To supplement the TCS Special Issue onTopologies of Culture (Jul-Sep 2012, 29.4-5), Simon Dawes interviews the issue’s editors about their use of topology, the extent to which we are witnessing a ‘topological turn’ in the humanities and the social sciences or the emergence of a ‘topological society’, and the implications of a topological approach for a critique of neoliberalism.
Simon Dawes: In your introduction to the issue, you present the topological turn as twofold: in terms of both cultural topology and topological culture. In what ways is culture itself becoming topological?
Celia Lury: The claim we make in the introduction is that we no longer live in or experience movement or transformation as the transmission of fixed forms in space and time but rather movement – organised in terms of ordering and continuity of transformation – composes the forms of social life itself. These dynamic, distinctively topological ‘abstractions’ emerge in practices of sorting, naming, numbering, comparing, and calculating. The effect of these practices is to introduce new continuities into a discontinuous world, linked to the topological forms of lists, models, networks, clouds, fractals and flows. There is a multiplication of relations of equivalence and difference and a radical expansion of the possibilities of establishing comparisons. Ordinal rankings or ratings, for example, are proliferating and increasing in importance not only in the economy but also in education, health, and popular culture, as they are used to derive and justify the allocation of resources. Such practices, we suggest, are changing how change itself is made legible: on the one hand, forms of social life are identified and made legible in terms of their capacities for change (rather than, for example, in terms of their typological characteristics), while on the other change is normalised as it becomes a shared condition in which more and more people are, variously, implicated, even if it is only as those whose exclusion is required for change to happen. In the multiplication of relations, change is established as continuous, normal and immanent, rather than as exceptional or externally produced. One can thus notice an ongoing expansion of the present through the maximization of entities to be taken into account. Importantly, this normalization of change is happening in such a way as to make dynamic social forms amenable to – indeed the only context for – economic and social innovation, intervention and decision-making. The future is anticipated; the past is made retroactively operable; and events are problematized, all in terms of the potential they offer for change in a multi-modal logic of possible worlds.
SD: Is ‘topology’ in this sense the same as the kind of topology elaborated in mathematics, or is there only a loose connection?
Luciana Parisi: In relation to the claim that culture is becoming topological, algebraic topology is not used as a metaphor or as a frame to represent changes in culture. Instead, it is used to describe culture as a matrix of changes; that is to embrace the operations and functions as well as the attributes and the dynamics that explain how culture is above all a process of change. This non-standard geometry crucially sustains that structures are not determined by points and by the distance between points. Instead points are determined by the vectorial forces that conjoin or not at the formation of a point. A structure itself is determined by the tendencies and the direction of vectorial forces as they mark a trajectory. If structural analysis has been central to the definition of culture, we propose that algebraic topology articulates an idea of structure in terms of continual transformation of forces and not in terms of specific points on a grid. It is important therefore to offer a scientific study of culture rather than an understanding of culture through scientific lenses. In this way, culture can produce its own scientific ideas. Our argument is that topology or non-standard geometry is intrinsic to the conception of topological culture and allows us to speak of the primacy of change in the analysis of cultural forms and forms of power.
CL: Exactly: it is active in specific cultural forms such as lists, networks and models, changing forms of relationality and their implication in processes of auto-spatialisation.
SD: How significant are media and technology to both aspects of this topological turn? Is culture also becoming topological in ways that are unmediated and unaffected by technology, and does cultural topology address areas of research that aren’t obviously technological?
LP: One can certainly look for expressions of cultural topology that are not mediated, but are instead determined by patterns of continual communication. However, our concern with the becoming topological of culture is necessarily a concern with how the computational transformation of technical machines and media into systems of organization, storage, transmission and control of information has led to a new form of culture defined by flows of data and by the rules, procedures, constrains through which they are ordered. So cultural topology for us is intrinsically affected by technology, to the extent that a technical machine is already a cultural, political and social universe that needs to be addressed. On the other hand, when speaking of cultural topology one is more generally speaking of a non-standard structure of organization that is not directly mediated by technology and its uses. One for instance can speak of the organization of geopolitical territories and boundaries, which change according to contingencies and are regulated by the topological function of homeomorphism, keeping checkpoints flexible but continuous. In the special issue, Mezzadra and Neilson’s research for instance explains these topological dynamics which are not directly technological, although they typically involve some technologically mediated activity, including, for example, searching data-bases.
