TallDave wrote:Theres a lot more to it than that. For instance, lets say you need to disassemble an asteroid with nanotech to get at the resources. Normal exponential growth of the replicators gives you a relatively short period of time but that number is false because it counts on all the replicators replicating constantly, when in fact the only replicators that will replicate will be those at or near the edge of the goo where they can get at disassembled raw resources with which to build offspring with. Thus instead of growing based on a cubic volume of replicators, it is growing merely based on a square exponent as the surface area expands.
That's an interesting point.
When I said time was the last scarce commodity, I was originally thinking of big projects like terraforming Mars and Venus, or building Dyson rings/spheres. The amount of overall energy required must increase very quickly as you reduce the desired time-to-completion, and even if your energy source is more or less inexhaustible you still can't push the time required below certain minimum values.
Right. Theres further limits. See, as we advance into the singularity, the demand for computational resources will continue to grow exponentially (hence why nanites would be needed to disassemble asteroids, to build orbiting computronium infrastructure). Eventually, the posthuman society will seek to disassemble the terrestrial planets. Mercury first, since its got the closest access to solar power, then Mars cause its a shallower gravity well than Venus, then Venus, then Earth. Google "Matrioskha Brain". Its a solar system where the plane of the ecliptic is a series of rings of computronium which are powered by waste photons emitted by the next ring inward, and which dumps waste heat to the next ring outward, with the rings all nested like a Matrioskha doll.
Now, disassembling the planets is more than getting eaten up by grey goo. At a certain depth, the magma will be too hot for nanites to deal with, even when made of diamond. The heat will swamp out the optical computers of the nanites with noise.
Mass disassembled on planetary surfaces needs to be moved into orbit, so a lot of energy needs to go into accellerating that mass to orbital and escape velocities to get into solar orbit. As the mass of the planet is reduced, this energy requirement drops, obviously, but it still delays the disassembly significantly, as does the need to cool the mantle and core of the planets. Geothermal energy will be utilized to power space elevators to move that mass into space.
Eventually the posthuman society will seek to disassemble the jovian planets. Getting all that mass out of those extremely deep gravity wells will take a LOT of energy and a LOT of time. over 200 years alone for Jupiter at maximum speed.
The singularity is not going to finish quickly.