Geo Lounge’s Elizabeth Borneman has a piece on Tissot’s indicatrix, which tends to turn up in discussions of map projections. (See, for example, this piece from Vox’s Johnny Harris, and the accompanying video.) And for good reason: it’s a useful visualization tool. All maps distort—representing a curved surface on a flat plane, et cetera, et cetera—but a grid of Tissot’s indicatrices superimposed on a world map will measure the distortion—linear, angular, by area—produced by that map’s projection. On the Mercator projection, the indicatrices remain perfect circles, but grow larger toward the poles; on equal-area equatorial projections, they maintain their size but squish into ellipses; on other projections they also angle left or right depending on how close they are to the edge. On compromise projections like the Robinson (see above), they do all three.
“A world map tells a lot about the person who has made it, or about the market it is made for,” says Frans Blok. The edges of equatorial projections are determined so as to put the map’s audience at the centre of the map: European maps put the Bering Strait at the edges, Australian and Asian maps the Atlantic, American maps break Asia in two. If, however, only the polar regions were habitable—or if you were making a map for penguins—you might use a polar projection centred on Antarctica.
“And no, for European use this map is less suitable. But there aren’t that many penguins living here,” says Blok. [ICA]
Education news website The 74 has its own coverage of the Boston schools/Peters map controversy (is it safe to call it a controversy?), with extensive quotes from Matthew Edney, who does not mince words. (Comparing both projections to Comic Sans? Ouch.) [Caitlin Dempsey]
Previously: More on Boston Schools and the Peters Map; The Peters Map Is Fighting the Last War; The Peters Projection Comes to Boston’s Public Schools; In Defence of the Mercator Projection; How the Mercator Projection Won the Internet.
With all this recent talk about map projections, it might be worth pointing out the existence of Flex Projector, a cross-platform Java application for creating map projections, now at version 1.0.6. Yes, creating: if you want to invent your own map projection and slap your own name on it, you can do that with this app; others certainly have. (You will need to have Java installed on your computer.) Heck, Tom Patterson’s Natural Earth projection was built with it. [GIS Lounge]
Previously: Shaded Relief World Map and Flex Projector.
Atlas Obscura’s Cara Giaimo has an in-depth look at the reaction to the decision by Boston public schools to adopt the Peters projection in teaching materials. It’s well worth taking the time to read; the general gist from several cartographers and commentators is that swapping the Mercator for the Peters isn’t that much of an improvement. Though it includes comments from yours truly (I was in touch for this article), Giaimo talks to people who actually do know what they’re talking about, including Mark Monmonier (who, again, literally wrote the book on the Mercator projection) and Matthew Edney (who spoke to WZON 3 about this topic earlier).
Joshua Stevens, NASA’s data visualization and cartography lead:
(2/2) Are kids being taught that? If so, adopting any *1* projection is counter to learning why *many map projections exist & have purpose*
— Joshua Stevens (@jscarto) March 23, 2017
Also on Twitter, and to emphasize how long this has been going on, Jeremy Crampton notes his 1994 paper, “Cartography’s Defining Moment: The Peters Projection Controversy, 1974–1990.” A sequel may be required.
News of Boston public schools’ decision to go with the Peters projection has gone viral over the past week, and my teeth have not stopped itching. Largely because this is very much old news: Arno Peters began promoting “his” projection 44 years ago, and the Peters map has been making the rounds in certain circles ever since then. This is not new, and the media is showing its feckless streak in its lack of awareness of that fact. After all, the West Wing episode with the Peters map in it was broadcast 16 years ago.
The Gall-Peters projection is just one of several rectilinear equal-area projections; that Peters promoted it as a tool of social justice and anti-colonialism made it awfully appealing to people who are concerned with such issues. (They are not wrong to be concerned with such issues.) But cartographers have generally always been appalled by the projection, by Peters’s rhetoric and by his general ignorance of what had gone before. (Peters’s map had already been described by James Gall in 1885; the Mercator projection’s insufficiencies as a wall map had long been known; and there were many other projections, from the Van der Grinten to the Mollweide to the Goode homolosine, that were already being used in the Mercator’s stead.)