SD: Isn’t there a danger that topology could be used to cover everything, or that recent interest in topology is just a case of the ‘emperor’s new clothes’? What’s significant about topology, as distinct from complexity, assemblage or chaos theory? Are there any prominent critics of the topological turn that you’re aware of, and how would you respond to their criticisms?
LP: Of course, as with any claim about a turn it is possible that topology mainly becomes just a new order-word, an intellectual checkpoint that homogenizes critical thought. The problem is not how topology is different from complexity or chaos theory. The problem instead is how to produce a scientific engagement with culture, according to which science does not inform culture, but culture itself becomes scientific and thus becomes expressive of ideas that are as valid as scientific statements. The intrusion of complexity theory or chaos theory as well as topology in cultural analysis then has to be considered not merely as a trend according to which cultural analysis just incorporates – without really understanding – scientific epistemologies. Instead, one has to insist that cultural expressions are modes of articulation of epochal changes that are themselves concerned with ideas of entropy, self-organization, inter-relations, continuity, etc. The question therefore is not topology versus chaos theory. These are instead a valid matrix of analysis and critical understanding of political, social, economical changes. The question therefore is why are these important when thinking at the place of culture or humanities vis-a-vis the sciences now.
Tiziana Terranova: I think that one of the best things this Special Issue can offer is exactly a relationship with science and mathematics that, as Luciana explains, is not about using science as a metaphor or as something that can be simply applied to culture. This reminds me of the argument that Ilya Prigogine and Isabelle Stengers made some years ago in Order Out of Chaos, where they argue for a non-reductionist, non-mechanicist science that could interact in a new way with philosophy, but we could also say with the human and social sciences. On the one hand, it is about seeing how culture can produce its own scientific concepts; on the other hand it involves entering a dialogue with those scientists and mathematicians who are themselves fighting against such reductionist applications of mathematics and science. Brian Rotmanand Xin-Wei Sha in this issue offer a model of this transformative conversation. But also Luciana’s notion of the generative power of contemporary culture which is producing its own scientific concepts is a very powerful idea. It is important to offer a possible model of this relationship at a time when the humanities and social sciences are under attack and are being asked to conform somehow to a rather obsolete, but still powerful, model of ‘doing science’ – what Prigogine and Stengers define as a reductionist, mechanistic, and deterministic science.
SD: Some of the writers in the issue seem to be positioning themselves in contrast to Alain Badiou. Could you say a little about the distinction between the approach set out in this issue and that of Badiou?
LP: It is interesting how these tensions between mathematical ontology and a topological ontology have been so distinctively although indirectly articulated in the issue. One of the crucial implications of topology is of course linked to the problem of infinity and how it gets resolved or addressed by a topological method of intuition versus one based on rationality, or a philosophical conception of a mathematical truth that cannot be directly experienced versus a topological notion of physical uncertainties defined by the directly lived, the gestured, the felt, the danced, or generally by experienced contingencies. In the issue, there is a certain inclination for the experienced and for a mathematics that accounts for the relation with the uncertainties of physical variations. However, more specifically for us, as stated in the introduction, it is important to acknowledge the superposition of these two tendencies of topological thought, one that accounts for a mathematical ontology that needs no further proof than mathematical axioms – and is therefore immanent to itself – and another that expresses the incompleteness of mathematics and its necessary relations to physics, and thus highlights the sense of topology as accounting for wholes and not just parts.
SD: In your co-written introduction to the special issue, you discuss the relationship between inclusion and exclusion, and refer briefly to an idea of the ‘commons’ emerging out of a ‘networked topological ethics of composition’ opposed to neoliberalism. Could you elaborate on this and tell us more about the implications of a topological approach for a critique of neoliberalism (in terms of the commons, the public sphere and inclusion/exclusion)?
