Gödel, Escher, Bach: An Eternal Golden Braid (52 page)

Achilles: But that doesn't tell which one is phony. I've worked, and so has my master, at trying to produce these two strings by following the String Manipulation Rules, but to no avail. Neither one ever turns up. It's quite frustrating. Sometimes you begin to wonder ...

Tortoise: You mean, to wonder if either one has Buddha-nature? Perhaps neither of them has Buddha-nature-and neither koan is genuine!

Achilles: I never carried my thoughts as far as that-but you're right-it's possible, I guess.

But I think you should not ask so many questions about Buddha-nature. The Zen master Mumon always warned his pupils of the danger of too many questions.

Tortoise: All right-no more questions. Instead, I have a sort of hankering to make a string myself. It would be amusing to see if what I come up with is well-formed or not.

Achilles: That could be interesting. Here's a piece of string. (
He passes one to the
Tortoise.)

Tortoise: Now you realize that I don't have the slightest idea what to do.

We'll just have to take potluck with my awkward production, which will follow no rules and will probably wind up being completely undecipherable. (
Grasps the loop
between his feet and, with a few simple manipulations, creates a complex string which
he proffers wordlessly to Achilles. At that moment, Achilles' face lights up.)
Achilles: Jeepers creepers! I'll have to try out your method myself. I have never seen a string like this!

Tortoise: I hope it is well-formed. Achilles: I see it's got a knot at one end.

Tortoise: Oh just a moment! May I have it back? I want to do one thing to it.

Achilles: Why, certainly. Here you are.

(Hands it back to the Tortoise, who ties another knot at the same end. Then the
Tortoise gives a sharp tug, and suddenly both knots disappear!)
Achilles: What happened?

Tortoise: I wanted to get rid of that knot.

Achilles: But instead of untying it, you tied another one, and then BOTH disappeared!

Where did they go?

Tortoise: Tumbolia, of course. That's the Law of Double Nodulation
(Suddenly, the two knots reappear from out of nowhere-that is to say, Tumbolia.)
Achilles: Amazing. They must lie in a fairly accessible layer of Tumbol they can pop into it and out of it so easily. Or is all of Tumbolia equally inaccessible?

Tortoise: I couldn't say. However, it does occur to me that burning string would make it quite improbable for the knots to come back such a case, you could think of them as being trapped in a deeper la of Tumbolia. Perhaps there are layers and layers of Tumbolia. that's neither here nor there. What I would like to know is how string sounds, if you turn it back into phonetic symbols. (As he hauls it back, once again, the knots pop into oblivion.)

Achilles: I always feel so guilty about violating the Central Dogma (
Takes out his pen
and code book, and carefully jots down the many sym triplets which correspond to the
curvy involutions of the Tortoise's string; when he is finished, he clears his voice
.) Ahem. Are you ready to hear w you have wrought?

Tortoise: I'm willing if you're willing.

Achilles: All right. It goes like this:

A certain monk had a habit of pestering the Grand Tortue (the only one who had ever reached the Enlightenment 'Yond Enlightenment), by asking whether various objects had Buddha-nature or not. To such questions Tortue invariably sat silent. The monk had already asked about a bean, a lake, and a moonlit night. One day, he brought to Tortue a piece of string, and asked the same question. In reply, the Grand Tortue grasped the loop between his feet and

Tortoise: Between his feet? How odd! Achilles: Why should you find that odd?

Tortoise: Well, ah ... you've got a point there. But please go on!

Achilles: All right.

The Grand Tortue grasped the loop between his feet and, with a few simple manipulations, created a complex string which he proffered wordlessly to the monk. At that moment, the monk was enlightened.

Tortoise: I'd rather be twice-enlightened, personally.

Achilles: Then it tells how to make the Grand Tortue's string, if you be, with a string draped over your feet. I'll skip those boring details concludes this way: From then on, the monk did not bother Tortue. Instead, he made string after string by Tortue's method; and he passed the method on to his own disciples, who passed it on to theirs.

Tortoise: Quite a yarn. It's hard to believe it was really hidden inside my string.

Achilles: Yet it was. Astonishingly, you seem to have created a well-formed string right off the bat.

Tortoise: But what did the Grand Tortue's string look like? That's the main point of this koan, I'd suppose.

Achilles: I doubt it. One shouldn't "attach" to small details like that inside koans. It's the spirit of the whole koan that counts, not little parts of it. Say, do you know what I just realized? I think, crazy though it sounds, that you may have hit upon that long-lost koan which describes the very origin of the Art of Zen Strings!

Tortoise: Oh, that would almost be too good to have Buddha-nature.

Achilles: But that means that the great master-the only one who ever reached the mystical state of the Enlightenment 'Yond Enlightenment-was named "Tortue", not "Tutor".

What a droll name!

Tortoise: I don't agree. I think it's a handsome name. I still want to know how Tortue's string looked. Can you possibly recreate it from the description given in the koan?

Achilles: I could try ... Of course, I'll have to use my feet, too, since it's described in terms of foot motions. That's pretty unusual. But I think I can manage it. Let me give it a go. (
He picks up the koan and a piece of string, and for a few minutes twists and
bends the string in arcane ways until he has the finished product
.) Well, here it is.

Odd, how familiar it looks.

