These projections, how do they make sense?

I can project a 3D item onto a 2D plane, but only observe it because I'm outside of that 2D plane. This is like expecting the 2D plane to see itself and deduce 3D-dimensionality from what it sees. Like a stickman. It would only be able to raycast from its eye in a circle. It could do so from multiple points on the plane, but still, how would it know that it is looking at the projection of a sphere?