# Crosscuts

From the Series: Topology as Method

My interest in topology is twofold. First, to discern whether, by analogy or directly, topological thinking might inform how some people arrange spatial relations and separations, which in turn might affect how they, and perhaps others, experience the meaning and relative value of their locations. Second, I am interested in how the co-existence of other ways of thinking, which are not topological, affects such spatial doings that have been informed by topological thinking. These two interests are different from drawing upon topology as a source of metaphors. Instead, I am exploring how topological logic might inform spatial relations and separations.

Drawing on this approach, the title of this text, “Crosscuts,” refers to the spatial effects of topological thinking in the world, starting from the premise that such thinking co-exists with other ways of thinking. Topology can be crudely defined as “the study of malleable shapes,” in contrast to Euclidean geometry, which is the study of rigid objects (Richeson 2008, 2). Topology provides a means to think about spatial abstraction differently: a cube can be described geometrically or topologically. Within topology, a cube is the same as a pyramid or sphere (imagine reshaping a plasticine cube); within geometry, they are different. Neither geometry nor topology changes the cube; but they change how people think about it, which might change what people do with it, how they classify it, and how they involve it in other things in their lives.

To demonstrate how this approach could be drawn upon in anthropology, I briefly describe four cross-cutting logics that inform how long-term residents of Lesvos locate themselves in the Aegean, as reflected in maps, ideas of nation, kinship, and an Archangel.

## Maps

Geographically, Lesvos is located in the north Aegean, opposite the Turkish coast. Politically, Lesvos is both a part of Greece and a part of the European Union and Schengen zone, which separates the island from Turkey in three ways: by state, by EU membership, and by Schengen regulations. Commonly available maps, including Google Maps, only partially show these multiple separations (they show state borders rather than EU/Schengen borders). Though they are not made visible on the maps, these three different kinds of separation are important to anyone crossing the Aegean Sea.

The state borders and EU borders follow a Euclidean geometrical logic, not a topological one: they mark what are intended to be rigid shapes, emphasizing separation and difference between the sides. In terms of actual maps, it is easy to see how Euclidian geometrical thinking has been directly drawn upon in constructing that particular cartographic form. Although the location of the lines is often disputed in the Aegean, the logic of rigid shapes is built into this kind of mapping. Yet Schengen, as an idea, is supposed to allow more flexibility of movement, removing state boundaries for people moving between states within the zone. There is an implied topological-geometrical crosscut within Schengen space.

## Nation

In the Aegean, the idea of nation has strongly informed the separation of Greece from Turkey after the final breakup of the Ottoman empire, which led to a compulsory exchange of populations that separated Greek Orthodox peoples from Turkish Muslim peoples (Hirschon 2003). This separation literally followed the political map and realigned people so that they now matched, and reinforced, that geometric logic of separation.

## Kinship

In the Aegean, the topological analogies that might be interesting for kinship are those of cutting and gluing: a shape can be deformed while remaining topologically the same unless it is cut or glued, at which point it becomes topologically different from what it was before. Within kinship, rules for separating relations from non-relations (cutting), and for creating new relations (gluing) are essential.1 The topological analogy here would imply that kinship is constantly morphing into something different; what stays the same is the logic, which is built upon relations and separations between the parts.

This built-in cutting/gluing logic, this axiomatic capacity for kinship to generate something different, means that principles of kinship can easily be borrowed for cutting and gluing purposes within other logics. At the moment of the political creation of contemporary Greece and Turkey as separate states, in the Aegean, kinship was strongly drawn into ideas of both nation (fatherland/motherland, blood, and soil) and religion: the teachings of both Orthodoxy and Islam are replete with genealogies taken from kinship, and religious affiliation was used as the basis for separating populations in the Lausanne Treaty. Kinship both crosscut and became indelibly entangled with both of them, generating a spatial logic of relations and separations across the Aegean.

## An Archangel

The Archangel Michael, more often called Taxiarchis (the Brigadier) within Greek Orthodoxy, is the Patron Saint of the Aegean within the Orthodox Church. He is also an Archangel within the Islamic and Jewish traditions. While religious affiliation was the criterion used to separate populations between the two sides of the Aegean, the Archangel remained on both sides. Both populations recognized the two Archangels as also being one Archangel, so he was already always on both sides, there was no way of separating him or removing him. By analogy, Michael/Taxiarchis could perhaps be described in topological terms: different shapes of the same Archangel, crosscut by the decidedly non-topological geometric logic of nations and maps: a national-cartographic separation crosscut by an Archangel connection.

### Note

1. A pair of Marilyn Strathern’s articles draw this out particularly clearly (see Strathern 1995, 1996).

### Acknowledgments

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 694482). See https://www.helsinki.fi/en/researchgroups/crosslocations.

## References

Hirschon, Renée, ed. 2003. Crossing the Aegean: An Appraisal of the 1923 Compulsory Population Exchange between Greece and Turkey. New York: Berghahn Books.

Richeson, David S. 2008. Euler’s Gem: The Polyhedron Formula and the Birth of Topology. Princeton, N.J.: Princeton University Press.

Strathern, Marilyn. 1995. The Relation: Issues in Complexity and Scale. Cambridge: Prickly Pear.

–––. 1996. “Cutting the Network.” Journal of the Royal Anthropological Institute 2, no. 3: 517–35.