Cao Chong's Elephant Weighing
Updated 2026-08-22
INTRODUCTION
English translation pending.
CORE DEFINITION
Recorded in the Records of the Three Kingdoms, the child Cao Chong was asked to weigh an elephant with no scale large enough. He loaded the animal onto a boat, marked the waterline, replaced the elephant with stones until the same mark was reached, and weighed the stones separately. The method is equivalent substitution: when a quantity cannot be measured directly, it is converted into a form that can, and the two are connected by a shared invariant, here the displacement of the boat.
SCAFFOLDING EFFECT
Reduce cognitive load
- Find the equivalent: look for a measurable stand-in connected to the target by an invariant. - Swap, do not estimate: replace the object rather than guessing at its size. - Check the invariant: confirm the equivalence actually holds before trusting the result.
Anchor fast decisions
Direct measurement fails because no instrument spans the object, but the boat's displacement responds to weight regardless of what causes it. Loading the elephant, marking the waterline, then substituting stones until the mark returns copies the same force onto objects that an ordinary scale can handle. The invariant, equal displacement, carries the elephant's weight into the stones, and the stones are measurable in parts.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
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Source support: Explicit
- zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E4%B8%89%E5%9B%BD%E5%BF%97verified
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