Let's lay out our playing pieces first.
1. The world's population is about 6.796 billion.
2. The area of all the world's land is about 57.5 million square miles.
3. The worldwide population density is about 118 people / square mile.
4. The population density of New York City is about 27,440 people / square mile.
5. The population density of Manhattan is much higher: 71,201 people / square mile.
Let's ask ourselves some questions:
Q: Name a country with a population density similar to that of the entire world.
A: Afghanistan is a good match: 118.6 people / square mile.
Q: Take all the people in New York City (8.363M) and spread them out at the same average density as the entire planet (118 ppl/sq.mi). How much space would they take up?
A: About 71,000 sq.mi. - an area about the size of North Dakota, Missouri, or the country of Cambodia, Syria, or Uruguay.
Q: Same question, only now you're taking just the people in Manhattan (1.635M) and spreading them out at the earth's average population density.
A: The population of Manhattan would take up about 13,900 sq.mi.- about the size of Taiwan or Moldova. No states are in the right range of size. Twice the size of Hawaii? Meh.
Q: What if we took those 1.635M people and spread them all over the planet? What would the average population density of Earth be?
A: 0.0284 ppl/sq.mi. Greenland, by comparison, has a population density of 0.067 ppl/sq.mi. Each person on earth would have 35 square miles all to themselves- approximately the size of the island of Anguilla or, ironically, an area about the size of Manhattan (33.77 sq.mi.) all to themselves.
Q: If you were to take the entire population of the world and pack it into a single large city with a population density similar to that of New York City (the Five Burroughs), how big would it be?
A: About 248,000 sq.mi. - about the size of Texas. And no country is the size of Texas.
Q: Same question, only now we're using the population density of Manhattan as a model. How big would our "World-Sized Manhattan" have to be?
A: 95,700 sq.mi. A little bigger than Indiana or the United Kingdom.
Q: Imagine that the entire planet is covered by an endless Manhattan-like cityscape. How many people would live in it?
A: Just over 4 trillion people.
Let's take those 4 trillion people and give them the following: 1/4th acre of farmland (in a vertical farm)- about 10k square feet. 1000 square feet of personal living space. A 2000 square foot share of open space. A 1000 square foot share of shared infrastructure space. 1000 square feet of structural space. Total area: 15,000 square feet. Let's assume a ten foot ceiling for all spaces. Total volume: 150,000 cubic feet. Of course, give that person a super-advanced MMO account and they could feel like they had a lot more space.
Q: How big would a spherical spaceship need to be to house the entire population of Planet "Super Manhattan" (4 trillion)?
A: 1046,448 feet or almost exactly 198 miles in diameter. That's a very small moon or average-sized asteroid. For comparison, Saturn's moon Mimas is about 25% larger. Ceres, the largest asteroid (now dwarf planet), is about 260% larger.
Q: What if you were to just put the present population of the planet (6.976B) in such a spherical space spaceship, only this time let's give them four times more space: 600,000 cubic feet per person.
A: The sphere would be almost exactly 200,000 feet in diameter or just under 38 miles in diameter.
Q: Don't be so generous. 150,000 cubic feet is excessive. Using aeroponics, virtual reality, and creative design, you could make a person quite comfortable in less than 50,000 cubic feet. How big would your sphere be then?
A: About 86,580 feet or 16.4 miles in diameter.
Yeah. That's a sphere, less than 17 miles in diameter, that comfortably houses the entire present population of the planet.
Q: What would it cost to build such a sphere?
A: About $1 in the year 2100. Why? Because if you can build in space and can use material from asteroids and get your energy from the sun, the only cost is labor. But if you can build a robot that can build another robot that can also build another robot- using free material and free energy- the only cost is the original robot, the original program, the cost of delivering it to a place with abundant free resources, and *time.* How long? Well, if you started at the center and built outward at a rate of one inch an hour, it would take you 115 years. So you'd have to build it faster than that. If you could build it at an average rate of an inch a minute, it would take just under two years. How much would your first robot cost? It might cost only 50 cents and weigh only a few grams- much of which would be a solar array that could double as a solar sail. If you bought it in space, you're already most of the way there. What's the other fifty cents for? I don't know. Maybe you want to buy two just in case one gets lost.
Q: What would it cost to build a bigger one?
A: Same amount. It would just take longer.
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