Analog Imagery in Mental Model Reasoning: Depictive Models

We investigated whether people can use analog imagery to model the behavior of a simple mechanical interaction. Subjects saw a static computer display of two touching gears that had different diameters. Their task was to determine whether marks on each gear would meet if the gears rotated inward. This task added a problem of coordination to the typical analog rotation task in that the gears had a physical interdependency; the angular velocity of one gear depended on the angular velocity of the other gear. In the first experiment, we found the linear relationship between response time and angular disparity that indicates analog imagery. In the second experiment, we found that people can also solve the problem through a non-analog, visual comparison. We also found that people of varying spatial ability could switch between analog and non-analog solutions if instructed to do so. In the third experiment, we examined whether the elicitation of physical knowledge would influence solution strategies. To do so, we manipulated the visual realism of the gear display. Subjects who saw the most realistic gears coordinated their transformations by using the surfaces of the gears, as though they were relying on the friction connecting the surfaces. Subjects who saw more schematic displays relied on analytic strategies, such as comparing the ratios made by the angles and/or diameters of the two gears. To explain the relationship between spatial and physical knowledge found in the experiments, we constructed a computer simulation of what we call depictive modeling. In a depictive model, general spatial knowledge and context-sensitive physical knowledge have the same ontology. This is different from prior simulations in which a non-analog representation would be needed to coordinate the analog behaviors of physical objects. In our simulation, the inference that coordinates the gear motions emerges from the analog rotations themselves. We suggest that mental depictions create a bridge between imagery and mental model research by positing the referent as the primary conceptual entity.