CSNB Map #2

Here is another constant-scale natural boundary map of Earth called “Ocean Watersheds.”

When the edge of a world map is a natural boundary, the shape of the map has physical meaning.

World maps with natural boundaries were discovered in the mid-twentieth century by a fascinating old coot named Athelstan Spilhaus, a polymath from South Africa who, according to his obituary, spent World War II in Burma and southwest China as a meteorological sciences adviser to not-yet-chairman Mao, spent the 50’s at Area 51 sending up experimental, extremely high altitude weather balloons and about whom, because of a popular Sunday funnies science-strip Spilhaus wrote, President Kennedy said, “The only science I ever learned I learned from Athelstan Spilhaus.”

Working ingeniously with scissors and tape, Spilhaus exploited conventional projection formulas, extending them here, cropping them there, along shorelines and tectonic features to make “world maps with natural boundaries,” the title — finally, the right words together! — of his last published paper, with cartographic luminary John Parr Snyder, of 1993. The trouble, if there was one, was that he and Snyder exploited conventional projections, which, extended beyond their usual limits, became grossly distorted at their peripheries. So, even though the edges of their maps had physical meaning, it was like looking at a map of the world through a fun-house mirror. For Spilhaus and Snyder, the problem became 1) of selecting a particular projection (from hundreds available) which would minimize the fun-house effect for a given projection, and 2) of accepting the limitation of boundary extent that the chosen projection allowed. So, they could (as they did in their 1993 paper) conceive of a world map edged by continental divides, and comment on the “obvious utility” of such a map — it would organize the world into its constituent watersheds, the basic units of geomorphology — but they could not figure out how to make it.

Earth\'s Ocean Watersheds copyright 1996 Chuck Clark all rights reserved

Here is the map they would like to have made.

Because the geometry for plotting points for csnb world maps is not a conventional (two parameter, x and y) projection system — csnb only projects the line of interruption (a single parameter, x) at a constant scale — the two problems that bedeviled Spilhaus and Snyder, extreme peripheral distortion and limited boundary selection, are moot. And — here’s the bonus, the beauty of the csnb approach to making world maps — when a world map’s natural boundary is drawn at a constant scale, the map’s shape has geometrically accurate physical meaning, like looking at your reflection in a flat mirror.

Land is white, water is blue, edge of map is continental (and sub-continental) divides, and the habitual perimeters of primary ocean currents (imagine holding your finger over the end of the water hose).
What is nice here is that at a single glance you see Earth’s complete surface in proper proportion, the world’s ocean and the lands that drain into it, all in proper shape and size.

From the point of view of a raindrop, falling on the map’s edge, everything is downhill (or swept along the current). From the point of view of the sailor, coming into port, walk inland as far as you want, but beware if you go over the top of the hill. And:

  • The overall proportion of land to water is accurate
  • The relative proportion of each ocean to the others is accurate
  • The proportion (and disposition) of land draining into each ocean is accurate
  • The proportions, shape and size of the particular watersheds, relative to each other, are accurate.
  • Continents are color-coded.
  • Straits (Bering and the various Indonesian) are shown with curvy hyperlines
  • Canals (Suez and Panama) are shown with straight hyperlines (Suez, a sea level canal, has a radius corner; Panama, a locked canal, has a hard corner).

Because no segment is very large in relation to the total surface, the map folds to a pretty good globe.

If you think about the words “constant” and “scale,” it’s obvious that any csnb world map, even when its segments are very large, has to fold up, at least to some sort of volume. More about that in later posts, where I’ll cover the “children” (more compact adaptions, prunings of the boundary tree) of this map.

5 Responses to “CSNB Map #2”

  1. Jack van Wijk Says:

    Great story! I worked on this also, see http://www.win.tue.nl/~vanwijk/myriahedral

  2. Chuck Clark Says:

    Yes, you certainly did, and you did it digitally! Only nitpick I see is you called it “coastline” map, when with just a bit more attention to the border (the interruption, it would be an ocean basin map. And far more accurate than anything I could make. All you need is software that extracts divides.

    We should talk.

  3. ingrid dabringer Says:

    Hi Chuck,
    I am an artist who paint on maps, (among many other things). Any chance I can work with some of yours maps?

    I am very interested in isolated waterbasin maps. I would like to paint these because I think the concept of nationalism would be much better served by waterbasin boundaries than the current ones we have going based on war.


  4. Chuck Clark Says:

    Yes, but.
    There are a few things we must come to an understanding on, in order for that to happen, but want to be encouraging.
    As well as a tangential item or two that might be of interest, for instance

    I know very little about the mit project (they found me) but they appear to be exploring the whimsical and the cultural aspects of mapping rather than the hard science niche I’m investigating.
    And I take it you’ve followed by site-link to Strange Maps, over at Big Think?
    Sounds to me you are interested in making derivative works. If these are strictly for educational or personal uses, you have my blessing with the requirement foe educational uses that you credit, i.e., identify the source of the maps (Chuck Clark architect, Atlanta, GA, rightbasicbuilding.com).
    We’ll have to talk if you envision commercial use.
    I’ll send you an email.

  5. L’Océan au centre du monde, ou la “projection de Spilhaus” – Compagnon de l'archipel : Didier Fradin Says:

    […] On peut arriver à de très artistiques représentations comme celle-ci, sans doute moins parlante, qui nous vient d’un architecte sur un site de cartographie […]

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