The Residue of Model Reduction

(perhaps omitting quantum mechanics). The significance of this observation for hybrid systems is that the nominal description involving discontinuity is merely a convenient approximation at the relevant time scale which involves the (unmodelled?) neglect of dynamics on any faster time scales — whose details are then necessarily lost in the process of model reduction. We will argue that some residue of these details must be retained to understand, in certain contexts, what will actually occur when these hybrid strategies are to be implemented in the real world. For example, at a familiar level we think of the thermostat in an electric heater as simply switching the element on or off discontinuously, but it is certainly possible to ‘open the box’ and consider in more detail, if desirable, the