Math CentralQuandaries & Queries


Question from Naresh, a student:

in a book, i got to read this :

Is it possible to pack the entire population of earth and everything that was created by
humankind in a cube whose edges are 2 miles long ?

Is it possible? Thanks.

That's a fascinating question Naresh.

Let's start by estimating the volume of human bodies alive today.

People weights vary widely, particularly if you include children and adults together. Let's say the average weight of a person alive today is 110 lbs.

How much is that in volume? The human body floats most of the time, but is pretty close to the density of water, so for an estimate, let's think of the human body as having a density of water (we are mostly made of water anyway). That's 62.4 lbs per cubic foot. Since 110/62.4 = 1.76 or so, that means the average person's body occupies 1.76 cubic feet of volume.

What is the entire population of earth? According to Wikipedia, it is currently a little less than 7 billion. So all the living human bodies on earth occupy 7 billion x 1.76 = 12.3 billion cubic feet of space.

How does that compare to a cube 2 miles on an edge? Such a cube is 2 x 2 x 2 cubic miles = 8 cubic miles. The humans are 12.3 billion cubic feet. To convert cubic feet into cubic miles, we divide 12.3 billion by
5280 three times (one time each for length, width and height). That makes 0.08 cubic miles.

All the humans alive on earth and we've only filled 1 per cent of the space in the box! Perhaps our estimates of people's weights is off, but not by a factor of 100, certainly! In fact, a recent estimate of the number of people that have ever lived on earth (all the people from the last several tens of thousands of years) is about 106 billion. That would bring us up to 1.27 cubic miles, or 16% of the available space.

Now though things start to become uncertain, because what does the phrase "everything that was created by humankind" include? It would probably include things like buildings, ocean liners, clothing, oil rigs, pyramids, and such, although you could also say that we are just assembling things in the environment into other forms. But what else that occupies volume? Would this include things like human waste, solid
and liquid? What about perspiration? I presume breath would not be included, but do our bodies "create" waste or are we just extracting nutrients from food and leaving the remainder, not really creating it?

I don't know the answers to these questions, so I'll leave it to you to
puzzle over them.

Stephen La Rocque.

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