Morphological Representation Hypothesis (MRH): Self-Supervised Representations for Physical Discovery from Information-Rich Observations

Physical discovery frequently begins with measurements that are spatially information-rich yet dynamically incomplete: a 2D passive tracer, projected column density, or an intensity field, rather than the full state variables appearing in first-principles equations. This raises two questions: *which patterns in an observation are interesting enough to become physical questions?* and *how can information in observations be used efficiently rather than compressed into degenerate summaries?* The first is traditionally called insight; the second is acute in information-rich physical data. Inefficient information use blinds observations to relevant structure and limits how competing theories can be tested. We propose the Morphological Representation Hypothesis (MRH): self-supervised learning (SSL) organizes the spatial and multiscale information in an observable into a physically meaningful representation that preserves physically relevant organization. In the Keller–Segel model, the learned embedding exhibits equation-space correspondence; in magnetohydrodynamic (MHD) turbulence, learned morphological neighborhoods exhibit lower average distances in dimensionless physical diagnostic space than density-matched or random neighborhoods. These results illustrate how learned morphological coordinates can organize physical information and support subsequent quantitative analysis and the formulation of physical questions.