The Short and Long Tail of Maps

At the Royal Observatory in Greenwich, a line in the ground marks the prime meridian: zero degrees of longitude, the line the whole world counts east and west from. Stand astride it and you have one foot in each hemisphere.

Now open the map on your phone. It disagrees. By GPS, zero longitude runs about 102 metres to the east of the telescope the line was drawn through. Nobody moved the line, and the phone isn't broken. Both are right, and in the long tail we'll see how.

That 102-metre gap is the whole subject in miniature. A map looks like a faithful picture of the world, but every map is a pile of decisions: what to keep, what to throw away, what to stretch, and where to put zero. The maps we use every day hide those decisions so well that we forget anyone made them. The rare and strange maps are where the decisions show.

First, the short tail: the handful of maps nearly everyone uses, and the questions they raise but rarely answer. Then the long tail: a fake town in upstate New York, a diagram that changed how Londoners travel, sea charts that are pessimistic on purpose, coordinates that point to two places at once, and charts made of sticks that never went to sea.

Part oneThe short tail

What is a map, actually?

A map is a drawing of a place that keeps a few true relationships and throws the rest away, so that someone can do a particular job. The throwing away is the point.

Lewis Carroll made the joke in 1893. In Sylvie and Bruno Concluded, a visitor boasts that his country once made a map at the scale of a mile to the mile. It was never unfolded, because the farmers said it would cover the country and shut out the sunlight. "So we now use the country itself, as its own map," he says, "and I assure you it does nearly as well."

Real maps shrink. On a 1:25,000 walking map, one centimetre stands for 250 metres. Shrink that far and the paper can't hold everything, so the mapmaker selects, simplifies and exaggerates. On a 1:250,000 road map, a road drawn as a line one millimetre thick would, at true scale, be a quarter of a kilometre wide. It gets drawn that thick anyway, because a driver needs to see it.

So every map answers a question, and different questions produce different maps of the same ground. A road map asks which roads connect. A walking map asks how steep the hill is. A metro diagram asks which line to take and where to change. A sea chart asks where the water is deep enough. None of them is the map of a place. The useful thing to ask of any map is what job it was built for, and what it gave up to do that job.

Which maps do most people use every day?

For most of us, "a map" now means the one on a phone. After that comes a small, stable handful: metro diagrams on station walls, road maps and road signs, the weather map on the forecast, and the world map on a classroom wall.

Phone maps run at a scale that's hard to picture. OpenStreetMap, a volunteer project we'll meet in a moment, publishes its traffic: in April 2026 its main map layer answered about 118 billion requests for map tiles, roughly 45,000 every second. That's one volunteer-run map, not Google's or Apple's.

The metro diagram is nearly as universal. London's 1933 design became, as the London Transport Museum puts it, a model for public transport companies across the world, which is why so many subway maps share its tidy angles and coloured lines. Weather maps are the odd ones out: they map something that won't hold still.

The world map on the wall is the one most people carry around in their heads, and it's the shakiest of the lot, because no correct version of it exists. When Boston's public schools swapped their Mercator maps for the Gall–Peters projection in 2017, some students' jaws dropped: Africa was suddenly huge and Europe small. Both maps were accurate. They were accurate about different things.

Who makes the maps we use?

Three kinds of mapmaker: governments, companies and volunteers. Each leans on the others.

The oldest are national mapping agencies. Britain's Ordnance Survey dates its birth to 21 June 1791, and the name gives away its origin. It was a project of the Board of Ordnance, the defence ministry of the day, and its early job was mapping England's southern coast against the threat of French invasion. In the United States, Thomas Jefferson created the Coast Survey in 1807 to chart the young country's waters. It's now an office of NOAA and still makes America's nautical charts. Agencies like these do the unglamorous work every other map stands on, such as defining the official coordinate systems that positions are measured in.

Companies came next. Google Maps launched in February 2005, and Apple, HERE and TomTom run maps of their own. In 2022 four rivals, Amazon Web Services, Meta, Microsoft and TomTom, founded the Overture Maps Foundation to build shared open map data, drawing partly on OpenStreetMap.

The volunteers are the newest. OpenStreetMap began in 2004 with Steve Coast at University College London, at a time when Britain's tax-funded map data wasn't freely available. The first street went in on 10 December 2004, after he cycled around Regent's Park with a GPS receiver. By 22 September 2026 the project had 10.9 million registered accounts and 10.9 billion mapped points. About 2.25 million accounts had actually edited it by mid-2025.

