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.

From cypherpunk spirits: the advance preparation time clause could possibly be removed from such a proof by including the knowledge that would be attained during preparation, directly within the definition of the algorithm.

> incompleteness theorems