288 • CHAPTER 10 Visual Imagery
How did you solve these problems? One approach to solving mechanical problems
is to use mental simulation, in which the operation of the mechanical system is mentally
represented. If you used this procedure for the fi ve-gear problem, you probably imagined
gear #1 turning clockwise, gear #2 turning counterclockwise, gear #3 clockwise, and so
on. Another way to solve the gear problem is by using a rule-based approach, which
would involve applying a rule such as “When one gear turns, the one next to it rotates in
the opposite direction” or “All odd-numbered gears rotate in the same direction.”
These two ways of solving the gear problem are analogous to the two sides of the
visual imagery debate we have been discussing in this chapter. The mental simulation
approach is analogous to the idea that visual imagery involves a spatial representation.
The rule-based approach is analogous to the idea that visual imagery involves a proposi-
tional representation. In our discussion of the imagery debate, we discussed a large amount
of evidence favoring the spatial representation explanation of imagery. However, things
are not as one-sided for solving mechanical problems. As we saw for the gear problem,
both spatial representation and rule-based approaches can be used to solve the problem.
Let’s now consider the water-pouring problem. The answer to this problem is that water
will start pouring from the wide glass fi rst. ● Figure 10.24a shows that this is the case, by
superimposing the narrow and the wide glasses. From this diagram, you can see that whereas
water is about to pour from the wide glass, it is still below the edge of the narrow glass. Thus,
the narrow glass would need to be tilted farther before the water will begin to pour.
You may have found that this problem was harder to solve than the fi ve-gear prob-
lem. In fact, Daniel Schwartz and Tamara Black (1999) found that when they asked
participants for the answer to the water-pouring problem, without giving them time to
either reason out the problem or use mental imagery, most of the participants answered
incorrectly that both glasses would pour at the same angle (Figure 10.24b). However,
when participants were told to close their eyes and imagine the glasses being tilted,
almost all of them were able to “see” that the narrow glass would have to be tilted
farther than the wide glass (Figure 10.24c).
This result is relevant to the tacit knowledge explanation that Pylyshyn used to
explain people’s performance in visual imagery tasks (see page 275). Because most
people do not know the answer to the water-pouring problem beforehand, its solution
by using imagery cannot depend on tacit knowledge.
The water-pouring problem, like the fi ve-gear problem, can be solved without using
imagery. One way to do this is to use a diagram like the one in Figure 10.24a. Imagery,● FIGURE 10.24 (a) The solution to the water-pouring problem, illustrated by
superimposing the wide and narrow glasses. This shows that when the glasses are
tilted at 25 degrees, the water is close to the edge of the wide glass, but that more tilt
is necessary before the water will reach the edge of the narrow glass. (b) Participants’
immediate predictions of the solution to the water-pouring problem, indicating the
percentage of participants who predicted which glass would need to be tilted more to
pour. (c) Participants’ solutions to the water-pouring problem after closing their eyes
and imagining the glasses being tilted. (Source: Based on data from D. L. Schwartz &
J. B. Black, “Analog Imagery in Mental Model Reasoning: Depictive Models,” Cognitive Psychology, 30,
154–219. Copyright © 1996 Academic Press, Elsevier Ltd. Reproduced by permission.)Narrow WidePercent participantsSame100500100500(a) (b)NarrowSame Wide(c)Water level
before tiltingWide glass Thin glassWater levels
after tilting 25°Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.