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This essay concerns the inevitability of contradiction and the resulting paradox that occurs in the modeling of complex phenomena in general and within medicine in particular. We address how encountering a logical impasse in the interpretation of experimental data using simple models, forces the development of next generation mega models, or theory, in order to resolve an empirical paradox. The challenge to overcome such a data-based complexity barrier was met in physics with the development of quantum mechanics at the beginning of the twentieth century in order to resolve the paradoxical properties light, resulting in a revolutionary new way to understand the physical universe. A no-less transformational understanding of the complex way the human body combats illness occurred in medicine somewhat earlier when Jenner determined that the way to protect against a life-threatening disease was to expose a patient to that very disease. What could be more paradoxical than a vaccine? This was the beginning of a science revolution in medicine, requiring the synthesis of multiple disciplines to understand what was demonstrably true about vaccinations. New theory entailed by the resolution of empirical paradox invariably leads to new kinds of knowledge that is incompatible with prior understanding and this was certainly the case in medicine. Herein it is argued that the source of complexity is criticality, which is the emergent collective behavior of natural systems, and it is the cooperative behavior of critical dynamics that ultimately resolves empirical paradox. Understanding how to systematically resolve such internal contradictions is a necessity if the progress of medical understanding is to outpace the technology on which much of today’s understanding is based.