The aesthetic appeal of mathematics

Mathematics

From conch shells to chrysanthemums: nature abounds with spectacular arrays of geometrical forms. Their visual forms can be translated into mathematical equations, enabling an intellectual understanding of the ways such geometric forms are created and replicated throughout the visual world. Translating visual forms into equations does more than satisfy thirst for computation, though. As the "science of total intellectual order," mathematics enables human beings to perceive order in the universe, to see neither a random collection of petals nor a smelly set of sea creatures ("Patterns, Order, and Chaos," p. 189). In addition to helping human beings perceive natural order in a frequently chaotic universe, mathematics also encourages several key functions including generalization, idealization, and abstraction. The equations the mathematician conceives can be applied to all similar conch shells, not just one or two; in fact, any spiral will follow certain trajectories and will be represented through similar mathematical symbols. Equations also stimulate the innate fascination with the ideal and the absolute. Circles, pyramids, spirals, and parabolas are transformed into ideal, nearly spiritual absolutes: like Plato's forms they are archetypal representations. Represented in the mundane world, circles, pyramids, spirals and parabolas are rarely as perfect as they are in the human mind. Finally, mathematics encourages abstraction, which liberates the mind to pursue open-minded and free thinking. Mathematics reveals the beauty of the natural world and by using mathematical equations human beings can create works of majesty and art.

S. Jan Abas notes that geometric forms predominate in medieval Islamic art not only because of the admonishment of anthropomorphized depictions of deity but also because of the intrinsic aesthetic value of mathematics. The stars and rosettes that pepper Islamic art and architecture serve several key symbolic and practical functions: they symbolize divine presence and intervention; they represent divine light and spiritual illumination; and they permit actual light to flow through physical spaces such as in mosques or palaces. The aesthetic value of the star patterns in Islamic art and architecture also serves a purpose: uplifting the heart and soothing the mind just as any work of art of vision of natural beauty can.

Islamic art not only demonstrates the symbolic significance of geometric forms and their psychological, social, religious, and aesthetic functions. In addition to these purposes, Islamic art also demonstrates symmetry. Symmetry's appeal is well-known: babies tend to favor faces with symmetrical features over those with lop-sided noses or askew eyes. Although absolute symmetry is by no means a prerequisite for beauty, symmetry is usually perceived with pleasure. The Spirograph forms, explicated by Karin Deck, are sublimely symmetrical.