Solving Problems by Analogy

Many hard problems have already been solved — just not in the form you are facing. An engineer's fix, a general's tactic, a biologist's trick may share the same underlying shape as your problem while looking completely different on the surface. Analogy is the bridge: carry the structure of a known solution across to a new case, and a wall becomes a doorway.

The catch is that people rarely cross the bridge on their own. We store problems by their surface details — tumours with medicine, armies with roads — so a matching solution sitting one shelf over goes unnoticed. Understanding why this happens, and how a small prompt changes it, turns analogy from lucky accident into a method you can use on purpose.

Source, target, and mapping

Analogical problem-solving has three parts. The target is the problem you face. The source is a problem you already know how to solve. Mapping is lining up the parts: this element of the source corresponds to that element of the target, so the source's solution suggests one for the target. Good mapping is about roles and relationships, not appearances.

Surface versus deep similarity

Two problems can look alike yet work differently, or look utterly different yet share a structure. Surface features are the concrete details — the objects, the setting, the vocabulary. Deep structure is the pattern of forces and constraints. A useful analogy matches on deep structure. The trouble is that human memory is organised largely by surface features, so the analogies we happen to recall are often the useless ones.

Why we miss useful analogies

Because retrieval is cued by surface detail, a perfectly matched source in another domain simply does not come to mind. Studies show that a hint — even a gentle nudge to "think about the story you just read" — dramatically raises the chance people apply an analogy they already possess. The lesson is that the knowledge is usually there; what fails is the search. So make the search explicit.

You must roll out a new policy across a large organisation, but pushing it everywhere at once triggers resistance and it collapses. Stuck, you deliberately ask: where has a single force, too strong to apply all at once, been delivered in parts instead? You recall how a vaccine campaign seeds many small local clinics that together reach the whole population. Mapping that structure across, you launch the policy through many small pilots that converge into full coverage. The domains differ entirely; the deep structure — divide one large force into converging small ones — is identical.

Analogy misleads when you map on surface resemblance. A manager reasons, "Our company is like a family, so I will run it as a strict parent runs children." The word family is a surface match; the deep structures — voluntary employment, professional accountability, adult peers — do not line up, and the parenting model produces resentment. A shiny analogy that shares only vocabulary is often worse than none, because it feels insightful while quietly importing the wrong constraints.

Mary Gick and Keith Holyoak studied analogical transfer using Duncker's "radiation problem": a patient has an inoperable tumour, and a ray strong enough to destroy it would also destroy the healthy tissue it passes through, while a ray weak enough to spare the tissue is too weak to destroy the tumour. The solution is to aim several weak rays from different directions so they converge and sum only at the tumour.

In their 1980 paper in Cognitive Psychology, Gick and Holyoak first had people read an analogous story about a general who captures a fortress by sending small groups of soldiers along many roads to converge on it. Reading the story helped — but only modestly on its own. Roughly a third of people who had read it spontaneously solved the radiation problem, while only about one in ten solved it with no story at all. When participants were given a hint to use the story, the solution rate rose sharply, to around three-quarters. Their 1983 follow-up showed that reading two different analogous stories, which encouraged people to extract the shared "convergence" schema, improved spontaneous transfer. The precise figures vary across their experiments, but the pattern is robust and widely replicated: people often hold a perfectly good analogy yet fail to retrieve it until they are prompted to look.

• "If I know the analogy, I will use it." Often you will not, until something cues you to search for it.
• "Similar-looking problems make the best analogies." Surface likeness is a weak guide; shared structure is what matters.
• "Analogies are just decoration for explaining ideas." They are also engines for generating solutions.
• "More detail in the source problem helps." Vivid surface detail can actually bury the structural match.

Take a problem you are stuck on and strip it to one abstract sentence naming no specifics — just the forces and constraints. Now ask three deliberately distant fields (nature, sport, history) how they handle that same structure. Write down one candidate source from each, then map its parts onto your problem and check whether the deep structure truly aligns.

Think Like a Maester: The answer to your problem may already exist in a field you have never studied — your task is to go looking for it.

1. What are the source, target, and mapping in analogical problem-solving?
2. How do surface and deep similarity differ, and which one makes an analogy useful?
3. In Gick and Holyoak's studies, why did most people fail to use the fortress story until hinted?
4. What did reading two analogous stories add, according to the 1983 follow-up?
5. Give an example of an analogy that misleads because it matches only on the surface.

Analogy lets you borrow a solution from a problem you have already cracked, even in a distant field — but only if you map on deep structure rather than surface resemblance, and only if you actually search. Gick and Holyoak's radiation-problem experiments showed the gap vividly: people who held a matching analogy usually missed it until prompted, and a simple hint or a second example lifted their success rate sharply. So make the search deliberate. Strip your problem to its bare structure, scan unrelated domains for the same pattern, and map the parts across with care.

• Framing and Defining Problems
• How Experts Solve Problems