2489: Bad Map Projection: The Greenland Special

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Bad Map Projection: The Greenland Special
The projection for those who think the Mercator projection gives people a distorted idea of how big Greenland is, but a very accurate idea of how big it SHOULD be.
Title text: The projection for those who think the Mercator projection gives people a distorted idea of how big Greenland is, but a very accurate idea of how big it SHOULD be.

Explanation[edit]

This is the fourth comic in the series of Bad Map Projections displaying Bad Map Projection #299: The Greenland Special. It came one and a half year after the third 2256: Bad Map Projection: South America (#358).

Map projections are different methods of representing the curved surface of the Earth on a two-dimensional map. There's no perfect way to do so. Because the Earth is not flat, any 2D map projection of it will always distort in a way the spherical reality, and a map projection that is useful for one aspect (like navigation, geographical shapes and masses visualization, etc.) will not be so for all the others. Typically a projection can represent only distances, areas or angles correctly, or at best imperfectly compromise two of these. The map choice should reflect the purpose you need to put it to, as it will necessarily distort (perhaps by twisting, skewing and/or resizing) those aspects it was not designed to show intact.

One such projection is the Mercator projection, which is designed so that all north-south lines of longitude are parallel to each other and all rhumb lines are consistent, which is most important in the time of map-based navigation. In reality, apart from the direct east-west directions, all the imaginary straight lines eventually meet at the poles which - even if they look parallel. The apparent distance between lines of latitude at the more extreme latitudes expands and the vicinity around each pole can never be drawn, as Mercator maps show geographic features plotted over ever larger map areas and distances than they should, for those nearer the poles, compared to those more equatorial. It is not possible to accurately compare the sizes of features across the globe using this projection, although the distortions can be effectively ignored for more local maps that do not plot a significant area of the globe (other than very close to the poles, historically not an issue) and along or between any given narrow strips of latitude away from the equator the comparison is between near equal scalings.

Greenland is a large island in the Arctic ocean and one of the nearest pieces of land to the north pole. The Mercator projection shows it to be significantly larger than it really is, compared to equator-straddling features such as Africa. It is therefore one of the most obvious inaccuracies of Mercator's map, if used (e.g.) in the classroom to teach physical geography (which perhaps would best use a representation that was consistent to area) rather than navigation.

The equal-area projections such as Mollweide or Tobler Hyperelliptical, the latter of which seems to extremely closely match the majority of the features evident upon the hand-drawn map, ensure that shapes contain the same relative proportion of area as they would upon the original spherical (or slightly spheroidal) surface, across all latitudes, but only by bending the directions and rescaling the distances ever more drastically the closer to the map edge (the anti-meridian to that the map is centred upon) you go. Unlike the Mercator projection, you can show the poles (as the extreme upper and lower limits of the rim) from an equatorially-centred view, and every point of the Earth is given one definite position (or two, where they lie exactly upon the crossing point between the left/right extremes of the map).

This comic's projection has retained this singular inaccuracy as a deliberate feature, though avoiding all other such inaccuracies of the Mercator projection by using a different projection elsewhere that is designed explicitly to avoid them. For example, a traditional Mercator map would show other polar areas such as Antarctica, southern South America, or even New Zealand as larger, but this map does not.

Although it may not be obvious, due to no land-masses being normally shown at/close-enough to the North Pole, the Mercatorish Greenland actually extends beyond the Elliptic map's northern limits into positions that do not even exist in reality - it does not even 'wrap around and over' the pole (like a bad toupée) but passes through it and the arbitrary back-edge meridian line and into purely imaginary space that does not exist upon the surface of the Earthly sphere. (For a flipped comparison, the lower 'curve' of Antarctica is not its coast, but merely the map's 'wrap-around' edge where a further step would have you stepping back onto the continent at a second point of this nominal edge. The true coast of Antarctica is only the rough upper edge, passing between the two points which each represent the one arbitrary 'wrap-around' coordinate that is opposite-but-adjacent on the map's oval edging, i.e. at ±180°E/W, but which otherwise has no particularly special quality 'on the ground'.)

The title text suggests that this map was created for people who believe Greenland should be larger. Whether these people believe it should be physically increased in size in some manner or should simply receive a greater share of the attention is unclear. One method for increasing its size would be to increase the coverage of its ice cap, which is currently decreasing in size due to increases in temperature. However, increasing Greenland's ice coverage to the size it appears on a Mercator map would involve covering the entire island and surrounding ocean with ice, which would be very problematic for Greenland's population[citation needed].

