Abstract
Topology is integral to a shift in socio-cultural theory from a linguistic to a mathematical paradigm. This has enabled in Badiou and Žižek a critique of the symbolic register, understood in terms of pure conceptual abstraction. Drawing on topology, this article understands it instead in terms of the figure. The break with the symbolic and language necessitates a break with form, but topologically still preserves a logic of the figure. This becomes a process of figuration, indeed a process of `deformation'. Badiou/Žižek will then presume a break with the symbolic for `the real'. But topology entails the centrality of not the real but the imaginary. With Castoriadis, this imaginary is understood as productive and social, and with Sloterdijk as spatial. In our times this is a self-organizing socio-technical imaginary. For Niklas Luhmann these socio-technical systems engage in coupling. They structurally couple with other social imaginaries. Their self-organization, going beyond pure functionality, operates through semantic excess: an excess that organizes the system and is their structure. Such structural coupling entails semantic exchange, consisting of not just information but also of images.
In what follows I want to address topology. It is widely agreed that topology is, in the first instance, less temporal than spatial. Topology takes us beyond the classical object and indeed beyond the classical subject. The classical object that we encounter – as most forcefully and powerfully delineated by Kant – is a form in something like a ‘container space’. As such it is ‘topographical’. Topology will take us beyond this classical object and form. Yet it will remain geometrical and spatial and as such does not take us beyond the figure. It will indeed give us a new paradigm of figure and object that is beyond form: a process of figuration, an object that is constantly in deformation. As spatial, as figural, topological objects seem most prone to relate to, to ‘couple’ with, a particular mode of subjectivity. This is a mode of subjectivity in which the imaginary, rather than the real or the symbolic, is the most prominent dimension. If the symbolic and the real work most pronouncedly in the register of time, it is the imaginary that is the most spatial of our faculties. It is the imaginary that encounters the object in its spatiality.
Many contemporary cultural thinkers, most notably Alain Badiou and Slavoj Žižek, as well as a number of conceptual artists, suggest that contemporary subjectivity engages with objects that are beyond experience. These authors take us beyond experience to an infinite temporality. They understand what is at stake here as a multiplicity of the real. I will insist, to the contrary, that topological thinking, and the topological character of so much of contemporary culture features not the real, but instead the imaginary. Let me make two preliminary points about the imaginary. First, if Emile Durkheim introduces culture as a question of the social symbolic, then as we will see below, it makes just as much sense to talk about a social imaginary. Second Durkheim’s symbolic functioned primarily to more or less stabilize and reproduce social relations. Such is also the case in Lacan’s psychoanalytic theory, both of the symbolic and the imaginary. In what follows I will identify two imaginaries: on the one hand, a ‘reproductive’ imaginary that is ensconced in the functioning of capitalism and the dominance of the commodity, and, on the other, a ‘productive imaginary’. This article will focus on this topological and productive imaginary, which is, I will suggest, at the heart of contemporary subjectivity. This imaginary is social and technological, and is engaged with topological objects. It is at the same time experienced and beyond experience.
At this juncture I need to be clear about my aims in the following. I am not making primarily an argument for the priority of space over time. Indeed the sort of self-organizing and co-evolutionary topology described below is also profoundly temporal. Topological objects do not, I will maintain, exist in time and space. Through their own energetics, they drive their own space and time. Topological space in its own self-transformation must be simultaneously temporal. My aim in this article is thus not to separate space from time, but to use notions of space to better understand the figure – or process of figuration – that is at the heart of topology, which, in turn, is tightly bound up with the imaginary, the social imaginary and its empiricist or a posteriori mode of operation. The complex of keywords in this is topology, the social imaginary, the figure and their, not rationalist but consistently inductive, empiricism. These elements work largely spatially, but a metaphysics of space is not at all at the centre of my argument. Indeed, though I will use the notion of the imaginary in a predominantly spatial and hence figural sense in this article, I am well aware of the temporality that is also driving the productive imaginary. Indeed this productive imagination is time in Heidegger’s Being and Time. Heidegger spends the entire second half of Being and Time’s companion volume, Kant and the Problem of Metaphysics, explicating this. But I want to break with the rigorous a priori of Heidegger’s imaginary for an empiricist imaginary: one that works less through some kind of transcendental argument than through imagings, mirroring, imitation – an imaginary that is fundamentally thus figural.
Topology: Mathematics and Figuration
Why ‘topology’? Topology is integral to the ‘mathematical turn’ in cultural and social theory. In cultural theory this is associated first and foremost with Badiou’s (2006) focus on post-Euclidean mathematics. As human beings begin to think in abstractions, they do so not just linguistically but mathematically. This is the case not only in the West, starting from the Pythagorean School, but also in Indian thought and the Arab world. Thought has thus historically been mathematical, linguistic and religious (Collins, 1998). Now, once again, we do not want to think, culturally or social scientifically, via only language or linguistic symbols but also via mathematical and religious symbols. Badiou (2004) has famously rejected what he sees as the ‘sophism’ of ‘linguistic’ thought for the truth instead of the mathematical. At the same time he has addressed the religious and the universal in his book on Saint Paul (Badiou, 2003). The point for us is that Paul’s strongly ontological Christianity most fully breaks with experience. The Synoptic gospels, Matthew, Mark and Luke, focused on the evidence, the miracle-based experience of possible redemption. In contrast, the Gospel of John and the thought of Saint Paul were focused on the beyond-experience, the Christian infinity of Death and Resurrection. For Badiou mathematics, since Georg Cantor’s scientific revolution, is important because it addresses infinity in nature: that is, it addresses natural infinities. These natural infinities take Badiou beyond an ontology and a politics of experience. When he addresses the religious, he does so to better engage with the infinite.
A half-century ago there was a similar turn of theory towards the realm of mathematics. Then, Cornelius Castoriadis and Jean François Lyotard, as well as Gilles Deleuze, were involved in debates in the context of the Bourbaki group in French mathematics. Again at stake was post-Cantorian mathematics. In The Critique of Pure Reason’s transcendental aesthetic, Kant understands time and space in terms of objects of experience. Thus knowledge depends on an experience of time in terms of algebra, in which numbers are the objects of experience, and space in terms of a Euclidean geometry, in which forms are the objects of experience. 1 Cantor’s set-theoretical revolution brings us to an encounter with a not theological but natural infinity: an infinity of infinities. Thus mathematics can be understood as beyond experience and beyond the object. This is the basis of Badiou’s critical theory. But its focus is temporality. Similarly with space there is the development of Riemannian geometry and topology, which takes us beyond Euclidean form into what Manuel Delanda (2002) has understood as ‘intensive science’. Thus mathematics leaves the realm of social science positivism and instrumental rationality and becomes also a basis for critique.
