Sanity Check (Plausibility Heuristic)
The technique of comparing the output of a mechanical process against real-world constraints. It prevents blind acceptance of absurd results (like -4 grams of water) by forcing a contextual evaluation of the outcome.
THE IDEA
The core heuristic is the Sanity Check—the habit of asking whether a result makes sense given the problem's context. The text illustrates this with a calculus exam where a student mechanically arrives at -4 grams for the weight of water in a jug. The instructor awards half credit to the student who recognizes the absurdity (demonstrating understanding) and zero credit to the student who simply submits the impossible number without comment. This highlights the distinction between procedural fluency and genuine understanding.
The author frames this within the 'math wars' between:
- Traditionalists: Emphasizing memorization, standard algorithms, and exact answers.
- Reformists: Emphasizing meaning, guided discovery, and approximation.
The sanity check belongs to a necessary middle ground. The author argues we must teach a mathematics that 'values precise answers but also intelligent approximation, that demands the ability to deploy existing algorithms fluently but also the horse sense to work things out on the fly'. A computer can perform an integral or a linear regression, but 'understanding whether the result makes sense—or deciding whether the method is the right one to use in the first place—requires a guiding human hand.'
Ellenberg warns against training students to become 'a very slow, buggy version of Microsoft Excel'. A plausibility check asks them to examine what a computed answer means before accepting it.
When to use it
Academic Grading: Award partial credit for recognizing an impossible result as well as for carrying out the procedure correctly.
Data Science: Examining summary statistics and simple cross-tabs before building complex models to validate basic plausibility.
Medical Diagnosis: Questioning a lab result that starkly contradicts a patient's clear physical symptoms, prompting a retest.
Financial Modeling: Evaluating whether a projection (e.g., 50% annual returns) passes a quick reality check against historical benchmarks before committing resources.
FROM THEORY TO EVERYDAY LIFE
In practice
The -4 Gram Jug of Water
A student works through a calculus problem about water flow and derives a final weight of -4 grams. A sanity check reveals that mass cannot be negative in this context. The student who flags this issue receives half credit; the student who circles it gets none, demonstrating the value of contextual evaluation.
Linear Regression in Business
A sales regression reports a perfect R-squared and a positive price coefficient. That combination prompts a data scientist to check the data, model specification, and interpretation. The coefficient alone does not prove an error: price may also vary with product quality or other factors.
A MOMENT TO REFLECT
Put it to work.
What is a common calculation or assumption in your work where the result could be technically correct but completely ridiculous?
How can you build a two-second 'plausibility check' into your next important analytical task?
When teaching a method or procedure, do you deliberately emphasize the final 'gut check' as much as the steps themselves?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- How Not to Be Wrong The Power of Mathematical Thinking (Ellenberg, Jordan)