[lucas_membrane]

I suspect that systems that defy understanding demonstrate something that ought to be a corollary of the halting problem, i.e. just as you can't figure out for sure how long an arbitrary system will take to halt, or even figure out for sure whether or not it will, neither can you figure out how long it will take to figure out what's going on when an arbitrary system reaches an erroneous state, or even figure out for sure whether or not you can figure it out.

[nil-sec]

I’m not sure about this. Define your “erroneous” state as “halt”. Now the question becomes, for a systems that halts, find out how it reached this state. The mathematical answer to this is simply the description of the Turing machine that produced this state. Whether you can understand this description or not isn’t relevant.