FIGURE 2.5 An information landscape depicting demographic similarities and differences between the 50 states. The high peak at the front represents California, which is very different from all other states. Image produced using a self-organizing map (neural network) and data from the 2000 Census.

2.4 THE THREE FUNCTIONS OF SPATIAL THINKING

Spatial thinking serves three purposes. It has (1) a descriptive function, capturing, preserving, and conveying the appearances of and relations among objects; (2) an analytic function, enabling an understanding of the structure of objects; and (3) an inferential function, generating answers to questions about the evolution and function of objects.

The power of spatial thinking resides in its capacity to provide an understanding of structure and of function. By an understanding of structure is meant a description of how something is organized—what part is where in relation to other parts. We can capture the arrangement of objects in space and speak about order, relation, and pattern. By function is meant an understanding of how and why something works. It can express how something changes with time (kinematics) and allow us to explain the reasons for the changing arrangements of time-varying spatial patterns (dynamics). Therefore, spatial thinking is not static. It is a dynamic process that allows us to describe, explain, and predict the structure and functions of objects and their relationships in real and imagined spatial worlds. It allows us to generate hypotheses, to make predictions, and to test their consequences.

The archetypal case of a spatial representation is a cartographic map, and we can see the three functions of spatial thinking at work in map reading and interpretation. The most commonly available map form, a road map, provides a two-dimensional picture of part of the world, depicting places and the roads that connect them. Spatial thinking is the analytical and inferential process that allows us to select a route connecting two places subject to criteria such that the route is easy to follow (e.g., contains a minimum number of decision points [intersections, turns, etc.]) and that it



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