Mark Gritter (markgritter) wrote,
Mark Gritter

Rapture Denied

I finished Rapture of the Nerds today, about which Marissa has more to say in her review. Their future is one in which the inner planets (except Earth, although the fate of Luna was not mentioned) have been disassembled to build orbiting computational substrates, which form a cloud around the sun in order to harvest its energy. Uploaded humans live at speeds greater than real-time.

I felt like the issue of lightspeed delay was mentioned but not really handled. Let's crunch some numbers. Or at least as many numbers as don't require me to perform calculus.

Let's assume the asteroid belt is included but no outer planets (which are mentioned as future work.) It doesn't make sense to disassemble Venus until you've scooped up all the small planetesimals first! So we're talking a radius of about R = 3.27 AU = 4.9*1011 meters. Although the past-rapture nerds could limit themselves to in-plane orbits, this is wasteful of sunlight so we should assume a sphere.

The speed of light is 3*108 m/s, so the maximum volume with which you can hold a conversation at 10ms round-trip latency has (5ms * c) radius = a mere 1500km. Now, 10ms latency is way less than humans need. But if you're living at 100x speedup then that's a perceptual second.

Suppose you want "common knowledge" (say, a fully-functional simulation of Earth) to be accessible at no more than a 1-second perceptual delay. How many times would a particular record need to be replicated within the cloud? R^3 / (1500km)^3 gives us about 3.5*1025 copies. This is the first hint that the computational infrastructure doesn't scale well.

(We can improve matters by sticking to the surface of a sphere rather than distributing nodes throughout its volume, but that makes the average case delay for uncommon information worse!)

Of course, if there are only say 1012 (a trillion) posthuman entities floating around, they can just take the data with them wherever they happen to be. But what about *uncommon* knowledge, like the consciousness of a particular individual?

Let's imagine the best possible case in which you're tucked neatly within the orbit of Mercury. By sending a signal a distance of D you can reach D^3/R^3 of the total storage capacity (at latency 2D/c). If data is uniformly distributed, then the probability of finding a unique datum within a given time limit is as follows:

ProbabilitySubjective seconds at 100x speedup
1%70,000 seconds (~19 hours)
2%24.6 hours
5%33 hours
10%42 hours
20%53 hours
50%72 hours

In other words, the Singularity is not like a universal jukebox so much as a universal you can find anything you want, but it'll probably take two days to get it. It seems a better bet for a Solar System-spanning electronic culture to run at slower than realtime.

The Galactic Alliance's death threat is stupid. Instead of threatening annihilation, they need only virtualize the human's operating system. If the (post-)humans are well behaved, then they get access to galactic technologies. If the monkeys can't play nice, they get shunted into a sandbox to rampage to their hearts' content, at progressively slower rates compared with realtime to conserve resources. The best part is, the newly virtualized entities won't be able to tell the difference! Sufficiently advanced civilizations ought to have solved mechanism design better than to resort to such crude penalties.
Tags: books, geek, mathematics, science fiction
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