Ever since Malthus, there has been a concern about overpopulation. I thought it would be an interesting excercise to see how much space the human population actually takes up. For example, how many oil tankers would it take to carry around the volume of humanity if converted to liquid. Let’s say there are 6 billion people on the planet and the average mass per person is 100 kg (this is an overestimate). Hence, the upper bound on the mass of humanity is kg, or a billion metric tons. Given that we are mostly water, we can assume that this is about litres. Taking the cube root gives metres or a kilometre. Thus, if we liquefied the mass of all humans, it would fit in a cube whose sides are a kilometre long. The largest oil tankers can carry about five hundred thousand metric tons, so two thousand oil tankers could cart around all of humanity. To put that into perspective, according to Wikipedia, the current fleet of oil tankers moves around 2 billion metric tons a year, so half the world’s fleet could carry around the world’s population.

Now, how much area would we take up if we were to stand side by side. Let’s say 6 people can fit into a square metre of space, then we would all be able to fit into a billion square metres or 1000 square kilometres, about the size of Hong Kong (according to Wolfram Alpha), or we could all fit 4 to a square metre onto the island of Oahu in Hawaii. If we each wanted about 100 square metres of space, then we would take up about a million square kilometres or about twice the area of France. Wolfram Alpha also tells me that there is about square kilometres of arable land in the world. If we assume that a square kilometre can feed 1000 people (10 people per hectare), then that puts the capacity of the earth at 15 billion people.

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