977: Map Projections

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Map Projections
What's that? You think I don't like the Peters map because I'm uncomfortable with having my cultural assumptions challenged?  Are you sure you're not ... ::puts on sunglasses:: ... projecting?


Map projections, or how to represent the spherical Earth surface onto a flat support (paper, screen...) to have a usable map, is a long-time issue with very practical aspects (navigation, geographical shapes and masses visualization, etc.) as well as very scientific/mathematic ones (involving geometry or even abstract algebra among other things). There is no universal solution to this problem, any 2D map projection will always distort in a way the spherical reality; many projections have been proposed in various contexts, each intending to minimize distortions for specific uses (for nautical navigation, for aerial navigation, for landmass size comparisons, etc.) but having drawbacks from other points of view. Some of them are more frequently used than other in mass media and therefore more well-known than others, some are purely historical and now deprecated, some are really obscure, etc.

Randall suggests here the idea that someone's "favorite" map projection can reveal aspects of their personality, and goes through a series of them and what they can mean:

The Mercator projection was introduced by Flemish cartographer Gerardus Mercator in 1569. The main purpose of this map is that at any point the vertical and horizontal scales are the same, so locally i.e. considering only a small part of the map, geographical features (shapes, angles) are well represented, which helps a lot in recognizing them on-the-field, or for local navigation in that small part only. For this reason that projection (or a close variant) is used in several online mapping services such as Google Maps, which means that people commonly see it nowadays. No angle distortion also means that a straight line on the map corresponds to a course of constant bearing (direction), which was very useful for nautical navigation during centuries (and thus made that projection very well-known).
However from a global point of view, this projection is radically incorrect in how it shows the size of landmasses (for instance Antartica or Greenland seem gigantic), and furthermore it always excludes a small region around each pole (otherwise the map would be of infinite height), so it doesn't provide a complete solution for the problem of map projection. The comic implies that people who like that projection aren't very interested with map issues, and typically use what they are offered without thinking a lot about it.
Van der Grinten
The Van der Grinten projection is not much better than the Mercator. It was adopted by National Geographic in 1922 and was used until they updated to the Robinson projection in 1988.
The Van der Grinten projection is circular as opposed to the Mercator projection. Circles look happier than squares, leading to the conclusion that people who like the projection are optimistic.
The Robinson projection was developed by Arthur H. Robinson as a map that was supposed to look nice. National Geographic moved to this projection in 1988, and used it for ten years, moving to the Winkel-Tripel in 1998.
The Beatles was a rock band that enjoyed great commercial success in the 1960s. The Beatles, coffee, and running shoes suggest an ordinary, easygoing lifestyle paralleled by the projection.
Also called the Fuller Map, the Dymaxion Map takes a sphere and turns it into an icosahedron, that is a polyhedron with triangular faces. It is far easier to unwrap an icosahedron than it is to unwrap a sphere into a 2D object and has very little skewing of the poles.
Randall associates the projection to geek subculture and niche markets:
  • Isaac Asimov was an American science-fiction writer, that (as well as publishing many textbooks) is considered the father of the modern concept of robots. He invented the Three Laws of Robotics. He also worked on more than 500 books throughout his career.
  • XML is the eXtensible Markup Language. It is used to represent data in a format that machines can read and understand, as well as being human-readable. In practice, XML is cumbersome to read.
  • Toed-Shoes are a favorite of Randall's to pick on. In society they are seen as a hipster clothing item.
  • Brought to the world by Dean Kamen, the Segway PT was supposed to be a device that changed the way cities were built. In reality, most principalities have put in place rules specifically against Segways, making them a frustration to own and use within the law (In some states in Australia, it is illegal to use them on public footpaths or roads). Also, the former owner of Segway Inc., the late Jimi Heselden, accidentally rode his Segway off a cliff in 2010.
  • 3D goggles are a very niche market only pursued by enthusiasts. In the 1990s the promise of virtual realities was very tantalizing, many companies attempted to perfect it, but fell short of the mark. Also the phrase "The grass is always greener on the other side of the fence." is relevant.
  • Dvorak is an alternate keyboard layout to QWERTY. Where QWERTY was invented to help keep manual typewriters from jamming (by placing the most used keys further away from each other), Dr. August Dvorak performed many studies and found the mathematically optimal keyboard layout to reduce finger travel for right handed typists. While technically better than QWERTY, QWERTY had become the standard. All the keyboards were laid out in QWERTY format, and retraining the brain after becoming a touch typist is extremely difficult.
Winkel Tripel
Proposed by Oswald Winkel in 1921, this map tried to reduce the three (German: tripel) main problems with map projections: area, direction, and distance. The Kavrayskiy projection is very similar to the Winkel Tripel and was used by the USSR, but very few in the Western world know of it.
The comic links this projection to hipster subculture. The whole point of hipsters is to avoid conforming to mainstream fashions. "Post-" refers to a variety of musical genres such as post-punk, post-grunge, post-minimalism, etc. that branch off of other genres.
Goode Homolosine
