Sator as linguistic destiny (Sator Square, Part 6)
Just as the discovery of the second Pompeian Rotas square in 1936 effectively foreclosed the historicity of a Christian solution, the meaninglessness of the Sator square—which should have ended debate altogether—has been discovered three times, by three scholars working independently, over the course of four years. Each time the finding was ignored. The history of this non-discovery is itself revealing—it tells you something about what happens when one gazes too long into the abyss of the square.
In 1965, Margherita Guarducci—the epigrapher who had published graffiti beneath the Vatican from the late third century written by people who believed they were at the tomb or shrine of Peter—published a study calling the Sator square uno scherzo grafico: “a graphic joke”. Her method was counter-anagram. She rearranged the same 25 letters into Satanic invocations and showed that the grid’s letters could produce devil-worship even better than the Lord’s Prayer. If the same raw material yields opposite messages with equal ease, the material carries no message. The response was silence.¹
Three years later, Paul Veyne arrived at the same conclusion from a different direction, making the argument methodological. Because the letters in this palindrome are so common, you can easily rearrange them into dozens of other meaningful phrases. He generated a flood of counter-readings in Latin, and as we saw in Part 2, Veyne constructed from the same twenty-five letters a second cross—PORTAE NOSTRAE—geometrically identical to Grosser’s PATERNOSTER, crossing at the shared ⟨N⟩.² If the method that finds one cross finds two, the method proves nothing. His verdict:³
le palindrome existe et l’anagramme n’existe pas—c’est nous qui la faisons exister.
The palindrome exists and the anagram does not; it is we who bring it into existence.
Again, silence.
Then, in 1969, Charles Douglas Gunn submitted a doctoral dissertation to Yale that proved the point by a third route—not linguistic this time, but computational.⁴
Gunn compiled a dictionary of more than two thousand Latin five-letter words and wrote a computer program to generate every possible 5×5 word square with the same fourfold symmetry as the Sator—the same word reading across, down, and both reversed.
The central “cross” requires a word that is itself palindromic. There are only 43 of these that are five letters long:⁵
AEAEA, AENEA, AEREA, INANI, MACAM, MADAM, MAGAM, MAIAM, MALAM, MANAM, MURUM, MUTUM, REFER, RENER, ROBOR, ROGOR, ROROR, ROTOR, SAGAS, SANAS, SAPAS, SATAS, SECES, SEDES, SEGES, SENES, SEPES, SERES, SIDIS, SIRIS, SITIS, SIVIS, SOLOS, SONOS, SUCUS, SUDUS, SUMUS, SUTUS, TAXAT, TEGET, TENET, TEPET, TEXET
The first and last words of the square must be a palindromic pair whose middle letters begin with one of the above, yielding this list of 35:⁶
Animo/Omina, Antea/Aetna, Arabo/Obara, Assam/Massa, Assum/Mussa, Aures/Serua, Essem/Messe, Iurem/Merui, Iesum/Musei, Iuras/Sarui, Iures/Serui, Maius/Suiam, Marem/Meram, Mares/Seram, Metor/Rotem, Metum/Mutem, Mites/Setim, Mitis/Sitim, Mures/Serum, Muris/Sirum, Mutas/Satum Mutis/Situm, Mutit/Titum, Mutus/Sutum, Natas/Satan, Nemus/Sumen, Neris/Siren, Orabo/Obaro, Rotas/Sator, Rutas/Satur, Samus/Sumas, Satis/Sitas, Satus/Sutas, Seius/Suies, Simus/Sumis
Of these narrowing options, Alberto G. Peano Casavola notes:⁷
If both the word for the second line and its reverse for the fourth one are required to be meaningful […], there are a few dozens of solutions listed by Gunn.
The program found solutions. Not one—a significant number of formally valid Latin squares can be assembled under those constraints. Additionally, Gunn’s program was able to identify three 5×5 squares composed entirely of palindromes:⁸

Not a single one besides the Sator left any trace in the historical record. None propagated. None was scratched on a wall, copied onto a parchment, carved into a tomb, or folded into a charm.
The most recent burial is Casavola’s. Writing in 2024, he cites both Guarducci and Gunn in his footnotes, only to read past their findings and construct his own 20-page receiver story—the square decoded through Virgilian palingenesis and Saturn’s pruning-knife.⁹ He does exactly what the square invites everyone to do: look into it and see one’s own reflection.
Though somehow missing his own point, of the three fully palindromic squares Gunn offered, Casavola concedes:¹⁰
Although they are much more symmetrical than the Rotas/Sator square, no ancient palindromist ever got excited about any of them and recorded it for us on stone, parchment or papyrus.
Gunn computed 2,264 valid squares if you allow nonsense words¹¹—If you require all five to mean something, the Sator is the only solution.
