It's a Jungle in There: How Competition and Cooperation in the Brain Shape the Mind (30 page)

A psychological study of the cheap-necklace problem showed that incubation helps lead to its solution. College students were assigned to three groups. One group worked on the problem nonstop for half an hour; 55% of the students in this group solved it. A second group worked on the problem for 15 minutes, had a half-hour break during which they did other things, and then worked on the problem for a final 15 minutes; 64% of the students in this group solved the problem. A third group had a 15-minute work period, a 4-hour break filled with other activities, and then a final 15-minute work session; 85% of the students in this group found the solution.
⁵

These results show that the more time a group had with a problem, the more likely they were to solve it. The outcome wasn’t due to the fact that participants who had more time to work on the problem came back with the solution; that wouldn’t have been interesting. What happened was more informative. Participants with breaks came back without having already solved the problem, but soon after returning to it were able to get it. It was as if, with more time away, there was more chance for the chick to nearly hatch.

I’ve likened working on problems to hens keeping their eggs warm, but what mechanism actually underlies incubation? It’s insufficient to say that the
mechanism is keeping potential solutions warm, for that doesn’t answer the question of what the warming does. It also leaves unanswered the larger question of how new solutions arise, which is the main question of interest.

The time to solve a problem reflects the time for neural cooperation and competition to reach a point where a solution becomes possible. The appropriate balance of power must be reached among ideas or idea components for solutions to emerge. Are there findings about problem-solving that shed light on this process?

Consider an activity that any child would love—pouring water into and out of jugs. The aspect of this activity that might challenge the youngster despite the initial appeal of the water play is the need to end up with a specific quantity. The target volume differs from the volume of any of the jugs, and no extra measuring cups are available. To solve the problem, what’s needed is a series of “jugular” additions and subtractions.

The table below shows a series of problems that a group of participants was given in a famous study of problem-solving that involved jug-to-jug water transfers.
⁶
All the problems except the eighth could be solved by first filling jug B, then emptying jug B into jug C, then emptying jug C and filling jug B again, then emptying jug B into jug C once more, and finally pouring jug B into jug A. The amount left over in jug B would be the target amount, given by the equation B – 2C – A = 100.

When this series of pours proved useful—that is, when it was adaptive to pour according to the procedure B – 2C – A—participants came to rely on it, using the procedure over and over again because it worked, as it did in problems 1–7. “If it ain’t broke, don’t fix it,” the participants seemed to say to
themselves, which was fine until the procedure no longer satisfied the task demand, in problem 8. Then things fell apart. Many participants failed to solve the eighth problem even though they had gotten better and better on the problems before.

What does this finding reveal about problem-solving? It shows that when a procedure proves useful, it dominates. This is fine as long as the procedure helps. But when it doesn’t help, despite having proven useful before, it still tries to rule the roost, so to speak, inhibiting the method that would work if given a chance.

Persisting with a method is called a
set
effect. The word “set” refers to the fact that you can get stuck in your ways. This can be helpful if the method proves useful, but it can be detrimental otherwise.
⁷

Here’s another example of a set effect. Try to unscramble each letter string so it makes a word.

kmli

recma

graus

foefce

teews

ikrdn

Once you get the idea that the solutions pertain to coffee-drinking, the solutions come in a rush, bursting forth like froth from an espresso machine. The time to solve anagrams like these, which are semantically organized, is much shorter than the time to solve anagrams that are not.

The effect I’ve just summarized illustrates a positive set effect. There are also negative set effects. One was illustrated earlier in the difficult transition to the eighth step of the jug-pouring exercise. Negative set effects are also seen in studies of
functional fixedness
. Here people tend to get mentally fixed in the functions they assign to problem elements.
⁸

Consider the problem of joining two hanging strings that are too far apart to be grasped simultaneously with outstretched arms. Present in the scene, besides the two hanging strings, are various objects: a chair, a jar with tacks, some other tacks lying on the floor, some pieces of paper, and a pair of pliers. How would you solve the problem?
⁹

An initial temptation might be to move the chair midway between the strings and climb up before reaching either one. But that does you no good. The distance between the strings is just what it was before. Whichever string is farther from you is just as out of reach as it was before you mounted the chair. Tossing things at one of the strings to drive it toward the other is a method that might cross your mind, but that strategy is iffy at best.

Eventually, people figure out what to do, but their ability to do so depends on their seeing that one of the extraneous objects in the scene can serve a function other than the one it normally does. Pliers are normally used for squeezing, but you can also tie pliers to a string and set the string in motion. Once the weighted string swings to and fro, you can walk to the other side, catch the pliers as they swing toward you, and join the cords.

Seeing the pliers as a tool for gripping rather than as a tool for swinging leaves you stuck, suffering from functional fixedness. Overcoming blindness to the alternative function that pliers can serve—being a weight rather than a squeezer—lets you solve the problem.

