Contracrostipunctus by Douglas Hofstadter (from Gödel, Escher, Bach: an Eternal Golden Braid)
note: if you like this dialogue, go buy the book! This transcription lacks the typography in the book that reveals exquisite hidden meanings and structure. Nevertheless, you'll notice still plenty of different levels of meaning in this entertaining story about records invented to break record players!
Achilles has come to visit his friend and jogging
companion, the Tortoise, at his home
Achilles: Heavens, you certainly have an admirable boomerang collection
Tortoise: Oh, pshaw. No better than that of any other Tortoise. And now would you like
to step into the parlor?
Achilles: Fine. (Walks to the corner of the room.) I see you also have a large collection of
records. What sort of music do you enjoy?
Tortoise: Sebastian Bach isn't so bad, in my opinion. But these days, I must say, I am
developing more and more of an interest in a rather specialized sort of music.
Achilles: Tell me, what kind of music is that?
Tortoise: A type of music which you are most unlikely to have heard of. I call it "music to
break phonographs by".
Achilles: Did you say "to break phonographs by"? That is a curious concept. I can just
see you, sledgehammer in hand, whacking on phonograph after another to pieces,
to the strains of Beethoven's heroic masterpiece Wellington's Victory.
Tortoise: That's not quite what this music is about. However, you might find its true
nature just as intriguing. Perhaps I should give you a brief description of it?
Achilles: Exactly what I was thinking.
Tortoise: Relatively few people are acquainted with it. It all began when my friend the
Crab-have you met him, by the way?-paid me a visit.
Achilles: ' twould be a pleasure to make his acquaintance, I'm sure. Though I've heard so
much about him, I've never met him
Tortoise: Sooner or later I'll get the two of you together. You'd hit it off splendidly.
Perhaps we could meet at random in the park one day ...
Achilles: Capital suggestion! I'll be looking forward to it. But you were going to tell me
about your weird "music to smash phonographs by", weren't you?
Tortoise: Oh, yes. Well, you see, the Crab came over to visit one day. You must
understand that he's always had a weakness for fancy gadgets, and at that time he
was quite an aficionado for, of al things, record players. He had just bought his
first record player, and being somewhat gullible, believed every word the
salesman had told him about it-in particular, that it was capable of reproducing
any and all sounds. In short, he was convinced that it was a Perfect phonograph.
Achilles: Naturally, I suppose you disagreed.
Tortoise: True, but he would hear nothing of my arguments. He staunchly maintained that
any sound whatever was reproducible on his machine. Since I couldn't convince
him of the contrary, I left it at that. But not long after that, I returned the visit,
taking with me a record of a song which I had myself composed. The song was
called "I Cannot Be Played on Record Player 1".
Achilles: Rather unusual. Was it a present for the Crab?
Tortoise: Absolutely. I suggested that we listen to it on his new phonograph, and he was
very glad to oblige me. So he put it on. But unfortunately, after only a few notes,
the record player began vibrating rather severely, and then with a loud "pop",
broke into a large number of fairly small pieces, scattered all about the room. The
record was utterly destroyed also, needless to say.
Achilles: Calamitous blow for the poor fellow, I'd say. What was the matter with his
Tortoise: Really, there was nothing the matter, nothing at all. It simply couldn't reproduce
the sounds on the record which I had brought him, because they were sounds that
would make it vibrate and break.
Achilles: Odd, isn't it? I mean, I thought it was a Perfect phonograph. That's what the
salesman had told him, after all.
Tortoise: Surely, Achilles, you don't believe everything that salesmen tell you! Are you
as naive as the Crab was?
Achilles: The Crab was naiver by far! I know that salesmen are notorious prevaricators. I
wasn't born yesterday!
Tortoise: In that case, maybe you can imagine that this particular salesman had somewhat
exaggerated the quality of the Crab's piece of equipment ... perhaps it was indeed
less than Perfect, and could not reproduce every possible sound.
Achilles: Perhaps that is an explanation. But there's no explanation for the amazing
coincidence that your record had those very sounds on it ...
Tortoise: Unless they got put there deliberately. You see, before returning the Crab's
visit, I went to the store where the Crab had bought his machine, and inquired as
to the make. Having ascertained that, I sent off to the manufacturers for a
description of its design. After receiving that by return mail, I analyzed the entire
construction of the phonograph and discovered a certain set of sounds which, if
they were produced anywhere in the vicinity, would set the device to shaking and
eventually to falling apart.
Achilles: Nasty fellow! You needn't spell out for me the last details: that you recorded
those sounds yourself, and offered the dastardly item as a gift ...
