View source for Sator Square

{{Short description|Roman-era word square with a Latin palindrome}}
{{Other uses|Sator (disambiguation){{!}}Sator}}
{{Use dmy dates|date=September 2022}}
[[File:Sator Square at Oppède.jpg|thumb|right|A Sator Square (laid out in the SATOR format), etched onto a wall in the medieval fortress town of [[Oppède|Oppède-le-Vieux]], France]]

The '''Sator Square''' (or '''Rotas-Sator Square''' or '''Templar Magic Square''') is a two-dimensional [[acrostic]] class of [[word square]] containing a five-word [[Latin]] [[palindrome]].<ref name=MRS/>  The earliest squares were found at Roman-era sites, all in ROTAS form (where the top line is "ROTAS", not "SATOR"), with the earliest discovery at [[Pompeii]] (and also likely pre-AD 62).{{efn|name=PS}}  The earliest square with Christian-associated imagery dates from the sixth century.{{efn|name=Coptic}} By the [[Middle Ages]], Sator squares existed in [[Europe]], [[Asia Minor]], and [[North Africa]].<ref name=MRS/><ref name=Fishwick/>  In 2022, the ''[[Encyclopedia Britannica]]'' called it "the most familiar lettered square in the Western world".<ref name=EB/>

A significant volume of academic research has been published on the square, but after more than a century, there is no consensus on its origin and meaning.<ref name=MRS/><ref name=RB/><ref name=ENC/>  The discovery of the "Paternoster theory" in 1926 led to a brief consensus among academics that the square was created by early Christians, but the subsequent discoveries at Pompeii led many academics to believe that the square was more likely created as a Roman word puzzle (per the [[Temple of Venus and Roma#Architecture|Roma-Amor puzzle]]), which was later adopted by Christians.  This origin theory, however, fails to explain how a Roman word puzzle became such a powerful religious and magical medieval symbol. It has instead been argued that the square was created in its ROTAS form as a Jewish symbol, embedded with cryptic religious symbolism, which was later adopted in its SATOR form by Christians.<ref name=MRS/><ref name=Fishwick/><ref name=Baines/> Other less-supported academic origin theories include a [[Pythagoreanism|Pythagorean]] or [[Stoicism|Stoic]] puzzle, a [[Gnostic]] or [[Orphism (religion)|Orphic]] or Italian pagan [[amulet]], a cryptic [[Mithraic]] or [[Semitic people|Semitic]] numerology charm, or that it was a device for assessing wind direction.<ref name=MRS/>

The square has long associations with magical powers throughout its history (and even up to the 19th century in North and South America), including a perceived ability to extinguish fires, particularly in Germany.  The square appears in early and late medieval medical textbooks such as the [[Trotula]], and was employed as a medieval cure for many ailments, particularly for dog bites and [[rabies]], as well as for insanity, and relief during childbirth.<ref name=MRS/><ref name=Fishwick/>

It has featured in a diverse range of contemporary artworks including fiction books, paintings, musical scores, and films,<ref name=ENC/> and most notably in [[Christopher Nolan]]'s 2020 film ''[[Tenet (film)|Tenet]]''.<ref name=vox/>  In 2020, ''[[The Daily Telegraph]]'' called it "one of the closest things the classical world had to a [[meme]]".<ref name=DT>{{cite web | newspaper=[[The Daily Telegraph]] | title=How Tenet was inspired by palindromes, the memes of the ancient world | first=Sam | last=Leith | date=30 August 2020 | access-date=20 September 2022 | url=https://www.telegraph.co.uk/films/2020/08/30/tenet-inspired-palindromes-memes-ancient-world/}}</ref>

==Description and naming==
[[File:Enigmatic inscription of St Peter ad Oratorium 400.jpg|thumb|right|Sator square (in ROTAS form) on the eighth-century facade of [[San Pietro ad Oratorium Abbey|Abbey of St. Peter ad Oratorium]] in Italy]]
The Sator square is arranged as a 5&nbsp;×&nbsp;5 grid consisting of five 5-letter words, thus totaling 25 characters. It uses 8 different Latin letters: 5 consonants (S, T, R, P, N) and 3 vowels (A, E, O).  In some versions, the vertical and horizontal lines of the grid are also drawn, but in many cases, there are no such lines.  The square is described as a two-dimensional [[palindrome]], or [[word square]], which is a particular class of a [[acrostic|double acrostic]].<ref name=EB>{{cite web | url=https://www.britannica.com/topic/SATOR-square | title=Sator square | website=[[Encyclopedia Britannica]] | access-date=17 September 2022}}</ref><ref>{{cite journal|title='Arepo' in the Magic 'Sator' Square|author=Griffiths, J. Gwyn|journal=[[The Classical Review]] |series=New Series |volume=21|issue=1|date=March 1971|pages=6–8 |doi=10.1017/S0009840X00262999|s2cid=161291159 }}</ref>

The square comes in two forms: ROTAS (left, below), and SATOR (right, below):<ref name=Fishwick/><ref name=Baines/>

{| style="font-family: monospace; margin: 0 0 0 0; line-height:90%"
|style="padding-left: 2em; line-height: 1.2em;"|
R O T A S <br />
O P E R A <br />
T E N E T <br />
A R E P O <br />
S A T O R
| style="padding-left: 4em; line-height: 1.2em;" |
S A T O R <br />
A R E P O <br />
T E N E T <br />
O P E R A <br />
R O T A S
|}

The earliest Roman-era versions of the square have the word ROTAS as the top line (called a ROTAS-form square, left above), but the inverted version with SATOR in the top line became more dominant from early medieval times (called a SATOR-form square, right above).<ref name=MRS/> Some academics call it a Rotas-Sator Square,<ref name=Fishwick>{{cite journal | journal=[[Harvard Theological Review]] | first=Duncan | last=Fishwick | volume=57 | issue=1 | date=1954 | title=On the Origin of the Rotas-Sator Square | pages=39–53 | publisher=[[Cambridge University Press]] | url=https://www.jstor.org/stable/1508695 | access-date=10 September 2022 | doi=10.1017/S0017816000024858| jstor=1508695 | s2cid=162908002 | url-access=subscription }}</ref><ref name=Baines>{{cite journal | title=The Rotas-Sator Square: a New Investigation | first=William | last=Baines | url=https://www.cambridge.org/core/journals/new-testament-studies/article/abs/rotassator-square-a-new-investigation/DCCDDD63AB4ECB9E8B028D3282F5B8FE | access-date=10 September 2022 | doi=10.1017/S0028688500014405 | date=July 1987 | volume=33 | issue=3 | pages=469–476 | journal=[[New Testament Studies]] | publisher=[[Cambridge University Press]]| s2cid=170226416 | url-access=subscription }}</ref> and some of them refer to the object as a [[rebus]],<ref name=MRS/><ref name=":0"/> or a [[magic square]].<ref name=Fishwick/> Since medieval times, it has also been known as a Templar Magic Square.<ref name=MRS/><ref>{{cite book | chapter-url=https://books.google.com/books?id=-mu8O8RMG6QC&dq=%22Templar+magic+square%22&pg=PA23 | pages=23–25 | chapter=A Brief History of Magic Squares: Templar Magic Square | author-link=Clifford A. Pickover | first=Clifford A. |last=Pickover | title=The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures across Dimensions | date=June 2002 | access-date=20 September 2022 | publisher=[[Princeton University Press]] | isbn= 978-0691115979}}</ref>

==Discovery and dating==
[[File:Acrostic Rotas-Sator Square - YDEA - 5755.jpg|thumb|One of the four Sator squares (all in ROTAS form) found at [[Dura-Europos]], [[Syria]], circa AD 200.]]
[[File:Sator Square Palestra Pompeii (CIL 8623 & 8622a-b).jpg|thumb|The oldest known square. Found in 1936 on a column in the {{ill|Palestra Grande|it}} (CIL 8623), it is now kept in the Pompeii Museum.<ref>{{cite web | website=Parco Archeologico di Pompei | url=https://pompeiicommitment.org/il-quadrato-del-sator-dalla-palestra-grande/ | title=Il Quadrato del Sator dalla Palestra Grande | date=2023 | access-date=14 June 2023}}</ref>]]
The existence of the square was long recognized from early medieval times, and various examples have been found in Europe, [[Anatolia|Asia Minor]], [[North Africa]] (in mainly [[Copts|Coptic]] settlements), and the Americas.<ref name=MRS/><ref name=":0"/> Medieval examples of the square in SATOR form abound, including the earliest French example in a [[Carolingian dynasty|Carolingian]] [[Bible]] from AD 822 at the monastery of [[Saint-Germain-des-Prés (abbey)|Saint-Germain-des-Prés]]. Many medieval European churches and castles have Sator square inscriptions.<ref name=MRS/><ref name=":0"/>

