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Learning To Think Spatially
Christaller brought these three streams of scholarship—necessity, history, and statistics—to bear on the problem of settlements. On the one hand, he was a theoretician, interested in explanations drawn from the intersections of geography, history, economics, and statistics and from the generalities of space. In so doing, he described himself as an “outsider” to all of these disciplines. On the other hand, he was an empiricist, drawn to the details of maps and regional landscapes, to the particularities of places (in this case, southern Germany in the 1930s).
What distinguished his particular approach was the interplay between theory and observation, driven by a remarkable capacity for spatial thinking. In his work, we can see a variety of complementary approaches: space as in graphics, space as in the description and analysis of patterns, space as in a structure for a model, and space as in algebraic relations in the form of hierarchies.
The observational component drew on the formative influences of his childhood. As he reports:
I continued my games with maps: I connected cities of equal size by straight lines, first of all, in order to determine if certain rules were recognizable in the railroad and road network, whether regular traffic networks existed, and, second of all, in order to measure the distances between cities of equal size. (Christaller, 1972, p. 607)
Maps again become tools for experimentation, the basis of a search for regularity, pattern, and rules. In this stage, Christaller was successful, identifying latticework patterns of spatial relationships that have become iconic and, to some geographers, beautiful: “Thereby, the map became filled with triangles, often equilateral triangles (the distances of cities of equal size from each other were thus approximately equal), which then crystallized as six-sided figures (hexagons)” (Christaller, 1972, p. 607).
He also identified a previously known spatial relationship whereby small towns were “… very frequently and very precisely 21 kilometers apart from each other.” The accepted explanation was based on a day’s travel by cart, the small towns serving as stopover points for travel between major cities. Understanding the reasons for the geometric pattern and this spacing regularity was the result of his theorizing, a step that took only nine months (see Figure 3.32).
The key to this step was an imaginative leap out of the real space of southern Germany into an abstract economic model of space: “a symmetrical plain, without obstructions such as rivers or mountain ranges, with a uniformly distributed population, in order to then determine where, under such conditions, the site of a central city or market would form” (Christaller, 1972, p. 608).
FIGURE 3.32 Diagram of a classic central place system (market areas: a K = 3 hierarchy). SOURCE: de Souza, 1990, p. 258.