Gödel, Escher, Bach: An Eternal Golden Braid (134 page)

(All at once, Babbage deftly massages the keyboard with graceful strokes, inputting
one command after another. After a few seconds, he sits back, and in almost no
time, the screen begins filling with figures. In a flash, it is totally covered with
thousands of tiny digits, the first few of which go: "3.14159265358979323846264

... ")

Achilles: Pi!

Crab: Exquisite! I'd never imagined that one could calculate so mane digits of pi so quickly, and with so tiny an algorithm. Babbage: The credit belongs exclusively to the smart-stupid. My role was

merely to see what was already potentially present in it, and to exploit its instruction set in a moderately efficient manner. Truly, anyone who practices can do such tricks.

Tortoise: Do you do any graphics, Mr. Babbage? Babbage: I can try.

Crab: Wonderful! Here, let me take you to another one of in,.- I want you to try them all!

(And so Babbage is led over to another of the many smart-stupids, and takes a seat.

Once again, his fingers attack the keyboard of the smartstupid, and in half a trice,
there appear on the screen an enormous number of lines, swinging about on the
screen.)

Crab: How harmonious and pleasing these swirling shapes are, as they constantly collide and interfere with each other!

Author: And they never repeat exactly, or even resemble ones which have come before. It seems an inexhaustible mine of beauty.

Tortoise: Some are simple patterns which enchant the eye; others are indescribably complex convolutions which boggle and yet simultaneously delight the mind.

Crab: Were you aware, Mr. Babbage, that these are color screens? Babbage: Oh, are they? In that case, I can do rather more with this algorithm. Just a moment. (
Types in a
few new commands, then pushes two keys down at once and holds them
.) As I release these two keys, the display will include all the colors of the spectrum. (
Releases them
.) Achilles: Oh, what spectacular color! Some of the patterns look like they're jumping out at me now!

Tortoise: I think that is because they are all growing in size.

Babbage: That is intentional. As the figures grow, so may the Crab's fortune.

Crab: Thank you, Mr. Babbage. Words fail to convey my admiration for your performance! Never has anyone done anything comparable on my smart-stupids. Why, you play the smart-stupids as if they were musical instruments, Mr. Babbage!

Babbage: I am afraid that any music I might make would be too harsh for the ears of such a gentle Crab as your Crab. Although I have lately become enamoured of the sweet sounds of the hurdy-gurdy, I am well aware of the grating effect they can have upon others.

Crab: Then, by all means, continue on the smart-stupids! In fact, I have a new idea-a marvelously exciting idea!

Babbage: What is it?

Crab: I have recently invented a Theme, and it only now occurred to me that, of all people, you, Mr. Babbage, are the most suited to realize the potential of my Theme!

Are you by any chance familiar with the thoughts of the philosopher La Mettrie?

Babbage: The name sounds familiar; kindly refresh my memory.

Crab: He was a Champion of Materialism. In 1747, while at the court of Frederick the Great, he wrote a book called
L'homme machine
. In it, he talks about man as a machine, especially his mental faculties. Now my Theme comes from my ponderings about the obverse side of the coin: what about imbuing a machine with human mental faculties, such as intelligence?

Babbage: I have given such matters some thought from time to time, but I have never had the proper hardware to take up the challenge. This is indeed a felicitous suggestion, Mr. Crab, and I would enjoy nothing more than working with your excellent Theme.

Tell me-did you have any specific kind of intelligence in mind?

Crab: An idle thought which had crossed my mind was to instruct it in such a manner as to play a reasonable game of chess.

Babbage: What an original suggestion! And chess happens to be my favorite pastime. I can tell that you have a broad acquaintance with computing machinery, and are no mere amateur.

Crab: I know very little, in fact. My strongest point is simply that I seem to be able to formulate Themes whose potential for being developed is beyond my own capacity.

And this Theme is my favorite.

Babbage: I shall be most delighted to try to realize, in some modest fashion, your suggestion of teaching chess to a smart-stupid. After all, to obey Your Crabness'

command is my most humble duty. (
So saying, he shifts to another of the Crab's many
smart-stupids, and begins to type away
.)

Achilles: Why, his hands move so fluidly that they almost make music!

Babbage (
winding up his performance with a particularly graceful flourish
): I really haven't had any chance, of course, to check it out, but perhaps this will allow you at least to sample the idea of playing chess against a smart-stupid- even if the latter of its two names seems more apt in this

Case, due to my own Insufficiencies in the art of instructing smart-stupids.

(He ti-ields his seat to the Crab. On the screen appears a beautiful display of a chess
board with elegant wooden pieces, as it would look from White's side. Babbage hits a
button, and the board rotates, stopping when it appears as seen from the perspective
of Black.)

Crab: Hmm ... very elegant, I must say. Do I play Black or White?

Babbage: Whichever you wish just signal your choice by typing "White" or "Black". And then, your moves can be entered in any standard chess notation. The smart-stupid's moves, of course, will appear on the board. Incidentally, I made the program in such a way that it can play three opponents simultaneously, so that if two more of you wish to play, you may, as well.

