Rate Distortion Control Theory, aimed at minimizing disjunction between what is wanted and what is achieved, and ‘ordinary’ control theory, based on the Data Rate Theorem and aimed at preventing instability, provide distinct, but related, perspectives on embodied systems, i.e., those that must act in, while becoming part of, an enfolding environment. We suggest here that deeper and more general mathematical concepts and concerns, in particular those related to more subtle symmetry-breaking phase transitions, can cover a far wider spectrum of possible dynamic behaviors and make significant contributions to the understanding, control, and remediation, of critical embodied systems across a broad range of scales and levels of organization.