The Goode Homolosine projection takes a different approach to skewing a sphere into a roughly circular surface. An orange peel can be taken off of an orange and flattened with fair success, this is roughly the procedure that John Paule Goode followed in creating this projection.
Common people make, what seems to be, fairly reasonable arguments that if normal people would run the United States, then the US wouldn't be in the trouble it is. This is from the belief that career politicians are simply out to make money and will only act in the interest of their constituency when their continued easy life is threatened (usually around election time).
Airline food is another, much maligned, problem. How do you store enough food to feed people on long airplane trips? The common solution is to use some kind of sub-standard microwave-able dinner. Randall is saying that the people in favor of the Goode Homolosine wonder why the airlines don't simply order meals from the restaurants in the airport, store that food, and serve it, rather than using frozen, and microwaved food.
Older cars burned oil like mad fiends and oil back then would become corrosive to the innards of an engine, so oil had to be changed often. But, with the introduction of synthetic motor oil and better designed engines, new cars only need their oil changed about ever 10,000 to 15,000 miles. Allegedly. Perhaps this is a conspiracy built by the collusion of the car manufacturers and big oil companies!
All of these references suggest that people who like the Goode Homolosine projection are fans of practical solutions to simple problems.
The Hobo–Dyer projection was commissioned by Bob Abramms and Howard Bronstein and was drafted by Mick Dyer in 2002. It is a modified Behrmann projection. The goal was to be a more visually pleasing version of the Gall-Peters.
As is discussed in the Gall-Peters explanation, the Gall-Peters was developed to be equal area, so that economically disadvantaged areas can at least take comfort in the fact that their country is represented correctly by area on maps.
Randall associates the Hobo-Dyer projection to "crunchy granola" — a stereotype associated with vegetarianism, environmental activism, anti-war activism, liberal political leanings, and some traces of hippie culture.
With the new general acceptance of homosexual, bisexual, and transgendered persons, some have begun to invent gender-neutral pronouns so that when referring to a person whose gender is not known they cannot be offended by being referred to by the wrong pronouns. In old English 'they' and 'their' were accepted gender-less pronouns that could replace 'he', 'she' as well as be used to represent a crowd. This usage is now considered archaic, so, a whole host of new pronouns are being invented in an attempt to keep from ever offending anyone ever again.
Plate Carrée
Also known as the Equirectangular projection that has been in use since, apparently, 100 AD. The benefit of this projection is that latitude and longitude can be used as x,y coordinates. This makes it especially easy for computers to graph data on top of it.
According to the comic, the projection appeals to people who find much beauty in simplicity.
A Globe!
In any good discussion there has to be at least one smart-ass. This is a comic about map projections, that is, the science of taking a sphere and flattening it into 2 dimensions. The smart-ass believes that we shouldn't even try: a sphere is, in fact, the perfect representation of a sphere.
To quote The Princess Bride: "Yes, you're very smart. Shut up."
Waterman Butterfly
Similar to the Dymaxion, the Waterman butterfly projection turns a sphere into an octahedron, and then unfolds the net of the octahedron, which was devised by mathematician Steve Waterman based upon the work of Bernard J.S. Cahill
Bernard Cahill published a butterfly map in 1909. Steve Waterman probably has the only extant "ready to go" map following the same general principles, though Gene Keys may not be far behind. Waterman has a poem with graphics in a similar vein to this xkcd comic that is worth reading.[1]
The Cahill/Keyes/Waterman projections are arguably the only map projections, thus far, that more or less equally balance the inevitable “all maps lie” distortions in size, shape and area.
The joke is that the person responding deeply understands map projections; anyone who knows of this projection is a person that Randall would like to get to know.
Peirce Quincuncial
The Pierce quincuncial projection was devised by Charles Sanders Peirce in 1879 and uses complex analysis to make a conformal mapping of the Earth, that conforms except for four points which would make up the south pole.
Inception was a 2010 movie about meta lucid dreaming. It has a complex story that is difficult to follow and leaves the viewer with many questions at the end, and almost needs to be watched multiple times to be understood.
The human brain is not well developed to deal with oddly obvious things. One example is that everyone has a skeleton, but everyone is surprised when a bone pokes through the skin after it has been broken. Another is the fascinating complexity of the human hand, a machine that is amazingly complex driven by a complex interplay of electrical and chemical signals and yet is the size of the hand and is so useful.
The Gall-Peters projection is mired in controversy, surprising for a map. James Gall a 19th century clergyman presented this projection in 1855 before the British Association for the Advancement of Science. In 1967, the filmmaker Arno Peters created the same projection and presented it to the world as a "new invention" that put poorer, less powerful countries into their rightful proportions (as opposed to the Mercator). Peters played the marketing game and got quite a few followers of his map by saying it had "absolute angle conformality," "no extreme distortions of form," and was "totally distance-factual" in an age when society was very concerned about social justice. All of these claims were in fact false. The polar regions are horribly distorted, and south of the Mediterranean Sea is "taller" than it should be.
Anyone who loves such a politically charged map that has become popular by way of marketing stunts, Randall would rather not have anything to do with.

