Theories, Problems and Evidence

The main consideration in any discussion of “Islamic geometrical design” should surely be the sheer breadth of this topic. With its extraordinary range of examples, drawn from centuries of development throughout the Islamic world, this is clearly a subject on which it is perilous to make sweeping generalizations. 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 Qu’rānic 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 clearly does have some basis as an influence, deriving from the strict Islamic adherence to the 2nd commandment, Exodus 20 (“You shall not make unto you any graven image …” etc.). But this explanation, by itself, is entirely inadequate in accounting for the particular forms that have been adopted in the Islamic world. 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 comes 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 principal sources of evidence will always lie in the surviving work itself, but even here there are problems, not least the fact that so much in the architectural record has been destroyed. In addition, 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.

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 upward. This is an art of decorative playfulness, largely deriving from 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 by the sophistication and complexity of their designs. In Islamic arts and crafts generally, technical virtuosity was always highly regarded.

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 below), and even of occasional cross-disciplinary meetings, but it seems far more probable that those who created these forms generally relied on their own informal, nonacademic working knowledge of plane geometry, which was clearly quite considerable. 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 the means of their construction almost amounting to a trade secret in many cases. Even the extent of specialization in these different decorative components (geometric, floriated arabesque, and calligraphic) and the methods of organizing these 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 (Fig. 1).

“One would enquire in vain for the masters who brought this system to its flowering, or those who opened up new ways for its development. This art is totally anonymous and it would contradict the artist’s noblest charge, which was the liberation of the spirit from the transitoriness of worldly ties.” - Ernest Kühnel

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 have meant that important parts of the archaeological record have been destroyed or seriously diminished. Apart from the terrible human costs, 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 recognizable – but the precise qualities that create these distinctive cultural qualities are often not so easy to pin down (Wade, 2018). Islam’s proclivity for geometric ornament is of course very much part of its character and part of what makes so instantly recognizable – 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 geometrical symmetries – these are its central principle. The overriding question in this topic has to be, Why and How did this preoccupation with geometrical and symmetry principles come about?

At the risk of being accused of the sort of generalizations mentioned earlier, my own instinct 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 was to later incorporate many of its themes into its own broad philosophical outlook. In fact, Classical Greek philosophies in general were to become very much part of the Islamic tradition. In its formative period, 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 would seem to have a strong bearing on the principle themes of Islamic art. The Greek author Plutarch, 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.” - Plutarch

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 our view, is quintessentially Platonic. Precisely how these lofty philosophical speculations were transmitted to those living at the lower, artisanal level of society is of course another matter entirely…