Understanding Psychology (10th Ed)

Survival Frame
Mortality Frame
feL82795_ch08_240-275.indd Page 255 9/6/10 3:45 PM user-f464
feL82795_ch08_240-275.indd Page 255 9/6/10 3:45 PM user-f464

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256 Chapter 
8 
Cognition and Language
analysis can be counterproductive. For example, sometimes the fastest route to the 
summit of a mountain requires a mountain climber to backtrack temporarily; a means-
end approach—that implies that the mountain climber should always forge ahead and 
upward—will be ineffective in such instances. 
For other problems, the best approach is to work backward by focusing on the 
goal, rather than the starting point, of the problem. Consider, for example, the water 
lily problem:
Water lilies are growing on Blue Lake. The water lilies grow rapidly, so that the amount 
of water surface covered by lilies doubles every 24 hours. On the fi rst day of summer, 
there was just one water lily. On the 90 th day of the summer, the lake was entirely 
covered. On what day was the lake half covered? (Reisberg, 1997)
If you start searching for a solution to the problem by thinking about the 
initial state on day 1 (one water lily) and move forward from there, you’re facing 
a daunting task of trial-and-error estimation. But try taking a different approach: 
Start with day 90, when the entire lake was covered with lilies. Given that the 
lilies double their coverage daily, on the prior day only half the lake was covered. 
The answer, then, is day 89, a solution found by working backward (Bourne et al., 
1986; Hunt, 1994).
 FORMING SUBGOALS: DIVIDING PROBLEMS INTO THEIR PARTS 
Another heuristic commonly used to generate solutions is to divide a problem into 
intermediate steps, or subgoals, and solve each of those steps. For instance, in our 
modifi ed Tower of Hanoi problem, we could choose several obvious subgoals, such 
as moving the largest disk to the third post. 
If solving a subgoal is a step toward the ultimate solution 
to a problem, identifying subgoals is an appropriate strategy. 
In some cases, however, forming subgoals is not all that help-
ful and may actually increase the time needed to fi nd a solu-
tion. For example, some problems cannot be subdivided. 
Others—like some complicated mathematical problems—are 
so complex that it takes longer to identify the appropriate 
subdivisions than to solve the problem by other means (Reed, 
1996; Kaller et al., 2004; Fishbach, Dhar, Zhang, 2006).