I don’t know about information theory’s distinctioning BUT I think after all this time I have a 0/1 distinction I can work with. Took me long enough: Foreground/Background. I reasoned it out while looking at mathematical morphology. Foreground is 1. Background is 0. BUT, it’s not absolute. Imagine foreground and background’s only distinction being from what’s “above the surface” (fore) and what’s “below the surface” (back)? Now, make the surface move up and down. With that, you have granularity.

I don’t know about information theory’s distinctioning BUT I think after all this time I have a 0/1 distinction I can work with. Took me long enough:
 
Foreground/Background. I reasoned it out while looking at mathematical morphology.
 
Foreground is 1.
Background is 0.
 
BUT, it’s not absolute. Imagine foreground and background’s only distinction being from what’s “above the surface” (fore) and what’s “below the surface” (back)?
 
Now, make the surface move up and down.
 
With that, you have granularity.
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