  However, note that some crucial assumptions are being made here. We are assuming, for instance, that a state of a system is characterized by the values of the crucial variables and that a physical state corresponds via these values to a point in state space. These assumptions allow us to develop mathematical models for the evolution of these points in state space and such models are taken to represent (perhaps through an isomorphism or some more complicated relation) the physical systems of interest. In other words, we assume that our mathematical models are faithful representations of physical systems and that the state spaces employed faithfully represent the space of actual possibilities of target systems. This package of assumptions is known as the faithful model assumption (e.g., Bishop 2005), and, in its idealized limit—the perfect model scenario—it can license the (perhaps sloppy) slide between model talk and system talk (i.e., whatever is true of the model is also true of the target system and vice versa). In the context of nonlinear models, faithfulness appears to be inadequate   (§3).