Big advertising displays did provide us something to think about: the drawing of a box--by which we mean a cube--brings us to look at foreshortening, which is also called a perspective projection. In an advert that involves the drawing of such things, we know that it is often done by an artist with an eye for such things. But, either taken on faith or by experience, we know that such things can be done by calculation.
If we are faithless, and haven't yet looked at Linear Algebra, we might yet look at the lines which go to make up a box, after calling one of the corners the origin. We might do so even if we are of little faith. But such things make us think about the shape of our eye, and thus we ask it to be invisible for a bit.
To start off with, then, we have eight points. We have to leave the matter of invisible lines to clever people. What we do know is that our angle of vision tends towards a full half circle. The trouble I have in thinking this through now, twenty-five years after I first did so, is that I can't be sure I didn't borrow from someone else's imagination, without their permission, so as to put myself outside myself.
To differentiate a perspective projection from an orthographic one, we note that there aren't any parallel lines when we foreshorten a cube. Each point may be described as a radial vector. By looking at them from one unit away from the plane, we come to what is called a perspective projection. By noting that the plane is in fact a sphere, we come to projections which in the one extreme are called fish-eye, and the other, long-angle.
Now, children: what's the difference between a business centre, and an arcade?
If you must block out the sunlight, and so insist that an arcade of shops is something which might be found in orbit, and then play games with those that are subsequently born by telling them that the rules must change if we put ourselves outside the world, and therefore we aught to start experimenting with new rules now, then we might see boys pointing at boxes and saying that what you see is what you get.
If I seem to be unrealistic in my writing sketches, I'm just putting myself out there. Witchell English is ideal for what goes on boxes, because it has no highest authority. Payment for publishing something wrong just gets us looking at a mommy en vir haar wil gevra om of ons dit net one more time kan doen, asseblief?