Readers of the first post on this subject will have seen that Daniel Miller, long a Himalayan “range ecologist,” and student of Tibetan ways and textiles, sent me a couple of images of a Tibetan rug he owns.
The first image was “head-on” and looked like this.
A second photograph of this rug, taken from an angled perspective looked like this.
Dan, who has been looking at Tibetan rugs for maybe 30 years plus, said he’d not previously seen this effect and wondered whether others of my readers might have.
So, we put these two images up in the first post on this site and asked. There have been a variety of responses and proposals.
A large number of folks with deep experience in Tibetan textiles said they had not seen this effect in other rugs. One experienced person said that he had seen it “lots of times.”
The explanatory proposals seem to group as follows:
1. Illusionistic effects produced by changing knot direction or pitch in different parts of the same weaving (e.g., asymmetrical open right and asymmetrical open left).
2. Illusionistic effects produced by varying such things as the width of squares or some other design area or device.
3. Illusionistic effects produced by change in perspective.
Several respondents suspected that this effect might have been reproduced by proposal 1.
Dan was asked to take pictures of the back of his rug to see whether that provided any hints about the likelihood that pitch of the knot might be implicated.
The question of whether this effect might be produced by the character of the weave is a legitimate one since examples of it are known. Rugs with silk pile famously produce dramatic differences viewed from opposite ends and there are rugs known in which the character of the weave produces different effects in different parts of the rug when viewed from different perspectives.
Matthew Polk, indicated that he knows of such an example:
“…I have seen a rug that produced an illusion due to direction of the knots. It’s a modern silk Isfahan owned by my sister and her husband. Viewed with the warps vertically the knots to the left of center face one way and to the right face the other. Viewed from one side the design on the near side is clear while the other side looks blank…”
Daniel Miller provided three additional images of his rug, including two of its back.
He reported that the knotting was “straight Tibetan weaving.” Here are his additional photos.
That seemed to indicate that this effect is not produced by “knot direction” or “pitch” and the like.
Next, were respondents who spoke to explanation 2: Illusionistic effects produced by varying such things as the width of squares or some other design area or device.
The Dutch scholar, Koos De Jong, who is about to publish a book on Chinese saddle covers, wrote to say that he is treating “illustionistic” effects in them.
He shared some images, the most accessible of which is from the McMullan Collection.
You can see that a kind of three dimensional effect is created by varying interior areas of the piece as well as the width of its outside borders.
Here is a 19th century U.S. hooked rug that exhibits a similar 3-D effect in the drawing of its field.
Color and shape of design elements have been used to create a three-dimensional effect.
A third example is a quilt.
Here the height or width of the rectangular design elements have been varied to create a distorting illusion.
Quite a few U.S. coverlets with “overshot” designs exhibit this kind of distortion. So do some Escher designs, like the one below.
When we look again at Daniel Miller’s Tibetan piece,
we can see that although colors vary, the shape and size of the squares do not. So, although color may be implicated in this illusionistic effect,
size and shape of its design elements are not. We need to look further for a real explanation and our third alternative, above, illusion created primarily by change in perspective seems to the one that offers the best chance of explanation.
I sent an image of what seemed to me a similar checkerboard rug to Wendel Swan and asked him to skew it as the image above of Daniel Miller’s piece is in the second paragraph. He did, but the distinctive visual effect we can see in Dan’s rug did not appear.
But Matthew Polk sent me the line image below, and said:
“Interesting optical illusion (ed. referring to the Tibetan rug) which I’ve not seen before. You can duplicate the effect by printing this page with the drawing below. Look at the page straight on and it’s much like your rug. However, turn the page so that you’re looking from a corner and tilt so that you’re viewing at a low angle then the quadrant pattern will appear.”
I followed Matthew’s instructions and a illusion effect like that in Dan’s rug appeared.
“The reason it works is this. When you look at the image straight on all the lines and spaces in each quadrant all have equal weight. When you view from a corner at a low angle the lines and spaces perpendicular to your view blur creating an almost monochrome effect in those two quadrants while the lines and spaces in the other two quadrants are aligned with your point of view remaining clear and distinct. This makes them suddenly jump out of the plane of view. One wonders whether the illusion was discovered accidentally then reused as a traditional design motif.”