We also see the importance of mathematics in cultural theory in the Kabbalistic thinking of Benjamin, of Gershom Scholem and indeed of Kafka. The messianic, the eschatological, of early Christianity is beyond experience. We encounter such Kabbalistic as well as Gnostic thought in Scholem and Hans Jonas (Handelman, 1991). Benjamin, through his breaking with (Kantian) experience, notably in ‘On Language as Such and on the Language of Man’ (1996b) and ‘Critique of Violence’ (1996a), developed such a critical eschatological politics. Benjamin, aware of his own effective innumeracy, deferred to his friend Scholem’s mathematical eschatology. In Kafka’s ‘angelology’, Benjamin observed there is hope, but not for us: there is hope only for the angels. Michel Serres’ angelology (1995), which is at the same time a theory of information, has its roots in his own mathematical thinking (Serres, 1968). As in Scholem, so in Serres, mathematical thought is not just very different from the more instrumental quantitative positivism of most of social science, it also is explicitly a critique of Newtonian and Kantian experience. Thus we can understand Serres’ magisterial Doctoral d’Etat dissertation on Leibniz’s mathematical models: if Newtonian mathematics were epistemological, then Leibniz’s calculus was ontological. For Leibniz and Serres, mathematics deals with the very structure of being.
This said, topology does not repeat the Deleuzian prism of virtual and actual. In this model we experience an actual which is generated by the virtual. Thus in the calculus-modelled process of differentiation and integration in Deleuze’s Difference and Repetition (2004) we encounter the virtual and the actual. Similarly, in Friedrich Kittler’s (1997) media theory, the algorithm generates what we experience on our screens. In topology, the virtual does not generate the actual. Instead there are topological surfaces and the topological figure. You cannot speak of a virtual figure or virtual surface because the virtual is not experienced and, on the contrary, generates the figure (surface). Topological entities instead deform into one another. I will want to define the topological object thus as a space of deformation (Günzel, 2007: 21). For example, a circle and a square are topological equivalents. They are not topographically equivalent, yet they belong to the same topological set. This is the set of their shared properties, such as being planar and having an inside and outside separated by a boundary. By definition, topological objects can be stretched or twisted into one another, but they cannot be torn or cut, as in the famous example of the donut that deforms into a coffee cup. So, unlike the virtual, which is beyond experience and the experienced actual, topological figures cut across the distinction of the virtual and actual. The movement, the process at stake is not the generation of an actual by a virtual, but the deformation of, as it were, two actuals into one another via their topological properties. For our purposes, then, the topological, unlike the virtual, is constitutively figural. 2 The topological object is a process, a space of figuration. This point is at the heart of this article. Because the virtual is beyond the actual that it generates, the virtual must belong to a problematique of the real. Because the topological objects are figures in deformation, they must belong to a paradigm of the imaginary.
Equally as important, topological space must be understood as not topographical space. A topographical object is a form, a fixed form. The topological object is anti-form, in-form, de-form. Topographical objects are located in, move in (topographical) space. Topological objects are not located in space at all. Topological objects are spaces. Topological objects do not move in space. They are instead spaces of movement. Topographical objects are forms that move in space. Topological objects are not forms, but themselves spaces: spaces of deformation. Here the single and three-dimensional as it were ‘container space’ of Newtonian physics and Kantian experience splinters into the multiplicity of spaces (Günzel, 2007: 23). In Kant’s Transcendental Aesthetic, space is exterior to – and time is interior to – subjectivity: to the unity of apperception. In this context, topological space is the form that intensifies, that infolds into the figure. For its part, the transformation of time works on the lines of McLuhan’s sensorium that is externalized into the global media environment. Thus time exteriorizes from the inside of the subject: the single Newtonian time of Kant’s subjective unity splinters into a multiplicity of temporalities.
So topology is a challenge to today’s temporalization of thought, from Deleuze to Badiou, from Derrida to Heidegger, from Žižek to Negri. This temporal dominance in cultural theory breaks with the unitary subject of the symbolic for a multiplicity that is rooted in the real. Topology’s geometric paradigm will also give us a subject as, this time spatial, multiplicity. As such it must deal in the register of the image, with the figure. 3 As such its deconstruction of unity must privilege the imaginary, the productive imaginary as itself a multiplicity. In as much as subjectivity is cognitive or moral it engages the world in a mode foregrounding the symbolic and the real. Inasmuch as it deals with art, media and urban space, it will foreground the imaginary. 4 Topology, while a systematic critique of form, is still a defence of the figure. Badiou gives us a critical theory of capitalism through an infinite temporality that subtracts from, that is beyond experience. Topology, as Lury (2012) insists, is a question of surfaces, of empirical surfaces. To start from such surfaces is to shift out of a priori modes of thought. Yet these surfaces infold (Deleuze, 1988). Topology is thus at the same time experienced and beyond-experience. Topology is like Foucault’s ‘man’: it is a transcendental-empirical double. It is at the same time finite and infinite. In this chapter, the sort of critical social topology we are addressing is thus, on the one hand, a method, and on the other a set of processes emerging in cultural and social life. In the culture industries and in technological media, and in the East, perhaps more than the West, social life itself is becoming more topological.
The Topological Animal
Sloterdijk’s Philosophical Anthropology
The entirety of Peter Sloterdijk’s Sphären is a cultural theory of space. If for Heidegger after the Kehre, language is the house of being, for Sloterdijk being itself is a house. Or better the house, or the sphere, is the space in which subjectivity is constituted and ontologically exists. The three volumes of Sphären are: Blasen (Bubbles) (1998), a ‘micro-spherology; Globen (Globes) (1999), a ‘macro-spherology’; and Schäume (Foam) (2004), a ‘plural spherology’. Volume 2, Globen, is largely concerned with the topographical: it addresses the single Kantian container space, which is the space of metaphysics, of onto-theology. Volume 3, Schäume (Foam), is explicitly topological. It makes sense to see volumes 1 and 3 as critiques of Globen, of the macro-spherology. They are critiques of metaphysics, which Sloterdijk understands, in large part, in terms of Plato’s Academy with its primacy of classical geometry.
Already in Sloterdijk’s first and massively influential book, Critique of Cynical Reason (1988), the figure of Diogenes the Cynic was dominant. Diogenes was excluded from the metaphysics and geometry of Plato’s Academy and de facto constituted hiss critique from the outside. Now volume 1 of Spheres is a critique of the assumptions of ‘the One’ of Plato’s metaphysics and the topography of Globen. This critique is launched in terms of a (proto-) inter-subjectivity of the intimacy of ‘the two’. This intimate inter-subjectivity works through its own characteristic media and micro-spheres. Here we see not so much ‘the One’ of the Beautiful (the Good) in Plato’s Republic as the micro-sphere of inter-subjective intimacy of erotic love between man and boy in the Phaedrus and Symposium. Here the Old Testament’s Genesis is re-read not in terms of the One of God as Yahweh, but instead as the intimate communicative inter-subjectivity of God and Adam. Here the intimacy of the couple dominates. There is no God without Adam (Sloterdijk, 2011: 42–3). Volume 3, for its part, is a critique of the Academic geometry of Platonic metaphysics from the point of view of a plural spherology: a critique of ‘the One’ from the standpoint of the modern multiplicity of today’s topological geometry.
