Why a Diagram is (Sometimes) Worth Ten Thousand Words

"Why a Diagram is (Sometimes) Worth Ten Thousand Words"
JILL H. LARKIN and HERBERT A. SIMON
COGNITIVE SCIENCE 11, 65-99 (1987)

We distinguish diagrammatic from sentential paper-and-pencil representations of
information by developing alternative models of information-processing systems
that are informationally equivalent and that can be characterized as sentential or
diagrammatic. Sententiol representations are sequential, like the propositions in
a text. Diagrammatic representations are indexed by location in a plane. Dia-
grammatic representations also typically display information that i s only implicit
in sentential representations and that therefore has to be computed, sometimer
at great cost, to make it explicit for use. We then contrast the computational effi-
ciency of these representations for solving several.illustrative problems in mathe-
matics and physics.
When two representations are informationally equivalent, their computational
efficiency depends on the information-processing operators that act on them.
Two sets of operators may differ in their capabilities for recognizing patterns, in
the inferences they can carry out directly, and in their control strategies (in par-
ticular, the control of search). Diagrammatic and sentential representations sup
part operators that differ in all of these respects. Operators working on one
representation may recognize features readily or make inferences directly that
are difficult to realize in the other representation. Most important, however, are
differences in the efficiency of search for information and in the explicitness of
information. In the representations we call diagrammatic, information i s orga-
nized by location, and often much of the information needed to make an infer-
ence i s present and explicit at a single location. In addition, cues to the next
logical step in the problem may be present at an adiacent location. Therefore
problem solving can proceed through a smooth traversal of the diagram, and may
require very little search or computation of elements that had been implicit.