Tortoise: Clever devil! You jumped ahead of the story! But that wasn't the end of the
adventure, by any means, for the Crab did r believe that his record player was at
fault. He was quite stubborn. So he went out and bought a new record player, this
one even more expensive, and this time the salesman promised give him double his
money back in case the Crab found a song which it could not reproduce exactly.
So the Crab told me excitedly about his new model, and I promised to come over
and see it.
Achilles: Tell me if I'm wrong-I bet that before you did so, you once again wrote the
manufacturer, and composed and recorded a new song called "I Cannot Be Played
on Record Player 2", based on the construction of the new model.
Tortoise: Utterly brilliant deduction, Achilles. You've quite got the spirit.
Achilles: So what happened this time?
Tortoise: As you might expect, precisely the same thing. The phonograph fell into
innumerable pieces, and the record was shattered.
Achilles: Consequently, the Crab finally became convinced that there can
be no such thing as a Perfect record player.
Tortoise: Rather surprisingly, that's not quite what happened. He was sure that the next
model up would fill the bill, and having twice the money, he--
Achilles: Oho—I have an idea! He could have easily outwitted you, by obtaining a LOW fidelity
phonograph-one that was not capable of reproducing the sounds which
would destroy it. In that way, he would avoid your trick.
Tortoise: Surely, but that would defeat the-original purpose-namely, to have a
phonograph which could reproduce any sound whatsoever, even its own selfbreaking
sound, which is of course impossible.
Achilles: That's true. I see the dilemma now. If any record player—say
Record Player X—is sufficiently high-fidelity, then when it attempts to play the song "I
Cannot Be Played on Record Player X", it will create just those vibrations which
will cause it to break. .. So it fails to be Perfect. And yet, the only way to get around
that trickery, namely for Record Player X to be of lower fidelity, even more
directly ensures that it is not Perfect. It seems that every record player is
vulnerable to one or the other of these frailties, and hence all record players are
Tortoise: I don't see why you call them "defective". It is simply an inherent fact about
record players that they can't do all that you might wish them to be able to do. But
if there is a defect anywhere, it is not in THEM, but in your expectations of what
they should b able to do! And the Crab was just full of such unrealistic
Achilles: Compassion for the Crab overwhelms me. High fidelity or low fidelity, he loses
Tortoise: And so, our little game went on like this for a few more rounds, and
eventually our friend tried to become very smart. He got wind of the principle
upon which I was basing my own records, and decided to try to outfox me. He
wrote to the phonograph makers, and described a device of his own invention,
which they built to specification. He called it "Record Player Omega". It was
considerably more sophisticated than an ordinary record player.
Achilles: Let me guess how: Did it have no moving parts. Or was it made of cotton? Or—
Tortoise: Let me tell you, instead. That will save some time. In the first place, Record
Player Omega incorporated a television camera whose purpose it was to scan any
record before playing it. This camera was hooked up to a small built-in computer,
which would determine exactly the nature of the sounds, by looking at the groovepatterns.
Achilles: Yes, so far so good. But what could Record Player Omega do with this
Tortoise: By elaborate calculations, its little computer figured out what effects the sounds
would have upon its phonograph. If it deduced that the sounds were such that they
would cause the machine in its present configuration to break, then it did
something very clever. Old Omega contained a device which could disassemble
large parts of its phonograph subunit, and rebuild them in new ways, so that it
could, in effect, change its own structure. If the sounds were "dangerous", a new
configuration was chosen, one to which the sounds would pose no threat, and this
new configuration would then be built by the rebuilding subunit, under direction
of the little computer. Only after this rebuilding operation would Record Player
Omega attempt to play the record.
Achilles: Aha! That must have spelled the end of your tricks. I bet you were a little
Tortoise: Curious that you should think so ... I don't suppose that you know Godel's
Incompleteness Theorem backwards and forwards, do you?
Achilles: Know WHOSE Theorem backwards and forwards? I've never
heard of anything that sounds like that. I'm sure it's fascinating, but I'd rather hear more
about "music to break records by". It's an amusing little story. Actually, I guess I
can fill in the end. Obviously, there was no point in going on, and so you
sheepishly admitted defeat, and that was that. Isn't that exactly it?
Tortoise: What! It's almost midnight! I'm afraid it's my bedtime. I'd love to talk some
more, but really I am growing quite sleepy.
Achilles: As am 1. Well, I'll be on my way. (As he reaches the door, he suddenly stops,
and turns around.) Oh, how silly of me! I almost forgot. I brought you a little
present. Here. (Hands the Tortoise a small neatly wrapped package.)
