Why is symmetry so satisfying?

In an early chapter of his interesting new book, Symmetry: A Journey Into the Patterns of Nature, Marcus du Sautoy describes a visit to the Alhambra, the great Moorish palace in Granada, Spain. He and his young son spend an afternoon identifying 14 different types of symmetry represented in paving patterns, ornamentation, and tile work. To the layman, the patterns may look simply like pretty forms, but to du Sautoy, who teaches mathematics at Oxford University, they are expressions of deep geometries that have their own names: gyrations, *333s, miracles, double miracles.

Du Sautoy's book is about mathematics, but his excursion to the Alhambra is a reminder that symmetry has always been an important part of architecture. Symmetry appears in small things and large: Floor tiles may be laid in symmetrical patterns; the design of door paneling can be symmetrical, and so can window panes. In frontal symmetry, the left side of a building's facade mirrors the right (the entrance usually being in the middle); in axial-plan symmetry, the rooms on one side of the axis are a mirror image of those on the other. If the women's restroom is on one side, chances are the men's is on the other. Sometimes not being symmetrical is important; the fronts and backs of buildings, for example, are intentionally different.

Symmetros is a Greek word, and ancient Greek architecture used symmetry as a basic organizing principle. As did Roman, Roman-esque, and Renaissance. Indeed, it is hard to think of any architectural tradition, Western or non-Western, that does not include symmetry. Symmetry is something that Islamic mosques, Chinese pagodas, Hindu temples, Shinto shrines, and Gothic cathedrals have in common.

Architectural Modernism thumbed its nose at tradition and firmly avoided symmetry. Being symmetrical was considered as retrograde as being, well, decorated. All exemplary Modernist buildings celebrated asymmetry: The wings of Walter Gropius' Bauhaus shoot off in different directions; the columns of Mies van der Rohe's Barcelona Pavilion are symmetrical, but you can hardly tell, thanks to the randomly spaced walls; nothing in Frank Lloyd Wright's pinwheeling Falling water mirrors anything else; and Le Corbusier's Ronchamps dispenses with traditional church geometry altogether. The facades of Philip Johnson's Glass House are rare instances of Modernist symmetry, although all the elements of the interior—kitchen counter, storage wall, and brick cylinder containing the bathroom—are carefully located off-center.

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