If we were all "upgraded infinitely", then we would know what everyone else knows.
No, we wouldn't be upgraded
infinitely. We would be upgraded
intelligently... as is most useful. An AI's idea of progress wouldn't be the blind, nonsensical raising of every bar... it would be a selective, smart raising of exactly just the bars that need to be raised (and not necessarily to their max potential, but their most
useful potential).
Plus, if we create an A.I. that can upgrade our intelligence to the point of being maxed out, we wouldn't need the A.I. anymore.
No idea what you're claiming.
However, we most-likely wouldn't be maxed out by any means (unless an AI did in fact decide that being maxed out would be best. Still, with a maxed out mind, our brains would have to think in an entirely new "flavor" in order for us to continue being
happy... meaning to say, don't think an A.I. would be dumb enough to leave us with regular old, broken human minds. It could change the very
dimension of thought, after which we'd see standard human thinking as a foreign concept... like the difference between morse code, and fluid, spoken language).
How does the AI world account for Turing's Halting Problem?
Assuming you mean that the Singularity could take too long (longer than the lifespan of the A.I.'s programmers), this is assuming that the A.I. wouldn't be in a responsive state
during the Singularity. (point being: the Singularity could even take all eternity, for all an A.I. programmer would care, as long as it could still communicate and respond to people while compiling new data. For example: technically, Google's archiving of the web will never be complete... but its database is usable at all times, so it doesn't really matter)
Also, someone (or some group) smart enough to be programming A.I. in the first place probably wouldn't use a "Turing complete" programming language, if they thought it would be an issue.
I don't understand the halting problem deeply, but I think I have the concept. By design, an A.I. would never stop trying to understand, anyway. The only important thing would be that it remains responsive while it "thinks", which would be the FIRST thing its designers nail down.