It might seem straightforward to pull out a map and measure the distance between two distant points, however, the larger the distance the bigger the distortion caused by traveling on the curved surface of the Earth as opposed to flat 2D space. So while the distance you measure to your neighbouring town won't be too bad, if you're measuring between London and Rio the curvature of the Earth will make a big difference to the distance that you'll travel. To help figure out the correct distance there's the haversine formula.

The haversine formula allows you to calculate the shortest distance between two points on a sphere using their latitudes and longitudes — this will be the arc between them on the great circle that includes both points. A great circle is a circle on a sphere with the same centre as the sphere, like the Equator. The haversine formula isn't perfect in practice, as Earth isn't a perfect sphere — see the 3 tallest mountains.

It was invented around two hundred years ago, together with tables to speed any calculations, to help sailors navigate.

The haversine formula

Jared Diamond’s classic Guns, Germs and Steel, proposes some remarkable hypotheses about how the pattern of history played out, notably trying to answer the question of why it was generally the Europeans that invaded much of the rest of the world rather than the other way around. One hypothesis, striking in its simplicity if you’ve ever looked at a world map, is the significant contribution of the general orientation of the major continents.

The Americas are largely lined up North–South, while Europe and Asia (Eurasia) are largely lined up East-West. An East-West alignment means the land generally has a more similar climate, day length and seasonal variations. The general logic goes that the similar latitude of an East–West alignment means animals, crops, as well as travel and trade, more easily spread across the continents than with a North–South alignment — of the Americas and Africa — which naturally encounters more different climatic zones.

As a simplified example, horses and other large animals and crops spread throughout the shared temperate latitudes of Eurasia. In contrast, South America’s only large domesticated animal, the thick-coated llama (and related species like the alpaca) couldn’t easily spread to North America through the impassable tropical barrier of the isthmus of Panama. They just aren’t built for it.

There are a lot of viewpoints on the theory, and Diamond includes many more factors of geopgraphy and others — like never being able to domesticate the zebra — that go towards answering his question of why Spain invaded the Americas and not vice-versa. But ever since reading it I’ve found this hypothesis hugely intriguing.

The continental axis hypothesis

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 mindbending mapping, 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

I grew up with the idea that there are developed countries and developing countries. There was the ‘rich’ world and the 'poor’ world. I didn’t actively consider it, it’s just always been there. And it’s wrong.

Hans Rosling, in his excellent book Factfulness, shows that wealthier countries tend to have smaller families and a low child mortality rate, whereas poorer countries were more likely to have larger families and a high child mortality rate. Plotting the spread of countries in 1965 gives a reasonable approximation of a cluster of 'developed’ countries with small families where most children live, and 'developing’ countries with larger families where more children die. But that’s in 1965.

The world has changed a lot since then and now that model of dividing up the world into two buckets just doesn’t hold true with the data any more. Most people in the world are somewhere in the middle.

And more useful than dismantling my worldview is providing a new model to replace it with. A model with 4 income levels instead of 2 and the number of billions of people who currently live in each level. It’s a model with most people somewhere in the middle.

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.

A world of 4 income levels

Everyone knows Everest is the highest mountain at a colossal 8,848m above sea level. But, depending on how you’re measuring, there are two other candidates for tallest mountain.

Mauna Kea is a volcano on the big island of Hawaii. In fact the whole island is made from volcano, so as a peak it rises from the base of the Pacific ocean to over 4,200m above sea level. Including the part of the mountain that rises from the sea bed it is over 10,000m tall.

Mt Chimborazo can also lay a claim to the tallest mountain. The Earth is not a perfect sphere — it bulges around the Equator meaning that points on the Equator are several kilometres further from the centre of the Earth than points further North or South. A bulging around the centre is a common shape for a spinning sphere due to the force exerted by the spinning. Sitting almost exactly on the Equator means that Chimborazo’s already enormous 6,263m from sea level makes its summit the furthest point on the Earth’s surface from the centre of the Earth.

I’m not totally sure if that means that at some point Chimborazo’s summit makes it the closest point to the sun, but it definitely sounds plausible! 

The 3 tallest mountains

In the UK and certain temperate latitudes there’s a period where the weather gets warmer and the season late for the winter crops, while the temperatures can still be too low for the Summer crops to get going. This period is known as the Hungry Gap — from late April, through May and a little of early June — as it’s hard to pick enough crops locally at that time of year to live off.

Ellen Warrell at Riverford Organic Farmers explains the Hungry Gap including ways to manage it. For example, did you know that “Trucking tomatoes over from Spain uses just a tenth of the carbon compared with growing them in the UK using heat.”

The Hungry Gap

All maps involve decisions. Whenever you compress real life onto something smaller and less detailed you have to choose what to keep in and what to leave out. And in the case of printing a map of the Earth, you have to figure out how to get something that is curved onto something that is flat, and this involves trade-offs and decisions as well. 3 dimensional space just doesn’t flatten to 2 dimensional paper without choices.

