A Sator Square (laid out in the SATOR-format), etched onto a wall in the medieval fortress town of Oppède-le-Vieux, France

The Sator Square (or the Rotas-Sator Square, or the Templar Magic Square) is a two-dimensional acrostic class of word square containing a five-word Latin palindrome.[1] 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-A.D. 62).[a] The earliest square with Christian-associated imagery dates from the sixth century.[b] By the Middle Ages, Sator squares had been found across Europe, Asia Minor, and North Africa.[1][2] In 2022, the Encyclopedia Britannica called it "the most familiar lettered square in the Western world".[3]

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.[1][4][5] The discovery of the "Paternoster theory" in 1926 led to a brief consensus amongst 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 (as per the Roma-Amor puzzle), which was later adopted by Christians. This origin theory, however, fails to explain how a Roman word puzzle then 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.[1][2][6] There are many other less-supported academic origin theories, such as a Pythagorean or Stoic puzzle, a Gnostic or Orphic or Italian pagan amulet, a cryptic Mithraic or Semitic numerology charm, or that it was simply a device for working out wind directions.[1]

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.[1][2]

It has featured in a diverse range of contemporary artworks including fiction books, paintings, musical scores, and films,[5] and most notably in Christopher Nolan's 2020 film Tenet.[7] In 2020, The Daily Telegraph called it "one of the closest things the classical world had to a meme".[8]

Description and naming

Sator square (in ROTAS-form) on the eight-century facade of Abbey of St. Peter ad Oratorium in Italy

The Sator square is arranged as a 5 × 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 double acrostic.[3][9]

The square comes in two forms: ROTAS (left, below), and the SATOR (right, below):[2][6]

R O T A S
O P E R A
T E N E T
A R E P O
S A T O R

S A T O R
A R E P O
T E N E T
O P E R A
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).[1] Some academics call it a Rotas-Sator Square,[2][6] and some of them refer to the object as a rebus,[1][10] or a magic square.[2] Since medieval times, it has also been known as a Templar Magic Square.[1][11]

Discovery and dating

One of the four Sator squares (all in ROTAS-form) found at Dura-Europos, Syria, circa A.D 200.
The oldest known square. Found in 1936 on a column in the Palestra Grande [it] (CIL 8623), it is now kept in the Pompeii Museum.[12]

The existence of the square was long recognized from early medieval times, and it has been found on the continent of Europe (including Asia Minor), in North Africa (in mainly Coptic settlements), and in the Americas.[1][10] Medieval examples of the square in SATOR-form abound, including the earliest French example in a Carolingian Bible from A.D 822 at the monastery of Saint-Germain-des-Prés. Many medieval European churches and castles have Sator square inscriptions.[1][10]

The first recognized serious academic study of the square was the 1881 publication of Reinhold Köhler [de]'s historical survey in Zeitschrift für Ethnologie [de], titled "Sator-Arepo-Formel", and a considerable body of academic research has been subsequently published on the meaning of the square.[1][10]

Up until the 1930s, a Coptic papyrus with the square in the ROTAS-form dating from the fourth or fifth century A.D. was considered the earliest version.[b][10][13] In 1889, British ancient historian 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 at Cirencester to be of Roman origin, however, his assertion was discounted by academics who considered it an "early medieval charm".[1][14]

Haverfield would be proved right by the 1931–32 excavations at Dura-Europos in Syria that uncovered three Sator square inscriptions, all in ROTAS-form, on the interior walls of a Roman military office (and a fourth a year later) that dated from circa A.D 200.[1][15]

Five years later in 1936, Italian archaeologist Matteo Della Corte [it] discovered a Sator square, in ROTAS-form, inscribed on a column in the Palestra Grande [it] (gymnasium) near the Amphitheatre of Pompeii (CIL IV 8623).[16] This discovery led to the reexamination of a fragment of a square, again in ROTAS-form, that Della Corte had made in 1925 at the house of Publius Paquius Proculus, also at Pompeii (CIL IV 8123). The square at the house of Publius Paquius Proculus was dated between A.D 50 and A.D 79 (based on the style of the interior), and the palestra square find was dated pre-A.D 62,[a] making it the oldest known Sator square to date.[1][10]

