> You mean, in that case tolerance to partition and availability should be perfect.
No. If a network is never partitioned, you don't need to write algorithms that can tolerate partitions. Therefore consistency and availability are possible.
> So this is the really interesting question. All the CAP theorem says is that (C,A,P) != (1.0,1.0,1.0). How close to (1.0,1.0,1.0) could we make (C,A,P)? If infinitely close, then we have achieved perfection by the limit, and the CAP theorem is rather pointless. If not, then what is the numeric limit?
I think you have misunderstood the theorem (at least, if my bachelor-degree-level understanding is correct). C, A, and P are not variables you can multiply together or perform mathematical operations on. They are more like booleans. "Is the web service consistent (are requests made against it atomically successful or unsuccessful)?" "Is the web service available (will all requests to it terminate)?" "Is the web service partition-tolerant (will the other properties still hold if some nodes in the system cannot communicate with others)?" These questions cannot be "0.5 yes". They are either all-the-way-yes or all-the-way-no.
> . . . and the CAP theorem is rather pointless
Not really. It is pointful for networks that experience partitions. It just doesn't apply to reliable networks. It also sort-of doesn't apply when an unreliable network is acting reliably, with the caveat that since it is not possible to tell in advance when a network will stop behaving reliably, you still have to choose between these three properties when writing your algorithms for when the network behaves badly.
> C, A, and P are not variables you can multiply together or perform mathematical operations on. They are more like booleans.
Right, but I wasn't restating CAP, just wondering about a follow on to CAP that considers the probability of remaining consistent, the probability of remaining available, and the probability of no failures due to network partitions in physical terms.
Is this not an interesting thing to consider? What if someone proves a hard limit on the product of these probabilities in some physical computation context? The CAP theorem is absolutely fascinating to me, especially if it has something real to say about the systems we can build in the future. The future looks even more distributed.
> It is pointful for networks that experience partitions. It just doesn't apply to reliable networks.
Is there such a thing as a "reliable" network when thousands or millions of computational nodes are involved? Are the routers and switches which connect such a network 100% available? If an amplification attack saturates some network segment with noise, what then?
As programmers, we desperately want things to work, and it's easy to greet something like CAP with flat out denial. I know I'm always fighting it. "It will never fail." No, it can and will fail.
I still don't understand what you mean when you say, "probability of remaining consistent," etc. Either you wrote the service so it system would always remain consistent or you didn't. Similarly with availability. Either the system will always return a result, or it may sometimes hang.
Maybe what you mean is the probability of whichever of C, A, or P you gave up actually becoming a problem? But I cannot imagine a physical law of the form you are referring to applying uniformly to these disparate properties. I wouldn't even know how to formulate it for consistency. For availability and partition tolerance it would just be, "Requests to this service will (availability: hang forever/partition-tolerance: return with errors) at a rate exactly equal to the probability of network failures."
With regards to your last point, there are no reliable networks, at least where I work. That doesn't mean there won't be.
Actually, C/A/P are more like variables you can multiply together. Even more accurately, they define a three-dimensional space with the CAP theorem (especially in Gilbert and Lynch's formal proof) only saying that you cannot be at the point that represents the maximum of all three. There are definitely tradeoffs or "mode switches" that can be made between C and A, and some even believe that you can give up some P to get more C/A. Personally I believe that the probability of partition is always non-zero in even the best designed and fully provisioned networks, even including those that are econonomically infeasible, and that those who choose to treat a small probability as zero to capture a performance advantage or position themselves as "more consistent" than competitors are being a bit dishonest, but those tradeoffs are being made.
> they define a three-dimensional space with the CAP theorem (especially in Gilbert and Lynch's formal proof) . . .
That's weird because I've read the proof and they speak only of boolean instances of C, A, and P in the proof. They give no examples of systems where any of the three variables have values other than zero or one.
No. If a network is never partitioned, you don't need to write algorithms that can tolerate partitions. Therefore consistency and availability are possible.
> So this is the really interesting question. All the CAP theorem says is that (C,A,P) != (1.0,1.0,1.0). How close to (1.0,1.0,1.0) could we make (C,A,P)? If infinitely close, then we have achieved perfection by the limit, and the CAP theorem is rather pointless. If not, then what is the numeric limit?
I think you have misunderstood the theorem (at least, if my bachelor-degree-level understanding is correct). C, A, and P are not variables you can multiply together or perform mathematical operations on. They are more like booleans. "Is the web service consistent (are requests made against it atomically successful or unsuccessful)?" "Is the web service available (will all requests to it terminate)?" "Is the web service partition-tolerant (will the other properties still hold if some nodes in the system cannot communicate with others)?" These questions cannot be "0.5 yes". They are either all-the-way-yes or all-the-way-no.
> . . . and the CAP theorem is rather pointless
Not really. It is pointful for networks that experience partitions. It just doesn't apply to reliable networks. It also sort-of doesn't apply when an unreliable network is acting reliably, with the caveat that since it is not possible to tell in advance when a network will stop behaving reliably, you still have to choose between these three properties when writing your algorithms for when the network behaves badly.