Gödel, Escher, Bach: An Eternal Golden Braid (115 page)

This kind of decision constantly crops up: How many levels should a system have? How much and what kind of "intelligence" should be placed on which level? These are some of the hardest problems facing
AI
today. Since we know so little about natural intelligence, it is hard for us to figure out which level of an artificially intelligent system should carry out what part of a task.

This gives you a glimpse behind the scenes of the Dialogue preceding this Chapter. Next Chapter, we shall meet new and speculative ideas for
AI
.

Contrafactus

The Crab has invited a small group of friends over to watch the Saturday
afternoon football game on television. Achilles has already arrived, but the
Tortoise and his friend the Sloth are still awaited.

Achilles: Could that be our friends, a-riding up on that unusual one-wheeled vehicle?

(The Sloth and Tortoise dismount and come in.)

Crab: Ah, my friends, I'm so glad you could make it. May I present my old and beloved acquaintance, Mr. Sloth-and this is Achilles. I believe you know the Tortoise.

Sloth: This is the first time I can recall making the acquaintance of a Bicyclops. Pleased to meet you, Achilles. I've heard many fine things said about the bicyclopean species.

Achilles: Likewise, I'm sure. May I ask about your elegant vehicle? Tortoise: Our tandem unicycle, you mean? Hardly elegant. It's just a way for two to get from A to B, at the same speed.

Sloth: It's built by a company that also makes teeter-teeters.

Achilles: I see, I see. What is that knob on it?

Sloth: That's the gearshift.

Achilles: Aha! And how many speeds does it have?

Tortoise: One, including reverse. Most models have fewer, but this is a special model.

Achilles: It looks like a very nice tandem unicycle. Oh, Mr. Crab, I wanted to tell you how much I enjoyed hearing your orchestra perform last night.

Crab: Thank you, Achilles. Were you there by any chance, Mr. Sloth? Sloth: No, I couldn't make it, I'm sad to say. I was participating in a mixed singles ping-ping tournament. It was quite exciting because my team was involved in a one-way tie for first place.

Achilles: Did you win anything?

Sloth: Certainly did-a two-sided Mobius strip made out of copper; it is silver-plated on one side, and gold-plated on the other. Crab: Congratulations, Mr. Sloth.

Sloth: Thank you. Well, do tell me about the concert.

Crab: It was a most enjoyable performance. We played some pieces by the Bach twins Sloth: The famous Job and Sebastian?

Crab: One and the same. And there was one work that made me think of you, Mr. Sloth-a marvelous piano concerto for two left hands. The

next-to-last (and only) movement was a one-voice fugue. You can't imagine its intricacies. For our finale, we played Beethoven's Ninth Zenfunny. At the end, everyone in the audience rose and clapped with one hand. It was overwhelming.

Sloth: Oh, I'm sorry I missed it. But do you suppose it's been recorded: At home I have a fine hi-fi to play it on-the best two-channel monaural system money can buy.

Crab: I'm sure you can find it somewhere. Well, my friends, the game is about to begin.

Achilles: Who is playing today, Mr. Crab?

Crab: I believe it's Home Team versus Visitors. Oh, no-that was last week. I think this week it's Out-of-Towners.

Achilles: I'm rooting for Home Team. I always do.

Sloth: Oh, how conventional. I never root for Home Team. The closer a team lives to the antipodes, the more I root for it.

Achilles: Oh, so you live in the Antipodes? I've heard it's charming to live there, but I wouldn't want to visit them. They're so far away.

Sloth: And the strange thing about them is that they don't get any closer no matter which way you travel.

Tortoise: That's my kind of place.

Crab: It's game time. I think I'll turn on the TV.

(He walks over to an enormous cabinet with a screen, underneath which is an
instrument panel as complicated as that of a jet airplane. He flicks a knob, and the
football stadium a ears in bright vivid color on the screen.)
Announcer: Good afternoon, fans. Well, it looks like that time of year has rolled around again when Home Team and Out-of-Town face each other on the gridiron and play out their classic pigskin rivalry. It's been drizzling on and off this afternoon, and the field's a little wet, but despite the weather it promises to be a fine game, especially with that GREAT pair of eighth-backs playing for Home Team, Tedzilliger and Palindromi.

And now, here's Pilipik, kicking off for Home Team. It's in the air! Flampson takes it for Out-of-Towners, and runs it back he's to the 20, the 25, the 30, and down at the 32.

