Off the Charts

The best of our data journalism

Marie Segger
Data journalist

This week our Graphic detail looks at how Russia might be dodging the oil price cap imposed by Western importers. Although official data show that its production and revenues are down, a report by the Centre for Research on Energy and Clean Air, a think-tank, suggests that China, India, Singapore, Turkey and the United Arab Emirates may be acting as middlemen. They buy Russia’s crude and sell refined oil to America, the EU and others that have implemented the price cap.

More of our data reporting this week:

Alex Selby-Boothroyd reported on the latest ranking of the world’s most liveable cities.
Rachel Dobbs looked at the consequences of shrinking sea-ice coverage in Antarctica.
Below Caroline Carter explains why coastlines are difficult to measure. She talked to Norway’s mapping agency about its growing shores and the country’s approach to tracing them.

Finally, a plug. If you want to join our data team, The Economist is hiring a political data scientist.

If you have any feedback for us, want to share interesting data or suggest what we should write about in a forthcoming edition of this behind-the-scenes newsletter, you can drop us a line at [email protected].

Why is Norway’s coastline growing?

Caroline Carter
News editor

One of the joys of working at The Economist is the opportunity to research and write about almost anything that interests you. I studied geography at university and have always been fascinated by maps. I have written about such topics as how Google shows different international borders to different users and how many oceans there are. So when I read that every time Norway’s coastline is measured, it becomes longer, I was intrigued.

Governments need to know where the boundaries of their countries lie. Land borders, negotiated by politicians and drawn up by cartographers, are often neat lines. Coastlines, which constitute at least part of the boundaries of 140 countries, can be more complicated. They are squiggly, re-position themselves at least twice a day and change seasonally. Some are shrinking because of climate change. Mapping them has long challenged surveyors. Measuring a straight line is simple. But measuring a curve requires assessing lots of short intervals and adding their lengths together.

Measuring the length of a coastline is not just difficult. The “coastline paradox” finds that it is actually impossible. In 1951 Lewis Fry Richardson, a British mathematician, was studying whether the length of neighbouring countries’ borders influenced the likelihood of them going to war. Mr Richardson noticed that Portugal and Spain recorded different lengths for their shared border and reasoned that was because the two countries were using different metrics. He also noticed that coastal measurements varied widely.

Britain’s coastline mapped at varying degrees of detail

Hence the “Richardson effect”: when measuring an imperfect line the shorter the ruler the longer its length. Richardson also proposed that if the ruler were infinitely small, the line it measured would be infinitely long. This idea was taken up by Benoît Mandelbrot, a Polish-born mathematician, in “How long is the coast of Britain?”, a paper published in 1967. Mandelbrot found that coastlines are statistically “self-similar,” meaning that parts of them show the same statistical (and visual) properties at many scales, so the closer you look, the more intricate a coastline becomes. (Coastlines can be considered as imperfect examples of the “fractal” pattern Mandelbrot developed a decade later.)

Zoom in and out of digital maps of Norway’s coast and you can see Mandelbrot’s self-similarity in action. The shore has curve upon curve and there are around 240,000 islands and more than 1,700 fjords. Improved cartographic technology allows more detail to be included. And, as Richardson’s rule says, the more features, such as inlets, coves and rocks, that are mapped, the longer the distance becomes. In the 1990s the Kartverket, Norway’s mapping agency, measured the coastline, on paper, to be 57,000km. Once the agency digitised its measurements, the length grew to 83,000km. In 2011 it had reached 101,000km. The latest estimate is 104,600km. By most sources that makes Norway’s coastline the world’s second-longest, after Canada’s. The next time it is measured it will be even longer. And Norway is not alone. Official estimates of the length of America’s coasts, for example, vary between 20,000km and 154,000km.

Martin Egger, a cartographer at the Kartverket, says that the agency is not particularly interested in the length of the coastline and does not publish an official estimate. It wants to provide sufficient detail for those who ply the country’s waters. The Kartverket makes its maps from aerial photographs but other countries use different technologies. Accurate mapping is expensive. Greenland’s landmass is six times larger than Norway’s and features a similarly intricate coastline but has not been mapped in the same detail. “I would not be surprised if the length of the coastline of Greenland was much longer than the Norwegian one,” said Mr Egger.