Domain-Specific Cognitive Systems Underlying Geometric Knowledge

The use of geometric properties of both large-scale environments (in navigation) and small-scale objects (in object recognition) has been found across many distantly related species of animals and from very early stages of development. We discuss the nature of these two systems of core spatial geometry, the specificity observed in each system in their geometric content, and their potential role in the development of abstract Euclidean concepts in humans. First, we present evidence that the geometric analysis of the navigable environment for the computation of orientation (often referred to ask the ‘geometric module’) is an evolutionarily ancient process that specifically takes as input extended 3D surfaces and computes their relative distances and directions but not angle or length relationships. We then show that the geometric analysis of manipulable objects is different from that of large-scale environments because angle, distance, and length relationships are successfully used in object-shape analysis, while directional relationship are not. While the two core systems shown above each represent a specific and limited subset of geometric properties, humans share universally Euclidean geometric intuitions, even in the absence of explicit training or education. We end by suggesting that our abstract representations of geometry may be constructed from the core spatial representations, which we share with other animals, through uniquely human linguistic and symbolic capacities.