Models and the real world · Perspectives
Can a representation be accurate and misleading at the same time?
Every flat map of the round Earth distorts something: areas, angles, distances or shapes. A map can be perfectly accurate for its purpose and still give a false impression. This question asks how mathematics helps us understand, and choose between, such trade-offs.
Claims
- Mathematics shows exactly what each projection preserves and distorts, so a well-chosen map is accurate knowledge for its purpose.
- Being misleading is a fault of the user, not the representation; knowing the method removes the problem.
Counterclaims
- Most people never learn how a map was made, so the choice of representation shapes their beliefs, for example about the size of countries.
- Choosing a representation can reflect political or cultural perspectives, so mathematics does not make the choice neutral.
Real-life situations from mathematics
The Mercator projection
Gerardus Mercator's 1569 map keeps compass directions as straight lines, which made it ideal for navigation, but it greatly enlarges areas far from the equator. Greenland appears similar in size to Africa, which is about fourteen times larger.
The Gall–Peters debate
In 1973 Arno Peters promoted an equal-area projection as fairer to countries near the equator. Cartographers pointed out that equal-area maps were already known and that his map distorted shapes, and the debate became as much about politics as mathematics.
Check dates and figures in a reliable source before you use them, and cite that source.
Use this in your TOK work
Essay. Excellent for titles about representation, perspective or whether knowledge can be neutral.
Exhibition. A Mercator wall map is one of the most popular and effective maths-linked objects; make your commentary specific about what it preserves and distorts.
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 language Perspectives
Different views of what mathematics is and whose it is.