Sator Square

sator square, also called sator-rotas square or rotas square, early Latin word puzzle or cryptogram. It is the most well-known example of a lettered magic square, with 25 letters that make up a five-by-five grid of acrostic Latin palindromes. The words found in a sator square are SATOR (“sower” or “planter”), AREPO (an unknown word, possibly a name), TENET (“to hold”), OPERA (“work” or “care”), and ROTAS (“wheels”). These words are often arranged in this order, but examples have also been found beginning with ROTAS and ending with SATOR; this variant is called a rotas square.

When the five words of a sator square are read horizontally, vertically, forward, in reverse, from bottom to top, or from top to bottom, they form a sentence: sator arepo tenet opera rotas. This sentence has been translated in numerous ways, with the most commonly cited being “The sower, Arepo, works (or holds) the wheels with care.” If read boustrophedon (Greek: “to turn like oxen”; zigzag) with the central word repeating, it can be read as sator opera tenet, tenet opera sator, which has been translated as “as you sow, so you shall reap” and, with a more religious bent, “the Creator preserves his works.” Such a reading has the advantage of eliminating the obscure AREPO, which occurs nowhere else in Latin. (Few of these readings apply to the rotas square.)

The oldest complete example of this cryptogram was a rotas square found in the ruins of Pompeii in 1936. This finding, carved into a column of Pompeii’s Palestra Grande, can be dated to before 62 CE, when an earthquake destroyed the structure. (A fragmentary rotas square was found at Pompeii in 1925.) Other rotas squares have been found throughout the Roman world, from Manchester, England, to the border city of Dura-Europos (now in Syria).

After the fall of Rome and the spread of Christianity throughout Europe, the rotas square was supplanted by the sator square, possibly because the square then began with sator (“sower”), referring to the parable of the sower in Matthew 13. Another Christian connotation was that the grid’s middle word, both vertically and horizontally, is always TENET, which can be read as the two arms of a hidden cross.

The sator square’s origin as a Latin puzzle became increasingly irrelevant as the symbol took on magical properties in European folklore. In the 12th century it could be found in medical books, often as a cure for rabies and fever. Sufferers were advised to carve the square’s words into the crusts of bread before ingesting it. The sator square was also often used as a charm for good fortune in medieval times. In the centuries following, it was adopted as a ward against fires; it was inscribed on the walls of German buildings to prevent their destruction. Sator squares accompanied European settlers to the Western Hemisphere, proliferating throughout North and South America in the 18th and 19th centuries. In the Allegheny and northern Appalachian mountains, German settlers continued to use sator squares as magic cures and prophylactics into the 20th century.

Beginning in the 19th century, Christian thinkers and puzzle enthusiasts tried to decode possible hidden meanings in the sator square. Perhaps the most popular was the Pater Noster theory, which finds the Latin name of the Lord’s Prayer, Pater Noster, written twice in cross form as well as four residual letters (two each of the letters a and o), which can be read as alpha and omega, the first and last letters of the Greek alphabet and how God identifies himself in the Book of Revelation. Independently proposed in the mid-1920s by three separate authors, the Pater Noster theory fell into disfavour with the discovery of the Pompeii rotas squares. Some academics have found a basis for the square’s origin as a Jewish symbol, pointing to the Hebrew letter tau as the central symbol rather than the cross. They also point to the large population of Jews who settled in Pompeii prior to and during the 1st century. Another theory places the square’s origins in Pythagoreanism and Stoicism. Others have argued it is a gnostic symbol developed from Egyptian words and imagery. Many such arguments hinge on tenuous theories about the meaning of AREPO, and no theory of the square’s origins has been widely accepted. It has even been noted that another magic square (ROMA-OLIM-MILO-AMOR), which does not form a sentence, was found at Pompeii, and, thus, the 1st-century Romans possibly just found magic squares to be fun.