Gödel, Escher, Bach: An Eternal Golden Braid (23 page)

(And so saying, the Genie picks up the Lamp, and stuffs it into a pocket concealed among the folds of his long ghostly robe which swirls out of the Lamp.)

As a sign of gratitude for your heroic deed, I would like to offer you, on the part of my Lamp, the opportunity to have any three of your wishes realized.

Achilles: How stupefying! Don't you think so, Mr. T?

Tortoise: I surely do. Go ahead, Achilles, take the first wish.

Achilles: Wow! But what should I wish? Oh, I know! It's what I thought of the first time I read the Arabian Nights (that collection of silly (and nested) tales)-I wish that I had a HUNDRED wishes, instead of just three! Pretty clever, eh, Mr. T? I bet YOU never would have thought of that trick. I always wondered why those dopey people in the stories never tried it themselves.

Tortoise: Maybe now you'll find out the answer.

Genie: I am sorry, Achilles, but I don't grant metawishes.

Achilles: I wish you'd tell me what a "meta-wish" is!

Genie: But THAT is a meta-meta-wish, Achilles-and I don't grant them, either. Achilles: Whaaat? I don't follow you at all.

Tortoise: Why don't you rephrase your last request, Achilles?

Achilles: What do you mean? Why should I?

Tortoise: Well, you began by saying "I wish". Since you're just asking for information, why don't you just ask a question?

Achilles: All right, though I don't see why. Tell me, Mr. Genie-what is a meta-wish? Genie: It is simply a wish about wishes. I am not allowed to grant meta-wishes. It is only within my purview to grant plain ordinary wishes, such as wishing for ten bottles of beer, to have Helen of Troy on a blanket, or to have an all-expenses-paid weekend for two at the Copacabana. You know-simple things like that. But metawishes I cannot grant. GOD won't permit me to.

Achilles: GOD? Who is GOD? And why won't he let you grant meta-wishes?

That seems like such a puny thing compared to the others you mentioned.

Genie: Well, it’s a complicated matter, you see. Why don’t you just go ahead and make your three wishes? Or at least make one of them. I don't have all I time in the world, you know ...

Achilles: Oh, I feel so rotten. I was REALLY HOPING wish for a hundred wishes ...

Genie: Gee, I hate to see anybody so disappointed that. And besides, metawishes are my favorite k of wish. Let me just see if there isn't anything I do about this. This'll just take one moment

(The Genie removes from the wispy folds of his robe an object which looks
just like the copper Lamp he had put away, except that this one is made of
silver; and where the previous one had 'L' etched on it, this one has 'ML' in
smaller letters, so as to cover the same area.)

I

Achilles: And what is that?

Genie: This is my Meta-Lamp ...

(He rubs the Meta-Lamp, and a huge puff of smoke appears. In the billows
of smoke, they can all make out a ghostly form towering above them.)
Meta-Genie: I am the Meta-Genie. You summoned me, 0 Genie? What is your wish?

Genie: I have a special wish to make of you, 0 Djinn and of GOD. I wish for permission for tempos suspension of all type-restrictions on wishes, for duration of one Typeless Wish. Could you ph grant this wish for me?

Meta-Genie: I'll have to send it through Channels, of course. One half a moment, please

(And, twice as quickly as the Genie did, this Meta-Genie removes from the
wispy folds of her robe an object which looks just like the silver MetaLamp, except that it is made of gold; and where the previous one had 'ML'

etched on it, this one has 'MML' in smaller letters, so as to cover the same
area.)

Achilles (
his voice an octave higher than before
): And what is that? MetaGenie: This is my Meta-Meta-Lamp. . .

(She rubs the Meta-Meta-Lamp, and a hugs puff of smoke appears. In the
billows o smoke, they can all make out a ghostly fore towering above
them.)

Meta-Meta-Genie: I am the MetaMeta-Genie. You summoned me,

0 Meta-Genie? What is your wish?

Meta-Genie: I have a special wish to make of you, 0 Djinn, and of GOD. I wish for permission for temporary suspension of all type-restrictions on wishes, for the duration of one Typeless Wish. Could you please grant this wish for me?

Meta-Meta-Genie: I'll have to send it through Channels, of course.