The first recognized serious academic study of the Sator square is the 1881 publication of {{ill|Reinhold Köhler|lt=Reinhold Köhler's|de}} historical survey in ''{{ill|Zeitschrift für Ethnologie|de}}'', which was titled "Sator-Arepo-Formel". Since then, a considerable body of academic research has been published on the topic.<ref name=MRS/><ref name=":0"/>

Until the 1930s, a Coptic papyrus with the square in the ROTAS form dating from the fourth or fifth century AD was considered the earliest version.{{efn|name=Coptic|The fourth- or fifth-century Coptic papyrus with a Sator square had no evidence of any Christian associations or Christian imagery; it would be another two centuries before the first Sator squares appeared that had additional Christian imagery that would definitively associate them as Christian.<ref name=MRS/>}}<ref name=":0"/><ref name=DA>{{cite journal | url=https://www.escholar.manchester.ac.uk/api/datastream?publicationPid=uk-ac-man-scw:1m1363&datastreamId=POST-PEER-REVIEW-PUBLISHERS-DOCUMENT.PDF | journal=[[Bulletin of the John Rylands Library]] | title=The Sator-Formula And The Beginnings Of Christianity | first=Donald | last=Atkinson | doi=10.7227/BJRL.22.2.6 | volume=22 | issue=2 | pages=419–434 | date=1938 | access-date=10 September 2022 | archive-date=7 December 2022 | archive-url=https://web.archive.org/web/20221207100542/https://www.escholar.manchester.ac.uk/api/datastream?publicationPid=uk-ac-man-scw:1m1363&datastreamId=POST-PEER-REVIEW-PUBLISHERS-DOCUMENT.PDF | url-status=dead }}</ref>  In 1889, British [[ancient historian]] [[Francis J. Haverfield|Francis Haverfield]] identified the 1868 discovery of a Sator square found in ROTAS form scratched on a plaster wall in the Roman settlement of [[Corinium Dobunnorum|Corinium]] at [[Cirencester]] to be of Roman origin; however, his assertion was discounted at the time by most academics, who considered the square to be an "early medieval charm".<ref name=MRS>{{cite journal | journal=[[Cryptologia]] | author-link=Rose Mary Sheldon | first=Rose Mary | last=Sheldon | url=https://indexarticles.com/reference/cryptologia/sator-rebus-an-unsolved-cryptogram-the/ | title=The Sator Rebus: An unsolved cryptogram? | pages=233–287 | doi=10.1080/0161-110391891919 | date=2003 | volume=27 | issue=3 | s2cid=218542154 | access-date=10 September 2022| url-access=subscription }}</ref><ref name=Hemer/>

Haverfield was ultimately proved right by the 1931–32 excavations at [[Dura-Europos]] in [[Syria]] that uncovered three separate Sator square inscriptions, all in ROTAS form, on the interior walls of a Roman military office (and a fourth a year later) that were dated from circa AD 200.<ref name=MRS/><ref name=Conimbriga/> 

In 1936, Italian archaeologist {{ill|Matteo Della Corte|it}} discovered a Sator square, also in ROTAS form, inscribed on a column in the {{ill|Palestra Grande|it}} (the gymnasium) near the [[Amphitheatre of Pompeii]] (''[[Corpus Inscriptionum Latinarum|CIL IV]] 8623'').<ref>{{cite web | website=[[Pompeii|Parco Archeologico di Pompei]] | url=https://pompeiicommitment.org/il-quadrato-del-sator-dalla-palestra-grande/ | title=The Sator Square from the Palaestra Grande | date=2023}}</ref> This discovery led  Della Corte to reexamine a fragment of a square, again also in ROTAS form, that he had made in 1925 at the house of Publius Paquius Proculus, also at Pompeii (''[[Corpus Inscriptionum Latinarum|CIL IV]] 8123''). The square at the house of Publius Paquius Proculus was dated between AD 50 and AD 79 (based on the decorative style of the interior), and the palestra square find was dated pre-AD 62 (and therefore the [[AD 62 Pompeii earthquake|earthquake of AD 62]]),{{efn|name=PS|Work by Italian archaeologist [[Amedeo Maiuri]] in 1938 showed that [[Graffito (archaeology)|graffito]] on the Pompeii palestra square column associated with the Rotas square were linked to graffito that would have predated the [[AD 62 Pompeii earthquake|earthquake of AD 62]]; this was later confirmed by German classical philologist {{ill|Friedrich Focke|de}} in 1948 based on an analysis of the [[stucco]] plastering of the specific palestra square columns.<ref name=Hemer/><ref name=Conimbriga/>}} making it the oldest known Sator square discovery to date.<ref name=MRS/><ref name=":0"/>

==Translation==

===Individual words===

The words are in Latin, and the following translations are known by scholars:<ref name=Fishwick/><ref name=Baines/>

:;{{lang|la|SATOR}}: (nominative noun; from {{lang|la|serere}}, "to sow") sower, planter, founder, progenitor ([[List of Roman agricultural deities#Other indigitamenta|usually divine]]); originator; literally 'seeder';<ref name=Fishwick/><ref name=Baines/>
:;{{lang|la|AREPO}} : unknown word, perhaps a proper name, either invented to complete the palindrome or of a non-Latin origin (see [[#Arepo interpretations|§ Arepo interpretations]]);<ref name=Fishwick/><ref name=Baines/>
:;{{lang|la|TENET}} : (verb; from {{lang|la|tenere}}, 'to hold') he/she/it holds, keeps, comprehends,  possesses, masters, preserves, sustains;<ref name=Fishwick/><ref name=Baines/>
:;{{lang|la|OPERA}} : (ablative [see [[wiktionary:opera#Latin|opera]]] singular noun) service, pains, labor; care, effort, attention;<ref name=Fishwick/><ref name=Baines/>
:;{{lang|la|ROTAS}} : ({{lang|la|rotās}}, accusative plural of {{lang|la|rota}}) wheels.<ref name=Fishwick/><ref name=Baines/>

===Sentence construction===
[[File:Grenoble - Sator 01.jpg|thumb|right|Sator form of the square on a door in [[Grenoble]], France]]
The most direct sentence translation is: "The sower (or, farmer) Arepo holds the wheels with care (or, with care the wheels)".<ref name=MRS/><ref name=":0"/><ref name=Hemer/><ref name=RB/><ref>{{cite book | title=The New Testament and Rabbinic Judaism | author-link=David Daube | first=David | last=Daube | page=403 | date=2011 | isbn=978-1610975100 | publisher=[[Wipf and Stock]]}}</ref> Similar translations include: "The farmer Arepo works his wheels",<ref name=M1>{{cite web|website=[[Pepys Library|Magdalene College Libraries]]|url=https://magdlibs.com/2019/11/19/sator-squares/|title=Sator Squares|first=Ellie|last=Swire|date=19 November 2019|access-date=13 October 2021}}</ref> or "Arepo the sower (sator) guides (tenet) the wheel (rotas) with skill (opera)".<ref>{{cite web | url=https://coriniummuseum.org/2021/07/the-sator-square-by-isobel-wilkes/ | website=[[Corinium Museum]] | first=Isobel | last=Wilkes | date=19 July 2021 | access-date=13 September 2022 | title=The SATOR Square}}</ref>

Some academics, such as French historian [[Jules Quicherat]],<ref name=":0"/> believe the square should be read in a [[boustrophedon]] style (i.e. in alternating directions).<ref>{{Cite book |last=Ceram |first=C. W. |year=1958 |title=The March of Archaeology |url=https://archive.org/details/marchofarchaeolo00cera |url-access=registration |publisher=Alfred A. Knopf |location=New York |isbn=0-3944-3528-1 |lccn=58-10977 | page=30}}</ref>  The boustrophedon style, which in Greek means "as the ox plows", emphasizes the agricultural aspect of the text of the square.<ref name=MRS/>  Such a reading when applied to the SATOR-form square, and repeating the central word TENET, gives SATOR OPERA TENET – TENET OPERA SATOR, which has been very loosely interpreted as: "as ye sow, so shall ye reap",<ref name=":0"/> while some believe the square should be read as just three words – SATOR OPERA TENET, which they loosely translate as: "The Creator (the author of all things) maintains his works"; both of which could imply Graeco-Roman [[Stoicism|Stoic]] and/or [[Pythagoreanism|Pythagorean]] origins.<ref name=MRS/><ref name=ENC/>

