Magic Squares, Cryptocrosses, and the Upcoming Movie ‘Tenet’

There is a mysterious set of words that appears in graffiti, inscriptions, amulets, and other forms all across the ancient Roman world. Commonly known as the Sator Square, it is a Latin palindrome — a phrase that reads the same forward and backward — arranged as a square of five rows and columns, and comprised of five words that are each five letters long. Because it reads the same regardless of which corner and which direction (horizontally or vertically) one reads it in, it is also a two-dimensional palindrome. There’s no consensus regarding its exact meaning and purpose, so that’s what we’ll be looking at in a moment. Here’s what it looks like:

Sator Square

This ancient enigma, normally little more than a footnote in history books, has been thrust into the popular spotlight by the entertainment press¹ due to the upcoming (we hope) July release of a new film by writer-director Christopher Nolan, whose previous body of work includes Memento, Inception, Interstellar, and the Dark Knight trilogy. Nolan’s films often use unconventional, nonlinear storytelling techniques, including nested stories (Inception) and even narratives that proceed backwards (Memento), to explore the elusive nature of reality. We can probably expect another unique perspective on reality in his next movie — called Tenet — which apparently involves espionage and time travel.

The film’s title, as you might have guessed, refers to the central word of the Sator Square above. The typography of the film’s logo and the mirrored imagery of its poster reflect the nature of a palindrome, and crew members were given cubes with the letters of the Sator Square engraved on them as gifts.

The logo for the movie Tenet

Since I’m writing about this puzzle on a Bible-related blog, you’ve probably also guessed that there might be a religious connection. We’ll get to that.

What Those Words Mean

I should first mention that there are two variants of this inscription. One goes SATOR–AREPO–TENET–OPERA–ROTAS, and the other takes the opposite order: ROTAS–OPERA–TENET–AREPO–SATOR. Whether the order matters or not, the versions beginning with ROTAS are the oldest, so it makes sense to treat that as the original form (Marcovich, p. 32). However, I’ll keep referring to it as the Sator Square, since that name seems to be more widespread.

Here’s a simplified summary of what the five words of the Square mean in Latin:
ROTAS = wheels, torments (noun: accusative plural) or rotate (verb: 2nd person singular)
OPERA = works, effort, or trouble (noun: nominative or accusative)
TENET = holds, keeps, preserves (verb: 3rd person singular)
AREPO = meaning uncertain
SATOR = sower, creator, progenitor (noun: nominative)

The difficulty with AREPO, which is not a known Latin word, has led to a wide variety of interpretation approaches. Most theories assume that it is a name. A competing explanation, that it was a loanword from Gallic meaning “plough”, goes back to a fourteenth-century Byzantine scribe but has no linguistic evidence to support it (Marcovich, p. 29). Taking AREPO to be a name, the sentence means something like “The sower Arepo holds the wheels with care” (Sawyer, p. 124) or “The sower Arepo protects against toils and torments” (Mercovich, pp. 33–34).

An older view of some scholars, no longer widely followed, was that the square might be read boustrophedon (which means the lines zig-zag, alternately read from left-to-right and right-to-left), with the central word TENET repeated. Doing so avoids the problematic word AREPO and produces SATOR OPERA TENET – TENET OPERA SATOR, which could be plausibly interpreted as “the Creator preserves his creation.” Many of the scholars who used to support this interpretation intended to read SATOR in a Christian or Jewish sense, with the sower either being Jesus or the Judeo-Christian God. Mercovich provides several reasons why this reading is not likely — particularly the facts that the oldest versions all begin with ROTAS and that boustrophedon texts never started right-to-left (for all this, see Mercovich pp. 30–34). It also makes little sense in light of the square’s likely purpose, which we shall examine below.

Where the Square Appears

The two earliest known appearances of the square are graffiti found at Pompeii, a city that was buried under volcanic ash in 79 CE, and at least one of them could be from earlier than 62 CE (Marcovich, p. 31). In addition to “countless” wall graffiti and inscriptions, it also appears on amulets, ostraca, potsherds, papyri, and parchments found across most of Europe, North Africa, and Asia Minor, and dated to a period spanning antiquity and the medieval era.

The Square’s Purpose

Miroslav Marcovich, the famous classical scholar (now deceased), argues convincingly that the square is a magic charm or formula intended to confer some kind of blessing or good luck. Numerous magic squares similar to this one are known from antiquity. The fact that the three basic vowels A E O are each repeated four times apparently reinforces its magical nature. The central word, TENET (meaning “preserve”), serves as the cruciform “spine” of the charm, crossing it both ways to protect it from evil influence (Marcovich, p. 34).

