{"id":1790582,"date":"2021-03-31T17:05:53","date_gmt":"2021-03-31T21:05:53","guid":{"rendered":"https:\/\/www.maproomblog.com\/?p=1790582"},"modified":"2021-03-31T17:05:53","modified_gmt":"2021-03-31T21:05:53","slug":"the-spherical-cow-projection","status":"publish","type":"post","link":"https:\/\/www.maproomblog.com\/2021\/03\/the-spherical-cow-projection\/","title":{"rendered":"The Spherical Cow Projection"},"content":{"rendered":"

Today is The Map Room<\/strong>\u2019s 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\u2019m 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\u2019t even taken geography since high school.)<\/p>\n

But that\u2019s not to say that I haven\u2019t picked up some<\/em> knowledge: I\u2019ve turned my longstanding interest in fantasy maps<\/a> into a few published articles<\/a> (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<\/em>. 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\u2019ve seen and read, has afforded me some perspective.<\/p>\n

Enough to call out obvious horseshit when I see it.<\/p>\n

<\/p>\n

Also, because I\u2019m not a cartographer, because I don\u2019t have that background or training, because my expertise is a hundred miles wide but a millimetre thick, I\u2019d be extraordinarily reluctant to tell cartographers that what they\u2019ve been doing for the past few centuries has been completely wrong<\/em>, and that I\u2019ve come up with something better that no one has ever thought of before\u2014<\/em>only for the something better to be utterly old and familiar to those who know what they\u2019re doing.<\/p>\n

I don\u2019t have that kind of chutzpah.<\/p>\n

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<\/a>, 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\u2019s homolosine, Mollweide and Van der Grinten projections, among others, by the mid-20th century.<\/p>\n

Even so, cartographers generally hated<\/em> 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\u2014Peters vs. Mercator\u2014and marketed the projection to credulous audiences (e.g. Boston schools as recently as four years ago<\/a>) as a solution to a problem that in truth was neither unsolved nor really a problem.<\/p>\n

Guess what? It\u2019s happening again.<\/p>\n

In 2007 a pair of physicists, David Goldberg and J. Richard Gott, published an article in Cartographica<\/em><\/a> in which they proposed a way of measuring and scoring map projections by six kinds of distortion\u2014area, 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<\/em>, had the best score: 4.563. (The lower the score, the better: a globe\u2019s score is zero. The Mercator\u2019s score is 8.296.)<\/p>\n

Last month, in an unpublished paper uploaded to Arxiv<\/a>, 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<\/em>.<\/p>\n

\"\"
North Pole on the front; South Pole on the back (Gott, Vanderbei and Goldberg).<\/figcaption><\/figure>\n

\u201cTo the best of their knowledge,\u201d says the piece from Princeton\u2019s communications office<\/a>, \u201cno 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.\u201d<\/p>\n

Except that maps showing the world in two hemispheres date back at least<\/em> as far as the 16th century (there\u2019s one on my wall) and polar azimuthal projections aren\u2019t exactly new either: they\u2019re splitting hairs awfully<\/em> fine to make that claim. Regardless, their double-sided map gets a score of 0.881 on their Goldberg-Gott scale.<\/p>\n

Matthew Edney was not impressed; as you might expect, he did not hold back. \u201cI am utterly and thoroughly gobsmacked,\u201d he wrote last month<\/a> in a piece that marvels at the claims made in the PR piece.<\/p>\n

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. […]<\/p>\n

Ultimately, once one has stripped away the immense amount of PR guff and hyperbole, there\u2019s little to recommend this as a \u201cnew\u201d and \u201cdifferent\u201d\u2014other than the proposal to paste the two halves together. And I\u2019m pretty sure I\u2019ve seen an eighteenth- or nineteenth-century hand-held fan with hemispheres drawn on either side \u2026<\/p>\n

They have really only reinvented the wheel.<\/p><\/blockquote>\n

In a separate piece<\/a> Edney has some questions about the parameters used in Goldberg and Gott\u2019s scoring system, a couple of which he finds dubious, along with the way they\u2019re tallied up.<\/p>\n

Someone coming in from outside the field to \u201csolve\u201d the map projection problem sounds an awful lot like Arno Peters all over again\u2014especially since their little paper has picked up a certain amount of media attention\u2014see coverage from The Verge<\/em><\/a> and the New York Times<\/em><\/a>\u2014that trumpets the possibility that this projection \u201cfixes\u201d flat maps, or the distorted view of the world that we get from flat maps.<\/p>\n

Hoo boy. That\u2019s a hell of a claim\u2014one we\u2019ve seen before. Except that Peters purported to solve map projections\u2019 problem of representation<\/em>. These professors sound like they\u2019re 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\u2019ve seen on Quora, for example, that insist upon this impossibility\u2014that there is such a thing as an \u201caccurate\u201d map projection\u2014is striking.)<\/p>\n

