this was expressed through the abstraction of trees; for Islamic artists,
through understanding geometry as a microcosmic rendition of the
cosmos.^18 Both systems convey intellectual meaning not through super-
ficial resemblance, but through structural verisimilitude. In opposing
European naturalism, Mondrian proposed a different system of represen-
tation that ended up–for reasons less arbitrary than one might imagine–
reframing those of the Islamic tradition.
The implicit preference for surface over structural verisimilitude in the
natural attitude of the Western tradition prefers explicit over implicit
meaning. Grabar thus explains:
A positive cultural explanation of geometry...argues that geometry is the visual
expression of a set of truths that dominated the traditional life of the Muslims until
the appearance of contemporary disruptions. Thus astrological configurations,
magical squares, cosmological considerations, and the central Muslim notion of
Unity (tawhid) are all seen as numerical ideas for which a geometric formulation is
not only possible, but even desirable. Many arguments of logic and fact exist
against this immediate interpretation of geometry, however appealing it is to a
curious mixture of Western orientalists and Islamic fundamentalists. The most
important objections are several. There does not exist, to my knowledge, a single
instance justifying the view that the Muslim community, theummah, as opposed
to individual thinkers, understood mathematical forms as symbolizing or illustrat-
ing a Muslim cosmology. Furthermore, we have no information to the effect that
viewers of complex designs on walls, ceilings, orfloors interpreted them in the
abstract and schematic formulas of the orderly sketches needed by the artists or
artisans to make their designs. Finally, although it has been shown that at least
contemporary artisans are well aware of the complex technology of their designs, I
do not know of many instances of a spectator or viewer being equally informed.^19
Grabar’s devaluation of“individual thinkers”as outliers to a single defining
truth suggests a static understanding of Islam, defined eternally through
doctrine. Yet knowledge is not always explicit, or even public. For example,
in the Ottoman Empire, geometric patterns circulated as guild secrets
associated with Sufibrotherhoods, where technical and spiritual knowledge
often required years of apprenticeship.^20 ‘Individual thinkers’are not excep-
tional; their overlapping discourses reflect widespread recognition of geo-
metry as perpetuating meaning. The difference between a cohesive Western
discourse of perspectivalism and one concerning Islamic geometry is not the
presence or absence of information, but the theorization that recognizes
relationships between individual thinkers as a discourse.
(^18) Blotkamp, 2001 : 100–101. (^19) Grabar, 1992 : 51. (^20) Necipoğlu, 1995 : 353.
Pattern as Pathology 273