## All Models Are Wrong

All models are wrong‘ is a common aphorism in statistics; it is often expanded as ‘All models are wrong, but some are useful.’ It is usually considered to be applicable to not only statistical models, but to scientific models generally. The aphorism recognizes that statistical or scientific models always fall short of the complexities of reality but can still be of use.

The aphorism is generally attributed to the statistician George Box, although the underlying concept predates Box’s writings. He offered the ‘ideal gas law’ as an example: ‘PV = RT relating pressure P, volume V and temperature T of an ‘ideal’ gas via a constant R is not exactly true for any real gas, but it frequently provides a useful approximation and furthermore its structure is informative since it springs from a physical view of the behavior of gas molecules.’

Statistician J. Michael Steele has commented on the aphorism: ‘… there are wonderful models — like city maps…. If I say that a map is wrong, it means that a building is misnamed, or the direction of a one-way street is mislabeled. I never expected my map to recreate all of physical reality, and I only feel ripped off if my map does not correctly answer the questions that it claims to answer.’

In 2013,  philosopher of science Peter Truran published an essay related to the aphorism, noting: ‘… seemingly incompatible models may be used to make predictions about the same phenomenon. … For each model we may believe that its predictive power is an indication of its being at least approximately true. But if both models are successful in making predictions, and yet mutually inconsistent, how can they both be true? Let us consider a simple illustration. Two observers are looking at a physical object. One may report seeing a circular disc, and the other may report seeing a rectangle. Both will be correct, but one will be looking at the object (a cylindrical can) from above and the other will be observing from the side. The two models represent different aspects of the same reality.’

Truran’s essay further notes that Newton’s theory of gravitation has been supplanted by Einstein’s theory of relativity and yet Newton’s theory remains generally ’empirically adequate.’ Indeed, Newton’s theory generally has excellent predictive power. Yet Newton’s theory is not an approximation of Einstein’s theory. For illustration, consider an apple falling down from a tree. Under Newton’s theory, the apple falls because Earth exerts a force on the apple—what is called ‘the force of gravity.’ Under Einstein’s theory, Earth does not exert any force on the apple. Hence, Newton’s theory might be regarded as being, in some sense, completely wrong but extremely useful. (The usefulness of Newton’s theory comes partly from being vastly simpler, both mathematically and computationally, than Einstein’s theory.)

In 1923, a related idea was articulated by the artist Pablo Picasso. ‘We all know that art is not truth. Art is a lie that makes us realize truth, at least the truth that is given us to understand. The artist must know the manner whereby to convince others of the truthfulness of his lies.’

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