It's not that the speed of light varies, it's that the "amount of computation" you can do varies. As you approach the center of the galaxy even the relatively efficient human brain starts to break down. The speed of light connection is that FTL requires so much computation that it breaks at a certain point relatively far out from the center. Other technologies have similar issues.
However, if you read carefully, and consider some of the consequences, it becomes clear that this is not a natural rule of the universe, but something technological, created by presumably one of the first civilizations to become highly technological as a defense against what would otherwise be a fairly vicious universe with constant high-tech civilizations fighting each other with frightfully powerful weapons, and perhaps a hint of compassion towards the not-yet-high-tech civilizations. That's why it can be manipulated with certain keys, in ways that would not be possible (lots of FTL signalling) if the Zones were truly a fundamental rule of the universe. (Notice also how the super-high-tech civilizations don't understand how the Zones work or why they exist, which if there were purely natural seems unlikely.) The Powers tend to last 10 years probably because that's how long it takes to either be accepted by the highly advanced civilization(s) that live in the galactic cores, or how long it takes to work out how to move there despite the Zones being in the way, or both. This creates an entrance gate against things like the main threat of the novel getting into your high-tech civ.
I don't deny I'm extrapolating a bit, but there's a lot of hints, especially if you add A Deepness in the Sky to the mix. Pham was probably sent from this central civ to fight A Fire Upon the Deep's main threat, if you read where he came from. The entire planet of A Deepness in the Sky is clearly from a super-high tech civ far beyond what Earth's depth could support, but it's from closer to the galaxy's core, not farther, which is why Pham went in to the galaxy's core after that story rather than out looking for more intelligent life. He in fact found it, or it found him, if you prefer.
Once you see there's a probably-even-beyond-Transcend civilization living under the Zones of Thought it mostly comes together.
I agree with a lot of this -- although I hadn't put the story about the galactic core together in the same way. A lot of this isn't made clear though. Can you point to some of the evidence you used to arrive at the conclusion that the high-tech civ is centered in the core, or that they're gating civilizations entering it? I think you might have picked up on some things I missed.
One correction: the Zones impact BOTH the speed of computation AND the laws of physics (whether FTL travel and communication are physically possible). They also make pretty explicit in Fire Upon the Deep that mechanical failure rates of certain complex systems (especially automation) increase rapidly as you approach the Slow Zone. And then within the Slow Zone they increase again as you approach the Unthinking Depths.
It is made explicit -- as you note -- that the Zones of thought are controlled somehow by the Countermeasure (or some Control System it speaks to). It is also clear that this system do not like the Blight and actively opposes it.
One other interpretation that struck me is that the Control System may have put in place the Zones of Thought simply because stars become so dense as one approaches the Galactic Core. Forcing the Transcend to the Galactic edges limits the rate at which any change can spread and allows for civilizations (and the System itself) to respond to threats such as the Blight.
"Can you point to some of the evidence you used to arrive at the conclusion that the high-tech civ is centered in the core, or that they're gating civilizations entering it?"
A high-tech civilization in the core is IIRC spelled out in A Deepness in the Sky because the planet there comes from the core. On its own that means nothing, but combined with A Fire upon the Deep it means there's more down there than the Upper Beyond realizes.
Gating civilizations entering it is a bit of my own interpolation. One alternative is that powers simply die out after 10 years because there is some reason they need to advance to the next level, but they're locked out by the Zones.
"BOTH the speed of computation AND the laws of physics (whether FTL travel and communication are physically possible)"
My read is that that is cause and effect, though, not two effects. The amount of computation you are allowed is limited; super high tech becomes impossible, then FTL, then our tech, then even any system that performs simple and meaningful mechanical computations. Even a car engine can be viewed as performing computations to stay running.
This is a particularly sci-fi element. I don't think it's immediately obvious how to separate the universe into "meaningful" computation and the sort of computation a stationary rock is "performing" as its atoms jiggle around, such that one can distinguish at the level of the laws of physics themselves between a rock and a car engine or other simple mechanical device. Then again, I'm not a superintelligent civilization with nearly unbounded resources and deeper access to the laws of physics than I have. (Arguably, under the circumstances, it could simply be an enormous computation of its own, in which they aren't doing it via clever rewrites of the universe, but basically by executive fiat, or, to put it another way, the standard may literally be "I know it when I see it" for some sufficiently intelligent "judge", rather than any sort of physical law.)
> This is a particularly sci-fi element. I don't think it's immediately obvious how to separate the universe into "meaningful" computation and the sort of computation a stationary rock is "performing" as its atoms jiggle around, such that one can distinguish at the level of the laws of physics themselves between a rock and a car engine or other simple mechanical device.
It sounds like what you’re asking boils down to “is entropy a real thing, or is it subjective / relative to our purposes and measurements.” And that the Zones essentially work by enforcing an “entropy quota” on things according to where they are in the galaxy- things in the Slow Zones must be very high-entropy (and somehow are forced to become so if they weren’t before) and things in the Transcend can be low-entropy in ways we couldn’t currently imagine.
IIRC the planet comes from the direction of the core, which the protagonists assume implies from the core... but it could have just been travelling through it, no?
As for the FTL limit, I always thought the causality is the reverse - that compute power that the Beyond has is because their computers run on the same physics that allows FTL travel.
If FTL was driven solely by compute, then you'd never have a clear boundary in the first place - just shorter and shorter hyperspace jumps, perhaps until the point where they become infeasible (because the amount of time it takes to make one, including compute, is more than just travelling there). But the way the book describes it, the boundary is qualitative, and FTL drives plainly don't activate once in the Slow Zone. Ditto for FTL comms.
Yes, that was my take too. "OnOff’s eccentric orbit had at least passed through those unseen depths." -- but the irony of the end of the book is that they're going to be going entirely the wrong way. The ellipse that describes its orbit is eccentric -- that means it can touch both points near the center of the galaxy and points outside the Slow Zone.
However, if you read carefully, and consider some of the consequences, it becomes clear that this is not a natural rule of the universe, but something technological, created by presumably one of the first civilizations to become highly technological as a defense against what would otherwise be a fairly vicious universe with constant high-tech civilizations fighting each other with frightfully powerful weapons, and perhaps a hint of compassion towards the not-yet-high-tech civilizations. That's why it can be manipulated with certain keys, in ways that would not be possible (lots of FTL signalling) if the Zones were truly a fundamental rule of the universe. (Notice also how the super-high-tech civilizations don't understand how the Zones work or why they exist, which if there were purely natural seems unlikely.) The Powers tend to last 10 years probably because that's how long it takes to either be accepted by the highly advanced civilization(s) that live in the galactic cores, or how long it takes to work out how to move there despite the Zones being in the way, or both. This creates an entrance gate against things like the main threat of the novel getting into your high-tech civ.
I don't deny I'm extrapolating a bit, but there's a lot of hints, especially if you add A Deepness in the Sky to the mix. Pham was probably sent from this central civ to fight A Fire Upon the Deep's main threat, if you read where he came from. The entire planet of A Deepness in the Sky is clearly from a super-high tech civ far beyond what Earth's depth could support, but it's from closer to the galaxy's core, not farther, which is why Pham went in to the galaxy's core after that story rather than out looking for more intelligent life. He in fact found it, or it found him, if you prefer.
Once you see there's a probably-even-beyond-Transcend civilization living under the Zones of Thought it mostly comes together.