Sensible units -- Per capita isn't enough (incomplete)

This is an incomplete snippet. If I complete it, I’ll add a link to the completed snippet here. Update: Here’s the finished version.

The world population is about 7.9 billion people.
The global GDP is about 90 trillion USD.
Global oil production is about 100 million barrels per day.
The US federal budget for the 2020 fiscal year was set at $4.79 trillion USD.

In this snippet we’ll take these statements, complete with their large and unwieldy numbers, and turn them into something a bit more tangible. A common (and very good strategy) for making large numbers tangible is to look at their per capita interpretation. Take the number, divide by the relevant population, and you start to get a better picture of what the number means. As we’ll see with our first example, this strategy isn’t always enough.

How do we make 7.7 billion people more tangible? Dividing by the world population here would be silly. The population is 1 person per capita. That’s not a useful statistic.

Instead, we can use space and time to make it more tangible.

Population in Space

Here are some numbers we may find useful (too big to make immediate sense of for now, but we can deal with that momentarily): The surface area of Earth is 196.9 million mi². Of that, 57.51 million mi² is land area, and only about 24.64 million mi² of that is habitable.

This gives us a global population density of 312 people per habitable square mile. Still not the most intuitive for two reasons: 1) a square mile is a pretty large area (Manhattan is 23 mi²; San Francisco is 47 mi²) and imagining 312 people scattered across it can be challenging, 2) the population density varies wildly across different regions (population density in Manhattan is 69,468 people per square mile; in San Francisco its 17,246 people per square mile).

We can deal with reason (1) pretty simply. 312 people per habitable square mile is 89353 square feet per person. The Manhattan population density equals 401 square feet per person. The San Francisco population density equals 1616 square feet per person.

It’s tempting to compare these “square feet per person” figures to typical apartment sizes in these regions. “Four hundred square feet per person,” we might be tempted to remark, “no wonder apartments in the city are so small!”

Before we do that though, we have to remember two things: First, Manhattan’s 23 mi² isn’t all apartment space; it also includes public infrastructure like roads and parks, and commercial spaces like stores and offices. Only a fraction of the space is available for living. Second, redeemingly, Manhattan is built up considerably. For every 10-story building built on 400 square feet of habitable land, we get nearly 4000 square feet of potential living space, not a mere 400.

We can turn to New York’s 2014 ten-year housing plan to add more color to these numbers. There were 3.4 million units across New York City in 2014.

A bit of Googling suggests the average apartment size in New York City is 700 square feet. Of course this is going to vary considerably by location and apartment type, and I don’t know how much we can trust this estimate. Still, let’s work with the number. Using the overall NYC population density of 27,000 people per square mile (1032 square feet per person)

Population in Time

TODO

Recapping the original statements

Here we take each of the original statements the way you might find it in a fact book, and we restate them in more tangible terms.

Original:

The world population is about 7.7 billion people.

Restated:

There is X square feet of habitable land per person globally (Y in a typical city, Z in a typical suburb)