Translation

Individual words

The words are in Latin, and the following translations are known by scholars:[2][6]

SATOR
(nominative noun; from serere, 'to sow') sower, planter, founder, progenitor (usually divine); originator; literally 'seeder'.[2][6]
AREPO
unknown word, potentially a proper name, either invented to complete the palindrome or of a non-Latin origin (see § Arepo interpretations).[2][6]
TENET
(verb; from tenere, 'to hold') he/she/it holds, keeps, comprehends, possesses, masters, preserves, sustains.[2][6]
OPERA
(ablative [see opera] singular noun) service, pains, labor; care, effort, attention.[2][6]
ROTAS
(rotās, accusative plural of rota) wheels. [2][6]

Sentence construction

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)".[1][10][14][4][17] Similar translations include: "The farmer Arepo works his wheels",[18] or "Arepo the sower (sator) guides (tenet) the wheel (rotas) with skill (opera)".[19]

Some academics, such as French historian Jules Quicherat,[10] believe the square should be read in a boustrophedon style (i.e. in alternating directions).[20] The boustrophedon style, which in Greek means "as the Ox plows", emphasizes the agricultural aspect of the square.[1] 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",[10] 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 Stoic and/or Pythagorean origins.[1][5]

British academic Duncan Fishwick observes that the translation from the boustrophedon approach fails when applied to a ROTAS-form square,[10] 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?".[1][10]

Arepo interpretations

The word AREPO is a hapax legomenon (i.e. it appears nowhere else in Latin literature). Some academics believe it is likely a proper name or potentially a theophoric name, that was adapted from a non-Latin word or was invented specifically for the Sator square.[10] French historian Jerome Carcopino believed that it came from the Gaulish word for a 'plough', however, this has been discounted by other academics.[c][10] American ancient legal historian David Daube believed that AREPO represented a Hebrew or Aramaic rendition of the ancient Greek for alpha (Ἄλφα) and omega (ω), giving the "Alpha-Omega" concept (cf. Isiah 44.6, and Revelation 1:8) from early Judeo-Christianity.[1] J. Gwyn Griffiths contended that the term AREPO came, via Alexandria, from the attested Egyptian name "Hr-Hp" (ḥr ḥp), which he took to mean "the face of Apis".[1][21] 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 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".[1][22][5]

Duncan Fishwick, amongst 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.[2]

Further anagrams

Attempts have been made to discover "hidden meanings" by the anagrammatic method of rearranging the letters of which the square is composed.[1]

Origin and meaning

The origin and meaning of the square has eluded a definitive academic consensus even after more than a century of study.[6][4][5] 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 ...".[13] Even by 2003, American academic Rose Mary Sheldon called it "one of the oldest unsolved word puzzles in the world".[1] 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.[23]

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.[1][2] Academics note the repeated association of Christ with the "sower" (or SATOR),[1] and the words of the Sator square have been discovered in Christian settings even in very early medieval times, including:

The Sator square appears in diverse Christian communities, such as in Abyssinia where in the Ethiopian Book of the Dead, the individual nails in Christ's cross were called: Sador, Alador, Danet, Adera, Rodas.[1] 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.[1]

While there is little doubt amongst academics that Christians adopted the square, it was not clear that they had originated the symbol.[1][14]

Paternoster theory

Lord's Prayer anagram from the 25 letters of the square, including the Alpha and Omega positioning of the residual As and Os.[2][24] There is an alternative layout proposed with the As and Os positioned at the extreme ends of the Paternoster cross,[5][25] and a Jewish option with the letters laid out in an X-shape (i.e. tau).[2]

During 1924–1926, three people separately discovered,[d] 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 As and two Os) could be placed in the four quadrants of the cross and would represent the Alpha and Omega that are established in Christian symbolism.[2][18] The positioning of the As and Os was further supported by the fact that the position of the Ts in the Sator square formed the points of a cross – there are obscure references in the Epistle of Barnabas to T being a symbol of the cross – and that the As and Os also lay in the four quadrants of this cross.[10] At the time of this discovery, the earliest known Sator square was from the fourth century,[b][1] further supporting the dating of the Christian symbolism inherent in the Paternoster theory.[2] Academics considered the Christian origins of the square to be largely resolved.[1][14][2][6][15]

