Today is The Map Room’s 18th anniversary. When I started this blog back in March 2003, it was as an exercise in self-education: I liked maps a lot, but knew very little about them, and thought that the blogging process would enable me to learn things and share what I learned with my readers. The idea that I’m some kind of map expert is just silly: I have no professional credentials whatsoever, not in cartography, not in geospatial, not even in illustration. (I haven’t even taken geography since high school.)

But that’s not to say that I haven’t picked up some knowledge: I’ve turned my longstanding interest in fantasy maps into a few published articles (with more still in the works or in press), so I will concede the point on that front. But in general what I do have is exposure. Over the past 18 years I have seen just about everything to do with maps, and so I know a little bit about just about everything. Not enough to be employed at any map-related job, but 18 years of paying attention, of synthesizing everything I’ve seen and read, has afforded me some perspective.

Enough to call out obvious horseshit when I see it.

Also, because I’m not a cartographer, because I don’t have that background or training, because my expertise is a hundred miles wide but a millimetre thick, I’d be extraordinarily reluctant to tell cartographers that what they’ve been doing for the past few centuries has been completely wrong, and that I’ve come up with something better that no one has ever thought of before—only for the something better to be utterly old and familiar to those who know what they’re doing.

I don’t have that kind of chutzpah.

Arno Peters did, though. In 1974 the German historian presented the Peters World Map (a retread of an 1855 equal-area projection by James Gall) as the antidote to a Mercator projection that emphasized temperate regions over the tropics: the Global West over the Global South. In doing so Peters was fighting a battle that, Mark Monmonier has argued, was mostly already won by the 1970s. The Mercator had long been seen as unsuitable for world maps, with wall maps and atlases already having moved on to the Goode’s homolosine, Mollweide and Van der Grinten projections, among others, by the mid-20th century.

Even so, cartographers generally hated the Peters map because it was foundationally ignorant: Peters was dabbling in map projections without understanding their history. He and his adherents invented a false dichotomy—Peters vs. Mercator—and marketed the projection to credulous audiences (e.g. Boston schools as recently as four years ago) as a solution to a problem that in truth was neither unsolved nor really a problem.

Guess what? It’s happening again.

In 2007 a pair of physicists, David Goldberg and J. Richard Gott, published an article in Cartographica in which they proposed a way of measuring and scoring map projections by six kinds of distortion—area, shape, distance, boundary cuts, flexion and skewness (the latter referring to bending and lopsidedness). According to their system, the Winkel Tripel projection, currently in use at National Geographic, had the best score: 4.563. (The lower the score, the better: a globe’s score is zero. The Mercator’s score is 8.296.)

Last month, in an unpublished paper uploaded to Arxiv, Goldberg and Gott, along with Robert Vanderbei, tried to come up with something better than the Winkel Tripel, and arrived at a pair of azimuthal equidistant projections centred on each pole and extending to the equator; the twist, as they see it, is to make the map double sided.

“To the best of their knowledge,” says the piece from Princeton’s communications office, “no one has ever made double-sided maps for accuracy like this before. A 1993 compendium of nearly 200 map projections dating back 2,000 years did not include any, nor did they find any similar patents.”

Except that maps showing the world in two hemispheres date back at least as far as the 16th century (there’s one on my wall) and polar azimuthal projections aren’t exactly new either: they’re splitting hairs awfully fine to make that claim. Regardless, their double-sided map gets a score of 0.881 on their Goldberg-Gott scale.

Matthew Edney was not impressed; as you might expect, he did not hold back. “I am utterly and thoroughly gobsmacked,” he wrote last month in a piece that marvels at the claims made in the PR piece.

Underpinning all this sheer stupidity and naivety are some serious points about what these astrophysicists understand maps to be. It is not that they are ignorant of the mathematical principles; two have published a paper in a map journal on their measures of map distortion (Goldberg and Gott 2007; also Gott, Mugnolo, and Colley 2007). But it seems that from their highly mathematicized perch they have realized that world maps are actually useful for imaging and visualizing the world. But they want the maps to also be as accurate as possible, according to their own idiosyncratic criteria. […]

Ultimately, once one has stripped away the immense amount of PR guff and hyperbole, there’s little to recommend this as a “new” and “different”—other than the proposal to paste the two halves together. And I’m pretty sure I’ve seen an eighteenth- or nineteenth-century hand-held fan with hemispheres drawn on either side …

They have really only reinvented the wheel.

In a separate piece Edney has some questions about the parameters used in Goldberg and Gott’s scoring system, a couple of which he finds dubious, along with the way they’re tallied up.

Someone coming in from outside the field to “solve” the map projection problem sounds an awful lot like Arno Peters all over again—especially since their little paper has picked up a certain amount of media attention—see coverage from The Verge and the New York Times—that trumpets the possibility that this projection “fixes” flat maps, or the distorted view of the world that we get from flat maps.

Hoo boy. That’s a hell of a claim—one we’ve seen before. Except that Peters purported to solve map projections’ problem of representation. These professors sound like they’re going after the impossible Holy Grail of map projections: to find the most perfect, least distorted map, the One True Map that will leave all others in its dust, the One Projection that can be used all the time and in every circumstance. (The number of questions I’ve seen on Quora, for example, that insist upon this impossibility—that there is such a thing as an “accurate” map projection—is striking.)

Only they’ve defined “most accurate” as “fewest distortions according to our own criteria.” In doing so they’ve reduced map projections to a simple math problem that ignores centuries of map history, to say nothing of real-world uses. In other words: a spherical cow—a model reduced to the point of oversimplification so that it works.

Because you’d be hard pressed to find an actual use case for their double-sided map of the world. As Edney points out, only half of the world is viewable at once: “The point of world maps is to show the whole earth, but one can’t see the entire earth, so the most accurate world map doesn’t show the whole earth” (which somehow doesn’t incur a penalty in their schema). And heaven forbid you should want your world map to show all of Africa, or South America, or Indonesia, at the same time.

Thing is—and regular readers will know I’m preaching to the choir here—there is no such thing as the perfect map projection. Only the right projection for the job at hand. The antidote to a given map projection’s distortion is a different map projection whose distortion is less problematic for what you’re trying to map. Some distortions you can live with in order to preserve fidelity elsewhere. I’m fond of the Equal Earth projection, but I wouldn’t use it if I wanted to emphasize the polar regions.

It’s a practical choice, in other words, one that I’ve come to understand, from my 18 years of paying attention to this, as a basic challenge of map design. One that you can’t simply come in and solve with math. It’s tempting to see this as a variant of the Dunning-Kruger effect—or at least the popular understanding of it: an inability to recognize your lack of ability—that in my experience seems to afflict an awful lot of physicists and engineers. Reduce the problem until it’s solvable, then solve it.

First, assume a spherical cow.

Interesting as an exercise, but not particularly useful.