I was thinking about the figures in Flatland. What actually determines a shape? Is it a line? A line is by itself, is infinitely thin. A shape is not defined by a line, it has an edge, a divider between inside and outside. I don’t think the residents of Flatland would confuse a bright spot with a triangular shape, with an actual triangle, even though it is an area of brightness bounded by a dimensionless edge, a line, if you will.  Why is that line different than the line that defines the triangle citizens of Flatland?

Triangle Bright Spot in Flatland Night
Photo