Those who have studied Islamic art and architecture for some time inevitably have asked sooner or later the following questions: How did they do that? Apart from the application of fundamental principles in geometry, how could they create most sophisticated and highly complicated geometric designs over extended areas in this stunning precision? And then, why did Muslims in the Golden Age of Islam do that? Who had taught them, and how? Where are the books and manuscripts? When and on what occasions met and collaborated scientists and artists in Islamic civilization?
In the early 1970s these simple questions struck a young and extraordinary talented Iraqi lady with a strong background in history and historiography when she searched for a suitable topic for a doctoral thesis at Harvard . These questions weren’t obvious at that time. When Wasma’a Chorbachi had explained her preliminary proposal and her desire of finding the relevant literature which had obviously been lost during the centuries, she was rather quickly turned down. Her advisor expressed his strong opinion that there was not such a thing. There had never been. His good advise was rather to expand her list of questions in order not to fail, for instance, including questions such as: Has the interest in science or geometry been part of the average cultured person’s background in the ninth or tenth century? What practical geometry had been developed by the tenth century? What caused the growth of this phenomenon? Geographically, where did it begin and in what directions did it spread?
A Needle in the Haystack
Wasma’a started her search taking advantage of the extensive resources of the Harvard library system. She read through catalogues and indices of manuscript collections available in libraries throughout the world. By the end of the week she had come across Kamāl al-Dīn Yūnis bin Man’a, one of the most outstanding teachers at the main school of the early 13th century in Mosul, Iraq (which has later been named after him, al-Madrasah al-Kamālīyah, ). Among his work was a commentary on an earlier work of one of the most eminent mathematicians and scientists of the Islamic world of the 10th century, Abū’l-Wafā al-Būzjānī. He lived in Baghdad from approximately 945 CE until his death in about 987 CE. The transliterated title of the main work was also more or less the title of Wasma’a’s PhD project: “A treatise on what the artisan needs of geometric problems”, while the title of Kamāl al-Din Yunis’ commentary was “Commentary on the geometry problems.” Thus, by the third week of her search Wasma’a Chorbachi had already been successful in achieving her first aim: to locate the relevant literature as regards the teaching of medieval artisans of the Islamic world by scientists.
Wasma’a’s next step was to travel to Europe and find and read the original manuscripts, in the Victoria and Albert Museum in London and the Bibliotheque Nationale in Paris where she had located a Persian translation of Abū’l-Wafā al-Būzjānī’s manuscript of the “Treatise on what the artisan needs of geometric problems.” In Paris, she found an unnamed, undated manuscript probably from the 14th century which clearly was of significantly greater importance than Abu’l Wafa’s work: “On interlocking similar and congruent figures.” Wasma’a writes:
“By the time I returned to Cambridge, I had located a range of written material, in the history of Islamic science and geometric design from the tenth century of the mid-nineteenth century, lying in library and museum storage rooms all over the world. In point of fact, my material turned out to be so convincing that it is now being used and propagated even by those who demonstrated such a strong sceptical attitude towards it at the beginning. Though locating the manuscripts took only two months, acquiring microfilms and/or photocopies of these documents without any backing or support took several years. Meanwhile, I was struggling to decipher the material, and to find an appropriate language in which to discuss it and describe the geometrical patterns with which it dealt.”
Studying the right language (while noticing that different people with different background will describe what they see by using different terminology) took years for Wasma’a. It foremost included Group Theory, Crystallography and Symmetry Notation, fields with which historians and art historians are not really familiar per se. Wasma’a strictly applied scientific reasoning, though. It is interesting reading her rebuttal of ‘esoteric’ reasoning in explaining the ‘meaning’ in Islamic art which became most popular in the mid 1970s. According to proponents, the “principle of the unity of being” was even “pushed to a point of scientific fallacy such as the claim that all geometric patterns of Islamic art are derivable through a single method of construction based on the subdivision of the circle, in order to declare this art work an example of the ‘Unity of Being’.” Divine Unity, or Tawhīd, as the driving force for geometric patterns. That didn’t make sense in her opinion.
