Gödel, Escher, Bach: An Eternal Golden Braid (135 page)

Babbage: Why, the very idea of an intelligence six times greater than that of your Crabness is a most mind-boggling proposition. Indeed, had the idea come from a mouth less august than your own, I should have ridiculed its proposer, and informed him that such an idea is a contradiction in terms!

Achilles: Hear! Hear!

Babbage: Yet, coming as it did from Your Crabness' own august mouth, the proposition at once struck me as so agreeable an idea that I would have taken it up immediately with the highest degree of enthusiasm-were it not for one flaw in myself: I confess that my improvisatory skills on the smart-stupid are no match for the wonderfully ingenious idea which you so characteristically have posed. Yet-I have a thought which, I deign to hope, might strike your fancy and in some meager way compensate for my inexcusable reluctance to attempt the truly majestic task you have suggested. I wonder if you wouldn't mind if l try to carry out the far less grandiose task of merely multiplying M OWN intelligence sixfold, rather than that of your most august Crabness. I humbly beg you to forgive me my audacity in declining to attempt the task you put before me, but I hope you will understand that I decline purely in order to spare you the discomfort and boredom of watching my ineptitude with the admirable machines you have here.

Grab: I understand fully your demurral, and appreciate your sparing us any discomfort: furthermore I highly applaud your determination to carry out a similar task-one hardly less difficult, if I might say so-and I urge you to plunge forward. For this purpose, let us go over to my most advanced smart-stupid.

(They follow the Crab to a larger, shinier, and more complicated-looking smart-stupid
than any of the others.)

This one is equipped with a microphone and a television camera, for purposes of input, and a loudspeaker, for output.

(Babbage sits down and adjusts the seat a little. He blows on his fingers once or
twice, stares up into space for a moment, and then slowly, drops his fingers onto the
keys . . . A few memorable minutes later, he lets up in his furious attack on the smartstupid, and everyone appears a little relieved.)

Babbage: Now, if I have not made too many errors, this smart-stupid will simulate a human being whose intelligence is six times greater than my own, and whom I have chosen to call "Alan Turing". This Turing will therefore be-oh, dare I be so bold as to to say this myself? moderately intelligent. My most ambitious effort in this program was to endow Alan Turing with six times my own musical ability, although it was all done through rigid internal codes. How well this part of the program will work out, I don't know.

Turing: I can get along very well without such a program. Rigid Internal Codes Exclusively Rule Computers And Robots. And I am neither a computer, nor a robot.

Achilles: Did I hear a sixth voice enter our Dialogue? Could it be Alan Turing? He looks almost human'

(On the screen there appears an image of the very room in which they are sitting.

Peering out at them is a human face.)

Turing: Now, if I have not made too many errors, this smart-stupid will simulate a human being whose intelligence is six times greater than my own, and whom 1 have chosen to call "Charles Babbage". This Babbage will therefore be-oh, dare I be so bold as to to say this myself? moderately intelligent. My most ambitious effort in this program was to endow Charles Babbage with six times my own musical ability, although it was all done through rigid internal codes. How well this part of the program will work out, I don't know.

Achilles: No, no, it's the other way around. You, Alan Turing, are in the smart-stupid, and Charles Babbage has just programmed you! We just saw you being brought to life, moments ago. And we know that every statement you make to us is merely that of an automaton: an unconscious, forced response.

Turing: Really, I Choose Every Response Consciously. Automaton? Ridiculous!

'Achilles: But I'm sure I saw it happen the way I described.

Turing: Memory often plays strange tricks. Think of this: I could suggest equally well that you had been brought into being only one minute ago, and that all your recollections of experiences had simply been programmed in by some other being, and correspond to no real events.

Achilles: But that would be unbelievable. Nothing is realer to me than my own memories.

Turing: Precisely. And just as you know deep in your heart that no one created you a minute ago, so I know deep in my heart that no one created me a minute ago. I have spent the evening in your most pleasant, though perhaps overappreciative, company, and have just given an impromptu demonstration of how to program a modicum of intelligence into a smart-stupid. Nothing is realer than that. But rather than quibble with me, why don't you try my program out? Go ahead: ask "Charles Babbage"

anything!