I also received a graphic from William Bateson. William’s version replicated the three-color variation of the Tibetan rug.
William’s viewing instruction was like Matthew’s: Print off the image. Lay it on a table and view it from a corner at a low angle.
I did and, again, an illusion, like that in Dan’s rug appeared.
About William’s graphic Matthewe Polk said:
“This graphic is a better representation of what’s happening in the carpet and works for the same reasons. Sighting at a low angle from a corner the viewer sees the long lines of white squares in two quadrants whereas the white lines cross the viewing angle at 90 degrees in the other two quadrants creating a visual contrast between the quadrants.”
William, subsequently, tested whether this illusion effect could be produced with a two color checker board and found that it could not.
About the graphic above, Matthew Polk said:
“The 2×2 graphic doesn’t work because the pattern is uniform across the entire rectangle.”
Explaining his sense of the requirements of a graphic that produces the visual effect in this Tibetan rug and wondering about other possibilities William said:
“I think it is necessary that the design be symmetric about both the major and minor axes, just as are both Polk’s and the Tibetan carpet.
“Now the question is whether other geometric design carpets–Tibetan and others–are symmetric in this way.
“In the Tibetan case, symmetry requires that the carpet have an odd number of rows and lines of squares in order to maintain (almost) the rule that no square touch another like-colored square except at diagonal corners. This rule is violated only around the center-most square.
“What do other three-colored, square-patterned weavings look like? Surely this has been discovered by cloth weavers.
“And, if Polk’s explanation works for lines and squares, how would it be manifest, if at all, in triangles or hexagons? Surely one of the TM regulars is a topologist.”
I asked Carol Bier, who has studied, curated and published on the relationships between mathematics and textile design. Her exhibition on “Symmetry and Pattern” at the TM a few years ago is still visible on Drexel University’s Math Forum.
Carol said: “
You’re right — it’s definitely visible and a very interesting phenomenon. It does seem to be related to perception and anamorphism, but I’m not sure it would be considered a topological effect since it is in the plane.
Here’s a definition of anamorphism, which seems to fit (http://dictionary.reference.com/browse/anamorphic, accessed 1/17/13):
an·a·mor·phic [an-uh-mawr-fik] Show IPA
1.Optics. having or producing unequal magnifications along two axes perpendicular to each other.
In one email, as we discussed his Tibetan piece and the effects visible in it, Dan Miller said in part:
“I wonder if the weaver of this blue checkerboard Tibetan rug had any idea of the illusion effect the design would have when the rug was taken off the loom and put on the floor and viewed from a corner at a low angle? Or, was the weaver just weaving a nice carpet with a geometric design? I guess we will never know.”
I decided to contact Jeff Spurr, with whom I’d had an exchange about weaver intentionality in another context. Jeff said in this previous exchange that he tended to see most of the effects we experience in rugs as the result of weaver intention.
But looking at the images of this rug and the things that had been said about it, he said:
“I have no basis for true judgement in regard to this particular phenomenon. There is no doubt that “tumbling blocks,” whether in a hooked rug or log cabin-style quilt, features an illusion of depth quite deliberately achieved. I am more inclined, in the case of the Tibetan rug to assume that the rather simple checkerboard was the intended design, and the added perspectival feature was incidental.”
Jeff also provided images and some words about two Borneo rattan mats (Punan ethnic group), and one African raffia textile (Kuba kingdom)] that exhibit effects related to that we see in the Tibetan rug.
“I am attaching a photo of one of the plainer Borneo mats in my collection.. It is somewhat easier if you zoom in a bit, but you will first note that the field design is a chevron; however, looked at just a bit differently -without the dramatic change in perspective demanded in the case of the Tibetan rug – and you will suddenly see it as a stepped design. Believe me, it works both ways, although the chevron design is basic.”
In the second example I am attaching, another principle seems to be at work. Rather than the challenges of simplicity, the complexity of this design defeats any attempt to see it in only one way, several options presenting themselves in turn.”
“The third image is of a large Kuba (Congo) raffia square in an incredibly rare technique, not the usual pile with contrasting lines of embroidery, but lateral floats about one-third inch long in contrasting black and natural creating the design. I know of only one other example in this technique (in the collections of the MFA Boston). Unfortunately, the lousy photo does not effectively reveal the remarkable “op” effects characteristic of this rare type. Unlike the other cases, this is simply “there,” but utterly unexpected given what we are used to from the standard pile examples and also those that are all in standard Kuba embroidery stitch.”
