This is a brief introduction into Planetary Magic Squares. My intention is to set the stage for a later post in which I will describe my methods for working with these Magic Squares to construct and charge sigils.
The mathematical definition of a Magic Square is an arrangement of distinct integers in a square grid in which the integers of each row, column and diagonal all add up to the same number. While a full exploration into the history of Magic Squares is beyond our current scope, suffice it to say that their use in mathematics and mysticism is well documented in Asia as early as the 7th century B.C.E.
By the early Renaissance, Magic Squares were popularized in Europe and made their way into western magical traditions via the later writings of Marsilio Ficino, Pico della Mirandola, and Cornelius Agrippa. Of primary importance to this post is a grouping of seven squares between the orders of 3 and 9 that were identified as planetary in nature. These were each attributed to one of the seven classical planets based on the emanation sequence of the kabbalistic sefirah associate with that planet.
|Order||Sefirot||Planet||Square||Sum of Rows||Total Sum||Magic Square|
|3||Binah||Saturn||3×3||15||45||Click to View|
|4||Chesed||Jupiter||4×4||34||136||Click to View|
|5||Gevurah||Mars||5×5||65||325||Click to View|
|6||Tiferet||Sun||6×6||111||666||Click to View|
|7||Netzach||Venus||7×7||175||1252||Click to View|
|8||Hod||Mercury||8×8||260||2080||Click to View|
|9||Yesod||Moon||9×9||369||3321||Click to View|
The number of rows and columns, the sum of the rows, and the total sum of the square were understood to represent certain magical principles of the planet in question. Through Hebrew gematria the numbers on the planetary grid could also be represented in Hebrew letters. As such, the practitioner was able to derive divine names associated with the planet using the square and sigils super-imposed on the square.
The construction of sigils from a name (or a name from a sigil) follows the basic rule that every number/letter of the name establishes a point on the sigil. Occasionally double letters are denoted with additional embellishments (such as humped lines) and the start and end of the name are sometimes marked by a circle and/or a small perpendicular line. Additionally, when the gematria value of the letters exceeds the highest number in the square, the value is divided by either 10 or 100 following standard Pythagorean reduction (i.e. Nun in Hebrew gematria is 50, but can also be represented as 5).
For example, the solar magical square is a 6×6, grid with each row, column and diagonal summing to 111 and the total sum equaling 666.
The intelligence of the Sun is called forth using the name Nachiel (gematria value of 111), and the spirit of the Sun answers to the name Sorath (gematria value of 666). These names have an associated sigil derived from the square itself.
Note that both the names Nachiel and Sorath contain Hebrew letters that enumerate higher than 36, the highest integer in the Magic Square of the Sun. The numeric value of these letters was reduced using the system of Pythagorean reduction described above. Additionally, with the sigil of Sorath, we see the use of the humped line (forming an “m”) to denote two repetitions of the same number. In the case of Sorath, the first six is for the letter Samekh (60, reduced to 6) and the second for the letter Vav (6).
The Magic Square for each planet along with its seal, intelligence sigil and spirit sigil can be found following the links in the table at the beginning of this post.