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==Explanation==
 
==Explanation==
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{{quote|
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{{incomplete|Created by a MAP THAT'S WAY BIGGER THAN IT'S SUPPOSED TO BE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
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"What a useful thing a pocket-map is!" I remarked.
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When talking about maps of the world, it's common to discuss the ways that it distorts the land areas that are depicted. All flat maps suffer from some kind of distortion, because the surface of a sphere cannot be flattened without stretching parts and possibly cutting it into pieces. Such discussion normally refers to the way that the shapes change or to the ''relative'' sizes of different land areas. For example, the {{w|Mercator projection}} makes land areas near the poles look larger than similar-sized areas near the Equator; a common complaint is that {{w|Greenland}} appears as big as {{w|Africa}} on the map, when Africa actually has 14 times more area than Greenland. The benefit of this projection, however, is that the landmasses maintain their overall shape, and it allows for easy course planning at sea since angles are preserved.
  
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"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?"
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The joke in this comic is that [[Cueball]] is comparing the size of Greenland on the map (usually on the order of centimeters or inches, unless you have a really big or really small map) with its real world size (about 650 miles  or 1,050 km across from east to west[https://www.britannica.com/place/Greenland]), rather than with the map's other landmasses, which Cueball deems misleading. Of course, this is absurd for an argument against the Mercator projection, as any projection of a map of the same size would be erroneous by Cueball's argument. Any world map that doesn't suffer from this distortion would have to be the size of the Earth's surface, which would make it useless.{{Citation needed}}
  
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"About six inches to the mile."
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The title text is about the fact that a horizontal line on a worldwide Mercator projection corresponds to a line of latitude. Most lines of latitude are thousands of miles (kilometers) long, but they become smaller and smaller approaching the poles, and in fact there ''is'' a line of latitude in a small-diameter circle around each pole whose length would equal the width of the map that Cueball is looking at. 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 one circle for each of the poles with a circumference of 1 m.
  
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"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''!"
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A map at a scale of 1:1 was discussed in Lewis Carroll's "Sylvie and Bruno Concluded":
  
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"Have you used it much?" I enquired.
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''"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?"''<br>
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''"About six inches to the mile."''<br>
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''"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!"''<br>
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''"Have you used it much?" I enquired.''<br>
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''"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."''
  
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"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}}}}
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Mercator projections have been mentioned previously in [[977: Map Projections]], [[2082: Mercator Projection]], and [[2613: Bad Map Projection: Madagascator]].
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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.
 
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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.
 
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[[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 [//britannica.com/place/Greenland about 650 miles] or 1,050 km across from east to west. Cueball deems this difference misleading, presenting it as a failure of this specific map or projection.
 
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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).
 
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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.
 
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The idea of a 1:1 map was expanded in {{w|Jorge Luis Borges}}'s "{{w|On Exactitude in Science}}".
 
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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==
 
==Transcript==
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{{incomplete transcript|Do NOT delete this tag too soon.}}
  
 
:[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 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.]

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