Humans exhibit a fundamental propensity to interact for social, cultural, technological, and other reasons. In this paper we seek to determine when the propensity to interact, expressed in the form of a spatial externality, becomes strong enough to induce agglomeration. We design an abstract world where the only possible reason for agglomeration is the spatial externality. In this world the uniform population distribution is a steady-state. Then to ask under what circumstances does a spatial externality induce agglomeration is to ask under what circumstances does it induce an instability of the steady-state: anything other than a uniform steady-state implies some agglomeration.