Well, it's an interesting space.
   The proposed pathological process is tasked basically with being
   unpredictable in the face of a prediction process that expects it to do
   so and has unlimited time to prepare.
   This prediction process could for example consider many possible shapes
   of environments, ecosystems, knowledge and research exposure the
   pathological process would be exposed to.
   The pathological process might for example generate new random
   universes, with random physical laws, and perform simulations within
   these in order to consider things unlikely to be predicted.
   How large is this space? Does it matter?
   Both systems will likely attempt to derive general descriptions of
   systems in which inferences can be made.
   I am very off track! Is this relevent? At what point is it relevent or
   not?
   No. Things are only relevent when they relate to challenges we might
   encounter in the real world.
   In reality, computational systems are relatively small. They exist in
   tiny algorithmic systems inside our larger universe. One can be fully
   observed by another, and two can mutually fully observe each other.
   An all-prediction program would then be tasked with sufficiently hiding
   its workings from pathological programs, and observing and preparing
   for their behavior in advance of engaging them. This is entirely
   possible only if it has access to all other program forms before it is
   tasked to work with them. The program's spec would provide it with that
   access.
   I don't know why Turing assumes that the predicted program can observe
   the predicting program. Have not read the paper. Don't know what
   concepts are within its scope.
   In reality, programs happen that are not observed by another given
   program prior to their execution, and such situations aren't usually
   considered interesting when trying to predict program behavior alone.
   Concept closes to writing a program which predicts whether another
   halts, which means writing something similar to an optimizing compiler
   and an algebraic solver. Some of the spaces of algebraic solution do
   indeed look unreasonable to solve given how many unproved mathematical
   theorems there are. Regardless, such an analyser would be incredibly
   useful for other tasks than the pathological one.