British academic Duncan Fishwick observes that the translation from the boustrophedon approach fails when applied to a ROTAS-form square;<ref name=":0"/> however, Belgian scholar [[Paul Grosjean]] reversed the boustrophedon rule on the ROTAS form (i.e. starting on the right-hand side instead of the left) to get SAT ORARE POTEN, which loosely translates into the Jewish call to prayer, "are you able to pray enough?".<ref name=MRS/><ref name=":0"/>

===Arepo interpretations===
The word AREPO is a [[hapax legomenon]], appearing nowhere else in attested Latin literature. Some academics believe it is likely a proper name, or possibly a [[theophoric name]], that was adapted from a non-Latin word or was invented specifically for the Sator square.<ref name=":0"/> French historian [[Jerome Carcopino]] believed that it came from the [[Gaulish language|Gaulish]] word for a 'plough'; however, this has been discounted by other academics.{{efn|Duncan Fishwick showed that this translation into plough was based on a "faulty knowledge of Latin, if not of Greek",<ref name=":0"/> and Fishwick's view was reinforced by French historian [[Robert Étienne]].<ref name=Conimbriga/>}}<ref name=":0"/> American ancient legal historian [[David Daube]] believed that AREPO represented a [[Hebrew language|Hebrew]] or [[Aramaic language|Aramaic]] rendition of the ancient Greek for [[alpha]] ({{lang|grc|Ἄλφα}}) and [[omega]] ({{lang|grc|ω}}), bespeaking the "[[Alpha and Omega|Alpha-Omega]]" concept (cf. [[Isaiah 44#Verse 6|Isiah 44.6]], and [[Revelation 1:8]]) from early Judeo-Christianity.<ref name=MRS/> [[J. Gwyn Griffiths]] contended that the term AREPO came, via [[Alexandria]], from the attested Egyptian name "Hr-Hp" (''[[wikt:ḥr|ḥr]] [[wikt:ḥp|ḥp]]''), which he took to mean "the face of [[Apis (egyptian mythology)|Apis]]".<ref name=MRS/><ref>{{cite journal|last=Griffith|first=J. Gwyn|title='Arepo' in the Magic 'Sator' Square|journal=The Classical Review|publisher=[[Cambridge University Press]] (CUP)|volume=21|issue=1|year=1971|issn=0009-840X|doi=10.1017/s0009840x00262999|pages=6–8|s2cid=161291159 }}</ref> In 1983, Serbian-American scholar [[Miroslav Marcovich]] proposed the term AREPO as a Latinized abbreviation of [[Harpocrates]] (or "[[Horus]]-the-child"), god of the rising sun, also called {{lang|grc|Γεωργός `Aρπον}}, which Marcovich suggests corresponds to SATOR AREPO. This would translate the square as: "The sower Horus/Harpocrates keeps in check toils and tortures".<ref name=MRS/><ref name=MM>{{cite journal |title=SATOR AREPO = ΓΕΩΡΓΟΣ ̔ΑΡΠΟΝ(ΚΝΟΥΦΙ) ΑΡΠΩΣ (''geōrgos arpon''[''knouphi''] ''arpōs''), arpo(cra), harpo(crates) | first=Miroslav | last=Marcovich | author-link=Miroslav Marcovich |journal=[[Zeitschrift für Papyrologie und Epigraphik]] |volume=50 |year=1983 |pages=155–171|jstor=20183770}}</ref><ref name=ENC/>

Duncan Fishwick, among other academics, believed that AREPO was simply a residual word that was required to complete what is a complex and sophisticated palindrome (which Fishwick believed was embedded with hidden Jewish symbolism, per the "Jewish Symbol" origin theory below), and to expect more from the word was unreasonable from its likely Jewish creators.<ref name=Fishwick/>

===Further anagrams===

Attempts have been made to discover "hidden meanings" by the [[Anagram|anagrammatic method]] of rearranging the letters of which the square is composed.<ref name=MRS/>

* In 1883, German historian [[Gustav Fritsch]] reformed the letters to discover an invocation to Satan:<ref name=MRS/><ref name=":0"/>
*:SATAN, ORO TE, PRO ARTE A TE SPERO
*:SATAN, TER ORO TE, OPERA PRAESTO
*:SATAN, TER ORO TE, REPARATO OPES
* French historian [[Guillaume de Jerphanion]] catalogued examples that were known formulas for an [[exorcism]] such as:<ref name=":0"/>
*:RETRO SATANA, TOTO OPERE ASPER, and the prayers
*:ORO TE PATER, ORO TE PATER, SANAS
*:O PATER, ORES PRO AETATE NOSTRA
*:ORA, OPERARE, OSTENTA TE PASTOR
* In 1887, Polish [[Ethnography|ethnographer]] [[Oskar Kolberg]] amended the strict anagrammatic approach by using abbreviations and thus deduced from the 25 letters of the Sator Square the 36 letters of the monastic rule: SAT ORARE POTEN (TER) ET OPERA(RE) R(ATI)O T(U)A S(IT),<ref name=":0"/> which he considered an ancient rule of the Benedictines; French historian Gaston Letonnelier made a similar approach in 1952 to get the Christian prayer: SAT ORARE POTEN(TIA) ET OPER(A) A ROTA S(ERVANT), which translates as: "Prayer is our strength and will save us from the wheel (of fate?)".<ref name=MRS/>
* In 1935, German art historian {{ill|Kuno von Hardenberg|de}} believed he discovered the relief the [[Rose of Sharon]] gave to [[Saint Peter]] for the sin of his denial of Christ, with the anagram PETRO ET REO PATET ROSA SARONA, which translates as "For Peter even guilty the rose of Sharon is open"; academics refuted his interpretation.<ref name=MRS/><ref name=":0"/>
* In 2003, American historian [[Rose Mary Sheldon]] listed some of the many diverse sentences that can be produced from anagrams of the square including her favorite: APATOR NERO EST, which would translate as saying that the Roman emperor [[Nero]] was the result of a virgin birth.<ref name=MRS/>

==Origin and meaning==

The origin and meaning of the square has eluded a definitive academic consensus even after more than a century of study.<ref name=Baines/><ref name=RB/><ref name=ENC/>  In 1938, British classical historian Donald Atkinson said the square occupied the "mysterious region where religion, superstition, and magic meet, where words, numbers, and letters are believed, if properly combined, to exert power over the processes of nature ...".<ref name=DA/>  Even by 2003, American academic Rose Mary Sheldon called it "one of the oldest unsolved word puzzles in the world".<ref name=MRS/>  In 2018, American ancient classical historian Megan O'Donald still noted that "most interpretations of the ROTAS square have failed to gain consensus due to failings", and, in particular, reconciling the archeological evidence with the square's later adoption as a religious and magical object.<ref name=MOD>{{cite journal | journal=[[Zeitschrift für Papyrologie und Epigraphik]] | url=https://www.jstor.org/stable/26603971 | first=Megan | last=O'Donald | title=The ROTAS "Wheel": Form and Content in a Pompeian Graffito | pages=77–91 | date=2018 | volume=205 | jstor=26603971 | access-date=10 September 2022}}</ref>

===Christian symbol===

====Adoption by Christians====

Irrespective of the theory of its origin, the evidence that the Sator square, particularly in its SATOR form, became adopted into Christian imagery is not disputed by academics.<ref name=MRS/><ref name=Fishwick/>  Academics note the repeated association of Christ with the "sower" (or SATOR),<ref name=MRS/> and the words of the Sator square have been discovered in Christian settings even in very early medieval times, including:

