I have read any number of discourses on Flatland in various attempts to introduce the concept(s) of dimensions in excess of the 4 normally sensed by humans.
Well, I object to all of these thought experiments on the ground that they all, and I mean ALL, are dishonest.
They all "pretend" that 2-dimensional entities can exist (can't, there's nothing there), and sense each other (quite impossible - no 3rd dimension into which sense organs project), and communicate (impossible, again, since there is nothing there).
In Flatland, even entities one atom thick cannot exist. The depth of Flatland is infinitely small as in non-existent.
But repeatedly, without criticism, all Flatland entities are discussed exactly as if they have a very, very, very tiny 3rd dimension (thus 3-dimensional). There is simply no such thing as a 2-dimensional physical entity. Just as a point has zero substance (how can it?) and is an imaginary concept, a 2-dimensional "world" cannot exist because it has zero depth: substance requires volume. Area times zero depth is zero. Thus, one pretends lines and circles and shapes can exist, but how? There is nothing there for them to be expressed in; they have no depth and thus no substance and thus don't exist.
All the physics popularizers that re-tell the Flatland analogies start with this false pretense that such "worlds" exist but they cannot, as I say, even conceptually. So what does that say about the various extrapolations and analogizing to multiple dimensions?
It bothers me.
I know, I know. It's just a good thought experiment that seems to help us get a grip on the the various effects of adding dimensions to a picture. It offers some fascinating metaphors and imagery.
But the whole edifice is founded on a perfect falsehood that any sort of Flatland can exist at all. Flatlanders don't exist, even conceptually. The book "Flatland" is based on a profound falsehood and is suspect from page one.
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