A study regarding the spontaneous use of geometric shapes in young children’s drawings

Studies on the ontogenetic origins of human knowledge provide evidence for a small set of separable systems of core knowledge dealing with the representation of inanimate and animate objects, number, and geometry. Because core knowledge systems are evolutionarily ancient, they can be investigated from a comparative perspective, making use of various animal models. In this review, I discuss evidence showing precocious abilities in nonhuman species to represent (a) objects that move partly or fully out of view and their basic mechanical properties such as solidity, (b) the cardinal and ordinal/sequential aspects of numerical cognition and rudimentary arithmetic with small numerosities, and (c) the geometrical relationships among extended surfaces in the surrounding layout. Controlled rearing studies suggest that the abilities associated with core knowledge systems of objects, number, and geometry are observed in animals in the absence (or with very reduced) experience, supporting a nativistic foundation of such cognitive mechanisms. Animal models also promise a fresh approach to the issue of the neurobiological and genetic mechanisms underlying the expression of core knowledge systems.

For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core cognitive systems for representing the shapes of large-scale, navigable surface layouts and of small-scale, movable forms and objects. Each of these systems applies to some but not all perceptible arrays and captures some but not all of the three fundamental Euclidean relationships of distance (or length), angle, and direction (or sense). Like natural number (Carey, 2009), Euclidean geometry may be constructed through the productive combination of representations from these core systems, through the use of uniquely human symbolic systems.