Suppose we want 16 earth-surfaces’ worth of human living space by the year 02050, in orbit around the sun, using an exponentially growing colony of 3-D printers that starts growing in 02029.
How much material is this? The classic approach is rotating space stations in order to provide artificial gravity of one gee. Suppose we don’t have a stronger material for this than music wire, whose free breaking length is 35 km (2700 MPa / (7.9 g/cc) / gravity). (We can hope that carborundum fiber (110 km), basalt fiber (183 km), monocrystalline iron whiskers (183 km), UHMWPE (378 km), carbon fiber (399 km), nanotube rope (4700 km), etc., are options, but maybe they won’t work out.) We can't use all the structure’s weight in tensile supports against its own centrifugal force, since we also want lakes and soil and stuff; suppose we use an “overhead factor” of 3.
(Ugh, I’m tangling up in mental knots trying to figure this out.)
So, uh, suppose our habitat soil and lakes etc. is about 10 meters deep, so we need about 20 tonnes of soil per square meter, plus another similar amount of our bargain-basement Victorian-era scrith, let’s say 64 tonnes per square meter in total. 149 million km², the Earth’s land surface, is then 9.5 × 10¹⁸ kg (9.5 zettagrams). 16 times that is 153 zettagrams, round it up to 200 zettagrams (2 × 10²⁰ kg), about 0.3% of the mass of the Moon, all of the mass of asteroid Pallas, or 7% of the mass of the main asteroid belt.
If the initial 3-D printer weighs 100 g in 02029, that’s a factor of 2 × 10²¹ growth in 21 years, which is fairly slow by the standards of bacteria and fungi, about 0.64% per day, doubling every 108 days. A human growing from 4 kg to 40 kg in 10 years is on average much slower, of course, but during their first 3 months after birth they grow perhaps from 3.5 kg to 6.5 kg, nearly the same speed.
At this speed, we have the following growth curve:
| 02029 | 02030 | 02031 | 02032 | 02033 | 02034 | 02035 | 02036 | 02037 | 02038 | 02039 |
|---|---|---|---|---|---|---|---|---|---|---|
| 100 g | 1 kg | 11 kg | 108 kg | 1.1 t | 11 t | 120 t | 1.2 Gg | 12 Gg | 128 Gg | 1.3 Tg |
| Gerbil | Rabbit | Pug | Dolphin | Narwhal | Three hippopotami | Blue whale | General Sherman | 2×Pando | La Tour CN | Golden Gate Bridge |
| 02040 | 02041 | 02042 | 02043 | 02044 | 02045 | 02046 | 02047 | 02048 | 02049 | 02050 |
| 13 Tg | 138 Tg | 1.4 Pg | 15 Pg | 150 Pg | 1.6 Eg | 16 Eg | 160 Eg | 1.7 Zg | 17 Zg | 180 Zg |
| 2×Great Pyramid | the humans | the fish | ??? | Lake Tahoe | Lake Ontario | Lake Tanganyika | Gulf of California | Gulf of Mexico | Arctic Ocean, or asteroid Euphrosyne | Indian Ocean, or asteroid Pallas |
As Machiavelli points out, any innovation is likely to provoke opposition from entrenched interests. Experience in 02020 has shown that existing human institutions are not equipped to stop or respond to exponential phenomena with doubling times of around a week, so this is probably a better benchmark to shoot for, although of course in this case the phenomenon is a liberatory phenomenon of human empowerment rather than an epidemic of a virus.
Having the seed on Earth is not equivalent to having it in orbit around the Sun; launching things into orbit is expensive and tightly surveilled. There are two likely ways to cross this bridge.
The first is to get a single spore off Earth as early as possible and grow it among the asteroids, which has the disadvantage that it requires access to space launch very early on, before a significant quantity of printers have been built. Worse, it’s not just space launch but actually escape velocity, which means launching not just a printer but a thruster that can provide the other half of the Δv. this would benefit from having as small a printer as possible, especially absent buy-in from the entrenched interests mentioned above; the Space Surveillance Network publicly catalogs 17480 objects mostly 10cm (1ℓ) or larger, so we’d have to assume objects down to 3cm are usually detectable even today, especially if they’re in LEO doing things like emitting plumes of plasma. So the target design size would probably have to be about 10g or less: the future of a galaxy contained in the mass of a coin.
The other possibility is to grow the 3-D printer ecosystem here on Earth until it can print abundant space launch resources, perhaps in 02040 or thereabouts. This avoids the risk of provoking opposition at an earlier, more fragile stage of the project, but it means that inevitably it will have to face opposition before making the leap off Earth, and consequently is at serious risk of being strangled in the cradle. It also limits the material and energy resources that will be available to the project during that time to what is available on Earth. However, everything done on Earth is enormously easier in some ways — to fix when it breaks, especially — and there are many resources on Earth that are hard to find elsewhere, such as microprocessors.