TT: Actually, it is not so much the ‘commons’ as ‘common notions’, which is Spinoza’s term for, as Deleuze put it in Spinoza: Expressionism in Philosophy, ‘the idea of what is common to the affected and affecting bodies, to the external bodies and to our own’. Common notions, explains Deleuze, are for Spinoza the means by which we can exercise reason in such a way as to become active and escape not only the tyranny of sad passions, such as powerlessness and anger, which define the conditions of our impotence, but also the limits of simply accumulating joyful passions in a casual way, without exercising our powers of reason to organize our encounters, define our agreements and disagreements, and increase our powers of action. Common notions are adequate ideas that we form – more or less general, more or less limited to our viewpoints – of our relations to our bodies from which a new power of action can flow. They are born out of an active engagement with the nature of relations. This power of action is defined as the power to form relations that increase our power of being. Deleuze is very strict in defining common notions in Spinoza as biological and not physical or mathematical ideas, but when thinking topologically about contemporary culture, that is, when thinking about a culture where connectedness, continuity, relationality, invariance and change are so central, it is possible to think about this as a plane of composition, that is as an ethical plane in the Spinozist sense, involving the interplay of passions and reason. If these relations of composition are thought topologically, as Brian Massumi does for example, when he draws on Simondon to speak about the ways in which affect connects distant regions and turns limits and boundaries into thresholds, you get a sense of a possible topology of composition of the common. Thinking for example of social networks in terms of open monads infolding whole networks of relations makes the notion of topological cultures as ethical spaces of experimentation more intriguing. In this sense, topology can be a new conceptual tool for practices of political subjectivation in network culture.
The question of political subjectivation in network culture is of course crucial for thinking the common as alternative to neoliberalism. Today, the political, social and cultural potential of networks tends to be seen in two opposing ways: as inherently emancipatory or as new modes of capture of subjectivity within what Jodi Dean has influentially defined as the ‘circuits of communicative capitalism’. And yet more often the emancipatory perspective has become a bit of a straw man, where we see a rising number of writings which emphasize the ways in which networks constitute us as neoliberal sad subjects: angry, disconnected, anxious, powerless. We have been told that the connectedness and continuities that new media bring us also separate us from our powers of being. They produce substantially powerless public spheres, which include us in an endless circulation of opinions and beliefs, while excluding us from the real locations of power; that is, global financial markets and national state capitalisms. There is an automatism to the recursive dynamics of topological cultures that, as we argue in this introduction, can and will unleash an indeterminate potential in the world, but how can networked subjectivity become active? How can the series of unpredictable events unleashed by topological continuity trigger something more, the becoming active that Deleuze-Spinoza was thinking about? What about the passions unleashed by ubiquitous, mobile communication and connected continuities? It is not just a question of inventing and mobilizing new topological forms organizing continuities among oppositional subjectivities. As Hardt and Negri have recently suggested, contemporary capitalism which operates according to a neoliberal political rationality in Foucault’s sense, enables this process of commoning to be produced, we could say, topologically, while also destroying it. Social networks are a very poignant example of that. How can networks, as topological surfaces of connections, fields of vector forces variably intersecting at specific points, become sites where not only ‘nuggets of enjoyment’ can be experienced, but where adequate ideas can be formed, expressing something common to a planet networked by neoliberal capital, allowing for the active formation of new agreements between bodies and more common notions defining alternative ways of constructing the continuum of change? I think that understanding networks topologically in the ways identified in this Special Issue allows us not to retreat back onto a Hegelian notion of totality and hence to instigate active experimentation with network culture as a an ethical plane of production of common notions.
SD: Finally, could you tell us a little about how each of you first got interested in topology? Which writers first got you thinking about topology, and how are you applying it (or how is it relevant) to your own research?