Spheres is at the same time Heideggerian and a critique of Heidegger. It is not so much Sein und Zeit (Sloterdijk, 1998: 345) as Sein und Raum. Dasein for Sloterdijk (2001) is first and foremost da, it is there; it is spatial. Even in Being and Time we are in a seemingly spatial world with Dasein before we move to the more temporal character of ‘thrown-ness’ and ‘anticipation’. Heidegger is a rigorous a priori thinker; Sloterdijk breaks with the a priori for a philosophical anthropology and a psychology. Where Heidegger talks about the condition of existence of ontological subjectivity, Sloterdijk is focused on what distinguishes humans from other animals. In Sein und Zeit’s famous chapter on Being-In, the key opposition is Vorhandenheit and Zuhandenheit, present-at-hand and ready-to-hand. For authentic Dasein we need the ready-to-hand. For Sloterdijk (2004: 364–5), what counts instead is the hand.
As animals with hands, we throw stones to keep enemies at bay. We build enclosures. We make tools. Crucial in this is the enclosure. Humans are the enclosure-building animals. Our building of enclosures echoes our original enclosure in the womb. This incubator and the early incubators of domestic living spaces give us humans a uniquely extended period of incubation. In classical philosophical anthropology, in Arnold Gehlen, the human differentia specifica is our Instinktarmut, a poverty of instincts (Sloterdijk, 2004: 229). This absence, this lack must somehow be filled. Human lack means we need security in a way that animals do not. Sloterdijk understands this security in terms of what he calls an ‘immunology’. But this lack is also a space of indeterminacy.
In mainstream sociology Peter Berger (1990) was a philosophical anthropologist. He addressed the security side of human Instinktarmut and suggested a sacred canopy to provide this security. For Sloterdijk in the age of onto-theology or metaphysics of volume 2 of Sphären, this security, this immunology, works through a cosmology of the One, based on the Platonic Good or the Judaeo-Christian God. But all of this security disappears when we are thrown into the multiplicity, what seems to be the void of modernity. In this void, in this ontological insecurity, what takes the place of the sacred and Platonic canopy is instead technology itself. The first of these pluri-spheres, the first case of immunology through foam and technology, is the greenhouse of London’s Crystal Palace, from the first International Expo of 1851 (Sloterdijk, 2004: 332).
Psycho-topology: Intimate Space and Unmediated Communication
The problem for Sloterdijk (1998: 343) is that in Heidegger’s Dasein there is no intimacy. 5 So we have human being and intimate space, its intimate protector/incubator. And like Gaston Bachelard’s Poetics of Space and Rachel Whiteread’s houses, it is the nooks and crannies of the house that are the object of the investment of desire (Sloterdijk, 1998: 9). Indeed, Sloterdijk begins the first volume of Spheres with a quote from Bachelard, one that rejects Platonic Academic geometry for the roundness of intimacy. The subjects and objects of Platonist metaphysics are rejected for what are the media of intimacy. With Thomas Macho (1993) Sloterdijk (2011: 291–5) disagrees with Freudian object theory. Before the oral, anal and genital phases of the Freudian proto-subject who is attached to, respectively, the breast, faeces and the mother as objects, are three more primordial stages. In the first of these, the foetus and mother connect through the placenta and the medium of blood. In a second phase the newborn connects with the world not through the mother’s breast but through the medium of breath. In the third stage through the medium of the newborn’s voice. In each pre-oral phase what is at stake is not objects but media spaces. As the ‘open animal’, only humans are topological. Only humans have worlds. Animals, even mammals, are born. Humans ‘come into the world’. As topological entities, human beings must be spaces of deformation. The lack – the space which the instincts do not fully determine – becomes topological.
Sloterdijk (2004: 388–9) draws on John Bowlby’s theory of attachment. Bowlby was an evolutionary psychologist and biologist. In this context we can understand humans as topological animals: as a highly evolved species (see Holmes, 1993) with high levels of neuro-plasticity (Malabou, 2004). Attachment and prolonged incubation may be tied to the development of such plasticity. To be the enclosure-building animal entails plasticity and incubation. In Sloterdijk’s philosophical anthropology, man is the enclosure-building animal. Other animals adapt to their environment, while humans build their environment. So other animals evolve in a process of adaptation to the environment. Because each of us builds their own environment, we do not evolve in this simple Darwinian fashion: instead humans co-evolve. Topological beings co-evolve. At a certain point in the evolution of species, we emerge as the co-evolving animals.
Lacan’s psychology also was influenced by philosophical anthropology (Jay, 1994). In the Mandarin editions of Lacan’s writings on the ‘mirror phase’, the imaginary is translated as the xiangxiang (想象). Here the first graph xiang (想) indicates thought and the second xiang (象) means appearance or image: the imaginary is a thought-image. This xiangxiang is the ideal ego of Lacan’s reproductive imaginary that reproduces capitalist relations of domination. This is an ideal unification of the subject, as ‘the One’ that all of Lacan’s work is directed against. Now there is another term in Mandarin for the imaginary, or the imagination, and this is the xiangxiangli (想象力). It is the same thought-image with a li (力) added on. This li means power, force, strength: both physically and spiritually. This second imaginary is not the reproductive but instead the productive imaginary. It is central to the late Lacan’s (2000) topological paradigm of subjectivity. This is to be found in the ‘Rings of String’ essay from the Twentieth Seminar. This late Lacan of the real is the mathematical and topology-influenced Lacan. In ‘Rings of String’ Lacan focuses on a familiar topological figure: the Borromean Knot. Borromean rings consist of three topological circles whose linkage forms a Brunnian link, in which the removal of any ring results in two unlinked rings. The Borromean Knot is comprised for him of rings of string. One of these rings – none of which is removable – is symbolic, one imaginary, and one real.
If Badiou’s mathematical multiplicity is rooted in the algebra of number, of post-object number, then Lacan’s is rooted in post-Euclidean geometry. The imaginary now is no longer identical with the ideal ego. Instead it inhabits a space of topological deformation. If the knot is a figure comprised of rings of the real, the symbolic and the imaginary, then subjectivity as multiplicity is not grounded solely in the real. This late Lacanian subjectivity is just as much symbolic and imaginary. It is a topological multiplicity of all three registers. The rings are topological equivalents. As such they must share properties and belong to the same set: the set of, not the real, but of the topological.