Tortoise: Really, you shouldn't have! Why, thank you very much indeed think I'll open it
now. (Eagerly tears open the package, and inside discovers a glass goblet.) Oh, what
an exquisite goblet! Did you know that I am quite an aficionado for, of all things, glass
Achilles: Didn't have the foggiest. What an agreeable coincidence!
Tortoise: Say, if you can keep a secret, I'll let you in on something: I'm trying to find a
Perfect goblet: one having no defects of a sort in its shape. Wouldn't it be
something if this goblet-let's call it "G"-were the one? Tell me, where did you come
across Goblet G?
Achilles: Sorry, but that's MY little secret. But you might like to know who its maker is.
Tortoise: Pray tell, who is it?
Achilles: Ever hear of the famous glassblower Johann Sebastian Bach? Well, he wasn't
exactly famous for glassblowing-but he dabbled at the art as a hobby, though
hardly a soul knows it-and this goblet is the last piece he blew.
Tortoise: Literally his last one? My gracious. If it truly was made by Bach its value is
inestimable. But how are you sure of its maker?
Achilles: Look at the inscription on the inside-do you see where the letters `B', `A', `C', `H'
have been etched?
Tortoise: Sure enough! What an extraordinary thing. (Gently sets Goblet G down on a
shelf.) By the way, did you know that each of the four letters in Bach's name is
the name of a musical note?
Achilles:' tisn't possible, is it? After all, musical notes only go from ‘A’ through `G'.
Tortoise: Just so; in most countries, that's the case. But in Germany, Bach’s own
homeland, the convention has always been similar, except that what we call `B',
they call `H', and what we call `B-flat', they call `B'. For instance, we talk about
Bach's "Mass in B Minor whereas they talk about his "H-moll Messe". Is that
Achilles: ... hmm ... I guess so. It's a little confusing: H is B, and B B-flat. I suppose
his name actually constitutes a melody, then.
Tortoise: Strange but true. In fact, he worked that melody subtly into one of his most
elaborate musical pieces-namely, the final Contrapunctus in his Art of the Fugue.
It was the last fugue Bach ever wrote. When I heard it for the first time, I had no
idea how it would end. Suddenly, without warning, it broke off. And then ... dead
silence. I realized immediately that was where Bach died. It is an indescribably
sad moment, and the effect it had on me was-shattering. In any case, B-A-C-H is
the last theme c that fugue. It is hidden inside the piece. Bach didn't point it out
explicitly, but if you know about it, you can find it without much trouble. Ah, me-there
are so many clever ways of hiding things in music .. .
Achilles: . . or in poems. Poets used to do very similar things, you know (though it's
rather out of style these days). For instance, Lewis Carroll often hid words and
names in the first letters (or characters) of the successive lines in poems he wrote.
Poems which conceal messages that way are called "acrostics".
Tortoise: Bach, too, occasionally wrote acrostics, which isn't surprising. After all,
counterpoint and acrostics, with their levels of hidden meaning, have quite a bit in
common. Most acrostics, however, have only one hidden level-but there is no
reason that one couldn't make a double-decker-an acrostic on top of an acrostic.
Or one could make a "contracrostic"-where the initial letters, taken in reverse
order, form a message. Heavens! There's no end to the possibilities inherent in the
form. Moreover, it's not limited to poets; anyone could write acrostics-even a
Achilles: A dial-a-logician? That's a new one on me.
Tortoise: Correction: I said "dialogician", by which I meant a writer of dialogues. Hmm
... something just occurred to me. In the unlikely event that a dialogician should
write a contrapuntal acrostic in homage to J. S. Bach, do you suppose it would be
more proper for him to acrostically embed his OWN name-or that of Bach? Oh,
well, why worry about such frivolous matters? Anybody who wanted to write
such a piece could make up his own mind. Now getting back to Bach's melodic
name, did you know that the melody B-A-C-H, if played upside down and
backwards, is exactly the same as the original?
Achilles: How can anything be played upside down? Backwards, I can see-you get H-C-A-
B-but upside down? You must be pulling my leg.
Tortoise: ' pon my word, you're quite a skeptic, aren't you? Well, I guess I'll have to give
you a demonstration. Let me just go and fetch my fiddle- (Walks into the next
room, and returns in a jiffy with an ancient-looking violin.) -and play it for you
forwards and backwards and every which way. Let's see, now ... (Places his copy
of the Art of the Fugue on his music stand and opens it to the last page.) ... here's
the last Contrapunctus, and here's the last theme ...
The Tortoise begins to play: B-A-C- - but as he bows the final H, suddenly,
without warning, a shattering sound rudely interrupts his performance. Both
he and Achilles spin around, just in time to catch a glimpse of myriad
fragments of glass tinkling to the floor from the shelf where Goblet G had
stood, only moments before. And then ... dead silence.