Landy, D. & Goldstone, R. L. (2007). Grounding symbol structures in space: Formal notations as diagrams. Proceedings of the Twenty-ninth Annual Conference of the Cognitive Science Society.(pp. 425-430). Nashville, TN: Cognitive Science Society.
[Winner of the 2007 Marr Prize for Best Student Paper at the 2007 Meeting of the Cognitive Science Society]
Although a general sense of the magnitude, quantity, or numerosity is common both in untrained people and animals, the abilities to deal exactly with large quantities and to reason precisely in complex but well-specified situations—to behave formally, that is—are skills unique to people trained in symbolic notations. These symbolic notations employ typically complex, hierarchically embedded structures, which all extant analyses assume are the product of concatenative, rule-based processes. The primary goal of this article is to establish, using behavioral measures on naturalistic tasks, that the some of the same cognitive resources involved in representing spatial relations and proximities are also involved in representing symbolic notations. In short, formal notations are used as a kind of diagram. We examine selfgenerated productions in the domains of handwritten arithmetic expressions and typewritten statements in a formal logic. In both tasks, we find substantial evidence for spatial processes even in these highly symbolic domains.