Why a Diagram is (Sometimes) Worth Ten Thousand Words

We distinguish diagrammatic from sentential paper-and-pencil representationsof information by developing alternative models of information-processing systems that are informationally equivalent and that can be characterized as sentential or diagrammatic. Sentential representations are sequential, like the propositions in a text. Dlogrammotlc representations ore indexed by location in a plane. Diogrommatic representations also typically display information that is only implicit in sententiol representations and that therefore has to be computed, sometimes at great cost, to make it explicit for use. We then contrast the computational efficiency of these representotions for solving several illustrative problems in mothematics and physics. When two representotions are informationally equivolent, their computational efficiency depends on the information-processing operators that act on them. Two sets of operators may differ in their copobilities for recognizing patterns, in the inferences they con carry out directly, and in their control strategies (in portitular. the control of search). Diogrommotic ond sentential representations sup port operators that differ in all of these respects. Operators working on one representation moy recognize feotures readily or make inferences directly that are difficult to realize in the other representation. Most important, however, are differences in the efficiency of scorch for information and in the explicitness of information. In the representotions we call diagrammatic. information is organized by location, and often much of the information needed to make on inference is present and explicit at a single location. In oddition. cues to the next logical step in the problem may be present at on adjacent location. Therefore problem solving con proceed through o smooth traversal of the diagram, and may require very little search or computation of elements that hod been implicit.