Looking under the hood at
beauty, complexity of cartograms

UPDATE: The Blog was a bit groggy this morning (it IS Monday, after all) so we didn't quite connect the interview Chicago Tribune Graphics Editor Steve Cavendish did last fall for that paper's Perspective section with Sunday's featured item about WorldMapper. We're very pleased to repost that interesting Q-and-A with Mark Newman ...

Q-and-A with WorldMapper's Mark Newman

Mark Newman sees the world a bit differently than the rest of us do.

Whereas you and I might see a map with borders, he sees algorithms and spatial representations. A University of Michigan physicist turned self-professed "map geek," Newman and a group of geographers in England have been turning data on topics such as population or mortality into a type of map called a cartogram.

Their WorldMapper project, which can be found at WorldMapper.org, takes information from the United Nations, the U.S. Census Bureau and other sources and puts them through a mathematical formula Newman developed a few years ago.

The result? Countries still have borders, but their area is now a visual representation of the data. Though cartograms aren't new, Newman's algorithm has given geographers an easier way to do them. In a recent conversation with the Tribune, he elaborated on his interest and how they work.

Q. Why are cartograms useful?
Cartograms are a striking way to visualize statistics on a map. By making countries, states or regions bigger or smaller according to their population or wealth or any other quantity of interest, we can see at a glance how different regions compare. All of the data we use in making our maps is freely available in the form of tables on the Internet, but tables aren't easy to read. These maps, on the other hand, allow people to take in the same data in a single, easily understood figure.

Q. You're a physicist. How did you get interested in mapping?
I do research on networks, such as computer networks and social networks, and first became interested in making cartograms as a tool for studying the spatial distribution of the nodes in some of these networks. Along with a colleague, Michael Gastner, I developed the computer technique used for making the maps. Only after we'd started making maps did we realize that this was something geographers were very interested in as well.

Q. There's some complicated math behind these maps. Can you give me a layman's explanation for it?
If we want to make a map in which the sizes of countries vary with, say, population, then we want to make countries larger -- spread them out more -- if they have larger populations.
We do this by making use of an analogy to the physical process of diffusion. (This is where the physics comes in.) Imagine dumping a bottle of black ink into a swimming pool. Initially, the ink would be concentrated in a small area -- very black -- while the rest of the water would be clear. As time goes by, however, the ink would spread out, and if we wait long enough it will end up uniformly distributed throughout the pool, with all the water being just slightly inky. This is the diffusion process.

In our work, we mimic the same process with population density. We let it spread out away from the places where it is highest -- the cities and greater metropolitan areas -- until it is uniform everywhere. And as it spreads we allow it to "carry along" the features of the map, such as country borders and coastlines, so that the countries with big populations expand while those with small populations remain small.

Q. Any surprises in the things you've mapped? What have you seen that you didn't expect?
The most surprising results for me have been in the sheer scale of things. Most of us know, for example, that the United States emits more greenhouse gases than other countries. We know that Africa has higher child mortality than does Europe or the Americas. We may even have seen the figures for these things in the newspapers or on TV.

But for me these maps bring home the true scale of things in a way that numbers on a page never really do.

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