(The Mercator projection, for its part, makes a crap wall map: its virtue is that rhumb lines—compass headings—are straight lines, making the Mercator ideal for navigation. It’s worth emphasizing that Mercator himself died in 1594. Again, see Monmonier’s book on the subject.)
Cartographers’ response to the Peters projection is essentially, usually (and correctly) that every map projection is a compromise, because every map projection is an attempt to represent a round planet on a flat surface. All maps, in other words, lie; or at least no map is exempt from lying; or at least the Mercator is no more a liar than any other projection. It’s essentially an effort in debunking—the tedious repetition of “well, actually” to a credulous audience that doesn’t care enough to listen all the way through. (And besides: the company selling the Peters map thoroughly agrees with them!)
For the latest examples of this, see Caitlin Dempsey’s piece on teaching context, and Andy Woodruff’s response to the latest round of this. They’re good pieces, worth reading—but I can’t help wonder whether something different needs to be tried. But then again: what problem are we trying to solve? Media and public credulity? The fact that the Peters projection, bluntly, sucks? The campaign—and it is a campaign—behind it?
But the campaign for the Peters map is increasingly irrelevant. In late 2015 I argued that the debate over the right projection for wall maps was the cartographic equivalent of fighting the last war. The Peters map was a 20th-century response to a 19th-century problem (the Mercator on wall maps) that had already largely been solved earlier in the century. Sure, there are still wall maps out there that use the projection (I’m looking in your direction, IKEA), but by and large it’s not used nearly as much as the Peters defenders would have you think.
But 21st-century mapmaking is not about wall maps: it’s about web maps. As I said in 2015:
Every online map service uses a variant of the Mercator projection called Web Mercator. Whatever its shortcomings—and there are many, owing to the fact that its calculations use a spherical Mercator model to save computational cycles—Web Mercator has become the de facto standard. And the size distortions at small scales that have made the Mercator projection the target of so much ire over the decades are simply moot for most use cases.
In many ways the past debates over the Mercator are moot: arguing over the right projection for wall-sized world maps—Mercator vs. Peters vs. Robinson—is fighting the last war. Mercator has become the default option for online mapmaking, simply because so many data visualization maps rely on Google Maps or OpenStreetMap for their base map layer. Other projections will be reserved for the professionals, people with access to more sophisticated mapmaking tools and the skill to use them, but for the most part, when data is mapped on the Internet, it’ll be mapped according to Mercator.
Zoom out in Google Maps or OpenStreetMap, and what do you see? The Mercator projection, with Greenland in all its inappropriately giant glory. (Apple Maps turns into a globe when you zoom out far enough, but Apple Maps are app-only.) The reason why this isn’t generally seen as a problem is that hardly anyone uses Google Maps as a world map: like topographic maps that use UTM, at close range Mercator works just fine.
While there are efforts under way to use other projections in web maps, it’s unlikely that the Mercator-vs.-Peters battle—a false dichotomy if there ever was one—will migrate to the digital arena.
In a development that just might make academic cartographers pull out their remaining hair in frustration, Boston’s public schools began using the Peters projection in social studies classes last week. The news coverage (see the Grauniad’s) is the usual straw man argument about the Mercator and the false dichotomy between it and the Peters, as though no other map projections have ever been used. (National Geographic has been using other projections since the 1920s, and currently uses the Winkel tripel. The last time I was at a map store, hardly any of the world maps for sale used the Mercator. See Mark Monmonier’s Rhumb Lines and Map Wars: A Social History of the Mercator Projection, which I reviewed in 2008.)
Randall Munroe is a bad man who is back with another bad map projection to make our eyes bleed. (If he does this often enough he’ll have enough for a book. Heaven forfend.) This one is, like his other maps, fiendishly subtle: it stretches and compresses countries to fit where their time zones ought to be, longitudinally speaking.