With the subsequent discovery of Sator squares at Pompeii, dating pre-79 A.D,[a] the Paternoster theory began to lose support, even amongst notable supporters such as French historian Guillaume de Jerphanion.[10][15] Jerphanion noted: that (1) it was improbable that many Christians were present at Pompeii, that (2) 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 symbol of the cross only appears from about A.D 130–131, and that (5) cryptic Christian symbols only appeared during the persecutions of the third century.[1][10][15]

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,[10][14][15] and the Paternoster theory as a proof of Christian origination lost much of its academic support.[1][10][6][15][24]

Regardless of its Christian origins, many academics considered the Paternoster discovery as being a random occurrence to be mathematically impossible.[13] Several examined this mathematical probability including German historian Friedrich Focke [de] and British historian Hugh Last, but without reaching a conclusion.[1] A 1987 computer analysis by William Baines derived a number of "pseudo-Christian formulae" from the square but Baines concluded it proved nothing.[6]

Roman word puzzle

There is considerable contemporary academic support for the theory that the square originated as a Roman-era word puzzle.[1][6][23] Italian historian Arsenio Frugoni found it written in the margin of the Carme delle scolte modenesi beside the Roma-Amor palindrome,[1] and Italian classist Margherita Guarducci noted it was similar to the ROMA OLIM MILO AMOR two-dimensional acrostic word puzzle that was also found at Pompeii (see Wiktionary for details on the Pompejan graffito), and at Ostia and Bolonia.[1] 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.[26] Duncan Fishwick noted the "composition of palindromes was, in fact, a pastime of Roman landed gentry".[10] American classical epigraphist Rebecca Benefiel, noted that by 2012, Pompeii had yielded over 13,000 separate inscriptions and that the house of Publius Paquius Proculus (where a square was found) had over 70 pieces of graffiti alone.[4]

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.[1] 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.[23]

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).[10] 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.[10][23][15] Some argue that this can be bridged if considered as a Pythagorean-Stoic puzzle creation.[1][5]

In 2018, Megan O'Donnell argued that the square is less of a pure word puzzle but more a piece of Latin Roman 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.[23]

Jewish symbol

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 tau "+" symbol).[2][5] It also parallels the Roman system of Cardo and Decumanus, being central road crosses through towns.[5]

Some prominent academics, including British-Canadian ancient Roman scholar Duncan Fishwick,[2] American ancient legal historian David Daube,[1] and British ancient historian Mary Beard,[27] consider the square as being likely of Jewish origin.[1]

Fishwick notes that the failings of the Paternoster theory (above) are resolved when looked at from a Jewish perspective.[2] Large numbers of Latin-speaking Jews had been settled in Pompeii, and their affinity for cryptic and mystical word symbols was well known.[2][10] The Alpha and Omega concept appears much earlier in Judaism (Ex. 3.14; Is. 41.4, and 44.6), and the letters "aleph" and "tau" are used in the Talmud as symbols of totality.[2][10] The Ts 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 ossuaries of both Hellenistic and early Roman times.[2][10] Fishwick highlights the central position of the letter N, as Jews attached significance to the utterance of the "Name" (or nomen).[2][10]

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).[2][10] The Paternoster word is not unique to Christianity, and also has roots in Judaism where several prayers refer to "Our Father".[2][10] 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".[2][10] The motivation for the creation square might have been the Jewish pogroms of A.D 19 or A.D 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).[2]

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".[25] 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.[25] 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.[25]

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");[4] American academic Rose Mary Sheldon attempted to catalog and review the most prominent works in a 2003 paper published in Cryptologia.[1] Amongst the more diverse but less supported theories Sheldon recorded were:

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".[1] 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 Clavicula Salomonis.[30]

