One of the challenges for perceptually grounded accounts of high-level cognition is to explain how people make connections and draw inferences between situations that superficially have little in common. Evidence suggests that people draw these connections even without having explicit, verbalizable knowledge of their bases. Instead, the connections are based on sub-symbolic representations that are grounded in perception, action, and space. One reason why people are able to spontaneously see relations between situations that initially appear to be unrelated is that their eventual perceptions are not restricted to initial appearances. Training and strategic deployment allow our perceptual processes to deliver outputs that would have otherwise required abstract or formal reasoning. Even without people having any privileged access to the internal operations of perceptual modules, these modules can be systematically altered so as to better subserve our high-level reasoning needs. Moreover, perceptually-based processes can be altered in a number of ways to closely approximate formally sanctioned computations.