time, if you’re reminded of things that are similar on the surface, they’re going to be relationally similar as well,” she explained. Remember how you fixed the clogged bathtub drain in the old apartment? That will probably come to mind when the kitchen sink is clogged in the new one.
But the idea that surface analogies that pop to mind work for novel problems is a “kind world” hypothesis, Gentner told me. Like kind learning environments, a kind world is based on repeating patterns. “It’s perfectly fine,” she said, “if you stay in the same village or the same savannah all your life.” The current world is not so kind; it requires thinking that cannot fall back on previous experience. Like math students, we need to be able to pick a strategy for problems we have never seen before. “In the life we lead today,” Gentner told me, “we need to be reminded of things that are only abstractly or relationally similar. And the more creative you want to be, the more important that is.”
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In the course of studying problem solving in the 1930s, Karl Duncker posed one of the most famous hypothetical problems in all of cognitive psychology. It goes like this:
Suppose you are a doctor faced with a patient who has a malignant stomach tumor. It is impossible to operate on this patient, but unless the tumor is destroyed the patient will die. There is a kind of ray that can be used to destroy the tumor. If the rays reach the tumor all at once at a sufficiently high intensity, the tumor will be destroyed. Unfortunately, at this intensity the healthy tissue that the rays pass through on the way to the tumor will also be destroyed. At lower intensities the rays are harmless to healthy tissue, but they will not affect the tumor either. What type of procedure might be used to destroy the tumor with the rays, and at the same time avoid destroying the healthy tissue?
It’s on you to excise the tumor and save the patient, but the rays are either too powerful or too weak. How can you solve this? While you’re thinking, a little story to pass the time: There once was a general who needed to capture a fortress in the middle of a country from a brutal dictator. If the general could get all of his troops to the fortress at the same time, they would have no problem taking it. Plenty of roads that the troops could travel radiated out from the fort like wheel spokes, but they were strewn with mines, so only small groups of soldiers could safely traverse any one road. The general came up with a plan. He divided the army into small groups, and each group traveled a different road leading to the fortress. They synchronized their watches, and made sure to converge on the fortress at the same time via their separate roads. The plan worked. The general captured the fortress and overthrew the dictator.
Have you saved the patient yet? Just one last story while you’re still thinking: Years ago, a small-town fire chief arrived at a woodshed fire, concerned that it would spread to a nearby house if it was not extinguished quickly. There was no hydrant nearby, but the shed was next to a lake, so there was plenty of water. Dozens of neighbors were already taking turns with buckets throwing water on the shed, but they weren’t making any progress. The neighbors were surprised when the fire chief yelled at them to stop, and to all go fill their buckets in the lake. When they returned, the chief arranged them in a circle around the shed, and on the count of three had them all throw their water at once. The fire was immediately dampened, and soon thereafter extinguished. The town gave the fire chief a pay raise as a reward for quick thinking.
Are you done saving your patient? Don’t feel bad, almost no one solves it. At least not at first, and then nearly everyone solves it. Only about 10 percent of people solve “Duncker’s radiation problem” initially. Presented with both the radiation problem and the fortress story, about 30 percent solve it and save the patient. Given both of those plus the fire chief story, half solve it. Given the fortress and the fire chief stories and then told to use them to help solve the radiation problem, 80 percent save the patient.