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In two previous posts, I introduced some considerations about the use of topology as a method in anthropology. The first of these presented conceptions of the body in relation to tattooing and the second offered a discussion of the notion of “house” as an analytic category. With this third post, I move up to the macro-level of borders between social or political entities.One key aspect of my interest in the question of borders and borderlands has to do with the issue of the outer limit of state territoriality. I take as a case study a “border” that never fully materialized according to international law (but which exists in many other ways as a boundary), the one between Tibet and China. I approach this Sino-Tibetan “border” through the lens of frontier dynamics that prompt us to rethink the associated binaries of core/periphery and Sino/Tibetan. In the border-space these binaries become distorted: neither simply distant nor proximate, and neither outside nor inside. In fact, the outside/inside divide becomes blurred and can hardly be disentangled from both “Tibet” and “China”—where does one end and the other start?Thinking about the Sino-Tibetan border(land) in this fashion is to move away from the constraints of topography and territory toward a more topological imagination, whereby the gap between the here and there is not so much a matter of actual distance than social relations, exchange, and interactions. The traditional vision of the topography of power has been shattered by many authors, leading to questions about the existence of clear “insides” and “outsides” of spatial authority. The conventional vision of a social landscape where the centre’s reach is limited within the remote periphery, and according to which horizontal relations and vertical hierarchies determine the equation of various topographies of power, is being increasingly questioned. There have been multiple attempts to reflect on these issues and to move away from spatial containers (such as the nation-state) and to explore what has been called “process geographies.” More unfamiliar forms of spatialization have been introduced, such as archipelagos, hollow rings, lattices, meshwork, or patchwork.According to these insights, borders are rather like porous membranes that do not so much separate an inside from an outside (of a political, cultural, ethnic unit) as mediate their relation and mutual exchanges. Borders are not so much containers as interfaces, “outer membranes” of state territoriality, of varied thickness and permeability (Billé 2017). Or, in other words, thinking topologically leads to problematizing differently the meaning of the hyphen in “Sino-Tibetan”: it can be likened to a Möbius strip where the two sides are in fact the same continuous surface.In the case of the Sino-Tibetan borderlands, the non-linear characteristic of this zone can be captured by a topological figure such as the Möbius strip that can perhaps help characterize how the constant “re-mapping” of such a border can be effectively addressed as spatial history. Using the Möbius strip as a metaphor enables us to challenge the fixity of the border and to point out its relational qualities: as a continuous surface, the Möbius strip aptly evokes the historical process through which border dynamics tend to produce new forms of territorialisation and re-ordering. If one starts on one side and follows the loop of the Möbius strip, one ends up on the other side, without having crossed a border. The Sino-Tibetan border, as an in-between place, substantiates the claim that the multiplicity of its constitutive relations “does not simply happen in the in-between” of power centres “but rather operates a topological continuum of the in-between” (Lury, Parisi, and Terranova 2012, 13, my emphasis). Thinking about in-betweenness in these terms leads to a productive deconstruction of the centre/periphery binary. Location is not what matters here as much as the relations themselves when deployed in a topological space whose features are expressed in a cultural vocabulary.The Möbius strip with its a priori paradoxical one-sidedness displays characteristics that, to go beyond mere metaphor, are congruent with processes that take place in the border zone. Firstly, this topological figure’s specificity is that the inside and outside are part of a single continuous space, yet they can nonetheless be identiﬁed as distinct sides at any one point or location. Secondly, there is a continuous exchange between what happens internally and what takes place outside. Thirdly, and because of this continuous exchange, sources of change are both internal and external, and produce transformations that allow relationships to be reproduced differently. In social topology, these continuities undergoing transformations constitute some of the main stimulating features as applied to power and its variable intensive reach (see Allen 2016), or more generally to how relations last despite continuous change (Martin and Secor 2014). When looking at the Sino-Tibetan border through this lens, what the Möbius topology points to—and this increasingly in the contemporary period—is that there is something else to see than two distinct sides reacting with one another, which is a movement between two interlocked conditions.[1]ReferencesAllen, John. 2016. Topologies of Power. Beyond Territory and Network. London: Routledge.Billé, Franck. 2018. “Skinworlds: Borders, Haptics, Topologies.” Environment and Planning D: Society and Space 36 (1): 60-77.Lury, Celia, Luciana Parisi, and Tiziana Terranova. 2012. “Introduction: The Becoming Topological of Culture.” Theory Culture Society 29 (4/5): 3–35.Martin, Lauren and Anna J. Secor. 2014. “Towards a Post-Mathematical Topology.” Progress in Human Geography 38 (3): 420-438. [1] I have pursued this exploratory work in my introductory chapter to the edited volume Frontier Tibet: Patterns of Change in the Sino-Tibetan Borderlands.