The Magazine

The Gothic Vision

Blueprints for technology in patterns of design.

Feb 2, 2009, Vol. 14, No. 19 • By DAVID GELERNTER
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We see better when we recognize and can name (at least for our own purposes) the things we see. If you can tell a delphinium from a daylily, or a Titian from a Rubens, or a Honda Civic from a Lotus Elise, you see the world in sharper focus than someone who can't.

Gothic architecture--which emerged near Paris in the 1140s, became a powerful artistic force in most of Europe and remained so through the early 1500s--has been studied seriously since the 19th century. No other style of art in Western history has had such an intensely magnetic (sometimes passionate, sometimes hypnotic) appeal. You might imagine that every aspect of Gothic worth recognizing has already been recognized. Not true. Ideas from computer science sharpen our focus on Gothic architecture. They help us identify a fundamental design gesture that historians have seen in particular cases, but haven't described as the widespread, general phenomenon it is--because they lack the intellectual or ideational vocabulary.

Software has already played a role in research and writing on medieval architecture. The eminent Alain Erlande-Brandenburg's recent book on the cathedral of Reims (2007) is part of the new "Grand témoins de l'architecture" series. Each book is based on a fabulously detailed software model, which allows one to study the building of interest from unexpected viewpoints. Of course, the practice of architecture has been in the hands of the computer-aided design industry for years; historical essays illustrated by sophisticated computer-generated images are common. Yet the best such images approach nowhere within miles of the detail, precision, and beauty of engravings from the studios of such 19th-century master medievalists as Augustus Pugin, Robert Billings, and Eugène Viollet-le-Duc.

Allow me to discuss technology as a source not of tools but ideas. Computer science is useful in this case because software happens to resemble Gothic architecture in an unexpected way--"recursive structure" is important to each.

A structure is said to be recursive if the shape of the whole recurs in the shape of the parts. Imagine a circle, for example, formed of welded links that are circles themselves. Each circular link could itself be made of smaller circles, and in principle you might have an unbounded nest of circles made of circles made of circles. This sort of structure is surprisingly important in software, and in Gothic architecture.

The idea of recursive structure didn't originate with modern computing, but came into its own there. It first appeared as a powerful tool for organizing digital information in a software application designed in the late 1950s by H.L. Gelernter, in the course of his pioneering work on artificial intelligence. This application inspired a related one called Lisp, where recursive structure is the basic organizing principle not only for data but for the program itself. Years later the mathematician Benoit Mandelbrot developed his highly influential work on fractal curves as descriptions of nature based, partly, on the idea of recursive structure.

In architecture, the idea occurs in a much simpler way.

Many churches terminate in a chevet: As you enter such a church and walk towards the rear, you reach a half-circular space called the apse. You might find separate chapels opening off (or "radiating from") the walkway or ambulatory that follows the outside perimeter of the apse.

The chevet at the Abbey of Saint-Denis (1144) is a recursive structure. Its half-circular perimeter is defined not by a simple curved line but by a series of scoops, each a radiating chapel--and itself (roughly) a half-circle. In other words, this chevet is a semi-circle of semi-circles.

Many chevets have approximately this shape--in which each chapel "becomes a paraphrase of the apse itself," as John Summerson puts it. But Saint-Denis realizes the idea in its purest form--appropriately; Gothic architecture first emerged at Saint-Denis in this very chevet, and nearby parts of the building.

The inside of the west or front façade at Reims Cathedral, probably designed in the 1220s, is one of the most celebrated compositions in medieval art. In a large pointed arch a rose window is lodged at the top like a helium balloon. Within this large arch, and below the rose, is a second, smaller arch with a smaller rose lodged at its top. Thus, another recursive structure: an arch with a rose and, nested within it, a smaller arch with a smaller rose.