Line up when the pieces arrived and the map in your pocket turns out to be a stack of inventions four centuries deep: Mercator's projection in 1569, Ordnance Survey in 1791, London's diagram in 1933, OpenStreetMap in 2004, Google Maps in 2005.

Why can't a flat map of the world be right?

Because a sphere is curved in a way that no bending can remove, and a flat sheet isn't. Carl Friedrich Gauss proved it in 1827.

Our hands already know this. Peel an orange and press the peel flat: it tears. Now pick up a floppy slice of pizza and curl the crust into a U: the tip stops drooping. Both are the same theorem.

Gauss found a kind of curvature that can be measured entirely from inside a surface, by an ant with a tape measure who never looks up. A flat sheet has none of it. A sphere has the same positive amount everywhere. And bending a surface without stretching or tearing it can never change that amount. Gauss called the result the Theorema Egregium, the "remarkable theorem". Curl a pizza slice across and, to keep its curvature at zero, it has to stay straight along its length, so the tip holds up. The orange peel would have to lose its curvature to lie flat, and it can't without tearing.

The ant can check this on Earth. Start at the North Pole and walk about 10,000 km in every direction. The circle you trace is the equator, about 40,075 km around. On a flat sheet, a circle of radius 10,000 km would be 2π × 10,000, about 62,800 km around. So a flat map that keeps every distance from the pole true has to draw the equator about 57 percent too long. The distortion has to go somewhere, and it always does.

Gauss wasn't doodling. He'd been asked in 1818 to survey the Kingdom of Hanover, invented an instrument for the job (the heliotrope, which flashed sunlight between survey stations), and his theory of curved surfaces grew out of that fieldwork.

So mapmakers choose. John Snyder's projection manual for the US Geological Survey puts it in one line: "No map can be both equal-area and conformal." An equal-area map, like Gall–Peters, keeps every country's size honest and bends the shapes. A conformal map keeps small shapes and angles true and lets sizes swell. Compromise projections spread the error around, so nothing is badly wrong and nothing is exactly right.

Why is a sailors' map from 1569 still on your phone?

Because Mercator's projection keeps angles true everywhere, which is exactly what a navigator needed in 1569 and exactly what a street map needs now.

Gerardus Mercator presented it in 1569 on a wall-sized world map whose Latin title promised a description of the Earth corrected for use in navigation. Its trick is that a course of constant compass bearing, a rhumb line, comes out as a straight line. A navigator could lay a ruler between two ports, read off the angle and hold it. Mercator probably found the spacing of his latitude lines by drawing; Edward Wright published the tables in 1599.

The price is size. On a globe the meridians meet at the poles; Mercator draws them parallel, so east–west distances are stretched more and more as we move away from the equator. To stop shapes from smearing, north–south distances are stretched by the same factor, 1/cos(latitude). Areas get that factor twice. The poles would be infinitely far away, so they're left off.

Place	Latitude	Lengths drawn	Areas drawn
Singapore	1°N	×1.00	×1.0
Cairo	30°N	×1.15	×1.3
New York	40.7°N	×1.32	×1.7
London	51.5°N	×1.61	×2.6
Helsinki	60.2°N	×2.01	×4.0
Tromsø	69.7°N	×2.9	×8.3
Longyearbyen, Svalbard	78.2°N	×4.9	×24
Top edge of a web map	85.05°N	×11.6	×134

Now Greenland. It runs from about 60°N to nearly 84°N, so it lives in the bottom rows of that table. We ran the numbers on Natural Earth's public-domain country outlines. Greenland covers about 2.15 million km² and Africa about 30 million, fourteen times as much. On a Mercator map, Africa's area is inflated by about 12 percent on average and Greenland's by about 16 times. Greenland ends up drawn roughly 5 to 6 percent bigger than Africa.

Why put this on a phone? When Google Maps first launched, it didn't use Mercator, and a Google employee later explained what went wrong: streets in high-latitude cities like Stockholm didn't meet at right angles on the map. A map we zoom into has to get every street corner right, everywhere, and only a conformal projection promises that. Mercator is the one conformal projection on which north is straight up everywhere, so the pieces of the map fit together in a simple grid. The cost lands on the zoomed-out world view, which nobody uses to find a café. In 2018 Google's desktop map started showing a globe when you zoom all the way out.

Mercator never left the sea, either. NOAA's current Coast Pilot still describes it as the projection used on most nautical charts, because a straight line between two points on it is a rhumb line. And its sideways cousin, the transverse Mercator, underlies Britain's National Grid and the worldwide UTM grid.

How does a phone map show the whole planet so fast?

It never shows the whole planet. It fetches only the few small squares on your screen, from a pyramid of squares cut in advance at every zoom level.

