 Of course, we do not have perfect models. But even if we did, they are unlikely to live up to our intuitions about them (Judd and Smith 2001; Judd and Smith 2004). For example, no matter how many observations of a system are made, there still will be a set of trajectories in the model state space that are indistinguishable from the actual trajectory of the target system. Indeed, even for infinite past observations, we cannot eliminate the uncertainty in the epistemic states given some unknown ontological state of the target system. One important reason for this difficulty follows from the faithful model assumption. Suppose the nonlinear model state space is a faithful representation of the possibilities lying in the physical space of the target system. No matter how fine-grained we make our model state space, it will still be the case that there are many different states of the actual target system (ontological states) that are mappable into the same state of the model state space (epistemic states). This means that there will always be many more target system states than there are model states for any computational models since the equations have to be discretized. In principle, in those cases where we can develop a fully analytical model, we could get an exact match between the number of possible model states and the number of target system states. However, such analytical models are rare in complexity studies (many of the analytical models are toy models, like the baker’s map, which, while illustrative of techniques, are misleading when it comes to metaphysical and ontological conclusions due to their simplicity). 