#54 Duncker's Radiation Problem

Analogies are the fuel for problem solving

Mar 04, 2022

Saturday, March 05, 2022

Let me start by asking you one of the most famous hypothetical problems in cognitive psychology posed by Karl Duncker in the 1930’s. While you read 54th edition of The Passion Pad, make sure you keep solving the problem in the backdrop of your mind. The problem is as follows -

Suppose you are a doctor and you have to treat a patient who has a malignant stomach tumor. Unless the tumor is treated in the next 24 hours the patient will die. There is a kind of ray that can be used to treat that tumor. If the rays reach the tumor all at once with a sufficient intensity, it would kill the tumor. Unfortunately, all the healthy tissues that come in the path of that ray towards the tumor will also get destroyed. At lower intensities the healthy tissues won’t be effected but that would not kill the tumor either. How would you destroy the tumor and save the healthy tissues at the same time?

While you try to save the patient, a little story to pass the time: Chief of the State Fire Department arrived at a woodshed fire, concerned that the entire village would burn if the fire isn’t extinguished quickly. There were no fire safety equipments available but the site was nearby a lake hence plenty of water was available. The local people in the neighbourhood were already taking turns by filling up buckets and throwing water to extinguish the fire. Suddenly the chief yelled at the people to stop and asked them to all go fill their buckets from the lake. When they returned, the chief made them stand in a circle around the burning shed and asked them to throw the water at a count of 3. Three…..Two……One…… Guess what? The fire was immediately dampened and thereafter extinguished.

Have you saved the patient? Here’s one last story before I come to the answer. There was a general who needed to capture a territory in the center of the country and free it from the brutal dictator. If the general could get all his troops at the same time at the fort, he would succeed. The roads radiated out from the fort like wheel spokes. However they were laden with mines, so only a small number group of soldiers could safely traverse any road. The general decided to split his troops into small groups and each traversed on a unique road leading up to the fort. They synchronised their watches so as to reach the fort together. The plan worked and the general captured the fort and overthrew the dictator.

Ahem Ahem. Patient? Don’t feel bad if you couldn’t, almost no one solves it at first. However when presented with the other two stories and asked to relate them with saving the patient, almost most of the people solve it. The answer is that you could direct multiple low intensity rays at the tumor from different directions, leaving the healthy tissues unharmed, converging at the tumor with enough intensity to destroy it.

It doesn’t matter if you were able to solve it or not, the important part is what it shows about problem solving. A gift of a single analogy from a different domain can make people think of solutions for a completely different problem from a completely different domain, as seen in this case. Statistics say that almost no one could solve the Duncker Radiation at first, but once they learned about the two stories, number of people coming up with the solution almost tripled. Analogies are the fuel for problem solving. If you are ever stuck in a problem, try thinking of analogies, try thinking in some other domain with which you have some familiarity and the see if the solution of that domain works with your current problem.

“If you need a large force to accomplish some purpose, but are prevented from applying such a force directly, many smaller forces applied simultaneously from different directions may work just as well.”