필사 모드: Why Maps Lie — From Mercator to the Search Algorithm

Introduction — Why Does Greenland Look the Size of Africa

Picture the world map on the classroom wall. Snow-white Greenland sits at the top, Africa sits low in the middle, and the two look roughly the same size. The actual figures are about 2.17 million square kilometres for Greenland and about 30.37 million for Africa. Africa is fourteen times larger than Greenland.

Calling this a mistake ends the conversation before it starts. The accurate statement is this: that map was never built to show area in the first place. It was a tool designed so that a 16th-century navigator could draw a compass bearing as a straight line, and for that purpose it deliberately sacrificed area. The problem begins when the tool is moved onto a classroom wall.

To doubt a map is also to doubt its maker. What goes in the middle, which way is up, which names get written, which lines are drawn solid — all of these are choices. And behind every choice stands somebody choosing.

A Sphere Cannot Become a Plane — The Gauss Proof

Start with the mathematics. Peel an orange and press the skin flat on a desk and it will always tear or overlap somewhere. This is not a question of dexterity but a theorem. In 1827 Carl Friedrich Gauss proved, in a paper on curved surfaces, that the degree to which a surface is curved is an intrinsic property measurable from within the surface itself, and that it cannot change unless the surface is stretched or compressed. He was so pleased with the result that he named it the remarkable theorem.

The consequence is brutally simple. A sphere and a plane have different intrinsic curvature. Therefore every flat map without exception distorts something. The choice is not whether to distort but what to distort.

Cartography has sorted these choices into families. Conformal projections preserve angles and local shape. Equal-area projections preserve the ratio of areas. Equidistant projections preserve distances from a chosen point. And compromise projections preserve none of them fully, spreading the total error evenly instead. One further cold theorem attaches to the list: no map can be conformal and equal-area at the same time.

There is even a tool that makes the size of the distortion visible. It is the indicatrix devised in 1859 by the Frenchman Nicolas Auguste Tissot. You place small circles of equal size all over the surface of the globe, project them, and watch how much each one swells and squashes. Lay Tissot indicatrices over a Mercator map and the circles balloon like snowballs as you move north from the equator, in plain sight.

The Defence of Mercator and the Counterattack of Peters

In 1569 the Flemish cartographer Gerardus Mercator published a large world map made up of eighteen separate sheets. The Latin title is long, but its heart is at the end: a description of the world corrected and adapted for the use of navigators. This map was not a portrait of the world but a navigational calculator.

The principle runs as follows. If you sail holding a constant compass bearing, on the globe you trace a spiral that winds toward the pole. To turn that rhumb line into a straight line on paper, you must stretch the spacing of the parallels by exactly the same ratio by which you spread the meridians apart. That ratio is the secant of the latitude. At 60 degrees, lengths double and areas quadruple; at 80 degrees, lengths alone stretch more than fivefold. Mercator approximated this expansion by geometric construction, and the man who supplied an accurate mathematical table was the Englishman Edward Wright in 1599. For a navigator this was a revolution. You could now cross an ocean following a line drawn with a ruler, watching nothing but a compass.

The trouble is that this navigational instrument spent the whole of the 20th century hanging in classrooms, in newspapers and behind news anchors. Alaska is five times smaller than Brazil yet looks comparable, and Europe is far smaller than South America yet does not look it. Researchers including the cartographer Mark Monmonier have argued that such visual habits quietly warp our sense of how the weight of the world is distributed. The international news story in 2017, when Boston public schools announced they would replace their world maps with an equal-area projection, belongs to the same argument.

The symbolic counterattack was a press conference in Bonn in 1973. The German historian Arno Peters unveiled his own world map and argued that existing maps had been inflating the developed nations of the northern hemisphere. The political message was powerful, and international relief agencies and United Nations bodies adopted the map. The reaction from cartographers, however, was frosty, for two reasons. First, the projection was essentially identical to one already published in 1855 by the Scot James Gall, which is why it is now called the Gall-Peters projection. Second, the price of preserving area is that shapes stretch badly, smearing the continents near the equator into long vertical smudges. In 1989 the major North American geographical bodies took aim at Mercator and Gall-Peters together, issuing a joint resolution against the use of rectangular world maps for general purposes.

