Thought on critical elements and The Axiom of Choice

I once said that encoding the Rubik's Cube solve into one's mind is like learning a level 1 spell in D&D- it is memorization and repetition, with layers added layer for instinct (mastery). 

The Axiom of Choice reminds me so much of that analogy. For the Cube, from a given starting state, there are an infinite number of conceptual ways to reach a completed state, if stacking all inefficient solves, with the only functional limit being how many times you can make moves before the Cube falls apart. Still, turning at random is extremely unlikely to result in a completed state, and it becomes clear that "any combination of moves" does not solve the cube. 

This is like my Lego analogy for prophecy, but with rotational permutations considered. Essentially, the pieces must fit, but can be rearranged. I could also see an architect in their domain just changing the colors of the cube for those in their domain, but this is not "solved," and other means of observation would prove that easily, which reminds me of Tetrachromatic Crossroads.