe of being without becoming.”

The Deleuzian ontology I have described in these pages is, on the contrary, one characterizing a universe of becoming without being. Or more exactly, a universe where individual beings do exist but only as the outcome of becomings, that is, of irreversible processes of individuation

Extensive Time: “…time divided into instants of a given extension or duration, instants which may be counted using any device capable of performing regular sequences of oscillations.”

Between the fastest vibrations of subatomic particles and the extremely long lifecycles of stars and other cosmic bodies, Iberall imagines a nested set of oscillations pulsating at increasingly longer time scales providing time with its metric structure

Just as there are nested spatial structures between the scale of individual cells and complex organisms (ex. tissues, organs, organ systems) or between organisms and demes and species, there is also a spectrum of time scales: sleep-wake cycles, reproductive cycles, breathing.

DeLanda describes Deleuze’s view of a “living present”, comprised of the “immediate past and future”.

He refers to this metric or extensive time by the name of ‘Chronos’, and writes:

[Deleuze:] In accordance to Chronos, only the present exists in time. Past, present and future are not three dimensions of time; only the present fills time, whereas past and future are two dimensions relative to the present in time. In other words, whatever is future or past in relation to a certain present (a certain extension or duration) belongs to a more vast present which has a greater extension or duration. There is always a more vast present which absorbs the past and the future. Thus, the relativity of past and future with respect to the present entails a relativity of the presents themselves in relation to each other… Chronos is an encasement, a coiling up of relative presents

DeLanda does not mean to make this an argument about subjective time. We know from famous relativity experiments (ex. one twin on Earth and one in orbit above earth) that time can be empirically asymmetric for two entities.

DeLanda discusses the concept of relevant changeone that I found familiar from Greer’s Mystery Teachings from a Living Earth- just as the surface of a lake affords a walking medium to a small insect but not to a large mammal, “certain cycles are simply too slow for them to appear as  changing or moving relative to a faster level, and vice versa, certain oscillations are much too fast for them to even count as existing for oscillators operating at longer time scales.

Relaxation time: the amount of time that a trajectory, temporarily dislodged from a stable state by an outside force, is returned to its attractor (assuming that it is still in the basin of attraction)

Briefly, on the “object relatively of [capacities/affordances] with respect to temporal scale”:

Iberall argues that whether a particular body appears solid or liquid to a given observer will depend on the ratio between relaxation and observational time scales, in the sense that for sufficiently long observational times the glass will appear to the observer as a flowing liquid. The inclusion of the observer in this description may give the wrong impression that something psychological is being discussed, but this impression dissolves once we realize that ‘observation’ is simply one particular instance of ‘interaction’. In other words, what counts here is the ratio of relaxation time to interaction time, a ratio that can be defined without including a human observer in the picture. In particular, we can let the liquid and glass interact with each other and speak of how solid the glass ‘appears’ to the liquid, and vice versa. The glass, given its long relaxation time scale relative to the scale of interaction with the liquid, will behave as a solid, affording the liquid, for instance, an obstacle to its flow, or affording it a channel in which to flow. The flowing liquid, in turn, will afford erosion to the glass. In short, what capacities the glass has to affect and be affected by the liquid will depend on their relative time scales, the characteristic durations of their relaxation to equilibrium.

Any individual entity experiences “lived present” that takes into account what other entities can afford it due to its temporal scale (whether other entities can be interacted with as a solid of liquid, for example). In this sense, even non-living things have a “lived experience.”

“[…] material and energetic processes give time its metric and measurable form by their possession of a characteristic time scale, specified either through relaxation times, or as I will do in the rest of this section, through the intrinsic period of nonlinear oscillations.”


The Nature of Intensive Time

On to intensive time. It might help to recall some of the themes from my last post, on rates of change (which are relative to each other) and assemblages (couplings between separate processes).

“A process may change too slowly or too fast in relation to another process, the relationship between their temporal scales determining in part their respective capacities to affect one another. Even when two processes operate at similar scales, the result of their interaction may depend on their coupled rates of change.”

Example, lifted from elsewhere:

Heterochrony (from the Greek hetero meaning “other” and chronos meaning “time”) describes a change in the timing of ontogenetic events between two taxa. These can be the result of relatively small genetic changes that may not even be alterations in DNA sequence, but in the timing of particular genes being expressed during development.