One quarter of a moment, please.

(And, twice as quickly as the Meta-Genie did, this MetaMetaGenie removes from the folds of his robe an object which looks

just like the gold MetaLamp, except that it is made of ...)

.

.

.

.

.

. .
{GOD}

.

.

.

.

( ... swirls back into the MetaMeta-Meta-Lamp, which the Meta-

Meta-Genie then folds back into his robe, half as quickly as the Meta-Meta-Meta-Genie did.)

Your wish is granted, 0 MetaGenie.

Meta-Genie: Thank you, 0 Djinn, and GOD.

(And the Meta-Meta-Genie, as all the higher ones before him, swirls
back into the Meta-Meta-Lamp, which the Meta-Genie then folds back
into her robe, half as quickly as the Meta-Meta-Genie did.)

Your wish is granted, 0 Genie.

Genie: Thank you, 0 Djinn, and GOD.

(And the Meta-Genie, as all the higher ones before her,

swirls back into the Meta-Lamp, which the Genie folds back into his robe,
half as quickly as the M Genie did.)

Your wish is granted, Achilles.

(And one precise moment has elapsed since he "This will just take one
moment.")

Achilles: Thank you, 0 Djinn, and GOD.

Genie: I am pleased to report, Achilles, that you r have exactly one (1) Typeless Wish-that is to sa wish, or a meta-wish, or a meta-meta-wish, as many "meta"'s as you wish-even infinitely many (if wish).

Achilles: Oh, thank you so very much, Genie. But curiosity is provoked.

Before I make my wish, would you mind telling me who-or what-GOD is?

Genie: Not at all. "GOD" is an acronym which stands "GOD Over Djinn".

The word "Djinn" is used designate Genies, Meta-Genies, Meta-MetaGen etc. It is a Typeless word.

Achilles: But-but-how can "GOD" be a word in own acronym? That doesn't make any sense!

Genie: Oh, aren't you acquainted with recursive acronyms? I thought everybody knew about them. \ see, "GOD" stands for "GOD Over Djinn"-which can be expanded as "GOD Over Djinn, O, Djinn"-and that can, in turn, be expanded to "G( Over Djinn, Over Djinn, Over Djinn"-which can its turn, be further expanded ... You can go as as you like.

Achilles: But I'll never finish!

Genie: Of course not. You can never totally expand GOD.

Achilles: Hmm ... That's puzzling. What did you me when you said to the Meta-Genie, "I have a sped wish to make of you, 0 Djinn, and of GOD"?

Genie: I wanted not only to make a request of Meta-Genie, but also of all the Djinns over her. 'I recursive acronym method accomplishes this qL

naturally. You see, when the Meta-Genie received my request, she then had to pass it upwards to I GOD. So she forwarded a similar message to I Meta-Meta-Genie, who then did likewise to t Meta-MetaMeta-Genie ... Ascending the chain this way transmits the message to GOD.

Achilles: I see. You mean GOD sits up at the top of the ladder of djinns?

Genie: No, no, no! There is nothing "at the top", for there is no top. That is why GOD is a recursive acronym. GOD is not some ultimate djinn; GOD is the tower of djinns above any given djinn.

Tortoise: It seems to me that each and every djinn would have a different concept of what GOD is, then, since to any djinn, GOD is the set of djinns above him or her, and no two djinns share that set.

Genie: You're absolutely right-and since I am the lowest djinn of all, my notion of GOD is the most exalted one. I pity the higher djinns, who fancy themselves somehow closer to GOD. What blasphemy!

Achilles: By gum, it must have taken genies to invent GOD.

Tortoise: Do you really believe all this stuff about GOD, Achilles?

Achilles: Why certainly, I do. Are you atheistic, Mr. T? Or are you agnostic?

Tortoise: I don't think I'm agnostic. Maybe I'm metaagnostic.

Achilles: Whaaat? I don't follow you at all.

Tortoise: Let's see . . . If I were meta-agnostic, I'd be confused over whether I'm agnostic or not-but I'm not quite sure if I feel THAT way; hence I must be meta-meta-agnostic (I guess). Oh, well. Tell me, Genie, does any djinn ever make a mistake, and garble up a message moving up or down the chain?

