Computing with Ambiguity

In a previous paper, emergence and ways of computing with emergence were discussed. Emergence goes hand in hand with ambiguity. Ambiguity, of a particular kind, is foundational in shape grammars. Shape grammars compute with shapes that have ambiguous or indefinite parts. This part ambiguity is exploited easily and well in shape grammar computations. Another kind of ambiguity is considered here. This is representational ambiguity—an ambiguity of the nature of the elements that make up shapes. Shapes are represented with elements—points, lines, planes, and solids—that can have ambiguous and fluid interpretations as material, conceptual, symbolic, or other entities. Like part ambiguity, representational ambiguity is integral to the beginning, exploratory stages of a design process. Among the best and most explicit treatments of representational ambiguity were those given by two prominent design theorists of the 20th century, Wassily Kandinsky and Paul Klee. Informal examples of representational ambiguity from the writings of Kandinsky and Klee are reviewed here. These are used to motivate ways of handling representational ambiguity computationally. New kinds of algebras for shape grammar computations that support some of the ambiguities suggested by Kandinsky and Klee, as well as other kinds, are proposed.