Cellular Geography

Abstract

Captain Ahab, in the film version of Moby Dick, searches for the white whale with the aid of a geographical map on which are noted sighting-frequencies within 5° cells bounded by lines of latitude and longitude. The written version of the story, dating from circa 1830, does not contain this scene, but the technique of recording geographical data in this fashion is increasingly popular today. One of the motivations for the use of such partitionings is their ‘objectivity’. It is also asserted that there are advantages for analysis purposes over the irregular spatial polygons defined by political jurisdictions. There is no doubt that there are notational simplifications; one can index a cell of an array in the same fashion as in matrix algebra. Thus the cell in the ith row and jth column becomes the cell i,j. Geographical data which pertain to that cell can be referred to by subscripts, as g _ij for example. If one lets G represent an N by M array of such cells then this can be considered isomorphic with a portion of the surface of the earth (if one deletes the poles and makes a convention about the edges). But one can also apply matrix algebra to this array and can obtain geographically interesting results. The major advantage however is pedagogical, and results from the fact that in such a scheme every country in the world has exactly the same number of neighbors. The analytical results can be extended to the more realistic variable-number-of-neighbors case but the insight is more easily gained in the cellular case.

A condensed translation of a lecture “Schachbrette Modelle in der Geographie” presented to the Arbeitskreis fur neue Methoden in der Regionalforschung, Wien, 17 April 1975.