by Terr » Fri Nov 12, 2010 7:55 pm
Pretty sure it's you, although I'm not sure if you mean "silly" as in "totally joking" or as in "devil's advocate". I'm being serious even if I misspoke slightly in my last post.
Before, I used 3 planets in 1D space and proved their final distances require a triangle, forcing the need for a 2D representation.
Similarly, I can use 4 planets in a 2D space to prove that their final distances create a tetrahedron, forcing the need for a 3D representation.
The pattern is clear, isn't it? You always need at least N-1 dimensions to model N planets, or else chance arrangements will break your math.