Deleuze as Networkologist: ‘The Logic of Sense’ and the Networkology of Events
by Christopher Vitale (crossposted at Networkologies)
I understand why it is that Difference and Repetition is Deleuze’s masterwork, but of the two works he produced in ’67, give me The Logic of Sense anyday. Then again, perhaps I’m biased, because its this book which, even to some extent more explicitly than in his book on Leibniz, namely, The Fold, in which he puts his cards on the table. And those cards are plain – following Leibniz and Whitehead, Deleuze is one of the original networkologists. Of course, this is precisely what needs to be explained.
First, though, a word on The Logic of Sense itself. What a strange book! Woven together from the works of Lewis Carroll and the Hellenic era Stoics (an obvious juxtaposition, no?), and ostensibly on language, this is the book where he more than any other takes on Lacan on his own terms, exploding Lacan’s structures from within (as opposed to inventing new ones in texts such as Anti-Oedipus). But more than anything else, this is a book about ethics, and specifically, the ethics of the event. In fact, Deleuze could have easily called the text, or at least its middle sections, ‘Being and Event.’ For the text starts with language, but towards the middle, it truly addresses what it means to be an event. The book climaxes addressing the sort of ethics required by events (via an extended analysis of what he calls, in an unwieldy turn of phrase, ‘counter-actualization’), and then proceeds, by means of an extended immanent critique of psychoanalysis, to reassemble a subject based on his ethics of the event. What is fascinating is just how many books exist in the multiplicity called Logic of Sense. For there is truly here a book on language, sense, and nonsense with Caroll, the Stoics, and Lacan; a book on subjectivity with the Stoics and Lacan; a book on ethics with the Stoics and Lacan; and a book on the metaphysics of the event. And it is only by means of their collision, overdetermination, and interpenetration that he was able to write any of these. Perhaps unsurprisingly, Deleuze performs with his text that which he describes.
What precisely, though, does Deleuze mean by event in this text? He often distinguishes between Event and event, and argues that all events are manifestations of the purity of Aion, an avatar of the virtual in this text. In fact, it seems that all events spring from a single event, the birth of birthing, so to speak, the donation of all that exists, namely, Aion and its descent into the world of linear time, or Chronos. And while it may be tempting to take this as pure metaphysics, Deleuze is clear that he is also talking about physics (in the non-meta sense). In ‘The Twelfth Series of the Paradox’ he engages with discourses on entropy and the genesis of the arrow of time, and he is quite clear that the ur-Event or ur-Singularity is clearly what physicists call the Big Bang. Deleuze’s event are singularities in the sense in which the term is used by physicists and mathematicians. And in ‘The Fifteenth Series of Singularities,’ Deleuze links his notion of the event with model of individuation described by Gilbert Simondon, in which potential energy serves as both a philosophical and scientific term. In the notes to this section, Deleuze refers specifically to Albert Lautman’s use of singularities to describe the behavior of vector fields, primary tools for the descriptions of the universe used by contemporary theoretical physics. Much of the discourse which Deleuze employs in the margins of his discourse is that employed by contemporary complexity science – fields, singularities, etc. Of course, Deleuze is interested in deploying these terms philosophically, to turn scientific functions into philosophical concepts. And this means that he is less than concerned to map out precisely the manner in which they relate, term for term, to their scientific uses. But if we do this, in fact, it actually becomes much easier, particularly for those not versed in the scientific/mathematical uses of these terms, to map the manner in which Deleuze describes an ontology of events.
In contemporary science, it is most common to describe the manner in which water transforms between solid, liquid, and gas by means of what is called a ‘phase diagram’, in which pressure and temperature indicate the vertical and horizontal axes on a graph.
The difference between the phases (solid, liquid, and gas) are represented by lines. The most essential part of this graph, however, is the one in which the three phases of water collapses into two, the famed ‘triple point.’ For once pressure is raised high enough, water skips the liquid phase entirely, and jumps from solid to gas in a process known as sublimation (famous from chemistry class via the ‘steaming solid’ of dry ice, or solid CO2).
