What Is a Model? A Deliberate Simplification That Earns Its Keep

A representation as complicated as the thing it represents would be no easier to reason about than the thing itself, so every model discards detail deliberately. Which detail is discarded is the modelling decision, and it determines what the model can answer and where it will mislead. A model of a planet's orbit treating it as a point mass is false, since planets have size and structure, and it is exactly right for calculating the orbit, while being useless for anything about tides. That pattern holds generally, and the standard formulation is that all models are wrong and some are useful, which is quoted so often that its content is easily lost. The content is that usefulness is relative to a purpose, so asking whether a model is correct is the wrong question and asking what it is good for is the right one.

Models take several forms and the differences matter for how they are checked:

• •Mathematical models, where relationships are expressed as equations and consequences are derived
• •Computational models, where a system is simulated step by step because the equations cannot be solved directly
• •Physical models, including scale models in wind tunnels and tanks, which use real physics at a different size
• •Animal models, where one organism stands in for another, which carries its own substantial assumptions
• •Statistical models, which describe patterns in data rather than mechanisms producing them
• •Conceptual models, which are qualitative pictures used for reasoning rather than calculation

Assessing a model means comparing its outputs with observations, and the standard practice has several parts because the obvious approach is inadequate. Fitting a model to data and then reporting how well it fits that same data proves very little, since a sufficiently flexible model will fit anything, which is overfitting and is the central hazard. The remedy is to withhold some data during fitting and test against it afterwards, or to test against data collected subsequently, which is why prediction is valued over explanation. Sensitivity analysis varies the assumptions to see which ones the conclusion depends on, and a conclusion robust to the uncertain assumptions is worth far more than one that hinges on them. Comparing several models built on different assumptions is more informative than refining one, since agreement between independent approaches is evidence and agreement within one approach is not.

A recurring hazard is that a model succeeds well enough that people stop distinguishing it from reality. Economic models built on simplified assumptions about behaviour have been used to design institutions, and where the institutions then shape behaviour to match, the model becomes self-confirming rather than validated. Performance measures derived from a model of what matters become targets, and once they are targets the behaviour they measure changes, which is the well-known observation that a measure ceases to be a good measure once it is used to judge. Diagnostic categories are models of clusters of symptoms and are frequently treated as discovered entities. The general point is that a model used to make decisions acts on the world it describes, which is a feedback no model includes in itself, and it is a reason to revisit assumptions periodically rather than only when the outputs look wrong.

Public argument about models, particularly in climate and epidemiology, is frequently conducted in terms that misunderstand what is being claimed. A model output is conditional, stating what follows given the assumptions, so a projection that does not come to pass may indicate a wrong model or a changed input, including changes made because the projection prompted action. A range of outcomes is the honest output and a single number is a summary of it, so reporting the central figure alone removes the most important information. Models are frequently used to compare options rather than to forecast, in which case the comparison can be reliable while the absolute numbers are not. And the criticism that a model is a simplification is never itself an objection, since that is what a model is, and a useful criticism has to identify a specific simplification and explain why it matters for the conclusion drawn.

Discarding detail is the purpose, so a model is deliberately false in chosen ways and its value depends on the question asked of it. Fitting data and reporting the fit proves little, which is why withheld data and prediction matter. A range is the honest output and a single number is a summary. Objecting that a model simplifies is not a criticism unless it says which simplification breaks the conclusion.