The ability of deep learning (DL) to improve the practice of medicine and its clinical outcomes faces a looming obstacle: model interpretation. Without description of how outputs are generated, a collaborating physician can neither resolve when the model's conclusions are in conflict with his or her own, nor learn to anticipate model behavior. Current research aims to interpret networks that diagnose ECG recordings, which has great potential impact as recordings become more personalized and widely deployed. A generalizable impact beyond ECGs lies in the ability to provide a rich test-bed for the development of interpretive techniques in medicine. Interpretive techniques for Deep Neural Networks (DNNs), however, tend to be heuristic and observational in nature, lacking the mathematical rigor one might expect in the analysis of math equations. The motivation of this paper is to offer a third option, a scientific approach. We treat the model output itself as a phenomenon to be explained through component parts and equations governing their behavior. We argue that these component parts should also be "black boxes" --additional targets to interpret heuristically with clear functional connection to the original. We show how to rigorously factor a DNN into a hierarchical equation consisting of black box variables. This is not a subdivision into physical parts, like an organism into its cells; it is but one choice of an equation into a collection of abstract functions. Yet, for DNNs trained to identify normal ECG waveforms on PhysioNet 2017 Challenge data, we demonstrate this choice yields interpretable component models identified with visual composite sketches of ECG samples in corresponding input regions. Moreover, the recursion distills this interpretation: additional factorization of component black boxes corresponds to ECG partitions that are more morphologically pure.