Medieval German Sator square fire disks
Oberhausmuseum
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.[1] An edict in 1743 by Duke Ernest Auguste of Saxe-Weimar-Eisenach required all settlements to make Sator square disks to combat fires.[1] By the fifteenth century the square was being used as a touchstone against fire at the Château de Chinon and Château de Jarnac [fr] in France.[10]

The square appears as a remedy during labour in the twelfth-century Latin medical text, the Trotula,[31] and was widely cited as a cure for dog bites and rabies in medieval Europe;[1] in both cases, the remedy/cure is administered by eating bread inscribed with the words of the square.[1][31] 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.[10] 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.[10]

The Long Lost Friend (1820)[32]

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.[1] Richard Cavendish notes a medieval manuscript in the 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."[33] 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.[1]

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,[1] and in enclaves of German settlers (or mountain whites) in the Allegheny Mountains who used the square to prevent fire, stop fits, and prevent miscarriages.[1] The Sator square features in eighteenth-century books on Pow-wow folk medicine of the Pennsylvania Dutch, such as The Long Lost Friend (see image).[32]

Notable examples

Roman

Roman second-century ROTAS-form squares
Cirencester, England
Manchester, England
Conímbriga Portugal

Early medieval

Examples of Coptic Sator square amulets, Papyrus Museum, Vienna

Later medieval

Samson and the Lion. A twelfth-century mosaic with the words of the square in a circle, Collegiate church of Saint Ursus, Aosta, Italy

Other

In popular culture

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,[37] 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),[5] and American artist Gary Stephan with Sator Arepo Tenet Opera Rotas (1982).[38]

British-American director Christopher Nolan's 2020 film Tenet, incorporates all the five of the names from the Sator square:[7]

American author Lawrence Watt-Evans notes that Sir Terry Pratchett named the main square in the fictional city of Ankh-Morpork in his Discworld book series, "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.[39]

The song Tenet by the Nordic neo-folk band Heilung is based on the Sator square. All its individual musical parts, melodies and instruments (and even at times the lyrics) play the same both forward and backwards.[40]

See also

Notes

  1. ^ a b c d Work by Italian archaeologist Amedeo Maiuri in 1938 showed that graffito on the Pompeii palestra square column associated with the Rotas-square, were linked to graffito that would have pre-dated the earthquake of A.D 62; this was later confirmed by German classical philologist Friedrich Focke [de] in 1948 based on an analysis of the stucco plastering of the specific palestra square columns.[14][15]
  2. ^ a b c d e The fourth or fifth century Coptic papyrus with a Sator square had no evidence of any Christian associations or Christian imagery, it would not be for another two centuries before the first Sator squares appeared that had additional Christian imagery that would definitively associate them as Christian.[1]
  3. ^ Duncan Fishwick showed that this translation into plough was based on a "faulty knowledge of Latin, if not of Greek",[10] and Fishwick's view was reinforced by French historian Robert Étienne.[15]
  4. ^ Most notable and impactful of the three was German priest, Felix Grosser who published in 1926;[2] German historian Christian Frank [de] published in 1924, and Swedish historian Sigurd Agrell published in 1927.[1]

