Proof that higher dimensions cannot exist within lower ones

[RQ]

Could higher dimensions really exist within lower ones? I mean the definition itself defies it, but why not? Well let us suppose that a cube existed within flatland. That cube would have 3 directions of independent motion, but the bionian universe would only have 2. Now what better way to picture this than a 3D drawing in the bionian world, and the 3D object (the cube) is within it. Now before you say that the cube is going to be outside the 2D drawing of a 3D bigger cube, I might add that to us trionians (and maybe above) it would still seem like a cube within a bigger cube. So, if we say that the 2D drawing is to represent two squares, with their corresponding corners connected, then it would have to point at two directions at once if it was extended in 3D, since if one of the squares were extended in the 3rd dimension towards us it would be pointing one way, but if it was extended away from us it would point in a different direction, so if we had the 3D cube, it would have to have a duplicate of itself since it is in 3 dimensions and the 2D drawing makes the cube go in two directions at once, which would violate the first law of thermodynamics. [/quote]

[Geosphere]

This post has tons of blind assumptions.

suppose that a cube existed within flatland
No. It can't. Don't bother supposing.

That cube would have 3 directions of independent motion
No, it can't, not there.

So, if we say that the 2D drawing is to represent two squares
No reason to say that.

makes the cube go in two directions at once, which would violate the first law of thermodynamics
No, it wouldn't. And the two directions at once is not founded here anyway.

Once you start with "a cube in flatland" the rest is wrong based on the incorrect supposition. You can prove anything once provided with a flawed supposition.

[RQ]

it's an assumption that it couldn't or doesnt

[RQ]

if a square existed as a visible 2D object in flatland, then a drawn hollow cube would also have to exist since to us it has a third dimension and perspective is what matters.