Particularly, in this chapter, we look to make an initial case for the argument that the tools of computational topology can be effectively utilized to explore questions of constitution, textuality, and performativity for critical IR. To that end, the first section lays out an argument about the possible utility of thinking geometrically about concept formation and reification for post-structuralist IR, and possible ways to do that work. The second section introduces the concept of democracy in IR, and argues that it might be possible to gain leverage on the dimensions of the concept using computational topology to evaluate existing data. The third section shows the method in action, and sketches out some of the possible ramifications for studying democracy from a critical perspective. The concluding section makes a case for the value-added both for political methodology and critical theory of methodological explorations like this.