  When are two collider events similar? Despite the simplicity and generality
of this question, there is no established notion of the distance between two
events. To address this question, we develop a metric for the space of collider
events based on the earth mover's distance: the "work" required to rearrange
the radiation pattern of one event into another. We expose interesting
connections between this metric and the structure of infrared- and
collinear-safe observables, providing a novel technique to quantify event
modifications due to hadronization, pileup, and detector effects. We showcase
how this metrization unlocks powerful new tools for analyzing and visualizing
collider data without relying upon a choice of observables. More broadly, this
framework paves the way for data-driven collider phenomenology without
specialized observables or machine learning models.