References

  1. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai aj ak al am an ao ap aq ar as at au av aw ax ay az ba bb bc bd be bf bg bh bi bj bk bl bm bn bo bp bq br bs bt bu bv bw bx by bz ca cb cc cd Sheldon, Rose Mary (2003). "The Sator Rebus: An unsolved cryptogram?". Cryptologia. 27 (3): 233–287. doi:10.1080/0161-110391891919. S2CID 218542154. Retrieved 10 September 2022.
  2. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai Fishwick, Duncan (1954). "On the Origin of the Rotas-Sator Square". Harvard Theological Review. Cambridge University Press. 57 (1): 39–53. doi:10.1017/S0017816000024858. JSTOR 1508695. S2CID 162908002. Retrieved 10 September 2022.
  3. ^ a b "Sator square". Encyclopedia Britannica. Retrieved 17 September 2022.
  4. ^ a b c d e Benefiel, Rebecca R. (2012). "Magic Squares, Alphabet Jumbles, Riddles and More: The Culture of Word-Games among the Graffiti of Pompeii". The Muse at Play: Riddles and Wordplay in Greek and Latin Poetry. De Gruyter. pp. 65–79. doi:10.1515/9783110270617.65. ISBN 978-3-11-027000-6. Retrieved 15 September 2022.
  5. ^ a b c d e f g h i j k l m Erwin Fahlbusch; Jan Lochman; John Mbiti; Jaroslav Pelikan; Lukas Vischer (February 2008). The Encyclodedia of Christianity. Vol. 5. William B. Eerdmans Publishing Company. pp. 755–757. ISBN 978-0802880055. Retrieved 16 September 2022. Entry: Word Square by Ulrich Ernst
  6. ^ a b c d e f g h i j k l m n Baines, William (July 1987). "The Rotas-Sator Square: a New Investigation". New Testament Studies. Cambridge University Press. 33 (3): 469–476. doi:10.1017/S0028688500014405. S2CID 170226416. Retrieved 10 September 2022.
  7. ^ a b c d e f g h i Wilkinson, Alissa (4 September 2020). "The ancient palindrome that explains Christopher Nolan's Tenet". Vox. Retrieved 13 October 2021.
  8. ^ Leith, Sam (30 August 2020). "How Tenet was inspired by palindromes, the memes of the ancient world". The Daily Telegraph. Retrieved 20 September 2022.
  9. ^ Griffiths, J. Gwyn (March 1971). "'Arepo' in the Magic 'Sator' Square". The Classical Review. New Series. 21 (1): 6–8. doi:10.1017/S0009840X00262999. S2CID 161291159.
  10. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai aj ak al am an ao ap aq ar as at au Fishwick, Duncan (1959). "An Early Christian Cryptogram?". CCHA. University of Manitoba. 26: 29–41. Archived from the original on 14 January 2021. Retrieved 13 October 2021.
  11. ^ Pickover, Clifford A. (June 2002). "A Brief History of Magic Squares: Templar Magic Square". The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures across Dimensions. Princeton University Press. pp. 23–25. ISBN 978-0691115979. Retrieved 20 September 2022.
  12. ^ "Il Quadrato del Sator dalla Palestra Grande". Parco Archeologico di Pompei. 2023. Retrieved 14 June 2023.
  13. ^ a b c d Atkinson, Donald (1938). "The Sator-Formula And The Beginnings Of Christianity" (PDF). Bulletin of the John Rylands Library. 22 (2): 419–434. doi:10.7227/BJRL.22.2.6. Retrieved 10 September 2022.
  14. ^ a b c d e f g h i j Hemer, Colin J. "The Manchester Rotas-Sator Square" (PDF). Faith and Thought. 105: 36–40. Retrieved 12 September 2022.
  15. ^ a b c d e f g h i j k l m n o Étienne, Robert (1978). "Le «Carre Magique» a Conimbriga (Portugal), The "Magic Square" in Conimbriga (Portugal)". Conimbriga. Scripta Antiqua. Vol. XVII. University of Coimbra. pp. 15–34. ISBN 9782356132987. Retrieved 13 September 2022.
  16. ^ "The Sator Square from the Palaestra Grande". Parco Archeologico di Pompei. 2023.
  17. ^ Daube, David (2011). The New Testament and Rabbinic Judaism. Wipf and Stock. p. 403. ISBN 978-1610975100.
  18. ^ a b Swire, Ellie (19 November 2019). "Sator Squares". Magdalene College Libraries. Retrieved 13 October 2021.