Only they\u2019ve defined \u201cmost accurate\u201d as \u201cfewest distortions according to our own criteria.\u201d In doing so they\u2019ve 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>\u2014a model reduced to the point of oversimplification so that it works.<\/p>\n

Because you\u2019d 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: \u201cThe point of world maps is to show the whole earth, but one can\u2019t see the entire earth, so the most accurate world map doesn\u2019t show the whole earth\u201d (which somehow doesn\u2019t 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.<\/p>\n

Thing is\u2014and regular readers will know I\u2019m preaching to the choir here\u2014there 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\u2019s distortion is a different map projection whose distortion is less problematic for what you\u2019re trying to map. Some distortions you can live with in order to preserve fidelity elsewhere. I\u2019m fond of the Equal Earth<\/a> projection, but I wouldn\u2019t use it if I wanted to emphasize the polar regions.<\/p>\n

It\u2019s a practical<\/em> choice, in other words, one that I\u2019ve come to understand, from my 18 years of paying attention to this, as a basic challenge of map design. One that you can\u2019t simply come in and solve with math. It\u2019s tempting to see this as a variant of the Dunning-Kruger effect<\/a>\u2014or at least the popular understanding of it: an inability to recognize your lack of ability\u2014that in my experience seems to afflict an awful lot of physicists and engineers. Reduce the problem until it\u2019s solvable, then solve it.<\/p>\n

First, assume a spherical cow.<\/p>\n

Interesting as an exercise, but not particularly useful.<\/p>\n","protected":false},"excerpt":{"rendered":"