And before the Sator, there was ROMA.
As I’ve mentioned before, Romans knew their city’s name reversed into amor—love. It is the kind of accident that invites play, and they played with it. Casavola documents at least three ancient attempts at a 4×4 ROMA word square, the earliest from Pompeii: grids built on the ROMA / AMOR axis, the interior cells filled with varying success.¹²
The 4×4 grid is forgiving—looser constraints, wider solution space, the palindromic engine already given by the language. Building these squares was a pastime, not an intellectual feat. Wall-scratching. Graffiti. Doodling with the formal structure of a puzzle.
This establishes the nursery. Someone filling 4×4 grids naturally wonders whether a 5×5 is possible. The step is obvious; the execution exponentially harder. At 5×5, Gunn’s enumeration shows the fourfold symmetry produces a small but real set of valid Latin squares. Most land on vocabulary no one would bother repeating. But one—by an accident of the Latin lexicon—lands on sator and tenet and rotas, and sounds like a statement about God.
The ROMA squares prove Romans were building word squares as a cultural practice. The Sator emerged not from a single mind but from a tradition of play already running on the smaller grid. The step up was natural. The survival of only one result was not. That asymmetry—widespread practice, singular survivor—is the fingerprint of selection, not authorship.
This changes the origin question. For 140 years, since Reinhold Köhler’s 1881 survey,¹³ scholars have asked: who composed the Sator square? Jews? Christians? Stoics? Mithraists? A bored legionary? The answer suggested by Gunn’s data is more unsettling: nobody composed it, because it composes itself.
The analogy is ecological. Many seeds can germinate in the same soil—Gunn showed the constraints permit a significant number of formally valid Latin squares. But most say nothing worth repeating. Selection is not about what can exist; it is about what survives. The Romans who scratched ROMA / AMOR squares on the walls of Pompeii were already working the 4×4 version of the problem. Someone—perhaps many someones, independently—tried a 5×5 grid, and the only meaningful solution propagated. This is why the authorship question produces nothing but receiver stories. There is no author to find. The square is a property of Latin.
Once the square exists, it becomes a mirror. Every community that encounters it sees its own theology reflected back. A Stoic reads it and finds the Logos spermatikos—the divine sower (sator) governing the cosmos with providential care (tenet opera rotas). A Roman poet steeped in Virgil’s fourth eclogue reads the return of Saturn’s golden age, the Saturnia regna, announced by wheels turning back to their origin. A follower of Mithras finds Saturn and his harpe—the pruning knife Casavola identifies with AREPO through three medieval glossaries—presiding over the highest initiation grade.¹⁴ A Jew in first-century Pompeii, if Nicolas Vinel is right, finds messianic prophecy¹⁵ encoded in the same letters that yield PATER NOSTER in a cross with Alpha and Omega at the terminals.¹⁶ A Christian reads the Son of Man with his sickle in Revelation 14, the sator of Matthew 13:37, the cross formed by the two TENETs.
None of these readings is wrong. But none of them are the “solution” either. They are projections—meaning supplied to a form that precedes all of them. Vinel’s Jewish-origin thesis is the most historically specific of the group, grounded in real evidence of Jewish presence in Pompeii, but it answers the question “who might have recognized meaning in this square?” rather than “who put meaning into it”. The distinction matters. What Vinel describes is an early act of reception, not an act of authorship. The square was already there, doing what it does: offering a surface legible as sacred without being legible as specific.
If the square were a message, you could not swap its words out without destroying it. But Coptic evidence shows you can do almost anything to those words, and the square keeps working.¹⁷

On certain witnesses, the square appears as ARETO / OTERA in place of AREPO / OPERA.¹⁸ Two of the five words replaced, two-fifths of the “message” simply gone. And nothing happens. The form persists. The sacred feeling endures. Copyists keep treating it as powerful, keep folding it into amulets, keep carrying it as protection.
Casavola offers a sharper alternative: the substitution may have been deliberate. If AREPO was understood as Saturn’s pruning-knife—his reading, grounded in medieval glossary entries linking aripus to gladius falcatus—then Coptic Christians may have swapped the word precisely because it carried pagan meaning they wanted to shed. The sator could be Christ; the harpe could not.¹⁹
But the Coptic witnesses do not stop at substitution. On a pair of healing amulets, the scribe glosses all five words as “the names of the nails which bound Jesus to the cross”—not corruption, not purge, but wholesale re-semanticization.²⁰ The same letters that may once have described a farmer at his plough now describe the instruments of the Passion. The tradition survives into Ethiopian Orthodoxy, where the five-nails reading persists to this day.
