Spatial Analysis through the Looking Glass

One of the delightful attractions that mathematics and geography have in common is that they offer fresh views of the world. Both fields of inquiry are circumspect almost by definition, and as soon as one looks around without prejudice, one discovers alternatives to one’s provincial world view. In mathematics, formalism and generalization are the seemingly sterile keys that open the gates to fertile fields of invention that, for its unexpected—even unexpectable—consequences, is indistinguishable from discovery. Formalism engenders the “what if” assumptions that lead to strange constructions, with their uncanny applicability to physics—non-Euclidean geometry, complex numbers, the Mandelbrot set. Generalization is the building of broader and broader analogies—the essence of cognition that Hofstadter has called ‘chunking” (Hofstadter 2002). The joy of mathematics is that one gets more than what one bargained for; one discovers connections that one did not anticipate. The net effect is that the familiar is seen anew, as a “special case”. In geography, one discovers cultural symmetry, and cultural asymmetry. One realizes that relations are not absolute, but dependent on location in space and in time. Unless one is very well indoctrinated, one develops a sense of the relative, even “accidental”, nature of one’s point of view. Science seeks to discover the laws which describe the rhythms and patterns of nature in time and space (Feynman 1967); in fact the essence of reality may be relations, or interactions, rather than any inherent objective attributes (Anandan 2003). In this spirit, I’d like to offer here an example of a geographic-analytic point of view that I think is a refreshing departure from the customary provincial point of view in spatial analysis.