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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.

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 Rotman and Xin-Wei Sha in this issue offer a model of this transformative conversation. 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.

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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.

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.

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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.

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The question of political subjectivation in network culture is of course crucial for thinking the common as alternative to neoliberalism. 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. Social networks are a very poignant example of that. 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.

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. 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.


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Luciana Parisi | Goldsmiths, University of London -

Naoki Fukui. Computing and Philosophy. Vincent C. Language As Disclosure. Carolyn Norman Slaughter. Machine Intelligence. Fundamental Issues of Artificial Intelligence. Simon Critchley. Reasoning about Preference Dynamics. Fenrong Liu. Playful Intelligence.

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