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

(Dana P.) #1
FIGURE 56. Cube with Magic Ribbons, by M. C. Escher (lithograph, 1957).

Achilles: Exactly.
Crab: I remember that picture. Those little bubbles always seem to flip
back and forth between being concave and convex, depending on the
direction that you approach them from. There's no way to see them
simultaneously as concave AND convex-somehow one's brain doesn't
allow that. There are two mutually exclusive "modes" in which one can
perceive the bubbles.
Achilles: Just so. Well, I seem to have discovered two somewhat analogous
modes in which I can listen to a fugue. The modes are these: either to
follow one individual voice at a time, or to listen to the total effect of all
of them together, without trying to disentangle one from another. I
have tried out both of these modes, and, much to my frustration, each
one of them shuts out the other. It's simply not in my power to follow
the paths of individual voices and at the same time to hear the whole
effect. I find that I flip back and forth between one mode and the
other, more or less spontaneously and involuntarily.


282 Prelude ...

Free download pdf