Geometries of Desire: Simulating René Girard’s Mimetic Theory

Abstract

In this paper, I develop the first computational model of René Girard’s mimetic theory, an influential account of the social psychology of imitation. Girard argues that many forms of desire are socially learned and ought to be understood in terms of a triangular relationship between a desiring subject (S), a mediator (M), and a desired object (O). Mimetic theory is widely applicable to advertising, social influence, identity formation, character psychology, financial markets, and geopolitical soft power. I begin by translating Girard’s framework into the formalism of directed graphs—what I call “mimetic networks”—by representing mediation and desire relationships between agents as directed out-links. I use simulation to explore network dynamics, demonstrating the conditions under which the model arrives at stability—what I term a “Nash Equilibrium of Desire.” I also explore the effect of cascades, narcissists, and self-mediating agents and show that mimetic networks have globally emergent properties—notably, the tendency for all agents to converge on a single, universal object of desire (“Convergence of Desire”). In the appendix, I develop a set of mathematical definitions and theorems regarding mimetic networks. This paper is aimed at an intentionally multi-disciplinary audience, including social scientists, complex systems and network theorists, philosophers, narratologists, and literary and cultural critics.