The title text makes a joke that goes to the familiar meme from CSI: Miami, in which the star, David Caruso starts on sentence, then puts on his sunglasses and then ends it with a corny pun. This internet meme has been mentioned previously by xkcd in comic 626 and possibly others.


What your favorite
Map Projection
says about you
[All of these are organized as Title, a copy of the particular projection underneath, and what it says about you under that]
  • Mercator
    • You're not really into maps.
  • Van der Grinten
    • You're not a complicated person. You love the Mercator projection; you just wish it weren't square. The Earth's not a square, it's a circle. you like circles. Today is gonna be a good day!
  • Robinson
    • You have a comfortable pair of running shoes that you wear everywhere. You like coffee and enjoy The Beatles. you think the Robinson is the best-looking projection, hands down.
  • Dymaxion
    • You like Isaac Asimov, XML, and shoes with toes. You think the Segway got a bad rap. you own 3D goggles, which you use to view rotating models of better 3D goggles. you type in Dvorak.
  • Winkel-Tripel
    • National Geographic adopted the Winkel-Tripel in 1998, but you've been a W-T fan since long before "Nat Geo" showed up. You're worried it's getting played out, and are thinking of switching to the Kavrayskiy. You once left a party in disgust when a guest showed up wearing shoes with toes. Your favorite musical genre is "Post–".
  • Goode Homolosine
    • They say mapping the Earth on a 2D surface is like flattening an orange peel, which seems enough to you. You like easy solutions.You think we wouldn't have so many problems if we'd just elect normal people to Congress instead of Politicians. You think airlines should just buy food from the restaurants near the gates and serve that on board. You change your car's oil, but secretly wonder if you really need to.
  • Hobo-Dyer
    • You want to avoid cultural imperialism, but you've heard bad things about Gall-Peters. You're conflict-averse and buy organic. You use a recently-invented set of gender-neutral pronouns and think that what the world needs is a revolution in consciousness.
  • Plate Carrée (Equirectangular)
    • You think this one is fine. You like how X and Y map to latitude and longitude. The other projections overcomplicate things. You want me to stop asking about maps so you can enjoy dinner.
  • A Globe!
    • Yes, you're very clever
  • Waterman Butterfly
    • Really? You know the Waterman? Have you seen the 1909 Cahill Map it's based— ...You have a framed reproduction at home?! Whoa. ...Listen, forget these questions. Are you doing anything tonight?
  • Peirce Quincuncial
    • You think that when we look at a map, what we really see is ourselves. After you first saw Inception, you sat silent in the theater for six hours. It freaks you out to realize that everyone around you has a skeleton inside them. You have really looked at your hands.
  • Gall-Peters
    • I hate you.



I have a Plate Carrée hanging on my wall myself. Never failed me yet. Davidy22[talk] 07:05, 2 February 2013 (UTC)

I like the Azimuthal Equidistant (equatorial aspect) the best. - not Pennpenn. 01:15, 17 December 2015 (UTC)

You can explore and compare different map projections and their distortions (using Tissot’s indicatrix and triangulation of sphere) in an interactive blog post The problem with maps by Michael Davis --JakubNarebski (talk) 14:58, 26 May 2017 (UTC)

Go check out that site carefully though most of the data is accurate, some of the media is not, for example the two side by side Google maps satellite images of cars and the text saying how a map projection changes the apparent size of the cars. Well if you open up both links you will see they are at different zoom levels, one at a scale of 50 feet per unit and the other at 100 feet so yes being twice the zoom the cars are going to appear larger then the image right next to it. 12:04, 23 August 2017 (UTC)

