Interested in disproving the halting problem and the incompleteness theorems.

Idea for halting problem: an algorithmic system that can predict the behavior of everything in the universe, with sufficient advanced preparation time, can always predict when a process will halt, because it will always be able to outpredict a pathologic example via its own pathological counterbehavior and advance preparation.
Idea for subproof of universe predictability: The universe is made of statistical processes based on measurable metrics. Probability trees are predictable.

I'm more interested in the logic challenges than formal proof, because I don't have the math. But maybe the nerd sniping can learn me some math.

I got to godel's incompleteness theorems from xkcd. I have a lot of math to learn.