This is the fascinating observation that it’s not straightforward to say how long a coastline is. If you were to measure the coastline of a country by using a ruler on a globe, you would come out with a vastly different number than if you were to pace around the edge. The closer you look, the more wiggles and squiggliness you come across and instead of converging on a more accurate length, the coastline just keeps getting longer. The smaller your ruler, the longer it gets.

This was originally spotted, incredibly, in the 1950s, by an Englishman, Lewis Richardson, when trying to check a theory he had that the likelihood of war between countries depended on the length of their shared borders. Remarkably, he found that the quoted lengths of borders varied significantly. While measuring on maps at different scales he saw that the smaller scale map he used, or the smaller the width of his calipers he was measuring with, the length systematically increased. When looking at coastlines, instead of borders, some countries had wigglier coasts and so the length increased at a faster rate with the scale — for instance, Norway’s coastline, with it’s crinkly fjords, increases faster than Britain’s, which in turn increases faster than South Africa’s, as he zoomed in. The rate of this increase later became known as its fractal dimension.

Long after Richardson’s research, Benoit Mandelbrot published a paper How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension that discussed how the wiggliness of something like a coastline at one scale can be repeated at smaller and smaller scales. The work led to the later term fractals. Many other things exhibit fractal-like behaviour such as river networks, borders, brains, frequencies, lightning or even the stock market.

More mind-bending mapping with the Mercator Projection, and the difference between Great Britain, the UK and the British Isles.

There’s a super section on this in Scale, by Geoffrey West.

The coastline paradox

From the Swedish plocka upp (pick up), plogging is the simple combo of picking up litter while out jogging. Litter in our environment is the responsibility of all of us and I’m still surprised by how much impact a small effort can make to tidy a place up. Plogging gives the multiple gratification of making your local area nicer and helping out Nature, while getting a decent workout and some fresh air to boot.

Maybe combine it with these other jogging sketchplanations: fartlek, London running kit, clingfilm your keys, run further, or, heck, swimrun for the adventurous.

Plogging

Ever had that feeling when people were saying well done or thank you for what you did, that you didn’t deserve it? It’s called imposter syndrome.

It’s a pernicious and pervasive feeling of doubting accomplishments and fear of being exposed as a fraud — any moment, everyone will wake up and realise you aren’t so great after all.

My thoughts: Hang in there, keep trying your best, stay humble, and don’t take things too seriously.

Get my new weekly sketch in your inbox

Imposter syndrome