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The well-known pendulum problem (Caramazza, McCloskey, and Green, 1981), like the one shown Figure 8, is adapted here for our first investigation. In the original problem, subjects were asked to draw how the pendulum bob would fall if the string is suddenly cut as the pendulum bob were at different locations on its path. Of particular interest is how the bob would fall if the string is cut when the bob is at mid-point O. According to their report, a large percentage (44%) of the subjects chose a vertical or straight-down path, rather than the physically correct projectile path. Physics tells us that the horizontal motion of the pendulum bob at mid-point O should not disappear at the moment when the string is cut but will continue to exist as the bob is falling to the floor. As a result, on leaving mid-point O, the bob should travel not only downward but also forward in the horizontal direction, i.e, through a parabolic trajectory.

We are interested in why the subjects chose such a physically incorrect answer and the cognitive apparatus responsible for such an answer. A straight-down response to the pendulum problem can not be explained by the impetus theory proposed by (McCloskey,1983) for the sudden disappearance of the horizontal impetus in such a response does not agree with the basic claim of the theory that an impetus has a tendency to continue (McCloskey, 1983). A more comprehensive and in-depth explanation appear to be needed.

We propose that the subjects represented the pendulum problem in term of its force mechanism consisting of two basic components: the horizontal motion and the dynamic equilibrium formed around the bob between gravity and the upholding force (i.e., tension) in the string. More specifically, before the string was cut, the action of gravity on the bob was dynamically balanced by the tension in the string; to represent the action of gravity on the bob in the swinging pendulum requires the representation of this dynamic equilibrium, and vice versa. In the meantime, the subjects also represented the movement of the bob before the string was cut. But, in conceiving the pendulum at the moment when the string is cut, the subjects were much more sensitive to the interruption of the dynamic equilibrium than to the pre-existing horizontal motion. In other words, the subjects had cognitively over-reacted to the action of gravity on the bob upon the cutting of the string and totally ignored the presence of the horizontal motion in conceiving the falling bob.

If the cognitive system is more sensitive to the interruption of the dynamic equilibrium than the horizontal motion, over-reactions to it may not be restricted to the subjects who gave the straight-down responses only. A trace of the difference in the subjects' cognitive sensitivity to the two different types of mechanical information (i.e., the interruption of the dynamic equilibrium and the horizontal motion) should also be found in responses that are not straight-down. Secondly, if the representation of the horizontal motion of the pendulum bob was merely repressed by the representation of the action of gravity on the bob, the horizontal motion should reemerge in the subjects' responses when gravity is prevented from pulling the bob down as the string is cut (see Figure 9(b)), i.e., the horizontal motion should be recoverable in the response of a subject in this new situation who has originally given a straight-down response.

In the first case, more extensive measurements of responses other than the straight-down responses would provide us the information which would either confirm or disconfirm our hypothesis. If the subjects who had given non-straight-down responses are not over-sensitive to the interruption of the dynamic equilibrium, the horizontal motion should be well preserved in their representation of the bob's subsequent motion, as a result, a continuous projectile trajectory should be their response. Otherwise, we expect at least some subjects to repress the horizontal motion to certain degrees in their responses which would then fall in-between a perfectly correct response and a straight-down response.

In the second case, by introducing a table into the original problem right beneath the pendulum's swinging bob, we would be able to test whether the representation of horizontal motion has really vanished or only temporarily been hidden. Subjects who believe the bob will drop straight down from the mid-point O ought to believe that the bob would hit the floor without horizontal motion. That is, aside from bouncing up and down, the bob should not move right or left after hitting the floor. Would these subjects then expect the bob to be completely stationary when the string is cut exactly at the point the bob skims the table? Or will these subjects "rediscover" the bob's horizontal motion in these circumstances?


It is possible that the representation of the previous horizontal motion was not destroyed in the cognitive system, but only subdued by the more salient representation of the dynamic discontinuity information and consequently stored away while a subject was drawing his or her straight-down or vertical response. The present experiment investigates this possibility.

The hypothesis for this experiment is that the representation of the horizontal motion was only temporarily stored away and a horizontal response, when given the opportunity, could be totally recovered later on the ground following the vertical response. An experimental stimulus, which is a modified version of a stimulus originally devised in (McCloskey, 1983), was adapted for this experiment. A drawn airplane was shown flying above the ground. The subjects were told that the wheel of the plane suddenly drops off and asked to draw first the path of the wheel both in the air and then on the ground. The question was how the wheel would roll on the ground in the responses of the subjects who had drawn straight-down paths in the first task. If these subjects had no representation of the horizontal motion while they were drawing their straight-down paths, the wheel should then stay where it lands on the ground. On the other hand, if the representation of the horizontal motion was stored away, a horizontal drawing should be expected to recover in their responses on the ground.


The dynamic discontinuities we have so far been dealing with are characterized by the mechanical situation in which a pre-existing dynamic relation in the dynamic context of an object suddenly came to a stop; consequently, the object had left one mechanical state and entered into a different mechanical state. In the pendulum problem, for example, the removal of the string, hence the static force in the string, enabled the bob to fall as gravity remained to act on the bob; in this case, the downward motion of the bob was not caused by any new external force, but by the gravity that had already been acting on the bob.

In the present experiment, I will focus a more common kind of dynamic discontinuity, namely, impact, in which one object hits another, exerting a force to the second object and, at the same time, also receiving a force from it. In a mechanical impact, the dynamic contexts of both objects suddenly change, a mutual dynamic relation is suddenly established, as a result, each object enters into a new mechanical state. However, in an impact, it is no longer the sudden removal of a pre-existing force which characterizes and distinguishes the change of the mechanical state of each object, but the emergence of a new force which has not been in the mechanical state of the object; In other words, the dynamic discontinuity that characterizes a mechanical impact is positive, in contrast to the negative dynamic discontinuities we have dealt with in the last two experiments.

In both positive and negative dynamic discontinuities, the dynamic context of an object is suddenly changed, with either the arrival of a new force or the removal of an old one. As a result, the object enters into a new mechanical state. Note, a new mechanical state does not necessarily imply that the object is now in a new kinematic state. For example, in the pendulum problem, at the moment immediately after the string was cut (point O) the pendulum bob had the same kinematic state as at the moment right before the string was cut. But, the mechanical states of the bob at these two moments were quite different because the dynamic state of the bob had changed drastically.

Recall, in Experiment 2, many subjects believed that a fast ball shot into a spiral tube would come out of the tube curving in the direction of the tube. Such a result was used by McCloskey to support his Impetus Theory. According to this theory, subjects believed that the ball travels in a curve because it carries a curved impetus, a dynamic primitive conceived by the cognitive system.

Our key question in the experiment is that, if a curved impetus carried by an object is an unique type of force as represented by the cognitive system, how would it represent this force in another object which, upon being hit by the first object, receives this force from this object and starts to move? The Impetus Theory tells us that an impetus can be imparted from one object to another, which is true not only for straight impetus, but also for the curved impetus. Then, would the transferred impetus in the second object also be conceived as curved? It certainly should be, following the Impetus Theory. What does it mean if the transferred impetus does not curve in people's responses? Does it mean that the Impetus Theory is false?