Today is The Map Room\u2019s 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… More<\/a><\/p>\n","protected":false},"author":1,"featured_media":1790591,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"autoblue_enabled":true,"autoblue_custom_message":"","autoblue_shares":[],"autoblue_post_url":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[29],"tags":[571,1475],"class_list":["post-1790582","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cartography","tag-map-projections","tag-toujfeat"],"jetpack_featured_media_url":"https:\/\/www.maproomblog.com\/xq\/wp-content\/uploads\/2021\/03\/goldberg-gott.jpg","jetpack-related-posts":[{"id":1788776,"url":"https:\/\/www.maproomblog.com\/2020\/04\/an-explorers-cartography-of-already-settled-lands\/","url_meta":{"origin":1790582,"position":0},"title":"An Explorer’s Cartography of Already Settled Lands","author":"Jonathan Crowe","date":"22 April 2020","format":"link","excerpt":"As you probably know, I\u2019m keenly interested in fiction where maps are part of the story. The latest example of this comes from my friend Fran Wilde, whose story, \u201cAn Explorer\u2019s Cartography of Already Settled Lands,\u201d went live on Tor.com this morning. This is a story that challenges our ideas\u2026","rel":"","context":"In "Maps and Literature"","block_context":{"text":"Maps and Literature","link":"https:\/\/www.maproomblog.com\/category\/maps-and-literature\/"},"img":{"alt_text":"An Explorer\u2019s Cartography of Already Settled Lands (cover)","src":"https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2020\/04\/an-explorers-cartography-200x300.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":1788711,"url":"https:\/\/www.maproomblog.com\/2020\/04\/star-maps-history-artistry-and-cartography\/","url_meta":{"origin":1790582,"position":1},"title":"Star Maps: History, Artistry, and Cartography","author":"Jonathan Crowe","date":"14 April 2020","format":"link","excerpt":"The March 2020 issue (PDF) of Calafia, the journal of the California Map Society, has as its theme the mapping of space. It also has something from me in it: my review of the third edition of Nick Kanas\u2019s Star Maps: History, Artistry, and Cartography. An excerpt: It\u2019s important to\u2026","rel":"","context":"In "Antique Maps"","block_context":{"text":"Antique Maps","link":"https:\/\/www.maproomblog.com\/category\/antique-maps\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2020\/04\/IMG_8122.jpeg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2020\/04\/IMG_8122.jpeg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2020\/04\/IMG_8122.jpeg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2020\/04\/IMG_8122.jpeg?resize=700%2C400&ssl=1 2x, https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2020\/04\/IMG_8122.jpeg?resize=1050%2C600&ssl=1 3x, https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2020\/04\/IMG_8122.jpeg?resize=1400%2C800&ssl=1 4x"},"classes":[]},{"id":1787849,"url":"https:\/\/www.maproomblog.com\/2019\/10\/cartography-the-ideal-and-its-history\/","url_meta":{"origin":1790582,"position":2},"title":"Cartography: The Ideal and Its History","author":"Jonathan Crowe","date":"1 October 2019","format":false,"excerpt":"Matthew H. Edney\u2019s Cartography: The Ideal and Its History (University of Chicago Press, April) is a full-throated jeremiad against the concept of cartography itself\u2014the ideal of cartography, which after 237 densely argued pages Edney says \u201cis quite simply indefensible.\u201d Or as the subtitle to the first chapter states: \u201cThere is\u2026","rel":"","context":"In "Book Reviews"","block_context":{"text":"Book Reviews","link":"https:\/\/www.maproomblog.com\/category\/book-reviews\/"},"img":{"alt_text":"Cartography (cover)","src":"https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2018\/10\/edney-cartography-ideal-history-210x300.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":513340,"url":"https:\/\/www.maproomblog.com\/2017\/12\/a-book-roundup-2\/","url_meta":{"origin":1790582,"position":3},"title":"A Book Roundup","author":"Jonathan Crowe","date":"19 December 2017","format":"link","excerpt":"The Routledge Handbook Out last month, the expensive, 600-page\u00a0Routledge Handbook of Mapping and Cartography\u00a0(Routledge). Edited by Alexander J. Kent (who co-wrote\u00a0The Red Atlas) and Peter Vujakovic, the book \"draws on the wealth of new scholarship and practice in this emerging field, from the latest conceptual developments in mapping and advances\u2026","rel":"","context":"In "Antique Maps"","block_context":{"text":"Antique Maps","link":"https:\/\/www.maproomblog.com\/category\/antique-maps\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2016\/11\/social-life-of-maps-142x150.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2016\/11\/social-life-of-maps-142x150.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2016\/11\/social-life-of-maps-142x150.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2016\/11\/social-life-of-maps-142x150.jpg?resize=700%2C400&ssl=1 2x, https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2016\/11\/social-life-of-maps-142x150.jpg?resize=1050%2C600&ssl=1 3x, https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2016\/11\/social-life-of-maps-142x150.jpg?resize=1400%2C800&ssl=1 4x"},"classes":[]},{"id":1786739,"url":"https:\/\/www.maproomblog.com\/2018\/11\/creative-cartography-making-art-with-discarded-maps\/","url_meta":{"origin":1790582,"position":4},"title":"Creative Cartography: Making Art with Discarded Maps","author":"Jonathan Crowe","date":"22 November 2018","format":"link","excerpt":"Creative Cartography: Since 2014, students of Ellen Meissinger's Art on Paper class at Arizona State University have taken discarded maps from ASU Library's Map and Geospatial Hub and put them to use as raw material for art projects. Every year since then those projects have been the subject of an\u2026","rel":"","context":"In "Art"","block_context":{"text":"Art","link":"https:\/\/www.maproomblog.com\/category\/art\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2018\/11\/asu-shi-magic-place-1024x792.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2018\/11\/asu-shi-magic-place-1024x792.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2018\/11\/asu-shi-magic-place-1024x792.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2018\/11\/asu-shi-magic-place-1024x792.jpg?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":1787764,"url":"https:\/\/www.maproomblog.com\/2019\/09\/p-j-mode-interviewed\/","url_meta":{"origin":1790582,"position":5},"title":"P. J. Mode Interviewed","author":"Jonathan Crowe","date":"20 September 2019","format":"link","excerpt":"JSTOR Daily interviews P. J. Mode, the map collector (and donor) behind Cornell University Library\u2019s P. J. Mode Collection of Persuasive Cartography. Mode began collecting maps in 1980, and proceeded in the usual manner until stumbling across what would become his niche. When I was looking at those maps in\u2026","rel":"","context":"In "Antique Maps"","block_context":{"text":"Antique Maps","link":"https:\/\/www.maproomblog.com\/category\/antique-maps\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2019\/09\/pjmode-plumb-pudding-gillray-1024x762.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2019\/09\/pjmode-plumb-pudding-gillray-1024x762.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2019\/09\/pjmode-plumb-pudding-gillray-1024x762.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.maproomblog.com\/xq\/wp-content\/uploads\/2019\/09\/pjmode-plumb-pudding-gillray-1024x762.jpg?resize=700%2C400&ssl=1 2x"},"classes":[]}],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.maproomblog.com\/wp-json\/wp\/v2\/posts\/1790582","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.maproomblog.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.maproomblog.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.maproomblog.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.maproomblog.com\/wp-json\/wp\/v2\/comments?post=1790582"}],"version-history":[{"count":10,"href":"https:\/\/www.maproomblog.com\/wp-json\/wp\/v2\/posts\/1790582\/revisions"}],"predecessor-version":[{"id":1790603,"href":"https:\/\/www.maproomblog.com\/wp-json\/wp\/v2\/posts\/1790582\/revisions\/1790603"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.maproomblog.com\/wp-json\/wp\/v2\/media\/1790591"}],"wp:attachment":[{"href":"https:\/\/www.maproomblog.com\/wp-json\/wp\/v2\/media?parent=1790582"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.maproomblog.com\/wp-json\/wp\/v2\/categories?post=1790582"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.maproomblog.com\/wp-json\/wp\/v2\/tags?post=1790582"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}