The triple point in such a diagram is in fact what Deleuze is talking about when he speaks of a singularity. The triple point indicates the change, in this case bifurcation, of two forms of the substance H2O into three. We see here the opening of a new territory within the same overarching territory known as water. As we follow the pressure and temperature down the chart, we would literally see a new type of water, namely, the liquid form, seem to all but spontaneously emerge from solid/gas water as if out of nowhere. Few examples on earth give better form to what Deleuze means by the virtual. This is also precisely what Bergson refers to in his writings as the work of intuition as method. That is, while we cannot see things like a triple point, we can map them via a sort of second-order cartography of water, precisely what we get with a phase diagram, because we intuit, by means of careful experimentation, that a virtual transition point must exist within the substance in question, even if we cannot see it. When Bergson says that intuition is not irrational, but strictly rigorous, this is precisely what he means. We cannot see a triple point, but we can intuit that is must be there.
A singularity is thus defined, in a mathematical sense, as a point which is both within a graph and outside of it. It is a paradoxical point, one which cannot be contained by the terms of the graph in question. If the graph is a line (a mathematical function), it is indicated by an ‘undefined’ point, while if the graph in question takes the form of a set, a singularity is indicated by the sort of point which Russell defined by his famous paradox (of the ‘barber who shaves himself’, or Lacan’s famous S1/master signifier). But if we are dealing with a more extended sort of graph, we have what physicists, following mathematician Rene Thom (of whose work Deleuze was also acquainted), calls a ‘bifurcation point.’ The term is perhaps unfortunate, because in fact there need not by two branches, and in fact, the term ‘branching point’ might work better. Either way, the triple point on our water graph is precisely what is at stake with this notion. A singularity is a place where something from without the domain in question impacts it from without. It is, to use a term employed by Lacan, extimate. For in fact, neither temperature nor pressure determine the fact that water changes radically at the triple point. The molecular structure of water, in relation to the more general conditions on planet earth and the physical universe, do. This is the sense in which the triple point is both within and without the temperature/pressure graph.
While water only has one node connecting the lines of its graph, a more complicated substance has much more complex connections of nodes and links – that is, a network. Take, for example, the manner in which the possible sounds made by the human voice are criss-crossed by multiple branching points which determine the territories carved by letters on our phonic capabilities, carving out the sounds we call vowels and consonants. And in fact, each language does this differently. The human phonic network is thus in this sense a hypernetwork, a series of networks superposed on top of each other. Nodes and links are what define the potential relations between territories on a plane.
So far, we have examined two types of events – the singularity of the Big Bang, and that of a physical substance. But Deleuze is quite clear there are more types of events, and its worthwhile to put these in a hierarchy. Firstly, there is the primordial event – the Big Bang. This event gives rise to subsidiary events, each of which gives shapes to territories, each of which become planes on which new events can give rise to new territories. Events give rise to networks which give rise to planes which are broken open by new events which start the process over again.
The first type of network is clearly physical, as we have seen with water, and Deleuze’s approach to the physical world is described, if obliquely, in the margins of this text and many others. Deleuze’s approach to science is consistently described in terms which have become seen as precursors to what today is called ‘complexity studies’ (as is described at length in Manuel DeLanda’s masterful Intensive Science and Virtual Philosophy). From here, however, we need to understand that there are not only static events, but dynamic ones. Of course, the distinction is relative. While humans have existed on planet earth, the triple point of water has remained at the same place, and is likely to remain there in the indefininte future, but if we think in the larger cosmological scale, the triple point of water was something which originally took time to unfold and develop as the universe expanded and evolved to its current form. Thus, while the triple point of water appears static to us, ultimately, it is dynamic. But in the smaller scale, the more common types of dynamic singularities are those which move on a regular basis.
A dynamic event is one which branches right before our eyes, which opens and closes territories on a plane as it goes. A simple example might be the opening up of the triple point of water as the universe began to cool and water eventually was allowed to settle down to the sort of meager temperature and pressures we see on planet earth. Beyond this is the individuation of any given water molecule, the existence of which is itself an event, an individuation. These of course range from simple individuations to the much more complex. Each individuated water molecule retains its structure over time, and is free to move around, beyond the virtual network of water, within the world of the actuality known as matter. Each individual molecule is itself an event, this time not only the virtual plane of water, but within its actual existence. Thus, there are virtual events (ie: triple point), and actual events (ie: individual water molecules).
But there are also higher level dynamic singularities, those which compose their own planes on the fly by deterritorializing substances determined by certain structural networks, and employing them as parts to give rise to an entirely new complex unity. For example, the construct a human being, water molecules need to be deterritorialized from their original locations in the world, and reterrirtorialized into the assemblage known as the human body. Deleuze calls each water molecule and each human body an event, this time under the name of an ‘individual’ (following Gilbert Simondon).
