How to Solve Unsolvable Problems in Physics

Real-world systems are complicated. Much more complicated than any fundamental physics model can handle. Take, for example, a simple glass of water. This glass of water has an unimaginable number of molecules, each made up of several individual atoms which are themselves made up of their own constituent particles. Trying to explain this system with, say, fundamental particle physics would be an impossible feat, even with access to all of the world's strongest supercomputers. So how do we go about solving these unsolvable problems? We resort to statistical mechanics!