Models and the real world · Methods and tools

How do the assumptions built into a model shape the conclusions it can reach?

Whether a population is modelled as growing exponentially or levelling off, or whether people are assumed to act independently, can decide what a model concludes. This question asks how far a model's results are discovered from data and how far they are built in by its assumptions.

Claims

Assumptions are stated openly and can be tested, so a good model makes its own limitations visible and its conclusions conditional.
Comparing models with different assumptions shows which conclusions are robust and which depend on one choice.

Counterclaims

Once results are reported, the assumptions are often lost, so readers take conditional conclusions as unconditional facts.
Modellers' own expectations can guide which assumptions seem reasonable, so a model may confirm what its makers already believed.

Real-life situations from mathematics

Malthus and population

In 1798 Thomas Malthus argued that population tends to grow geometrically while food supply grows arithmetically, predicting recurring famine. Changes in farming technology and birth rates meant his assumptions did not hold as he expected.

Logistic versus exponential growth

Fitting early epidemic or population data with an exponential model and with a logistic model can give similar fits at first but very different forecasts later, which is why the choice of model must be justified.

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 assumptions, bias or the reliability of predictions in the human and natural sciences.

Exhibition. Two graphs from the same data, one fitted exponentially and one logistically, show how assumptions decide conclusions.

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 Methods and tools

How mathematical knowledge is produced and justified.