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

The tragedy of the commons is the all too common outcome of individuals making use of a shared resource and one of the true challenges of our times. The original scenario referred to commons land that soon becomes overgrazed as each individual tries to maximise their value from the share resource. The tragedy is that the overgrazed land is then ruined for all.

We see the effect, perhaps most perniciously, with invisible or hidden shared resources such as taking water from underground aquifers for irrigation, or overfishing of fish stocks in the sea. The same effect is at work with problems such as littering, or washing plastics into the sea, or polluting the atmosphere — while it’s easier for any individual to take another fish, leave their litter on the ground, let pollution run into a river or the sea, or not worry about air pollution, the tragedy is it can have the effect of ruining them for all of us.

When shared resources are moderated or governed fish stocks can be managed to recover, water supplies to replenish or pollution to be naturally treated.

For more, check out this 5 min video on the tragedy of the commons by TED-Ed.

The tragedy of the commons

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.

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 1965 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 1965.

The world has changed a lot since then, and that model of dividing the world into two buckets no longer holds true with the data. Most people in the world are somewhere in the middle.

And more helpful than dismantling my worldview was providing a new model to replace it: a model with 4 income levels instead of 2 and the number of billions of people living at 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

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, and 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.

Seasons

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 range around a star that’s not too hot and not too cold to support life. If you were looking for planets that may support life as we know it in distant solar systems it seems a good idea to look for planets in the Goldilocks Zone.

The Goldilocks Zone

Which is kind of amazing. The magnetic field is produced by some remarkable result of the convection of molten hot iron alloys in the core of the Earth. Kind of hard to really get your head round if you’re sitting calmly at your desk or walking on a nice stable surface. Periodically, the poles switch round it seems but at the moment the magnetic South pole is actually near the point we’d normally call the geographical North pole. They’re pretty close, but the geographic axis doesn’t exactly coincide along the geographic axis of rotation of Earth. And the lines of force go from magnetic North to magnetic South so your compass needle is actually pointing towards magnetic South. Remember iron filings and bar magnets from physics class?

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