In 1569 Gerardus Mercator created a map that brilliantly solved a pressing problem — that of being able to follow a straight line while sailing and it correspond to a straight line on the map. His map also did a good job of preserving the shape of countries. But to do this you have to stretch the areas at the top and bottom of the Earth. Because most of the land on Earth is in the Northern hemisphere, and because that land is generally further north than the land in the southern hemisphere is south, it has the effect of enlarging Northern countries such as Europe, the US and Canada, Scandinavia and Russia as compared to countries closer to the equator and in the Southern hemisphere.

Most world maps you see are still similar to Mercator’s projection. In fact Google Maps desktop used it until just recently. It could well be that this distorts our worldview by emphasizing Northern countries in size and therefore importance. When I see a more size accurate Gall-Peters projection I have to say it’s hard to argue.

The Mercator projection

Are caused by the Earth’s tilt. As the Earth goes around the sun, the tilt of Earth’s axis — 23.5 degrees — causes at different times of the year, the two hemispheres, North and South, to be either tilted towards the sun or away from it.

In Winter, and closer to the Poles, because light from the sun hits at a greater angle, the solar energy gets spread over a larger area. This makes it weaker, cooler and gives rise to Winter.

In Summer, and closer to the equator, light from the sun hits more directly and so is concentrated on a smaller area making it stronger.

The tilt also means that the number of daylight hours is greater in the Summer than in the Winter, and hence the amount of time it gets heated, which also contributes to the seasons.

Seasons are reversed in the two hemispheres, so if it’s Winter in the Northern Hemisphere it’s Summer in the Southern and vice-versa. The further from the equator you go, the bigger the effect of the seasons. So, temperatures in Ecuador stay relatively constant throughout the year, while the poles experience extremes of 24-hour daylight or 24-hour night and great freezes and great thaws.

PSThis is a correction to my original Seasons sketchplanation which implied that temperature difference was more due to the increased distance from the sun due to the tilt. This is not correct, and it’s taken me, embarrassingly, a long time to right it. Thanks to Adrián Fernández Martínez, marjancek and Reasons2AvoidAndroid for putting me straight. 

Seasons

Nature’s greatest snow machine, where crazy amounts of snow can fall in huge snowstorms on the downwind — leeward — side of a lake. Where the effect is pronounced, such as on the East of some of the Great Lakes in the US, it can generate regions known as snow belts because of the amount of snow they receive.

It works kind of like this: cold air blows over a lake. As the cold air passes over the warmer lake it picks up water vapour from the lake and it warms. This causes it to rise and in turn cool, such that when it reaches the downwind side of the lake it is now a lot of cold moist air which can cause some incredible snowstorms, like 2–3 inches of snow per hour. Satellite pictures like these show it in action pretty clearly. If the land rises after the lake the air can cool faster and increase the effect — and also cause a rain shadow — and if there’s a whole lot of convection and the air is rising fast you can get what’s called thundersnow — a thunderstorm in a snowstorm. I know.

Find weather interesting? Me too. You might also be interested in: Dirty thunderstorms, thunderclouds, yesterday’s weather (applying weather forecasting to software engineering), rain shadow, lenticular clouds, know your cirrostratus from your altocumulus, and British weather.

Lake-effect snow

There are only two double-landlocked countries: Liechtenstein and Uzbekistan. Their claim to fame is that not only are they landlocked with no access to the high seas themselves, but they are also surrounded by countries that are themselves landlocked. Another way to put it is that you have to cross two national boundaries before you can reach water connected to the oceans.

Double-landlocked countries

From the prefix iso meaning equal and khronos meaning time it literally means equal times. And whereas maps are usually put together with lines of equal distance you can either construct maps, or overlay maps as here, with lines of equal time. The overlay view gives you time contours rather than, say, altitude contours. Handy for checking things like commuting distance. I like how you find little islands where there is fast transport in and out like trains or planes.

You can explore time maps of London at mapumental.

Isochrones

A clever means of categorizing the size of rivers. It does this by looking at joins of tributaries. Each time two tributaries of the same order join together then the river goes up in order. So the start of a stream from a spring is the outermost branch — first order. When two first orders join together, the river is classified as second order and so on.

The largest river by Strahler stream order classification is the Amazon at twelfth order. This means that at least two order 11 rivers had to merge together before the river emptied into the sea.

Strahler stream order: Streams, rivers, the Amazon and how to organise them.

If you were to dig straight down from where you’re standing and pass straight through the centre of the Earth and keep on digging — you’d now be tunnelling up I guess — where you come out would be your antipode. Though most of them would first have you springing a leak at the bottom of the ocean, so be careful.