That was Mool in on the tackle for Home Team.

Crab: A superb runback! Did you see how he was ALMOST tackled by Quilker-but somehow broke away?

Sloth: Oh, don't be silly, Crab. Nothing of the kind happened. Quilker did NOT tackle Flampson. There's no need to confuse poor Achilles (or the rest of us) with hocus-pocus about what "almost" happened. It's a fact-with no "almost" 's, "if "'s, "and" 's, or

"but" 's.

Announcer: Here's the instant replay. Just watch number 79, Quilker, come in from the side, surprising Flampson, and just about tackle him!

Sloth: "Just about"! Bah!

'Achilles: Such a graceful maneuver! What would we do without instant replays?

Announcer: It's first down and 10 for Out-of-Town. Noddle takes the ball, hands off to Orwix-it's a reverse-Orwix runs around to the right, handing off to Flampson-a double reverse, folks!-and now

Flampson hands it to Treefig, who's downed twelve yards behind scrimmage. A twelve-yard loss on a triple reverse!

Sloth: I love it! A sensational play!

Achilles: But, Mr. S, I thought you were rooting for Out-of-Town. They lost twelve yards on the play.

Moth: They did? Oh, well-who cares, as long as it was a beautiful play?

Let's see it again.

( ... and so the first half of the game passes. Towards the end of the third quarter, a
particularly crucial play comes up for Home Team. They are behind by eight points.

It's third down and 10, and they badly need a first down.)

Announcer: The ball is hiked to Tedzilliger, who fades back, looking-for a receiver, and fakes to Quilker. There's Palindromi, playing wide right, with nobody near him.

Tedzilliger spots him and fires a low pass to him. Palindromi snatches it out of the air, and- (
There is an audible groan from the crowd
.)--oh, he steps out of bounds! What a crushing blow for Home Team, folks! If Palindromi hadn't stepped out of bounds, he could've run all the way to the end zone for a touchdown!

Let's watch the subjunctive instant replay.

(And on the screen the same lineup appears as before.)

The ball is hiked to Tedzilliger, who fades back, looking for a receiver, and fakes to Quilker. There's Palindromi, playing wide right, with nobody near him. Tedzilliger spots him, and fires a low pass to him. Palindromi snatches it out of the air, and-

(
There is an audible gasp from the crowd.
)-he almost steps out of bounds! But he's still in bounds, and it's clear all the way to the end zone! Palindromi streaks in, for a touchdown for Home Team! (The stadium breaks into a giant roar of approval.) Well, folks, that's what would've happened if Palindromi hadn't stepped out of bounds.

Achilles: Wait a minute ... WAS there a touchdown, or WASN'T there?

Crab: Oh, no. That was just the subjunctive instant replay. They simply followed a hypothetical a little way out, you know.

Sloth: That is the most ridiculous thing I ever heard of! Next thing you know, they'll be inventing concrete earmuffs.

Tortoise: Subjunctive instant replays are a little unusual, aren't they?

Crab: Not particularly, if you have a Subjunc-TV.

Achilles: Is that one grade below a junk TV?

Crab: Not at all! It's a new kind of TV, which can go into the subjunctive mode. They're particularly good for football games and such. I just got mine.

Achilles: Why does it have so many knobs and fancy dials?

Crab: So that you can tune it to the proper channel. There are many channels broadcasting in the subjunctive mode, and you want to be able to select from them easily.

Achilles: Could you show us what you mean? I'm afraid I don't quite understand what all this talk of "broadcasting in the subjunctive mode" is about.

Crab: Oh, it's quite simple, really. You can figure it out yourself. I'm going into the kitchen to fix some French fries, which I know are Mr. Sloth's weakness.

Sloth: Mmmmm! Go to it, Crab! French fries are my favorite food. Crab: What about the rest of you?

Tortoise: I could devour a few.

Achilles: Likewise. But wait-before you go into the kitchen, is there some trick to using your Subjunc-TV?

Crab: Not particularly. Just continue watching the game. and whenever there's a near miss of some sort, or whenever you wish things had gone differently in some way, just fiddle with the dials, and see what happens. You can't do it any harm, though you may pick up some exotic channels. (
And he disappears into the kitchen
.) Achilles: I wonder what he means by that. Oh well, let's get back to this game. I was quite wrapped up in it.

