kilobug comments on Server Sky: lots of very thin computer satellites - Less Wrong
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There is something that feels "wrong" for me in this proposal, it's that it doesn't account for Moore's law. Sending objects to space is expensive (even with a launch loop or a space elevator, it would still be expensive, even if much less than with traditional rockets), so you can't renew the "server sky" every few years. But with Moore's law, computers a few years ahead are much more powerful than the computers of now. Launch "server sky" now, and with Moore's law, in 10 years, we can make servers 32 times faster... but we can't change the ones in orbit.
Other problem is the ping : with a distance of 12789 km, you get at best a ping 85ms, assuming no other delay and that the nearest satellite can answer you directly, which will rule out many possible usages.
In a recent reply to the comments on Brin's post, Keith Lofstrom mentions using obsolete sats as ballast for much thinner sats that would be added to the arrays as the manufacturing process improves.
He acknowledges that ping times are going to be limited, and lower than you can theoretically get with a fat pipe, but it is still much better than you get with GEO.
For lots of processor-heavy things (mining bitcoin, rendering animations, what have you) it isn't especially crucial. High frequency stock trading is probably out.
The key thing about those isn't that they're processor heavy; it's that they're very parallelizable, and have minimal data dependencies between subtasks. For an example of something that isn't like this, calculating scrypt hashes is very processor-heavy, but is provably Hard to parallelize.
I suspect that most interesting calculations will bottleneck on communication latency.