The talk is based on a 1990 Phys. Rev. milestone paper Scientists attempt to understand physical phenomena by constructing models. A model serves as a link between scientists and nature, and one basic goal is to develop models whose solutions accurately reflect the nature of the physical process. But a dynamical model uses simplifying assumptions and approximations. The question of whether a model accurately reflects nature is one constantly faced by scientists. I will argue that there exist levels of mathematical difficulty, brought from the theory of dynamical systems, which can limit our ability to represent chaotic processes in nature using deterministic models. Specifically, in such cases, no model of such a system produces solutions of reasonable length that are realized by nature. Furthermore, for these processes, the numerical solutions of the models do not approximate any actual model solutions.