Thinking about problems don't provide new information. It's the same basic fallacy as assuming a really really powerful AI could deduce QM from a few minutes of webcam footage.
That's sort of a technical non-sequitur, no? I would imagine that a sufficiently advanced AI could deduce QM from a few seconds of real time, given that it could ask questions of any resolution. Or, equivalently, a large amount of webcam footage.
In either case, the emphasis is on conclusions being bought in the currency of experience.
I brought it up because people actually believe it. As you noticed both resolution and time are important limitations. You don't get to arbitrarily examine things at any resolution or for any length of time. Stick a AI up to a webcam at 648x480 @ 30 cycles per second pointed at a brick wall and it's not going to be able to say comment on politics in the middle east.
Or in a more down to earth example, if we stop building ever higher energy particle accelerators there are things we simply don't get to know.