Announcer: It's fourth down for Out-of-Town, with Home Team receiving. Out-of-Town is in punt formation, with Tedzilliger playing deep. Orwix is back to kick-and he gets a long high one away. It's coming down near Tedzilliger

Achilles: Grab it, Tedzilliger! Give those Out-of-Towners a run for their money!

Announcer: -and lands in a puddle-KERSPLOSH! It takes a weird bounce! Now Sprunk is madly scrambling for the ball! It looks like it just barely grazed Tedzilliger on the bounce, and then slipped away from himit's ruled a fumble. The referee is signaling that the formidable Sprunk has recovered for Out-of-Town on the Home Team 7! It's a bad break for Home Team. Oh, well, that's the way the cookie crumbles.

Achilles: Oh, no! If only it hadn't been raining ... (
Wrings his hands in despair
.) Sloth: ANOTHER of those confounded hypotheticals! Why are the rest of you always running off into your absurd worlds of fantasy? If I were you, I would stay firmly grounded in reality. "No subjunctive nonsense" is my motto. And I wouldn't abandon it even if someone offered me a hundred-nay, a hundred and twelve-French fries.

Achilles: Say, that gives me an idea. Maybe by suitably fiddling with these knobs, I can conjure up a subjunctive instant replay in which it isn't raining, there's no puddle, no weird bounce, and Tedzilliger doesn't

fumble. I wonder ... (
Walks up to the Subjunc-TV and stares at it.)
But I haven't any idea what these different knobs do. (
Spins a few at random
.)

Announcer: It's fourth down for Out-of-Town, with Home Team receiving. Out-of-Town is in punt formation, with Tedzilliger playing deep. Orwix is back to kick-and he gets a long high one away. It's coming down near Tedzilliger Achilles: Grab it, Tedzilliger! Give those Out-of-Towners a run for their money!

Announcer: -and lands in a puddle-KERSPLOSH! Oh-it bounces right into his arms!

Now Sprunk is madly scrambling after him, but he's got - good blocking, and he steers his way clear of the formidable Sprunk, and now he's got an open field ahead of him.

Look at that, folks! He's to the 50, the 40, the 30, the 20, the 10-touchdown, Home Team! (
Huge cheers from the Home Team side
.) Well, fans, that's how it would have gone, if footballs were spheres instead of oblate spheroids! But in reality, Home Team loses the ball, and Out-of-Towners take over on the Home Team 7-yard line. Oh, well, that's the way the ball bounces.

Achilles: What do you think of THAT, Mr. Sloth?

(And Achilles gives a smirk in the direction of the Sloth, but the latter is completely
oblivious to its devastating effect, as he is busy watching ,the Crab arrive with, a large
platter with a hundred and twelve-nay, a hundred-large and delicious French fries,
and napkins for all.)

Crab: So how do you three find my Subjunc-TV?

Sloth: Most disappointing, Crab, to be quite frank. It seems to be badly out of order. It makes pointless excursions into nonsense at least half the time. If it belonged to me, I would give it away immediately to someone like you, Crab. But of course it doesn't belong to me.

Achilles: It's quite a strange device. I tried to rerun a play to see how it would have gone under different weather conditions, but the thing seems to have a will of its own!

Instead of changing the weather, it changed the football shape to ROUND instead of FOOTBALL-SHAPED! Now tell me-how can a football not be shaped like a football?

That's a contradiction in terms. How preposterous!

Crab: Such tame games! I thought you'd surely find more interesting subjunctives. How would you like to see how the last play would have looked if the game had been baseball instead of football?

Tortoise: Oh! An outstanding idea!

(The Crab twiddles two knobs, and steps back.)

Announcer: There are four away, and---

Achilles: FOUR away!?

Announcer: That's right, fans-four away. When you turn football into baseball, SOMETHING'S got to give! Now as I was about to say, there are four away, with Out-of-Town in the field, and Home Team up. Tedzilliger is at bat. Out-of-Town is in bunt formation. Orwix raises his arm to pitch-and he gets a long high ball away. It's heading straight for Tedzilliger

Achilles: Smash it, Tedzilliger! Give those Out-of-Towners a home run for their money!

Announcer: -but it seems to be a spitball, as it takes a strange curve. Now Sprunk is madly scrambling for the ball! It looks like it just barely grazed Tedzilliger's bat, then bounced off it-it's ruled a fly ball. The umpire is signaling that the formidable Sprunk has caught it for Out-of-Town, to end the seventh inning. It's a bad break for Home Team. That's how the last play would have looked, football fans, if this had been a game of baseball.