Mindware Strategy: Problem Solving By Analogy
The first matrix problems are solved by finding similarities of the sort X is to Y as P is to Q, (where you have to find Q).
In the first problem, the relationship is based on analogous transformations: ‘inner shape > outer shape’ and ‘outer shape > inner shape’.
In the second problem, which is harder, the relationship is ‘inner white shape > outer white shape’ and ‘outline shape reflected vertically’.
To solve this kind of problem, what is essentially is that you are generate lots of possible alternative relationships and don’t get fixated on something. Your n-back working memory training should help with this.
Duncker’s Radiation Problem
If you used the ‘capture the fortress’ scenario to help you solve the surgery problem (called ‘Duncker’s Radiation Problem’), you were using a problem-solving-by-analogy strategy. In analogical problem solving you re-represent a problem in terms of some other process or situation you know better.
Analogies occur when there are parallels between two different situations – where one situation is like another in certain respects.
In the problem you just did, one research study showed that only 10% could solve the surgery problem with no help. After hearing the ‘capture the fortress’ problem, 30% could then solve the surgery problem. When it was hinted that the two stories were related, 75% got the answer to the surgery problems. Hearing the story isn’t enough: you have to notice the analogy.
Steps to solving problems by analogy
Here are the steps
- First you have to notice the analogous relationship
- Then you have to map the relevant features of the relationship in your own mind
- Then you have to apply the mapping to generate a solution.
In this problem
- The surgeon corresponds to the general (both are in command)
- The tumour corresponds to the fortress (both must be destroyed)
- The mines correspond to the healthy tissue (neither may be disturbed)
- The radiation corresponds to the army (both are available resources)
Insight About The Analogy
You may have had a ‘flash of insight’ about the shared ‘structure’ of the solution – which can be represented like this:
Expert Problem Solving
Experts routinely solve problems analogically, and some of the deepest scientific insights are based on analogical reasoning. For example, Niels Bohr’s model of the atom made an analogy between the atom and the solar system.
If you get into a habit of noticing underlying similarities between different types of problems and situations, this will help both your ability to solve problems and your ability to understand new material (based on your existing understanding of analogous things).