By slightly generalizing a notion of rank originally introduced in the context of metric tame dynamical systems by Glasner and Megrelishvili, we define an ordinal valued rank for the action of Aut(M) on the space of types over M, where M is a model of some theory T. We then investigate the relationship between this rank and the dividing lines in the model theoretic hierarchy, in particular we characterize NIP theories as those with non-infinite rank and stable theories as those with rank 0. This is joint work with Daniel Max Hoffmann.