Socio-topology
Once we are in the realm of philosophical anthropology, it follows that the human’s ‘world’ is just a variant of the environment of all biological beings. Being in the world is one mode of being-in-the-environment. For Sloterdijk in our plural modernity of ‘foam’, Heidegger’s being-in-the-world is displaced by system-in-the environment. This move – from phenomenology to nonlinear systems – is widespread in socio-cultural theory. Thus Luhmann has drawn on Maturana and Varela to reconstitute Husserl’s time consciousness as a system–environment relationship. And Bernard Stiegler has drawn on Gilbert Simondon to reconstitute a phenomenology with roots in Husserl, Heidegger and Derrida as a technological phenomenology. In Sloterdijk this seems to hinge on phenomenology’s ‘horizon’ being reconstituted as topology’s atmosphere. If Husserl, Heidegger and phenomenology give us a horizon on which subjectivity constitutes meaning, then co-evolutionary topological systems give us atmospheres.
The horizon, like the ‘world’, is metaphysical. The atmosphere is physical and metaphysical. In topology we have (self-built) environments and atmospheres. In Renaissance painting there was a perspectival horizon. 6 The visitor experienced this from the outside. In contemporary art, for example Olafur Eliasson’s 2003 Weather Project in Tate Modern’s Turbine Hall, the sun and this weather is experienced by the visitor (from the inside) as an atmosphere. Signally, the 2006 Shanghai Biennale on Hyper Art and HyperDesign was one of the first major contemporary art events in China in which Mainland Chinese visitors started to outnumber westerners. While western visitors mostly looked at the show’s installations from a critical distance, large numbers of local visitors entered into the inside of the installations, crawling under and about them and taking photos. In a sort of architectural turn in art led by Gordon Matta Clark and now Beijing artist Liu Wei, nature and culture, the physical (cf. load bearing-ness in both Matta Clark and Liu Wei) and metaphysical are merged. With, again, McLuhan, we are inside the media, inside the object.
For Heidegger, death was the horizon on which we constitute the meaning of our beings. In our topological modernity this horizon of our finitude has exploded: it is shattered into an infinity of atmospheres, in which we must constitute our fragile and plural meanings. In these atmospheres we both breathe and constitute meaning. The effective afterword to Spheres’ three volumes is Sloterdijk’s (2006) Im Weltinnenraum des Kapitals: Für eine philosophische Theorie der Globalisierung: if capital has for centuries effectively accumulated extensively as Globen, now it must accumulate intensively. Hence globalization, außenweltlich process, has now become innenweltlich. So we move from a topographical to a topological regime of capital accumulation. Here capital accumulates as atmospheres themselves. Topography may give us two-dimensionality, actor-networks and the network society, but now we move to the épaisseur of atmospheres as capital accumulates intensively. In the plural spherology of contemporary foam we are individuated into our own bubbles and those very bubbles mediate our communication. We move from a psychology to a sociology, and now it is these topological spaces that communicate with one another. Our capsules separate us from one another, but they also make us multiple as subjectivities. They cut both ways: they open and close and burst.
We are these topological systems we construct. Communication takes place, when it does, not in a topological space but between topological spaces. These are atmospheres of isolated individuation. Yet atmospheres can also be shared. Thus pivotal for Sloterdijk (2004: 342) in the transition to modernity’s foam is the Crystal Palace from the First World Exposition in London 1851. In their physicality these atmospheres constitute humans above all in terms of ‘breathability’ (Latour and Gagliardi, 2006), and, in Schäume, considerable text is devoted to how human beings can breathe in space stations. The Crystal Palace was a particular site of incubation: a container in which transplanted plants from tropical regions might survive. There is an artificial breathability in this constructed greenhouse: it is a site of a ‘multi-naturalism’. It is a shared atmosphere, such as that of project-networks in design and the culture industries; like file-sharing networks. Another such shared atmosphere, which is actually called an atmosphere (kuqi) by its participants, is the Japanese video-tagging metadata platform in Japan, Nico Nico Douga. Here participants write on video content as it streams (Bachmann, 2011). We become topological subjectivities in Sloterdijk’s plural spherology. We are our technologies, our tastes, our lifestyles and brands, our literal spaces. These are constantly under deformation, always a different figure showing, yet having their topological equivalent the structures of meaning comprise us as singular ‘rings of string’. Further, like foam, these are fragile and always threatening to burst.
These structures of meaning are what Niklas Luhmann addresses in, as Sloterdijk (2004: 328f.) notes, his assumption of the excess of semantics over function. Luhmann’s topological modernity will supersede an earlier topographical modernity – described by Talcott Parsons – in which function as distinct from semantics was driving social systems. For Luhmann, social systems have both functional and semantic levels. In contemporary societies the semantic – which is also a question of communication – overflows the functional (Koschorke and Vismann, 1999). It is this semantic excess that provides the power that drives the morphing of topological spaces, topological objects. Thus Parsonian functionally driven systems are involved in a logic of reproduction and external causation from the environment. Luhmann’s topological systems are involved in a logic of production, of a self-organization driven by semantic overflow (Schützeichel, 2003). The above-mentioned co-evolution of contemporary topological subjectivities works through what Varela and Luhmann saw as the ‘structural coupling’ of these systems.
With semantic excess, structure breaks loose from function. Function still reproduces, but structure produces. The old structural functionalism very well described topographical modernity – every structure had a function: the church, the family, etc. In late and topological modernity, the driving structures are now the semantic structures, for us also information structures, and finally structures of the imaginary. This is an imaginary in excess of function that drives media culture, consumer culture, and the knowledge and information society. It drives not real but intellectual property, in its chronic invention. Not only does structure break loose from function, but structure becomes deeper; the depth of surfaces that are spaces in themselves. And they no longer just reproduce, they invent, they produce. In functionalism and topographical modernity the system was organized from the outside, while now, in the presence of this semantic excess, the system is organized, driven and caused from the inside. The old topographical functionalism, the ideal-ego paradigm of the Lacanian imaginary, was one of the functions. Now this function itself becomes topological, becomes productive and drives the self-invention of the system.
The Imaginary
We encounter the imaginary in, for example, the work of Emile Durkheim and Walter Benjamin: in both cases, curiously, in the context of religion. In Emile Durkheim’s Elementary Forms of Religious Life (2008), there is an imaginary and a symbolic. The symbolic is a social symbolic. But the imaginary, for Durkheim, is very distinctly an individual phenomenon, it happens at the level of individual psychology. Durkheim is very much the rationalist, his Comtean positivism standing in opposition to the empiricism of the contemporaneous British anthropology. So, for Durkheim, the symbolic is rationalist and the imaginary empiricist: the symbolic resolutely a priori, Durkheim’s social a priori and the imaginary a posteriori. For Durkheim the symbolic fixes social relations, it makes society and social continuity possible (Alexander, 2005). In comparison, the imaginary and images are fleeting, protean.
