Oatmeal Agitante

I'm not familiar enough with group theory or topology to comment on those. Among the rest, it seems to break down into 2 forms

1. Instantiate the halting problem in X. (trivial) 2. X produces pseudorandom behavior which can't be predicted. (maybe not)

Instantiating the halting prob. can be how you *prove* undecidability in probs of interest for other reasons; I've seen that.

in those cases I always feel let down because the halting problem usually isn't a "pragmatic" usage of a system

One practical example is that you cannot write a truly optimal compiler. https://en.wikipedia.org/wiki/Full_employment_theorem …

Although you may think that cases to worry about are rather pathological.

Yes, actually compilers are one of the motivators for my intuition

sophisticated manipulation of programs in turing complete language, switching b/w representations, it all works