P3D Re: Escher, stereo, impossibility

[Bruce Springsteen <bsspringsteen@xxxxxxxxx>]

It should come as no surprise that I have been a student of Escher's art
for a couple of decades.  I have copies of most of the principal books on
his work, including "The Magic Mirror of M.C. Escher" by that pseudonymic
purveyor of pseudoscopes, Bruno Ernst (a.k.a.  J. A. F. de Rijk - thanks
to Abram for the inside story!)

The fascination in most of Escher's work comes from his play with the
paradoxical nature of pictures.  R. L. Gregory describes pictures as
having a "dual reality", an essential quality of all  pictorial
representations.  We may see a picture as a flat collection of marks on a
surface - a 2 dimensional thing, but we also interpret (perceive) these
marks as the representation of solid, 3-dimensional things.  Optical
illusions such as the Penrose staircase & tribar, the 2 or 3-pronged fork,
and Escher's many examples all exploit the difference between seeing an
object, and seeing a 2-dimensional image of that object.  By violating
conventions of perspective and connectivity, these illusions deliver
contradictory cues about the depth of the objects presented, exploiting
the absence of stereoscopic cues to relative distance.  This fluctuation
and confusion in how the mind will interpret a picture is the game - the
pleasant and bewildering ambiguity of not knowing how to make a stable,
plausible interpretation about how a pictured object looks in 3D reality.

Which is why I have ambiguous feelings about stereoscopic
reinterpretations of Escher's art.  On the one hand, the images that
present no spatial impossibility, just improbability, are pleasant to
view.  But the enjoyment of the original works is largely in the power of
2-D representation to elicit sensations of depth - stereo rather misses
the point of the game.  Further, in the case of "impossible" images like
"Belvedere", "Waterfall", "Convex and Concave" and others where the
uncertainty of depth relationships is the whole idea, an arbitrary
decision by a conversion artist to create a stereo depth cue for parts
that are depth-ambiguous is both impossible and pointless, and spoils the
image for me.  On the other hand, the technical accomplishment of trying
it at all is indeed impressive.  So my feelings on this are somewhat
"multistable" as well.

I recently saw a pop-up book of Escher images, where the pages fold out
into 3D layers, and I thought "Boy, does that book miss the point!"  Now I
feel basically the same way about stereo conversions of Escher.  The
examples of stereo conversions of impossible objects are neither
persuasive, nor interesting as the originals, to my thinking.  By
definition, a depth-impossible object cannot be presented in stereo, and
the examples I've seen, by A. Girling and Udo S. and Holten, only
demonstrate that fact.  I welcome examples that prove me wrong, and am
willing to explain why the examples cited don't succeed, if the topic is
of interest to anyone besides Abram and me ;-)

Respectfully,
Bruce   
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