Individuals, however, are relatively permanent constructions, but there are those which are much more fleeting, more basic, continually vanishing as they go, and these Deleuze terms ‘aleatory points’. For example, the speaker within a conversation knits together words and meanings on the fly, drawing from planes of phonic material and the networks of meanings used by culture, suturing together matter from various planes in temporary series which we call sentences. Human bodies, ‘individuals’ in Deleuze’s terms, support these aleatory points, but these points vanish as soon as someone is no longer speaking. In this sense, aleatory points are the simplest constructions, individuals the more complex version thereof, and beyond this, Deleuze indicates a third layer of complexity, which he calls persons. Persons are individuals which have memory and a sense of self.
All events, thus, are both static and dynamic. Some last for most of the duration of the universe (such as the triple-point of water), while others barely last longer than a conversation. Some events give birth to chains of others on various other fields, or even give rise to entire other fields in the process as these new events draw multiple fields into novel conjunctions via deterrirotirialized elements, while other events stay stable and are relatively speaking dead-ends. But one things is clear. All that exists, from the physical world to the world of meaning, is composed of internetwined networks of networks, and these networks, operating on different planes of different ‘densities’ (or abilities to interpenetrate) are continually traversed by the most dynamic types of events which continually hop between territories. Thus, we have networks which are relatively free agents, and others which act as the terrains upon which the others operate. There are no firm distinctions, only shades of grey, as events continually give rise to other types of events. And in the process, territories continually fold and unfold as events give rise to ever new types of combinations and logics of worlds. All of this arises from the Big-Bang, the original branching point, which gave rise to the branching points which gave rise to matter and memory, organic and inorganic, living and inert, conscious and unconscious, meaning, feeling, etc. And as each arises from the branchings within that which came before, new potential for second level combinations arises as more dynamic types of events lift off from the upper levels and transgress the order of layers, entering into transverse combinations.
What do such transverse events look like? Take a simple example. When I utter the word ‘water’, I combine elements carved out of the phonic capabilities of the human vocal species by the phonemes of the English language and I tie them to: the graphic sequences indicated by the word ‘water’ in the roman alphabet, my intention to say this word as an event in mental space, the particular glass of water sitting on my table that I am indicating with this word, all the physical determinations (ie: triple point) that make it possible for water to exist in this world, as well as all the networks – physical, organic, meaningful, etc., that these are tied to indirectly – to which they are connected. By simply uttering this word, I connect incalculable numbers of elements together, giving rise to events on each of these territories, each of which is controlled by the events that govern the lines of force which determine the potentials for transformation on a given plane.
The world is, for Deleuze, an intertwined series of layer of networks within networks. Which is not to say that Deleuze says all of this in anything like a systematic fashion. But all of this is present, if in the margins, of Deleuze’s texts. All of which produces the basis upon which it becomes possible to put Deleuze’s work into discourse with the contemporary manifestations of the science of networks. For in fact, Deleuze was not here to see the internet, nor the more developed forms of globalized capital, nor networked approaches to the mind and artificial intelligence. And while his networkology of events is in fact central to his metaphysics, it fascinates me that few beyond DeLanda have truly pursued this approach to Deleuze before.
Whether or not this means that I am simply seeing the networkological in Deleuze because I want to, or because I am truly employing a Deleuzian buggery of Deleuze via his approach to commentary, is a bit hard to say. To me, however, it seems that all this is in fact the core of Deleuze, the ramifications of which play out in various forms in his works. But it also seems there is much to do to draw out the philosophy of networks, not only from his work, but from a wide variety of sources beyond Deleuze, including figures such as Leibniz, Whitehead, Simondon, as well as a variety of scientific sources.
Either way, the task is to articulate the philosophy of networks on its own plane, one which is not burdened by the needs of fidelity to a Deleuzian corpus and its peculiar concerns or terms. This is where terms such as node, link, topology, field, individuation, and other terms and concerns I describe in my Networkologies – A Manifesto depart from Deleuze and build a new edifice on their own plane. But the debt to Deleuze is, without question, enormous. The task, of course, is to shatter Deleuze, recast him, rework him, and start from scratch on a new plane composed of the detritus. This, it seems to me, is much of the work to be done to develop a philosophy of networks. Why we need a philosophy of networks, however, is the topic for another post, one which addresses ethics and politics of the event.