“The general public unfortunately remains unaware of this. If in these books, that are now readily available on the market, their authors had made clear that the presented views were modern understandings of old forms, turning them into symbols, there would be no reason to object. The problem lies in presenting these modern mystical views as historical truths, as if these symbols were the meanings at the time the art forms were created. The non-Islamicist who is exposed to these books [for example, I. El-Said’s Geometric Concepts in Islamic Art; L. Bakhtiar’s Sufi: Expressions of the Mystic Quest] will anachronistically assume that a modern interpretation is the historical truth. Where does one draw the line between true historical research and the creation of and attribution of symbolic meaning to forms from the past? How can we redeem the geometric shapes, forms and patterns from the shrouds of mystical interpretations in order to see the precise scientific design at their basis?”
Describing the visual perception and linguistic or even fashionable semiotics further served only to confuse the interested layman in particular in the 1970s .
In a comprehensive case study Wasma’a Chorbachi deconstructs one of several amazing brick pattern on one of the two Seljuq Kharraqan tomb towers (1093 CE) in the vicinity of Qazvin in northern Iran which consists, at first sight, of V-forms, X-forms as well as dots, but which, at second sight, comprises an extremely popular geometric structure, a square within a square within another square. I have described this pattern, which can be found, for instance, several times on the western and southern iwans of Esfahan’s Great Mosque , and how it may be created in another posting on this blog. It’s construction in five steps had been described in a systematic, scientifically correct, way in the above mentioned, unnamed, undated Paris manuscript No. 169 “On interlocking similar and congruent figures”, Wasma’a had been working on.
What follows is another case study of the Persian manuscript folio 192b about a similar structure of a kind of pinwheel which fascinates “in its use of a strict algorithm with irrational numbers.” It shows how the principles may lead to different designs which probably have been considered from a pure esthetic point of view.
“The science of symmetry of patterns tell[s] us that there are 17 different periodic two-dimensional groups and 7 groups periodic in a singular direction (string or ribbon), also that each of these groups could have an infinite number of different designs. As seen, these Islamic geometric manuscripts give us samples of the infinite design variations of the basic 17 periodic groups; these documented geometric problems or examples in turn could be the basis for developing many new sets of design.”
See Dr. Wasma’a Chorbachi’s homepage here.
 This posting is about a remarkable text by Wasma’a K. Chorbachi which was based on two lectures given at MIT, Cambridge, in November 1987 and had been published in Computers Math Applic 1989; 17: 751-789: In the Tower of Babel: Beyond Symmetry in Islamic Design. It deals with a lot of questions which I have asked myself (and many others) since I became fascinated of Islamic art and architecture in recent years.
 Despite his Arabic name, Wasma’a’s advisor considered Kamāl al-Dīn Yūnis a member of the Nestorian Church which had been revived in Iraq in the 12th century. Dr. Chorbachi explains her dismay with considerable prejudices as well. I suppose it is not entirely correct that the annoying response of her supervisor reflected a general ignorant attitude towards the achievements of the Islamic world in the West after WWII, as she describes it. Ignorant supervisors are frequently found in Academia, even at Harvard. It might in fact be the case that in particular Americans are in essence Eurocentric. Not to forget that the 1970s were a decade of great technological and scientific achievements mainly coming from the US, which were very much occupied in proxy wars of the Cold War, for instance in Vietnam. Islamic art and architecture may not have been regarded a fruitful field where scientific breakthroughs had to be expected. In any way, Wasma’a continued her search and found quite a lot of information about Kamāl al-Dīn Yūnis. I have to admit that in spite of considerable search of the internet, I could not identify the scholar yet.
 Mystic interpretations of Islamic geometric patterns are still prevalent in many esoteric circles in the West. When trying to talk about new discoveries or searches, for instance, the search for quasi-crystalline patterns, one generally faces incomprehension among people with a general interest in Islamic art and art historians. The “meaning” of the stunning patterns is of greater importance than the question, how could it be created. And whether it has been chosen for esthetic reason only.
 Interestingly, Wasma’a mentions 1122 CE as construction date of the iwans, i.e., after Assassin rebels had set the mosque on fire in 1121. She also mentions that the iwans were re-decorated in 1800. In fact, restoration and repair of the structures and tessellations constantly takes place. The celebrated decoration of, for instance, the western iwan is usually considered to be Timurid (15th century) or Safavid (16th and 17th century).
See ArchNet for further pictures of the two Kharraqan tomb towers.