The Information Geometry of Emergent Disease

Understanding complex disease requires a theory of emergence—how system-level pathology arises from molecular interactions. This effort has been hindered by a lack of mathematics capable of representing the stochastic, multi-scale, and causally asymmetric nature of biological systems. Here, we establish information geometry as the foundational framework for this task. We demonstrate that its intrinsic structures—statistical manifolds, the Fisher-Rao metric, and dually flat connections—directly encode the probabilistic nature of omics data, define invariant distances between clinical states, and formally separate mechanistic parameters from phenotypic outcomes. This mathematical correspondence supplies the missing first principles needed to transform medical AI from a correlative tool into a formal instrument for causal discovery, shifting the paradigm from fitting data to decoding the architecture of emergent disease.