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

(Dana P.) #1
Hemiolia and Escher

In Verbum (Fig. 149), oppositions are made into unities on several levels.
Going around we see gradual transitions from black birds to white birds to
black fish to white fish to black frogs to white frogs to black birds ... After
six steps, back where we started!Js this.a reconciliation of the dichotomy of
black and white? Or of the trichotomy of birds, fish, and frogs? Or is it a
sixfold unity made from the opposition of the evenness of 2 and the
oddness of 3? In music, six notes of equal time value create a rhythmic
ambiguity-are they 2 groups of 3, or 3 groups of 2? This ambiguity has a
name: hemiolia. Chopin was a master of hemiolia: see his Waltz op. 42, or
his Etude op. 25, no. 2. In Bach, there is the Tempo di Menuetto from the
keyboard Partita no. 5, or the incredible Finale of the first Sonata for
unaccompanied violin, in G Minor.
As one glides inward toward the center of Verbum, the distinctions
gradually blur, so that in the end there remains not three, not two, but one
single essence: "VERBUM", which glows with brilliancy-perhaps a symbol of
enlightenment. Ironically, "verbum" not only is a word, but means
"word"-not exactly the most compatible notion with Zen. On the other
hand, "verbum" is the only word in the picture. And Zen master Tozan
once said, "The complete Tripitaka can be expressed in one character."
("Tripitaka", meaning "three baskets", refers to the complete texts of the
original Buddhist writings.) What kind of decoding-mechanism, I wonder,
would it take to suck the three baskets out of one character? Perhaps one
with two hemispheres.


FIGURE 52. Rippled Surface, by M. C. Escher (lino-cut, 1950).
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