Blindness to novel applications is just what you’d expect if you subscribe to the view that it’s a jungle in there. Mental demons with narrow self-interests get excited by relevant stimuli. The sight of pliers activates demons related to gripping and squeezing, and they inhibit other demons with which they normally compete, such as demons that swing rather than squeeze.
¹⁰

If the source of functional fixedness is what I’ve just said—cognitive creatures squelching other cognitive creatures—then there’s a theoretically motivated antidote to such functional fixedness. By activating mental creatures who get turned on by swinging, it should be possible to help would-be problem-solvers overcome the fix they’re in. This expectation is borne out: Giving hints to participants in problem-solving tasks helps them find solutions more quickly. For example, encouraging people to swing their arms helps them solve the two-string problem.
¹¹

Another example of a hint helping to fix functional fixedness comes from another problem studied by cognitive psychologists. This is the problem of mounting a candle on a wall. Part of the challenge is to leave the candle on the mount, burning brightly for as long as the wick will last. The materials you can work with are a candle, matches, and a box of tacks. Think about the problem for a while. The solution is given a few paragraphs from now.

One of the things that make the candle-on-the-wall problem hard is the way it’s presented. The way the objects are shown can obscure the path to its
solution. Showing the box filled with tacks makes the problem harder to solve than showing the box empty, with the tacks lying beside it.
¹²

What makes the tacks-free box less taxing? When the box is filled, you’re more likely to see it just as a container. But when the box is empty, you’re more likely to see it as something that can serve some other relevant function, such as providing a base of support. Once you realize the box can support the candle, it’s relatively easy to see that the tacks can be used to pin the box to the wall. If the box is pinned right-side-up rather than upside-down, it can even collect the melted wax, which may be appreciated by the homeowner whose residence you’ve turned into a haunted house.

The discovery that people are more likely to solve the candle-on-the-wall problem when the box is empty than when it’s full is a classic finding in the problem-solving literature. It was one of the first demonstrations of functional fixedness. As it happens, the demonstration can also be seen as one of the first indicators of an important finding that led to a Nobel Prize in Economics. The finding came from two cognitive psychologists, Amos Tversky and Daniel Kahneman, who showed that the way a question is framed strongly affects the answer it receives.
¹³

A dramatic example of this framing effect, as it’s called, pertains to the probability that people express willingness to donate their organs in case of traffic accidents. When you renew your driver’s license in the United States and Germany, you check a box to indicate that you’re willing to donate your organs. The acceptance rate, on average, is 14%. In other countries, such as France and Poland, when people renew their driver’s licenses, they check a box to indicate that they’re
not
willing to donate their organs. Then only 10% say they’d be unwilling to donate, so 90% of the respondents say, in effect, “Sure, you can have my organs if I die.”
¹⁴
Amazingly, then, the logically equivalent question—“Are you
willing
to donate your organs?” or “Are you
unwilling
to donate your organs”—yields totally different outcomes.

What accounts for this amazing effect of the way the same question is framed? The surface features of the problem activate demons who take over the thought process. Demons for willingness to donate take over in one framing, whereas demons for unwillingness to donate take over in the other. Similarly, in the candle problem, demons favoring containment are activated by the
sight of a box holding thumbtacks, and those agents inhibit agents favoring support. Conversely, demons favoring support are activated by the sight of a box
not
holding thumbtacks, and they inhibit demons who favor containment. Framing effects are expected, then, if it’s a jungle in there. Creatures given a leg up try to tie down creatures who get no helpful kick.

Solving problems benefits from the openness of mind called “creativity.” Consider one form of creativity that arises in connection with another problem commonly studied in cognitive psychology—the 9-dot problem. The problem begins with an innocent-looking diagram—a 3 × 3 array of dots. If you undertake the problem, you try to connect the 9 dots with 4 straight lines. A further constraint is to do so without lifting the tip of your pencil from the drawing surface. Try the problem if you wish. Here, for your drawing enjoyment, are the nine dots.

. . .

. . .

. . .

People are often flummoxed by the 9-dot problem. They try paths that leave them frustrated. No matter how the series of four straight lines is drawn—whether it includes a diagonal from the top left to the bottom right or a diagonal from the bottom left to the top right—the lines fail to intersect some of the dots. This is true as long as all the lines fit within the imaginary box joining the outer dots of the matrix. But it’s that imaginary box that hems you in. Your imagination limits you, for you see a box, or your mind imposes one. A box is for containment, for keeping things inside. Once you think outside the box, you can solve the problem. If you let your pencil go beyond the box’s borders (a box that was never mentioned), you can join the nine dots with four straight, connected lines.
¹⁵
This example is often used in creativity workshops. When people are encouraged to “think outside the box,” the box referred to is often the one from the 9-dot problem.
¹⁶

It’s important not to blame yourself for failing to think outside the box. If you attempt the 9-dot problem and can’t solve it, you’re unlikely to become more creative by castigating yourself for being less creative than you’d like. In fact, a damning attitude is likely to curtail creativity, not inspire it. Being down doesn’t help the creative juices flow. Being up and lighthearted has the opposite effect. People exposed to comedy routines display measurable increases in creativity, as do people tipsy from alcohol.
¹⁷

Disappointingly, it often takes in-your-face directives to help people solve problems. This fact about thinking was established in relation to the problem of killing a tumor with radiation beams. The challenge was to kill the tumor without damaging the surrounding tissue. The researchers who did this study told people who would work on the problem a story about multiple invading armies attacking a fort from many sides.
¹⁸
The multiple armies could slip through enemy lines on the way to the fort and could then join the other forces at the fort to capture it. Would people hearing the story see the connection to the radiation problem?