Tortoise: Yes, isn't that so? I wonder where I saw it before? Achilles: I know! Why, this is YOUR string, Mr. T! Or is Tortoise: Certainly not.

Achilles: Of course not-it's the string which you first handed to me, before you took it back to tie an extra knot in it.

Tortoise: Oh, yes-indeed it is. Fancy that. I wonder what that implies.

Achilles: It's strange, to say the least.

Tortoise: Do you suppose my koan is genuine?

Achilles: Wait just a moment ...

Tortoise: Or that my string has Buddha-nature?

Achilles: Something about your string is beginning. to trouble me, Mr.Tortoise .

Tortoise (
looking most pleased with himself and paying no attention to Achilles
): And what about Tortue's string? Does it have Buddha nature? There are a host of questions to ask!

Achilles: I would be scared to ask such questions, Mr. T. There is something mighty funny going on here, and I'm not sure I like it. Tortoise: I'm sorry to hear it. I can't imagine what's troubling you. Achilles: Well, the best way I know to explain it is to quote the words of another old Zen master, Kyogen.

Kyogen said: Zen is like a man hanging in a tree by his teeth over a precipice. His har grasp no branch, his feet rest on no limb, and under the tree anotl person asks him: "Why did Bodhidharma come to China from India?" the man in the tree does not answer, he fails; and if he does answer, falls and loses his life. Now what shall he do?

Tortoise: That's clear; he should give up Zen, and take up molecular biology.

Mumon and Gödel

What Is Zen?

I'M NOT SURE I know what Zen is. In a way, I think I understand it very well; but in a way, I also think I can never understand it at all. Ever since my freshman English teacher in college read Joshu's MU out loud to our class, I have struggled with Zen aspects of life, and probably I will never cease doing so. To me, Zen is intellectual quicksand-anarchy, darkness, meaninglessness, chaos. It is tantalizing and infuriating. And yet it is humorous, refreshing, enticing. Zen has its own special kind of meaning, brightness, and clarity. I hope that in this Chapter, I can get some of this cluster of reactions across to you. And then, strange though it may seem, that will lead us directly to Godelian matters.

One of the basic tenets of Zen Buddhism is that there is no way to characterize what Zen is. No matter what verbal space you try to enclose Zen in, it resists, and spills over. It might seem, then, that all efforts to explain Zen are complete wastes of time. But that is not the attitude of Zen masters and students. For instance, Zen koans are a central part of Zen study, verbal though they are. Koans are supposed to be "triggers" which, though they do not contain enough information in themselves to impart enlightenment, may possibly be sufficient to unlock the mechanisms inside one's mind that lead to enlightenment. But in general, the Zen attitude is that words and truth are incompatible, or at least that no words can capture truth.

Zen Master Mumon

Possibly in order to point this out in an extreme way, the monk Mumon ("No-gate"), in the thirteenth century, compiled forty-eight koans, following each with a commentary and a small "poem". This work is called "The Gateless Gate" or the Mumonkan ("No-gate barrier"). It is interesting to note that the lives of Mumon and Fibonacci coincided almost exactly: Mumon living from 1183 to 1260 in China, Fibonacci from 1180 to 1250

in Italy. To those who would look to the Mumonkan in hopes of making sense of, or

"understanding", the koans, the Mumonkan may come as a rude shock, for the comments and poems are entirely as opaque as the koans which they are supposed to clarify. Take this, for example:' -

FIGURE 46. Three Worlds by M. C. Escher (lithograph, 1955)

Koan:

Hogen of Seiryo monastery was about to lecture before dinner when he noticed that the bamboo screen, lowered for meditation, had not been rolled up. He pointed to it. Two monks arose wordlessly from the audience and rolled it up. Hogen, observing the physical moment, said, "The state of the first monk is good, not that of the second."

Mumon's Commentary:

I want to ask you: which of those two monks gained and which lost? If any of you has one eye, he will see the failure on the teacher's part. However, I am not discussing gain and loss.

Mumon's Poem:

When the screen is rolled up the great sky opens,

Yet the sky is not attuned to Zen.

It is best to forget the great sky

And to retire from every wind.

Or then again, there is this one:2

Koan:

Goso said: "When a buffalo goes out of his enclosure to the edge of the abyss, his horns and his head and his hoofs all pass through, but why can't the tail also pass?"

Mumon's Commentary:

If anyone can open one eye at this point and say a word of Zen, he is qualified to repay the four gratifications, and, not only that, he can save all sentient beings under him. But if he cannot say such a word of Zen, he should turn back to his tail.

Mumon's Poem:

If the buffalo runs, he will fall into the trench;

If he returns, he will be butchered.

That little tail

Is a very strange thing.

I think you will have to admit that Mumon does not exactly clear everything up. One might say that the metalanguage (in which Mumon writes) is not very different from the object language (the language of the koan). According to some, Mumon's comments are intentionally idiotic, perhaps meant to show how useless it is to spend one's time in chattering about Zen. How ever, Mumon's comments can be taken on more than one level. For instance, consider this :3

Koan:

A monk asked Nansen: "Is there a teaching no master ever taught before?"

Nansen said: "Yes, there is."

"What is it?" asked the monk.

Nansen replied: "It is not mind, it is not Buddha, it is not things."