* Jesuit historian [[Jean Daniélou]] claimed that the third century [[Irenaeus|Bishop Irenaeus of Lyons]] (c. AD 200) knew of the square and had written of "Him who joined the beginning with the end, and is the Lord of both, and has shown forth the plough at the end".<ref name=MRS/>  Some academics link Irenaeus with creating the association of the five words in the square to the five wounds of Christ.
* The [[Berlin State Museum]] houses a sixth-century bronze amulet from Asia Minor that has two fish turned toward one another on one side, and a Sator square in Greek characters in a checkerboard pattern on the other side.  Written above the square is the word "ICHTHUS", the Greek for fish but also a direct [[Ichthys|term for Christ]]; it is the earliest known Christian annotated Sator Square.{{efn|name=Coptic}}<ref name=MRS/>
* An illustration in an early Byzantine bible gives the baptismal names of the three [[Magi]] as being: ATOR, SATOR, and PERATORAS.<ref name=MRS/><ref name=":0">{{cite journal |last=Fishwick |first=Duncan |date=1959 |title=An Early Christian Cryptogram? |url=https://www.umanitoba.ca/colleges/st_pauls/ccha/Back%20Issues/CCHA1959/Fishwick.htm |journal=CCHA |publisher=[[University of Manitoba]] |volume=26 |pages=29–41 |archive-url=https://web.archive.org/web/20210114111747/https://www.umanitoba.ca/colleges/st_pauls/ccha/Back%20Issues/CCHA1959/Fishwick.htm |archive-date=2021-01-14 |access-date=13 October 2021}}</ref>
* In [[Cappadocia]], in the time of [[Constantine VII]] (913–959), the shepherds of the [[Nativity of Jesus]] are named: SATOR, AREPON, and TENETON.<ref name=MRS/><ref name=":0"/>

The Sator square appears in diverse Christian communities, such as in [[Abyssinia]] where in the '' [[Bandlet of Righteousness|Ethiopian Book of the Dead]]'', the individual nails in Christ's cross were called: Sador, Alador, Danet, Adera, Rodas.<ref name=MRS/> These are likely derived from even earlier [[Coptic Christian]] works that also ascribe the wounds of Christ and the nails of the cross with names that resemble the five words from the square.<ref name=MRS/>

While there is little doubt among academics that Christians adopted the square, it was not clear that they had originated the symbol.<ref name=MRS/><ref name=Hemer/>

====Paternoster theory====
[[File:Palindrom PATERNOSTER.svg|thumb|[[Lord's Prayer]] anagram from the 25 letters of the square, including the [[Alpha and Omega]] positioning of the residual ''A''s and ''O''s.<ref name=Fishwick/><ref name=History>{{cite book | url=https://books.google.com/books?id=oUFFAQAAQBAJ&dq=The+Rotas-Sator+Square%3A+a+New+Investigation&pg=PA1002 | title=Encyclopedia of Early Christianity | edition=2nd | first=Everett | last=Ferguson | author-link=Everett Ferguson | page=1002 | quote=Rotas Sator (first century): Although the result is striking, the interpretation rests on the unlikely assumptions, and a non-Christian meaning is more probable. | isbn=978-0815333197 | publisher=[[Routledge]] | date=1999 | access-date=16 September 2022}}</ref> There is an alternative layout proposed with the ''A''s and ''O''s positioned at the extreme ends of the Paternoster cross,<ref name=ENC/><ref name=NV/> and a Jewish option with the letters laid out in an X-shape (i.e. tau).<ref name=Fishwick/>]]

During 1924 to 1926, three people separately discovered,{{efn|Most notable and impactful of the three was German priest Felix Grosser, who published in 1926;<ref name=Fishwick/> German historian {{ill|Christian Frank|de|Christian Frank (Heimatforscher)}} published in 1924, and Swedish historian [[Sigurd Agrell]] published in 1927.<ref name=MRS/>}} or rediscovered, that the square could be used to write the name of the [[Lord's Prayer]], the "Paternoster", twice and intersecting in a cross form (see image opposite).  The remaining residual letters (two ''A''s and two ''O''s) could be placed in the four quadrants of the cross and would represent the [[Alpha and Omega]] that are established in [[Christian symbolism]].<ref name=Fishwick/><ref name=M1/> The positioning of the ''A''s and ''O''s was further supported by the fact that the position of the ''T''s in the Sator square formed the points of a cross – there are obscure references in the ''[[Epistle of Barnabas]]'' to [[Tau cross|T being a symbol of the cross]] – and that the ''A''s and ''O''s also lay in the four quadrants of this cross.<ref name=":0"/>  At the time of this discovery, the earliest known Sator square was from the fourth century,{{efn|name=Coptic}}<ref name=MRS/> further supporting the dating of the Christian symbolism inherent in the Paternoster theory.<ref name=Fishwick/>  Academics considered the Christian origins of the square to be largely resolved.<ref name=MRS/><ref name=Hemer/><ref name=Fishwick/><ref name=Baines/><ref name=Conimbriga/>

With the subsequent discovery of Sator squares at Pompeii, dating pre-79 AD,{{efn|name=PS}} the Paternoster theory began to lose support, even among notable supporters such as French historian [[Guillaume de Jerphanion]].<ref name=":0"/><ref name=Conimbriga/>  Jerphanion noted that (1) it was improbable that many Christians were present at Pompeii, (2) [[Christianity in the 1st century|first-century Christians]] would have written the square in Greek and not Latin, (3) the Christian concepts of Alpha and Omega only appear after the first century, (4) the [[Christian cross variants|symbol of the cross]] only appears from about AD 130–131, and (5) cryptic Christian symbols only appeared during the [[Persecution of Christians in the Roman Empire|persecutions of the third century]].<ref name=MRS/><ref name=":0"/><ref name=Conimbriga/>

[[Jérôme Carcopino]] claimed the Pompeii squares were added at a later date by looters. The lack of any disturbance to the volcanic deposits at the palestra, however, meant that this was unlikely,<ref name=":0"/><ref name=Hemer/><ref name=Conimbriga/> and the Paternoster theory as a proof of Christian origination lost much of its academic support.<ref name=MRS/><ref name=":0"/><ref name=Baines/><ref name=Conimbriga/><ref name=History/>

Regardless of its Christian origins, many academics considered the Paternoster discovery as being a random occurrence to be mathematically impossible.<ref name=DA/> Several examined this mathematical probability including German historian {{ill|Friedrich Focke|de}} and British historian [[Hugh Last]], but without reaching a conclusion.<ref name=MRS/> A 1987 computer analysis by William Baines derived a number of "pseudo-Christian formulae" from the square but Baines concluded it proved nothing.<ref name=Baines/>

===Roman word puzzle===

There is considerable contemporary academic support for the theory that the square originated as a Roman-era word puzzle.<ref name=MRS/><ref name=Baines/><ref name=MOD/> Italian historian [[Arsenio Frugoni]] found it written in the margin of the ''Carme delle scolte modenesi'' beside the Roma-Amor palindrome,<ref name=MRS/> and Italian classicist [[Margherita Guarducci]] noted it was similar to the ROMA OLIM MILO AMOR two-dimensional acrostic word puzzle that was also found at Pompeii (see [[wikt:oiim|Wiktionary]] for details on the Pompeiian graffito), and at Ostia and Bolonia.<ref name=MRS/> Similarly, another ROTAS-form square scratched into a Roman-era wall in the basement of the [[Basilica di Santa Maria Maggiore]] was found alongside the Roma-Amor, and the Roma-Summus-Amor, palindromes.<ref name=Basilica/> Duncan Fishwick noted the "composition of palindromes was, in fact, a pastime of Roman landed gentry".<ref name=":0"/>  American classical [[Epigraphy|epigraphist]] Rebecca Benefiel noted that by 2012, Pompeii had yielded more than 13,000 separate inscriptions and that the house of Publius Paquius Proculus (where a square was found) had more than 70 pieces of graffiti alone.<ref name=RB>{{cite book | title=The Muse at Play: Riddles and Wordplay in Greek and Latin Poetry | pages=65–79 | first=Rebecca R. | last=Benefiel | doi=10.1515/9783110270617.65 | chapter=Magic Squares, Alphabet Jumbles, Riddles and More: The Culture of Word-Games among the Graffiti of Pompeii | publisher=[[De Gruyter]] | access-date=15 September 2022 | url=https://www.academia.edu/5111444 | date=2012| isbn=978-3-11-027000-6 }}</ref>

A 1969 computer study by Charles Douglas Gunn started with a Roma-Amor square and found 2,264 better versions, of which he considered the Sator square to be the best.<ref name=MRS/>  The square's origin as a word puzzle solved the problem of AREPO (a word that appears nowhere else in classical writing), as being a necessary component to complete the palindrome.<ref name=MOD/>

