Editing Sator Square (section)

==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", which directly translates as a [[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|Constantine VII Porphyrogenitus]] (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, that (2) [[Christianity in the 1st century|first-century Christians]] would have written the square in Greek and not Latin, that (3) the Christian concepts of Alpha and Omega only appear after the first century, that (4) the [[Christian cross variants|symbol of the cross]] only appears from about AD 130–131, and that (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 as 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 gave an emphasis on 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/>