The lesson here is not which projection is correct. It is that a map that looks politically correct cannot escape distortion either, and that choosing a projection is a question of purpose rather than of morality.

What Goes in the Middle — The Politics of Centre and Up

Even once the projection is settled, the decisions are not over, because you still have to choose where to cut the map. Put Europe and Africa in the centre and push the Pacific out to both edges, and the Americas and Asia end up as far apart as they can possibly be. Put the Pacific in the centre instead, and the Atlantic splits while Asia and the Americas face each other. That the textbook maps of Korea and Japan, of Australia and New Zealand, mostly take the second option is the natural choice of countries that would rather not be shoved to the margin. The same planet is drawn, but the neighbourly relations of the world change.

Even the reference line was settled by a meeting. At the International Meridian Conference held in Washington in October 1884, delegates from 25 nations voted on the proposal to make Greenwich the prime meridian. The result was 22 in favour, 1 against and 2 abstentions; the vote against came from San Domingo, and the abstentions from France and Brazil. France went on insisting on the Paris meridian for some time afterwards and only accepted Greenwich time in practice in 1911. Zero degrees of longitude was not fixed by nature but by the fact that the charts of the leading maritime power already used Greenwich.

The rule that up means north is not a universal constant either. The Tabula Rogeriana, made by al-Idrisi in 12th-century Sicily for Roger II, has south at the top. The medieval European mappa mundi put east at the top, and the English word orientation, which comes from the Latin for the direction of sunrise, is a fossil of that habit. The south-up world map published by the Australian Stuart McArthur in 1979 was a joke and an argument aimed precisely at this arbitrariness. Australia violates no law of physics by sitting at the top rather than the bottom.

The centre of a map is not the centre of the world but the spot where its maker is standing. If some arrangement feels natural to us, that means we have been looking at it for a long time, not that it is right.

Names and Lines — When a Map Becomes a Weapon

This is also why a single place name can become a diplomatic incident. The volume on the limits of oceans and seas published by the International Hydrographic Organization long served as the basis for naming on national charts, and the dispute between Korea and Japan over one of its entries has run for decades. That the organization decided in 2020 to move to a new system using numeric identifiers instead of names shows how delicate an exercise of power naming really is. The argument over whether to say Persian Gulf or Arabian Gulf has exactly the same character.

Digital maps handle the problem in a new way: by hiding it. The major online maps today draw borders differently depending on the country you connect from. Connect from India and Kashmir appears as Indian territory with a solid line; connect from elsewhere and dotted lines and disputed-territory labels appear. The rendering of Crimea likewise changes with the region of access. Several maps now exist simultaneously for one planet, and each viewer believes the screen in front of them is the fact of the matter.

Lines can summon actual physical force. When Nicaraguan soldiers entered the area around Calero Island, which Costa Rica claims as its territory, in November 2010, the commander on the ground cited the border shown on an online map. The boundary data on that map was in error and was corrected soon afterwards, but the troops had already moved. The International Court of Justice found for Costa Rica in 2015.

Historical borders come with received wisdom that needs correcting too. The explanation that Africa was carved up with a ruler at the Berlin Conference of 1884 is widespread but inaccurate. What the Berlin Conference settled was mostly rules. It made effective occupation a requirement for a claim, declared free trade in the Congo basin, and recognised the rule of Leopold II over the Congo. Most of the actual boundary lines were drawn over the following fifteen years or so in individual treaties between the powers. What happened in that conference hall was not the execution of the partition but the issuing of a licence to partition. The outcome was no different, but responsibility for it spreads far more widely. The case of Cyril Radcliffe, who drew the partition line of India in 1947 as a lawyer who had never set foot in the country, finished the job in five weeks, and saw the result published only two days after independence, belongs to the same family.

