Emptiness and topology

This is a contribution to the roundtable ‘Twisting the Fabric of Sovereignty: Torsions, Distortions, and the Topological Imagination’ organized by Franck Bille and Rebecca Bryant as part of the American Anthropological Association conference in Toronto in Nov 2023.

Roundtable abstract: Too often, the term topology is used as a synonym for ‘network’ and as a result tends to remain abstract and disembodied. Yet a topological space can offer much theoretical mileage when mobilised as originally conceptualised in mathematics on account of its unique spatial characteristics – notably those that it “maintains in the process of distortion and transformation (bending, stretching, squeezing, but not breaking)” (Blum and Secor 2011). In foregrounding the physicality of space, this view of topology brings it into conversation with the growing literature on materiality and three-dimensionality and can illuminate the tension between physical, political, and cultural realms. In this session, we are particularly interested in holes, knots, folds, and other irregularities in the fabric of political space, and how these are produced and maintained. We invite ethnographic and conceptual contributions on all forms of spatial interruptions. This may include exclusion zones, breakaway states, anthropogenic subsurface structures, enclaves, gated communities, buffer zones, and no-go zones, to name only a few potential topological configurations.

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In this contribution, I am going to try thinking about emptiness as a topological configuration. I’ve been working on emptiness as a social-spatial formation and as an ethnographically derived analytical category for some years now, but I have not thought about it through the lens of topology. I will begin by considering emptiness via the feature of topological space emphasised in the description of this roundtable, namely the sameness that is maintained despite distortions. I take this to be a suggestion that there is analytical traction in asserting the sameness of seemingly differential space, that emphasizing sameness is somehow important in the current historical moment. If this is indeed so, I would like to understand why. It seems to me that turning to topology has been consequential for scholars who have taken it up over the years. If Edmund Leach turned to mathematical abstraction in 1961 to correct for the Eurocentrism of some of his colleagues, STS scholars, as pointed out by Noortje Marres, wanted to contest the notion that society and technology are different spheres. One could argue that technological changes have made it possible to produce space in ways that was not possible before, accessing depths of earth and space in ways that demand we adapt our spatial thinking. But, still, why turn to topology now and via the category of sameness. One possible answer to the question of why sameness is analytically consequential – and one that in my view could justify the mobilization of topological spatial imaginary as an analytical device – is that it allows to zoom in on the distorting force, such as sovereign power, in contexts where its operations may be obscured if one assumes difference rather than sameness. So, let’s try this with regard to emptiness.

Emptiness – and the associated emptying – are terms used by residents of towns and villages in eastern Latvia to describe radical reconfigurations of place-constituting relations that entail people leaving, schools and hospitals closing, services and shops shutting down, and transportation routes being cancelled. Importantly, emptiness does not mean that there is nothing there. There is a lot, and you can read more at emptiness.eu. In the process of emptying, place-constituting relations between people and material environment change so radically that the place becomes strange, unfamiliar, nausea-inducing to its long-term residents. Yet, they also recognise that it is the same place. For example, residents of Lielciems, a former monotown near Latvia’s border with Russia find themselves amidst too much space. They are surrounded by empty apartments and abandoned allotments. They talk about them by talking about the time when space was scarce, when all apartments and allotments were taken, and when one had to wait in line to get them. Now, one woman told me, you can just walk outside and start digging to plant potatoes. Nobody will stop you. It’s not like there is not enough space, she added. My neighbour – and pretty much everyone else in the stairwell – used the empty first floor apartments for storage and the empty fifth-floor apartments for hanging laundry.  As they did so, they felt simultaneously estranged from this place and attached to it; it seemed very different to them, and yet it was the same.

