Sator Square Non-Starters

Failed solutions to an ancient rebus (The Mysterious Square, Part 1)

The so-called Sator Square, a palindromic grid of letters which can be read beginning at any of the four corners, has captured people’s imaginations for millennia. Early in its history, those who ostensibly understood it inscribed it widely, and it eventually came to have a cultural value similar to that of the Icelandic Rune Staves I have also written about. More recently, lacking a key to its understanding, scholars and layfolk have theorized about its meaning. So, in something of a turnabout from my posts about the Witham Sword, I wanted to evaluate some of the different solutions to this mysterious square.

The text reads:


This appears to be some type of Latin phrase, and has puzzled many since it first started appearing. And appear it did, reaching a status some have described as memelike long before the intertubes began trading in such stuff. Its earliest appearances seem to have been in the Italian Peninsula, but it has been seen in France, Portugal, and as far away as England and Syria. There is even a runic inscription that shows the square Although somehow this has been characterized and spread across the internet as being a runestone, it is (as can be seen in the image, below) carved into wood—the bottom of a bowl of some kind, partly missing, but which doubtless finished the Square.

Then, as I noted, the secret of the square seems to have been lost. The earliest known attempt at a decipherment of the Square came from a Byzantine scribe in the 14th century, but there have been many since. The 19th century saw a boom in scholarly efforts, which continued until last century when they dropped off, with codebreakers either feeling it to be unsolvable or being satisfied with the efforts already made.

On the unsolvable front, Rose Mary Sheldon has provided us with an exhaustive 34-page bibliography of the solutions posited, titling her work, “The Sator Rebus: An Unsolved Cryptogram”.¹

Let’s turn to just a few of the solutions Sheldon considers to have failed. First there’s that of that first Byzantine scribe, who broke it down thus:

σάτορ—ὁσπεἱρων [sower]
άρέπο—ἄροτρον [plough]
τένετ—ϰραεί [holds]
ὄπερα—ἔργα [works]
ρότας—τροχούς [wheels]

There are problems, of course. Mainly these are around arepo, which would continue to bedevil would-be codebreakers as we shall see. The scribe here claims is ἄροτρον (L. arepum, of which arepo would be an inflected form) supposedly meaning “plough”, although it is found in no other source. Some have suggested a borrowing from a Gaulish or Celtic term, *arepos, which again is nullibiquitous. The asterisk in *arepos is used by linguists to mark a reconstructed word—that is, one that is unattested but conjectured to exist. Wanting arepo to mean plow or opera rotas to somehow imply it seems a clear case of confirmation bias: “it says ‘sower’ so it must say ‘plow’.” I think given the brevity of the rebus, the inclusion of such redundancies would actually be quite undesirable. Still, it lives on in many modern interpretations which hold that the phrase’s full translation, with the other words translating in order as “the sower”, “to hold”, “works”, and “wheel”, is therefore:

The sower holds the plough, the works, the wheels.

Others have decided that arepo is a proper name, again choosing to set aside the fact that it’s a hapax legomenon, and so render the phrase:

The sower Arepo holds the works, the wheels.

They somehow feel that “the works, the wheels” implies a plow even though the plows of the appropriate time in no way resembled such a description. Frustration with the word led some to dismiss it as a term like abracadabra—without meaning, but while some such terms are attested, it’s a far from satisfying conclusion. Abracadabra, rather seems to derive from ΑΒΛΑΝΑΘΑΝΑΛΒΑ (ablanathanalba), a palindromic term associated with the rooster-headed anguipede, ΑΒΡΑΣΑΞ (Abrasax). Ad repo, “I creep towards” is another interpretation that has been suggested but results in still worse nonsense. Yet another suggestion is the Latinized and shortened name of the popular god of good luck from Graeco-Roman Egypt, Harpocrates (Har-pa-khered, “Horus the Child”).

To get from Harpocrates to Arepo, elide the initial ⟨h⟩ (the Greek is Ἁρποκράτης), inject a vowel ⟨e⟩ to break up the consonant cluster rp, drop the entire second half, and Robert is your father’s brother. The meaning (in a charitable reading) thus becomes a decently apotropaic formula:

The sower Harpocrates keeps in check toils and tortures.

Never mind that the god is nowhere depicted as a “sower”, appearing in Egyptian stelae perched on a crocodile’s back, snakes clutched in his outstretched hands—an image that calls to mind Herakles…. And later, and especially in the Graeco-Roman context as a child with a finger pressed to his lips. Marcus Terentius Varro was apparently the first to describe the gesture thus:²

[…] Harpocrates digito significat, ut taceam.

[…] Harpocrates with his finger makes a sign to me to be quiet.

However it is important to note that this pose actually relates to the form of the hieroglyph for “child”, and did not have a meaning relating to silence or secrecy in its original context. This sometimes-winged figure was later conflated with Cupid—Cupid with a uraeus on his head, though later forms morphed it into a topknot. If anything, he is shown holding a cornucopia—the polar opposite of the idea of sowing.

