Images that convert culture into physical space have a durable appeal, and numbers make it possible to literalize a spatial representation of culture by measuring the “distances” between cultural artifacts. But do cultural relationships really behave like physical distance? There are good reasons to think the analogy is imperfect, and a number of alternative geometries have been proposed—extending, in a few cases, to a systematic distinction between the mathematics of “embodied experience” and “epistemic experience” (Chang and DeDeo 2020). We test several proposed alternatives to spatial metrics against ground truth implicit in human behavior. While it is sometimes possible to improve on distance metrics, we do not yet find evidence that the information-theoretical measures recommended as appropriate for epistemic questions are generally preferable in the cultural domain.