Antipodes

The union jack flag is made up of the Saltire of St Andrew for Scotland, and St Patrick for Ireland — a saltire is the heraldic name for the diagonal cross-look — together with the cross of St George for the Kingdom of England. As Wales was a principality at the time the flag was created, not a kingdom, it is not represented in the design.

Before Ireland’s emblem was added there was actually an earlier flag back in 1606— the original union flag — with just Scotland and England present.

The Union Jack

This is generally the source of much confusion. Even amongst those who live over here. If you look carefully at the description of the United Kingdom you’ll see it’s the United Kingdom of Great Britain and Northern Ireland. And the British Isles is the group of islands as a whole including all of Ireland too.

The source I liked best for this explaining this and much more, was Project Britain.

For much further confusion, think for a moment why there’s a UK passport, Great Britain in the Olympic games, and in football we compete as England, Wales, Scotland and N. Ireland separately. 🤔

Great Britain, the United Kingdom and the British Isles: what’s the difference?

The key to getting the whole thing the right way round in my mind is to remember that you need to cling tight (tite) to the ceiling. Once that’s established, you have a letter C in stactite that fits cling and ceiling. And stalagmites, with its cheeky G, naturally then is the other one which would grow on the ground. Sorted?

Stalactites, Stalagmites

And, let’s face it, most of us are more likely to encounter camels in the Middle East and Africa than trekking around the Gobi Desert. The wild bactrian camel is sadly on the critically endangered list.

And, there is this simpler way to remember the difference that a reader passed on to me: dromedary is one hump like a D on its side, and bactrian is two humps like a B on its side. Simples.

Camel identification: 1 hump dromedary, 2 humps bactrian

There’s stiff competition for the original and the most authentic British cream teas between Devon and Cornwall and the Southwest of England. However, you can tell each apart by the preference to go for jam on top, or under the cream. Cream on top = Cornwall. Jam on top = Devon. If you haven’t had one on location, I recommend you give it a try.

Cream tea: Cornwall vs Devon

Divergent (Mid-Atlantic ridge, The Rift Valley), Convergent (The Andes, The Himalayas) and Transform (San Andreas fault, Dead Sea Transform). There are some sub-varieties but these are the main ones. Which makes natural sense, so there’s no remembering to do, when you have two contacting plates - they can either be pushing together, pulling apart or rubbing past each other.

Incidentally, the idea that the giant continents move around all the time, enough to pull apart South America and Africa, and thrust up the Himalayas, obvious as it may seem now, was once not at all obvious. And if you stand on the ground in a big landscape, it’s kind of amazing to think of just what an amazing notion it was to propose. I read about it in Bill Bryson’s, A Short History of Nearly Everything for which I found a relevant excerpt online - The Earth Moves (pdf) - should you be interested in the characters that had the courage to seriously propose it.

Tectonic plate interaction boundaries

Northern hemisphere only. Follow the last two of the Big Dipper.

Use the Southern Cross to find South

From various sources I have learned that mandarins are the original, from China, and were rather fancy and therefore only suitable for high society, which included mandarins (bureaucrats).

Satsumas are a type of mandarin cultivated in the Japanese district of Satsuma.

Clementines are named after Father Clément Rodier who may have cultivated the variety himself.

And tangerines are so named as being from Tangiers in Morocco, one of the places where mandarins were first imported into Europe.

Origins of mandarins

Know your poles

California is a nice example both stitching up the Central Valley and Nevada. And in Washington State if you need a bit more sunshine, just try driving East.

Rain shadow

V-shaped, formed by a river and U-shaped after carving by a glacier. Plus variations thereof.

I believe you get canyons when the land is going up and the river is cutting down. A nice frame shift I saw in a nature program was to not think of the river as moving, but instead think of the river as stationary and the land (the continental plates) as moving around it. You’ll get a canyon when the land is pushing up and the river is cutting down. Much like pushing a block of cheese up through a cheese wire. OK the cheese is my analogy which is why it’s not as good.

Had a helpful comment from Austin correcting and explaining, “canyons are formed any time the weathering action of some force (i.e. a flowing river) greatly outpaces the surrounding environment’s eroding forces. For example, the grand canyon is so deep because it never rains in the desert, and wind doesn’t erode as quickly as water.”

Shapes of Valleys

My own little mnemonic to remember which direction the sun rises and which it sets. Surprisingly helpful for figuring out what direction you are facing — by where the sun is and the rough time of day. Also, for figuring out what time it’s likely to be in a different country — is it earlier in the morning for them or later in the day?

I’ve also always wondered if the East/West coast of America is fundamentally affected by the sun — the East coast gets the sea sunrises, great for early birds catching worms, and the West coast gets the sea sunsets, great for romantic evenings and all night parties. Who knows.

Sketchplanations tagged with geography