The Map That Did Not Need to Be Accurate — The Medieval Mappa Mundi

Most people laugh the first time they see a medieval European world map. Waterways are drawn inside a circle in the shape of a T, with Asia filling the upper half, Europe at the lower left and Africa at the lower right. Jerusalem sits at the centre and the Garden of Eden is drawn at the top. Geographically it looks useless.

But this map was not made to help anyone find a road. The T-O diagram that Isidore of Seville included in his Etymologies in the early 7th century was a picture explaining the structure of the world, and the Hereford Mappa Mundi, made around 1300 and still surviving, is closer to a theological encyclopedia, arranging biblical events, legendary peoples and real cities on a single sheet of vellum more than 1.3 metres across. Time and space are layered on one surface. The question these maps set out to answer was not where do I go but what are we in the middle of.

Europeans of the same period had a different set of maps for actually going to sea. These are the portolan charts that appear from the end of the 13th century. Compass bearing lines radiate across them, and the accuracy of their Mediterranean coastlines is startling even measured against modern surveys. The same society used two kinds of map for two different purposes with no sense of contradiction whatsoever, because a map that holds a worldview and a map for steering a ship were never the same object.

One more piece of received wisdom, as a bonus. The story that medieval people believed the earth was flat is not true. The sphericity of the earth had been known since antiquity, and Bede in the 8th century and the treatise on the sphere by Sacrobosco, a university textbook in the 13th century, both take it for granted. The image of a flat-earth Middle Ages is closer to a 19th-century invention. The dramatic scene was made up in the 1828 Columbus biography by Washington Irving, and 19th-century authors pushing the narrative that religion and science have always been at war set the image in place. It is no accident that the T-O map is round either. The Isidore diagram was printed at Augsburg in 1472, as printing spread across Europe, which also gives it the distinction of being the first map printed in Europe.

The Mapmakers of Today — Web Mercator and Search Rankings

When online map services adopted tiling in 2005, the world became a Mercator world all over again. This projection, called Web Mercator, calculates as though the earth were a perfect sphere while taking its coordinates from an ellipsoidal datum. Strictly speaking it is therefore not even conformal, and it cannot be used for geodetic computation. The international registry of coordinate systems refused for some time to assign it a code at all.

It was adopted anyway for practical reasons. It is easy to slice recursively into square tiles, neighbourhood shapes survive when you zoom or rotate the screen, and north always points up. For someone finding a route these are perfect properties. The moment you put the whole earth on one screen, though, the distortions of the 16th century come straight back. The default world image of billions of people has been standardised once again on a navigational projection. Major services only began adding a switch to a globe at low zoom levels around 2018.

The more fundamental change is not in the projection but in the index. On a paper map the maker decided what to include, and that decision was disclosed to some degree by the legend and the scale. On a digital map, what becomes visible is decided by search ranking, ad bidding and personalisation signals, and those rules are not disclosed. Two people standing in the same spot and typing the same query see different shops. A map is no longer a picture; it is the result of a query.

In this situation the old questions of cartography come back wearing new clothes. Who left what out. Which roads were drawn thick. Which names surface first. This is also why efforts to build map data in the open, as OpenStreetMap does, matter. Making it possible to see where the editorial power sits is itself a political choice.

In Closing — A Map Is Not a Photograph of the World but an Argument About It

To sum up. The moment you flatten a sphere, distortion is unavoidable, and so the remaining question is what to keep and what to throw away. That choice always has a purpose, and a purpose always has somebody holding it. Mercator threw away area for navigators, Peters threw away shape for a political message, and the map services of today throw away other things for rendering speed and advertising revenue. None of them is neutral, and the map that claims neutrality is the most suspect of all.

So next time you look at a map, it is worth adding one question. What was this map made for? The route the blue dot on the screen traces to your destination, the world map hanging behind the news, the neighbourhood boundary drawn by a property app — all of them are pictures that have passed through somebody's purpose. A map is not a photograph of the world but an argument about it, and an argument can always be answered. Simply knowing that leaves us a little less governed by the argument.