Fishwick still considered this interpretation unproven and clarified that the apparent discovery of the Roma-Amor palindrome written beside the 1954 discovery of a square on a tile at Aquincum was incorrectly translated (if anything it supported the square as a charm).<ref name=":0"/> Fishwick, and others, consider the key failing of the Roman puzzle theory of origin is the lack of any explanation as to why the square would later become so strongly associated with Christianity, and with being a medieval charm.<ref name=":0"/><ref name=MOD/><ref name=Conimbriga/>  Some argue that this can be bridged if considered as a [[Pythagoreanism|Pythagorean]]-[[Stoicism|Stoic]] puzzle creation.<ref name=MRS/><ref name=ENC/>
 
In 2018, Megan O'Donnell argued that the square is less of a pure word puzzle but more a piece of Latin Roman [[Graffito (archaeology)|graffito]] that should be read ''figuratively'' as a wheel (i.e. the ROTAS), and that the textual-visual interplay had parallels with other forms of graffito found in Pompeii, some of which later became adopted as charms.<ref name=MOD/>

===Jewish symbol===
[[File:Palindrom TENET.svg|thumb|The central cross created by the vertical and horizontal TENET words, has both Christian and Jewish symbolism (e.g. the "[[tau cross]]", or the Hebrew [[Taw|tau]] "+" symbol).<ref name=Fishwick/><ref name=ENC>{{cite book | url=https://books.google.com/books?id=lZUBZlth2qgC&dq=sator+square&pg=PA756 | title=The Encyclodedia of Christianity | volume=5 | quote=Entry: Word Square by Ulrich Ernst | pages=755–757 | author1=Erwin Fahlbusch | author2=Jan Lochman | author3=John Mbiti |author4=Jaroslav Pelikan | author5=Lukas Vischer | isbn=978-0802880055 | date=February 2008 | access-date=16 September 2022 | publisher=[[William B. Eerdmans Publishing Company]]}}</ref> It also parallels the Roman system of ''Cardo and Decumanus'', being central road crosses through towns.<ref name=ENC/>]]

Some prominent academics, including British-Canadian ancient Roman scholar Duncan Fishwick,<ref name=Fishwick/> American ancient legal historian [[David Daube]],<ref name=MRS/> and British ancient historian [[Mary Beard (classicist)|Mary Beard]],<ref>{{cite web | url=https://www.goodreads.com/author/show/97783.Mary_Beard/blog?page=49 | access-date=12 September 2022 | title=Were there Christians at Pompeii? The sator word-square evidence | date=30 November 2012 | first=Mary | last=Beard | author-link=Mary Beard (classicist) | website= | quote=It is much more likely that we are dealing with a Latin-speaking Jewish slogan here, and there is plenty of evidence for Jews in the Vesuvian towns (including a kosher version of garum, the Roman staple of rotten fish sauce). "Alpha" and "omega" are well known in Jewish literature, and "our father" is perfectly compatible with a Jewish cultural background (and are found as that in Jewish prayers).}}</ref> consider the square as being likely of Jewish origin.<ref name=MRS/>

Fishwick notes that the failings of the Paternoster theory (above) are resolved when looked at from a Jewish perspective.<ref name=Fishwick/>  Large numbers of Latin-speaking Jews had been settled in Pompeii, and their affinity for cryptic and mystical word symbols was well known.<ref name=Fishwick/><ref name=":0"/> The Alpha and Omega concept appears much earlier in Judaism (Ex. 3.14; Is. 41.4, and [[Isaiah 44#Verse 6|44.6]]), and the letters "[[aleph]]" and "[[Taw|tau]]" are used in the [[Talmud]] as symbols of totality.<ref name=Fishwick/><ref name=":0"/> The ''T''s of TENET may be explained not as Christian crosses, but as a Latin form of the Jewish "tau" salvation symbol (from Ezekiel), and its archaic form (+ or X) appears regularly on [[Ossuary|ossuaries]] of both [[Hellenistic]] and early Roman times.<ref name=Fishwick/><ref name=":0"/> Fishwick highlights the central position of the letter ''N'', as Jews attached significance to the utterance of the "Name" (or nomen).<ref name=Fishwick/><ref name=":0"/>

In addition, Fishwick believes a Jewish origin provides a satisfactory explanation for the Paternoster cross (or X) as the configuration is an archaic Jewish "tau" (+ or X).<ref name=Fishwick/><ref name=":0"/> Fishwick draws attention to some liturgical prayers in Judaism, where several prayers refer to "Our Father".<ref name=Fishwick/><ref name=":0"/> None of these liturgical prayers, however, can be dated to before [[Jesus]].<ref>[https://www.chabad.org/library/article%20cdo/aid/542330/jewish/How-Old-Is-the-Kaddish.htm How Old Is the Kaddish? - Chabad.org]</ref><ref>[https://www.studylight.org/encyclopedias/eng/tje/l/lords-prayer-the.html Lord's Prayer, the; The 1901 Jewish Encyclopedia]</ref> Fishwick concludes that the translations of the words ROTAS OPERA TENET AREPO SATOR are irrelevant, except to the extent that they make some sense and thereby hide a Jewish cryptic charm, and to require them to mean more is "to expect the impossible".<ref name=Fishwick/><ref name=":0"/> The motivation for the creation square might have been the Jewish [[pogroms]] of AD 19 or AD 49; however, it fell into disuse only to be revived later by Christians facing their own persecution, and who appreciated its hidden Paternoster and Alpha and Omega symbolism, but who focused on the SATOR form (which emphasized the "sower", which was associated with Christ).<ref name=Fishwick/>

Research in 2006 by French classical scholar Nicolas Vinel drew on recent discoveries on the mathematics of ancient magic squares to propose that the square was a "Jewish cryptogram using Pythagorean arithmetic".<ref name=NV/> Vinel decoded several Jewish concepts in the square, including the reason for AREPO, and was able to explain the word SAUTRAN that appears beside the square that was discovered on the palestra column in Pompeii.<ref name=NV>{{cite journal | url=https://www.cairn-int.info/article-E_RHR_2232_0003--the-hidden-judaism-of-the-satorsquare.htm?contenu=article | title=The Hidden Judaism of the Sator Square in Pompeii | first=Nicolas | last=Vinel | date=April 2006 | volume=223 | issue=2 | page=3 | journal=Revue de l'histoire des religions | doi=10.4000/rhr.5136 | s2cid=170115926 | access-date=16 September 2022| url-access=subscription }}</ref>  Vinel addressed a criticism of the Jewish origin theory – why would the Jews have then abandoned the symbol? – by noting the Greek texts that they also abandoned (e.g. the [[Septuagint]]) in favor of Hebrew versions.<ref name=NV/>

===Other theories===

The amount of academic research published on the Rotas-Sator square is regarded as being considerable (and even described by one source as "immense");<ref name=RB/> American academic [[Rose Mary Sheldon]] attempted to catalog and review the most prominent works in a 2003 paper published in ''[[Cryptologia]]''.<ref name=MRS/> Among the more diverse but less supported theories Sheldon recorded were:

* Several German academics have written on the links of the square to [[Pythagoreanism]] and [[Stoicism]], including philologist {{ill|Hildebrecht Hommel|de}}, historian {{ill|Wolfgang Christian Schneider|de}}, and Heinz Hoffman, among others.<ref name=MRS/><ref name=Fishwick/> Schneider believed the square was an important link between [[Etruscan religion]] and Stoic academic philosophy.  Hommel believed that in the Stoic tradition, the Ephesian word AREPO would be discarded, and the square would be read in the boustrophedon style as SATOR OPERA TENET, TENET OPERA SATOR, translating as "The Creator preserves his works".<ref name=MRS/><ref name=ENC/> German scholar {{ill|Ulrich Ernst|de}} writing the Sator square's entry in ''The Encyclopedia of Christianity'' found this theory persuasive,<ref name=ENC/> but [[Miroslav Marcovich]] refuted the translation.<ref name=MM/>
* Several academics link the square to [[Gnosticism|Gnostic]] origins, such as Jean Doignon, Gustav Maresch, [[Adolfo Omodeo]], and {{ill|Hildebrecht Hommel|de}}.  English [[Egyptology|egyptogolist]] [[J. Gwyn Griffiths]] explains AREPO as a personal name derived from the Egyptian name "Hr-Hp", and sources the square to an Alexandrine origin where a gnostic tradition employed acrostics.<ref name=MRS/><ref name=ENC/>
* Some academics link the square to [[Orphism (religion)|Orphic cults]], including Serbian historian [[Milan Budimir]] who linked the Greek form of AREPO to the name Orpheus.<ref name=MRS/><ref name=Fishwick/>
* Italian academic Adolfo Omodeo linked the square to [[Mithraic]] origins as the Roman-era discoveries were in military locations with whom it was popular, while academic historian Walter O. Moeller attempted to derive a Mithraic relationship using perceived mathematical patterns in the square, but his arguments were not considered convincing by other academics.<ref name=MRS/><ref name=Fishwick/><ref name=Moeller>{{cite book | title=The Mithraic Origin and Meanings of the Rotas-Sator Square | first=Walter |last=Moeller | date=December 1973 | isbn=978-90-04-03751-9 | publisher=[[Brill Publishers]]}}</ref><ref>{{cite book|last=Ferguson|first=Everett|title=Backgrounds of early Christianity|url=https://books.google.com/books?id=3tuKkxU4-ncC&pg=PA590|year=2003|publisher=Wm. B. Eerdmans Publishing|isbn=978-0-8028-2221-5|pages=590–}}</ref>
* Norwegian [[classical philology|philologist]] [[Samson Eitrem]] took the last half of the square starting at ''N'' to get: "net opera rotans", which translates as "She spins her works", interpreting it to be a feminine being (i.e. [[Hecate]]), a demon, or even the square itself rotating on its TENET spokes, thus giving a peasant Italian pagan origin with the square as a wind indicator.<ref name=MRS/><ref name=Fishwick/>
* Some academics such as Swiss archeologist {{ill|Waldemar Deonna|fr}} have proposed that it is a numerical number square, which would also imply a [[Semitic people|Semitic]] origin.<ref name=MRS/> A significant issue is that the square is in Latin, and Romans did not have the ciphered number system of the Greeks or the Semites. However, if the letters are [[Transliteration|transliterated]] to Greek, and then assigned ciphered numbers, the word TENET can be rendered as 666, the [[number of the beast]].<ref name=MRS/> Walter O. Moeller analyzed the resultant numerical combinations to assert that the square was made by Mithraic numerologists.<ref name=MRS/><ref name=Moeller/>
* In 1925, Zatzman interpreted the square as a Hebraic or Aramaic [[Apotropaic magic|apotropaic formula]] against the devil, and translated the square to read: "Satan Adama Tabat Amada Natas".<ref name=MRS/>
* In 1958, French historian [[Paul-Louis Couchoud]] proposed a novel interpretation as the square being a device for working out wind directions.<ref name=MRS/>

==Magical and medical associations==
In 2003, [[Rose Mary Sheldon]] noted: "Long after the fall of Rome, and long after the general public had forgotten about classical word games, the square survived among people who might not even read Latin. They continued to use it as a charm against illness, evil and bad luck. By the end of the Middle Ages, the 'prophylactic magic' of the square was firmly established in the superstition of Italy, Serbia, Germany, and Iceland, and eventually even crossed to North America".<ref name=MRS/>  The square appears in versions of several popular magical manuscripts from the early and late Middle Ages, magical text such as the ''[[Tabula Smaragdina]]'' and the ''[[Key of Solomon|Clavicula Salomonis]]''.<ref>{{cite book| title=Magical Manuscripts in Early Modern Europe: The Clandestine Trade in Illegal Book Collections | date=December 2017 | doi=10.1007/978-3-319-59525-2 | publisher=[[Palgrave Macmillan]] | url=https://www.researchgate.net/publication/319954207 | first1=Bernd-Christian |last1=Otto | first2=Daniel |last2=Bellingradt | access-date=10 May 2023 | isbn=978-3-319-59524-5 | chapter=Appendix A | pages=134–135}}</ref>
{{multiple image
|align=right
|total_width=400
|header=Medieval German Sator square fire disks
|image1=OHM - Feuerteller 02.jpg
|caption1=[[Veste Oberhaus|Oberhausmuseum]]
|image2=2019-04-05 Regionale Staatsbibliothek Augsburg 72.jpg
|caption2=State and City Library, Augsburg
}}
In Germany in the Middle Ages, the square was inscribed on disks that were then thrown into fires to extinguish them.<ref name=MRS/> An edict in 1743 by [[Ernest Augustus I, Duke of Saxe-Weimar-Eisenach|Duke Ernest Auguste of Saxe-Weimar-Eisenach]] required all settlements to make Sator square disks to combat fires.<ref name=MRS/>  By the fifteenth century the square was being used as a touchstone against fire at the [[Château de Chinon]] and {{ill|Château de Jarnac|fr}} in France.<ref name=":0"/> 

The square appears as a remedy during labour in the twelfth-century Latin medical text the [[Trotula]],<ref name=SB/> and was widely cited as a cure for dog bites and [[rabies]] in medieval Europe;<ref name=MRS/> in both cases, the remedy/cure is administered by eating bread inscribed with the words of the square.<ref name=MRS/><ref name=SB/> By the sixteenth century, the use of the square to cure insanity and fever was being documented in books such as ''De Varia Quercus Historia'' (1555) by Jean du Choul, and ''De Rerum Varietate'' (1557) by [[Gerolamo Cardano]].  Jean du Choul describes a case where a person from [[Lyon]] recovered from insanity after eating three crusts of bread inscribed with the square.<ref name=":0"/>  After the meal, the person then recited five paternosters for the five wounds of Christ, linking to the Christian imagery believed encoded into the square.<ref name=":0"/>

[[File:Sahor areto.jpg|thumb|''[[Pow-Wows; or, Long Lost Friend|The Long Lost Friend]]'' (1820)<ref name=DK/>]]

Scholars have found medieval Sator-based charms, remedies, and cures, for a diverse range of applications from childbirth, to toothaches, to love potions, to ways of warding off evil spells, and even to determine whether someone was a witch.<ref name=MRS/> [[Richard Cavendish (occult writer)|Richard Cavendish]] notes a medieval manuscript in the [[Bodelian Library|Bodleian]] says: "Write these [five sator] words on in parchment with the blood of a Culver [pigeon] and bear it in thy left hand and ask what thou wilt and thou shalt have it. fiat."<ref>{{cite book | author-link=Richard Cavendish (occult writer) | first=Richard | last=Cavendish | title=The Black Arts: A Concise History of Witchcraft, Demonology, Astrology | date=1983 | page=130 | edition=40th | publisher=[[TarcherPerigee]] | isbn=978-0399500350 | url=https://books.google.com/books?id=NQwsi3s1cpUC&dq=sator+square&pg=PA130 | access-date=17 September 2022}}</ref>  Other examples include Bosnia, where the square was used as a remedy for [[aquaphobia]], and in Iceland, it was etched into the fingernails to cure [[jaundice]].<ref name=MRS/>

There are examples from the nineteenth century in South America, where the Sator square was used as a cure for dog bites and snake-bites in Brazil,<ref name=MRS/> and in enclaves of German settlers (or [[mountain white]]s) in the [[Allegheny Mountains]] who used the square to prevent fire, stop fits, and prevent miscarriages.<ref name=MRS/>  The Sator square features in eighteenth-century books on [[Pow-wow (folk magic)|Pow-wow folk medicine]] of the [[Pennsylvania Dutch]], such as ''[[Pow-Wows; or, Long Lost Friend|The Long Lost Friend]]'' (see image).<ref name=DK>{{cite book | title=A History of Magic, Witchcraft, and the Occult | date=August 2020 | publisher=[[DK (publisher)|DK]] | isbn=978-1465494290 | first=Suzannah |last=Lipscomb | author-link=Suzannah Lipscomb | url=https://books.google.com/books?id=PSnkDwAAQBAJ&dq=sator+square+magic&pg=PT526 | access-date=26 September 2022 | quote=Sator Square amulet: This early Christian magical tool called the Sator Square shows words that are readable backward or forwards. In his book on pow-wows, Johann George Hohman stated that the Sator Square possessed properties that could extinguish fires as readily as protect cows from witches.}}</ref>