At zoom level 0, the entire world is a single image 256 pixels on a side. For that to work the world has to be a square, and Mercator obliges if we cut it off at 85.0511° north and south, the latitude at which the map is exactly as tall as it is wide. (The number is arctan(sinh π), the sort of fact that makes a certain kind of person very happy.) Everything closer to the poles simply isn't on the map.

At zoom 1 that square splits into four tiles. At zoom 2 each of those splits into four again. Every level quadruples the count, so zoom level z has 4 to the power z tiles, and each pixel spans half the distance it did one level up.

Zoom	Tiles to cover the world	Ground per pixel at the equator	Fits on screen
0	1	156 km	The whole world
3	64	19.6 km	The largest country
10	1,048,576	153 m	A metropolitan area
16	4,294,967,296	2.4 m	A street
20	1,099,511,627,776	15 cm	A mid-sized building

Add up every level from 0 to 19 and there are 366,503,875,925 possible tiles. Google's engineers put it this way in 2010: it takes "more than 360 billion tiles to cover the whole world at 20 zoom levels".

Yet a phone only ever needs a screenful. A screen roughly 400 points wide and 800 tall holds two or three tiles across and four or five down, so even with a margin for scrolling it asks for a few dozen images out of hundreds of billions. That's the whole trick: the map of the world is enormous, and your view of it is tiny.

Mercator's stretch shows up here too. Away from the equator a pixel covers less ground, by the cosine of the latitude: at zoom 17 it spans about 1.2 m at the equator but 0.74 m in London.

In the big apps, most of the pictures have gone. In 2010 Google rebuilt its Android app around vector tiles, which it described as blueprints of the map rather than finished images; the phone does the drawing. Google said this took more than 100 times less data across all zoom levels, and that zooming could now stop when your fingers stopped instead of snapping to the next level. The pyramid is still there; in those apps it holds geometry. OpenStreetMap's main layer still serves pictures.

Part twoThe long tail

The short tail hides its decisions well. In the long tail, the decisions are the whole story.

Why would a mapmaker invent a town?

To catch copiers. Two honest maps of the same place ought to look alike, so it's hard to prove one was traced from the other. A detail that exists nowhere except on your own map works like a fingerprint.

The most famous is Agloe, New York. Otto G. Lindberg and Ernest Alpers of the General Drafting Company scrambled their initials into a name and put it at a dirt-road junction in the Catskills. The New York Times traced it to a free road map handed out at Socony gas stations in 1925; many retellings say the 1930s.

Then the fake became real. In 1930 a business called Agloe Lodge Farms bought land there and ran a fishing lodge under the name; a local paper later reported that an early guest from a map firm had told the owner to "put the place on the map". When Agloe turned up on a Rand McNally map, the popular story goes, General Drafting cried foul, and Rand McNally pointed to the Agloe General Store as proof the place existed.

That's where the legend runs ahead of the record. Darlene Beers, whose family owned the land, told the Times Herald-Record in 2016 that there never was a general store, only the lodge, and that the family suspected the buyers were a front for Rand McNally. The local historical society found a postcard of the lodge and nothing about a store. Accounts don't even agree on whether there was ever a lawsuit.

What survives every version is the mechanism. A name invented to expose copying ended up naming a real building, because a map said it was there. Agloe stayed on Esso and Exxon road maps into the late twentieth century, and on Google Maps until Google removed it in March 2014.

Not every mapmaker plays this game. When the Automobile Association paid Ordnance Survey £20 million in 2001 to settle a copyright dispute, OS said it had spotted the copying through "fingerprints" of its own drawing style, and that deliberate mistakes were off the table because "it would mislead our customers". Commercial street atlases are another matter. OpenStreetMap's wiki lists trap streets such as a Lye Close that appears in an A–Z of Bristol and nowhere on the ground.

OpenStreetMap's own defence is to avoid copying entirely. Its contributors are asked not to consult other maps; they work from their own surveys and GPS traces, and trace aerial imagery the project has permission to use.

A trap street shows something the phone map hides: every map has an author, and an author's work can be copied.

What does the Tube map get wrong on purpose?

Nearly all of the geography. Distances, curves and compass directions are bent or dropped. What's kept is the order of stations along each line and where the lines meet. A map that keeps only connections like that is called topological.

It was drawn by Harry Beck, a draughtsman who had worked for the Underground and was out of a job in 1931. In his spare time he redrew the network using only horizontal, vertical and 45-degree lines, and blew up the crowded centre so station names were easier to read. The publicity office handed it back in 1931 and accepted it a year later. The first pocket edition came out in January 1933. Maps then were printed in batches of 10,000 to 20,000; Beck's first run was 750,000, enough to last until the summer.

