By beauty of shape I want you here to understand not what the multitude understands by this expression, like the beauty of living things or of paintings resembling them, but something alternatively rectilinear and circular, and the surface and solids which one can produce from the rectilinear and circular, with compass, set-square and rule. Because these things are not, like the others, conditionally beautiful, but are beautiful in themselves.
From years of familiarity with the geometric mode in Islamic Art and Architecture it seems to me that one of the more interesting aspects of this genre is precisely that there is no single 'Key to Islamic Pattern', but rather a whole variety of ways of achieving geometric complexity. Regional variations have resulted in many distinct modes and families of pattern and symmetry types, not to mention differing attitudes towards geometric 'purity'. This is perhaps the most fascinating aspect of this art because it seems to beg the question 'What are the constant criteria in this broad aesthetic tradition?'. That is to say, what was it that kept the Islamic preoccupation with geometric pattern going as an essential artistic expression for such a long period, across a whole range of craft productions, over such a vast geographical area?
My own feeling, as I hope I have made clear, is that the Islamic dedication to symmetry and geometric ornament, both derive ultimately from the aesthetic ideals of a particular Classical philosophical tradition, namely that of Platonism, which had been thoroughly absorbed into mainstream Islamic thought at a very early stage of its cultural evolution, but which was later driven out as a Philosophy by religious intolerance. In short, Islamic geometricism, with its delight in the endless play of abstract geometrical shapes on the Euclidean plane, is an essentially Platonic art-form.
This, as I say, is a personal view - and from an academic perspective I realise that it is a hopelessly generalised one. It suffers as much from an insufficiency of continuant examples of geometric design as it does from a lack of documentary evidence – however, for the reasons cited above, all investigations into this subject are confronted by these same problems. There is little real evidence for the involvement of academic mathematicians in the elaboration of Islamic geometric art (which doesn’t mean that there was none, see Postscript A), and the notion of doctrinal influence is at the very least questionable (see Postscript B on the ‘Sunni Revival’ thesis). Nevertheless, as I stated at the beginning of these notes, there must be a compelling reason for the adherence to strong symmetrical arrangement and highly geometric modes of decoration in the art and architecture of the Islamic world. This aesthetic tendency seems to have been fastened on at an early stage of Islamic cultural confidence (and was indeed an expression of it) - and once this particular aesthetic trajectory had been settled upon, in which decorative forms had become a primary means of cultural expression, it was natural that the inherited late-Classical decorative elements would be embellished and made more complex over the generations.