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.

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