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Do higher planes of existence imply higher dimensionality?

So, in my verse, there are 3 different planes of existence and a hierarchy in which all the cosmology sits upon. The Middle Plane of Existence views the plane below it as lower/bottom existence. However, I'm not sure if this would imply a higher dimensionality. So the Lower Plane is 4D, and would this make the Middle Plane 5D?
 
depends, you need to explain more the difference between those planes of existence
Each Plane views the one below it as inferior, however characters from the middle plane are capable of interacting with the higher plane, and its not in reference to universes/dimensions/worlds
 
Each Plane views the one below it as inferior, however characters from the middle plane are capable of interacting with the higher plane, and its not in reference to universes/dimensions/worlds
I wouldn't even say it is a dimensional difference if this is the case. Just seems like the world is structured like that..
 
Each Plane views the one below it as inferior, however characters from the middle plane are capable of interacting with the higher plane, and its not in reference to universes/dimensions/worlds
Okay but what "inferior" means? Is it like some racist thing or like less powerfull? Can you explain a bit?
 
Better Explanation: It's the hierarchy of each Plane in which the multiple realms and higher planes of existence sit, there are three main planes of existence with the higher planes being referred to as such.


Okay but what "inferior" means? Is it like some racist thing or like less powerfull? Can you explain a bit?
 
Better Explanation: It's the hierarchy of each Plane in which the multiple realms and higher planes of existence sit, there are three main planes of existence with the higher planes being referred to as such.
So it's just georaphy? If the only thing about "inferiority" is just a stataments that says so then this isn't a difference in dimensionality.
 
It's too vague, it's like "being" bottom of barrel but with statement being inferior to the rest. Without explanation of how they (the middle) are able to interact with the higher. And the exception implies a quantifiable difference instead of a dimensional one. In general, to qualify higher dimensionality, n-dimension need to explicitly embed and encompass an arbitrary number of n-1 dimensions.
 
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