Durkheim criticizes the empiricists’ focus on dreams. Yet the imaginary is largely what is at work in dreams. The symbolic tends to represent rationally, through the categories of an emergent logic, while the imaginary represents proto-logically or illogically, through what Freud sees as sublimation, condensation and over-determination. The symbolic works through determination in its symbols, while the imaginary works through under-determined or over-determined representations, which, as in dreams, condense and merge. The symbolic works through the clear and distinct, the imaginary through what we might call the dazed and confused. The protean nature, the plasticity, of such images and such an imagining-capacity is incipiently topological.
Benjamin’s (1996b) ‘On Language’ features, on the one hand, human language and, on the other, the language of things. Like Durkheim, Benjamin too insisted that non-humans have imaginaries while only humans partake of the symbolic. Benjamin’s thing-language only utters images, operates mimetically, through the imaginary. Thing-language images do not classify, cannot analyse, unlike the language of man. The language of things, for Benjamin, also does not judge. It is such judgement – the shift to a language of judgement – that causes man’s Fall from the Garden of Eden. Eve listened to the serpent and ate fruit from the tree of knowledge. In doing so she engineered a shift in human language from the proper nouns of naming, from this God-given language of singularity, to a judging language of the common noun: a language that brings particulars under universals. Such a language of judgement put humans in the place of God and led to the Fall. But the language of things and the imaginary does not judge. Benjamin’s things communicate through the imaginary in a figural mode of representation. Humans encounter these communications and the task of Benjamin’s translator is discursively to translate these thing images again into singularities, into the proper. Our point is that both Durkheim and Benjamin give us a rationalist, a priori and symbolic language of judgement as counterposed to an imaginary, shared also by non-humans, an indeterminate and over-determinate language of images that can never work analytically, can never subsume particular under universal. The language of things is a posteriori.
Productive Imaginary: From Kant to Heidegger
Kant (1929: 142–3) develops the faculty of the imagination (Einbildun-gskraft) – the schemata of the imagination – in the first edition of The Critique of Pure Reason. The ‘schemata’ of the imagination mediate between intuition and the understanding. Intuition is a passive faculty, taking in and representing the manifold through the categories of time and space. The imagination works in productive syntheses on the intuition’s representations and then presents these to the understanding. The concepts or the categories of the understanding are not genres under which are determined specifics or particulars. They are instead more like logical operations such as cause, identity, relation and syllogism that enable us to subsume particulars under universals. The schema of the imagination work similarly. They are not contents nor forms, but an enabling frame. In judgements of the beautiful, the faculty of the imagination is in consonance with the understanding. In judgements of the sublime the faculties are in a relation of dissonance: now the perception is too much for the understanding, leaving the imagination to deal with it. Kant calls judgement Urteilskraft, just as the imagination is Einbildungskraft. He does not call the understanding Verstandeskraft, but just Der Verstand. So judgement is shot through with this power, of making images. Indeed Marxian labour-power, as Arbeitskraft, seems to be modelled on the actual productive capacities of the imagination. The early Marx’s connection to the Romanticism-influenced young Hegelians would have fostered this. The imagination and labour-power are more productive than is the understanding: imagination working with the raw materials of intuition.
Kant’s third critique is less a priori than the first and second critiques. Only in the third critique does Kant not start from the subject in general, from the transcendental unity of apperception, but instead from singular, feeling subjectivity. Only the third critique is critique of judgement in a strict sense. With Castoriadis (1987) we see that a priori notions of being, justice and politics are determinate in a way that a productive and topological imaginary is not. Once a given social imaginary is constituted, it operates less through a priori deduction or a posteriori induction than through what Gilbert Simondon calls transduction (Stiegler, 2007). 7 Transductive systems consist of a constellation of ‘social facts’ inductively emergent from social relations. Then these same facts metamorphose into quasi-determinate norms that help steer the system. Kant understood ‘Enlightenment’ in terms of the ‘what can I know?’, the ‘what should I do?’ and the ‘what can I hope?’ (Palmquist, 2011). In this the what-can-I-know maps onto the first critique and the faculty of the understanding. And the what-should-I-do is homologous to the ethics of practical reason and the faculty of reason. The what-can-I-hope, for its part, connects to judgement and the imaginary. The what-can-I-hope is – for example, for Marx and Benjamin – the basis of critical theory. Kant further notes that the third critique and judgement is a ‘bridge’ between the first and second critiques. Now we see the double role of the imaginary: as, first, a schema that connects the intuition and the understanding; and, second, as the mediator between understanding and reason, between necessity and freedom.
For Fichte and Schelling this productive imaginary goes further. Their idealism and a priorism 8 forgets that Kant was trying to square the circle between empiricism and rationalism in his synthetic a priori. Kant’s a priori synthetic judgements try to bring what were previously the mutually exclusive and seemingly exhaustive a priori analytic judgements of rationalism and the posterior synthetic judgements of empiricism. With Fichte and Schelling, who were Romantics and idealists, the imagination is the primordial a priori (Kearney, 1988). Now the imaginary is not just a bridge but the condition of possibility of both understanding and reason. Fichte’s and Schelling’s a priori is not the condition of possibility but the principle of production of what we encounter. For them Kant’s productive imaginary actually generates not just art but nature and social life too. Now Kant’s transcendental and synthetic unity of apperception that allowed knowledge of the world becomes an equally transcendental and synthetic unity of world production. This is Fichte’s ‘Ich’, his literal subject that ‘posits’ the world. Kant and the Romantics saw this is a question of ‘determination’. In the one case determination by a cognitive a priori, in the other from a productive a priori. Kant’s productive imagination synthesizes from the raw materials given to the intuition. Fichte and Schelling’s imaginary does not synthesize from the empirical. For them, there is no empirical apart from what is produced from out of the ‘Ich’ itself.
