I saw a discussn of Flatland somewhere here earlier.
Here's some quotes from that discussion which may bear some relevance to this subject:

Quote Originally Posted by Rota
I said the same thing in an old grade-school science paper. Time is the 5th dimension of existence.


The first 3 are the typical height, width, and depth. The 4th is mass, because you can have a box that is 1 foot cubed, but it has to be made of "something" in order to tangibly exist. The 5th is time, because if the box did not exist before now, and it doesn't exist at this moment, and it will never exist any time after now, then the box simply does not exist.
Quote Originally Posted by Bree Fletcher
Here: I'd like to introduce you to my good friend, A. Square. He lives in Flatland, a wonderful, two-dimensional country with his two-dimensional family and friends. One day, A. Square was approached by a visitor. However, this visitor didn't come in through the front door, he appeared in Square's house, first as a point, then as an expanding circle. This would be the Sphere, a denizen of a new place called Spaceland. Square simply could not comprehend it; how could there be space "up" or "down" from his current location? However, the Sphere eventually took A. Square out of Flatland, so that he could see that Flatland was indeed just tw parts of a three-dimensional world...

Am I making sense, here?
Quote Originally Posted by Rota
Your friend square is still a three dimensional object. Let's say you know him as a pretty green square with only height and width. You merely cannot make out his "depth," but I can assure you it is there. If he is on paper, then his depth is measurement of the crayon's wax, the pencil's graphite, the pen's ink, or the marker's dye. If he is on TV, then his depth is just a few electrons deep of the excited electrons producing the green color.

If there was no depth, then you could not perceive him. You cannot measure a truly 2 dimensional object. You can walk right through any spacial area that you would like to imagine a 2 dimensional figure exists. It MUST have the third dimension to be comprehended in the glory of it's 2 large dimensions. We all laugh and mock it's pathetic, measly, visually inadequate third dimension.

Mr. Square cannot deny his third dimension, no matter how small. Without it, he would not exist.
EDIT:

Darn it Rota stop being faster than me