Xperiential and F Ormal M Odels of G Eographic S Pace

This paper is concerned not with space and spatial relations as objective entities of the world, but rather with human experience and perception of phenomena and relations in space. The goal arising from this concern is to identify models of space that can be used both in cognitive science and in the design and implementation of geographic information systems (GISs). Experiential models of the world are based on sensorimotor and visual experiences with environments, and form in individual minds as the associated bodies and senses experience their worlds. Formal models consist of axioms expressed in a formal language, together with mathematical rules to infer conclusions from them. The paper reviews both kinds of models, viewing them each as abstractions of the same 'real world.' The review of experiential models is grounded in recent developments in cognitive science, expounded by Rosch, Johnson, Talmy, and especially Lakoff. Among other things, these models suggest that perception and cognition are driven by schemata and other mental models, often language-based. These models form a framework for a review of models of small-scale spaces filled with everyday objects. The ways in which people interact with such spaces is in sharp contrast to the bit-by-bit experience with geographic (large-scale) spaces during wayfinding and other spatial activities. The paper then addresses the issue of the 'objective' geometry of geographic space. If objectivity is defined by measurement, this leads to a surveyors' view, and a near-Euclidean geometry. The paper then relates these models to issues in the design of GISs. To be implemented on digital computers, geometric concepts and models must be formalized. The idea of a formal geometry of natural language is discussed, and some aspects of it are presented. Formalizing the link between cognitive categories and models on the one hand, and geometry and computer representations on the other is a key element in the research agenda. 2 INTRODUCTION Spatial relations do not exist in the real world; rather, they exist in minds, to aid in making sense of the world, and in interacting with it. Our concern therefore is not with space and spatial relations as objective entities of the world, but rather is with human experience and perception of phenomena and relations in space. This is a strong statement, and one which appears to be at odds with the positivist paradigm. However, in this paper, we present an approach from cognitive science, and apply it …