Hetrochronous processes arise from “interplay between rate-dependent phenomena (like chemical reaction and diffusion effects) and rate-independent phenomena” such as enzymes, which control rates (enzymes are catalysts).

The fact that embryological development is all about rates of change which are coupled or uncoupled through the action of genes and gene products, suggests that the processes underlying embryological development may be viewed as a kind of ‘computer program’. But this metaphor should be used carefully because there are different kinds of computer programs presupposing different forms of time, some using sequential or serial time, others departing sharply from these linear forms of temporality.

Stuart Kauffman:

It is a major initial point to realize that, in whatever sense the genomic regulatory system constitutes something like a developmental program, it is almost certainly not like a serial-processing algorithm. In a genomic system, each gene responds to the various products of those genes whose products regulate its activity. All the different genes in the network may respond at the same time to the output of those genes which regulate them. In other words, the genes act in parallel. The network, in so far as it is like a computer program at all, is like a parallel-processing network. In such networks, it is necessary to consider the simultaneous activity of all the genes at each moment as well as the temporal progression of their activity patterns. Such progressions constitute the integrated behaviors of the parallel-processing genomic regulatory system.

If there were a sequential, linear order in the embryological process, then new structures could only be developed at the end of a sequence (“terminal addition”), but because various processes in embryonic development occur in parallel, “new designs may arise from disengaging bundles, or more precisely, from altering the duration of one process relative to another.” Again, this is heterochrony– the most well-known case is the process of neotony. Deleuze finds neotony interesting also because it demonstrates a case where the loss of features can generate novelty, not just the addition of features- Darwinian evolution isn’t a march forward to more and more complexity necessarily [or, I’ll step in, if it is, that is the result of more diversity and more interaction, not an inherent drive in a linear evolutionary process.] Relationships of evolutionary fitness are ever-changing.

[S]ymbiosis is defined as an assemblage of heterogeneous species which persists for long periods, relative to the generation times of the interacting organisms, and which typically leads to the emergence of novel metabolic capabilities in at least one of the partners. The emphasis on long duration is due to the need for coevolution between the partners, both of which need to have exerted selection pressures on each other biasing
the long-term accumulation of their genes and bodily traits.


Photosynthesis, the ability to ‘bite’ into solar radiation to produce chemical energy stored in sugars, and respiration, the ability to tap into a reservoir of oxygen as fuel to burn these sugars, are both thought to have emerged through cellular level symbioses with micro-organisms. At larger scales, examples include the autonomous communities of micro-organisms which line the guts of hervibores allowing them to digest cellulose, the bacteria that allow legumes to fix nitrogen, and the fungi which permit many plant roots to get access to phosphorous. In all these cases, novel capabilities to exploit otherwise unavailable resources have come about not through a slow and gradual accumulation of favourable mutations but through an accelerated process: meshing the capabilities of two or more heterogeneous populations of organisms followed by the subsequent coevolution of the partners

” When discussing intensive processes Deleuze usually divides the subject into singularities and affects, but sometimes he uses an alternative and equivalent formulation in terms of speeds and affects: speeds of becoming and capacities to become.


The Virtual Spacetime

[In the last chapter] I described the elements which, according to Deleuze, constitute the content of a nonmetric continuum: changing populations of virtual multiplicities (conceived as complex ideal events) and a quasi-causal operator which assembles this heterogeneous population into a plane of consistency. This particular breakdown of the contents of the virtual is, of course, speculative, and as such, it may very well turn out to be wrong. There is, as I said, an empiricism of the virtual, even if it does not (and should not) resemble the empirical study of the actual. But while the specific solution which Deleuze proposes may turn out to be inadequate, he should get credit for having adequately posed the problem. In order to get rid of essentialist and typological thinking it is not enough to denounce the transcendent and affirm the immanent. Replacing Plato’s transcendent essences with Aristotle’s immanent natural states, for example, gets us out of essentialism but not of typological thought. One must also give mechanisms of immanence (however speculative) to explain the existence, relative autonomy and genetic power of the virtual.

The Quasi-Causal Operator is a topic I didn’t do proper justice to last round. The quasi-cause merely affects multiplicities but doesn’t generate them. There are two immanence mechanisms of this operator:

  1. Pre-Actualization: Assembling multiplicities together by creating convergent/divergent relations amoung the ordinal series emanating from them. This would “endow multiplicities with a minimum of actuality” and trigger the first of a cascade of broken symmetries into actuality.
  2. Counter-Actualization: Extracting virtual events from intensive processes, unflattening multiplicities and allowing them to progressively unfold and differentiate without fully actualizing them.


