Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
A Generative Theory of Shape
Generative theory of shape has two properties regarded as fundamental to intelligence - maximizing transfer of structure and maximizing recoverability of the generative operations. These two properties are particularly important in the representation of complex shape. The primary goal of this theory is the conversion of complexity into understandability. For this purpose, a mathematical theory is presented of how understandability is created in a structure. This is achieved by developing a group-theoretic approach to formalizing transfer and recoverability. To handle complex shape, a new class of groups is developed, called unfolding groups. These unfold structure from a maximally collapsed version of that structure. A principal aspect of the theory is that it develops a group-theoretic formalization of major object-oriented concepts such as inheritance. The result is an object-oriented theory of geometry. This talk will address the theory presented in his latest book, A Generative Theory of Shape.