Probably starting with Flatland it has been very popular to explain higher dimensional concepts by analogy to an interaction between beings in 2 space and 3 space.

To me a true 2D universe has zero extension in the third dimension and for all practical purposes (even if such a world did exist inside our 3D space) it would be impossible for either world to interact with the other except in the most hypothetical thought experiment manner.

For instance, the atoms (and everything else) in the 2D world must be 2D and somehow confined to the plane of their universe.

The idea that we could take a 2D object that is infinitely thin and turn it upside down to reverse it in 2D space so that it became its mirror image is absurd.

We are talking INFINITELY thin, not just very thin. ZERO thickness

Supposing we could even detect an infinitely thin being... and with god-like powers we succeed in flipping it out and back into its own dimensional space by breaking and then restoring whatever forces were confining it to that space... the idea that with infinitely thin eyes it could see anything of its own world from above is again ridiculous.

I know some people have thought about his as I have seen it suggested that a two dimensional world should be allowed some degree of 'thickness' in the third dimension.

My point here is not really about the use of the metaphor in order to explain the concept of dimensions -

it does seem to be a useful way for beginner to understand the concept, and some geometrical progressions help to understand higher dimensional geometries.

My real point is the question of whether our third dimensional space has any thickness in any higher dimensions.

I am not referring to string theory, although I suppose that is the first thing that comes to mind.

I am questioning whether anything that has ZERO extension in a particular dimension can be considered 'real' from the perspective of that dimension.

Holographic theories that propose that the universe is a holographic projection of information contained in the 2D boundary of the universe seem to me to be the opposite of common sense.

As I see it, it is higher dimensions that give reality to lower dimensions not vica versa.

Please excuse the inadequacy of my wording for this next sentence, I hope you will get the gist of what Im saying .

Without the existence of infinite dimensional space in which lower dimensional space can exist, it seems to me that there will always be this problem of thinness to deal with.

Eleven or thirteen dimensional string theory still would mean that in the 14th dimension the universe is infinitely thin.

Okay Ive made a fool of myself now, I think I'll shut up before I sound even more confused