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. Dio-grommatic 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 mothe-matics 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. 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. 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. "a picture is worth 10,OOO words" is a Chinese proverb. On inquiry, we find that the Chinese seem not to have heard of it, but the proverb is certainly widely known and widely believed in our culture. To understand why it is advantageous to use diagrams-and when it is-we must find some way to contrast diagrammatic and non-diagrammatic representations in an information-processing system.