Heidegger gave an entire year of lectures on Kant just before he wrote Being and Time. A year after Being and Time he shows that he understands Dasein in the paradigm of the imagination in Kant and the Problem of Metaphysics (1997). Already schooled by Husserl, whom Heidegger and his contemporaries read as breaking with the Kantian unknowability of noumena, Heidegger had to settle accounts with Germany’s predominant neo-Kantianism. The neo-Kantians had an empirical reading of Kant. For them synthetic a priori judgements were primarily synthetic judgements, that dealt with facts only loosely mediated by the intuition of a transcendental aesthetic, and not at all further determined or synthesized by the imagination. They turned to the second edition of The Critique of Pure Reason, in which the Einbildungskraft all but disappears. Heidegger goes back to the a priori Kantianism of the Romantics and idealists. Heidegger refashions subjectivity (Dasein) on the paradigm of the imagination. At stake is the existential a priori of ontological subjectivity: the condition of possibility of neither cognition (a priori synthetic judgements) nor moral action but of ontological existence. Heidegger is engaging not so much with experience (whether cognitive or aesthetic) but with being on the level of human subjectivity of existence. This existential a priori drives Being and Time. This ontological existence, in contrast to Kant’s subjectivity (transcendental and synthetic unity of apperception), is not general but singular, is not a question of abstract observation but of an embedded life-world. This ontological subjectivity is driven by the productive imagination. 9
Yet Heidegger’s productive imagination is fundamentally temporal. It works very much like Husserl’s phenomenological subjectivity. This is a critique of Newtonian time in which every moment is just a present and in which time is reversible, in which time is seen in terms of an object moving mechanically though container space. In contrast, for Husserl each perceived now also contains a past and present, a primary retention and a primary protention. In addition each present is modified, indeed bracketed through the operation of an imagined (i.e. not perceived) secondary protention and secondary retention (Stiegler, 2009). For Husserl this imaginary yields phenomenological knowledge, for Heidegger ontological existence. In Being and Time the secondary retention comes with thrown-ness (Geworfenheit), the secondary protention with anticipation. Both are the condition of possibility of ontological subjectivity, which is Besorgen (‘care’). The Kantian subject was outside of time, while his object was in Newtonian, mechanistic time. For Heidegger, both subject and object (Seiende) are in an existential world and time. Dasein is now not universal but singular and relates to beings, now not as particulars but as other singularities. Subjectivity, as care, relates to beings thus, not in a scientific attitude but via a poetics. Here only human beings, only Dasein, have the secondary and properly imaginary protention. This imagination makes the care of beings possible, and it imagines subjectivity’s own proper death. Dasein as existential imaginary is both singular and finite.
Towards the Social Imaginary
Cornelius Castoriadis’s The Imaginary Institution of Society (1987) is an insistent, sociological and spatial critique of Heidegger. Most important, Castoriadis breaks with Heidegger’s a priorism. For him (1987: 257–60) every a priorism, from Kant to Heidegger, must presume an unacceptable determinism. Heidegger and, for that matter, Kant never stop speaking of determination: of bestimmen or Bestimmungen. For Kant the ultimate condition of possibility of experience and judgement is Reason (Vernunft), on which understanding is contingent. Reason and its practical, active movement drive the show. So at stake are not just the ‘epistemological’ determinations of positivist causation and analysis, but also ontological determination. For Castoriadis the social imaginary cannot be an imaginary or an imagination if it is determined. The imaginary and social imaginary must not operate in the manner of an original or ‘primordial’ determinant. Thus Dasein and the wealth of categories in Sein und Zeit – from anticipation to thrown-ness to care, to world – are determinations of Being. But Being itself is not time here. Dasein instead is time. Being, Castoriadis (1987: 198–9) notes, determines the time that Dasein and beings and indeed the imaginary are.
Castoriadis insists on a move from the individual subject to a social dyad. Leibniz’s a priorism of plural substance, the monad, is another such determinism: the monad cannot have doors and windows and hence cannot enter into relations of inter-subjectivity, cannot be the basis of a social imaginary. Every modern body of a priorist thought, starting from the substantial a priorism of Descartes, Spinoza and Leibniz, presupposes an individualism of the subject. It can never, as Simmel (1994) noted, be inter-subjective, dyadic or sociological. In Kant and Heidegger, subject and substance part ways. The Kantian subject as unity of apperception and Heideggerian Dasein are not substances. They are instead conditions of possibility of, on the one hand, experience, and, on the other, ontological existence. As such, again, both presume the single subject and not the dyad. Indeed Husserl’s phenomenology can never give us a transcendental inter-subjectivity, without the entire phenomenological conceptual apparatus breaking down. Every modern a priori must thus start from a transcendental subject and not an inter-subjectivity. To begin from the dyad, we must, as Alfred Schutz (1967) understood, descend from the transcendental to the empirical. It is necessary to move from time’s interiority to the exteriority of space.
The imagination in Heidegger’s Kantbuch is fundamentally temporal. This is the problem for Castoriadis and for us. The imaginary in Heidegger loses all spatiality: it loses the dimension of the figure. The imaginary in Heidegger is heteronomously determined by Being itself. The social imaginary needs to break with this determining a priori of Heidegger’s Being. The social imaginary is largely self-determining: as dyad and multiplicity, it is also inter-determining. The social imaginary comprises non-monadic subjectivities with windows and doors. The social imaginary for Castoriadis (1987: 146f.) is the site at which the chain of signifiers ends. It is comprised of pure signifieds, the core and impossible-to-enunciate meanings at the heart of a social multiplicity. This set of pure signifieds drives the self-determination of the social. It is comprised of not images but imagings. It produces images in its self-transformation. As a process of largely self-determining figurations, the social imaginary is also temporal. It is not in space, but it is a space; as process it exists not in time but is a temporality.
In the 21st century, this social imaginary takes the form of a system. There was always technology. But there is a tipping point at which human subjects become integrally ensconced in human–technical systems – with the predominance of ubiquitous media, a range of technologies, the image-society, brands and consumer capitalism. Social systems, once rightly described as structural-functional by Parsons, become increasingly communications systems, Luhmann’s (1987) semantic systems. The structure of these systems is the semantic surplus over function. It is this that drives and self-organizes the systems. Again, unlike Parsons’ functional systems, which were largely valid before the predominance of technological culture, these semantically over-determined systems begin to produce their own environments. So we are dealing now with a multiplicity of environments that are themselves topological, psychic and social imaginaries. These topological imaginaries relate to one another through structural coupling. This presumes an openness to semantic interchange between subjectivities and between subjects and objects. It also presumes a coupling on a structural level, on the level of fundamental meanings. In the context of communications, media, design, art and technology such coupling is often largely on the level of the imaginary. In such a world objects communicate to us through images, while we as subjects translate and engage in symbolic exchange with the objects.
