Box 1. Rationality in stone

From the following article:

Triumph of the medieval mind

Philip Ball

Nature 452, 816-818(17 April 2008)



The twelfth-century renaissance gave rise to the artistic style now known as Gothic. In architecture this is characterized by hierarchical, orderly structures based on symmetry and proportion. Vaults and spires soar to unprecedented heights, yet the masonry, linked into a web of delicately balanced forces, seems almost weightless, flooded with light from immense coloured windows.

Some historians — most influentially Erwin Panofsky in the 1940s4 — have suspected a link between this style and the emerging belief in cosmic order. If a medieval church was in some sense a representation of heaven on Earth, they argue, then changes in church design must have something to tell us about how the Middle Ages conceptualized the cosmos. If the world was "God's discourse to man", in Umberto Eco's words, then cathedrals "actualized a synthetic vision of man, of his history, of his relation to the universe".

Panofsky proposed that the nascent French universities and academies in and around Paris influenced the Gothic architecture that originated here. Both architects and scholars, he said, used division and subdivision "to make the orderliness and logic of their thought palpably explicit"4. In the 1950s, historian Otto von Simson gave Panofsky's argument greater force when he scrutinized the role of geometry in the relationship between the intellectual and architectural worlds.

Von Simson argues that the first Gothic "marks and reflects an epoch in the history of Christian thought, the change from the mystical to the rational approach to truth"5. Historian of technology Lynn White agrees: "The transition from Romanesque to Gothic charts the passage from an age indifferent to the investigation of nature to one deeply concerned with it."

Today many historians consider Panofsky's argument to have been overstated, even misplaced. Some identify socioeconomic conditions as the principal force behind Gothic church building. Others say that geometry in architecture amounted to little more than convenient rules of thumb, lacking mathematical foundation. The truth probably lies somewhere in between.

A link between building and theology was sometimes explicit. To the scholars of Chartres, God was the great architectus, who used geometrical schemes to construct the Universe. Some medieval writers distinguished between the 'theoretical' geometry of the cathedral schools and universities, governed by mathematical proof, and the 'practical' geometry that could be used mechanically for constructing pillars and vaults. Builders probably had little need of mathematical understanding: they could draw and interpret plans encoded in sequences of operations that could be learnt by rote and passed on orally.

Triumph of the medieval mind SONIA HALLIDAY PHOTOGRAPHS

Chartres Cathedral may reflect an appreciation of cosmic order.

A fifteenth-century builders' handbook gives prescriptions for how to construct regular polygons, or to find the centre of a circle from an arc, with compass and ruler, with no indication that the writer knew of, or felt the need for, Euclid's proofs.

Yet classical geometry and pythagorean symbolism do sometimes emerge in masonry. For example, medieval sculptors often used a lens-shaped figure called the vesica piscis to frame Christ seated in majesty. The shape is found in Ars geometriae et arithmeticae by the early sixth-century Roman writer Boethius as the overlap between two equal circles whose circumferences pass through one another's centres. Boethius explains that this construction, which can be made with a pair of compasses, may be used to make the most 'perfect' of triangles, the equilateral. So the shape would have been used to frame the figure of Christ not simply because it was pleasing and convenient but for its symbolic connotations.