Editing 2911: Greenland Size

{{comic
| number    = 2911
| date      = March 25, 2024
| title     = Greenland Size
| image     = greenland_size_2x.png
| imagesize = 262x304px
| noexpand  = true
| titletext = The Mercator projection drastically distorts the size of almost every area of land except a small ring around the North and South Poles.
}}

==Explanation==
{{quote|
"What a useful thing a pocket-map is!" I remarked.

"That's another thing we've learned from ''your'' Nation," said Mein Herr, "map-making. But we've carried it much further than ''you''. What do you consider the ''largest'' map that would be really useful?"

"About six inches to the mile."

"Only ''six inches''!" exclaimed Mein Herr. "We very soon got to six ''yards'' to the mile. Then we tried a ''hundred'' yards to the mile. And then came the grandest idea of all! We actually made a map of the country, on the scale of ''a mile to the mile''!"

"Have you used it much?" I enquired.

"It has never been spread out, yet," said Mein Herr: "the farmers objected: they said it would cover the whole country, and shut out the sunlight! So we now use the country itself, as its own map, and I assure you it does nearly as well."|{{w|Lewis Carroll}}|{{w|Sylvie and Bruno Concluded}}}}

Because the {{w|Earth}} is {{w|Empirical evidence for the spherical shape of Earth|curved}}, all flat maps have some distortion. (A common comparison is flattening an orange peel, which cannot be done without tearing or stretching or wrinkling parts of it). Different {{w|map projection}}s can distort different {{w|Map projection#Metric properties of maps|metric properties}}, such as distances, areas, and angles, while leaving others intact. It can be desirable to preserve different metrics in different applications.

The {{w|Mercator projection}}, depicted in the comic, prioritizes depicting correct angles. This allows for easy course planning at sea, and makes shapes fairly accurate. In exchange, Mercator is often criticized for distorting size: distances near the poles look larger than the same distance near the {{w|equator}}. A common complaint is that {{w|Greenland}} appears as big on the map as {{w|Africa}}, when Africa actually has 14 times as much area as Greenland. When these size distortions are presented out of context, they can create bias and misconceptions about different places.

[[Cueball]]'s dialogue leads the reader to expect this complaint. However, instead of comparing ''relative'' sizes of two landmasses within the map, [[Cueball]] compares the ''absolute'' sizes of the depiction of Greenland and the actual Greenland. On a typical world map, Greenland might be centimeters or inches across. Judging from the human characters, the mapped Greenland in this comic might be 10 cm across. In real life, Greenland is about 650 miles or 1,050 km across from east to west ([//britannica.com/place/Greenland source]). Cueball deems this difference misleading, presenting it as a failure of this specific map or projection.

Of course, this is absurd. The purpose of any map is to present information at a scale (usually much more compactly) at which it is easy to read and interpret. Any actual-size world map would have to be the size of the Earth's surface, in which case it would have few uses. In addition, if a map includes a {{w|Scale (map)|scale}}, it enables the user to use the ratio to calculate the actual size of the places depicted (though this would not be possible on a Mercator projection, since the map-to-reality scale is not constant).

The title text is about the fact that regardless of the size of the map there ''is'' a certain point where the area on the map is equal to the area at the actual pole at that latitude. This is because a horizontal line on a worldwide Mercator projection corresponds to a line of latitude. While most lines of latitude are thousands of miles (kilometers) long, they become smaller and smaller approaching the poles. As long as the projection (and choice of how much map to print) includes the pole (a point of zero length) expanded out as a measurable edge of the map, there will be a line of latitude around each pole whose length would equal the width of the map that Cueball is looking at (though the specific line would be different depending on the size and precise geometry of the map). If Cueball's map were 1 m wide, then this line of latitude would be at 89.999998568° N or S - that is, the line of latitude there would be a circle with a circumference of 1 m around each of the poles. Of course, in order for the map to actually include (say) the northern of those latitude lines as well as the equator, it would have to be over 3 meters tall.

The idea of a 1:1 map was expanded in {{w|Jorge Luis Borges}}'s "{{w|On Exactitude in Science}}".

Mercator projections have been mentioned previously in [[977: Map Projections]], [[2082: Mercator Projection]], and [[2613: Bad Map Projection: Madagascator]]. The misleading size of Greenland on the Mercator projection is also the object of [[2489: Bad Map Projection: The Greenland Special]].

==Transcript==

:[Cueball and White Hat are looking at a world map on the wall showing a Mercator projection, with Cueball gesturing with his hand towards the map.]
:Cueball: This map is really misleading about the size of Greenland.
:Cueball: It's actually '''''much''''' bigger than that - it's hundreds of miles across.

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Comics featuring White Hat]]
[[Category:Maps]]
[[Category:Geography]]