Genie: This does happen; it is the most common cause for Typeless Wishes not being granted. You see, the chances are infinitesimal, that a garbling will occur at any PARTICULAR link in the chain-but when you put an infinite number of them in a row, it becomes virtually certain that a garbling will occur SOMEWHERE. In fact, strange as it seems, an infinite number of garblings usually occur, although they are very sparsely distributed in the chain.

Achilles: Then it seems a miracle that any Typeless Wish ever gets carried out.

Genie: Not really. Most garblings are inconsequential, and many garblings tend to cancel each other out. But occasionally-in fact, rather seldom-the nonfulfillment of a Typeless Wish can be traced back to a single unfortunate djinn's garbling. When this happens, the guilty djinn is forced to run an infinite

Gauntlet and get paddled on his or her rump, by GOD. It's good fun for the paddlers, and q harmless for the paddlee. You might be amused by the sight.

Achilles: I would love to see that! But it only happens when a Typeless Wish goes ungranted?

Genie: That's right.

Achilles: Hmm ... That gives me an idea for my w Tortoise: Oh, really? What is it? Achilles: I wish my wish would not be granted!

(At that moment, an event-or is "event" the word for it? --takes place which
cannot be described, and hence no attempt will be made to describe it.)
Achilles: What on earth does that cryptic comment mean?

Tortoise: It refers to the Typeless Wish Achilles made.

Achilles: But he hadn't yet made it.

Tortoise: Yes, he had. He said, "I wish my wish would not be granted", and the Genie took THAT to be his wish.

(At that moment, some footsteps are heard coming down the hallway in
their direction.)

Achilles: Oh, my! That sounds ominous.

(The footsteps stop; then they turn around and fade away.)

Tortoise: Whew!

Achilles: But does the story go on, let's see. or is that the end? Turn the page and let’s see.

(The Tortoise turns the page of "Djinn and Tonic", where they find that the
story goes on ...)

Achilles: Hey! What happened? Where is my Genie: lamp? My cup of espresso? What happened to young friends from the Convex and

Concave worlds? What are all those little lizards doing hi

Tortoise: I'm afraid our context got restored incorrectly Achilles.

Achilles: What on earth does that cryptic comment mean?

Tortoise: I refer to the Typeless Wish you made.

Achilles: But I hadn't yet made it.

Tortoise: Yes, you had. You said, "I wish my wish would not be granted", and the Genie took THAT to be your wish.

Achilles: Oh, my! That sounds ominous.

Tortoise; It spells PARADOX. For that Typeless wish to be

granted, it had to be denied – yet not to grant it would be to grant it.

Achilles: So what happened? Did the earth come to a standstill? Did the universe cave in?

Tortoise: No. The System crashed. Achilles: What does that mean?

Tortoise: It means that you and I, Achilles, were suddenly and instantaneously transported to Tumbolia. Achilles: To where?

Tortoise: Tumbolia: the land of dead hiccups and extinguished light bulbs. It's a sort of waiting room, where dormant software waits for its host hardware to come back up. No telling how long the System was down, and we were in Tumbolia. It could have been

moments, hours, days-even years.

Achilles: I don't know what software is, and I don't know what hardware is. But I do know that I didn't get to make my wishes! I want my

Genie back!

Tortoise: I'm sorry, Achilles-you blew it. You crashed the System, and you should thank your lucky stars that we're back at all. Things could have come out a lot worse. But I have no idea where we are.

Achilles: I recognize it now-we're inside another of Escher's pictures.

This time it's
Reptiles
.

Tortoise: Aha! The System tried to save as much of our context as it could before it crashed, and it got as far as recording that it was an Escher picture with lizards before it went down. That's commendable.

Achilles: And look-isn't that our phial of poppingtonic over there on the table, next to the cycle of lizards?

Tortoise: It certainly is, Achilles. I must say, we are very lucky indeed.

The System was very kind to us, in giving us back our popping-

tonic-it's precious stuff!

Achilles: I'll say! Now we can pop back out of the Escher world, into my house.

Tortoise: There are a couple of books on the desk, next to the tonic. I wonder what they are. (
He picks up the smaller one, which is
open to a random page.
) This looks like a moderately provocative book.