Every map is an argument

Take an orange, eat it carefully, and try to flatten the peel onto a table without tearing it.

You can't. Not by pressing, not by clever cutting, not by being patient. A sphere and a flat sheet are different kinds of surface, and no amount of skill gets you from one to the other with everything intact. Carl Friedrich Gauss proved this properly in 1827, and gave the result a name that sounds like boasting because it was: the Theorema Egregium, the remarkable theorem. Curvature is baked into a surface. You can't press it out.

Which means every flat map of the world is wrong. Not sloppy — wrong by necessity, in a way that can be measured. The only choice a mapmaker gets is which kind of wrong to accept, and that choice is where the arguments start.

You get to keep some properties, never all of them

There are four things a map might preserve: shape, area, distance and direction. You can have some. You can't have the set.

A conformal projection keeps angles right locally, so small shapes look correct — a bay looks like that bay. It pays by wrecking area. An equal-area projection keeps relative sizes honest, so a country covering one per cent of the planet covers one per cent of the paper. It pays by shearing and squashing shapes. You cannot have both at once anywhere except in trivial cases; that's not a limitation of current technique, it's arithmetic. Equidistant projections keep true distances, but only measured from one or two chosen points, which tells you something about who such a map is drawn for.

There's a lovely tool for seeing this. In the nineteenth century Nicolas Auguste Tissot worked out that you can scatter tiny circles across the globe and then draw what each one becomes on the flat map. On a conformal map they stay circles and swell enormously towards the poles. On an equal-area map they all keep the same area and turn into ellipses of increasingly violent eccentricity. The distortion doesn't hide. People just don't usually put the circles on.

So there's no neutral map. There's only a set of trade-offs somebody made, usually for a reason, and usually without writing the reason in the corner.

Mercator was a machine for not dying at sea

Gerardus Mercator published his world map in 1569, and the full Latin title says exactly what it's for: a new and enlarged description of the Earth, corrected and adapted for the use of navigators.

Here's the problem he was solving. A sailor steering a constant compass bearing doesn't travel in a straight line across the globe — the path curves, and it's called a rhumb line or loxodrome. On most maps that path is a curve you'd have to construct with instruments and trigonometry, on a heaving deck, possibly at night. Mercator stretched the spacing between lines of latitude at exactly the rate needed to compensate for the way the meridians had been forced apart into parallel lines. The effect is that any straight line you rule between two points on the chart is a constant bearing. Lay a ruler down, read the angle, steer it.

That's an extraordinary piece of design, and it saved a great many lives. It also has a price, and the price is enormous.

Because the stretch grows the further you get from the equator, area inflates without limit towards the poles. Greenland is about 2.2 million square kilometres. Africa is about 30 million. On a Mercator map they look comparable. Greenland is roughly the size of the Democratic Republic of the Congo and no more, and almost nobody's mental image of the world reflects that. The poles themselves can't be drawn at all — they'd be infinitely far up the page — so Mercator world maps just get chopped off somewhere in the eighties of latitude and the top of the planet quietly ceases to exist.

None of that mattered to the person Mercator built it for. A navigator doesn't care how big Greenland looks. A navigator cares about the bearing.

The trouble began when a chart designed for a specific technical job got hung on classroom walls as a general-purpose picture of the world, which it never claimed to be, and stayed there for four centuries.

The Peters fight was about who's allowed to choose

In 1973 the German filmmaker and historian Arno Peters held a press conference to launch a world map he presented as a correction of a distorted, Eurocentric worldview. His map was equal-area. Countries near the equator, which is where most of the world's poorer nations happen to sit, occupied their honest share of the sheet. Aid agencies, churches and development organisations adopted it in large numbers.

Cartographers went up like a rocket, and their objections are worth separating, because two of the three are technical and one isn't.

First: the projection wasn't new. James Gall had published essentially the same construction in the 1850s, which is why it's now generally called Gall–Peters. Second: equal-area came at a brutal cost to shape, stretching landmasses near the equator into long vertical smears and flattening high latitudes, and several cartographers said publicly that the continents looked like wet laundry hung out to dry. Third, and this is the one that wasn't really about geometry: the profession disliked being told by an outsider that its standard products carried a political message.