You'll often read that Beck borrowed the look of the electrical circuit diagrams from his old job in the signal engineers' office. It's plausible, but the London Museum says only that he was "probably" inspired by them. Treat it as a good guess.

The price of clarity is distance. Leicester Square to Covent Garden is 0.3 km, the shortest gap between any two Tube stations, and on the diagram it looks like any other hop.

Does that matter? In 2011 Zhan Guo of New York University used London Underground's own passenger data from 1998 to 2005 to see how riders chose between routes. Distance on the map was twice as influential as actual travel time, even for the most experienced riders. The diagram describes the network, and then it steers the people using it.

For years Beck got little credit. Since 2001, every Underground map has carried a line saying it is an evolution of his 1931 design.

Why do sea charts show the water at its shallowest?

Because the depths on a chart are measured down from a deliberately low water level, called chart datum. The chart is built to err on the safe side.

The sea's surface rises and falls, usually twice a day, so a chart has to choose a zero. By international agreement it's a level so low that the tide will not frequently fall below it. In Britain that's roughly the Lowest Astronomical Tide, the lowest level predicted under average weather. To get the real depth, you add the height of the tide, from a tide table, to the number on the chart.

Here's how that plays out, with illustrative numbers. The chart shows 1.8 m at a harbour mouth. The tide table says today's low water is 0.6 m and high water is 4.9 m. So the water there will be 2.4 m deep at low tide and 6.7 m deep at high tide. A boat that needs 2 m can cross at any time today. A boat that needs 3 m has to wait for the tide to come in. The printed figure is almost always a floor.

The United States makes a slightly different bet. NOAA charts measure from mean lower low water, the average of each day's lower low tide. Being an average, it gets undercut on some days. Where it sits depends on the local tides: at North Channel, New York, the chart's zero is 0.93 m below mean sea level, and at Bayou La Batre, Alabama, only 0.25 m.

Heights go the other way. The clearance under a bridge is measured up from mean high water, so the real gap is usually bigger than printed. Depth and height are both pessimistic, in opposite directions, on purpose.

The averages take patience. NOAA computes its tidal datums over a 19-year window because the Moon's orbit goes through an 18.6-year cycle that influences the tides. The US still uses the 1983–2001 window. The next one, 2002–2020, is proposed for release in 2029, to account for land movement, sea level rise and changes in the tides themselves.

One more twist. On British maps, the land has a different zero: heights are measured from mean sea level at Newlyn in Cornwall, averaged over 1915–21. So a British coastline sits between two zeros, the land's near mid-tide and the sea's down near the lowest tide.

How can the same coordinates point to two different places?

Because latitude and longitude only mean something relative to a chosen model of the Earth, called a datum, and different countries and eras chose different models.

Earth isn't a perfect sphere. It's slightly squashed, and its gravity is lumpy. To turn it into coordinates, surveyors choose an ellipsoid of a particular size and pin it in a particular position. Ordnance Survey's traditional maps use one defined in 1830 by George Airy, later Astronomer Royal, and fitted to Britain; only the patch of it under Britain has ever been used. GPS uses WGS 84, fitted to the whole planet. Ordnance Survey's own guide warns that systems in common use "can disagree on the coordinates of a point by more than 200 metres".

Let's work one through. Take Big Ben at 51.5007°N, 0.1246°W in WGS 84, the system your phone uses. Now read the same two numbers as OSGB36, the system behind Ordnance Survey's traditional maps. Using the seven conversion parameters Ordnance Survey publishes, which are good to about 3.5 m, that second point comes out about 57 m north and 112 m west of the first: 125 m away. Every digit was copied correctly. The mistake was in the one thing the numbers didn't say.

That also explains Greenwich. In 1884 an international conference recommended that the prime meridian pass through the Airy Transit Circle, a telescope at the Royal Observatory designed by the same George Airy. Its astronomers found "straight down" using a basin of mercury, which settles level with local gravity. Gravity at Greenwich leans very slightly, so their vertical leaned too. GPS measures from the centre of the Earth, which ignores such local lumps. A 2015 paper in the Journal of Geodesy showed that this lean, the "deflection of the vertical", is the right size and direction to account for the 102-metre gap. The line didn't move. The definition of "down" did.

Even a good datum drifts, because the ground moves. In Britain, WGS 84 coordinates creep about 2.5 cm a year to the north-east as the continent carries everything along. Australia moves about 7 cm a year, fast enough that in 2017 it shifted its official coordinates 1.8 m to catch up with itself.

