Gaudí's Sagrada Família and the magic square of the Passion façade

The magic square summing to 33 on the Passion façade of the Sagrada Família: from Dürer to Subirachs, numbers and symbols in Gaudí's basilica.

On the Passion façade of the Sagrada Família, beside the scene of the kiss of Judas, a grid of sixteen numbers is carved. Adding them by rows, by columns or diagonally always gives 33, the age that Christian tradition attributes to Christ at the moment of his death. It is one of the most photographed details in Barcelona, and one of the few examples of a magic square on a great contemporary sacred building.

A building site lasting more than a century

The basilica was begun in 1882 to a design by Francisco de Paula del Villar. The following year the project passed to Antoni Gaudí, who transformed it radically and devoted the rest of his life to it, until his death in 1926. Gaudí personally completed only part of the Nativity façade. He conceived the building as a Bible in stone: three façades for the Nativity, the Passion and the Glory, eighteen towers dedicated to the apostles, the evangelists, the Virgin and Christ. In 2010 the church was consecrated by Pope Benedict XVI.

Subirachs and the Passion façade

The Passion façade was entrusted in 1986 to the Catalan sculptor Josep Maria Subirachs, who worked on it for about twenty years. His angular, almost abstract style deliberately contrasts with the naturalistic exuberance of the Nativity. The scenes are read in a serpentine path, from the Last Supper to the laying in the tomb. The magic square stands at the level of the betrayal, as a kind of numerical seal on the drama that is beginning.

From Dürer to Barcelona

Subirachs's square derives from a famous model: the one Albrecht Dürer engraved in 1514 in Melencolia I, where the constant sum is 34 and the two central numbers of the bottom row indicate the very year of the engraving. To obtain 33, Subirachs lowered four numbers of the original square by one. The result is not a perfect magic square in the mathematical sense, because some numbers repeat and others are missing.

This choice shows clearly the nature of the symbol: what matters is not arithmetical purity but meaning. In the Renaissance tradition magic squares were associated with the planets and appeared in treatises on natural magic, such as the De occulta philosophia of Cornelius Agrippa. In Barcelona the same device is placed at the service of Christian meditation on the span of Christ's life.

Numbers and architecture

Gaudí too reasoned in numbers and geometries: the columns branching like trees, the ruled surfaces such as hyperboloids and paraboloids, the hierarchy of the towers' heights translate a symbolic order into built form. The tower of Jesus, the tallest, was designed to rise above all the others as a sign of the centrality of Christ. There is no need to attribute secret doctrines to him to recognise an architect who thought of structure itself as religious language.

The small square of the Passion, the work of a late twentieth-century sculptor, thus converses with a sixteenth-century German engraving, with Renaissance treatises on magic and with an ancient tradition of sacred numbers. It does so inside a building that continues to grow and that, phase after phase, adds new layers of meaning. Whoever stops before that grid may read in it an arithmetical game, a learned quotation or a prayer in figures.