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Any effective model of a nontrivial portion of the nervous system cannot possibly account in detail for the activity of individual cells. We have developed an approach to modeling cortical systems by taking advantage of the regularities of the macrostructure and the stochastic nature of the spatial microstructure and temporal activity. A gross linear or nonlinear description is found for the local activity of neural tissue. If the local activity can be described by a function which is linear in space and time, then this can be convoluted with any spatiotemporal input pattern to predict the output. When applied to the cerebellar cortex this approach has resulted in a model analogous to an anisotropic spatial filter with interesting temporal properties. The model predicts that the cerebellar cortex will enhance the detail (in space and time) of any input pattern. However, the form of the spatial transfer function depends on the temporal frequency of the input and vice-versa.