The magic square on the Passion façade: keys to understanding it

While admiring the Passion façade and all of Subirachs’ sculptural work, more than once visitors are surprised to discover a series of numbers inside a square and wonder what they mean.

Well, it is a magic square, but in this case, it is a very special one. In this article, we’ll try to explain why.

A magic square is a series of numbers on a square grid, placed so that any row, column or diagonal line always adds up to the same number. This sum is known as the magic constant of the square.

Magic squares start with 3×3 grids, as there’s no possible solution to a 2×2 grid and a 1×1 grid doesn’t make sense.

Normally, this means putting correlating whole numbers into the grid: for a 3×3 grid, the numbers from 1 to 9; for a 4×4 grid, the numbers from 1 to 16. Starting from these rules, the magic constant cannot be chosen and depends on the sum of the numbers used. For example, in a 3×3 magic, square where the sum of 1+2+3+4+5+6+7+8+9=45, each row, column and diagonal line sums 45/3 = 15; in a 4 x 4 magic square, where the sum of all the numbers from 1 to 16 is 136, the magic constant is 136/4 = 34. So, for a 5×5 square, the constant is 65; for a 6×6, it’s 111; and for a 7×7, 175.

The Sagrada Família magic square, however, is 4×4 and doesn’t meet these basic initial conditions. On the one hand, it doesn’t have all the numbers from 1 to 16 (it is missing the 12 and 16) and some numbers are repeated. On the other hand ―and herein lies the symbolic key―, the magic constant isn’t 34 but 33.

Subirachs took an existing magic square, from German painter Albrecht Dürer’s engraving Melencolia I, and adapted it, repeating the numbers 14 and 10 instead of 12 and 16, to make it add up to 33, the age Jesus is traditionally believed to have been executed. And we say traditionally believed because, historically, this has never been confirmed 100%. Nevertheless, it is true that 33 is also a symbolic number, and not at all random, based on the importance of the number 3 in the Christian world, as the symbol of the trinity.

Melencolia I, Albrecht Dürer. France National Library.

Nevertheless, Dürer’s engraving was a very special starting point for Subirachs. In addition to coming up with the magic constant by adding up the rows, columns and diagonal lines, it can also be obtained with many other combinations. Likewise, the author added a sort of signature or colophon: the two numbers in the centre of the bottom row, 15 and 14, are the year he made this piece.

The square at the Sagrada Família also has some of these characteristics and, so, in addition to the rows, columns and diagonals, there are many other options that add up to the magic constant of 33.

For some examples, see the ones marked here in different colours, which are the most notable combinations of four numbers that add up to 33:

Plus, in the magic square at the Sagrada Família, there is also a sort of hidden subliminal signature: adding up the numbers that repeat and looking at their correspondence in the Roman alphabet, we get the initials INRI.

The initials INRI means Iesus Nazarenus Rex Iudaeorum (Jesus of Nazareth King of the Jews). This is the sign that Pontius Pilate wrote on the Jesus’ cross and here, his signature.

Subirach chose these four numbers because there is one from each row, column, diagonal and quadrant, and also because the sum of these repeated numbers is 48, or four times twelve. All within the symbolic framework of what the numbers represent.

MAGIC SQUARES, A FASCINATION WITH NO KNOWN USE

Magic square have been recorded as far back as the third millennium BC in ancient China. According to legend, offerings had to be put into a 3×3 grid in order to calm the irate gods. Similar combinations are also known from Indian, Egyptian, Arab and Greek culture. The various civilisations have attributed astrological and divine properties to these squares, which were often represented on talismans, and have been tied to the sun, moon and planets in our solar system. In the western world, they were introduced sometime in the 14^th century by the Arabs and the Greek monk Moschopoulos. From then, they have drawn in great mathematicians like Pascal, Leibnitz and Euler, who dedicated several works to them despite the fact that they have no known use.

The basic 3×3 square is quite simple to create, even for those who aren’t expert mathematicians. By finding groups of three numbers that add up to 15, we see that only the number 5 can go in the centre, which must participate in four different combinations that add up to the magic constant (row, column and two diagonals). Continuing in the same manner, we find the numbers that have to go in the corners and on the sides. This will give us the one possible solution, although by turning it different ways we come up with eight possible variants.

The 4×4 square, however, is much more complicated, with 110 possible solutions that, turned different ways, give us 880 variants. Dürer’s is one of these. They all have 34 as the magic constant, but we can see that some solutions are more magical than others in terms of the number of possible combinations that add up to 34.

The square at the Sagrada Família has a total of 310 combinations that add up to 33. Here are the seventeen possible combinations of three numbers:

With four numbers, there are 88 possible combinations that add up to 33; with five, there are 131; and with six, 66. With seven numbers, there are eight different combinations:

As 1+2+3+4+5+6+7+8=36, more than 33, there’s no possible group of eight numbers or more that can add up to the magic constant of 33.

MAGIC SQUARES TODAY

Dan Brown’s best-selling novel The Lost Symbol, which takes place in Catalonia, Barcelona and at the Sagrada Família, also uses Dürer’s magic square as a key to the puzzle to be solved. The author uses an anagram of Isaac Newton with the same seven letters as his name in Latin, Isaacus Neuutonus, reorganised to spell out the message “Jeova Sanctus Unus”. If we put these letters in the same order as the seven numbers in Dürer’s famous magic square, they are encrypted as:

As you can see, centuries and centuries go by but magic squares are here to stay. And at the Sagrada Família we have a very special one that will go down in history.