Places like this, emptying places, tend to be subject to radically different interpretations. Not all places, by the way, are subject to such radically different interpretations. If most of the residents of Lielciems see emptying as a loss caused by the mutable subject of ‘they’, other people and institutions – from transient dark tourists to environmentally concerned progressives and from spatial planners to the Latvian military – see it as an opportunity that has emerged, when distortions, such as Soviet industrialisation, for example, have been removed. The environmentally conscious see it is an opportunity for rewilding. The Latvian military sees it as an opportunity for creating a buffer zone on the imperial fault line between Russia and Europe. When these subjects look, they see an entirely different place than Lielciems’ residents, but there is no sameness in their gaze.

It seems to me that the residents who focus on absent presences, on that which should be there but is not (like people, buildings, services), exhibit a topological spatial imaginary. By holding the past place next to the present, they call attention to the distorting forces that have changed this place beyond recognition while also keeping it the same. The residents of Lielciems are not nostalgic for the past, as their critics would have it. They are pointing to the distorting forces without necessarily giving a full narrative of them. As I noted, sometimes they simply refer to these distorting forces as ‘they’. The onlookers – the planners, the tourists, the environmentalists – use a different spatial imaginary, one that folds the emptying places into planning regions, urban-rural configurations, and so forth. They flatten the voluminous space of emptiness and obscure the distorting forces. But what makes the voluminous nature of emptiness visible is the spatial and temporal imaginary of the subject who lives it. Insisting on the sameness and difference of the place as they do also recognizes the temporal dimension of emptiness as a topological configuration. The past and the present appear simultaneously next to each other even as they are arranged in a before and after configuration, and the past’s future has a much stronger hold on the residents’ spatial-temporal imaginary than the future of the present. I hope you have not lost me by now…. What I want to say is that here sameness does not lie in objectively identifiable properties of space or time, but in the lived experience of the residents of the emptying places. Insisting on the sameness of the place alongside its difference, then, is possibly a form of embedded critique.

So far, I’ve run with the topological imaginary of a place staying the same while changing. I have not taken it up as a method of abstraction as Edmund Leach did. I have not used it as an analogy, which would require a much more thorough understanding of mathematics than I can claim. But I also have not used it merely as a metaphor. I’ve used topological imaginary as a heuristic or, as John Phillips puts it, as “a kind of beam that throws a diaphanous light over states of affairs, illuminating otherwise unnoticed relations between elements”. It has helped me to think about the specificity of the spatial imaginary of the residents of Lielciems in relation to the spatial projections of those who see Lielciems as they pass through or look from afar.

But given my primary commitment to emptiness as an ethnographic category rather than to topology as an analytic, I also want to think about the limits of topological spatial imaginary and thus the limits of sameness. When does sameness break? Annemarie Mol and John Law write that it is when space, which they understand to be fluid, cannot absorb what it encounters. Rob Shields, writing about the seven bridges of Koningsburg, remarks how the war – World War II – led to the solution of the problem of Seven Bridges – what was once a mathematical problem was completely altered by politics. When Russians moved in where Germans once had resided, the sameness of the place was radically reconfigured. In Lielciems, too, when the current residents will be gone, gone will be their topological spatial imaginary, and the place will not be both different and the same, it will be only different or only the same, depending on who will be looking. Seeing it as both same and different will then require a differently positioned gaze and abstraction. This is to stay that, if we are to think of place – and not only space – topologically, we have to account for people as one of the properties that constitutes its sameness.

Moreover, if we think that relationality is the ontology of topology, that as a shape changes, the relations between coordinates stay the same, then if those relations are cut by closure of borders or war, that is, by sovereign power, then new relations are forged, thus altering the place. What would be the stakes, then, if instead of the sameness of Lielciems, I would insist on holding difference in view. Would it lead me to analysis of rupturing forces instead of distorting forces? Or, lead me to ask when does a distorting force become a rupturing force and whether it stays the same as it undergoes this transition? So, in the end, I have not talked as much about sovereignty as I initially thought I would. But I have urged attention to distorting forces, suggesting that one of them is sovereign power that itself becomes distorted and transformed as it is extended, resisted, or desired in Lielciems.