I think dimensionality can actually be pretty visible - 1-dimensional is case-by-case learning, 2-dimensional is normative, 3-dimensional situational and 4-dimensional futuristic. Each one is less specific and more context-dependent than the previous one. So when we're faced with an unknown situation, we're able to use what we learned via a stronger functions, because it's flexible and adaptable, but what we learned by a weaker one is useless in comparison, as in this area we need experience and familiarity with the matter first (which always helps, but it's an essential difference early on).
A really lame analogy (purposefully revolving around abilities unrelated to socionics):
1-d - learning how to draw a line with a pencil.
2-d - learning how to use a pencil.
3-d - learning how to draw.
4-d - learning how to represent an object.
The point of that pattern is, 1-d is most specific and 4-d most generic. You may start with learning to draw a specific object with a specific tool, but depending on the "mode" of learning (dimensionality) you effectively learn this, to use a tool, to draw in general, or the most vague yet widely applicable "creating a representation". And when you're faced with a new situation - for example 3d modeling - only the latter would be of any use to get started in the area, though of course not nearly as good as an actual experience.
So to 1-d, higher dimensions seem to generalize what's learned, to project it onto other things; to 4-d, lower dimensions seem too specific, not making full use of it.
An element with dimensionality is simply how much we can learn from its type of information; so 4-d Ni would be able to "predict" development of unknown situation based on its generic observations of indirect consequences, while 1-d Ni would assume a known situation to develop as they know it to have once (not necessarily "lived through it"), and an unknown one to be unpredictable.