Maps and Projections

The Inevitable Distortion

Gauss proved that a sphere cannot be flattened onto a plane without distortion. Every projection saves one property by sacrificing others:

There is no neutral map. The choice of projection is an argument.

Mercator's Bargain

Mercator's projection (1569) keeps constant compass bearings as straight lines—a navigator's dream. To stay conformal, vertical stretch must match horizontal stretch at every latitude. The cost is massive area inflation at poles: Greenland looks as large as Africa, though Africa is $\approx 14 \times$ larger.

Beyond Math: Rhetoric & Power

Projections are just the math layer. Maps also use rhetoric: centring (what sits in the middle), orientation (north is just a convention), naming, line weight, and blankness (erasing indigenous peoples).

Mapping makes land administrable. Cadastral surveys replace overlapping customary rights with fixed boundaries to tax land. Colonial maps created states before realities caught up.

Pitfall: Treating a specialized tool like Mercator as "what the world looks like" turns a map into covert propaganda.