Oct 15, 2009
In the novel Flatland, the sphere fails to enlighten the square about the existence of a 3rd dimension. In the end the sphere simply gives up and pushes the square out of its current plane. This make him hover above his flat world and see it from a 3rd dimension point of view.
This never made sense to me for two reasons. First, this is an easy way out of solving the problem of explaining the 3rd dimension to a 2D being. Second, the square does not acquire a new sense of vision because he is outside of his original plane. He would still see the world through a flat input. What he would see would be incomprehensible to him, the same way the sphere was appearing, morphing and disappearing by intersecting with his plane. All 3D shapes would still look like that to him and all 2D shapes (from his plane or any plane) would look like points and, occasionally, lines.
Is it possible to explain the 3rd dimension using only only 2D terms and their relation to 1D and 0D? That's one of the things that I'm working on...
My poor brain