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Learning to Think Spatially: GIS as a Support System in the K-12 Curriculum
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SPATIAL THINKING IN EVERYDAY LIFE, AT WORK, AND IN SCIENCE 91
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).
Copyright © National Academy of Sciences. All rights reserved.
FIGURE 3.32 Diagram of a classic
central place system (market areas: a K
= 3 hierarchy). SOURCE: de Souza,
1990, p. 258.