==Notable examples==

===Roman===

* The oldest Sator square was found in November 1936, in ROTAS form, etched into column number LXI at the {{ill|Palestra Grande|it}} near the [[amphitheatre of Pompeii]] (''CIL IV 8623''). Graffiti associated with the particular columns predates the [[AD 62 Pompeii earthquake]],{{efn|name=PS}}<ref name=Hemer/><ref name=Conimbriga/> making it the oldest known square. It also has additional graffiti just below it, with the words SAUTRAN and VALE (''CIL IV 8622a-b'').<ref name=MRS/><ref name=":0"/>
* Another Sator square was also found in October 1925, in ROTAS form, etched onto the wall in a bathroom of the house of Publius Paquius Proculus (Reg I, Ins 7, 1), also at Pompeii (''CIL IV 8123'').  The style of the house, which is associated with [[Nero]]'s reign, dated the square to between AD 50 and AD 79 (the destruction of the city).<ref name=MRS/><ref name=":0"/><ref name=Conimbriga/>
* A Sator square was found in 1954, in ROTAS form, etched onto a roof tile of the second-century Roman Imperial governor's house for [[Pannonia Inferior]] at [[Aquincum]], near [[Budapest]], Hungary. There has been debate over whether a second partial inscription found beside the square is part of the Roma-Amor palindrome (thus affirming the Roman puzzle origin theory), but it seems unlikely.<ref name=":0"/><ref name=Conimbriga/>

{{multiple image
|align=right
|total_width=500
|header=Roman second-century ROTAS-form squares
|image1=Rotas square from Cirencester.jpg
|caption1=[[Corinium Dobunnorum|Cirencester]], England
|image2=Manchester museum sator square.JPG
|caption2=[[Manchester]], England
|image3=20110908 P1080767 Amuleto Museo Conimbriga.jpg
|caption3=[[Conímbriga]] Portugal
}}

* A Sator square was found in 1978, in ROTAS form, etched on a fragment of Roman pottery at a Roman site at [[Manchester]] that was dated circa AD 185.<ref name=Hemer>{{cite journal | journal= [[Science and Christian Belief|Faith and Thought]] | url=https://biblicalstudies.org.uk/pdf/ft/rotas_hemer.pdf | title=The Manchester Rotas-Sator Square | first=Colin J. | last=Hemer | volume=105 | pages=36–40 | access-date=12 September 2022}}</ref>
* Four Sator squares were found in 1931–32, all in ROTAS form, etched on the walls of military buildings, at [[Dura-Europos]] in [[Syria]], dated circa AD 200.<ref name=MRS/><ref name=":0"/><ref name=Hemer/><ref name=Conimbriga/>
* A Sator square was found in 1868, in ROTAS form, scratched onto a plaster wall in the Roman Britain settlement of [[Corinium Dobunnorum]] at [[Cirencester]].<ref name=Hemer/><ref name=Conimbriga/>
* A Sator square was found in 1971, in ROTAS form, etched onto an [[Roman brick|unfired brick]] at the Roman city of [[Conímbriga]] in Portugal that was dated from the second century.<ref name=Conimbriga>{{cite book | url=https://books.openedition.org/ausonius/8207?lang=en | access-date=13 September 2022 | volume=XVII | chapter=Le «Carre Magique» a Conimbriga (Portugal), The 'Magic Square' in Conimbriga (Portugal) | pages=15–34 | title=Conimbriga | date=1978 | author-link=Robert Étienne | first=Robert | last=Étienne | series=Scripta Antiqua | publisher=[[University of Coimbra]]| isbn=9782356132987 }}</ref>
* A Sator square was found in 1966–71, in ROTAS form, scratched into a Roman-era wall during excavations of the [[Basilica di Santa Maria Maggiore]] in Rome (along with the Roma-Amor, and the Rome Summus Amor palindromes).<ref name=Basilica>{{cite journal|last=Magi|first=Filippo|title=Il calendario dipinto sotto S. Maria Maggiore| year=1972| volume=16 |journal=Arte e Archeologia | publisher=[[Vatican Publishing House|Libreria Editrice Vaticana]] |isbn=9788820943790}}</ref>

===Early medieval===
[[File:Wien, Papyrusmuseum (45030276345).jpg|thumb|Examples of Coptic Sator square amulets, Papyrus Museum, Vienna]]
* The earliest Sator square post-Roman times was the 1899 discovery of a ROTAS-form square inscribed on a Coptic papyrus by German historians Adolph Erman and Fritz Krebs in the [[Berlin Papyrus Collection]] of the [[Berlin State Museums]] (then the {{Lang|de|Königlichen Museen}}); it has no other explicit Christian imagery.<ref name=MRS/><ref name=DA/>
* The earliest Sator square with explicit additional Christian imagery is a sixth-century bronze amulet from Asia Minor that has two fish turned toward one another on one side, and a Sator square in Greek characters in a checkerboard pattern on the other side.  Written above the square is the word "ICHTHUS", which directly translates as a [[Ichthys|term for Christ]].  It is also in the Berlin State Museums.{{efn|name=Coptic}}<ref name=MRS/>
* One of the earliest examples of a Sator square in a Christian church is the SATOR-form marble square on the facade of the circa AD 752 Benedictine [[Capestrano#San Pietro ad Oratorium Abbey|Abbey of St Peter ad Oratorium]], near [[Capestrano]], in [[Italy]].<ref name=MRS/>
* The earliest example from France is a SATOR-form square found in a [[Carolingian dynasty|Carolingian]] [[Bible]] from AD 822 at the monastery of [[Saint-Germain-des-Prés (abbey)|Saint-Germain-des-Prés]].<ref name=MRS/><ref name=":0"/> There are ninth- to tenth-century examples in Codex 384 from [[Monte Cassino]], and a square was found written into the margin of a work titled ''Versus de cavenda Venere et vino found'', which is part of Codex 1.4 of the Capitolare di Modena.<ref name=MRS/>
* One of the earliest examples of the square being applied to medical beliefs is from the twelfth-century Latin medical textbooks the [[Trotula]], where the translated text advises: "[98] Or let these names be written on cheese and butter: + sa. e. op. ab. z. po. c. zy. e pe. pa. pu c. ac. sator arepo tenet os pera rotas and let them be given to eat".<ref name=SB>{{cite web | url=https://sarahemilybond.com/2016/01/04/power-of-the-palindrome-writing-reading-and-wordplay-part-ii/ | title=Power of the Palindrome: Writing, Reading, and Wordplay (Part II) | date=4 January 2016 | access-date=13 September 2022 | first=Sarah E. | last=Bond | author-link=Sarah Bond | publisher=[[University of Iowa]]}}</ref>  In a similar vein, a thirteenth-century parchment from [[Aurillac]] offers a Sator-square chant for women in childbirth.<ref name=":0"/>

===Later medieval===
[[File:Aosta Sant Orso Mosaico 02.JPG|thumb|''Samson and the Lion''.  A twelfth-century mosaic with the words of the square in a circle, [[Collegiate church of Saint Ursus]], [[Aosta]], Italy]]

* Twelfth-century French examples are found on the wall of the Eglise Saint Laurent at {{ill|Château de Rochemaure|fr}}, and in the keep of [[Château de Loches]].<ref name=MRS/><ref name=":0"/>
* A Sator square in SATOR form was found on a block set into the doorway facade of a fortified wall in the largely abandoned medieval fortress town of [[Oppède|Oppède-le-Vieux]], in France's [[Luberon]]; the old town itself dates from the twelfth or thirteenth century and was abandoned by the seventeenth century.<ref name=vox/>
* Many medieval Italian towns and churches have squares.  The twelfth-century church of San Giovanni Decolatto in Pieve Terzagni in [[Cremona]] has fragments of a floor mosaic that included a square.<ref name=MRS/> [[Valvisciolo Abbey]] has letters forming five concentric rings, each one divided into five sectors. One appears on the exterior wall of the [[Siena Cathedral|Duomo]] in [[Siena]]. Inside the church of [[Acquaviva Collecroce]] is a stone with the square in a ROTAS form.  Others include the church of the [[Campiglia Marittima#Churches|Pieve of San Giovanni]], the [[Collegiate church of Saint Ursus]], the [[Ascoli Satriano|Cathedral of Ascoli Satriano]], and the Church of San Lorenzo in Paggese in [[Marche]].<ref name=vox/>
* The square is found in diverse locations all over later medieval France, including fifteenth-century examples at the [[Château de Chinon]], the {{ill|Château de Jarnac|fr}}, as well as in the courthouse in [[Valbonnais]].<ref name=":0"/>
* A Sator square in SATOR form is in the medieval [[Rivington Church]] in [[Lancashire]], England.<ref>{{cite book | first=John |last=Rawlinson | title=About Rivington | edition=3rd | date=March 1981 | publisher=Nelson Brothers| page=42 | isbn=978-0950061528}}</ref>
* The phrase appears on the [[rune]] stone Nä Fv1979;234 from [[Närke]], [[Sweden]], dated to the fourteenth century. It reads "sator arepo tenet" (untranscribed: "sator ¶ ar(æ)po ¶ tænæt).<ref name=Runforum>{{cite web|url=http://www.runforum.nordiska.uu.se/samnord/|title=amnordisk runtextdatabas|publisher=Runforum Uppsala|date=20 December 2010|access-date=13 February 2014|url-status=dead |archive-url=https://archive.today/20120525193554/http://www.runforum.nordiska.uu.se/samnord/ |archive-date=25 May 2012}}</ref> It also occurs in two inscriptions from [[Gotland]] (G 145 M and G 149 M), which contain the whole palindrome.<ref name=Runforum/>

