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Crosshatching in the Crosshairs

Brian Hayes

THE GRID BOOK. Hannah B. Higgins. 300 pp. The MIT Press, 2009. $24.95, paper.

We live on a planet wrapped in a fishnet of meridians and parallels. To get along in this world, we learn to navigate the streets and avenues of a city, the aisles of a supermarket, the columns and rows of a spreadsheet. At the airport we glance at the tabular listing of departing flights (columns and rows again), then solve minor problems in coordinate geometry to find gate B18 and seat 23C. Grids and networks are everywhere. Even our entertainments present themselves as arrays of squares: the chessboard, the Scrabble board, crossword puzzles, Sudoku.

In The Grid Book, Hannah B. Higgins looks into the cultural significance of all these crosshatch patterns and other geometric devices for organizing space and time. Higgins’s field is art history, and so she gives generous attention to manifestations of the grid in the arts: Piet Mondrian makes an appearance, the cubists get their due, and there’s a whole chapter on the evolution of perspective drawing. But Higgins also explores more widely, touching on city planning, writing and printing, weaving, mapmaking, musical notation, accounting, and of course the Web.

She begins with the brick, the modular building unit of several civilizations in the past 10,000 years. The first bricks were “hand-formed like loaves of bread,” she says.

During the next millennium, they would become more regular in size and shape and take on thumb indentations, concave pocks that made them more receptive to the mud mortar. . . . One imagines a field of concealed thumbprints, elemental self-portraits, tucked away inside these ancient walls.

In the further millennia since then, bricks have become still more regular and standardized; the thumbprints are gone. And yet the brick—emblem of industrial uniformity, all right angles and sharp corners—also serves to build fluid, curvilinear forms. Higgins quotes, or perhaps slightly misquotes, the architect Louis Kahn: “If you think of a brick, for instance, you say to brick ‘What do you want, brick?’ And brick says to you, ‘I like an arch.’”

Having begun with the common brick, Higgins turns near the end of her story to other standardized rectangular objects: the shipping container and the cardboard carton. The economic revolution brought about by the 40-foot cargo container is now well known, but it’s still a story worth telling. Perhaps less familiar is the tale of Kellogg’s Corn Flakes: It was the first consumer product to come prepackaged in a cardboard box. In both cases an important element of the innovation was the possibility of stacking and packing without waste of space.

Higgins misses a few squares of the great grid. In the chapter on bricks she might well have discussed bond patterns—the various ways of arranging the long and short faces of bricks in a wall—a topic that would have nicely illuminated her theme. In the discussion of perspective drawing she has occasion to mention René Descartes, “whose Analytic Geometry (1637) demonstrated for the first time that geometry could be explained algebraically.” But then she drops the subject without pausing to note that the Cartesian plane marked the very invention of the grid in its modern mathematical form, with orthogonal axes assigning each point on the plane a pair of coordinates. Elsewhere, too, when the topic turns mathematical, Higgins is not always surefooted. Her account of fractal geometry is incoherent, and she introduces Pythagoras as someone “famous for figuring the area of the triangle.”

But if this is not a mathematically sophisticated book, it is nonetheless an informative and sometimes provocative meditation on the place of geometry in human life. In an afterword, Higgins observes that grid lines can sometimes look like the bars of a jail cell, confining and constraining us. But then she takes a walk across her campus (the University of Illinois at Chicago) and recalls that the gridlike array of cubical buildings was erected on the rubble of an earlier neighborhood, whose grid in turn replaced the original Chicago street network that was swept away in the fire of 1871:

Each grid has a weave of its own that can be put to the task of reinforcing existing social structures as well as bending them and breaking them apart. The brick wall is a grid surface warmed by palms that produces a sense of permanence as well as its opposite, rubble.

Brian Hayes is Senior Writer for American Scientist. He is the author most recently of Group Theory in the Bedroom, and Other Mathematical Diversions (Hill and Wang, 2008).

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