The row ran for years. In 1989 seven North American geographic bodies issued a joint resolution urging publishers and the media to stop using rectangular world maps of any kind for general purposes, Mercator and Gall–Peters alike, on the grounds that they all misrepresent the planet badly. That's an unusual document. It's a professional body conceding that map choice has consequences for what people believe, while refusing the particular fix on offer.

Judge Peters however you like — the historical claim that Mercator was designed to flatter Europe doesn't hold up, since it was designed to hold a bearing. But notice what the whole episode demonstrates. Two groups fought bitterly, in public, for two decades, over which distortion the world's schoolchildren should grow up with. Nobody behaves like that about a neutral instrument.

What most publishers actually did was retreat to compromise projections that are neither conformal nor equal-area and just try to look reasonable. Arthur Robinson built one in 1963 by eye rather than by formula, adjusting it until it seemed right, and National Geographic used it from 1988 before switching in 1998 to the Winkel Tripel, devised by Oswald Winkel in 1921 and named for the three things it tries to minimise at once without perfecting any of them.

Everything you don't see was removed by somebody

Distortion is the famous problem. Selection is the bigger one.

A map at any usable scale has to leave out almost everything. Cartographers call it generalisation, and it's a set of deliberate operations: choosing what classes of thing appear at all, smoothing coastlines, merging clusters of buildings into a blob, straightening rivers, dropping the smaller settlements, exaggerating a road so it's wide enough to see when at true scale it'd be thinner than the ink.

That last one is worth sitting with. On a 1:250,000 road map, a drawn road two millimetres wide represents a corridor five hundred metres across. The road is not that wide. It's drawn wrong on purpose because a correctly-scaled road would be invisible, and a map you can't read is worse than a map that lies a bit.

Borges wrote the joke version in 1946: an empire whose cartographers grew so skilled they made a map at one-to-one, covering the territory exactly, useless, eventually left to rot in the desert. Lewis Carroll had got there first in 1893, with the punchline that the farmers objected because it would block the sunlight, so they use the country itself as its own map and it does nearly as well. Alfred Korzybski put the same point in a sentence in 1931 that's been repeated ever since: the map is not the territory.

The practical consequence is that somebody, somewhere, decided which categories of thing exist. Footpaths but not desire lines. Churches but not mosques, or both, or neither. Formal settlements but not informal ones — vast neighbourhoods in some cities have appeared on official maps only recently, and their absence had real effects on whether services reached them. Left off isn't the same as not there.

Some things get left off on purpose

And then there's deliberate omission, which is more common than you'd think.

Military sites vanish from national mapping in a lot of countries, sometimes replaced by plausible fields. British Ordnance Survey maps have historically blanked sensitive installations. Soviet civilian maps were systematically falsified for decades — towns shifted, rivers moved, coastlines redrawn — while accurate versions existed for military use.

Commercial mapmakers do something stranger. They insert fake entries to catch copiers: a street that doesn't exist, a bend that isn't there, a village invented from initials. The best-known is Agloe, New York, made up by two men at a map company from an anagram of their initials. Years later somebody built a shop at the crossroads and called it the Agloe General Store, because the map said there was a place there. A fictional town willed itself into existence by being drawn.

Disputed territory is where omission turns into diplomacy. Publishers routinely produce different editions of the same map for different national markets, with borders drawn to match the position of the government in each place — solid lines here, dashed lines there, a whole region attached to one country in one edition and another elsewhere. Digital map providers do this too, serving different border rendering depending on which country you're looking from. Both approaches are choices. There's no version of that page that offends nobody, which is precisely the point.

The centre and the top are decisions too

North is not up. There's nothing in physics that says so.

Medieval European world maps often put east at the top, towards Jerusalem and the rising sun — which is where the word "orientation" comes from. The great twelfth-century map made by al-Idrisi for Roger of Sicily has south at the top, in the standard practice of Islamic cartography of the period. Chinese maps had their own conventions. North won partly because of the compass and partly because the states that ended up printing the most maps were in the northern hemisphere, and it hardened into a convention so complete that a south-up map now reads as a provocation. Stuart McArthur published one in 1979 with Australia at the top and called it a Universal Corrective Map, which tells you how he expected people to react.