  19. ^ Wilkes, Isobel (19 July 2021). "The SATOR Square". Corinium Museum. Retrieved 13 September 2022.
  20. ^ Ceram, C. W. (1958). The March of Archaeology. New York: Alfred A. Knopf. p. 30. ISBN 0-3944-3528-1. LCCN 58-10977.
  21. ^ Griffith, J. Gwyn (1971). "'Arepo' in the Magic 'Sator' Square". The Classical Review. Cambridge University Press (CUP). 21 (1): 6–8. doi:10.1017/s0009840x00262999. ISSN 0009-840X. S2CID 161291159.
  22. ^ a b Marcovich, Miroslav (1983). "SATOR AREPO = ΓΕΩΡΓΟΣ ̔ΑΡΠΟΝ(ΚΝΟΥΦΙ) ΑΡΠΩΣ (geōrgos arpon[knouphi] arpōs), arpo(cra), harpo(crates)". Zeitschrift für Papyrologie und Epigraphik. 50: 155–171. JSTOR 20183770.
  23. ^ a b c d e O'Donald, Megan (2018). "The ROTAS "Wheel": Form and Content in a Pompeian Graffito". Zeitschrift für Papyrologie und Epigraphik. 205: 77–91. JSTOR 26603971. Retrieved 10 September 2022.
  24. ^ a b Ferguson, Everett (1999). Encyclopedia of Early Christianity (2nd ed.). Routledge. p. 1002. ISBN 978-0815333197. Retrieved 16 September 2022. Rotas Sator (first century): Although the result is striking, the interpretation rests on the unlikely assumptions, and a non-Christian meaning is more probable.
  25. ^ a b c d Vinel, Nicolas (April 2006). "The Hidden Judaism of the Sator Square in Pompeii". Revue de l'histoire des religions. 223 (2): 3. doi:10.4000/rhr.5136. S2CID 170115926. Retrieved 16 September 2022.
  26. ^ a b Magi, Filippo (1972). "Il calendario dipinto sotto S. Maria Maggiore". Arte e Archeologia. Libreria Editrice Vaticana. 16. ISBN 9788820943790.
  27. ^ Beard, Mary (30 November 2012). "Were there Christians at Pompeii? The sator word-square evidence". Retrieved 12 September 2022. 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).
  28. ^ a b Moeller, Walter (December 1973). The Mithraic Origin and Meanings of the Rotas-Sator Square. Brill Publishers. ISBN 978-90-04-03751-9.
  29. ^ Ferguson, Everett (2003). Backgrounds of early Christianity. Wm. B. Eerdmans Publishing. pp. 590–. ISBN 978-0-8028-2221-5.
  30. ^ Otto, Bernd-Christian; Bellingradt, Daniel (December 2017). "Appendix A". Magical Manuscripts in Early Modern Europe: The Clandestine Trade in Illegal Book Collections. Palgrave Macmillan. pp. 134–135. doi:10.1007/978-3-319-59525-2. ISBN 978-3-319-59524-5. Retrieved 10 May 2023.
  31. ^ a b c Bond, Sarah E. (4 January 2016). "Power of the Palindrome: Writing, Reading, and Wordplay (Part II)". University of Iowa. Retrieved 13 September 2022.
  32. ^ a b Lipscomb, Suzannah (August 2020). A History of Magic, Witchcraft, and the Occult. DK. ISBN 978-1465494290. Retrieved 26 September 2022. 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.
  33. ^ Cavendish, Richard (1983). The Black Arts: A Concise History of Witchcraft, Demonology, Astrology (40th ed.). TarcherPerigee. p. 130. ISBN 978-0399500350. Retrieved 17 September 2022.
  34. ^ Rawlinson, John (March 1981). About Rivington (3rd ed.). Nelson Brothers. p. 42. ISBN 978-0950061528.
  35. ^ a b "amnordisk runtextdatabas". Runforum Uppsala. 20 December 2010. Archived from the original on 25 May 2012. Retrieved 13 February 2014.
  36. ^ Wilde, Jane (1888). "Evil Eye". Ancient Legends Mystic Charms & Superstitions of Ireland. National Library of Ireland. pp. 18–23. ISBN 9783849673604. Retrieved 16 September 2022.
  37. ^ "Note astigiane in prima mondiale applaudite ad Atene". La Stampa (in Italian). 27 February 2020. Retrieved 13 October 2021.
  38. ^ "Sator Arepo Tenet Opera Rotas (1982) by Gary Stephan". Metropolitan Museum of Art. Retrieved 17 September 2022.
  39. ^ Watt-Evans, Lawrence (July 2008). The Turtle Moves!: Discworld's Story Unauthorized. BenBella Books. p. 44. ISBN 978-1933771465. Retrieved 29 September 2022.
  40. ^ "Heilung's palindrome, Tenet". Sputnik Music.

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