Magic squares of the planets: numbers that become seals

A magic square is a grid of numbers arranged so that the sum of every row, every column and both diagonals is always the same. It is a mathematical object, but for centuries it was also a magical one. In the Renaissance the squares were associated with the seven planets and became the basis for constructing seals and characters, that is, a genuine script born from numbers.

From the Arab world to Europe

Magic squares were known in China and India, and in the medieval Islamic world they were studied both as mathematical problems and as talismanic tools. In Arabic treatises on the magic of letters, such as those attributed to Ahmad al-Buni, who died in 1225, squares appear beside the names of God and the letters of the Arabic alphabet. Through Latin translations and Hebrew manuscripts, this knowledge reached Europe in the late Middle Ages.

The most famous arrangement is found in the second book of Heinrich Cornelius Agrippa's De occulta philosophia, printed in full in 1533. Agrippa presents seven squares, one per planet, of increasing size: that of Saturn has three cells per side, Jupiter four, Mars five, the Sun six, Venus seven, Mercury eight and the Moon nine. Each square is accompanied by seals and the names of planetary intelligences and spirits.

How a name becomes a sign

The link between numbers and letters passes through Hebrew, in which every letter also has a numerical value. The name of a planetary intelligence could therefore be translated into a series of numbers. By joining the corresponding cells on the square with a continuous line, one obtained a broken path: that path was the character of the spirit, its graphic signature.

For names with values too high for a small square, the numerical reduction of the Kabbalah of nine chambers, Aiq Bekar, was used, which brings the letters back to values from one to nine. The square thus became a kind of machine for writing signs, in which mathematics and theology worked together. Many characters in later grimoires derive from this procedure, even when their origin has been forgotten.

Dürer's square

One of the most famous magic squares in the history of art appears in Albrecht Dürer's engraving Melencolia I, dated 1514. At the top right, above the winged figure lost in thought, there is a square of four cells per side, in which the sum of every row, column and diagonal is thirty-four. In the two central cells of the bottom row appear the numbers 15 and 14, which form the date of the work.

The four-by-four square was, in Agrippa's tradition, that of Jupiter, a planet considered beneficent and able to temper the influence of Saturn, lord of melancholy. Many scholars have read the presence of the square in the engraving in the light of this doctrine, although the overall meaning of the work remains a matter of debate.

The magic squares of the planets show in exemplary fashion the logic of esoteric alphabets: turning knowledge into signs, and signs into instruments of contemplation. In a grid of numbers the Renaissance saw the order of the cosmos reflected, and in a line traced upon it the invisible signature of the celestial powers.