As insolvable problems go, it’s right up there with attempts to square the circle. Try as you might, it is impossible to render a three-dimensional object (the Earth, say) on a two-dimensional surface (a world map) without distortion.
Take for example the Mercator projection, still one of the most widespread ways of depicting the world on a map. Because of its cilindrical projection method, areas near the poles are shown much larger than they actually are. In a Mercator projection, Greenland is about the same size as Africa, while in fact Africa’s area is 14 times that of Greenland’s.
All sorts of other map projections have been devised since Mercator’s (practical because it allowed for rhumb lines – used in nautical navigation – to be drawn as straight lines), but none of them have managed to eliminate completely the distortion inherent in converting 3D to 2D.
Chuck Clark has found a novel way to reduce the distortion, though. The Atlanta architect has long been fascinated by world maps, and has devised a way to produce constant-scale natural boundary world maps. All the continents (and the oceans) are shown in a true scale. But to do the maps justice, you will need a pair of scissors, a bit of folding and some glue…
“The art historian Erwin Panofsky (…) called this prototopology, which means merely that the map, when properly folded, resembles the object”, Mr Clark explains on his website.
This prototopological map (constant-scale natural boundary map is even more of a mouthful) of the Earth is an early example of Mr Clark’s csnb maps, and concentrates on the watersheds: the outer edge of the map is constituted by (sub)continental watersheds. For example, north of the rift splitting open Europe, water flows to the Atlantic, south of it, water flows into the Mediterranean.
“What is nice about this map is that at a single glance you see the Earth’s oceans and the lands that drain into them, all in proper proportion, shape and size”, says Mr Clark.
For more information, more recent maps (without graticules) and future updates, check Mr Clark’s brand spanking new weblog: Right Basic Building.
Amazing. Kind of reminds me of the Dymaxion map (of which Wikipedia has a nice entry – I don’t remember if it has been featured on strangemaps yet) – where it’s usually the land mass that is depicted as continous. The watershed idea was a nice twist. Now for some interesting surfing on Rightbasicbuilding…
Jørgen
Comment by Jørgen — May 19, 2008 @ 5:06 pm
‘Athelstan Spilhaus’ was also interested in maps using natural boundaries. John Snyder’s Map Projection Bibliography contains references to the published works of Spilhaus and it can be found Here:
http://www.csiss.org/map-projections/index.html
Comment by Paul B. Anderson — May 19, 2008 @ 5:33 pm
Thank you, Paul, for the Spilhaus reference. You’ll find several more respectful mentions of him over at my http://www.rightbasicbuilding.com blog.
I was fortunate to have three fascinating phone conversations with Spilhaus in the year before his passed away that challenged me to unbcover what was different in our approaches to unwrapping the surface. Out of that came my title of “constant-scale” addition to his coining of phrase “natural boundaries. I’m quite disappointed never to have met JP Snyder, but i did recently get a chace to chat with Snyder’s amanuensis Alden Colvocoresses. He immediately pointed out how constant-scale natural boundary maps would be useful in maps of mines, although I’m not sure myself what he was getting at, as a mine is so small relative to the surface of then earth.
Comment by Chuck Clark — May 19, 2008 @ 6:15 pm
Delightful!
Comment by Anton Sherwood — May 19, 2008 @ 8:19 pm
Too America-centred for my taste.
Comment by Bo — May 19, 2008 @ 8:44 pm
Yo, Bo,
Can’t say as I blame you. Go on over to http://www.rightbasicbuilding.com for the version that reverses this map’s edge and middle disposition. That is, Africa and Asia instead of being the perimeter watersheds are the central land mass, surrounded by (the ocean and) watersheds of the Americas.
Comment by Chuck Clark — May 19, 2008 @ 9:16 pm
This really has opened a can of worms. I mean, the whole point of having a map is to read it AND for it to represent reality. If it fails to do one of these two things it’s not doing its job. Yes, this map DOES represent reality but is it readable? On the other hand, is it not readable because of what we’re used to?
Mercator look out!
Raf
http://uzar.wordpress.com/
Comment by Raf Uzar — May 20, 2008 @ 6:06 am
“Try as you might, it is impossible to render a three-dimensional object (the Earth, say) on a two-dimensional surface (a world map) without distortion…the distortion inherent in converting 3D to 2D.”
Sorry to be picky but that should read, “to render a curved three-dimensional object on a plain two-dimensional surface”. To render the surface of a cube on a plain two-dimensional surface is no problem at all.
Comment by Thony C. — May 20, 2008 @ 6:15 am
I see I’m not the first one to notice your omission of Fuller’s Dymaxion map. This is professed to be the most distortion free projection. Is this not true? I noticed Clark’s site didn’t mention it either…
Comment by Rob C — May 20, 2008 @ 1:03 pm
Yes, that’s a little bit better phrased, Thony C., but let’s not be too hard on our host here.
One person I know, and he’s a mathematician so he ought to know what he’s talking about, says the most accurate language for referring to the surface of “the Earth, say” is to call it a “two dimensional surface embedded in three-space.” The dilemma for the cartographer is to un-embed it, to transform it, the two dimensional sureface, to two-space.
what constant-scale natural boundary world mapping does is push all the distortion into the map’s middle, where it expresses itself as shrinkage, compared to the scale (the metric) at the map’s edge.
