Problem Calculus: Semantically Homogeneous vs Semantically Heterogeneous

My previous Problem Calculus and Cognitive Complexity outlines assert that spaces should be path connected in order to avoid complexity.  I think that this concept can be related to Semantically Homogeneous and Semantically Heterogeneous.  The argument is that Semantically Homogeneous spaces approximate path connected spaces AND the quality that you need in a space to have an easily understood space is a semantically homogeneous space.

So what's the difference between a function that looks like "func(x : int, y : int, z : int ) -> int" and a function that looks like "func( p : point3d ) -> int".  The problem calculus argument is that they are probably the same.  The source spaces for both functions are semantically homogeneous.

  

The source space involves three different dimensions that all "belong" together.  The space is one coherent component.

In order to create a semantically heterogeneous space, you can take the same function from before "func(x : int, y : int, z : int ) -> int", but instead of having the input parameters representing a point in 3D space you can have it represent some 2D point in a family of 2D spaces.

Here we have what appears to be the same thing, but the problem calculus diagram is radically different.  

Semantically homogeneous spaces are easy to comprehend because the dimensions that go into them only mean one thing.  Semantically heterogeneous spaces are hard to comprehend because the different dimensions can all indicate something potentially different.  Each different thing needs to be considered separately from the other things.  And this can become arbitrarily difficult as the space contains arbitrary more concepts that need to be understood on a case by case basis.

Here's an example of a space that is composed of a color dimension and an intensity dimension.  The space is semantically heterogeneous because the meaning of the intensity dimension changes meaning depending on what color is present.  The basic idea is the same, but the eventual output is going to be radically different.

Ideally, I think that path connected spaces probably provide a better theoretical basis, however having to worry about constructing topological spaces is probably more work than it's worth.  Additionally, there is going to be some difficulty in ensuring that the function used to show that the space is path connected is the "right" one.  There may be a space that is difficult to comprehend, but a sufficiently clever individual can figure out a function that shows that it's path connected.  Semantically homogeneous vs heterogeneous is hopefully easier to determine objectively.