4.5
Diasporic Experience and the Need for Topological Methods
Historically, architecture has struggled with how to represent movement, as it inevitably also encapsulates time, and architectural representation has traditionally remained static.1 However, in order to account for movement within architecture, it is not simply a question of being able to represent dynamic situations, it is also the very nature of architectural space, conceptualised through the constraints of Euclidean geometry, that needs to be questioned. Although space as a concept has exploded in cultural theory, geography and many other disciplines, including also architectural theory, in the practice of architecture it remains a container, bounded and secure in its three dimensions. Movement provokes a crisis in this containerised space.
Movement can, of course, occur at different scales – the movement of populations across borders, or the movement of a person across a city street. Often, these two scales collide: a migrant body moving through a street in a European city negotiates both these scales at once, a space that is impossible to define in standard Euclidean terms. As space of this kind cannot readily be represented, the inhabitations that create such spatial conditions remain hidden to the traditional gaze of the architect. Yet, it is not only the (in)visibility of these spaces that is important, but also their operation. Space of this kind needs to be conceptualised as the product of particular sets of relations to notions of scale, time and belonging. It is, therefore, directly related to the production of subjectivities and the often precarious and ambivalent nature of migrant lives. In order to operate with what I shall call migrant space, an approach is required that can switch scales and emphasis, from the intimate to the institutional, from the local to the global, and from systems to bodies.
This switching of scale is also related to the way in which change is conceptualised in contemporary society. Whereas traditionally society was considered mostly static, change being thought of as extensive and atypical, in the recent ‘topological turn’ in social theory, change is considered normal and immanent.2 This requires a shift in the way cities are understood. If change and movement are the norm, then the switching of scales and the different modes of belonging that migrants embody must also be understood as part of the course. Multiple and often conflicting subjectivities that encompass staccato modes of belonging, loyalties that are (dis)loyal, the foldedness of time that results from mixing nostalgias with contemporary trans-local connections, are becoming more prevalent in all our lives. For migrants and diasporas, these conditions are the result of displacement, but, in a globalised world, such responses do not necessarily require physical displacement. In fact, such modes of inhabiting are typical of a topological tendency in contemporary culture that not only reveals itself in situations relating to notions of home and belonging, but in many other aspects of our social lives.3
In the context of migration, these effects reveal themselves most forcefully in the different ways that notions of belonging, of inclusion and exclusion are affected. The ease with which relations can be made across large distances, yet are fragmented in topographic proximity, is a classic example. These trans-local connections described by Appadurai not only create relations, they also fragment them.4 Often, this fragmentation is only described at the level of social integration, but it is also related to the way in which states are functioning within Europe. On the one hand, economically driven processes are creating pockets of ‘the global inside the national’, through processes of denationalisation;5 on the other hand, the very system upon which modern Europe was constructed is fragmenting. The idea of a contiguous European territory, defined through the Westphalian system of states, was built precisely to create a static and peaceful order, resting upon the idea of inclusion and exclusion as binary metrics and on a notional equality of all states.6 With the power of global capital and the unevenness of development, this idea of equality is being systematically eroded. The faltering of the Westphalian project can, therefore, be related to the new ways in which Europe is being reconstituted through new relations, less dependent on proximity, which also have a profound effect on its diasporic populations.
Topology, surface and mediation
Such phenomena require different methods of analysis and intervention, a new understanding of the social. If change is thought of as immanent, we require an approach that is recursive and iterative. Practices of mediation and affect take on important functions, as they are able to negotiate a shifting terrain. Such practices are related to the changing role of the surface in contemporary society,7 where change occurs quickly and is reacted to almost immediately. As Adkins and Lury state, this move to the surface had already occurred in the 1920s in the sociologist Siegfried Kracauer’s description of modern society. In his essay The Mass Ornament, Kracauer describes the appearance of masses through a reading of the Tiller Girls8 as ornamental phenomena. ‘The ornament, detached from its bearers, must be understood rationally. It consists of lines and circles like those found in text books on Euclidean geometry.’9 It perhaps comes as no surprise that Kracauer was trained as an architect. This reductive description of the surface through recourse to three fixed co-ordinates chimed with the description of a mass society where the Tiller Girls became a ‘fraction of a figure’,10 and the audience became spectator. If, in modern society, the surface was Euclidean, Adkins and Lury ask what model of the surface is required in contemporary society. Here, the surface becomes folded and describes a space that is non-Euclidean. For architecture too, the modern project has been a ‘turn to the surface’ that foregrounds questions of mediation, such as the mediation of architecture through the machine, functionality, etc. Adkins and Lury’s question is pertinent for us as well. In this model of a complex and non-linear society, on what type of surface is mediation taking place? The concept of the surface is fraught in architecture; on the one hand, it conjures images of shiny buildings and literally folded and undulating surfaces of installations and plazas. On the other hand, the surface as metaphor is the place where social relations occur. However, following Lury, how can the surface also be thought of as method? The topological tendency described above as the changing role of the surface is simultaneously a concept and a mode of enquiry. In the practice of architecture, it translates into methods that can both represent and intervene in the spatial.
These are topological methods. Topology is a branch of modern mathematics, the study of spaces ‘reduced’ to surfaces.11 It is the study of continuity and connectivity through continuous deformations. In other words, topology is concerned with those instances where change and movement do not break connections and relations. Topology has several branches, but the most general is point-set theory, which studies the properties of topological spaces. It is still a contested area, where much of the argument centres around the problem of the continuum, first defined by Georg Cantor as: ‘How many points are there in a straight line . . .’ or ‘How many different sets of integers do there exist?’12 Different approaches to point-set theory provide very different attitudes to this as yet unanswerable question. For some, this is a question of connectedness, or the openness of a set; for others, it is the constitution of the set itself that is problematic.13 For the mathematician Brian Rotman, categories and arrows are more useful than sets, as they are inherently relational, and what is included in a category is defined by external relations. There is no originary or primordial belonging to a set, even an open one, as was the case with the former viewpoint. The definition of such an inclusion is, for Rotman, a diagrammatic problem that must be approached through vectors: ‘in contrast to the fixity of sets and the membership relation, arrows and composition connote movement or transformation’.14
Movement is inherent in topology, described as categories and relations. But, even in thinking of the topological through sets and memberships, what remains is a very different approach to the idea of measurement. As Sha writes: ‘Topology provides an anexact (in Deleuze’s sense) mode of articulation, that does not need numerical measure, equations, exact data, statistics.’15 It is this relation to measuring, a precision that is allowed to remain fuzzy, that is so useful for a way of thinking of space as movement in architecture. As Lury states, in topology, the two properties conflated in Euclidean mathematics, order and value, are brought together in relation to each other:
In the topological thinking of multiplicity, however, ordering and value are brought together without reference to an external measure, but rather by – or in – relations in which the performative capacities of number to order and value are locally combined in different ways to produce spaces more general than those described by Euclid.16