Gödel, Escher, Bach An Eternal Golden Braid by Douglas R. Hofstadter

(Dana P.) #1

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 if nowhere-that is to say,
Tumbolia.)
Achilles: Amazing. They must lie in a fairly accessible layer of Tumbolia if
_ 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 the
string would make it quite improbable for the knots to come back. In
such a case, you could think of them as being trapped in a deeper layer
of Tumbolia. Perhaps there are layers and layers of Tumbolia. But
that's neither here nor there. What I would like to know is how my
string sounds, if you turn it back into phonetic symbols. (As he hands 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 symbol-
triplets which correspond to the curvy involutions of the Tortoise's string; and
when he is finished, he clears his voice.) Ahem. Are you ready to hear what
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 ques-
tions 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 begin
with a string draped over your feet. I'll skip those boring details. It
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.


A Mu Offering 243

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