Btw, this comic is given in What Does Earth Look Like? of Vsause where these projections are discussed. --Ата (talk) 10:38, 3 September 2017 (UTC)


Dymaxion is clearly the best. There's nothing like a map made out of an unfolded d20. Alpha (talk) 19:43, 23 February 2013 (UTC)

Makes you wonder what if a dodecahedron had been used instead of an icosahedron. --Quicksilver (talk) 18:02, 17 August 2013 (UTC)
Here you go: http://www.progonos.com/furuti/MapProj/Normal/ProjPoly/Foldout/Dodecahedron/dodecahedron.html - Frankie (talk) 16:40, 23 July 2015 (UTC)

Peirce Quincuncial has 4 non-conformal points, but not the 4 corners, which are the south pole, but instead are the 4 midpoints of the sides. These are on the equator and seem to be 90 degrees apart.--DrMath 06:30, 30 August 2013 (UTC)

I love Peirce Quincuncial, yet I slept throughout that "Inception". 11:36, 27 January 2014 (UTC)
I'm surprised nobody thought of "really looking at your hands" as a hint that person that likes this projection is under influence of LSD or similar drug. As this surely is a thing that you do. (and you'll think of it next time you smoke your joint - inception!) -- 17:29, 7 December 2014 (UTC)

Plus it has a picture of a man looking at his hand and a man looking at the man looking at his hand. I used Google News BEFORE it was clickbait (talk) 14:39, 22 January 2015 (UTC)

xkcd 1051's title text - "meta lucid dreaming". I really got excited that there was an article about and ironically, it leads to meta and lucid dreaming separately. 21:23, 25 March 2014 (UTC)BK201

The common video game trope of "the far east of the world is connected to the far west, and the far north likewise to the far south" is popularly resolved by saying that those game worlds are toroidal shapes. (For a particular reference, I am thinking of the SNES and PSX era Final Fantasy games (4-9.)) But sometime in the last year, I got the idea that you could also resolve that geographical conflict (and claim they are spherical) by the logic that the "world map" you see in those games (where they have one) is a Peirce Qunincuncial map. Is my logic sound? Boct1584 (talk) 15:31, 28 March 2015 (UTC)

The explanation for the Peirce Quincuncial seems to miss the fact that Randall is implying that anyone who likes this map is most likely high. Getting lost in deep thought over things like your hands, or sitting in a dark theater for 6 hours to wrap your head around Inception...these are all very stereotypical "has smoke a lot of marijuana" behaviors. (talk) (please sign your comments with ~~~~)


In actual fact, the Waterman butterfly map used a truncated octahedron based upon the mathematics of close packing of spheres and is not at all based upon any of CaHill's work/math. -- steve waterman (talk) (please sign your comments with ~~~~)

Perhaps the explanation should mention that Waterman himself signed up at forum.xkcd.com and vigorously denied that his map has anything to do with Cahill. At the time, it was unclear whether the account was really Waterman, or just a troll trying to make him look bad. - Frankie (talk) 21:39, 25 March 2014 (UTC)
Kavrayskiy VII

Kavrayskiy is the best projection, despite being so far out of the mainstream that no-one west of Ukraine has seen one for the past 20 years. (talk) (please sign your comments with ~~~~)

Wow, I looked into it and it really seems like an excellent projection. It's been a while since I've looked at projections but I think it's my new favourite as it has everything that I've been looking for in a projection. It's a more accurate (in extremes) and more pleasing Robinson projection that still has a reasonable amount cut off the top. Also, the indicatrix for it is very simple, as is the formula, and simple things please simple minds (like mine, apparently) -- without taking it to an extreme like the equirectangular projection does. I swear I've come across it before, but then again I grew up in a country which wasn't far from the Eastern Bloc. 14:51, 5 November 2014 (UTC)

To be fair, what is drawn is an orthographic azimuthal projection.-- 18:59, 14 December 2014 (UTC)

GLOBES ARE THE BEST although my enormous Winkel Tripel hasn't done too bad. (talk) (please sign your comments with ~~~~)

Airline food is never microwaved, and is chilled rather than frozen. Also the problems aren't limited to storage and re-heating, there are technical considerations with low air pressure, dehydrated air etc. and concerns over strong smells. I edited the relevant section. AmbroseChapel (talk) 07:00, 11 September 2017 (UTC)

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