Patterns of Infinity

If we probe deeper into any phenomena – astronomy, the cycle of life, mathematics, we arrive at the concept of infinity. It is the most abstract of abstractions, although mathematicians have tried to devise ways to measure and rationalize infinity.

Trying to make sense of the infinite is a bit like trying to contain the uncontainable. Contemplating infinity inevitably led all civilizations and all religions to the concept of God.  The art of most religions express God as an image or a symbol, perhaps to make it more accessible to devotees, leaving it to the philosophers to come to terms with the nature of infinity.

The exception is Islamic Art, which from its earliest expressions of Quranic calligraphy, to the architectural design  of mosques,  made infinity the cornerstone of its expression.

While most art continued on a human centric pathway, culminating in the cult of the individual, Islamic art remained rooted to an interconnected cosmic order, exploring more and more complex patterns of infinity in two dimensional patterns and dazzling three dimensional arabesques and muqarnas in architecture. 

The interlacing Islamic patterns without beg inning or end , simultaneously intoxicating and restraining,  reflecting no specific ideas, not leading the eye in a particular direction, present unbroken rhythm and endless interweaving for quiet  contemplation of an infinite and all-encompassing  cosmic force in perpetual motion. Islamic calligraphy, while defining specific words, interlace in an equally compelling rhythm. The position of the reed pen at the beginning and ending of the formation of each letter is in the initial position of writing Aleph – the first letter of the Arabic alphabet, implying all begins and ends with Aleph or Allah. 

What distinguishes Islamic art is its intrinsic relationship to geometry and mathematics.  Geometry was considered by the ancient Greeks as essential to the understanding of logic and philosophy . The Motto on the entrance to Plato’s Academy read “Let none ignorant of geometry enter my door.”

Islamic scholars studied Euclidian geometry and mathematics from the Greeks as evidenced  in the Fihrist (Catalogue) written by the 10th century Baghdad court librarian al-Nadı¯m. There is much speculation but little evidence  of the exact origins and subsequent development of Islamic patterns. Yet the use of these patterns spread across the Muslim world from Spain to India, from North Africa to the Oxus, spanning many centuries. 

The Turkish historian Alpay Özdural  presents  two mathematical sources: “On the Geometric Constructions Necessary for the Artisan”  by Abu ‘l-Waf al-Buzjani (ca. 940-998), and an anonymous work, “On Interlocks of Similar or Corresponding Figures”  (ca. 1300) to suggest  collaboration between mathematicians and artisans in the Islamic world.

The works of Plotinus were translated into Arabic as early as the 9^th C  and Turkish Art Historian, Gülru Necipoglu, suggests the influence of his concept of ‘The One’  who has no manifestation and can only  be experienced, or known, through contemplation, is eternally present in all existence, inspiring both rapt contemplation and ecstatic, creative extension.

However, the actual evolution of patterns from the simple geometric patterns of Great Mosque of Kairouan,in the 9^th C to the  dizzying muqarnas of Al Hambra, Granada,  remains an enigma for researchers. 

In 2007 Harvard physicist Peter Lu, concluded “medieval Islamic artists produced intricate decorative patterns using geometrical techniques that were not understood by Western mathematics until the second half of the 20th century”. The set theory of infinity developed in the 19 C by Georg Cantor  was pre shadowed by Ibn e Sina in the 11^th C. The question remains: How did artisans intuitively produce complex pattern sets that could be extended infinitely in perfect symmetry and with mathematical accuracy? 

Allama Iqbal wrote in his diary: A mathematician cannot but a poet can enclose infinity in a line.

Titus Burckhardt suggests that contemplating the patterns on the Mosque of Cordoba, or of Ibn Ṭūlūn in Cairo, encapsulates the Islamic concept of Divine Unity and may be enough to answer the question “What is Islam?”

 

Durriya Kazi

March 28, 2021

 durriyakazi1918@gmail.com