 By contrast, most uses of computation in science and ordinary practice deal with concrete computation: computation in physical systems such as computers and brains. Concrete computation is closely related to abstract computation: we speak of physical systems as running an algorithm or as implementing a Turing machine, for example. But the relationship between concrete computation and abstract computation is not part of the mathematical theory of computation and requires further investigation (cf. Curtis-Trudel forthcoming-a, for an argument that abstract and concrete computation cannot be given a unified account).  Questions about concrete computation are the main subject of this entry. Nevertheless, it is important to bear in mind some basic mathematical results.