Uzar in the previous post makes the essence of my novelty explicit: “This really has opened a can of worms.” And then he continues by musing on “readability.”
Yes, Raf Uzar, it is “not readable” only because of what you are used to. This map may send you to The Atlas of Earth Watersheds, where you would find each riverbasin displayed disembodied, each on a page to itself. Many who focus on watersheds find this perfectly adequate. But if they wonder about context — what does this drain into, what is next door over the hill, this map or one similar (jump to my website) may be just the ticket.
Don’t forget that anything new is always disconcerting. Think about Joseph von Fraunhofer’s lines of the spectrum back in the early nineteenth century, before we knew what they meant. Or the masks of Picasso that show sides and front of a head at the same time. In this map you are seeing the rest of the world in terms of the watersheds of Africa and Asia.
Comment by Chuck Clark — May 20, 2008 @ 1:24 pm
[...] A map. [...]
Pingback by Pseudo-Polymath » Blog Archive » Tuesday Highlights — May 20, 2008 @ 1:51 pm
How do you decide what to do with the internal seas and endorheic basins? For example, you’ve got the Caspian (and Volga drainage) attached near the Scandinavian coastline, but it could also be placed almost halfway around the map at the Iranian coast.
It seems that these drainages could be connected to the rest of the map at any place along their border. Arguably, they could even float freely off to one side of the map!
Comment by Ken — May 20, 2008 @ 2:58 pm
Well, again, Rob C, let’s not be too hard on our host for introducing the cartographic property of distortion in a manner that lets the casual reader jump to the conclusion we’re playing a game judged exclusively on who most minimizes distortion.
Professor Fuller made a fine map and, given his surpassing talent for self-promotion, even more finely professed its various properties as admirable, even unique.
And, if Spilhaus were to go at a Bucky map with his scissors and tape — or, I suspect if we had been flies on the wall when Bucky gave his classified spiel to the U.S. Senate, Bucky reached for the scissors himself — we could cut this map along any number of natural boundaries like continental divides or mid-ocean ridges and rearrange the clippings into a Bucky-ball natural boundary map of the world. Let’s stick for the moment with tectonic boundaries: Spilhaus did something similar with an unfolded tetrahedron world map. Within the limitations of the Spilhaus tetrahedron or the Bucky-ball, you may rearrange the pieces many different ways.
Here’s the rub: whatever arrangement you make, cut it out and fold it up and you’ll always get a Bucky-ball (or a tetrahedron). You cannot CHANGE the distortion either way, increase or decrease. What the can of worms I’ve tumped over lets you do is precisely that. Change the distortion to so minimal that the folded object is (to quote a NASA scientist referring to constant-scale natural boundary maps of highly irregular asteroids) “exactly” a copy of the originating object. Or change the distortion to so extremal (like this map posted here) that the folded object resembles a mis-shapen burrito, or worse if we were continue “zipping up” its edges.
Do not be badgered into thinking that the map with the least distortion is the best map. The best map is that map which puts a meaningful boundary — a boundary germane to your map’s purpose — at the edge, and ONLY that meaningful boundary at the edge. (See my rant on tectonic-edged maps over at my blog.) Now, given such-and-such boundary, the map will have the least possible distortion when that boundary is at a constant scale. And map-users following the procedures of csnb do not have to waste time wading through the library of conventional projections hoping to find one that is a lucky fit to their circumstances.
Worms!
Worms running every which where!
Now what?
I yield the balance of my time for redirect.
Comment by Chuck Clark — May 20, 2008 @ 3:28 pm
Ken, you rock! Terry Gross herself couldn’t pose a better question.
The Caspian Basin (and Volga drainage) is, like other inland basins, attached at its spout.
That is, at the spot where, God forbid, it were to fill up, it would spill over into the sea. The Caspian basin has many spouts, but the lowest one is back up the Volga into that lake — name escapes me as I write — just east of St. Petersburg. From there it seemed a tossup if the flow would go into the Gulf of Bothnia or off to the north, so I pruned the tree (stopped the map boundary) there.
Same holds true for all the other inland basins. That’s why they can’t, or shouldn’t, “float freely off to one side of the map.” If we use the analogy for mapping of peeling the orange, that would be like tearing off a piece of the rind.
But Ken raises another good point about connecting them “at any place along their border.” We could split hairs and say Ken might better have said “at any other SPOUT along their border,” but let’s pretend we dam up the outlet to the north, cut a deep trench someplace else, and punch the csnb (constant-scale natural boundary) “make map” button. The Caspian magically (any new technology sufficiently advanced is indistinguishable from magic — thank you, Arthur Clarke) separates at the dam and reconnects at the new trench.
The map responds to changing conditions. Walk along a continental divide somewhere, move around a few critical rocks and the map responds. This is maybe not so vivid an example, but if we had used as the map edge meteorological divides — which change by the hour — instead of topographical divides, we’d get an animated world map framed by changing weather conditions, the various “basins,” low pressure areas, moving around not unlike my clumsy dammed-and-trenched Caspian example.