And when there's no datum, or no data at all, you get Null Island. Zero latitude, zero longitude in WGS 84 is open sea in the Gulf of Guinea. Software that fails to make sense of an address can return "0,0", and the point gets plotted there anyway, so this empty patch of ocean collects misplaced records from all over the world. In 2011 the public-domain dataset Natural Earth drew a one-square-metre island there to help analysts spot the errors, though the joke is older. The only fixed object at 0,0 is a weather buoy, station 13010, nicknamed Soul. Fittingly, 0,0 is only there in WGS 84. In another coordinate system, zero lands somewhere else.

What did Marshall Islanders map with sticks?

Ocean swells: how the steady trade-wind swell bends around an island and crosses itself behind it, a pattern a navigator can feel through the hull long before land is in sight.

The Marshall Islands are 34 low coral atolls and islands in two chains stretching over 800 km, and a coconut palm on an atoll can be seen from only about 20 km offshore. Navigators could spend days out of sight of land. So they read the sea instead. (The charts are sometimes called Polynesian, but the Marshalls are in Micronesia.)

The charts were lashed from the midribs of palm fronds, with shells marking the atolls and curved sticks marking swells. There were three kinds: the mattang, an abstract model for teaching how islands disturb swells; the meddo, showing real islands in part of a chain; and the rebbelib, covering most of one chain or both. Individual charts varied so much that only the navigator who made one could fully interpret it.

Here's the surprising part: they didn't go to sea. The charts were used to teach students and studied before a voyage, but navigators set sail without them and steered by the motion of the canoe. A missionary published the first notice of the system in 1862, and early scholars read the objects as ordinary charts of islands and courses. In the 1890s a German naval officer, Captain Winkler, persuaded navigators to explain them, and estimated that the first sign of an island could be felt in the swells fifty or sixty miles out.

In a study published in 2009, one of the last traditional navigators, Captain Korent Joel, worked with anthropologists and oceanographers to test that knowledge with wave buoys, satellite images and computer models. They confirmed one of the key signals: crossing wave trains that extend tens of kilometres behind an island, made as the swell bends around it.

These are the strangest maps in this essay, and maybe the purest. They show a process instead of a coastline, and the real map was never the sticks. It was in the navigator's head.

Back at the line

Each map in the long tail makes one decision out in the open. Agloe shows that a map has an author. Beck's diagram keeps the order of stations and drops the distances. Sea charts choose which way to be wrong. Datums show that even zero is a choice. The stick charts keep the waves and leave out the land.

The map on your phone makes all of those decisions too. It keeps angles and gives up area. It cuts the world into a square pyramid of tiles, with the poles trimmed off. It measures from WGS 84's idea of down, and it was assembled from the work of government surveyors, companies and millions of volunteers. It just hides the seams very well.

Which brings us back to Greenwich, where a line in the ground and the phone in your hand disagree by 102 metres, and neither of them is wrong.

The short and long tail of Maps

Part oneThe short tail

What is a map, actually?

Which maps do most people use every day?

Who makes the maps we use?

Why can't a flat map of the world be right?

Why is a sailors' map from 1569 still on your phone?

How does a phone map show the whole planet so fast?

Part twoThe long tail

Why would a mapmaker invent a town?

What does the Tube map get wrong on purpose?

Why do sea charts show the water at its shallowest?

How can the same coordinates point to two different places?

What did Marshall Islanders map with sticks?

Back at the line

Links in this essay

The short and long tail of Water Transport

The short and long tail of WWE Moves

The short and long tail of File Formats

Part oneThe short tail

§What is a map, actually?

§Which maps do most people use every day?

§Who makes the maps we use?

§Why can't a flat map of the world be right?

§Why is a sailors' map from 1569 still on your phone?

§How does a phone map show the whole planet so fast?

Part twoThe long tail

§Why would a mapmaker invent a town?

§What does the Tube map get wrong on purpose?

§Why do sea charts show the water at its shallowest?

§How can the same coordinates point to two different places?

§What did Marshall Islanders map with sticks?

§Back at the line

Links in this essay

The short and long tail of Water Transport

The short and long tail of WWE Moves

The short and long tail of File Formats

What is a map, actually?

Which maps do most people use every day?

Who makes the maps we use?

Why can't a flat map of the world be right?

Why is a sailors' map from 1569 still on your phone?

How does a phone map show the whole planet so fast?

Why would a mapmaker invent a town?

What does the Tube map get wrong on purpose?

Why do sea charts show the water at its shallowest?

How can the same coordinates point to two different places?

What did Marshall Islanders map with sticks?

Back at the line