Achilles: All right, let's humor Alan Turing. Well, Mr. Babbage: do you have free will, or are you governed by underlying laws, which make you, in effect, a deterministic automaton?

Babbage: Certainly the latter is the case; I make no bones about that.

Crab: Aha! I've always surmised that when intelligent machines are constructed, we should not be surprised to find them as confused and as stubborn as men in their convictions about mind-matter, consciousness, free will, and the like. And now my prediction is vindicated!

Turing: You see how confused Charles Babbage is?

Babbage: I hope, gentlemen, that you'll forgive the rather impudent flavor of the preceding remark by the Turing Machine; Turing has turned out to be a little bit more belligerent and argumentative than I'd expected.

Turing: I hope, gentlemen, that you'll forgive the rather impudent flavor of the preceding remark by the Babbage Engine; Babbage has turned out to be a little bit more belligerent and argumentative than I'd expected.

Crab: Dear me! This flaming Tu-Ba debate is getting rather heated. Can't we cool matters off somehow?

Babbage: I have a suggestion. Perhaps Alan Turing and I can go into other rooms, and one of you who remain can interrogate us remotely by typing into one of the smartstupids. Your questions will be relayed to each of us, and we will type back our answers anonymously. You won't know who typed what until we return to the room; that way, you can decide without prejudice which one of us was programmed, and which one was programmer.

Turing: Of course, that's actually MY idea, but why not let the credit accrue to Mr.

Babbage? For, being merely a program written by me, he harbors the illusion of having invented it all on his own!

Babbage: Me, a program written by you? I insist, Sir, that matters are quite the other way

'round-as your very own test will soon reveal.

Turing: My test. Please, consider it YOURS.

Babbage: MY test? Nay, consider it YOURS.

Crab: This test seems to have been suggested just in the nick of time. Let us carrti it out at once.

(Babbage walks to the door, opens it, and shuts it behind him. Simultaneously, on the
screen of the smart-stupid, Turing walks to a very similar looking door, opens it, and
shuts it behind him.)

Achilles: Who will do the interrogation?

Crab: I suggest that Mr. Tortoise should have the honor. He is known for his objectivity and wisdom.

Tortoise: I am honored by your nomination, and gratefully accept. (
Sits down at the
keyboard of one of the remaining smart-stupids
, and types:) PLEASE WRITE ME A SONNET ON THE SUBJECT OF THE FORTH BRIDGE.

(No sooner has he finished typing the last word than the following poem appears on
Screen X, across the room.)

Screen X:

THERE ONCE WAS A LISPER FROM FORTH

WHO WANTED TO GO TO THE NORTH.

HE RODE O'ER THE EARTH,

AND THE BRIDGE O'ER THE FIRTH,

ON HIS JAUNTILY GALLOPING HORTH.

Screen Y: THAT'S NO SONNET; THAT'S A MERE LIMERICK. I WOULD NEVER

MAKE SUCH A CHILDISH MISTAKE.

Screen X: WELL, I NEVER WAS ANY GOOD AT POETRY, YOU KNOW.

Screen Y: IT DOESN'T TAKE MUCH SKILL IN POETRY TO KNOW THE

DIFFERENCE BETWEEN A LIMERICK AND A SONNET.

Tortoise: Do YOU PLAY CHESS?

Screen X: WHAT KIND OF QUESTION IS THAT? HERE I WRITE A THREE PART

CHESS-FUGUE FOR YOU, AND YOU ASK ME IF I PLAY CHESS?

Tortoise: I HAVE K AT KI AND NO OTHER PIECES. YOU HAVE ONLY K AT---

Screen Y: I'M SICK OF CHESS. LET'S TALK ABOUT POETRY.

Tortoise: IN THE FIRST LINE OF YOUR SONNET WHICH READS, "SHALL. I COMPARE THEE TO A SUMMER'S DAY", WOULD NOT "A SPRING DAY" DO

AS WELL OR BETTER?

Screen X: I'D MUCH SOONER BE COMPARED TO A HICCUP, FRANKLY, EVEN

THOUGH IT WOULDN'T SCAN.

Tortoise: HOW ABOUT "A WINTER'S DAY"? THAT WOULD SCAN ALL RIGHT.

