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The Role of Diagrams and Diagrammatic Affordances in Analogy David Latch Craig (david.craig@arch.gatech.edu) College of Architecture, Georgia Institute of Technology Atlanta, GA 30332-0155 USA Nancy J. Nersessian (nancyn@cc.gatech.edu) College of Computing, Georgia Institute of Technology Atlanta, GA 30332-0280 USA Richard Catrambone (rc7@prism.gatech.edu) School of Psychology, Georgia Institute of Technology Atlanta, GA 30332-0170 USA Abstract We argue that problem solvers can, in certain cases, solve target problems by transforming perceptual simulations of solutions to analogous source problems. We further argue that source diagrams may facilitate the process, but only if they convey physical affordances consistent with the necessary transformations. We conducted an exploratory study in which participants were asked to solve a source and a target problem. We identified two properties of extemporaneously drawn source diagrams – view and configuration – that were highly correlated with the production of analogous solutions to the target problem. We speculated that view and configuration influenced the ease with which certain simulated transformations were performed. The results of two additional experiments in which the view and configuration of source diagrams were independently controlled further support the claim. Introduction In this paper we explore the functioning of diagrams in analogical problem solving. Specifically, we investigate how contextual aspects of diagrams – things ranging from depicted physical details to intrinsic properties like perspective, orientation and scale – might afford the kind of simulated physical transformations needed to convert a solution to one problem into a solution to another. In the next two sections we briefly outline our claims concerning diagrams, simulations and affordances, and how they might relate to analogy. In the remaining sections we present the findings of three experiments designed to both illustrate and test those claims. Diagrams, Simulations and Affordances One way external diagrams can function in problem solving is by scaffolding perceptual, or analog, simulations in the perceptual and motor cortices of the brain (Barsalou, 1999; Glenberg, 1997). Perceptual simulations have been found to facilitate spatial reasoning (e.g., Kosslyn, 1994) as well as various forms of conceptual reasoning (e.g., Barsalou, Solomon & Wu, 1999; Glenberg & Robertson, 2000; Stanfield & Zwaan, 2001; Fincher-Keifer, 2001). They could potentially benefit problem solving by facilitating the testing and general exploration of candidate solutions. We argue that the way a diagram is drawn affects not only what is perceptually simulated but also how the resulting simulation can be perceptually transformed. A long history of findings, dating back to Cooper and Shepard’s (1973) chronometric studies of mental rotation, support the basic premise that simulations are transformed through simulated motor activity. More recently, researchers have found that simulated transformations are motorically structured and constrained. The ease with which imagined body parts are mentally rotated, for example, parallels the ease with which those parts can be rotated in actuality (Parsons, 1987). In addition, concurrent motor activity consistent with simulated transformations of imagined objects tends to make those transformations faster and more accurate, while inconsistent activities produce interference (Wexler, Kosslyn & Berthoz, 1998). Generally speaking, simulated transformations appear to be constrained in the same way real interaction with the physical world is constrained. Insofar as contextual aspects of diagrams would help determine the physical properties of simulated objects (e.g., texture, shape, mass, etc.) and the context in which they are perceived (e.g., perspective, orientation, scale, etc.), those aspects act as transformational affordances by facilitating certain simulated transformations and inhibiting others. A finding that illustrates the idea that diagrams convey transformational affordances comes from a study by Schwartz and Black (1996) in which people were shown a diagram of two gears meshed together, one larger than the other, and asked whether two marks, one on the circumference of each gear, would eventually line up if the gears were rotated. By comparing response times against the initial angular disparity of the marks, Schwartz and Black were able to identify different strategies used to complete the task, one of which appeared to be perceptually simulating the two gears rotating together. Ultimately, Schwartz and Black were able to constrain the strategy people used |