Who invited to the party all these worms?
http://strangemaps.wordpress.com/2008/05/19/274-mercator-never-did-this-a-prototopological-world-map/trackback/
Comment by Chuck Clark — May 20, 2008 @ 3:53 pm
[...] 274 – Mercator Never Did This: A Prototopological World Map [...]
Pingback by Mijn nieuws van 20 mei 2008 | Verbeelding — May 20, 2008 @ 5:31 pm
Is there a word for the opposite of “spouts”, i.e. the points where lands separated by water would first meet if the sea falls far enough?
Comment by Anton Sherwood — May 20, 2008 @ 11:04 pm
It Makes Me Nauseous!
Comment by Lurker — May 21, 2008 @ 1:58 am
I’m thankful for phonics. Having seen it map it’s all too tempting to read the title as: PROCTOLOGICAL map.
Comment by Bart Hall (Kansas, USA) — May 21, 2008 @ 11:16 am
What are those red lines running through the Americas? I thought they were mountain ranges — there seem to be lines where the Appalachians, the Rockies, the Sierra Madres, and the Andes are. However there are no mountains running east-west across the American Upper Midwest (aka the “Plains States”), nor does there appear to be any mountains running parallel to the north of the Amazon River.
Comment by Wilson — May 22, 2008 @ 5:15 am
Wilson: “those red lines running through the Americas are the lines that separate the various watersheds.
This is often BUT NOT ALWAYS a chain of mountains. Thus you see on the map red lines running where you know mountains are, but you also see other red lines running through rolling plains or, as in the case of the lines “running parallel to the north of the Amazon River [Basin]” even lower topography. whatever turns the water counts as a divide.
Comment by Chuck Clark — May 22, 2008 @ 4:45 pm
Next question, then: what criteria determined which watershed lines are shown and which are not? For example, what is significant about the line approaching Hudson’s Bay from the southwest?
Comment by Anton Sherwood — June 4, 2008 @ 12:46 am
[...] object the Earth, say on a two-dimensional surface a world map without distortion. Take for exhttp://strangemaps.wordpress.com/2008/05/19/274-mercator-never-did-this-a-prototopological-world-map…June 4: Lifestyle Briefs The Herald BulletinThe Associates of Anderson Christian School will have [...]
Pingback by maps of continents — June 5, 2008 @ 12:25 am
[...] out this blog, which features strange maps and their function. I must admit I find it fascinating. This map, in particular, is a startling reminder that reality differs greatly from our perceptions thereof; [...]
Pingback by Wasabi Rhetoric » Blog Archive » Google maps got nothin’ on this — June 6, 2008 @ 4:46 am
OK, Anton, I can answer that. You ask what is significant about the [red] line to the SW of Hudson’s Bay. Answer: it was geodesically handy. Jump over to my blog (link above) and look up the Watershed Children maps. There you’ll find this map and the map edged by the redlines in the middle of this map. Given the imposition of constant scale at map edge, I needed a bit more map interruption (more red line) to keep the coastline turning around nicely. The extreme inlet-shape of Hudson’s Bay is what provoked the red-branch you wonder about.
As far as it being a significant divide on a local scale, it’s not. As far as it being a significant divide on a large scale (”in the large,” as Marston Morse might recommend we say), that is, in relation to the sizes of the pieces as they exist on the globe, it is. Significant, that is.
But as for the mapping program of constant-scale natural boundary, any branch could be extended or shortened per the whim of the map-user. On these two maps, i was going for whatever branches were needed to keep the coastline — and, more importantly, the body of water defined by the coastline (your Hudson’s Bay) — turning around on itself, cartographically speaking. Here the distance across the projection becomes the ruling characteristic for how many short branches as the one you question get added in.
In short, it’s the big picture that sets the significance of any particular divide, not the significance of the topography at the divide itself. It just so happens that across most of our world, large-scale significance and small-scale significance happen to align. Earth has lots of mountain chains. In those regions where there are no extreme topographic divides, I take what’s there anyhow.
On other roughly spherical worlds, as the Moon, or Venus, this is not the case. I’ll post some maps of these worlds over on my blog in a day or two; come take a look.
Comment by Chuck Clark — June 7, 2008 @ 7:14 pm
[...] (Strange Maps) m3t00 on 08-07-10 at 01:06:am in design, environment, international | tag(s): cartography | permalink | RSS feed | comment or trackback | [...]
Pingback by != » The Map is almost the terrain — July 14, 2008 @ 3:42 am
شات سودي
Comment by y22icom — March 11, 2009 @ 9:13 pm
دردشة فله
Comment by y22icom — March 11, 2009 @ 9:13 pm
شات
Comment by y22icom — March 11, 2009 @ 9:15 pm
thank you
Comment by Tony — May 4, 2009 @ 3:42 am
thanks for this map
good
luck
…
Comment by Solomon — May 11, 2009 @ 8:55 am
merci
Comment by aspicco . — May 17, 2009 @ 6:41 am
Muchas gracias
Comment by sun — July 4, 2009 @ 7:39 am