There would be a communication lag, but why is that an issue? When you're figuring out a problem, you don't come to a conclusion instantly. You use different parts of your brain in order to come to a logistical conclusion.
Signals in your brain travel from inbetween 1 and 270 miles an hour, yet even though your brain has a physical size and speed limit, you're still conscious aren't you? I think it would work the same way with a unified brain within a Dyson Sphere. Just because there's significant lag between different parts of its mind, doesn't mean the mind can't be unified and coherent. I mean, we're talking about a damn godlike intelligence here.
I just don't see how you could reconcile an enormously fast clock speed with 16 minute lag. The gap must be orders of magnitude more extreme than what exists in a human brain.
True. I just think different parts of its brain would work towards different goals, and they would later connect to solve greater problems.
Like, a part of its brain figures out an aspect of said problem, it's communicated to another part of the sphere (8 minutes away), then the former part is temporarily "turned down" (not shut off completely, just operating at lower activity), while the part of the brain it sent the data to can work on a separate asset of the problem. Obviously it wouldn't just be 1 part working at a time, but it's a superintelligent AI so it constantly has to use a significant amount of brainpower to make sure its mind stays coherent.
I guess an example would be deciding to raise your hand infront of your face. The decision making part of your brain makes the decision. You send signals to the parts that control your hand to go up. The part of the brain that receives visual input sees your vision is now blocked. The reasoning part of your brain says your vision is blocked because of your hand. Your brain registers this event as non-important, therefore it is sent to short-term memory. No parts of your brain are completely "turned off", but different parts of your brain are used for different things. This all happens in about a second, but for a super AI, a similar action (obviously with a level of complexity orders of magnitude greater) the reasoning takes 100,000 seconds
So even though there is significant lag, the problems it's solving would be ones that take higher orders of magnitude in time to solve (say, a decade of working at one problem) rather than our problems that take, say, a couple hours. After all we only live ~80 years, it would live well over 1,000,000,000 years.
As a whole, it's mind moves slower than ours, but it can simulate an entire human intelligence in a square millimeter. It doesn't need to constantly think as a whole.