orientation is often critical to identifying what something is, for example, distinguishing a letter M from a W, a b from a d, or a diamond from a square. Similarly in science and engineering, ascertaining orientation is an essential spatial judgment: in chemistry, for identifying molecules and predicting their behavior; in geology, for identifying rock strata and inferring the conditions that produced them; in building design, for identifying sources of light and predicting their seasonal and daily changes.

Representations: The Relations Between Dynamic Entities The world is not static, and the mind finds ways to encode, interpret, and represent moving objects. Evaluating characteristics of a dynamic entity is also done with respect to other entities or to a frame of reference. Dynamic features that can be evaluated include the following:

  • direction of movement,

  • manner of motion,

  • speed or acceleration, and

  • intersection or collision.

Evaluating direction of movement can be critical for survival: Is an object headed toward me? Is that beast turning around? Note that encoding change in size can underlie perception of direction of movement; thus, if something is growing larger, it is likely to be coming closer. The direction in which something animate is going is a clue to the organism’s intent: Is the motion toward a restaurant or a movie theater? Evaluating direction of movement underlies scientific reasoning as well, for example, the directions of tectonic plates or weather fronts.

Evaluating manner of motion is important for understanding the world; manner of motion distinguishes one animal from another—indeed, one individual human being from another. Running, swaggering, stumbling are all clues to the state of another person. Differences in manner of motion distinguish different physical entities, the weight and shape of rocks for example. Manner of motion can diagnose an unhealthy heart or, on a more abstract level, an irregular electroencephalogram (EEG).

Each of these judgments about relations among dynamic entities plays a role in everyday interactions in the world, in walking along crowded streets and in driving on the highway; in avoiding flying objects or trying to catch them in baseball (McBeath et al., 1995) or return them in tennis. These judgments underlie scientific inferences as well, in understanding the operations of a machine, anticipating weather conditions, or predicting traffic flows and bottlenecks.

Transformations of Representations of Entities These encoding operations establish mental representations of the spatial world. A powerful feature of spatial thinking is transforming, manipulating, and operating on representations. By mentally extrapolating a path of movement, we can predict time and place of arrival. By mentally rotating an object, we can determine whether it will fit into a room, a dishwasher, or a suitcase. By mentally extending a line in a graph, we can detect a trend.

According to the dominant theory of mental imagery, the mental operations that we perform on actual and mental representations are internalizations of the physical changes that we perceive as we interact in the world (Finke and Shepard, 1986). In the world, things move in different manners and directions; they change shape, color, and texture in regular and predictable ways. For this reason, many mental transformations parallel the changes encoded in forming mental representations of changing entities. Anticipating these changes is critical to interacting with the world. Anticipating changes entails mentally enacting those changes. The extraordinary flexibility of the human mind then allows these mental spatial operations to be applied to imagined stimuli as well as to perceived ones, providing the means not only to anticipate states and processes in the world, but

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