…what the accompaniment is supposed to sound like? 🙂
Its atomic view of the mind and intelligence may have been disputed and displaced, but Godel, Escher, Bach: The Eternal Golden Braid by Douglas Hofstadter is sheer pleasure to read, from whatever little I have read from it. Its elusively simple and amazingly well-written but the book mimics its contents (on life, nature and the mind) on multiple levels in achieving its (their) intriguing elusiveness. What better way to explain meaning than by creating it? No wonder the book won a Pulitzer! A friend summed it up best when I was trying to explain what the book is about to him.
“Its a very simple idea basically, but you have to be a genius to understand its simplicity” category pola
I am reproducing here an excerpt for everyone’s pleasure. It is titled Sonata for Unaccompanied Achilles. This excerpt and similar dialogues throughout the book, refer to the Achilles and Tortoise paradox by Zeno of Elea.
Art referred to in the excerpt: Sonata for Unaccompanied Violin by Bach & Mosaic II by Martin Escher.
இப்போ, யாம் பெற்ற இன்பம்!
Sonata for Unaccompanied Achilles
The telephone rings; Achilles picks it up.
Achilles: Hello, this is Achilles.
Achilles: Oh, hello, Mr.T. How are you?
Achilles: A torticollis? Oh, I am sorry to hear it. Do you have any idea what caused it?
Achilles: How long did you hold it in that position?
Achilles: Well, no wonder it’s stiff, then. What on earth induced you to keep your neck twisted that way for so long?
Achilles: Wondrous many of them, eh? What kinds, for example?
Achilles: What do you mean, “phantasmagorical beasts”?
Achilles: Wasn’t it terrifying to see so many of them at the same time?
Achilles: A guitar!? Of all things to be in the midst of all those weird creatures. Say, don’t you play the guitar?
Achilles: Oh, well, its all the same to me.
Achilles: You’re right; I wonder why I never noticed that difference between fiddles and guitars before. Speaking of fiddling, how would you like to come over and listen to one of the sonatas for unaccompanied violin by your favorite composer, J.S. Bach? I just bought a marvelous recording of them. I still can’t get over the way Bach uses a single violin to create a piece with such interest.
Achilles: A headache too? That’s a shame. Perhaps you should just go to bed.
Achilles: I see. Have you tried counting sheep?
Achilles: Oh, oh, I see. Yes, I fully know what you mean. Well, if it’s THAT distracting, perhaps you’d better tell it to me, and let me try to work on it, too.
Achilles: A word with the letter ‘A’, ‘D’, ‘A’, ‘C’ consecutively inside it… Hmm… What about “abracadabra”?
Achilles: True, “ADAC” occurs backwards, not forwards, in that word.
Achilles: Hours and hours? It sounds like I’m in for a long puzzle, then. Where did you hear this infernal riddle?
Achilles: You mean he looked like he was meditating on esoteric Buddhist matters, but in reality he was just trying think up complex word puzzles?
Achilles: Aha! – the snail knew what this fellow was upto. But how did you come to talk to the snail?
Achilles: Say, I once heard a word puzzle a bit like this one. Do you want to hear it? Or would it just drive you further into distraction?
Achilles: I agree — can’t do any harm. Here it is: What’s a word that begins with the letters “HE” and also ends with “HE”?
Achilles: Very ingenious — but that’s almost cheating. It’s certainly not what I mean!
Achilles: Ofcourse you’re right — it fulfills the conditions, but it’s a sort of “degenerate” solution. There’s another solution that I had in mind.
Achilles: That’s exactly it! How did you come up with it so fast?
Achilles: So here’s a case where having a headache might actually have helped you, rather than hindering you. Excellent! But I am still in the dark on your “ADAC” puzzle.
Achilles: Congratulations! Now maybe you’ll be able to get sleep! So tell me, what IS the solution?
Achilles: Well, normally I don’t like hints, but all right. What’s your hint?
Achilles: I don’t what you mean by “figure” and “ground” in this case.
Achilles: Certainly I know Mosaic II! I know ALL of Escher’s works. After all, he’s my favorite artist. In any case, I’ve got a print of Mosaic II hanging on my wall, in plain view from here.
Achilles: Yes, I see all the black animals.
Achilles: Yes, I also see how their “negative space” — what’s left out — defines the white animals.
Achilles: So THAT’s what you mean by “figure” and “ground”. But what does that have to do with the “ADAC” puzzle?
Achilles: Oh, this is too tricky for me. I think I’M starting to get a headache.
Achilles: You want to come over now? But I thought —
Achilles: Very well. Perhaps by then I’ll have thought of the right answer to YOUR puzzle, using your figure-ground hint, relating it to MY puzzle.
Achilles: I’d love to play them for you.
Achilles: You’ve invented a theory about them?
Achilles: Accompanied by what instrument?
Achilles: Well, if that’s the case, it seems a little strange that he wouldn’t have written out the harpischord part, then, and had it published as well.
Achilles: I see — sort of an optional feature. One could listen to them either way — with or without accompaniment. But how would one know what the accompaniment is supposed to sound like?
Achilles: Ah, yes, I guess that it is best, after all, to leave it to the listener’s imagination. And perhaps, as you said, Bach never even had any accompaniment in mind at all. Those sonatas seem to work very well indeed as they are.
Achilles: Right. Well, I’ll see you shortly.
Achilles: Good-bye, Mr.T.