About the Spilhaus Projection

Le Cartographe

This image went a bit viral earlier this week. Some context. It’s from an August 2015 blog post at Le Cartographe, in which Alexandre Nicolas discussed (and rendered, above) a projection produced in 1942 by South African oceanographer Athelstan Spilhaus. In Spilhaus’s oceanic projection, centred on Antarctica, the world’s oceans form a single, uninterrupted body of water. Which, you know, it is. The continents form the edges of the map; there is … some … spatial distortion. As Alexandre wrote in 2015, “This projection is rarely used and it’s a real shame!”

Previously: The Penguin Projection (speaking of Antarctica-centred projections).

More on Equal Earth

Equal Earth projection in colour

The Gall-Peters projection is a second-rate projection with first-rate public relations; cartographers’ responses to the projection that focused on its cartographic shortcomings ended up missing the point. Something different is happening with the Equal Earth projection, which was announced last month as a response to Gall-Peters: an equal-area projection with “eye appeal.” It’s getting media traction: the latest news outlet to take notice is Newsweek. So, finally, there’s an alternative that can be competitive on the PR front, without having to mumble something about all projections being compromises until the eyes glaze over.

It’s turning up in GIS packages, too: in D3, in G.Projector and in proj4. There’s even a t-shirt.

Previously: The Equal Earth Projection; Equal Earth Updates.

The Equal Earth Projection

In 2014 cartographer Tom Patterson and his colleagues, Bojan Šavrič and Bernhard Jenny, introduced the eponymous Patterson projection, a cylindrical projection that reduced polar exaggeration while maintaining the familiar shape of continents.1 Patterson, who recently retired from the U.S. National Park Service, has teamed up with Šavrič and Jenny to produce a new projection: the Equal Earth projection.

This projection can be seen as the cartographer’s response to the Peters map: in fact, the team created it in reaction to the furor over the Gall-Peters projection being adopted by Boston public schools. “Our message—that Gall-Peters is not the only equal-area projection—was not getting through,” the authors wrote in the International Journal of Geographical Information Science (mirrored here). “We searched for alternative equal-area map projections for world maps, but could not find any that met all our aesthetic criteria.” Citing their own research into map readers’ projection preferences, they decided against projections like the Eckert IV, Mollweide and sinusoidal and opted to make their own: “a new projection that would have more ‘eye appeal’ compared to existing equal-area projections and to give it the catchy name Equal Earth.”

The end result is a Robinson-like pseudocylindrical projection that nevertheless preserves area—and, like the Robinson, is nicer to look at than a cylindrical equal-area projection like the Gall-Peters. It’s actually kind of impressive that they were able to square that particular circle. The article details their decision-making process and the math behind the projection and is worth a read. It’ll be interesting to see whether this map gains any traction. I wish it well.

Previously: The Patterson Projection; The Peters Projection Comes to Boston’s Public Schools; The Peters Map Is Fighting the Last War; More on Boston Schools and the Peters Map; The 74 on Boston Schools and the Peters Map.

New (17 Aug): Equal Earth Updates.

Google Maps Switches to 3D Globe at Small Scales

Google

Web mapping uses Web Mercator. As Kenneth Field points out, this is fine at large scales, but at small scales you end up replicating the problem of using the Mercator projection on a wall map of the world.1 Zoom out in Apple Maps: using the map layer you get a Mercator; using imagery you get a virtual globe (basically, an orthographic projection you can spin). Ditto in Google Earth. But Google Maps, after some tests and starts, now does this in its map layer—and not just in Chrome, either. This means, among other things, that Antarctica is usably visible, as are the Arctic regions—and, of course, Greenland is its proper size at small scales.

The Urbano Monte Map in 20 Different Projections

More on Urbano Monte’s 1587 world map, which, you may remember, the Rumsey Collection digitally assembled into a single map from 60 manuscript pages. Now Visionscarto has taken it a step further, with a web tool that reprojects a map into other projections, taking the map’s original polar azimuthal equidistant projection and transmogrifying it into 20 other projections. Yes, sure, the Mercator is one of them, but so are the Goode Homolosine, the Hammer—even the Dymaxion. The tool is available on both the Visioncarto and Rumsey Collection websites. [David Rumsey]

Previously: Urbano Monte’s 1587 World Map, Digitally AssembledVan Duzer Assesses Urbano Monte’s Work.

Tissot’s Indicatrix

Tissot’s indicatrices superimposed on the Robinson projection. Map by Eric Gaba. Wikimedia Commons.

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.

The Penguin Projection

“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.

Frans Blok

“And no, for European use this map is less suitable. But there aren’t that many penguins living here,” says Blok. [ICA]

The 74 on Boston Schools and the Peters Map

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 MapThe Peters Map Is Fighting the Last WarThe Peters Projection Comes to Boston’s Public SchoolsIn Defence of the Mercator ProjectionHow the Mercator Projection Won the Internet.

Flex Projector

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.

More on Boston Schools and the Peters Map

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:

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.

Previously: The Peters Map Is Fighting the Last WarThe Peters Projection Comes to Boston’s Public SchoolsIn Defence of the Mercator ProjectionHow the Mercator Projection Won the Internet.

The Peters Map Is Fighting the Last War

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.

Previously: The Peters Projection Comes to Boston’s Public Schools; In Defence of the Mercator Projection; How the Mercator Projection Won the Internet.

The Peters Projection Comes to Boston’s Public Schools

Gall-Peters projection (Wikimedia Commons)

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.)

xkcd’s Time Zone Map

Randall Munroe, “Bad Map Projection: Time Zones,” 15 February 2017. xkcd.

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.

Dirty Reprojectors

Maps online invariably use the Web Mercator projection. The Dirty Reprojectors project aims to change that, at least in Mapbox. Anand Thakker explains.

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]