Theories, Problems and Evidence

David Wade

Carved marble revetment
Fig. 1 Carved marble wall-panel from the Umayyad palace at Madinat az-Zahra in Muslim Spain; circa. 950 CE/340 AH

The main consideration in any discussion of ‘Islamic geometrical design’ should surely be the sheer breadth of this topic. With its extraordinary range of example, drawn from centuries of development throughout the Islamic world, this is clearly a subject on which it is perilous to make sweeping generalisations. But appreciation of the intrinsic qualities of this art-form has not always been accompanied with the sort of careful evaluation that it obviously deserves. In fact it has to be said that the ‘geometric mode’, as a theme in Islamic decorative art, has endured more than its fair share of gratuitous interpretations and misconceptions. Among the more common of these are –

  1. that the resort to geometric and ‘arabesque’ patterns are entirely due to the Quranic prohibition on image-making;
  2. the belief that these designs are constructed according to some underlying symbolic meaning;
  3. the notion that theoretical mathematicians were involved in their creation.

The first of these assertions does have some basis as an influence (see Background note #2 - The Religious Dimension) but this explanation, by itself, is entirely inadequate in accounting for the particular forms that have been adopted. As for the other propositions, there is no evidence at all for the use of symbolism of any kind in Islamic geometrical or vegetal designs, and precious little for any connection with the discipline of ‘pure’ mathematics in the former.

It should also be said that there are other important aspects of this broad subject that remain obscure (and contentious), and are likely to remain so. Such as, precisely when and where the distinctive Islamic decorative canon first come into being, the extent to which it drew on late-Classical forms, and whether it had doctrinal associations, as some have claimed – or indeed, was influenced by religious or philosophical ideas at all. Obviously, the principle sources of evidence will always lie in the surviving work itself, but even here there are problems, not least the fact that so much has been destroyed (see below). But also it is frequently unclear whether a specific example of decorative art is wholly attributable to the artists and artisans involved in making the work, or had been determined by the tastes of those who commissioned it. Moreover, there is seldom any good evidence to indicate the realities of the creative processes involved, especially in large-scale projects where, for instance, it may be difficult to assign the relative contributions of the architect of a monument and those employed to decorate it.

Carved marble revetment
Fig. 2 Carved wooden panel from the Al-Aqsa mosque, Jerusalem; Umayyad period

In all probability the setting of aesthetic priorities and the contributions of the different agencies involved in grander schemes are likely to have varied enormously. However, it seems most likely that innovations in the particulars of vegetal arabesque and geometrical pattern were usually developed from the artisan level upwards. This is an art of decorative playfulness, largely created, I suspect, out of the creative genius of individual artist/craftsmen, who were keen to impress patrons (and their peers) with their creative skills, both in the particular medium that they were working in and in the sophistication and complexity of their designs; in Islamic arts and crafts generally ‘technical virtuosity became prized’.1

As for speculation regarding the extent to which mathematicians proper advised on the creation of geometric patterns, again, there is some small evidence of contributions of this kind in the form of geometrical manuals that were intended to be read by craftsmen (see Postscript A below), and of occasional cross-disciplinary meetings, but it seems far more probable that those who created these forms generally relied on their own informal working knowledge of plane geometry, which was clearly quite considerable2. There are no biographical accounts of architects from the formative periods of Islamic art and architecture, let alone artisans – and unsurprisingly, the latter have left few documents detailing their work practices. Moreover, there are no indications at all that either were influenced by an overarching theory of any kind. The geometric patterns, arabesques and calligraphy that have played such an important role in this art were usually created within workshop traditions that were handed down through generations. The unwritten rules of this decorative canon, and the skills involved in creating it, would have become second nature to the artist/craftsmen involved and probably guarded as a trade secret in many cases. Even the extent of specialisation in these different decorative components, and the methods of organising them into a finished production are simply not known. It is unlikely though that the Islamic ornemanistes who created geometric designs were at all familiar with the more technical geometrical knowledge required by architects or those involved in civil engineering, town-planning, land-surveying etc.. Their artistic geometry was primarily concerned with elegant appearance, not mathematical exactitude; approximations were often acceptable here, if the final effect justified it.

