Analogical thinking is what we do when we use information from one domain (the source or analogy) to help solve a problem in another domain (the target). Experts often use analogies during the process of problem solving, and analogies have been involved in numerous scientific discoveries. However, studies of novice problem solvers show that they often have difficulty in recognising that one problem can be used to solve another. A problem that has been studied by several researchers is Duncker's (1945) radiation problem. In this problem, a doctor has a patient with a malignant tumour. The patient cannot be operated upon, but the doctor can use a particular type of ray to destroy the tumour. However, the ray will also destroy healthy tissue. At a lower intensity the rays would not damage the healthy tissue but would also not destroy the tumour. What can be done to destroy the tumour?
Only about 10% of people manage to spontaneously generate a solution to this problem. In two papers Gick and Holyoak (1980 and 1983) explored the conditions under which participants would solve the radiation problem following exposure to an analogy. Some participants were presented with the following story:
A small country was ruled from a strong fortress by a dictator. The fortress was situated in the middle of the country, surrounded by farms and villages. Many roads led to the fortress through the countryside. A rebel general vowed to capture the fortress. The general knew that an attack by his entire army would capture the fortress. He gathered his army at the head of one of the roads, ready to launch a full-scale direct attack. However, the general then learned that the dictator had planted mines on each of the roads. The mines were set so that small bodies of men could pass over them safely, since the dictator needed to move his troops and workers to and from the fortress. However, any large force would detonate the mines. Not only would this blow up the road, but it would also destroy many neighbouring villages. It therefore seemed impossible to capture the fortress. However, the general devised a simple plan. He divided his army into small groups and dispatched each group to the head of a different road. When all was ready he gave the signal and each group marched down a different road. Each group continued down its road to the fortress so that the entire army arrived together at the fortress at the same time. In this way, the general captured the fortress and overthrew the dictator.
Reading this story led to a slightly higher, though not much higher, proportion of people thinking of the convergence solution - about 30%. When given a hint that the story might be of use in solving the radiation problem, but without making explicit reference to a possible analogy, then the solution rate was 92%. Solutions were also facilitated by asking participants to read two, rather than just one, problem analogues.