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Explaining the world one sketch at a time

Sketchplanations makes complex ideas simple with clear, insightful sketches. Explore topics from science, creativity, psychology, and beyond explained in pictures.

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Learn something new in a sketch each Sunday

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The coastline paradox: a map of the UK dividing up the coastline with ever smaller rulers shows how the coastline length dramatically increases

The coastline paradox

The coastline paradox 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 to 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 callipers he measured 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, and even the stock market. There’s a super section on this in Scale, by Geoffrey West. Also see: The Mercator Projection The difference between Great Britain, the UK and the British Isles
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Imposter Syndrome illustration: even as an appreciative audience applaud, an award recipient at the rostrum on stage questions whether they actually deserve this recognition.

Imposter syndrome

Ever had that feeling when people said "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 your accomplishments and fear of being exposed as a fraud — at 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. And accept compliments.
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Plogging illustration: a happy jogger runs along with a bin bag in hand. Whenever they see litter, they stop to pick it up and pop it in the bag.

Plogging

Plogging—from the Swedish plocka upp (pick up)—is the simple combo of picking up litter while out jogging. Litter in our environment is all our responsibility, and I’m still surprised by how much impact a small effort can make on tidying up a place. 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 or There is no away
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The Trust Equation illustration: set out as a mathematical equation, we understand that the trust we have in someone professionally is proportional to how credible they are in their field, how dependable they are and how safe you feel around them. That trust is inversely proportional to how self-orientated they are.

The trust equation

What is the trust equation and what makes you trust someone in a professional context? I liked this simple equation by Charles Green, which makes it a combination of how credible, reliable, and how intimate — or how safe you feel with that person — divided by the self-orientation of the person — are they focused on their interests, or simply paying more attention to themselves vs being genuinely interested in you and your success. Depending on how you scored this abstract model, I guess that would mean that trust is either undermined by someone focusing on their own interests or strengthened the more they are focused on yours. More at Trusted Advisor. Also see: The most beautiful equation HT: Buzz Pearce
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Tax Freedom Day illustration: a year-long scale from January to December shows how long into the year it takes for different countries to cover the bill for public services through income tax. After that point, the money you earn is for you to spend however you like.

Tax freedom day

If you took all the taxes a country pays each year on one hand, and all the money that people earn on the other, tax freedom day represents the day after which the country’s taxes would be paid by its citizens and the remaining earnings free to spend as they wish. It’s a national average as each individual’s tax freedom day would be different, though in principle you can calculate your own. Given taxes vary between countries, each country has a different tax freedom day — though it’s not easy to compare as calculations tend to differ. In the US it’s calculated by the Tax Foundation.
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Beyond developing and developed world views: a world of 4 income levels from Sketchplanations, Factfulness and Gapminder

A world of 4 income levels

I grew up with the idea that there are developed countries and developing countries, the “rich” world and the “poor” world. I didn’t actively consider this teaching. It’s just always been there. And it’s wrong. In his excellent book Factfulness, Hans Rosling shows that wealthier countries tend to have smaller families and a low child mortality rate. In contrast, poorer countries are more likely to have larger families and a high child mortality rate. Plotting the spread of countries in the 1960s gives a reasonable approximation of a cluster of “developed” countries with small families where most children survive and a cluster of “developing” countries with larger families where more children die. But that was in the ’60s. The world has changed a lot since then, and that model of dividing the world into two buckets no longer fits the data. Most people in the world are somewhere in the middle. And more helpful than dismantling a worldview is providing a new model to replace it: a model with four income levels instead of two. The numbers reflect most people’s reality, with most of us somewhere in the middle. Related Ideas to A world of Four Income Levels Also see: The Destiny Instinct The Continental Axis Hypothesis For more, check out the Factfulness book, or Gapminder. And you could do much worse than watch Hans’ entertaining TED talk: the best stats you’ve ever seen.
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