Our understanding is incomplete, however, without knowing the identity of this Arepo. Whoever Arepo is, he or she must be the guardian deity whose protection this charm invokes (ibid.). We’ll look at that shortly; but first, there is another potential Christian interpretation that needs to be examined.

The Supposed Pater Noster Cryptocross

The Sator Square has a long history of people coming up with Christian anagrams to explain its true meaning, but one in particular stands out. In the 1920s, three scholars independently discovered that the letters of the Square could be rearranged to form the words PATER NOSTER AO (alpha omega) in the shape of a cross:

Pater Noster, of course, is Latin for “Our Father” and refers to the Lord’s Prayer, which begins with those two words in Latin translations of the Bible. This discovery solidified, in the minds of many scholars at the time, the notion that the Square was Christian in origin. The apparent Latin words, including the troublesome AREPO, could be ignored, and the Square could instead be treated as a cryptocross.

To explain what a cryptocross is, a brief summary of early Christian archaeology is in order. Contrary to what one might expect, there is no evidence of the cross being used as a Christian symbol (in art, tomb inscriptions, etc.) prior to Constantine, even though it was widely used by other religions and cultures. Symbols found frequently in early Christian settings include the anchor, dove, boat, fish, Good Shepherd, and Orante, but the cross is nowhere to be seen. In order to resolve the discrepancy between the assumption that Christians always venerated the crucifix and what the evidence actually tells us, some scholars have resorted to finding cryptocrosses — crosses hidden inside other symbols and art for reasons not fully explained. The problem with such an approach is that if you try hard enough, you can find crosses everywhere. Intersecting lines in a picture of an anchor or a tree, the crosshatches on a roll of bread, the letter tau (T) in someone’s name, and so on. Thus, it has also been suggested that the Sator Square is a cryptocross used by Christians for its secret meaning. (For all this, see Graydon F. Snyder, Ante Pacem: Archaeological Evidence of Church Life before Constantine, 1985, especially pp. 60ff. See also Moeller, 1973, pp. 2–3, for examples of cross symbolism in other religions predating Christianity.)

There is no solid evidence to support the existence of cryptocrosses, and church historian Graydon F. Snyder concludes that the evidential grounds for interpreting the Sator Square as an anagram for Pater Noster are easily dispensed with. Even if the anagram were intended, it could belong to any number of Roman cults that used cross symbolism, and the discovery of early versions at Pompeii rules out any Christian connection (Snyder, p. 63; Charlesworth, App. IV). After all, we have no physical evidence for Christianity from the first century whatsoever.

A few scholars have proposed that the anagram had Jewish origins. However, this seems unlikely, since there is no prayer in Jewish tradition called Pater Noster, and for this anagram to be deliberate, those words must be of fundamental importance to the originator (Hofmann, p. 558.24ff, cited by Marcovich, p. 37).

Furthermore, the anagram is unsatisfying, as it leaves out two A’s and two O’s. As Charlesworth notes, to deal with the leftover letters by suggesting “that they represent Alpha and Omega smacks of special pleading,” and the only book of the Bible to associate alpha and omega with Christianity, Revelation, was written well after the date of the earliest Sator Squares (Charlesworth, App. IV).

Ultimately, the Pater Noster anagram is almost certainly a sheer coincidence.

If Not Christian, Then What?

If the Sator Square is indeed a magical charm and not a Christian cipher or cryptocross, then who is Arepo? The main candidates are as follows.

Horus — The Egyptian god Horus was the god of magic, with epithets that include ‘averting evil’, ‘protector’, and ‘saviour’ (Marcovich, p. 39). Horus was adopted into Greco-Roman religion as a personification of the rising sun under the name Harpocrates, which meant ‘Horus the Child’. The name was often abbreviated as HARPOS or HARPON in Greek, and numerous Latin variants existed — all beginning with A, since latin had no H. According to Marcovich, the transition from HARPOS in Greek to AREPO in Latin is “an easy one”, since it was already common enough to insert extra E’s into words to make them easier to pronounce (a phenomenon called anaptyxis). So far, this appears to be the most promising candidate, especially since Harpocrates was extremely popular in Pompeii, where the oldest Sator Squares are found (Marcovich, p. 42).

Apis — In an article published almost 50 years ago, Egyptologist J. Gwyn Griffiths proposed that Arepo was the latinized version of the Egyptian name Hr-Hp, which means “face of Apis”. Griffiths, who believed the square to be Christian, admitted that this explanation did not attach “any conceptual significance” to the name Arepo, and he did not explain who this Arepo was supposed to be or why a personal name would appear in the Square (Griffiths, pp. 6–8). Historian Walter O. Moeller, in a book published soon afterward, concurred with the Apis interpretation but believed the Square to be Mithraic in origin (see bibliography below). One reason Moeller connects the Square to Mithraism is that the Egyptian deity Apis was represented as a bull, and a slain bull plays a central role in Mithraic symbolism. However, few (if any) scholars have been swayed by Moeller’s arguments. Marcovich counters that using a theophoric personal name rather than the deity’s name makes little sense (Marcovich p. 46, n. 87).

