If you change the underlying physics, computational power can change quite a bit. The best-known example of this is that quantum computers are widely believed to be more powerful than classical computers. An even more striking example, though less well known, is that certain non-linear variants of quantum mechanics allow NP-complete problems to be solved in polynomial time. This result was written up here: http://arxiv.org/abs/quant-ph/9801041
We could imagine, then, that what's going on is that the Universe really runs according to the laws of one of these non-linear variants of quantum mechanics, but the power-beyond-the-powers has arranged so that at the length scales that can be probed by the races in Vinge's story things look effectively like standard (linear) QM.
The thing that bothers me a bit about the Zones: how is it that humans think? We are, after all, just machines. So if AI can't be built, then how is human consciousness possible?
I'd be interested to know what (if any) response Vinge has to this. A possible-but-not-very-satisfactory response is that life on Earth is really an artifact from another Zone, and one that goes beyond ordinary Slow Zone capabilities. What prevents us from building AI is that we can't reproduce those capabilities. Seems a bit of a stretch.
I'm no expert on the field, but I believe the optimality of Grover's algorithm strongly suggests that the upper bound on the speedup from quantum computing is quadratic (and I apologize if I'm fudging something here). I have no idea about non-linear QM - really over my head - so I suppose I'll have to concede that point.
I agree with you that having conscious carbon but not conscious silicon is arbitrary and silly. Once we understand the brain better we'll surely be able to build one. Again, not something that should depend on location, nanomachines or not.
The optimality of Grover's algorithm doesn't in any way suggest that the upper bound on speedup is quadratic. That result only applies to one very particular class of problems: unstructured (oracle) search problems. There are other oracle problems for which the speedup is known to be exponential. For non-oracle problems the situation isn't yet clear, although many people believe the speedup will be exponential. That will be true if factoring isn't in BPP, for instance.
We could imagine, then, that what's going on is that the Universe really runs according to the laws of one of these non-linear variants of quantum mechanics, but the power-beyond-the-powers has arranged so that at the length scales that can be probed by the races in Vinge's story things look effectively like standard (linear) QM.
The thing that bothers me a bit about the Zones: how is it that humans think? We are, after all, just machines. So if AI can't be built, then how is human consciousness possible?
I'd be interested to know what (if any) response Vinge has to this. A possible-but-not-very-satisfactory response is that life on Earth is really an artifact from another Zone, and one that goes beyond ordinary Slow Zone capabilities. What prevents us from building AI is that we can't reproduce those capabilities. Seems a bit of a stretch.