> The halting problem tells us that it’s plausible that that instinct is right - that for some programs, you really can’t do some other analysis of the program that tells you what it’s going to do. You have to just run it.

This isn't quite right. The halting problem says that you can't just run it. If you just run it, you will not learn whether or not it halts after any finite amount of time.

Also I don't see how this is related to uncertainty bounds.