I think Dr. Spilhaus would be very pleased with the map you created for Watersheds “M” with Currents. Keep up the great works!

Look at my main menu, click on any of the Earth tectonic maps; they use as map boundary various lines of trenches and mid-ocean spreading centers.

The crania maps also use boundary systems that are not strictly topographic ridges and valleys. And in CSNB map #2, the water interruptions are not elevationally derived either — they are edges of slipstreams.

I haven’t done it, but systems drawn from political boundaries (or any other geographic situation) would work; the main thing is to have a global focus, what Marston Morse called “in the large.” (Morse invented Morse Theory (so named by his admirers) a mathematical method of keeping track of all the critical points on an essentially globular object; Morse himself called it A Calculus of Variations in the Large. Morse Theory, with later improvements, continues to be basic for study of dynamics on 2-D surfaces embedded in three-space, things like earth’s climate, tectonics and global hydrology.)

When I look at Tobler’s material, I don’t see a global focus — many important phenomena don’t rise to the in-the-large category. Nothing in that to be ashamed of, and a world map showing, for example, this Tobler material wouldn’t, I think, add anything to the discussion. Maybe I’m not looking at the same maps you are?

Not that there aren’t global issues within demography and economics; it’s just that Tobler’s horizon, at least in the maps you cite, is too low to benefit from putting it on a world map of any projection, conventional or novel. Think about it this way: those USA maps he uses to show the data, they also have a “boundary” at the edge of the map, which limits rather than enlarges the scope. This is fine if your focus is regional. CSNB maps only come into play when a subject is “in the large.”

Not sure if that really helps. You tell me.

Another thing worth clarifying: much of this fuzzy geographical data like demography and economics may be organized topographically. The data has density and scarcity, which generate contour lines, which generate ridges and valleys, which are meat and potatoes for constant-scale natural boundary mapping.

Not to change scale over-much in a post on Earth ocean currents, but pardon me a moment while I Google-image-search electron density and imagine what those objects (and maps) would look like in a CSNB projection . . .

And then there are all sorts of possibilities with edges of slipstreams . . . Jupiter & Saturn; what else? You tell me . . .

The elevation maps of other planetary bodies are neat, but I’m thinking specifically of Waldo Tobler’s maps of demographic and economic flows. http://csiss.ncgia.ucsb.edu/clearinghouse/FlowMapper/

Though I was working on CSNB Map #2 by 1994, & CSNB #1 in 1990, I didn’t stumble on Spilhaus’ work until 1996. As far as my own precedents, Spilhaus gets credit for hoisting the phrase “natural boundaries” (my terms were nowhere near as articulate), and Snyder gets credit for teaching me the importance of where a projection system locates “constant scale.”

I put together the two concepts.

In 2005, Mike Purucker added the necessary hyphen in “constant-scale” (it’s an adjective modifying “natural boundaries”).

I never met Snyder, though I’m told he was very particular about starting a project; you had to be very specific about what you wanted him to do. Spilhaus I talked to a couple of times in his last year — he’d just turned eighty-six when I tracked him down (I think that conversation is recounted somewhere on this blog, if not, then in my 2003 ISPRS paper Visual Calculus or Perceptual Fribble? — World Maps with Constant Scale Edges . . .). He was mentally strong, and continued working on a new ocean-centered map right up until his passing.

http://books.google.com/books?id=GEHVbeZwLGQC&printsec=frontcover&dq=spilhaus&cd=1#v=onepage&q=&f=false

That’ll teach me to keep track of my acronyms.
ACSM is, I believe, the American Congress on Surveying and Mapping.
The CGIS is the The Cartography and Geographic Information Society Journal.
Slips my mind at the moment which library I tracked it down in. It may not be online.

I had thought that CSNB#2 had been drawn by Mr. Spilhaus, and the interruptions in the oceans were arbitrary.

Where would I find a copy of Spilhaus & Snyder’s paper?

If I understand correctly, the difference between “M” and what I’m calling “Spilhaus” is that “M” keeps the oceans contiguous.

There are places in the middle of the ocean that aren’t “contiguous.” They are kind of like continental divides, where a drop of rain might end up going north with one current or south with another.