Geometry as Transfer

Abstract

It is generally accepted that intelligent action involves considerable use of transfer. For example, Carbonell [1] has argued that learning proceeds by analogical reasoning; Rosch [12] has argued that categorization proceeds by seeing objects in terms of prototypes; and Leyton [9] has argued that the human perceptual system is organized as a hierarchy of transfer. The role of geometry is also seen as fundamental to the representations produced by the cognitive system. For example, Gallistel [2] has elaborated the powerful role of geometry in animal learning and navigation; Lakoff [3] has emphasized the role of geometry in semantics; and Leyton [9] has proposed an extensive role for geometry in causal explanation. We bring together the two above factors, transfer and geometry, in the book, Leyton [10], by developing a generative theory of shape in which transfer is a fundamental organizing principle. In this approach, transfer is basic to the very meaning of geometry. The purpose of the present paper is to give an introduction to this transfer-based theory of geometry.