Posts tagged ‘Dymaxion Map’

March 17, 2012

Mapping the World

A year ago today, I posted a short entry on world maps. More specifically, it was about alternative world map projections. (A projection is the way in which the globe or any portion of it is represented on a flat surface.) Mostly, when people think of the map of the world, they have the Mercator projection in mind. It looks like this.

The Mercator projection was created by Gerardus Mercator, a 16th century Flemish cartographer. Its strength was that it was useful for European maritime navigators. Remember, this is the dawn of colonialism. In a good example of how science and politics can be married, Mercator provided the Europeans with a tool for navigation, and in turn, they disseminated his map all over the world and made it the dominant mode of representation of the globe. Which is one of the reasons I said that when the words ‘world map’ pop up, people think of the Mercator projection.

The strengths of the projection are also its weaknesses. From a cartography standpoint, it gets one too many things wrong: it places the equator too low (it’s not in the middle), it distorts the northern parts of the globe too much (giving a false sense of size to small northern countries), it is Eurocentric, and it places the northern hemisphere on top, encouraging thinking of the northern hemisphere as dominant. (I should say that these are the most common criticisms leveled at the map. There are probably more, and not everyone would accept all of them as valid. But that’s not the point here.)

The Gall-Peters projection fixes some of these problems. This, we are told, is more ‘accurate’.

Then there are other, more whacky projections that further fix some of the Mercator map problems. In the last entry I gave two of these. The Peirce projection, also known as the Quincuncial projection

and the Buckminster Fuller Dymaxion Map projection


(Bear with me here, I’m not just recycling old material.)

A week or so ago, a university professor named Gene Keyes, commented on my original entry. He offered a link to his own article of criticism of the Dymaxion map in favor of the Cahill-Keyes projection. You can read all his arguments in detail here and here. I have myself only skimmed through the linked articles and I think I got the gist of the criticism. Apparently, decades before Buckminster Fuller created his Dymaxion map, Bernard J.S. Cahill was solving the same problems and came up with his own solution to the projection problems of the Mercator map. His solution is remarkably similar to Fuller’s later solution, and according to Keyes, Cahill’s is better.

According to Mr. Keyes, there are seven ways in which the Dymaxion Maps is deficient. They are:
1) Asymmetry of layout

2) Irregularity of graticule

3) Bad distortion of Korea and vicinity; also Norway

4) Poor scalability: the larger a Dymaxion map, the worse it looks

5) Anti-metric measurements; triangle edges have unstated irrational metric length of 7,048.89 km

6) Poor to zero comparison with any equivalent globe

7) Poor synoptic globe-and-map learnability

The Cahill projection (which Mr. Keyes would later amend to make the Cahill-Keyes projection) suffers from none of these problems. (I should add that this is all according to Mr. Keyes; not that I necessarily have any problems with his criticisms.)

The Cahill 1909 projection.

The Cahill-Keyes 1975 projection.

Now, I am not a cartographer, nor even a geographer. I don’t know what some of the words in those seven criticisms mean, and the only understanding I have of the concepts is through a superficial reading of Keyes’ article. I am ignorant of the issue, to say the least.

But there is something else. (And this is what this entry is really about.) I have no problem with criticizing the Mercator map or indeed the Dymaxion map. They might be more or less accurate, relative to other maps, they might be more or less suitable depending on the need. However, the claim from Cahill and Keyes is stronger (and Fuller probably fits this ideological criterion as well). Says Keyes:
Map-design-seekers are often asked: for what purpose do you want to use it? The conventional wisdom is that you must go with many different projections. Cahill begged to differ, and I concur:
I want a single, general purpose, world map projection, with high fidelity to a globe, suitable at all scales from smallest to largest, good for one country or the whole planet. I want a world map and globe as a synoptic pair, comparable to each other at a glance, or in detail. I want geography learners at any age to be able to grasp the globe and world map as readily as do-re-mi.

One map, one purpose. This is where my amateurish admiration for various projections and Cahill and Keyes’ project diverge.

This, I dare say, is not possible. For one, it just doesn’t seem likely that humanity will give up on the Mercator map. Somehow, for some reason or another, we seem to be invested in it. It is a convention that has been around long enough that it just might stick with humanity, even through massive civilizational changes. There is a decent argument to be made that we are currently going through one such civilizational shift, like the Middle Ages giving way to the Renaissance, or the Persian empire giving way to the Greek civilization. And if the Mercator map survives the change, and is able to transfer itself into the new age, it might be around for a very long time. Not as the only projection, but as the dominant one, the one people have in their heads when the words ‘world map’ are uttered.

(And if your conception of the civilization shift is tied to the change from analog to digital, then the fact that Google uses Mercator’s map – a fact that Keyes himself points out – has to be a strong argument for the projection surviving the jump.)

