TORTOISE: It certainly is. And now, in just a moment, comes an organ point.
ACHILLES: Isn’t an organ point what happens when a piece of music slows down slightly, settles for a moment or two on a single note or chord, and then resumes at normal speed after a short silence?
TORTOISE: No, you’re thinking of a “fermata”—a sort of musical semicolon. Did you notice there was one of those in the prelude?
ACHILLES: I guess I must have missed it.
TORTOISE: Well, you have another chance coming up to hear a fermata—in fact, there are a couple of them coming up, toward the end of this fugue.
ACHILLES: Oh, good. You’ll point them out in advance, won’t you?
TORTOISE: If you like.
ACHILLES: But do tell me, what is an organ point?
TORTOISE: An organ point is the sustaining of a single note by one of the voices in a polyphonic piece (often the lowest voice), while the other voices continue their own independent lines. This organ point is on the note of G. Listen carefully, and you’ll hear it.
ANTEATER: There occurred an incident one day when I visited with Aunt Hillary which reminds me of your suggestion of observing the symbols in Achilles’ brain as they create thoughts which are about themselves.
CRAB: Do tell us about it.
ANTEATER: Aunt Hillary had been feeling very lonely, and was very happy to have someone to talk to that day. So she gratefully told me to help myself to the juiciest ants I could find. (She’s always beets most generous with her ants.)
ACHILLES: Gee!
ANTEATER: It just happened that I had been watching the symbols which were carrying out her thoughts, because in them were some particularly juicy-looking ants.
ACHILLES: Gee!
ANTEATER: So I helped myself to a few of the fattest ants which had been parts of the higher-level symbols which I had been reading. Specifically, the symbols which they were part of were the ones which had expressed the thought “Help yourself to any of the ants which look appetizing.”
ACHILLES: Gee!
ANTEATER: Unfortunately for them, but fortunately for me, the little bugs didn’t have the slightest inkling of what they were collectively telling me, on the symbol level.
ACHILLES: Gee! That is an amazing wraparound. They were completely unconscious of what they were participating in. Their acts could be seen as part of a pattern on a higher level, but of course they were completely unaware of that. Ah, what a pity—a supreme irony, in fact—that they missed it.
CRAB: You are right, Mr. T—that was a lovely organ point.
ANTEATER: I had never heard one before, but that one was so conspicuous that no one could miss it. Very effective.
ACHILLES: What? Has the organ point already occurred? How can I not have noticed it, if it was so blatant?
TORTOISE: Perhaps you were so wrapped up in what you were saying that you were completely unaware of it. Ah, what a pity—a supreme irony, in fact—that you missed it.
CRAB: Tell me, does Aunt Hillary live in an anthill?
ANTEATER: Well, she owns a rather large piece of property. It used to belong to someone else, but that is rather a sad story. In any case, her estate is quite expansive. She lives rather sumptuously, compared to many other colonies.
ACHILLES: How does that jibe with the communistic nature of ant colonies which you earlier described to us? It sounds quite inconsistent, to me, to preach communism and to live in a fancy estate!
ANTEATER: The communism is on the ant level. In an ant colony all ants work for the common good, even to their own individual detriment at times. Now this is simply a built-in aspect of Aunt Hillary’s structure, but for all I know, she may not even be aware of this internal communism. Most human beings are not aware of anything about their neurons; in fact they probably are quite content not to know anything about their brains, being somewhat squeamish creatures. Aunt Hillary is also somewhat squeamish; she gets rather antsy whenever she starts to think about ants at all. So she avoids thinking about them whenever possible. I truly doubt that she knows anything about the communistic society which is built into her very structure. She herself is a staunch believer in libertarianism—you know, laissez faire and all that. So it makes perfect sense, to me at least, that she should live in a rather sumptuous manor.
ILLUSTRATION BY THE AUTHOR.
TORTOISE: As I turned the page just now, while following along in this lovely edition of the Well-Tempered Clavier, I noticed that the first of the two fermatas is coming up soon—so you might listen for it, Achilles.
ACHILLES: I will, I will.
TORTOISE: Also, there’s a most curious picture facing this page.
CRAB: Another one? What next?
TORTOISE: See for yourself. (Passes the score over to the Crab.)
CRAB: Aha! It’s just a few bunches of letters. Let’s see—there are various numbers of the letters “J,” “S,” “B,” “m,” “a,” and “t.” It’s strange, how the first three letters grow, and then the last three letters shrink again.
ANTEATER: May I see it?
CRAB: Why, certainly.
ANTEATER: Oh, by concentrating on details, you have utterly missed the big picture. In reality, this group of letters is “f,” “e,” “r,” “A,” “C,” “H,” without any repetitions. First they get smaller, then they get bigger.. Here, Achilles—what do you make of it?
ACHILLES: Let me see. Hmm. Well, I see it as a set of uppercase letters which grow as you move to the right.
TORTOISE: Do they spell anything?
ACHILLES: Ah… “J. S. BACH.” Oh! I understand now. It’s Bach’s name!
TORTOISE: Strange that you should see it that way. I see it as a set of lower-case letters, shrinking as they move to the right, and… spelling out… the name of… (Slows down slightly, especially drawing out the last few words. Then there is a brief silence. Suddenly he resumes as if nothing unusual had happened.) — “fermat.”
ACHILLES: Oh, you’ve got Fermat on the brain, I do believe. You see Fermat’s Last Theorem everywhere.
ANTEATER: You were right, Mr. Tortoise—I just heard a charming little fermata in the fugue.
CRAB: So did I.
ACHILLES: Do you mean everybody heard it but me? I’m beginning to feel stupid.
TORTOISE: There, there, Achilles—don’t feel bad. I’m sure you won t miss Fugue’s Last Fermata (which is coming up quite soon). But, to return to our previous topic, Dr. Anteater, what is the very sad story which you alluded to, concerning the former owner of Aunt Hillary’s property?
ANTEATER: The former owner was an extraordinary individual, one of the most creative ant colonies who ever lived. His name was Johant Sebastiant Fermant, and he was a mathematiciant by vocation, but a musiciant by avocation.