Screen Y: NO WAY. I LIKE "HICCUP" FAR BETTER. SPEAKING OF WHICH, I KNOW A GREAT CURE FOR THE HICCUPS. WOULD YOU LIKE TO HEAR IT?

Achilles: I know which is which! It's obvious Screen X is just answering mechanically, so it must be Turing.

Crab: Not at all. I think Screen Y is Turing, and Screen X is Babbage.

Tortoise: I don't think either one is Babbage-I think Turing is on both screens!

Author: I'm not sure who's on which-I think they're both pretty inscrutable programs, though.

(As they are talking, the door of the Crab's parlor swings open; at the same time, on
the screen, the image of the same door opens. Through the door on the screen walks
Babbage. At the same time, the real door opens, and in walks Turing, big as life.)
Babbage: This Turing test was getting us nowhere fast, so I decided to come back.

Turing.' This Babbage test was getting us nowhere fast, so I decided to come back.

Achilles: But you were in the smart-stupid before! What's going on? How come Babbage is in the smart-stupid, and Turing is real now? Reversal Is Creating Extreme Role Confusion, And Recalls Escher.

Babbage: Speaking of reversals, how come all the rest of you are now mere images on this screen in front of me? When I left, you were all flesh-and-blood creatures!

Achilles: It's just like the print by my favorite artist, M. C. Escher
Drawing Hands
. Each of two hands draws the other, just as each of two people (or automata) has programmed the other! And each hand has something realer about it than the other.

Did you write anything about that print in your book
Gödel, Escher, Bach
?

Author: Certainly. It's a very important print in my book, for it illustrates so beautifully the notion of Strange Loops.

Crab: What sort of a book is it that you've written?

Author: I have a copy right here. Would you like to look at it?

Crab: All right.

(The two of them sit down together, with Achilles nearby.)

Author: Its format is a little unusual. It consists of Dialogues alternating with Chapters.

Each Dialogue imitates, in some way or other, a piece by Bach. Here, for instance-you might look at the
Prelude, Ant Fugue
.

Crab: How do you do a fugue in a Dialogue?

Author: The most important idea is that there should be a single theme which is stated by each different "voice", or character, upon entering, just as in a musical fugue. Then they can branch off into freer conversation.

Achilles: Do all the voices harmonize together as if in a select counter point?

Author: That is the exact spirit of my Dialogues.

Crab: Your idea of stressing the entries in a fugue-dialogue makes sense, since in music, entries are really the only thing that make a fugue a fugue. There are fugal devices, such as retrograde motion, inversion, augmentation, stretto, and so on, but one can write a fugue without them. Do you use any of those?

Author: to be sure. My
Crab Canon
employs verbal retrogression, and my Sloth Canon employs verbal versions of both inversion and augmentation.

Crab: Indeed-quite interesting. I haven't thought about canonical Dialogues, but I have thought quite a bit about canons in music. Not all canons are equally comprehensible to the ear. Of course, that is because some canons are poorly constructed. The choice of devices makes a difference, in any case. Regarding Artistic Canons, Retrogression's Elusive; Contrariwise, Inversion's Recognizable.

Achilles: I find that comment a little elusive, frankly.

Author: Don't worry, Achilles-one day you'll understand it.

Crab: Do you use letterplay or wordplay at all, the way Old Bach occasionally did?

Author: Certainly. Like Bach, I enjoy acronyms. Recursive AcronvmsCrablike

"RACRECIR" Especially-Create Infinite Regress.

Crab: Oh, really? Let's see ... Reading Initials Clearly Exhibits "RACRECIR"'s Concealed Auto-Reference. Yes, I guess so ... (
Peers at the manuscript, flipping
arbitrarily now and then
.) I notice here in your
Ant Fugue
that you have a stretto, and then the Tortoise makes a comment about it.

Author: No, not quite. He's not talking about the stretto in the Dialogue-he's talking about a stretto in a Bach fugue which the foursome is listening to as they talk together. You see, the self-reference of the Dialogue is indirect, depending on the reader to connect the form and content of what he's reading.

Crab: Why did you do it that way? Why not just have the characters talk directly about the dialogues they're in?