This summer I read the entire collected fiction of Jorge Luis Borges, an Argentinian author from the early/mid 20th century who dealt philosophical themes.
Today we have the short story "The Disk." Read it. It's fun and doesn't take long. A woodcutter meets a beggar who claims to possess the Disk of Odin, an object with "but one side." The woodcutter kills the beggar, but in the process the Disk falls to the ground, up-side-down (or perhaps "only-side-down"). The woodcutter is never able to find it.
What would it mean to be a three dimensional object with only one side? In the afterward, Borges calls the Disk the Euclidean circle "which has but one face," but what does this mean? The Euclidean circle is just a two dimensional circle, like the kind you can draw on a piece of paper. In the two dimensional world (since this is where the circle lives), it has no faces since the face we see is on the plane of the z axis.
But consider this. Draw a circle on a piece of paper, a light circle with a pencil, and then turn the piece of paper over. Magic, the circle is gone. This is a cheap trick, since you can still see the paper that the circle is drawn on, but this is a start. Now imagine that the circle isn't drawn on a piece of paper, but just is (or that it's drawn on an invisible paper). If you were to turn it over in this case, the circle would appear to vanish, since you would have lost the background on which it is drawn that makes the everyday circle-on-a-paper case so trivial.
That's what I can get out of this - my take on 3D objects with but one side. Thoughts?