There are a lot of hints about how the Zones work, spread through both books.
The overall picture seems to be this:
* What we think of as the "laws of physics" in any given Zone are actually a kind of VM layer, running on top of some (unknown) physics.
* The implementation is done through extraordinarily tiny machines. What we see as quarks, leptons etc (and the laws they follow) are in reality complex machines made of far smaller constituents.
* The implementation was probably done by some power-beyond-the-powers that lives in the center of the galaxy. It uses the Zones as a protective device - civilizations in the Slow Zone, the Beyond and the Transcend have only relatively limited abilities, unless they can break through the virtualization layer. (That, incidentally, is why the Blight is such a threat in AFUTD, and why the Zones change so much in response.)
If you read both books with this set of ideas in mind, a whole lot of otherwise puzzling scenes and one-off observations in the books make a great deal more sense. There's no reason to call the Zones unscientific.
Yeah, I agree except for the last parenthetical remark -- I don't recall any evidence for it in the text. Why would the powers-squared need us to invoke them for their own security? I suppose it was more about protecting the wildlife preserve, to the extent it makes any sense to us.
Given what we know in the realm of complexity theory, I see no justification for arbitrary thresholds in computing power based on space. Nanomachines can change matter but they can't change math, and the fact of the matter is we know a reasonable amount about what we can compute (and how long it takes) and what we can't. Either P = NP or it doesn't, for example; we don't know which, but we're pretty sure the answer doesn't change dependent on where you're standing. Leaving the galactic plane isn't going to enable me to solve the halting problem.
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.
If you push any science fiction hard enough, you will find something impossible in the real universe. If this is your criterion, stop reading science fiction. You need to cut them at least a little slack.
Further, I don't think you are correct it your interpretation. My interpretation was: What changes is not what is computable and what is not, but what bandwidth the components are capable of communication with each other at. Bandwidth limitation limits the power of distributed computational systems, and when you're limiting things at the atomic level that includes the brain. And it is implied that it was constructed this way.
Yes, that's probably impossible. It's probably also impossible that there is a computational threshold above which you can do FTL.
You might be right about the bandwidth thing - been a while since I've read it - but it doesn't change the fact that crypto algorithms suddenly breaking (for non-brute-force reasons - again, you're saying it's bandwidth and not computing power) or AI suddenly becoming possible once you're saturated in a different mixture of nanomachines doesn't make sense.
I cautiously disagree with this, by the way:
>If you push any science fiction hard enough, you will find something impossible in the real universe.
What in Accelerando is impossible? Even more generously, what in it violates our current understanding of physics?
Faster than light travel. We do not actually know how to build computronium and it probably won't have the exact parameters given in the novel; real computronium may be many orders of magnitude less powerful. We do not know that living on Saturn is feasible from any engineering point of view. We do not know that there is any level of technology that will enable us to build a living adult human-like body in a matter of days as described in the book, as the ape manifestation of Manx was created. We do not know the limits of nanotechnology. We do not know that there is a path from humanity to post-humanity that still includes entities that were at one point human. We do not know what the limits of intelligence are. Is "Accelerando" really possible, or is it merely hiding in the unknowable more cleverly than older science fiction authors?
Bear in mind I often cite Accelerando as an example of sci-fi that is mostly possible (excepting the faster-than-light bit), but it's more that we can't currently prove it impossible than that it is guaranteed possible. We can't eliminate it on scientific grounds but there will be engineering limits in the real universe, too, and there's no guarantee that anything like that is actually possible. And the probability that the social implications of everything Accelerando laid out are correct is effectively zero, no offense to Stross, as nobody can really work it out.
We further do not know that we are not actually living in a simulation in which the "magic" parameter is merely set to 0, but switchable tomorrow on the whim of the Great Simulator. If you do not like the Zones of Thought today, well then the Accelerando-computronium can simulate it adequately enough to meet the criteria of the story one way or another. Given that this actually happens in Accelerand itself, I'm not even stretching; consider A Fire Upon the Deep as Accelerando fan fiction if it makes you feel better.
I'm advocating being a little more careful what nits you pick not because I'm a hippy who just wants to bask in the glow of the work, but because I've gotten to be a master nitpicker over the years. Nothing's perfect.
Can't remember where I read it, but another way to look at the Zones was that it breaks the idea and occurance of a technological singularity from a temporal to a spatial dimension.
I thought the zones being unknowable was part of the story.
The Magellanic Cloud aliens created (or at least can manipulate) the zones to stop transcendental "things" like The Blight from destroying all sentience (and then becoming a problem for the Cloudies?).
The zones are two things: a few layers of "play nice, you guys" and a cheap way of avoiding singularity issues muddling up the plot.
