Three demonstrations are presented and used to support a number of apparently unrelated claims about the internal rejresentations that people have when they perceive or imagine a spatial structure. The first demonstration illustrates properties of the spatial working memory that enables us to integrate successive glimpses of parts of an object into a coherent whole. The second demonstration shows that our ability to generate a mental image is severely limited by the form of our knowledge of the shape of an object. The third shows that the shape representation which we create when we attend to a whole object does not involve creating the kinds of shape representations for the parts of the object that we would form if we attended to them and saw them as wholes in their own right. The real motivation for this medley of demonstrations and for the interpretations offered is that these phenomena can all be seen as manifestations of a particular kind of parallel mechanism which is described briefly in the last section.