From molecular motions within a cell to gene expression and neural activity, the living world is a teeming dance of heterogenous, interconnected components. But how can we understand the remarkable diversity of biological forms and functions? And what is the role of a physical perspective? I address these questions on the scale of entire organisms where the effects of such dynamics are quantifiable through posture tracking from deep machine vision. I describe a framework which fuses dynamical systems, statistical physics and information theory with precision measurements to identify important behaviors and their meaning, and I demonstrate this approach in the wiggling of the nematode C. elegans. We find a low-dimensional and chaotic phase space with a symmetric Lyapunov spectrum, and spanned by three sets of unstable orbits corresponding to forward, reverse and turning locomotion. Within this space, we construct a Markov dynamics which is also predictive of long-time behavior transitions. Our “inverse” approach, where observed behavior is used to infer underlying dynamics, offers a general strategy with which to seek effective theories and emergent principles of complex, evolved systems.