In short, the first task of the quasi-causal operator is what Deleuze calls a condensation of singularities, a process involving the continuous creation of communications between the series emanating from every singularity, linking them together through non-physical resonances, while simultaneously ramifying or differentiating the series, ensuring they are linked together only by their differences. The mesh of one-dimensional continua that results would constitute the spatial aspect of the virtual. To this, a temporal dimension, which Deleuze calls ‘Aion’, should now be added.

Quoth Deleuze:

[The specification of the virtual] implies, on the one hand, a space of nomad distribution in which singularities are distributed (Topos); on the other hand, it implies a time of decomposition whereby this space is subdivided into sub-spaces. Each one of these sub-spaces is successively defined by the adjunction of new points ensuring the progressive and complete determination of the domain under consideration (Aion). There is always a space which condenses and precipitates singularities, just as there is always a time which progressively completes the event through fragments of future and past events.

Adjunction: borrowed by group theory pioneer Evaiste Galois. “the operation Galois defined as ‘adjunction of fields’ is an abstract operation very closely related to the idea of the progressive differentiation of a space through a cascade of symmetry-breaking transitions.”

In other words, the successive determination of sub-spaces to which Deleuze refers is simply the progressive unfolding of multiplicities through a series of symmetry-breaking events. The form of temporality involved in this unfolding, however, should be conceived in a very different way from that in which actual bifurcation events occur. The latter involve a temporal sequence of events and stable states, the sequence of phase transitions which yields the series of stable flow patterns conduction–convection–turbulence, for example. Moreover, as each bifurcation occurs, only one of the several alternatives available to the system is actualized. For example, in the transition to the convection regime, either clock or anti-clockwise rotating convection cells may emerge, but not both. Indeed, at every bifurcation there are alternatives that are physically unstable (unlike the two options for convection cells both of which are stable) which means that even if they are actualized they will not last very long and will be destroyed by any destabilizing fluctuation. In a virtual unfolding, on the other hand, the symmetry-breaking events not only fully coexist with one another (as opposed to follow each other), but in addition, each broken symmetry produces all the alternatives simultaneously, regardless of whether they are physically stable or not.

This virtual form of time, involving the idea of absolute simultaneity (or absolute coexistence) would seem to violate the laws of relativity. In relativistic physics two events cease to be simultaneous the moment they become separated in space, the dislocation in time becoming all the more evident the larger the separating distance. There are two reasons, however, why this should not be an objection to Deleuze’s conception of virtual time. The first and most obvious reason is that in virtual space there are no metric distances, only ordinal distances which join rather than separate events. Much as the notions of spatial ‘length’ or ‘area’ lose their meaning when we move away from Euclidean geometry to other ways of specifying the relations of proximity defining a space, so should the notions of ‘stretch’ or ‘lapse’ of time separating non-simultaneous events be meaningless in the context of a
nonmetric temporality. But there is a second and more important reason why relativistic constraints on absolute simultaneity, such as the constraint on the maximum speed at which causal signals may travel, should not apply to the virtual. The temporality of the virtual should not be compared to that of the processes governed by the laws of relativity, but to the temporality of the laws themselves. Unlike experimental laws (like Boyle’s law of ideal gases) which simply record laboratory regularities, fundamental laws (such as Newton’s or Einstein’s) are not mere mathematical re-descriptions of experience.57 Although physicists do not usually speculate about the ontological status of fundamental laws, to philosophers these laws are supposed to be eternal, and to be valid simultaneously throughout the universe. In other words, in philosophical discussions fundamental laws enjoy the same form of timelessness as immutable essences. And it is this form of time that the virtual is supposed to replace.

But how do we conceive of a nonmetric form of time? It’s obviously not the current present, and it can’t be a timeless dimension of beings without becoming (essentialist heaven). Instead, Deleuze suggests that the virtual must be populated “exclusively by pure becomings without being.”