And then there is a small papyrus sheet from the late sixth or early seventh century, folded into an amulet packet against venomous creatures.²¹ The Sator square appears on it alongside the alpha-leôn square—the four living creatures of Revelation—the names of the three Magi, and Psalm 118. No gloss, no interpretation, no indication the scribe understood the Latin at all. The square sits in a Christian assemblage the way a stone sits in a wall: structurally present, semantically inert, doing its work by being there.
Three witnesses, three relationships to the same five words. One community swaps them. One re-reads them as the nails of Christ. One copies them alongside scripture without comment. And in every case the square keeps working—because its potency never lived in any single interpretation. It lived in the form being legible as sacred without being legible as specific. The square travels without its meaning intact, because the meaning was never the cargo.
22 Coptic specimens survive across four centuries and multiple sites—too consistent for scribal error, too widespread for a single line of transmission. In every case, the three load-bearing words hold: SATOR, TENET, ROTAS. Everything else is ornament. The Copts proved it by stripping the ornament away and finding that the sacred feeling survived intact.
The Sator debate has been running since 1881 and it keeps stalling because it keeps asking the wrong question. “Who made it?” presupposes a composer with an intention. But the form generates itself. The right question is: why does this seed take root in so many different soils? The answer is in the vocabulary. By pure combinatorial accident, the only meaningful 5×5 Latin palindrome happens to land on three words that span the concerns of every theology: creation (sator), governance (tenet), and cosmic cycles (rotas). A divine agent who creates, who holds, who turns the wheels—that is the minimum viable god.
Any monotheist or providentialist can read their own version into it because the sentence describes the job specification for a supreme being without naming a candidate. AREPO may have felt too narrow to the Copts—to Saturn, to a billhook, to a specific mythology. So they dropped it. This is why the square outlasted every specific interpretation. The less specific it became, the more universally it could be received.
The Sator square is not a message. It’s a mirror. This is the third case study in a pattern that keeps recurring in this series and beyond it. The Ægishjálmur is not a Viking-age survival but an early-modern syncretic creation—a form that travels the continental sigil-magic pipeline and is received as indigenous. The Sator is not a Jewish cryptogram, or a Christian prayer, or a Stoic maxim—it is a linguistic accident received as all three. In both cases, the form precedes the meaning. In both cases, the search for an original author is a category error.
Whoever first scratched the Rotas square on a column in Pompeii may have thought they were recording a clever solution to a word puzzle. They were. But the puzzle had only one answer, and the answer happened to describe God. Everything that followed—the legionary amulets, the Coptic parchments, the Nubian archbishop’s tomb, the Italian church mosaics, the Icelandic grimoires, the healing charms—is the history of people encountering that accident and mistaking it for a revelation. The square has no author. It has only receivers. And every receiver, including every scholar who has tried to solve it, has looked into the grid and seen exactly what the grid was always going to show them: their own idea of who holds the wheels.
Read previous articles in the Sator Square series
Part 2: Sator Square Non-Starters
Part 3: And the Rotas Go ’Round
Part 4: Blessings Through Sator
Part 5: Loosening “Tenet”’s Hold
Notes
- Margherita Guarducci, “Il misterioso ‘quadrato magico’”, Archeologia Classica, 1965.
- Felix Grosser, “Ein neuer Vorschlag zur Deutung der Sator-Formel” (“A New Proposal for Interpreting the Sator Formula”), Archiv für Religionswissenschaft, 1926.
- Paul Veyne, “Le carré Sator ou beaucoup de bruit pour rien” (“The Sator Square, or Much Ado About Nothing”), Bulletin de l’Association Guillaume Budé: Lettres d’humanité, December 1968.
- Charles Douglas Gunn, The Sator-Arepo Palindrome: An Inquiry into the Composition of an Ancient Word Square, 1969.
- Ibid.
- Ibid.
- Alberto G. Peano Casavola, The Coherent Meaning of the ROTAS/SATOR Squares/Sentences Until Magicians Messed It Up, 2024.
- Gunn, 1969.
- Casavola, 2024.
- Ibid.
- Gunn, 1969.
- Casavola, 2024.
- Reinhold Köhler, “Sator-arepo-formel”, Zeitschrift für Ethnologie, 1881.
- Casavola, 2024.
- [Nicolas Vinel, “The Hidden Judaism of the Sator Square in Pompeii”, Revue de l’histoire des religions, April 2006.]
- Grosser, 1926.
- P. 982: Sator-Amulett, seventh century, Berliner Papyrusdatenbank.
- KYP M450, 530–570, KYP M226 976–1025, Österreichische Nationalbibliothek.
- Casavola, 2024.
- P. Heid. Inv. 685, 951–1000, Heidelberg Library.
- P.CyYBR inv. 1792, sixth–seventh century CE, Beinecke Rare Book and Manuscript Library, Yale Papyrus Collection.










