Brand new member here followed the link from slashdot - with a humble contribution.
A Simple Harmonic Ring
with apologies to Douglas Hofstadter
Achilles: Good day, Mr. Tortoise.
Tortoise: Why, same to you.
Achilles: I can’t help but notice that lovely ring you are wearing.
Tortoise: It is lovely, isn’t it? It was a gift from my dear friend Moebius.
Achilles: That certainly is an unusual pattern inscribed around the border.
Tortoise: Well, strictly speaking it isn’t a pattern; it’s an ancient Elvish language.
Achilles: Really? The beauty of the lettering is such that it can scarcely be distinguished from the decorative pattern that surrounds it.
Tortoise: Yes, if one does not detect the frame message there is very little which separates the “set of language-characters on ancient Elvish rings” from the “set of decorations on rings”.
Achilles: Also, part of the message is obscured by the unusual way in which it wraps around the body of the ring, like a serpent.
Tortoise: Oh yes, I’m afraid Moebius has a certain disdain for designs which create a distinction between front-sides and back-sides; he claims to have invented a new ring design which has neither front nor back!
Achilles: I must confess I hardly see the value in that.
Tortoise: For my part I cannot comment, for he is a dear friend and by far a superior engineer. In that regard, in fact, he may be said to run rings around me!
Achilles: Fair enough, dear Tortoise. I am most curious, however, to know what the inscription says. Have you been able to translate it?
Tortoise: Oh yes, it is quite simple if you are familiar with Elvish. It states “One ring to rule them all.”
Achilles: How very odd indeed. One ring to rule them all? All of whom, I wonder?
Tortoise: I suspect it is not so much a whom as it is a what! A ring to rule all rings, I surmise.
Achilles: A ring to rule all rings? Such folly!
Tortoise: Why is this folly, my dear friend?
Achilles: Surely you must see, Mr. Tortoise, that a ring to rule all rings must also be considered the ruler of itself! Unless what we have here is not in fact a mere ring, but some kind of greater, lord of rings.
Tortoise: No, Moebius was quite clear on the subject; while it may not be the most ordinary of rings, it is a ring all the same, and must be considered to be a member of “the set of all rings”.
Achilles: More and more puzzling. I must insist that this cannot be an ordinary ring at all, despite appearances, but must be a meta-ring of an entirely different class.
Tortoise: But that would imply that there exists an endless hierarchy of meta-rings to rule the rings, and meta-meta-rings to rule the meta-rings, and so forth.
Achilles: True enough I suppose. May I examine it? Perhaps a clue is held elsewhere in the pattern, a hidden field-message of sorts.
Tortoise: Most certainly, here you are.
(Achilles examines the ring.)
Achilles: Aha! I seem to have discovered another message intertwined with the original. Would you be so kind, dear Tortoise, as to apply your linguistic skill to this new message?
Tortoise: Nothing would please me more!
(Tortoise also examines the ring.)
Tortoise: I think I have it! Not only that, but the hidden message seems to read differently forward and backward! Truly a wealth of information you have uncovered, my friend!
Achilles: It was nothing, really - please share with me what it is the new message says.
Tortoise: Surely. Read the usual way, from left to right, it reads “This ring may not be worn on ring finger A.”
Achilles: Another puzzle it seems! Please do go on.
Tortoise: Of course. From right to left, it reads “This message conveys no information.”
Achilles: Conundrum upon conundrum. If only Xeno, with his knowledge of paradox, existed in this world to aid us rather than holding the almost supernatural position of being the author of the characters upon which this parody is based!
Tortoise: Speaking of which, have you ever noticed the similarity between the words “paradox” and “parody”?
Achilles: I can’t say I have, but thank you so much for bringing it to my attention - perhaps it ties in with this ring matter in some way.
(Just then, J. R. R. Tolkien appears with a blinding flash.)
Tortoise: My goodness, who is that? I’m so sorry, but a blinding flash seems to have left me temporarily unable to see for myself.
Tolkien: I’ll take that now.
(Tolkien grabs the ring away from the Tortoise and disappears in another, equally blinding flash.)
Achilles: I’m not sure, but whoever it was seems to have taken your ring.
Tortoise: Ah well, perhaps I am the unknowing owner of the “ring finger A” which the ring warned about. Or rather the meta-ring. Or meta-meta-ring.
Achilles: Perhaps, perhaps. Oddly enough, I am just now recalling a story I heard some time ago involving rings and ring fingers and hidden messages and such. Would you like to hear it over some tea?
Tortoise: That would be delightful, please do share your story - I have had enough of our own ring adventure for now.
Achilles: All right. It concerns two dear friends, named Akilees and Tortuce.
*Akilees: Good day, Mr. Tortuce.
Tortuce: Why, same to you.
Akilees: I can't help but notice that lovely ring you are wearing.
...*
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