The Mystifying ‘Sator Square’: a Combination of Mathematics, Symmetry, and Religions
By: Richard Bruschi
Tags: Mystery, Sator Square, Culture, Religion, History

The Mystifying ‘Sator Square’: a Combination of Mathematics, Symmetry, and Religions

Dating back to the 1st century AD and somewhat common in archaeological finds in Europe, this magic square’s significance and symbolism are still a mystery

The Sator Square in Oppede, France. Photo from Wikipedia.

Overview

A ‘palindrome’ is a sequence of numbers or letters, hence actual words too, which reads the same both forward and backwards (the word is from the Greek ‘can be read both ways’). When used appropriately in a grid they can create a ‘word square’, so that you read the same words and those words in the same order either if you read it left to right, right to left, up to down, or down to up. This is the letters’ version of a ‘magic square’, a grid which has only integers and that gives you the same addition results whichever order you follow in a row, column, or two diagonals. In case letters are used, it’s technically not a ‘magic square’ although it’s informally called so for the parallel in principles. Furthermore, a word square is a special type of ‘acrostic’, a case when a form of writing takes form so that the first letter of each line spells a word out.

The Sator Square is a unique ‘word square’.

The square is formed by the five Latin words SATOR, AREPO, TENET, OPERA, ROTAS. As you can see, this creates a palindrome, and the word at both centerlines, ‘tenet’, forms a ‘palindrome cross’.

Where

The oldest Sator Square is on a column in Pompei and has been inscribed before the infamous eruption of 79 AD, but it has been found numerous times all over Europe and across many monuments different in historic time, style, and destination. It’s in the Basilica di Santa Maria Maggiore in Rome, in Roman ruins in Cirencester in England, in Santiago de Compostela, in the Certosa di Trisulti, the castle of Rochemaure in France, in Syria and Sweden — just to name a few. One thing that seems certain is that the Sator Square is found in many Christian religious buildings and it hasn’t been found before the advent of the religion.

What, why, and who

Every aspect of this word square is unclear. First of all, the meaning of the single words.

The word sator is a noun that means ‘sower’ or ‘farmer’, and is an image for ‘father’ as in ‘creator’. The image of an almighty farmer is present in Latin writers’ work right before the advent of Christianity. In the 1st century BC the word sator appears in Cicero’s De natura deorum (‘On the nature of the Gods’) regarding the natural world, mentioning the themes of fecundity and nourishment, as Cicero’s stoicism philosophy brings about the Logos spermatikòs (‘seminal logos’, the generative principle of the universe). In Cicero’s time and culture the Roman Saturn was the god of agriculture (again the image of ‘farmer’ and ‘sower’). It’s something to keep in mind as although written as ‘SAUTRAN’, they would link it to Saturn (written under the oldest of the Squares). Also, someone noticed that Saturn’s consort is Opis, sometimes called Ops, from which opus comes, the plural form of which is opera.

Saturn as depicted in the House of the Dioscuri at Pompeii, Naples Archaeological Museum. Photo by Carole Raddato CC BY-SA 2.0.

In the 1st century AD sator is used to reference the Roman Jupiter, father of all the gods and humans. Being also Venus’ father and therefore grandfather of Aeneas, from whom the Roman people descended according to Virgil’s Aeneid, he gave celestial origins to the Romans and their Empire. By the end of the century, sator referred to the supreme divinity in Latin literature, referencing both Saturn or Jupiter.

The philosopher Philo of Alexandria would coincide the Logos to the Biblical ‘Word of God’ (the Greek word logos means ‘word’, among other similar meanings) and therefore to Christ perhaps for the first time, referencing John’s Gospel (John 1:1): “In the beginning was the Word, and the Word was with God, and the Word was God.”

Clearly there are other links to Christianity. The image of ‘farmer’ for example, as God’s word ‘sows’ humanity through Adam at the beginning, or the sickle harvests at the end of times. Also, the image of the ‘almighty father’.

The word arepo is the most elusive. It doesn’t appear anywhere in the Latin world, therefore most experts consider it a name, although even this name is not found anywhere else. Interpretations so far have been a bit far fetched and difficult to sustain, such as identifying it as the abbreviation of aripennis, a small plot of land. Du Cange (full name Charles du Fresne, sieur du Cange, 1610–1688) an expert in ancient latin, included in his glossary of Medieval Latin the word aripus, which he interpreted as a farmer sickle or billhook. This would reconnect to Saturn, as that instrument is one of his iconographic symbols. The sickle/billhook is also associated with the Greek titan Kronos who, according to Hesiod, used it to evirate his father Uranus.

