Abstract: I will discuss "biological simplicity"---new laws of (statistical) physics emerging in complex living systems. I will give examples of such laws in systems with many interacting components, such as brains or viral-immune co-evolution. Trying to understand these laws in the framework of statistical physics of the more traditional, inanimate world will open up somewhat unexpected connections between the existence of biological simplicity and the success of modern machine learning in building models of big data sets. Finally, completing a full circle, I will discuss how random matrix theory, originally used by Wigner to explain spectra of heavy nuclei, may hold an explanation for some of these emergent laws.