Nor would this be unusual for the human race. Just think of our concept of the day, the seasons, the year. Why would the day be divided into two twelve unit parts? It is a convention the Babylonians came up with 3000 (?) years ago, and it’s still with us (in a slightly changed form). Why should there be four seasons, and why should they be in the order they are in? If the Indian model of seasons had become dominant, we would perhaps only have two: wet and dry. If you exclude crop growing, we city dwellers (and of late we have become the majority, didn’t you know) could easily divide the year into more than four seasons: heating season, rainy season, falling in love season (for all I care), cooling season, melancholy season, shopping and partying season (to give an outrageous example). Why should the year have twelve months, and why should they have the number of days they have? (And don’t get me started on leap years.) Why would the 9th, 10th, 11th, and 12th months of the year be called the seventh, eighth, ninth and tenth (September comes from the Latin for seven, October from eighth) … ?

In fact, after seizing power, the French revolutionaries made up a new “rational” calendar, whereby the year had ten months. (The Russian revolutionaries were more modest in their attempts: they only switched from the Julian to the Gregorian calendar.) Why ten? Because we live in a world that uses the decimal system. Something that Keyes himself mentions as a strength of the Cahill projection over the Fuller projection. But why should this be better? What if future generations abandon the decimal system? (Perhaps in favor of the binary?) (Needless to say, the revolutionary calendar did not take.) And why should a sphere have 360 degrees? Why not 400? (In fact, I heard from someone once that the Russians had cannons during WWII that used a 400 degree circle, making a right angle 100, not 90 degrees.)

While these measurements sound arbitrary and irrational, they are vestiges of a time when their use was actually the most effective way of solving a specific problem. They have far outlived their usefulness, and are now simply convention. (Some have survived, and others have not, e.g. Roman numbers.) The Mercator projection falls neatly into this category, and there is little reason to think that it will not be just another in a long line of examples of this human phenomenon.

And this might be fine. Is there really a problem with the idea of a minute having sixty seconds? Or does anyone in America feel angst about the idea that water freezes at 32 degrees Fahrenheit? Or do those using Celsius really have a problem with their system of measurement being tied to physical properties of water (and not oxygen for example, or lead)?

This is not to say that Mercator map doesn’t have its problems. As I mentioned before, it does. Its problems can be discussed and other projections used to solve them. But the idea of a “better” map replacing and completely suppressing the use of Mercator’s map, just seems unlikely to me.

There are further reasons why I don’t think the Cahill-Keyes projection could become “the one” map.

I can think of one aspect according to which the Mercator (and the Peters) projection might best (I have to be careful here) the Peirce, Fuller, and Cahill. And that’s time. For someone who has a sister six time zones away, and friends two, three, four time zones before and after him, the passage of time seems mapped better on a cylindrical projection rather than the Quincuncial one or an unfolded icosahedron.

Further, it needs to be said that all these projections are heavily biased towards landmasses. That makes sense given that we think of ourselves as land creatures. But what if we once again become a civilization of maritime navigators? And I don’t mean like in Mercator’s time. I mean like the Polynesian civilization which used stick charts as maps of ocean swells and currents. The charts also map islands, but more to show how they interrupt ocean swells rather than give any significant detail of the landmass.

And what of potential space travel? This might sound like science fiction, but I am not convinced that space travel now is that dissimilar from what sailing around the world was in 1480, the year Ferdinand Magellan was born. In a hundred years, the attempt to make “the one” projection of Earth might turn out to be the equivalent of trying to clearly divide arable land in England at the end of the 15th century – a parochial endeavor that will ultimately have no place in the larger map.

March 17, 2011

Ever More Maps

Apparently, maps are important.

Also, I wish I could remember the name of the book about Copernicus I heard about. In an interview, the author said that Copernicus got the idea for his big ‘reversal’ from a map he was studying. So, apparently, maps are important.

In the above video, the cartographers are promoting the use of the Peters projection. A projection I prefer more than the Peters is Buckminster Fuller’s Dymaxion map. Not only does it have no up-down aspect, but it distorts either the landmass or the world oceans less, and can be packed into a cuboctahedron to closer resemble the obloid sphere that is Earth. See…

Dymaxion map as an unfolded icosahedron

When you open it up, it can be set up to place all the landmasses as one piece (like in the image above):

Or you can open it up to show the world oceans in one piece.

Another projection I really like is the Quincuncial projection developed by the philosopher Charles Sanders Peirce in the 19th century.

It distorts the distance between the landmasses (like between South America and Africa), but it preserves the proportions of the continents better than Mercator and Peters. Also, no up and down here either.

Over at Cosmic Variance, the physicist Sean Carroll offers a few links about map projections (beyond nerdy), and explains one of the reasons for the quincuncial projection being his favorite. The closing line of the piece is the best though. “All of which is simply to say: if Charles Sanders Peirce were alive today, he would definitely have a blog.”

(more projections)