Abstract: When are two collider events similar? In this talk, I will answer this question by introducing a natural metric between the radiation patterns of events. The metric is based on the well-known earth mover’s distance (EMD), and intuitively is the minimum “work” required to rearrange the energy flow of one event into the other. The EMD allows one to resolve the structure of an abstract "space of events" using a variety of tools for analyzing and visualizing events. Using jets at the LHC as an extended case study, I will highlight connections to the space of infrared and collinear safe observables, classification, dimensionality of event manifolds, and to machine learning and data visualization more broadly.