Concluding Illustrations: Culture Industry and the Chinese Economy
The culture industries are such imaginary-driven topological systems. In cultural objects, a range of products are topological equivalents in that they have a set of shared properties, e.g. the Virgin brand, or Apple or Google. Here the products that de-form into one another find their topological equivalence in the brand. This equivalence is marked in intellectual property: in copyright and, in particular, trademark (Lury, 2004). Not so much the real property of the commodity or the means of production, intellectual property is the shared property of the morphing contemporary cultural object. It may, for example, be the intellectual property in the algorithm that drives the de-forming images on your screen. Here the generative entity of the topological equivalents is this algorithm. At stake here, again, is not the post-object of the real (which is a post-object temporality). Indeed both Castoriadis and Lyotard were in disagreement with the pure Cantorian mathematics of the Bourbaki group. For Bourbaki the core of this is a pure mathematical axiomatic. It is this that is at the heart of Badiou’s real. Castoriadis objected: the first axiom must somehow be imagined. For Lyotard too the axiomatic cannot fully exclude the figural. In this sense, through fundamentally breaking with form and container space, the mathematics of the social imaginary is incipiently topological.
This topological object that is the brand or algorithm is still an object. And as such it operates spatially: not in a space but as a space, as for example in the brand environment described by Moor (2007). All of this is irreducibly figural in that we are dealing with the metamorphosing faces and figures of products, which then fold inward to the intensive locus of their structural equivalence. These topological, hence deformational, object-spaces then couple, not only with one another, but with a range and a succession of psychic and social imaginaries. These subjectivities, as topological spaces, are atmospheres. They are incubators and cocoons and more or less breathable. To the extent that these foam-like encapsulated topological subjectivities couple, they form social imaginaries. This is again through information and image and exchange. In, for example, Luke Fowler’s image and music and video file-sharing platform Shadazz we see such an inter-breathable atmosphere, a shared imaginary. We see social imaginaries in atmospheres of, for example, project-networks in architecture, art and the culture industries. We encounter them in larger-scale urban imaginaries, city topologies. It is this that is the stake in Lefebvre’s (co-)production of urban space.
This is the world, the cultural world of our increasingly topological modernity. It is a world in which capital itself operates increasingly not through the linearity of the symbolic and the commodity, but through the logic of the self-organizing social imaginary and intellectual property. This is a world in which capital accumulates through the sort of individualization that is constituted when Globen, when the topographical universal mind and topographical subjectivity, shatters into a million fragments like the exploding heads in David Cronenberg’s Scanners. After which each of these heads in its capsule, in its individualized atmosphere, is integrated into now self-organizing micro-circuits of capital. Yet Peter Murphy et al. (2010) have made a telling distinction between how the imaginary and symbolic work.
They distinguishes between (cognitive) judgement on the one hand and imagination on the other. For Murphy, judgement works through analysis while the imagination works through synthesis. If judgement comes across two entities, it separates them out, analyses them and identifies their distinctive characteristics. If the imaginary comes across these two elements, it finds a way to synthesize them, to cobble them together and to make something. This is how Schumpeter, Murphy continues, understood the creatively destructive entrepreneur. Schumpeter’s entrepreneur, that fourth factor, indeed fourth figure of production, is not a Judaeo-Christian creator. The entrepreneur is in a situation: he is not putting pre-assembled means and ends together as in the classical model of economic and social action. He comes across whatever elements or resources are lying about and, in one way or another, he manages to assemble them together. He synthesizes something. He, with a number of others, makes something. This is the productive and social imaginary. In a neoliberal age, Schumpeter’s social entrepreneur has been transmogrified, as Foucault (2008) notes, into Gary Becker’s ‘human capital’. Here, even difference has come under the spell of neoliberal capitalism’s self-accumulation. Schumpeter’s difference of invention becomes your obligation to accumulate your own human capital.
If the culture industries give us one illustration of the topological, then Bruno Latour in his above-mentioned co-edited Atmosphères de la politique gives us at least an implicit topology in the book’s notion of atmosphere. Latour in the book brings Sloterdijk and François Jullien, among others, together. But Jullien, perhaps the West’s leading cultural theorist of China, does not really there develop a notion of atmosphere that works in Chinese culture. Let me, by way of a concluding illustration, make an attempt to do this here. Giovanni Arrighi (2008) has at length argued that Adam Smith, and not Karl Marx, gives us a window on the Chinese economy. Arrighi rightly reads Smith and classical political economy as empiricist, in contrast to the rationalism of neoclassical (and neoliberal) economics. Arrighi contends that, in comparison to western neoliberalism, the Chinese economy works in such an empiricist mode. The implication is that the Chinese economy features not just such empiricism but an enhanced role for the imaginary: that it is largely an economy of not ‘the sphere’, but instead of atmospheres.
Michel Foucault in The Birth of Biopolitics (2008) also understands classical political economy of liberalism as effectively empiricist while there is only the governmentality of the body with neoclassicism and neoliberalism. 10 Adam Smith indeed worked very closely with David Hume and was the student of empiricist moral philosopher Francis Hutcheson. Smith’s contemporary, Immanuel Kant, rejected Hutcheson’s ‘moral sense theory’ in The Critique of Practical Reason for his own a priori morality. Smith, in The Theory of the Moral Sentiments insists instead on a rigorously a posteriori morality (see Haakonssen, 2002). Yet he too disagrees with his teacher. Smith says morality works not through a sixth, moral sense, indeed not directly through sense perception at all. It works, Smith specifies, instead through the imagination. We cannot sense what another person feels. We can only imagine it. Smith saw this as happening through a sort of ‘mirror’. At stake here, as Arrighi recognizes, are much more embedded economic relations, characteristic of Chinese economic relations, in which the moral and the economic are not to be analytically separated. Arrighi explicitly and Foucault implicitly see this in contradistinction to the disembedded and individualist western neoliberal economy.
The Chinese economy is also famously empiricist in its rejection of the set of a priori principles embodied in the ‘Washington Consensus’. Following such principles has led to the brutal and all-at-once privatization, cuts in welfare spending and abolition on capital controls that were enacted in Russia, Mexico, Argentina and elsewhere. In China, in contrast, there was the trial-and-error development of a Special Enterprise Zone in Shenzhen and Xiamen; and later local and experimental initiatives in local–state public investment in Shanghai-Pudong in the 1990s and now, from 2007, in the ‘Chongqing Model’. Jullien himself focuses on the Taoist wu wei of classical Chinese thought, which he contrasts to the centrality of action of the you wei in Greek thought. But there is a very similar you wei at the centre of Max Weber’s theory of social action. This is no coincidence because Weber’s zweckrational and wertrational action categories are explicitly not empirical but instead rational.
