Gaze and Geometry: comparing two languages of vision from Medieval Eastern and Modern Western visual compositions

Abstract

Islamic patterns from the medieval era are non-figurative displays of repetitive geometric shape relations on architectural surfaces. They are historically created as designs of a particular cultural setting and are said to be representations of infinity. Extensive research delineates elaborate geometric construction processes for these patterns based on a grid of circles, practically drawn using a compass, and lines that emerge from the intersections of these circles. Compositions deliver rich visual fields to the viewer while the application of these geometric constructions on actual materials alleviate the resulting visual effects. The designs can be assumed to reflect how visual fields and seeing are understood in their cultural and intellectual context. Among the rare evidence to corroborate this assumption, Kitāb al-Manāẓir offers a theory of vision based on the geometry of light as early as 1028. Written by the mathematician Ibn Al-Haytham, the manuscript constitutes a backdrop to the geometric construction processes that the Islamic patterns built up from, and provides remarkable insights to gaze at that time. Similar to how artists such as Gyorgy Kepes in early 20th century was inspired by the then-new science of psychology to formulate a “Language of Vision” in art based on basic elements of point, line and plane, and how their spatial relations are perceived, could one correlate Ibn Al-Haytham’s calculations and terminology to the ideation of Islamic geometric patterns as visual designs? This paper aims at formulating a grammar for the geometric patterns based on Ibn Al-Haytham’s calculations and terminology in Kitāb al-Manāẓir in order to reveal their language of vision.