We have eliminated the "town" level: conceptually it was useful, but can just
as well be done without. Figure 144 looks just like the diagram for Drawing
Hands: a Strange Loop of two steps. The division markers are arbitrary,
even if they seem natural to our minds. This can be further accentuated by
showing even more "collapsed" schematic diagrams of Print Gallery, such
as that in Figure 145.inclusion + depiction
FIGURE 145. Further collapse of Figure 143.This exhibits the paradox of the picture in the starkest terms. Now-if the
picture is "inside itself", then is the young man also inside himself? This
question is answered in Figure 146.inclusion + depiction + representation
FIGURE 146. Another way of collapsing Figure 143.Thus, we see the young man "inside himself", in a funny sense which is
made up of compounding three dis-tinct senses of "in".
This diagram reminds us of the Epimenides paradox with its one-step
self-reference, while the two-step diagram resembles the sentence pair each
of which refers to the other. We cannot make the loop any tighter, but we
can open it wider, by choosing to insert any number of intermediate levels,
such as "picture frame", "arcade", and "building". If we do so, we will have
many-step Strange Loops, whose diagrams are isomorphic to those of
Wateifall (Fig. 5) or Ascending and Descending (Fig. 6). The number oflevels
is determined by what we feel is "natural", which may vary according to
context, purpose, or frame of mind. The Central Xmaps-Dog, Crab,
Sloth, and Pipe-can all be seen as involving three-step Strange Loops;
alternatively, they can all be collaps-ed into two-or one-step loops; then
again, they can be expanded out into multistage loops. Where one per-
ceives the levels is a matter of intuition and esthetic preference.
Now are we, the observers of Print Gallery, also sucked into ourselves by
virtue of looking at it? Not really. We manage to escape that particular
vortex by being outside of the system. And when·we look at the picture, we
see things which the young man can certainly not see, such as Escher's(^716) Strange Loops, Or Tangled Hierarchies