Transcript[edit]

Bad Map Projection #299:
The Greenland Special
Equal-area map preserves size everywhere except Greenland, which uses the Mercator projection.
[A drawn world map, perhaps the Tobler hyperelliptical projection, except for Greenland which is of a typical Mercator appearance and sized at almost the size of Africa, to almost entirely fill the space between Canada and Iceland. It extends up well beyond the nominal location of the North Pole, while its southern tip has an apparent latitude comparable to that of Spain or the vicinity of Virginia.]
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Discussion

I want this map, but s/Greenland/Alaska (because that is how big Alaska should be) Orion205 (talk) 05:38, 15 July 2021 (UTC)

What are you trying to say? Beanie talk 09:50, 15 July 2021 (UTC)
s/Greenland/Alaska is the syntax to swap Greenland and Alaska in programs such as SED. Orion205 want's "The Alaska Special" map projection. 172.69.42.50 21:32, 15 July 2021 (UTC)

Hi, User:Beanie, sorry I've been messing with your well-intentioned Transcript edits, with my own well-intentioned ones. I seem to have difficulty with the Edit Conflict page not being very helpful (on this wide but short small screen, and a browser that wants me to resubmit things and lose newer stuff if I even think of switching windows mid-edit), especially when it seems we're each pushing little changes in very short intervals (often takes longer to tap in the edit-Summary!), and I'm formally not changing that any more. Except that it's so descriptive, I absolutely wouldn't object to some other way of describing the 'Supertitle', like a Subtitle but above the in-comic main title-scrawl, for example. (I only 'reverted' that back over because it was easier than trying to snipe in all the other retweaks it looked at one point that I needed to reapply when I couldn't work out why it was submitting so 'wrong'.) You've probably safely and sanely un-nuked my 'nuke' by the time I've added this comment, of course, but I can't know for sure yet... ;) 141.101.99.177 10:24, 15 July 2021 (UTC)

Ah well, I'm trying to conform to the usual style of transcripts. I will compare this to other examples of 'Bad Map Projections', in hope of styling the transcript right :). Beanie talk 10:35, 15 July 2021 (UTC)
I would say that two of those others are contrary to the general Transcript format that people have been arguing about recently, and the third is much closer to how the other edit looked (albeit for a bottom-titled). Not my place to retro-edit en-mass, though. Just commentary. And do we put links in the Transcript, these days? If not in the main Explanation, maybe as Trivia? Whatever. 162.158.159.48 15:37, 15 July 2021 (UTC)

Projection[edit]

Does anyone know which projection the rest of the map is? Djbrasier (talk) 13:10, 15 July 2021 (UTC)

The non-Greenland map projection is very close to **Kavraiskiy 5** (not 7) except the South Pole is rounded like Mollweide. - Frankie (talk) 12:09, 15 July 2021 (UTC)
I have a strong suspicion that it's projection which doesn't map ANY part of globe to the area North Greenland occupies. -- Hkmaly (talk) 14:12, 16 July 2021 (UTC)
Uh, hullo. I just made that very same point (NPI!) as part of one of my edits. And if you overlay the Tobler map (in particular) it is clearly a very decent match to at least a very close relative in that elliptical family (with the poles being points on the edge-oval, not stretched out to lines and reinforcing the non-equal-areaness of the suggested Kavrayskiy types). Only one person knows for sure, though, and apparently Randall doesn't read here (or at least care to comment, SFAIK), so consider this just a bit of mapgeek speculation. 162.158.159.42 14:31, 16 July 2021 (UTC)
FWIW, Kavrayskiy 5 is an equal area map very similar to Tobler Hyperelliptical except at the poles. - Frankie (talk) 01:59, 17 July 2021 (UTC)

New xkcd up: Pre-Pandemic Ketchup 162.158.78.64 15:08, 16 July 2021 (UTC)

Ideally, we should overlay the xkcd map to Tobler (not K5, the poles - or at least the visible bits at the south - are clearly different in the same way K5 is to Tobler) in the same way. I'm sure the other day I saw an assertion it was K7 (clearly wrong, to my eyes) but not sure it was even here (edited out?) so let me just reinforce my objection to that without any obvious reason in case it gets read by the same people who share my other relevent lurking/participatory habits. 141.101.99.13 09:00, 19 July 2021 (UTC)
Before I totally forget, and long after I should probably have completed the job, for reference I created https://imgur.com/a/ZJ5aCSa (easier to put there than upload here, when I did it). It shows the close match between the Tobler map (ripped from Wiki, and rescaled to the line drawing without being reproportioned) except for probable drawing differences. The 'real' Iceland is actually under the Mercator Greenland (again, ripped from Wiki, needed slight rotation as well as rescaling) forcing the drawn one to be moved. Svalbard could not be matched despite other near-latitude features working well and there's some other minor coastal disagreements (greater or lesser area under the illustrated version). This is perhaps not the bestest-of-best-fits, to the pixel, but it is close. (I did not upload the x2 version of the image, but rescaled back down first. Intended to perfect things before any unveiling, with the ultimate possibility of fully animating transitions between the various display options as well, without making a super-huge .gif as a result.)
The Mollweide and various Kavrayskiy versions mismatched (or, if you prefer, are systematically unmatchable) notably more from the xkcd so, yes, it's very much a Tobleresque original, or some projection I didn't get my hands on to compare. And the remaining 'errors' are from the redrawing process itself.
Finally, I splined in some revised continuations of the Tobler latitude/longitude marks to try to be consistent with their actual passage over/round the Mercatorial Greenland bit. Which was tricky (east-westings winding up and through the gap between G and UK in particular) and might not be how others might have done it, but was a lot easier than trying to overlay the relevent Tissot markings. - So that's how it is, for anyone who is still following this. Enjoy? 162.158.155.157 20:55, 24 July 2021 (UTC)