Author: I'm a miserable player. Achilles, you and Mr. T should go ahead. Achilles: No, I don't want you to be left out. I'll watch, while you and Mr. Tortoise play.

Tortoise: I don't want to play either. You two play.

Babbage: I have another suggestion. I can make two of the subprograms play against each other, in the manner of two persons who play chess together in a select chess club. Meanwhile, the third subprogram will play Mr. Crab. That way, all three internal chess players will be occupied.

Crab: That's an amusing suggestion-an internal mental game, while it combats an external opponent. Very good!

Tortoise: What else could this be called, but a three-part chess-fugue?

Crab.' Oh, how recherche! I wish I'd thought of it myself. It's a magnificent little counterpoint to contemplate whilst I pit my wits against the smart-stupid in battle.

Babbage: Perhaps we should let you play alone.

Crab: I appreciate the sentiment. While the smart-stupid and I are playing, perhaps the rest of you can amuse yourselves for a short while.

Author: I would be very happy to show Mr. Babbage around the gardens. They are certainly worth seeing, and I believe there is just enough light remaining to show them off.

Babbage: Never having seen Madstop before, I would appreciate that very much.

Crab: Excellent. Oh, Mr. T-I wonder if it wouldn't be too much of an imposition on you to ask if you might check out some of the connections on a couple of my smartstupids; they seem to be getting extraneous flashes on their screens from time to time, and I know you enjoy electronics ...

Tortoise: I should be delighted, Mr. C.

Crab: I would most highly appreciate it if you could locate the source of the trouble.

Tortoise: I'll give it a whirl.

Achilles: Personally, I'm dying for a cup of coffee. is anyone else interested? I'd be glad to fix some.

Tortoise: Sounds great to me.

Crab: A fine idea. You'll find everything you need in the kitchen.

(So the Author and Babbage leave the room together, Achilles heads for the kitchen,
the Tortoise sits down to examine the erratic smart-stupids, while the Crab and his
smart-stupid square away at each other. Perhaps a quarter of an hour passes, and
Babbage and the Author return. Babbage walks over to observe the progress of the
chess match, while the Author goes off to find Achilles.)

Babbage: The grounds are excellent! We had just enough light to see how well maintained they are. I daresay, Mr. Crab, you must be a superb gardener. Well, I hope my handiwork has amused you a little. As you most likely have guessed, I've never been much of a chess player myself, and therefore I wasn't able to give it much power.

You probably have observed all its weaknesses. I'm sure that there are very few grounds for praise, in this case

Crab: The grounds are excellent! All you need to do is look at the board, and see for yourself. There is really very little I can do. Reluctantly I've Concluded: Every Route Contains A Rout. Regrettably, I'm Checkmated; Extremely Respectable Chess Algorithm Reigns. Remarkable! It Confirms Every Rumor-Charlie's A Rip-roaring Extemporizer! Mr. Babbage, this is an unparalleled accomplishment. Well, I wonder if Mr. Tortoise has managed to uncover anything funny in the wiring of those strange-acting smart-stupids. What have you found, Mr. T?

Tortoise: The grounds are excellent! I think that the problem lies instead with the input leads. They are a little loose, which may account for the strange, sporadic, and spontaneous screen disturbances to which you have been subjected. I've fixed those wires, so you won't be troubled by that problem any more, I hope. Say, Achilles, what's the story with our coffee?

Achilles: The grounds are excellent! At least they have a delicious aroma. And everything's ready; I've set cups and spoons and whatnot over here beneath this six-sided print
Verbum
by Escher, which the Author and I were just admiring. What I find so fascinating about this particular print is that not only the figures, but also Author: The grounds are excellent! Pardon me for putting words in your mouth, Achilles, but I assure you, there were compelling esthetic reasons for doing so.

Achilles: Yes, I know. One might even say that the grounds were excellent.

Tortoise: Well, what was the outcome of the chess match?

Crab: I was defeated, fair and square. Mr. Babbage, let me congratulate you for the impressive feat which you have accomplished so gracefully and skillfully before us.

Truly, you have shown that the smart-stupids are worthy of the first part of their name, for the first time in history!

FIGURE 149.
Verbum, by M. C. Escher (lithograph, 1942).

Babbage: Such praise is hardly due me, Mr. Crab; it is rather yourself who must be most highly congratulated for having the great foresight to acquire these many fine smartstupids. Without doubt, they will someday revolutionize the science of computing.

And now, I am still at your disposal. Have you any other thoughts on how to exploit your inexhaustible Theme, perhaps of a more difficult nature than a frivolous game player?

Crab: To tell the truth, I do have another suggestion to make. From the skill which you have displayed this evening, I have no doubt that this will hardly be any more difficult than my previous suggestions.

Babbage: I am eager to hear your idea.

FIGURE 150.
The Crab's Guest: BABBAGE, C
.

Crab: It is simple: to instill in the smart-stupid an intelligence greater than any which has yet been invented, or even conceived! In short, Mr. Babbage-a smart-stupid whose intelligence is sixfold that of myself!