Same but different

In an early chapter of his interesting new book, Symmetry: A Journey Into the Patterns of Nature, Marcus du Sautoy...

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 Al Hambra, 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.

Symmetry appears in small things and large: Floor tiles may be laid in symmetrical patterns; the design of door panelling can be symmetrical, and so can window panes. In frontal symmetry, the left side of a building8217;s faccedil;ade 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 women8217;s restroom is on one side, chances are the men8217;s is on the other.

Symmetros is a Greek word, and ancient Greek architecture used symmetry as a basic organising principle. As did Roman, Romanesque, 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 Gropius8217; Bauhaus shoot off in different directions; the columns of Mies van der Rohe8217;s Barcelona Pavilion are symmetrical, but you can hardly tell, thanks to the randomly spaced walls; nothing in Frank Lloyd Wright8217;s pinwheeling Fallingwater mirrors anything else; and Le Corbusier8217;s Ronchamps dispenses with traditional church geometry altogether8230; Yet without occasional symmetry, all those angles and squiggles start to look the same.

Why is architectural symmetry so satisfying? As Leonardo da Vinci8217;s famous drawing demonstrated, it reflects the human body, which has a right side and a left, a back and a front, the navel in the very centre. Du Sautoy writes that the human mind seems constantly drawn to anything that embodies some aspect of symmetry.

Excerpted from Witold Rybczynski8217;s 8216;Mirror images8217; in Slate