The next major direction of exploration came from the idea that the inscription should be read boustrophedonically. The term means “as (plowing) oxen-turn”, therefore referring to a reading that alternates directions, so:


The image of plowing oxen probably was a temptation to employ this type of reading, but it’s just more fruit of the poison arepo tree. And again applying a generous amount of imagination to the reading, we can interpret this as the New Testament dictum:

As ye sow, so shall ye reap.

This solution also has its share of issues: first, inscriptions in boustrophedon appeared only in the prehellenic Greek (until 510 BC) and archaic Etruscan (until 480 BC) periods, coinciding with the advent of the Phoenician-based alphabet into those cultures, before they had settled on a single reading direction; left-right for Greek and right-left for Etruscan. So these predate the first known appearance of the square by just about 500 years.

Second, in boustrophedon inscriptions the letters themselves are typically reversed to show the reading direction. Such inscriptions also invariably begin left to right, while this solution requires a right-to-left start. That is, this solution would require the versions beginning with sator to be the older, original form, which contradicts all evidence. Indeed, the desire to read the cryptogram boustrophedonically may have actually prompted the current dominance of the sator-first form.

Finally, the symmetry of the square is a major element of its magic, or at any rate, aesthetics. The 5×5=25 form is destroyed by the 30-letter reading required for the boustrophedon to work. Furthermore, the words arepo and rotas are omitted entirely in this solution, which seems like taking the easy way out.

As you may have also noticed, we have now entered a realm where interpretations are based on the idea that the inscription is a Christian one. And the locations it has been found in suggest such an association, as they include Benedictine and Cistercian abbeys, a cathedral, an Anglican church, and a private chapel.

And many other seeming links to Christian tradition have been noted in potential solutions: An old Cappadocian tradition gave the shepherds of the Nativity the names Sator, Arepon, and Teneton. An old Byzantine biblical tradition calls the Three Magi Ator, Sator, and Peratoras. And the Ethiopians and Abyssinians invoke the Savior by enumerating the five nails of the Cross: Sador, Alador, Danet, Adera, and Rodas.

Attempts were also made to read the opening lines of the square as a set of abbreviations, similar to those I used in my solution for the Witham Sword:

SAlvaTOR A REx Pontifex O


SATOR A Rerum Extremarum Principio Omni

Of the two the first is execrable and the second only somewhat less so but again nowhere apart from this posited solution to the Square are these words found together—a fairly clear sign that there was no such phrase to code into a rebus.

One solution that seems to satisfy many interprets the Square as an anagram for Pater Noster, the opening words of the Lord’s Prayer, with a leftover pair of ⟨A⟩s and ⟨O⟩s as Alpha and Omega, representing God’s omnipresence.

Some aver that this could not possibly be a coincidence, that this must be the solution. However, when it comes to anagrams, quite a few attractive ones are possible—and some even manage to use all the letters—including:

  • Oro te, oro te, pater, sanas.
  • O pater, ores pro aetate nostra.
  • Ora, operare, ostenta te pastor.
  • Retro, Satana, toto opere asper.
  • Satan, oro te pro arte, a te spero.
  • Satan, ter oro te, opera praesto.

However all of these Christian associations are easily swept aside by the fact that the earliest known versions of the Square are graffiti from Pompeii. Two such were found in the city in separate locations and written in different hands and were buried in the ash of an exploding Vesuvius, giving a clear and irrefutable terminus ante quem of 79 AD. Not only was there no known Christian population in the city by that time, 1. It is not known how long before 79 AD the inscriptions were made—one of them has at least one responding graffito, so it had to have stood there for at least a while, and 2. If this were a Christian cryptogram it would likely have had to have been formulated and dispersed from other larger communities and there is zero evidence for this.

On top of this, the language of the early New Testament was either Aramaic or Greek—some debate remains as to whether Greek was originally used or if there was an Aramaic urtext—with the earliest possible date for the Gospels in any form being around 40 AD. That accomplished, a Latin translation would have to have been undertaken—for which, I might add, there is also no evidence until the Vetus Latina, a hodgepodge of translated sections from the 2nd century at the earliest. Then a cryptogram relating to such a text would need to be created and disseminated even to places with a negligible Christian community community, all within a maximum of 39 years. The whole hypothesis is pretty sketchy—even accepting the several unproven bits, the timeline just doesn’t work.

In fact, the discovery of the first of the Pompeiian Squares in 1936 was more likely the cause of the decline of scholarship on the issue more specifically than the cases I mentioned earlier—nearly everything had to be simply thrown away. The second, while actually found in 1925, was in much worse shape, coming from a ruined house, and was only able to be identified via the model of the other graffito. In Part 2, I’ll get to a theory I do credit, and why.

Read Subsequent Articles in this Series

Part 2: And the Rotas Go ’Round

Addendum: Loosening “Tenet”’s Hold


  1. In Cryptologia, 2003.
  2. Marcus Terentius Varro, De Lingua Latina, 5.10.

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