Towards a modeling view of computing

The view that the brain computes is a working hypothesis in cognitive and brain sciences. But what does it mean to say that a system computes? What distinguishes computing systems, such as desktops and brains, from (arguably) non-computing systems, such as stones, stomachs and tornadoes? This question has generated an intense and lively discussion in recent years, and, as expected, there is no consensus over the answer. In fact, it is far from clear that there is only a single notion in play; it might well be the case that the term "computation" invokes very different notions in different contexts. Most accounts of computing are "structural", in the sense that they take it that the difference between computing and non-computing has something to do with the structure of the mechanism, e.g., that computing processes have an algorithmic structure. I present the structural view of computing in section 1. As it turns out, however, the structural approach cannot account for much of the computational work in cognitive and brain sciences; I discuss this claim in section 2. There is thus a need for an alternative approach to computing, one that can take into account the current enterprises in computational cognitive neuroscience. My aim in section 3 is to sketch such an alternative, which is the modeling view of computing. The key feature of the modeling view is that computing consists in an isomorphism between the "inner" relations, defined over the representing states, and "outer" relations, defined over the represented states.