Geography is often mistaken for a list of capitals and rivers. Human geography asks a different kind of question: why are people, places and activities arranged the way they are, and what difference does that arrangement make? To ask these questions well you need a few tools for thinking about space.

Location, site and situation

Geographers describe location in two ways. Absolute location is a position given by a coordinate system such as latitude and longitude; it does not change. Relative location describes a place by its connections to other places, and it changes whenever those connections do.

A related pair of terms explains why cities grow where they do. Site means the physical features of the place itself: its soil, water supply, slope, harbor or defensive hill. Situation means a place's position relative to the routes, resources and other places around it. Singapore has a cramped site with little fresh water, yet its situation at the southern end of the Strait of Malacca has helped make it rich.

Scale

Scale has two meanings. Map scale is the ratio between distance on the map and distance on the ground. A map at 1:10,000 shows a neighborhood in detail; a map at 1:10,000,000 shows a continent with almost no detail. The scale of analysis is the level at which a question is studied, from a household to the whole planet. Patterns can appear or vanish when the scale changes. A country can look prosperous on average while some of its regions are poor, and a city that looks diverse as a whole can be made of neighborhoods that are each highly segregated.

A similar problem appears whenever data are grouped into areas. The modifiable areal unit problem is the way results shift depending on how the boundaries for counting are drawn. Draw the zones one way and a cluster of crime or disease appears; draw them another way and it dissolves.

Every flat map distorts

The Earth is close to a sphere, and in 1827 the mathematician Carl Friedrich Gauss proved that a curved surface of this kind cannot be flattened without stretching or tearing. Every map projection must therefore distort some mix of area, shape, distance or direction. Mapmakers choose which errors to accept for a given purpose.

The most famous choice was made by the Flemish cartographer Gerardus Mercator in 1569. The Mercator projection keeps compass directions true, so a line of constant bearing appears as a straight line, which made it ideal for sailors. The price is that areas swell enormously toward the poles. Equal-area projections, such as the one promoted by the German historian Arno Peters in 1973, keep sizes correct but squash and stretch shapes. Peters argued that Mercator maps made Europe and North America look more important than the tropics. Many cartographers agreed about Mercator's flaws but objected that Peters oversold his own map as uniquely fair. Compromise projections, such as the Robinson (1963) and the Winkel tripel, accept a little of every distortion so that none becomes severe.

Maps as arguments

A map is not a photograph. Someone decided what to include, what to leave out, where to center the world and which way is up. Placing north at the top is a convention, not a law of nature: many medieval European maps put east at the top, and the twelfth century world map of al-Idrisi put south there. A choropleth map shades whole areas according to a value such as income or vote share, and it can mislead, because large, thinly populated areas dominate the eye while small, crowded ones nearly vanish.

Geographers also study the maps in people's heads. A mental map is a person's inner picture of places, and it is often inaccurate in revealing ways: people tend to enlarge places they know well and shrink places they ignore. In 1970 the geographer Waldo Tobler stated what is now called the first law of geography, the idea that all things are related but nearby things are more closely related than distant ones. A closely related idea, distance decay, holds that interaction between places usually falls as distance grows, whether the interaction is trade, commuting or friendship.

Worked example: Greenland and Africa

On a standard Mercator world map, Greenland looks roughly as large as Africa. In fact Africa covers about 30 million square kilometers and Greenland about 2.2 million, so Africa is roughly fourteen times larger. Africa straddles the equator, where Mercator's distortion is smallest, while Greenland sits far to the north, where the projection stretches areas many times over. The same effect makes Alaska look far larger than Mexico, though Mexico is actually bigger.

None of this means Mercator lied. His map does exactly what it was built to do, which is to help sailors hold a course. The trouble began when a navigation tool became the default picture of the world on classroom walls, quietly teaching generations of children that high-latitude countries were bigger than they are. An equal-area map is the right choice for comparing sizes, while a version of Mercator is still used by online street maps, because at the scale of a city block it keeps shapes and angles accurate. Before trusting a map, ask what it was made to do.