Every Map Is an Argument

Mercator's 1569 world map is titled, in full, Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendate Accommodata. A new and fuller representation of the terrestrial globe, properly adapted for use in navigation.

The purpose is in the title, and the purpose is not "show what the world looks like." It is a working instrument, built so that a line of constant compass bearing comes out straight. Everything the projection is criticised for is the price of that one feature, and Mercator knew the price when he paid it.

I want to look at five maps, or objects that behave like maps, because the same thing is true of every representation anyone makes. A view is a set of decisions about what to preserve and what to sacrifice, and the decisions are almost never visible in the output.

Gerardus Mercator, Nova et Aucta Orbis Terrae Descriptio, Duisburg, 1569. Eighteen copper-plate sheets, assembled 202 × 124 cm. Public domain, via Wikimedia Commons.

What Mercator actually traded

The trade is exact and it is arithmetic. Linear scale grows as the secant of the latitude, so area grows as the secant squared. At sixty degrees, lengths double and areas quadruple. At seventy, areas are inflated by about eight and a half times. At eighty, by thirty-three.

The familiar complaint is that Greenland appears roughly the size of Africa. That is true of the appearance. Greenland is 2,166,086 square kilometres. Africa is about 30,365,000. The real ratio is fourteen to one.

Worth pausing on, because the number cuts both ways. People say "Mercator lies about size" as if the distortion were a bug. It is the exact and unavoidable consequence of the feature that made the map worth printing, which is that a navigator could lay a ruler on it and steer the bearing.

A projection does not have errors. It has a budget, and it spends it somewhere.

The fight that followed, and why the cartographers were angry

The Gall-Peters projection. Areas are correct; shapes are not. Image by Strebe, CC BY-SA 3.0, via Wikimedia Commons.

In May 1973, at a press conference in Bonn, the historian Arno Peters presented an equal-area world map and argued that Mercator made wealthy Europe and North America look large relative to poorer Africa and South America. The political point landed, and the map spread through aid agencies, churches and schools.

The cartographic profession's reaction is usually told as establishment defensiveness. It was partly that. But the substantive objection was narrower and fairer than the telling suggests: Peters claimed his was the only area-correct map, which was false, and the same projection had been presented by James Gall to the British Association in 1855, more than a century earlier.

Then, in 1989, seven North American geographic organisations published a joint resolution. It is worth reading in full, because it does not say what people assume it says:

WHEREAS, frequently seeing a greatly distorted map tends to make it "look right," THEREFORE, we strongly urge book and map publishers, the media and government agencies to cease using rectangular world maps for general purposes or artistic displays. Such maps promote serious, erroneous conceptions by severely distorting large sections of the world, by showing the round Earth as having straight edges and sharp corners, by representing most distances and direct routes incorrectly, and by portraying the circular coordinate system as a squared grid. The most widely displayed rectangular world map is the Mercator (in fact a navigational diagram devised for nautical charts), but other rectangular world maps proposed as replacements for the Mercator also display a greatly distorted image of the spherical Earth.

That last clause is aimed at Peters. The resolution condemns both maps, in the same sentence, for the same reason. It is not a pro-Peters document and it is not a pro-Mercator one. It is an argument that a rectangle is the wrong container.

There is a line in there I have quoted to people in meetings: frequently seeing a greatly distorted map tends to make it look right. Familiarity is doing the work that accuracy is assumed to be doing. That is true of every default view anyone ships.

Before north was up

The Hereford Mappa Mundi, about 1300. A single sheet of vellum, 64 × 52 inches. Hereford Cathedral. Public domain, via Wikimedia Commons.

The Hereford map puts east at the top and Jerusalem at the centre. It is tempting to file that as medieval error, and it is not. Hereford Cathedral's own description says what the object is for: it records how thirteenth-century scholars interpreted the world in spiritual as well as geographical terms.

The centring is the content. A map that places Jerusalem in the middle is asserting that the world has a middle and naming it. Put north at the top instead and you have made a different assertion, one so familiar that it reads as no assertion at all.

The diagram that admitted it was a diagram

Harry Beck was out of work when he offered the London Underground an unsolicited redrawing of its map in 1931. The publicity department turned it down as too radical. Beck's own account of the moment is the best sentence in this article:

My Underground map was handed back to me, and it seemed like that was the end of it.