A cypher — It is possible that AREPO is a codeword for another name. Marcovich provides several other examples of ancient magic squares, and they often contain words that are meaningless or encoded and can only be understood with special insight into the square’s religious context. There’s an ancient Coptic healing square, for example, that consists of four four-letter words intended to represent the four beasts from Revelation 4:7 and Ezekiel 1:10.² However, in place of the word for eagle (AETOS), it has PHONE, meaning “voice”. The connection is that the eagle serves as the voice of God in Rev. 8:13. Without this knowledge, the square makes no sense. If AREPO is also a cypher of some kind, we might simply lack the background knowledge to identify what it refers to. 

Gibberish — Some scholars have concluded that AREPO is just magical-sounding gibberish like “abracadabra”. The late French historian Henri Polge concluded that it was “un artifice lexicale”, a made-up word. Marcovich counters that if the inventor were free to invent a name, ARENO would work better, since its counterpart ONERA works better in context than OPERA (“The sower Areno checks any burden or torment”).

Christian Adoption of the Sator Square

Even if the Sator Square’s origins are pagan, as is very likely, it became popular as a Christian magical formula in later centuries — especially in Egypt. A Coptic abjuration spell from the tenth century, for example, quotes both the Sator Square and the aforementioned square with the four beasts in order to heal a certain girl.³ A sixth- or seventh-century Coptic amulet uses the same two magical squares as well as the Coptic names of the three Wise Men to protect against snakebites.⁴ Several more examples can be given. None exhibit any knowledge of the Sator Square’s origins or meaning; they simply quote it and various other sacred names and spells in order to produce the desired magical effect. Similarly, an ancient codex of spells from Nag Hammadi called “The Magical Book of Mary and the Angels” uses the Sator formula in three of its spells. In one of them, the five words of the formula are said to be the names of the five nails used to crucify Jesus, which surely points to creative invention and not inside knowledge of the Square’s meaning. (See Meyer, pp. 367–368.) In medieval Europe, the Sator Square was sometimes inscribed on an amulet and worn to protect against witchcraft (Bellingradt and Otto, p. 135), or written on cloth and placed over a woman’s womb to aid in childbirth (Kieckhefer, p. 78). The Square was also used as a decorative motif in numerous medieval churches, including the eighth-century Abbey of St. Peter ad Oratorium in L’Aquila, thirteenth-century Siena Cathedral in Siena, and eighth-century Valvisciolo Abbey in Latina. Though most inscriptions of the Square are found in Italy, examples have been found in locales as distant as Britain and Sweden.

The Rotas Square at St. Peter ad Oratorium

The widespread use of the Square in churches and the coincidence of the Pater Noster anagram have kept alive the notion that the Square is somehow a Christian symbol. Although I have no special knowledge of the plot of Tenet, the public attention that the film ends up bringing to this historical curiosity is likely to reinforce this notion, particularly among people with a penchant for historical mysteries and religious conspiracies.


  1. Examples include “Why Nolan’s Next Movie Is Titled ‘Tenet’ — and It’s Not Just Because It’s a Palindrome” by Release News and “Let’s wildly speculate about Christopher Nolan’s ‘Tenet’” by
  3. Vienna K 7093
  4. Yale 1792


  • Miroslav Marcovich, “SATOR AREPO = GEORGOS HARPON”, Studies in Graeco-Roman Religions and Gnosticism, 1988.
  • John F.A. Sawyer, Sacred Languages and Sacred Texts, 1999.
  • Graydon F. Snyder, Ante Pacem: Archaeological Evidence of Church Life before Constantine, 1985.
  • J. Gwyn Griffiths, ‘Arepo’ in the Magic ‘Sator’ Square, The Classical Review, Vol. 21, No. 1, 1971.
  • Walter O. Moeller, The Mithraic Origin and Meanings of the Rotas-Sator Square, 1973.
  • James H. Charlesworth, The Good and Evil Serpent, App. IV.
  • Heinz Hofmann, PW RE, Suppl.-Bd. xv, 1978.
  • Marvin Meyer, “Ritual in the Magical Book of Mary and the Angels”, Practicing Gnosis: Ritual, Magic, Theurgy and Liturgy in Nag Hammadi, 2013.
  • Daniel Bellingradt, Bernd-Christian Otto, Magical Manuscripts in Early Modern Europe, 2017.
  • Richard Kieckhefer, Magic in the Middle Ages, 1990.

Other Reading

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