“Unlike actual becomings which have at most an intensive form of temporality (bundles of sequential processes occurring in parallel) a pure becoming must be characterized by a parallelism without any trace of sequentiality, or even directionality. Deleuze finds inspiration for this conception of time in phase transitions, or more exactly, in the critical events defining unactualized transitions. When seen as a pure becoming, the critical point of temperature of 0C, for example, marks neither a melting nor a freezing of water, both of which are actual becomings (becoming liquid or solid) occurring as the critical threshold is crossed in a definite direction. A pure becoming, on the other hand, would involve both directions at once, a melting–freezing event which never actually occurs, but is ‘always forthcoming and already past.’”

Deleuze: “‘Time itself unfolds . . . instead of things unfolding within it… [Time] ceases to be cardinal and becomes ordinal, a pure order of time”

Actual time is made exclusively out of presents. “A pure becoming would imply a temporality that always sidesteps the present, since to exist in the present is to be […].

[Virtual] temporality must be conceived as an ordinal continuum unfolding into past and future, a time where nothing ever occurs but where everything is endlessly becoming in both unlimited directions at once, always ‘already happened’ (in the past direction) and always ‘about to happen’ (in the future direction). And unlike actual time which is asymmetric relative to the direction of relative pasts and futures, a pure becoming would imply a temporality which is perfectly symmetric in this respect, the direction of the arrow of time emerging as a broken symmetry only as the virtual is actualized.


Whether one views the latter in terms of relaxation times or in terms of the intrinsic period of nonlinear oscillations, the processes occurring in actual time always have a time scale of limited duration and yet are potentially infinite, in the sense that a particular sequence of cycles may go on pulsing for ever. Virtual time, on the other hand, would be nonmetric in the sense that it is unlimited in the past and future directions in which it unfolds, but always finite like the instant without thickness that performs the unfolding.64 The time of the virtual would be constituted entirely by what, from the point of view of metric time, cannot be but singularities: a maximum and a minimum, events of unlimited duration (the unfolding of multiplicities) and events of zero duration (the operation of the quasi-cause). The quasi-causal operator would have to:

“bring about the correspondence of the minimum time which can occur in the instant with the maximum time which can be thought in accordance with Aion. To limit the actualization of the event in a present without mixture, to make the instant all the more intense, taut, and instantaneous since it expresses an unlimited future and an unlimited past.”

Clearly, space has had the advantage of more than a century of mathematical work to grant it some more prevision than time has.

The quasi-causal operator must also “extract singularities from the present”, because we still need an explanation as to where multiplicities come from if they are not eternal essences.

In my post on the first chapter, I demonstrated how a multiplicity defines a space of its own, defined by N degrees of freedom and no more dimensions outside of that (there’s no N+1 space where everything is embedded). The quasi-cause, “unlike a transcendent source of unity which must operate from a supplementary [N+1] dimension”, actually operates at N-1 dimensions.

The operation of pre-actualization would give multiplicities not only a certain autonomy from the intensive processes acting as their real causes, it would also endow these impassive and sterile effects with whatever morphogenetic power they enjoy. In other words, preactualization would not only explain how an unactualized singularity belonging to a physical system with multiple attractors would subsist as a potential alternative state, it would also explain how the singularity that is actualized gets its power to attract in the first place. To the extent that linking multiplicities together and endowing them with productivity foreshadows the intensive processes which follow down the symmetry-breaking cascade, the quasi-causal operator is referred to as a ‘dark precursor’.75 The operation of counter-actualization, on the other hand, would operate in the opposite direction, up the cascade from the intensive towards the virtual. I said in Chapter 2 that some areas of the world, those defined by processes which are nonlinear and which operate far from equilibrium, do not conceal the virtual underneath extensities and qualities but rather reveal it, or allow it to express itself.76 These areas would represent a spontaneous movement towards the virtual which is still physical and corporeal but which may be given a boost making it reach the level of a pure virtuality. To the extent that counter-actualization accelerates an escape from actuality which is already present in some intensive processes, the quasi-causal operator is referred to as a ‘line of flight’.

“By the extension of singularities into series and the creation of convergent and divergent relations among those series the quasi-causal operator is the ‘dark precursor’, which gives multiplicities a certain autonomy from intensive processes and endows them, even as impassive and sterile effects, with morphogenetic power.”

Deleuze steps back again as the chapter closes, distancing himself from holding firm to Deleuzes answer so much as praising him for having so valiantly posing the question. The final chapter, “Virtuality and the Laws of Physics”, a view of the epistemological side of Deleuzian ontology.