A science of topography: From qualitative ontology to digital representations

Mountains are among the most prominent of geographic features (Smith and Mark, 2001). They also have social and emotional significance, serving as objects of worship in many cultures and as landmarks in many more. And, of course, mountains provide challenges to adventurers and scientists alike. Thus it should come as no surprise that geomorphologists and other environmental scientists have been drawn to mountains in conducting their research. But what exactly are mountains; what is their ontology, or the nature of their reality? Certainly, mountains are not among the most typical examples of objects. Typical objects (apples, people, cars) have distinct, complete, closed boundaries that separate them spatially from their surroundings. Mountains, in contrast, have crisp boundaries only with the atmosphere above. Where they meet the earth below and laterally, typical mountains do not have crisp boundaries that separate them sharply from their surroundings. Instead, each mountain blends gradually into neighboring mountains, or fades into foothills or plains and into the body of the Earth beneath (which itself is a prototypical object, its boundary being constituted by an irregular crust whose surface has concave and convex regions).i But do mountains exist as objects of study in their own right? Cartographers have long avoided the problems raised by the absence of crisp boundary delimitations in the case of mountains by representing the latter indirectly. The summit of the mountain is often marked on a map by a point symbol, which may have an associated name or elevation. In addition, the general shape of the mountain may be indicated by contours or hill shading, but the limits (horizontal