Further interconnection is found in Virgil’s Eclogues, where he foresees Saturn’s return to Earth marking the beginning of a new golden age. In his text he writes “The new great order of the ages is born”, “justice (virgo in Latin, also the ‘Virgin’) returns, return of Saturn’s reign”, and “a new lineage is sent down from high heaven.”. This has been later taken by Christians as a clear announcement of the birth of Jesus Christ,

The last three words have been somewhat considered deciphered. The word tenet is a verb and means ‘holds’, ‘understands’, and ‘sustains’. Opera could mean ‘with care’ or another meaning linked to work, as the word comes from opus meaning ‘work’ or ‘effort’. Rotas is usually translated as ‘wheels’, with a literal or metaphorical meaning such as ‘celestial wheels’. This plays into the interpretation of opera as ablative, thus translating the whole square sentence as “The farmer Arepo holds the wheels with effort”, shifting to focus on rotas with all its mystical, religious, and mythological connotations.

The aforementioned translation has been taken to its metaphorical meaning and rephrased as “The Creator of the lands holds the celestial wheels”, in the sense the creator rules over the land and fate. This would play into the connection of the heavens with earth symbolized by a cross, which in the Square is formed by the aforementioned palindrome cross with the two tenet.

Most think that the Sator Square has been created not by Christians for various reasons. Christians used the Greek language until about the 3rd century AD, so they wouldn’t have used Latin. Also, the earliest Square would have been carved in Pompeii at some point during the 1st century AD with an extremely unlikely presence of early Christians in the city. This would therefore suggest that its widespread presence in medieval churches is because it had been assimilated and adapted at a later stage. Nevertheless, there are strong connections and unlikely coincidences that create a strong connection between the Square and Christianity, although how remains a riddle.

The ‘Pater Noster’ arrangement of the Sator Square. Image from Wikipedia.

Three scholars apparently independently saw the five words as an anagram and rearranged the letters while maintaining Christian symbology, specifically the cross. The letters formed a cross reading ‘PATER NOSTER’, obvious reference to the most important Christian prayer, from top to bottom and left to right, and between the arms the letters ‘A’ and the ‘O’ (each repeated twice) which link to the symbology of ‘Alpha’ and ‘Omega’, the beginning and the end, as described in the Book of Revelation (commonly known as the Apocalypse of John). As indicated in a study published by the Cambridge University Press, the chances that this was accidental are exceptional. Lastly, some see in the central letter ’N’ the initial of Nazarenus, referring to Jesus, and notice that the ‘T’, the symbol deriving from the Greek tau representing the cross and in ancient times a symbol of resurrection, are flanked by an ‘A’ and an ‘O’.

An unusual reference is found in the Ethiopian Coptic ‘Prayer of the Virgin in Bartos’ in what is known as the Coptic Magical Papyri. Describing how Christ was crucified with five nails, the text named them Satōr, Aredō, Dened, Ōdera, Rōdos. The words are almost identical and the different letters have been written, in Greek or Coptic, with letters that still bear one or the other link with Jewish or Christian symbolism. The Papyri is dated later in the centuries though, so this too could have been a later assimilation of the words.

Although not of Christian origins, the Sator Square has connections to Judaism, perhaps giving a hint on some aspects of the identity of its creators.

Nicolas Vinel sees the Latin inscription as a Jewish cryptogram. He makes a connection between the bronze altar built by Moses under divine instruction, as described in the Book of Exodus (27:1–2), and the Square. Besides the mathematical explanation (it involves the locus pythagoricus of Iamblichus) it suggests that: the sum of rows and columns equals 65. The numbers involved are 13 + 26 + 26. Vinel, through the Hebraic gematria (‘gematria’ is an alphanumeric code of assigning a numerical value to a name, word, or phrase based on its letters), found that these numbers are important because they refer to the Jewish divinity. 13 is the numerical value of ehad (‘One’); 26 the value of the Tetragrammaton (the Jewish divinity name transliterated in four letters as YHWH or JHVH); and 65 the value of Adonai.

A final interpretation for the proponents of the Jewish origins of the Sator Square also point out that under the oldest of the Squares the name is, as mentioned at the beginning, not Saturn but ‘Sautran’. The letter ’N’ in epigraphy symbolizes the bronze snake, an identification mark and a symbol of salvation for the Diaspora. ‘Sautra’ is an imperative of the Hebrew root str, ‘to hide’, the infinitive absolute of which is SATOR.

Open mystery

There has been a lot written on the “magical” Sator Square. Some even connect it to Mithraism (also known as ‘Mithraic mysteries’, a Roman mystery religion centered on the god Mithras). Mithraic Mysteries. There has been no definitive conclusion. It doesn’t help that the earliest recovered example of the Square begins with ROTAS rather than SATOR.