Michael Ranney and Paul Thagard
Cognitive Science Laboratory Princeton University 221 Nassau Street Princeton, NJ 08542
Students of reasoning have long tried to understand how people revise systems of beliefs (see Wertheimer, 1945, for example). We will describe a computational model of how experimental subjects revise their naive beliefs about physical motion. We maintain that people often change their beliefs in ways driven by considerations of explanatory coherence. After describing instances in which subjects change their beliefs while learning elementary physics, we show how their belief revisions can be modeled using ECHO, a connectionist computer program that uses constraint-satisfaction techniques to implement a theory of explanatory coherence.
Ranney ( 1987a) investigated belief change in naive subjects learning elementary physics by using feedback provided on a computer display. Subjects were asked to predict the motion of several projectiles and then explain these predictions. The physical contexts were quite simple, involving objects that were either thrown or released in various ways. Analyses of verbal protocol data indicate that subjects sometimes underwent dramatic belief revisions while offering predictions or receiving empirical feedback. We will describe two kinds of revisions.
Consider "Pat," an individual who was asked to offer predictions about events including (a) the motion of a heavy object dropped by a briskly walking man and (b) the motion of a heavy object thrown obliquely upward. Using episodic memories and men- tal imagery, Pat initially predicted that the object dropped by the man would fall straight down (relative to the ground). This belief is a common finding in the naive physics literature ( McCloskey, Washburn, & Felch, 1983). Although she entertained the correct prediction, that the dropped object might curve forward due to the object's forward "force" (velocity), she preferred to stay with the straight-down belief.
Several tasks later, when faced with the upward-throw" situation, Pat noted a similarity between it and the "walking-drop" task -- one that eventually spawned a belief revision. While she offered the correct parabolic trajectory as a prediction for the upward-throw, she noted that, at the parabola's zenith, the upwardly thrown object is comparable to that just released by the walking man. That is, at the apex of the thrown object's trajectory, it has an exactly-horizontal motion, as does the just-dropped object. Pat then mentioned that this observation was not "consistent" with what she said before and, if she were to be consistent, the thrown object would "stop" its horizontal motion and "then just fall straight down" from the zenith of the parabola. This "curving-up-then-straight-down" trajectory was not consistent with her past experience of falling objects.
Pat then realized that her memory-driven description of the ball dropping straight down from the walking man involved beliefs that were incoherent with her beliefs about the parabolic motion of thrown bodies. After a period of ignoring the incoherence, Pat stated that she had "constructed a consistent theory of how these things move." Remarkably, she went on to reject her straight-down prediction for the walking-drop task and accept the belief that the path would have a "slight forward" arc combining the "forward force" and gravity. Eventually, Pat generalized this notion, discriminating among the breadths of the arcs of several laterally released projectiles.
A second kind of systematic belief revision occurred in subjects who offered predictions, received feedback, and provided explanations for a set of tasks in which pendulum-bobs were released from their supportive strings during various points in a swing. This set of tasks was adapted from stimuli used by Caramazza, McCloskey, & Green, ( 1981). Because of the similarity among several of the subjects, we will amalgamate them into a composite subject "Hal."
Hal predicted that, at the extreme "endpoint" of a swing, a released bob will travel laterally and (even-