A Link between Cartographic Theory and Mapping Practice: The Nearest Neighbor Statistic

C ARTOGRAPHERS and map makers are concerned with the accurate portrayal, by automated equipment, of the form of a quantitative distribution for which they have a finite number of values distributed at points in an area.' More often than not these data, or control points, are irregularly spaced, and the research worker has several alternative automated methods that he can use to construct, or infer, the form of the distribution. Although a different map may be produced by each of these different methods, no readily available answers to many practical questions exist. On the one hand, underlying the various methods we have the basic concepts, many of which are quite simple, and certain general relative statements may be deduced from these concepts. On the other hand, procedures that facilitate the application of the various cartographic methods have been devised for the map maker and are almost universally used. These procedures usually consist of "rules of thumb," which are not necessarily deduced from the basic concepts of a mapping technique, and in most instances it has been the practical procedures that have been modified to permit automation.2 The principal reason for the practical procedures is that the statements deduced from the various mapping-technique theories are defined only in gross relative terms that machines cannot handle, and for the most part these statements are of little use to the practicing map maker. Commonly the statements deduced from theory have paralleled the practical procedures, though neither has shown great advances, and the teaching of cartography has tended to perpetuate this parallel development by focusing on the theory in lectures and on the practical procedures in laboratory work. Rarely have the two been related.