If having two dimensions, height and width, means that a diagonal line is just a tiny line up connected to a tiny line across, repeated on a level so small we don't notice and the line appears diagonal, does that mean that everything in our 3D world is almost 'pixelated' at a really microscopic level?
Sorry, I'm having problems describing what I mean but see if you can make any sense of that. =)
There may be a debate over whether spacetime is continuous or granular: I will have to leave that to others. But there seems to be a problem with saying that a diagonal line is a microscopic staircase. If it was, then the diagonal of a one inch square would be two inches long, when in fact its length is the square root of two.