Becoming Euclid: Connecting Core Cognition, Spatial Symbols, and the Abstract Concepts of Formal Geometry

Abstract

Humans alone are capable of formal geometry, like the one outlined in Euclid’s Elements. We can conceive of points so infinitely small they have no size and lines that extend so infinitely far they never end. And yet, we conceive of such “points” and “lines” without having ever perceived them. Where, then, do such geometric concepts come from? This dissertation asks whether and in what way phylogenetically ancient and developmentally precocious “core” geometric representations guiding navigation and form analysis in humans may come to support uniquely human symbolic and abstract geometric thought. It does so by investigating children’s capacity for interpreting the geometric information presented in simple maps and pictures in the context of the scenes and objects that these symbols represent. The dissertation comprises three papers, framed by an introduction and a concluding chapter. Paper 1 (Dillon, Huang, & Spelke, 2013) investigates whether young children’s use of core geometric information to navigate scenes and analyze the shapes of visual forms correlates with their ability to use geometric information presented in simple overhead maps of fragmented triangular environments. Paper 2 (Dillon & Spelke, 2015) probes the connections between young children’s use of core geometry and their interpretation of highly realistic photographs and perspectival line drawings of scenes and objects. Paper 3 (Dillon & Spelke, 2016) measures the flexibilities, limitations, and automaticity with which children use core geometry when interpreting pictures of scenes and objects. The concluding chapter reevaluates children’s engagement with spatial symbols in light of these three papers, proposing an account of how this engagement changes through development and how such developmental change might provide clues to the origin of abstract geometric reasoning. While the three papers concern children’s comprehension of the geometry in spatial symbols, the concluding chapter also speculates on how our production of spatial symbols might reflect the core systems of geometry and, as a result, might explain a peculiar dearth in the representation of large extended surfaces (“landscapes”) throughout the history of human pictorial art.