@Article{,
author = {Jill Larkin and Herbert Simon},
title = {Why a diagram is (sometimes) worth ten thousand words},
journal = {Cognitive Science},
year = {1987},
OPTvolume = {11},
OPTpages = {65-99},
}
This paper compares the ease of computation with sentential and diagrammatic representations with the same informational content.
Simon 1978: Informational equivalence: all the info in one is inferrable from the other.
Simon 1978: Computational equivalence: informationally equivalent plus any inference in one is just as easy and fast as the same inference in the other. [p67]
[p71] Though everyone sees the pieces on a chessboard, the master sees things other don't-- such as "open files," a line of adjacent vacant squares running from your side to the opponent's.
[72] They have a pulley problem for which everyone observed grabs a paper and pencil and makes a diagram.
In both conditions productions do the inference. In the sentential condition, there is a representation where each component gets its own symbol. In the diagrammatic representation, [78] objects are not represented explicitly, only locations. In the pulley example, the primary difference found between the 2 representations was that the diagrammatic one required less search. [72] In the sentential representation, it's necessary to hold lots of values in working memory while searching. [76]
In the diagrammatic representation, when one location is attended to, all information there is attended to. Anything referenced in one location can be attended to with a switch. [78]
The first example is a pulley system. The second is a geometry problem with of triangle congruency [82]. The finding here is that the changes that need to be made to the representation are easier to make with the diagram rep than the sentential. In this problem, the triangles are emergent shapes of the mentioned elements. Search is not the big problem here, recognition is. To get the new data structure, the program uses perceptual inference rules [85].