 In our ordinary discourse, we distinguish between physical systems that perform computations, such as computers and calculators, and physical systems that don’t, such as rocks and raindrops. Among computing devices, we distinguish between more and less powerful ones. These distinctions are of both practical and theoretical importance: a supercomputer can compute in minutes what would take decades on a laptop, while a calculator cannot do certain things that a laptop can do, even in principle. What grounds these distinctions? What is the principled difference, if there is one, between a rock and a calculator, or between a calculator and a computer? Answering these questions is more difficult than it may seem.