If we could hook everyone up to virtual reality, and give them 8 cubic

feet of space (1 foot by 1 foot base times up to 8 feet height), we

could fit a world population of 7 billion into a cube with sides of

about 3826 feet (less than a mile), much smaller than most people

would think.

Even if the world population grows at 3% (it’s actually closer to 1.1%

now), the cube’s side would increase by only about 38 feet per year,

at least for now. This rate would increase by 4.5 inches per year

every year.

By the year 5497, the cube’s side’s velocity, excluding relativistic

effects would be the speed of light. Of course, it’s impossible to

reach the speed of light, so this just shows relativistic effects

would become significant by 5497.

By the year 6132, the cube’s side would be accelerating at an uncomfy

5g (again neglecting relativistic effects).

Of course, building something 3826 feet high would be difficult

(world’s tallest building is currently only 2723 feet), so what if we

gave everyone 1 sq ft, but didn’t try stacking them on top of each

other?

For now, we’d need a square that’s 16 miles on each side (about half

the size of the city of Hong Kong), growing at a rate of about 0.25

miles per year, accelerating at about 19 feet per year per year.

Of course, by 4495, the square’s side would be accelerating at an

uncomfy 5g, and, before that, in 4099, the square’s side would be the

speed of light (again ignoring relativistic effects).

Supporting calculations: https://github.com/barrycarter/bcapps/blob/master/sphere-of-humanity.m

I was originally going to describe a “sphere of humanity”, thus the

title of this blog post. However, constructing a large sphere seems

even harder than constructing a large cube, so I changed it to

cube. But, since “sphere of humanity” sounds way cooler, I left the

blog title as is.