Cognitive Scaffold

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MENTAL MODEL · M12539

Duncker's Radiation Problem

Duncker's Radiation Problem
Learn & MetacognitionHigh supportCognitive Psychology
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Updated 2026-08-16

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INTRODUCTION

English translation pending.

CORE DEFINITION

Karl Duncker introduced the radiation problem to study problem solving and functional fixedness. A patient has an inoperable tumor, and rays strong enough to destroy it would also destroy the healthy tissue they pass through. The accepted solution is to direct several weak beams from different angles so that they converge at the tumor, delivering a lethal dose there while each path stays harmless. The qualification is that the problem tests how a situation is represented: most subjects solve it after a fortress-and-generals analogy is supplied, but not before.

SCAFFOLDING EFFECT

psychology

Reduce cognitive load

- Distributed force: when one large intervention would cause damage, split it into weak inputs that converge. - Representation check: if the problem looks unsolvable, restate it and see whether new moves appear. - Analogy transfer: borrow the structure of a solved distant problem and map it onto yours.

anchor

Anchor fast decisions

The obstacle is not a missing fact but a fixed representation: the ray is treated as a single object that must travel one path at full strength. Reframing it as many weak sources removes the trade-off between effectiveness at the target and safety along the path. The mechanism generalizes, because any problem whose binding constraint is concentration can be reopened by redistributing the same total effort across several partial approaches.

MINIMUM ACTION

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Source support: Explicit

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    en.wikipedia.orghttps://en.wikipedia.org/wiki/Candle_problemZH · Explicit
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