Models and the real world · Methods and tools

If every mathematical model leaves something out, how can models produce knowledge?

A model keeps some features of a situation and ignores others so the mathematics can be done. The statistician George Box made the point that all models are wrong, but some are useful. This question asks how a deliberately incomplete picture can still give knowledge, and how we tell when a model has left out too much.

Claims

Simplifying is what makes knowledge possible: a model that included everything would be as complicated as the world and explain nothing.
Models can be tested against data, and a model that predicts well, within stated limits, gives reliable knowledge about those limits.

Counterclaims

Users of a model often forget its assumptions, so its conclusions can be trusted beyond the range where they hold.
Choosing what to leave out is a judgement, and different modellers can make different choices that lead to different conclusions.

Real-life situations from mathematics

COVID-19 epidemic models

In March 2020 epidemic models from Imperial College London projected deaths under different policies and influenced the UK's decision to introduce a lockdown. The models were praised and criticised for their assumptions about how people would behave.

SIR models in the classroom

The simple SIR model splits a population into susceptible, infected and recovered groups. It captures the rise and fall of an epidemic but ignores ages, places and behaviour, which is both its power and its limit.

Check dates and figures in a reliable source before you use them, and cite that source.

Use this in your TOK work

Essay. Fits titles about models, simplification or prediction across the natural and human sciences. Your IA modelling experience is a strong personal example.

Exhibition. A screenshot of an epidemic curve from 2020 is a powerful object for a prompt about the reliability or consequences of knowledge.

Link it to the prescribed title or the exhibition prompt you are working on, in your own words. See using maths examples in your essay and choosing exhibition objects.

Themes and study heading

Knowledge and politics Knowledge and technology Methods and tools

How mathematical knowledge is produced and justified.