Determining dimensionality has broader implications.
Perhaps the most interesting piece is how dimensional reduction relates to abstraction, forming the basis for cognition and symbolic reasoning. The research of Judy DeLoache found that children below the age of 2 1/2 display 'dimensional confusion' - but once this hurtle is cleared, human children rapidly acquire a capacity for reasoning with symbols.
My insight is that what is learned at that point is a skill with dimensional reduction. The ability to distinguish a 2-d picture from a 3-d scene is a gateway skill to higher learning, because that way the idea of 'writing' information onto a surface actually makes sense. And this notion has made its way into a number of my previous essays, and other published papers before and since their appearance.
But the idea that nature also determines dimensionality dynamically is a kind of validation for the constructivist view that observation and measurement are another face of imagination and construction. This validates also the quantum mechanical view that observation is creation. That is; on some level, learning and creativity are the same - the universe and its inhabitants are at play.
Have Fun,
Jonathan