Mereology of Visual Form

Visual forms come in countless varieties, from the simplicity of a sphere, to the geometric complexity of a face, to the fractal complexity of a rugged coast. These varieties have been studied with mathematical tools such as topology, differential geometry and fractal geometry. They have also been examined, largely in the last three decades, in terms of mereology, the study of part-whole relationships. The result is a fascinating body of theoretical and empirical results. In this paper I review these results, and describe a new development that applies them to the problem of learning names for visual forms and their parts.