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Wonder Constant Labs
Journal
Method1 min read

Models Are Tools, Not Truth

A model earns its keep by being useful under stated conditions — not by being right in general, which no model is.

Modelling & SimulationMathematics

Every model is wrong somewhere. That is not a failing to be apologised for; it is what a model is. A model is a deliberate simplification chosen so that something becomes computable, and the simplification is the whole point. The question is never whether a model is true. It is where it holds, how well, and how you would notice when it stopped.

State the conditions, not just the fit

A fit reported without its conditions is close to meaningless. The same estimator that behaves beautifully inside the range you sampled can produce confident nonsense a short distance outside it, and nothing in the fitted parameters will warn you.

m̂(x) = Σᵢ K((x − xᵢ)/h) · yᵢ ⁄ Σᵢ K((x − xᵢ)/h)

A kernel-weighted average — the estimator used in the figures on this site. It is entirely determined by the observations near x, which is exactly why it should not be trusted where there are none.

So the reporting standard we hold ourselves to is: the model, the data it was fitted on, the range over which it was checked, the residuals, and the conditions under which we expect it to fail. A model published without the last two is a claim, not a tool.

A model is a useful compression of reality, not reality itself.

There is a practical benefit to treating models this way. If a model is a tool rather than a belief, replacing it costs nothing but work. If it has become a position, replacing it costs face — and that cost is paid, eventually, by the accuracy of the result.