It was not. A trial run of five hundred copies went out in 1932; the full edition in 1933 ran to seven hundred thousand and was reprinted within a month. He was paid ten guineas for the card artwork and five for the poster, although the sources disagree and at least one account says he was never actually paid.

What Beck removed was geography: true scale, true position, surface detail. What he kept was sequence, interchange and direction, plus one piece of the real world, the Thames, as an anchor. The result is not a map and does not claim to be. It is a diagram of a network, and its usefulness comes precisely from having thrown the terrain away.

I would show it to you, but I cannot. The design is Transport for London's copyright, licensing is administered on their behalf, modification is prohibited, and Beck died in 1974, so the term runs to the end of 2044. That is worth knowing if you have ever been handed a "just use the tube map style" brief.

The lesson underneath is the one I actually use. Beck's diagram is honest because the distortion is obvious. Nobody has ever walked between two stations using it and felt deceived, because it never offered to be a map. Mercator is dangerous for the opposite reason: it looks like a picture of the world, so people read it as one.

The lies cartographers told on purpose

Mapmakers are supposed to have inserted fake streets to catch copiers. Most of what is told about this is folklore, so here is what survives checking.

Table 1. Four stories, two of which hold up.

The court case is the one that matters, and it kills the whole practice as a legal strategy. The judge's reasoning:

To treat "false" facts interspersed among actual facts as fiction would mean that no one could ever reproduce actual facts without risk of violating a copyright.

The Ordnance Survey settlement is usually cited as the great trap-street victory. It was a twenty million pound settlement in March 2001 covering over three hundred million copies of AA products, and the Survey proved copying by fingerprinting its own cartographic styling, road widths and similar, not by planting anything. Their own freedom-of-information response says it flatly: there are some publishers who put deliberate mistakes in their maps, and we don't do that.

Agloe, the paper town that supposedly became real when someone opened a general store there, is the version everybody knows. The town is real enough as an invention: Otto Lindberg and Ernest Alpers of the General Drafting Company placed it at a dirt crossroads in the 1930s, the name an anagram of their initials. The lawsuit is not documented. The Colchester Historical Society searched its files in 2012 and found a postcard for "Agloe Lodge on the Beaverkill" and nothing at all about a general store. Longtime residents say there never was one.

Mount Richard is the better story anyway, because the Denver Public Library archivists found the actual object and are honest about what they cannot know. A fake peak on the continental divide in the southwest corner of Boulder County, probably drawn by a county draftsman named Richard, surviving at least two years before anyone noticed. Whether Richard was protecting his work or just wanted a mountain named after him, as the library puts it, remains unknown.

Video. "The World of Ptolemy and the Birth of the Cartographic Atlas," Library of Congress.

What this does to anything with a default view

Three things I hold with different confidence.

• Certain. A default is an argument that has stopped being audible. Whatever projection, sort order, date range, currency, unit or baseline a system opens with, most users will never change it, and a majority of them will take it as neutral. The 1989 resolution is right that familiarity converts distortion into apparent correctness.

• Fairly confident. Beck's honesty is available and underused. A view that visibly abandons fidelity is safer than one that quietly compromises it. If a chart is schematic, make it look schematic. The danger zone is the representation that is accurate enough to be believed and wrong enough to mislead.

• Least confident, but I keep finding it true. The argument about which projection is correct is the wrong argument, exactly as the cartographers said. There is no correct one. There is only a stated purpose, and a distortion budget spent in service of it. A chart without a stated purpose is not neutral. It is a chart whose purpose nobody wrote down.

A deep dive into one map that makes all of this visible at once, the Catalan Atlas of 1375, is on my Korean blog: 베이니월드.

Sources

Mercator's title, sheet count and legends, and the secant-squared area relation: the 1569 map's scholarly record and the standard treatment of the projection. Greenland's area from Statistics Greenland, Greenland in Figures 2022; Africa's from Britannica. The 1989 resolution was published as "Geographers and cartographers urge end to popular use of rectangular maps," The American Cartographer 16 (1989), 222 to 223. Hereford: Hereford Cathedral. Beck: London Transport Museum and Transport for London. The Ordnance Survey settlement and its denial of trap streets: Ordnance Survey FOI 231143. Mount Richard: Denver Public Library. Agloe's missing store: Colchester Historical Society.

One thing I could not verify and have not printed: the names of the seven organisations that signed the 1989 resolution. The wording is confirmed from two independent reproductions; the signatory list is not published anywhere I could reach. What is confirmed is that the North American Cartographic Information Society declined to endorse it.