In a very important sense, the disembedded and instrumental neoclassical economic actor that, as Callon (1995) comments, is prevalent in western economies is at the same time Sloterdijk’s ‘sphere’. Its background assumptions – from Laozi’s (and Jullien’s) wu wei, of not action but situated activity – is the ‘atmosphere’. Wang Hui in his 现代中文思想的兴起 (The Rise of Modern Chinese Thought, 2007) argues explicitly against Weber in outlining a distinctly Chinese mode of modernity. Wang Hui sees the basis of this in Confucianist civilization. His focus is in particular on the Confucianist ‘rites and music’ or ‘rites and ceremonies’(儀禮). Here the rites and music are again the background assumptions that serve as a basis for action. Some 300 years later in Zhuangzi the rites and ceremonies are much more secularized, yet still follow, as Schwartz (1985) noted, a logic of wu wei. They are a set of background assumptions, implicit knowledge. They are a sort of spatio-temporal atmosphere, rather than the focused ‘sphere’ of subject-verb-object, goal-directed. The latter, which is assumed in neoclassical economics and classical sociology, is at the heart of western neoliberal economic and social action. Thus in the particular modernity and economy of China we see an empiricism of the social imaginary: an a posteriori of atmospheres. This can bring us to speculate that perhaps the East was topological well before the western world. Maybe whatever new version of the topological imagination is emerging in the West is also implicitly a process of ‘easternization’. Perhaps the question of topology is at the same time the question of what Gunder Frank (1998) so presciently called ‘re-Orient’. 11
Indeed, there are strong parallels between the figure in deformation in Chinese and in western art. François Jullien’s 2009 book, entitled The Great Image Has No Form, or On the Nonobject through Painting, is a study mainly of landscape painting in Song Dynasty China. It is, as is the rest of Jullien’s work, in contrast to say Wang Hui’s above-mentioned Confucianism, fundamentally Daoist. 12 In Jullien’s Great Image we see the Song painters such as Dong Yuan and Guo Xi, as well as Yuan and Qing artists Zhao Mengfu and Shitao, portray an image in deformation. We see mountains dissolve into clouds, and the sparseness of disintegrating trees. These are, as in our above descriptions of topology, figures in movement whose form is in the process of disappearance yet never quite does disappear into the full indifferentiation of the Dao. This is an art of figuration and the figure but not form. Its very process of deformation lends to its space indeed a temporality, one that at the same time belies understanding the topological as simply spatial, but instead incorporating a complex space-time. It is not just the form of the materials of art that are a figure in deformation, but the object itself being rendered which is at the same time a nonobject. The landscapes, the mountains and trees and clouds are in a movement of disintegration. Here the differentiation and light of the yang is always tending to the dark side and indistinction of the mountain’s yin. The object itself is also understood as topological: less in the western sense of the life drive of higher levels of energy and organization, but instead of the entropic death instinct. Yet this is a death instinct with its own proper qi, its own energy of regeneration.
Fast forward to contemporary Shanghai and we see Yang Fudong’s video-art cycle Seven Intellectuals in a Bamboo Forest. The rural and mountainous setting of much of this work is not just about intellectuals in exile. It is also a question of the (in)significance of the human subject-object in the landscape, in a landscape that is as much featureless void as comprised of mountains. Indeed the Mandarin term for landscape is shanshui (山水) or literally ‘mountain-water’. This has been echoed in Isaac Julien’s work with Yang in Julien’s nine-screen video installation, Ten Thousand Waves, shot in the even more rugged and hostile mountains of Guangxi province. Here, as in classical Song art, there is always an implicit movement from the unity and light of the form to the multiplicity, darkness and void of the formless. Yet formlessness or the pure multiplicity of the real and the void are never achieved. 13 There is instead still figuration: the object and figure in a process of deformation.
We see a similar figure in deformation in Francis Bacon’s above-mentioned paintings as described by Deleuze. There are arguably two Deleuzes: an early and perhaps middle Deleuze of Logic of Sense and especially Difference and Repetition (2004) and a late ‘topological Deleuze’ of Bacon (2003) and The Fold: Leibniz and the Baroque (1988). The Deleuze of Difference and Repetition (2004) is the theorist of the virtual and the actual as described by the very best of the Deleuze scholars (see DeLanda, 2002; Massumi, 2002). In important ways the dichotomy of virtual and actual are quite similar to Badiou’s (and Žižek’s) dichotomy of real and symbolic. In both there is a beyond-experience of the real (virtual), which is conceived along the lines of pure multiplicity. A pure multiplicity does not have features, and thus cannot be experienced. But in Chinese landscape painting the Dao is never a pure multiplicity, never a pure darkness or void, but always incorporates at the same time the featured-ness of the yang, and thus, though not actual, can nonetheless be experienced. Deleuze’s baroque culture is also not an unexperienceable virtual but instead an infolded object. In The Fold, Deleuze focuses on El Greco’s painting. In the baroque the unity of objects becomes infolded multiplicities, and the pure multiplicity of El Greco’s pure light becomes object, undergoes figuration. Deleuze describes El Greco in a register similar to McLuhan’s contrast of ‘light-on’ media, such as the novel, and light-through media, such as television, computers (and indeed mediaeval stained-glass church windows). Thus El Greco’s paintings are understood in terms of a light-through of pure light as distinct from the light-on straightforward actual of the Renaissance. This is not a question of actual versus virtual or real versus symbolic but instead of the topological. The topological is experienced, yet is always in a process of infolding into what is beyond experience. This also is what Deleuze (2003: 13–14) calls, in contrast to figurative art, Francis Bacon’s figure in deformation. We recall here that for (early) Deleuze multiplicity is a plenitude while for Badiou it is emptiness or void. My point is that neither can be experienced. In The Fold, middle and late Deleuze, however, multiplicity is experienced. Indeed the notion of ‘fold’ is derived from ‘manifold’, and manifold, in German Mannigfaltigkeit, is multiplicity. If the object thus infolds then multiplicity is no longer a virtual but is instead experienced. And topological objects, unlike virtual objects, can be experienced.
This brings us back again to the imaginary, which stands somewhere in between the indistinction of the real and the clear and distinct representation of the symbolic. The imaginary works though imitation and thus stands in contrast to the rules and deductive operations of the symbolic. The imaginary and social imaginary is never clear and distinct: like Lyotard’s figural it works through a dreamlike paradigm. The imaginary’s spatial under- and over-determination is overlain by its temporal under- and over-determination, in which past and future are brought into the present. The imagination, we recall, for Kant puts a first frame on the indeterminate multiplicity of the outside world; before this a further more analytic determination is imposed by the concepts of understanding (the symbolic). Thus, if topography works in the clear and distinct, in the register of the actual, of the symbolic, and the real operates in the void, the pure multiplicity of what is beyond experience, then topology works in the not-so-clear and distinct, the only partially determined, or alternatively in the dreamlike over-determination, in the logic of deformation of the (social) imaginary.
Footnotes
Acknowledgements
This article is informed by and draws on research from the project ‘Metadata in the Age of Ubiquitous Media’. This project is part of the Goldsmiths Spaces of Media Research Programme, funded by the Leverhulme Foundation. I would like to thank the Leverhulme, Programme Director James Curran and project co-investigators Yuk Hui and especially Goetz Bachmann.