Associating these words with the elevation promised in the Quran, they
transform pragmatic knowledge acquired from the ancients into a means
of ensuring the education of the true Muslim soul. Explicit in the treatise’s
conclusion, this unconscious infusion of knowledge extends from geome-
try and music to knowledge of the heavenly spheres and ultimately of God.
Know, O brother, that the study of sensible geometry aids skillfulness in the arts, whilst
the study of intellective geometry and the knowledge of the properties of numbers and
figures help in grasping the manner by which the heavenly bodies affect the lower
natural entities, and also in understanding how the sounds of music affect the souls of
the listeners. Studying the manner by which these two types influence their effects is a
prerequisite to knowing the way by virtue of which the separate [i.e. incorporeal] souls
impact the embodied souls in the realm of generation and corruption. Those who study
intellective geometry have a way to reach knowledge of it through God’saidand
guidance.^51
Geometry could describe the movement of music because of the shared
mathematical principles underlying both. Both music and geometry insinuate
themselves into the perceiver through this inherent structure, one inextricably
representing the other. For them, harmonies relied on the employment of
several‘virtuous ratios’which transcended specific media, applying as well to
music, speech, or form as to the soul. These geometries take different forms for
different senses: whereas they recognize visual perception as depending on
straight lines, they understand aural perception as taking place through circular
ones that inform systems of poetic–musical notation. Akkach rightly warns
that,“while major premodern Arabic sourcesprovide detailed exposition of the
close correspondence between prosodiccircles and musical cycles, the corre-
spondence of these to the geometric patterns and spatial structures of Islamic
architecture remain speculative and conjectural.^52 Alternatively, this disparity
may reflect cultural emphasis: while our modern oculocentrism leads us to
imagine geometry visually and consider sound analogously, the extensive
discussion of the geometry of sound in poetics and music allows for visual
geometry to function supplementarily.
The epistles of the Brethren of Purity circulated widely among intellectuals as
well as artisans, perhaps informing the use of geometric surface treatment
inculcating perception of God. Geometry demonstrates the agency of God
without taking recourse to the semiotic distinction between signifier and
signified. Whereas outwardly mimetic representation of the divine presumes(^51) El-Bizri, 2012 : 159. (^52) Akkach, 2018 : 181.
286 Mimetic Geometries