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?
7 comments:
great story, thanks for sharing. Jamie
hmm I have a couple disagreements with your thoughts. First, I don't see where you got the z-axis existence of the face of the Euclidean circle. Why can't it just exist in the Euclidean circle in 2d?
Now if you want to bring this 2d face into the 3d world, your circle-on-paper example does a terrible job of capturing the rather elegant nature of this disk with "but one side." The blank side of the paper is still the other side of the circle, visible lines or not. What makes Borges' disk so special is that every visible sign of the disk disappears when it is turned over. This little act has no place in the human mind - it's completely impossible. Now, what I think would have made the disk even more fascinating is if it would have disappeared physically as well. Unfortunately, this is not the case, as the woodcutter could still feel the cold disk in the beggar's hand.
However, I find it interesting that the visible side of the disk is never actually clearly seen. Only gleams were seen. And again it sucks that the invisible side still exists physically, because then the woodcutter has an even better excuse for never finding it. How big can his house be? If one could touch the invisible side, I imagine he would have found it in a matter of hours if not minutes.
And finally, perhaps Borges made the invisible side tangible on purpose. But I can't think of why...and think about why the disk gleamed when the woodcutter touched it. Did he move it slightly and he caught glimpse of the other side? But how is that possible, assuming the disk was way below eye level?
Always contrariwise!
1. The euclidian circle is a two dimensional beast. The x-axis goes left to right on the paper, the y-axis goes top to bottom on the paper. The face of the circle has left-right and top-bottom dimensions, but the way it faces is away from the paper. Away from the paper is the z-axis.
As for the rest, why can't stories be clear with a transparent meaning? Stupid Borges.
I saw the parallels between people's desires to cling to ideas (religion), and they're willingness to murder for it. To the result of what?
Alan,
#1 - Don't write out "#1" unless you have a #2
#2 - I'm not stupid. I know what a euclidian circle is. I wasn't asking for a definition, I was making a finer point about the disc not needing to be 3d - next time I'll make my point more blunt for you.
#3 - Ouch?
#2 p00ned!
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