Robert J. Bradbury wrote:
> No, the theory of gravity imposes a limit on the scale of computing
<and assorted related comments>
Yes, the density of a computational structure is significantly limited by the need to avoid forming an event horizon. Yes, long communication delays limit the scale on which you can mobilize resources to attack a single closely-coupled problem. Neither of these facts places much of a limit on the useful size of a computing system.
Why not? Well, for starters, most really hard problems do not require close synchronization between computing nodes. Most of the ideas I've heard for how SIs might pass the time would be quite amenable to being spread across a large network of computing nodes. The only real constraint is that the time to pass messages from one side of the node to the other must be a reasonably small fraction of the time needed to solve the problem.
Also, an SI civilization can reasonably be expected to think about more than one thing at a time. Since we have already discovered several fields that seem to have the potential for developing to an arbitrarily large degree of complexity (namely mathematics, social interaction, arts & literature, and military and economic competition), there is reason to believe that SIs might actually have lots and lots of different things to think about. The space occupied by the entire civilization will therefore be limited by the details of the socioeconomic tradeoff between deeper computing resources and social coherence.
As for your arguments from energy conservation, well, I really don't see that they are relevant except in the closed, doomed universe scenario (in which case SI conservation efforts should be much more all-encompassing, as I noted earlier). If you have figured out how to salvage, leave, or otherwise outlive the universe, or if you are desperately looking for said solution, what you care about is maximizing throughput.
That means you don't use stars for energy. What you want is a small, dense energy source - say, a small black hole that you can drop matter into. Surround that with a thick shell of high-temperature computronium, along with all the hardware needed to feed matter into the black hole, collect the radiated energy, and cool the whole system (obviously, the scale of the whole structure will be determined by the maximum energy density your energy collection system can handle). Ideally the black hole should be a small fraction of the structure's mass, so you get to devote lots of matter to doing computations. Lastly, cover the surface of the device with the most high-density communication system you can build.
Now you have a single computing node. Build a few million more of them, and with a bit of careful calculation you can arrange them in a constellation a few tens of light-years across without any danger of gravitational collapse. Add in a few hundred thousand solar masses of very large spacecraft (to collect fuel, build new black holes of the optimum mass, and carry off old ones that are too big to be useful), and you've got a credible first approximation of an SI civilization.
Depending on what assumptions you make about the limits of technology I could see an optimal computing node being anywhere from a few Earth masses to several solar masses. The spacing between nodes would be chosen to maximize the overall density of the constellation without risking gravitational collapse - and we don't really care how much energy it takes to maintain the ideal separation, as long as it doesn't cause enough of a cooling problem to impair the throughput of the nodes.
Billy Brown, MCSE+I