shared by the views (Tversky, 2003). Expertise in dealing with three-dimensional representations is, like pattern recognition, also domain specific.

Buildings and devices are three-dimensional structures; so architects and product designers face the challenge of three-dimensional thinking. They cope with the challenge by externalizing thought to the sketch-pad or computer screen, working with a series of two-dimensional slices. This is, of course, what radiologists do; they examine two-dimensional images of the human body. For architecture, there is a canonical set of two-dimensional slices: plan, elevation, and cross section. The slices facilitate design by simplifying a three-dimensional problem to a standard set of two-dimensional ones. Each slice serves different functions in the design process (Arnheim, 1977; O’Gorman, 1998). Plans or overviews capture spatial relations among the rooms of a building or among the buildings, open spaces, and paths of a complex. They are important for understanding the functions of the structure because they show the proximity of rooms or buildings to each other and ways to navigate among them. Elevations show how a building or complex will appear; the outside skin establishes the aesthetic value of the building. Finally, cross sections show how the infrastructure—for example, plumbing, heating and air-conditioning systems—interconnects parts of the structure.

Design in architecture is facilitated by partitioning three-dimensional space into two-dimensional representations. Architects typically begin with sketches of plans or overviews of the site. Early in the process, architects like to keep designs sketchy, literally and figuratively. They do not want to commit too soon to specific shapes or exact spatial relations. Sketches are a test bed for architects (Goldschmidt, 1994; Schon, 1983). Architects begin with an idea and turn it into a sketch. When they inspect the sketch, they often see spatial features and relations that they did not explicitly design, but that were a consequence of other design decisions (Suwa et al., 2001). Unintended spatial features and relations have implications that may or may not be desirable. As a consequence of such discoveries, architects revise ideas. They re-sketch the building and critically reexamine the new sketches. Architects interact with the sketches in a kind of conversation that refines their ideas (Goldschmidt, 1994; Schon, 1983). Experienced architects are more expert at this conversation. They get more new ideas from examining sketches than do novice architects. They see more functional implications than do novices (Suwa and Tversky, 1997). For example, experts see functional information such as changes in traffic flow and lighting throughout the day and year. Novice architects are less likely to make functional inferences from sketches. As is true for pattern recognition, considerable experience is needed to “see” behavior or function in sketches. For pattern recognition, the necessary information is in the depiction; experts learn to pay attention to the right features in the right organization. In the case of architecture, information about traffic flow or lighting is not in the depiction; it must be inferred from the depiction. The inference process is analogous to the expertise required to read written text or music. The sounds and meanings of words and notes must be derived from the depictions, and this process requires training and practice.

As architects’ ideas become more refined, sketches become more specific. The three-dimensional task of the architect is, therefore, simplified by the set of two-dimensional layers. It turns out, however, that simplification—division into planes—serves design in another important way because the different planes also correspond to differing sets of design considerations. Plans determine how people will navigate a building; elevations determine how a building will look; cross sections determine how the infrastructure is organized.

Air traffic control is another profession that requires spatial thinking in three dimensions. The process is even more difficult because of the added dimension of time; controllers must operate in three-dimensional space-time. Aircraft are in motion, so controllers must keep track of the changing positions of numerous aircraft at different and changing altitudes, speeds, and directions. As in the case of commuting routes on the ground, the key to success in the air is simplifying the

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