One way to understand the topography of the cerebral cortex is that "like attracts like." The cortex is organized to maximize nearest neighbor similarity. This principle can explain the separation of the cortex into discrete areas that emphasize different information domains. It can also explain the maps that form within cortical areas. However, because the cortex is two-dimensional, when a parameter space of much higher dimensionality is reduced onto the cortical sheet while optimizing nearest neighbor relationships, the result may lack an obvious global ordering into separate areas. Instead, the topography may consist of partial gradients, fractures, swirls, regions that resemble separate areas in some ways but not others, and in not a lack of topographic maps but an excess of maps overlaid on each other, no one of which seems to be entirely correct. Like a canvas in a gallery of modern art that no two observers interpret the same way, this lack of obvious ordering of high-dimensional spaces onto the cortex might then result in some scientific controversy over the true organization. In this review, the authors suggest that at least some sectors of the cortex do not have a simple global ordering and are better understood as a result of a reduction of a high-dimensional space onto the cortical sheet. The cortical motor system may be an example of this phenomenon. The authors discuss a model of the lateral motor cortex in which a reduction of many parameters onto a simulated cortical sheet results in a complex topographic pattern that matches the actual monkey motor cortex in surprising detail. Some of the ambiguities of topography and areal boundaries that have plagued the attempt to systematize the lateral motor cortex are explained by the model.