hypothetically exit the realm of matter, becoming open to higher forms of
knowledge and, ultimately, theology. Following the intellectual, noetic role
for geometry that Proclus proposed in his commentary on Euclid’s geo-
metry, they saw geometry as permitting the soul to“separate itself from this
[corporeal] world in order to join, thanks to its celestial ascension, the
world of spirits and eternal life.”^44
While the Brethren did not propose the idea of space as pure abstraction,
which emerged in the thought of ibn al-Haytham, they were thefirst to
imagine motion as a means of developing a line from a point moving to
another point, and the surface as this line rotating around one of the
points.^45 Following Plato’s discussion inTimaeusof the triangle as the
root of all rectilinear surfaces, they emphasized it as the foundation of
polyhedral geometry. However, their demonstrations were mathematically
incorrect, and they only tangentially mention Plato’s association between
the forms and the four elements.^46
Rather than introducing Platonic metaphysics into Islam, they promote
geometry as integral to mortal creativity. They discuss how animals such as
bees and spiders make habitation according to their natures–bees produce
hexagons, while spiders thread their webs rectilinearly and then stitch their
lines curvilinearly. Both model human endeavor.“Some people generate a
given art from their own proper talent and intelligence without being
preceded by anyone else, whilst most makers acquire their art by way of
demonstration and learning under mentors.”^47 These examples link geo-
metric practice to Quranic references to nature. One passage exhorts
humanity to follow the example of the bee under the inspiration of God
(Q16:68–69). Conversely, another warns humanity to refrain from any
protection outside that of God, comparing humanity to“spiders building
themselves houses– the spider’s is the frailest of houses”(Q29:41).^48
Approximately concurrently with al-Tabari’s restriction of Bukhari’s
Hadithcondemning representation to the representation of beings with a
soul, the Brethren thus establish an appropriate range for human creativity.
Like al-Tabari, they thus recognize innate or learned human creativity as a
natural gift of God without ignoring its pride-inducing danger. In various
discourses, the Quranic comparison between human and apian inspiration
also served as a model for calligraphy and engineering.^49(^44) Necipoğlu, 1995 : 191. (^45) El-Bizri, 2012 : 44 n. 103, 101–103.
(^46) Plato, 2008 :46–52; El-Bizri, 2012 : 126. (^47) El-Bizri, 2012 : 131.
(^48) Abdel-Haleem, 2004 : 254. (^49) Berlekamp, 2011 : 40.
284 Mimetic Geometries