===Other===

* [[Jane Wilde|Lady Jane Francesa Wilde]]'s anthology of Irish folklore, ''Ancient Legends Mystic Charms & Superstitions of Ireland'' (1888), includes the tale of a young girl who is enchanted by a poet using the spell of a Sator square written on a piece of paper in blood.<ref>{{cite book | url= https://www.libraryireland.com/AncientLegendsSuperstitions/Evil-Eye-5.php | access-date=16 September 2022 | first=Jane | last=Wilde | author-link=Jane Wilde | date=1888 | chapter=Evil Eye | publisher=[[National Library of Ireland]] | title=Ancient Legends Mystic Charms & Superstitions of Ireland | isbn=9783849673604 | pages=18–23}}</ref>
* The Sator square, with some letters changed, features in eighteenth-century books on [[Pow-wow (folk magic)|Pow-wow folk medicine]] of the [[Pennsylvania Dutch]], such as ''[[Pow-Wows; or, Long Lost Friend|The Long Lost Friend]]'' (see image earlier).

==In popular culture==
[[File:Trisulti - Sator, quadrato magico - panoramio.jpg|thumb|[[Filippo Balbi]] (circa 1860)]]
The Sator square has inspired many works in the arts, including some classical and contemporary composers such as works by Austrian composer [[Anton Webern]] and Italian composer [[Fabio Mengozzi]],<ref>{{cite news|title=Note astigiane in prima mondiale applaudite ad Atene|url=https://www.lastampa.it/asti/2020/02/27/news/note-astigiane-in-prima-mondiale-applaudite-ad-atene-1.38520837|newspaper=[[La Stampa]]|language=it|date=27 February 2020|access-date=13 October 2021}}</ref> writers such as Brazilian writer [[Osman Lins]] (whose novel ''Avalovara'' (1973) follows the structure of the square), and painters such as American artist [[Dick Higgins]] with ''La Melancolia'' (1983),<ref name=ENC/> and American artist [[Gary Stephan]] with ''Sator Arepo Tenet Opera Rotas'' (1982).<ref>{{cite web | url=https://www.metmuseum.org/art/collection/search/632979 | access-date=17 September 2022 | title=Sator Arepo Tenet Opera Rotas (1982) by Gary Stephan | website=[[Metropolitan Museum of Art]]}}</ref>

Director [[Christopher Nolan]]'s 2020 film ''[[Tenet (film)|Tenet]]'' has a story structure that mimics the square's concept of interlinked multiple directions of meaning, and  incorporates all five of the names from the Sator square:<ref name=vox>{{cite web|url=https://www.vox.com/culture/21419050/tenet-explained-sator-square-nolan|last=Wilkinson|first=Alissa|title=The ancient palindrome that explains Christopher Nolan's Tenet|website=[[Vox (website)|Vox]]|date=4 September 2020|access-date=13 October 2021}}</ref>
*The main antagonist is named Sator.<ref name=vox/>
*The artist who created the forged Goya drawings was named Arepo.<ref name=vox/>
*''Tenet'' is the title of the film as well as the secret organization that works to save the world.<ref name=vox/>
*The opening scene is set at an [[opera house]].<ref name=vox/>
*Sator owns a construction company called Rotas.<ref name=vox/>

American author [[Lawrence Watt-Evans]] notes that [[Terry Pratchett|Sir Terry Pratchett]] named the main square in the fictional city of [[Ankh-Morpork]] "Sator Square", in a deliberate reference to the symbol.  Watt-Evans notes that the ''[[Discworld]]'' series is full of other incidental references to unusual symbols and concepts.<ref>{{cite book | title=The Turtle Moves!: Discworld's Story Unauthorized | author-link=Lawrence Watt-Evans | first=Lawrence | last=Watt-Evans | date=July 2008 | publisher=[[BenBella Books]] | isbn= 978-1933771465 | page=44 | url=https://books.google.com/books?id=YSFEwHD6FQ0C&q=%22sator+square%22&pg=PT55 | access-date=29 September 2022}}</ref>

== See also ==<!-- Please respect alphabetical order -->

*[[Abracadabra]], a second-century Roman [[magic word]]
*[[Abraxas]], a mystical word in [[Gnosticism]]
*''[[Nipson anomēmata mē monan opsin]]'', a fourth-century Byzantine palindrome
*[[Paser Crossword Stela]]
*''[[The Book of the Sacred Magic of Abramelin the Mage]]'', a medieval book that contains word squares

==Notes==
{{notelist|30em}}

==References==
{{Reflist}}

== Further reading ==
* {{cite journal | journal=[[Cryptologia]] | author-link=Rose Mary Sheldon | first=Rose Mary | last=Sheldon | url=https://indexarticles.com/reference/cryptologia/sator-rebus-an-unsolved-cryptogram-the/ | title=The Sator Rebus: An unsolved cryptogram? | pages=233–287 | doi=10.1080/0161-110391891919 | date=2003 | volume=27 | issue=3 | s2cid=218542154 | access-date=10 September 2022| url-access=subscription }}
* {{cite journal | journal=[[Harvard Theological Review]] | first=Duncan | last=Fishwick | volume=57 | issue=1 | date=1954 | title=On the Origin of the Rotas-Sator Square | pages=39–53 | publisher=[[Cambridge University Press]] | doi=10.1017/S0017816000024858 | jstor=1508695 | s2cid=162908002 | url=https://www.jstor.org/stable/1508695 | access-date=10 September 2022| url-access=subscription }}
* {{cite journal | title=The Rotas-Sator Square: a New Investigation | first=William | last=Baines | url=https://www.cambridge.org/core/journals/new-testament-studies/article/abs/rotassator-square-a-new-investigation/DCCDDD63AB4ECB9E8B028D3282F5B8FE | access-date=10 September 2022 | date=July 1987 | volume=33 | issue=3 | pages=469–476 | journal=[[New Testament Studies]] | publisher=[[Cambridge University Press]]| doi=10.1017/S0028688500014405 | s2cid=170226416 | url-access=subscription }}

==External links==
{{Commons category}}
{{scholia}}
* ''[http://www.umanitoba.ca/colleges/st_pauls/ccha/Back%20Issues/CCHA1959/Fishwick.htm An Early Christian Cryptogram?] {{Webarchive|url=https://web.archive.org/web/20100802010729/http://www.umanitoba.ca/colleges/st_pauls/ccha/Back%20Issues/CCHA1959/Fishwick.htm |date=2 August 2010 }}'' Duncan Fishwick, [[University of St. Michael's College]] (1959)
* ''[https://books.openedition.org/ausonius/8207#ftn14 The "Magic Square" in Conimbriga (Portugal)]'' [[Robert Étienne]], [[University of Coimbra]] (1978)
* [https://pompeiicommitment.org/il-quadrato-del-sator-dalla-palestra-grande/ Square found in 1936 in the Palestra Grande on column (II 7)], Parco Archeologico di Pompei, inv. 20565 (2023) 

{{Archaeological site of Pompeii}}
{{Dura Europos}}
{{Amulets and talismans}}
{{Witchcraft}}
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