The centre is a decision as well. A map centred on the Atlantic splits the Pacific down both edges and puts Europe and Africa in the middle; standard maps in Japan, China, Australia and New Zealand centre the Pacific instead and slice the Atlantic, and the world looks genuinely different — the Americas move east, and Asia stops being on the margin.

Even the numbers have an origin story. Longitude has to be measured from somewhere and there's no natural zero, so for centuries different countries used different prime meridians. In 1884 an international conference in Washington voted for Greenwich, largely because most of the world's shipping already used British charts. France abstained and carried on using the Paris meridian for another quarter of a century. The grid on your map is the result of a vote.

Names are the loudest argument on the sheet

Get two people to agree on the shape of a coastline and you still won't get them to agree on what to call the water next to it.

The body of water between Korea and Japan is labelled differently depending on who published the map, and the disagreement has occupied diplomats for decades. The gulf between Iran and the Arabian peninsula has two names in active competition. The islands in the South Atlantic that Britain calls the Falklands are the Malvinas in Argentina and much of Latin America. In Northern Ireland, whether you write Derry or Londonderry is read instantly as a statement, which is why some publishers write both.

Renaming is one of the first things newly independent or newly assertive states do, and it's not decoration. Bombay became Mumbai in 1995, Madras became Chennai in 1996, Calcutta became Kolkata in 2001. Colonial-era names across Africa and Asia were replaced wholesale after independence. Australia moved to dual naming for Uluru, the name it had for a very long time before someone attached a colonial official's name to it, and the dual form is now standard.

Cartographers have a technical vocabulary for this — an endonym is what locals call a place, an exonym is what outsiders call it — and the vocabulary doesn't dissolve the problem. Every gazetteer has to pick. Picking is taking a position, and writing both names is also taking a position, and leaving the label off entirely is a third one.

Digital maps changed the default view

Something significant happened in 2005 and hardly anyone noticed the projection.

Web mapping settled almost universally on a variant of Mercator, usually called Web Mercator. The reasons are engineering: it's conformal, so shapes stay right at every zoom level and streets meet at the correct angles when you're navigating; it maps neatly onto square tiles that halve cleanly as you zoom; and it makes the maths cheap enough to run smoothly on a phone. Which means the most-viewed map in human history is a sixteenth-century navigation projection, chosen again, for essentially the same reason — it's excellent for getting from here to there.

It has the same failing at global zoom, so Greenland went on looking continental until desktop map services started rendering a globe when you pull far enough back.

The deeper change is the default itself. Nobody sees the whole world any more. The map opens on you, at street level, north-up, with a search box, and the wider planet is somewhere behind fifteen scroll wheels. Paper maps forced you to see a region in one glance and to see everything on that sheet, including things you weren't looking for. A search-driven map shows you what you asked for, plus whatever's in the database, plus whatever the ranking puts near the top.

Which relocates the old question rather than answering it. "What gets left off" used to mean what the cartographer omitted. Now it mostly means what isn't in the index — a business that never registered, a path nobody traced, a settlement no surveyor has visited. Volunteer projects like OpenStreetMap fill enormous gaps, and their coverage follows their contributors, so places with lots of enthusiastic mappers are mapped in loving detail and places without them aren't.

How to read one

The title of this piece isn't a slogan about maps being propaganda. Most maps are made honestly by people trying to be useful.

It's the narrower claim that the evidence above supports. A map is a chain of decisions — projection, centre, orientation, scale, what classes of thing exist, which names, which borders, what's suppressed, what the software indexed — and every link had alternatives, and the alternatives serve different people. Put together, those choices make a case about what the world is like and what's worth noticing in it. That's an argument, whether or not anyone meant it as one.

So a few habits. Find the projection, usually printed small in the margin, and ask what it sacrificed. Check where the centre and the top are. Ask who commissioned the thing — national mapping agencies often began as military or tax projects, and the Ordnance Survey is named after the Board of Ordnance for exactly that reason. Look at what's labelled and what's blank, and treat blank as data rather than emptiness. Watch out for maps coloured by area when the subject is people, because land doesn't vote, doesn't get ill and doesn't buy anything.

Then use it anyway. A map that argues is still the best tool anyone's built for holding a large amount of the world in your head at once.

You just want to know what it's arguing.