Tuesday, October 26, 2004

Speaking of Escher...

Print Gallery, lithograph, 1956.

"Mystery of Print Gallery solved", the official M.C.Escher site i linked to the other day triumphantly titles.
This so-called mystery of what ought to be in the blank center of this famous painting never actually had been one, as can be demonstrated from various sources.
One source, for example, is Bruno Ernst's omnipresent text The Magic Mirror Of M.C.Escher, where the author points out that in Escher's final print, 1969's Snakes, it is not necessary to continue the painting to what may seem like infinity, because it is enough to simply suggest this possibility.

Snakes, woodcut, 1969

As we can see here(click picture for an enlargement), the rings at the center of the painting could go on into infinity as they would do in other earlier Escher works, and it is our awareness of this fact that dispenses the artist from actually representing it.
Escher recognizes his own limits, the approximation to infinity is literally that: an approximation, and even the finest artisan in the world could not achieve the detail needed.

The same thing happens in Print Gallery, where each side of the painting is amplified four times as much in the next. The center of the work would theorically show another approximation to infinity, with the same image repeated on and on. This, however, was not the point Escher wanted to make. Since he wanted to represent the amplification of images closing in on each other, what happened in the center was utterly irrelevant, and portraying it would have been a useless distraction.

The aforementioned "news headline" is interesting anyway, as it links to a completely mathematical explanation to the problem, Escher and the Droste Effect which i particularly recommend to anyone studying or interested in maths-related disciplines. It explains some of the aforementioned topics with insightful computer-generated images and a pdf article which, although i was only barely able to grasp most of the maths, is quite a good read.