Problem Representation.

M. Minard, Carte figurative des pertes successives en hommes de l’Armée Française dans la campagne de Russie 1812-1813, 1869.

For external problem representation, we have provided a simple distinction between sentential representations, in which the data structure is indexed by position in a list, with each element “adjacent” only to the next element in the list, and diagrammatic representations, in which information is indexed in a plane, many elements may share the same location, and each element may be “adjacent” to any number of other elements. While certainly not the complete story on this important representational issue, this simple distinction lets us demonstrate the following reasons why a diagram can be superior to a verbal description for solving problems:

 - Diagrams can group together all information that is used together, thus avoiding large amounts of search for the elements needed to make a problem-solving inference. 

- Diagrams typically use location to group information about a single element, avoiding the need to match symbolic labels.

- Diagrams automatically support a large number of perceptual inferences, which are extremely easy for humans. 

None of these points insure that an arbitrary diagram is worth 10,000 of any set of words. To be useful a diagram must be constructed to take advantage of these features. The possibility of placing several elements at the same or adjacent locations means that information needed for future inference can be grouped together. It does not ensure that a particular diagram does group such information together. Similarly, although every diagram supports some easy perceptual inferences, nothing ensures that these inferences must be useful in the problem-solving process. Failing to use these features is probably part of the reason why some diagrams seem not to help solvers, while others do provide significant help.

J. H. Larkin and H. A. Simon, “Why a Diagram is (Sometimes) Worth Ten Thousand Words,” Cogn. Sci., vol. 11, no. 1, pp. 65–100, Jan. 1987, p.98-99.