[codeulike]

Its worth thinking about the idea that we are actually made of highly sophisticated self-replicating nanotech machines, and although they've been pretty successful for the last few billion years, they're still nowhere near good enough to achieve exponential growth that consumes all matter.

Maybe someone somewhere has already explored the theory that nanotech that could re-shape all matter around it is probably impossible due to the energy challenges inherent in re-shaping arbitrary atoms.

[ragebol]

Hasn't the world population of humans been increasing exponentially? And consuming, well, not all matter but still quite a lot? Once we have the technology (and will) to mine asteroids that'll even get worse.

[ben_w]

Roughly approximating exponential, but slowing down. And even then with a generational period of… well, of one generation.

Bacteria in the right conditions can do that in 30 minutes.

A hypothetical 1kg clanking replicator that eats moon rock and sunlight and replicates in 1 month would dismantle the moon in just over 6 years. Make it grey goo with a unit size of 1mg while keeping the replication time of a month and it takes 8 years to fully disassemble the moon.

[philipkglass]

Can you avoid running into power limits that would greatly slow the initial exponential progress?

Each square meter of moon receives a time-averaged sunlight input of about 340 watts [1]. The surface area of the moon is 3.79 * 10^13 m^2 [2]. The most efficient silicon solar cell is 27.6% efficient [3]. The gravitational binding energy of the moon is 1.2 * 10^29 joules [4].

Putting all those factors together, gravitational disassembly of the moon will take

(1.2 * 10^29) / (0.276 * 3.79 * 10^13) = 1.15 * 10^16 seconds, or 364 million years.

It will take longer if you model the moon as a shrinking core where all sunlight collection and replication takes place. It can go faster if the replicated units become part of a Dyson swarm beaming power down for disassembling what remains of the moon.

Gravitational disassembly of the moon in 8 years requires an average power of 476 exawatts (10^18 watts). It also seems like you would run into thermal limits trying to turn the moon into more clanking replicators, even if you did have exawatt scale beamed power from your Dyson swarm; you can't beam so much power down that the replicators melt from waste heat before they can finish building.

[1] https://en.wikipedia.org/wiki/Earth%27s_energy_budget#Incomi... -- Earth and its moon are roughly the same distance from the sun, so Earth's top-of-atmosphere solar input is a good approximation to the moon's surface solar input.

[2] https://en.wikipedia.org/wiki/Moon

[3] https://www.nrel.gov/pv/insights/assets/pdfs/cell-pv-eff-cry...

[4] https://www.universetoday.com/121421/how-could-we-destroy-th...

[philipkglass]

I made a critical mistake in my initial "364 million years" estimate -- I forgot to include the wattage per square meter.

Corrected:

(1.2 * 10^29) / (340 * 0.276 * 3.79 * 10^13) = 3.4 * 10^13 seconds, or 1.07 million years.

[ben_w]

> Can you avoid running into power limits that would greatly slow the initial exponential progress?

I doubt it, for all the reasons you give, though I agree the first choice is to do this as part of building a Dyson swarm.

I don’t even know if the interior of the moon is cool enough right now even without the extra heat from manufacturing; but then, I wouldn’t expect to know — I only have a GCSE grade B in chemistry, so I can be sure whoever does invent a von Neumann mechanism, it won’t be me.

[goatlover]

It's projected to level out sometime around mid century and then start declining. And that's because birth rates decrease to a below replacement level everywhere women are granted the freedom to control their reproduction, which is a global trend.

[onceUponADime]

Physics doesent take a break because you are tiny.. replicator weight would crush other replicators.

[Symmetry]

True but both genetic and mimetic evolution are pushing us to going back to having lots of children in the modern environment. Agreeableness in particular of the Big Five correlates with having kids and there are a lot of religion out there telling their followers not to use birth control. It might be that our current non-Malthusian era of history is going to be an aberration.