Almost all web mapping libraries render maps using Web Mercator, making an assumption that you generally can’t change out-of-the-box. This has advantages, but it posed a real challenge for us when we set out to build the Washington Post’s live election results map, where using the Albers USA projection was an important requirement. To meet that requirement, we built a pipeline to pre-process geometries.
It’s a bit of a kludge, a way of fooling Mapbox into showing a different projection—latitude/longitude coordinates aren’t accurate any more—but it’s an impressive stab at a real problem. The Dirty Reprojectors web app demonstrates the possibilities, with all the projections available through the d3-geo and d3-geo-projection libraries. [James Fee]
This morning’s post about the AuthaGraph World Map reminded me of Buckminster Fuller’s Dymaxion map (which after all was explicitly referenced by its creator). Designer Brendan Ravenhill has produced a version of Fuller’s map in the form of a magnetic folding globe. Wired: “Like Fuller’s original map, Ravenhill’s globe can exist in two or three dimensions. Laid flat, it’s a series of 20 triangles that show Fuller’s projection as a single landmass. The back of each triangle features a magnet so you can fold the map into an angular globe. ‘Really it’s a toy, but a toy that has a lot of resonance and importance,’ Ravenhill says.” $15 each, in three colours. [Sociative GIS]
Japan’s Good Design Awards have been announced for 2016, and the Grand Award has gone to an unusual map. The AuthaGraph World Map “is made by equally dividing a spherical surface into 96 triangles, transferring it to a tetrahedron while maintaining areas proportions and unfolding it to be a rectangle.” Follow that? Sphere to tetrahedron to rectangle.
The brainchild of designer Hajime Narukawa, the AuthaGraph map was first released in 2010. What’s it for? In many ways it’s sort of a Japanese Peters projection: it aims to maintain the relative sizes of the continents. From the page selling the map outside Japan:
Every world map that has been invented since the Mercator Projection was first revealed in 1569 can be divided into two groups. One group fits the world into a rectangle by distorting the continents. The other group corrects the distortion, but at the cost of the rectangular shape. This is what drove Narukawa to create a map which is rectangular like the Mercator Projection map, and yet correctly projects the continents like the Dyxmaxion Map (revealed in 1946).
In a June 2015 piece for Al Jazeera America, history Ph.D. candidate Nick Danforth offered a contrarian opinion piece in defence of the Mercator projection. The usual (i.e. Peters) critique of the Mercator is that it emphasizes northern countries at the expense of equatorial countries. Danforth questions the premise behind that critique:
I first sided with the Mercator against its critics when, on one of the rare occasions I thought about Greenland, I realized just how rarely I thought about Greenland. Despite seeing it hanging there like a giant icy sword of Damocles atop every wall map, we just don’t seem to care about it. Antarctica, too, is massively inflated on the Mercator, to the point that it’s as big around as the entire earth. But few would argue that mapmakers intended to depict it as a superpower. Meanwhile, if maps lead us to ignore Africa, they should also lead us to treat cartographically bloated Canada as one of the most important countries in the world. We don’t.
He goes on to argue that if the Mercator projection was a reflection of European power, Africa would have been emphasized, not minimized.
Of all the problems with criticizing the way our maps depict Africa, the most ironic is that it ignores the continent’s history of colonialism. Consider the motives of a colonial-era British cartographer—perhaps the kind of guy who made this bold, colorful propaganda map […] showing off the queen’s dominions.
His incentive, if anything, would have been to make Africa appear as large as possible, since Britain then ruled a large share of it. With India along the same latitude, expanding the size of the earth’s equatorial region would have been a perfect way to color more of the map imperial pink.
Previously: How the Mercator Projection Won the Internet.
Further reading: Rhumb Lines and Map Wars: A Social History of the Mercator Projection by Mark Monmonier (my review).