remarkable. Bach and Escher are playing one single theme in two different
"keys": music and art.
Escher realized Strange Loops in several different ways, and they can
be arranged according to the tightness of the loop. The lithograph Ascend-
ing and Descending (Fig. 6), in which monks trudge forever in loops, is the
loosest version, since it involves "so many st~ps before the starting point is
regained. A tighter loop is contained in Waterfall, which, as we already
observed, involves only six discrete steps. You may be thinking that there is
some ambiguity in the notion of a single "step"-for instance, couldn't
Ascending and Descending be seen just as easily as having four levels (stair-
cases) as forty-five levels (stairs)? It is indeed true that there is an inherent
FIGURE 7. Hand with Reflecting Globe. Self-portrait by M. C. Escher (lithograph,
19351.