LP: I became interested in topology through the analysis of the changed structure of power, defined by Deleuze and Guattari as a smooth space or as apparatuses of capture. Central to the articulation of this structure is Deleuze’s notion of differential, which also subtends his notion of the fold. This notion develops the idea of the infinitesimal from Leibniz and sustains Deleuze’s conception of the immanent relation between the virtual and the actual. Deleuze’s notion of the fold specifically had been adopted in digital architecture such as in the work of Greg Lynn and others, whereby Leibniz’ s differential calculus is re-articulated to discuss the importance of the curve over the line in digital aesthetics. However it has been with and through the study of Whitehead’s notion of extension and of his atomic conception of time that the notion of topology has become central to my research and to my book Contagious Architecture. In addition, Deleuze’s notion of the fold is also important so as to re-think structures and structural approaches to culture. Brian Massumi in Parables of the Virtual is explicit about how topology offers a new understanding of structure for cultural analysis. Similarly, my reading of and through quantum mechanics, chaos theory, and information theory had led me to study the shift from standard to non-standard geometry more closely. The history of topology as a scientific systematization of the problem of the infinite and indetermination has been at the centre of my most recent research in the investigation of the aesthetic of digital power.
TT: Obviously I got interested in topology by working on computer networks, and specifically on Internet protocols. Around more or less the same time that I published Network Culture, Alexander Galloway produced a very influential perspective on protocols as a new form of power, but seeing networks, and specifically Internet protocols, topologically, that is as implicated in the production of a space of continuity and differentiation, I think topology also allowed me to say also something different about protocols and informational space. In my previous work, topology was linked to physics, that is thermodynamics and chaos theory, in order to stress the interplay between protocols and the active powers of differentiation of network culture. Since then, network topology has definitely taken a ‘social’ turn, linking back to previous social science work on social networks. Further engaging with topological thinking in the work of co-editing this Special Issue has definitely helped me to engage with the question of the spatiality of networks in new ways, and I think this is going to show in my new work.
CL: My interest was crystalized by a lecture I heard given by Manuel De Landa – I suddenly saw how topology addresses so many concerns that are fundamental for contemporary social science. How could I not be interested? And once you become aware of the conceptual vocabulary it affords, you can see its significance for contemporary social and cultural theory everywhere. It is not new: it has, just for example, contributed to and transformed understandings of continuity and change, which are sometimes thought in opposition to each other, and brings them together. It has informed the identification and analysis of dynamic social forms such as networks, models, flows, lists, diagrams and foam. And, in conjunction with an account of boundaries which acknowledge how they both divide and connect, provided a vocabulary of modes of relating – of partial connection, of the mereographic, the transitive and the transductive – that augments the existing modes of the mechanical and the organic. In doing all this, it opens up new ways to consider the relations between ones, parts and wholes. The claim that we make in the introduction – that we are witnessing the emergence of a topological society is, I think, an exciting further step. It proposes the importance of an investigation and analysis of the social, political and economic implications of a topological society in terms of social differentiation, inclusion and exclusion, social mobility and so on, and makes it possible to think about new forms of engagement, participation, critique and intervention.
Celia Lury is Director of the Centre for Interdisciplinary Methodologies, University of Warwick. She was co-ordinator of the research network A Topological Approach to Cultural Dynamics (www.atacd.net). Her recent publications include Inventive Methods (co-edited with Nina Wakeford; Routledge) and Global Culture Industry: The Mediation of Things (with Scott Lash; Polity).
Luciana Parisi convenes the MA Interactive Media: Critical Theory and Practice at the Centre for Cultural Studies, Goldsmiths, University of London. In 2004 she published Abstract Sex. Philosophy, Biotechnology and the Mutations of Desire (Continuum Press). She has recently completed a monograph, Contagious Architecture. For an Aesthetic Computation of Space (MIT Press, March 2013).
Tiziana Terranova is Associate Professor of Sociology of Communications and New Media at the University of Naples ‘L’Orientale’, where she is also the director of the PhD programme in cultural and postcolonial studies. A member of the TCS editorial board, she is the author of Network Culture: Politics for the Information Age (Pluto Press, 2004) and numerous essays on the cultural politics of new media.