This is John Howe, talking again:
If you print off Jeff’s three examples and view them from various angles you will see that Spurr 1 exhibits effects similar to those in the Tibetan rug when viewed a) directly into a short side and b) directly into a long side, with the piece positioned square with your line of vision.
When viewed from a corner at a low angle, both Spurr 2 and Spurr 3 exhibit effects similar to those in the Tibetan rug. These effect are clearer in Spurr 3 because its design elements have more width.
Spurr 2 speaks to another aspect of related visual phenomena. It is generally admitted that lighter colored design devices are experienced as being closer than darker ones. But if you look at Spurr 2 from two different (and not opposing) corners you will see that the light colored devices are more prominent in one perspective and the darker colored ones are so when viewed from the other perspective. This demonstrates that the phenomenon that Matthew Polk first described and replicated is stronger than is the effect of light vs dark coloration.
Wendel Swan sent me two images of a contemporary rug woven by the textile authority Belkis Balpinar.
“…I have no doubt that she both intended and achieved optical illusions.
On the left, it seems to mound up
while on the right
the same rug seems to spiral downward.
“The effect is due to the perspective of the viewer.”
And to push such things a little further, Doug Klingensmith, a materials scientist and textiles collector in California, sent me another example, with comment. He said:
“The effects you discuss strike me as sort of cognitive psycho-physiology – combining the nature of optical perception and the predispositions in the mind of the viewer – intentionally fooling a trained brain a-la M.C. Escher, or just accidentally triggering a neurological response with a particular pattern and angle.
“Perhaps there are studies in optical physiology that identify the way in which our eye/brain system is fooled.”
Here are two photos that Doug provided “…of the same room with the same black lines painted on the wall –
Doug said: “…only the viewing angle is changed. I have seen some things like this in real space and it is trippy.”
As I was about to “go to press” with this Part 2 post, one experienced participant in these discussions said that 1) I had “gone on” a bit about this effect (and that is true), and 2) that he felt that the effects being discussed often do not rise to a level that merits their description as “optical illusions.”
My own thought is that, no matter how they are most properly described, there is something interesting to be seen, here, and they have been the occasion for at least moderate pondering by some pretty experienced folks, so I’m glad that Dan Miller brought his Tibetan rug and its visual effect to our attention, and find that I have enjoyed poking about for knowledgeable indications of what and why it is.
My thanks to the participants named here, and to others, who wrote me, and often provided me with additional examples, on the side, for their contributions.
Now, since we’re finished, let me pass on three sidewalk chalk drawings that Doug Klingensmith also sent me that show how quickly a conversation like this can go out of control.
R. John Howe
Related, Recently, or About to be Published, Books
Daniel Miller (ed,), “Auspicious Carpets: Tibetan Rugs and Textiles,” Blurb, 2009, available in paper-based copy or on-line.
Rupert Smith, “Secrets of Tibetan Weaving: The Greensmith Collection,” Karma Trinley Darchen, 2012
Koos de Jong, “Dragon and Horse*. Saddle Rugs and Other Horse Tack from China and Beyond,” (publication pending as described by de Jong below).
*) This publication is the outcome of a sound art-historic research, by which all published saddle rugs were compared with representations of similar rugs in Chinese painting, sculpture and applied arts in order to produce a reliable typology.
The book contains two volumes, one in English with all the images, the other with just the text in Chinese. Part one, chapter 1-6, deals with the chronological development of the Chinese saddle rug, part two, chapters 7-12, with the saddle rugs per origin. Anticipated is a format of L 30,3 W 22,5 cm, ca. 250 images (ca. 150 full-colour and 100 small supportive images), 10 maps and appendixes (technical information, reading list, glossary, index, photographic archive resources and colophon); in total ca. 50.000 words and 220 pages.
Published by myself, a total of 2000 copies will be printed and distributed by CA Design in Hong Kong. The publication is planned in March-April 2013.
It will be a strictly non-profit publication, meaning that it is completely financed by me, without any other public or private funding. Aiming at the widest possible distribution both in the Western world and China, it will be sold at cost-price.