Carved wood panel
Fig. 3 Carved wooden panel from the Al-Aqsa mosque, Jerusalem; Umayyad period

However, the paucity of evidence on these and other matters bedevils Islamic art-historical studies. Islam’s long cultural heritage has endured more than its share of the ravages of time, and the many terribly destructive events in Islamic history has meant that important parts of the archaeological record have been destroyed or seriously diminished. Apart from the human cost, this presents serious difficulties in determining the artistic evolution of Islamic decorative art, particularly the paths of its developments from its earlier, more derivative, styles through to the mature forms.

Islamic Art, in common with the artistic productions of other great cultures, has stylistic features that render it instantly recognisable – but the precise qualities that create these distinctive cultural qualities are often not so easy to pin down. Islam’s proclivity for geometric ornament is of course very much part of its character, and part of what make it recognisable – but this form of artistic expression is essentially a component of a broader theme, namely that of symmetry. Many other cultures use symmetries of course, but in Islam it is a sine qua non. Islamic art is not simply suffused with symmetries; symmetry is its central principle (figs. 1-4)3. The overriding question in this topic has to be Why and How did this come about?

At the risk of being accused myself of the sort of generalizations that I riled at earlier, my own instincts regarding the origins and continued use of the geometrical mode in Islamic art and architecture is that it reflects the aesthetic ideals of a Classical philosophical tradition that had been thoroughly absorbed into mainstream Islamic thought at an early stage of its development. I refer, of course, to the intellectual speculations that began with Pythagoras, were consolidated by Plato, and continued by the Neo-Platonists of Late Classicism. The very fact that Islam had expanded into this sphere of Hellenised Late Antiquity, meant that Neo-Platonism was the first major philosophy that it encountered, and it later incorporated many of its themes into its own broad philosophical outlook. In fact the principle Classical Greek philosophies were to become very much part of the Islamic tradition; much of Plato and Aristotle in particular were found to be acceptable, indeed perfectly compatible with core Islamic beliefs.

That a central concept of the Platonic stream of thought involved the association of Ideal Forms and Beauty, and that it was preoccupied with the purity of geometric forms as an expression of these concepts, seems to me to have a strong bearing on the principle themes of Islamic art. The Greek author Plutarch 4, long before the advent of Islam, and speaking like a true Pythagorean, epitomized this association of geometry and spirituality within Platonic tradition – ‘The function of geometry is to draw us away from the world of the senses and of corruption to a world of the intellect and the eternal. For the contemplation of the eternal is the end of philosophy as the contemplation of the mysteries is the end of religion.’ Could there be a more perfect description of the underlying intentionality behind the extraordinary variety of geometric designs, and the continuous process of artistic exploration of this mode for hundreds of years within the Islamic sphere? With its pure geometries, perpetually playing out their symmetrical dances on the stage of the Euclidean plane this genre, in my view, is quintessentially Platonic. Precisely how these lofty philosophical speculations were transmitted to those living at the artisanal level of society is another matter.

  1. Oleg Grabar, ‘The Formation of Islamic Art’, Yale, 1973.

  2. I can draw on my own experience here. I have managed to decipher and recreate a great many of the more complex of Islamic patterns without the benefit of any formal training in geometry whatsoever. I have found that it is largely a matter of intuiting the rules of this geometric game (plus a modicum of determination and patience).

  3. Neither Islamic craftsmen or mathematicians were aware however of symmetry principles or symmetry-groups in the formal, modern sense; these are relatively recent, 19th & 20th century, discoveries.

  4. Plutarch (1st century CE), was himself a Platonist and was fully aware that the Pythagoreans were the originators of the distinctly religious attitude towards mathematics that was adopted by Plato.