Sator rebus: An unsolved cryptogram?*, The

sator rebus: An unsolved cryptogram?*, The

Sheldon, Rose Mary

ABSTRACT: The sator square is one of the oldest, unsolved word puzzles in the world. Examples of the square and numerous variations on it, have been found in Europe, the Middle East, Africa, and the Americas. Examples date from first-century Rome to the nineteenth century. Many questions have plagued scholars: Who composed it? What do the words mean? How has it been used in magic, religion, medicine and superstition ever since? Does the solution lie with mathematicians, philologists or theologians? All these questions remain unsolved, but the number of attempts by scholars to answer them grows yearly.

KEYWORDS: Palindromes, cryptograms, rebus, sator-arepo, charms, Christian symbolism, acrostics, word games, magic squares, superstition, Latin word squares, Greekword squares.

These five words formed into a square, sometimes referred to as the Templar Magic Square, constitute one of the oldest unsolved word puzzles in the world.

The sator square has a history of at least two millennia and has appeared on all five continents. When written out as a sentence, the words form a palindrome.

As a square, the five words can be read consecutively either horizontally or perpendicularly. They appear in inscriptions in both of the versions; called the sator square (left) and the rotas square (right). The initial letter of each word spells the first word, the second letter of each word spells the second word, the third letter of each word spells the third word and so forth for the other two words. A translation of the Latin words themselves yields little. “The Sower Arepo (whatever that may mean) holds the wheels with care. “What does this message mean? Where did it come from? Is the square a cryptogram? And most importantly, can it be solved? After close to 150 years of scholarly commentary, no one has put forward a convincing solution. One scholar describes it as inhabiting the “mysterious region where religion, superstition, and magic meet, where words, number, and letters are believed, if properly combined, to exert power over the processes of nature… “1

Even recent books on the subject of magic squares only mention it briefly.2 It is my intention to place this enigma before the cryptographic community not only because of its historical interest, but also to assemble the ever-growing bibliography for easy reference in the hope that a solution may lie with the mathematically-minded rather than the philologists, ethnographers and pious theologians who have traditionally studied the problem. I have included bibliography in the text by topic rather than relegate it to footnotes in order to make it easier for the reader to reference the previously published solutions. Each entry is accompanied by a summary of the contents. A full bibliographical treatment by list in alphabetical order will appear in my forthcoming work.3

With the age of printed books, mention of the square became more widespread, and people began suggesting solutions for this ancient puzzle. Efforts to decipher the sator-formula date as far back as the fourteenth or fifteenth century. The Bibliotheque Nationale in Paris possesses a manuscript of Byzantine origin with an attempt at a translation. This is listed along with others in a comprehensive article by Dr. S. Seligman:

Dr. S. Seligman, “Die Satorformel,” Hessische Blatter fur Volkskunde 13(1914), 154-183.

He has done an historical study of the sator rebus, and gives an interesting survey of the German examples of the formula. The majority of these are to be found on medals and plaques. He also discusses the various theories of origin. Here we will be examining them chronologically. Serious modern investigation of its origin and nature began in 1881 with an article by Reinhold Kohler: “Sator-Arepo-Formel,” Zeitschrift fur Ethnologie 13 (1881), 301-306 and Kleine Schriften 3, 564. Since 1881, rarely has a year gone by when someone has not published a possible solution. The simplest approach was to translate the five words and then turn them into a meaningful sentence as we tried in the beginning of this article. The most frustrating aspect of this exercise, however, was that one of the words, Arepo, has no firmly established meaning. From the outset then, all constructions of the square that aimed at a direct rendering of all five words were open to question. This led some scholars to deny the possibility of producing an acceptable translation. Others advanced the idea that arepo is a nonsense word coined to provide letters needed for whatever anagram they had produced for the square, the most famous being the pater noster solution (see below). The various meanings of arepo are also discussed below in the summary of the articles in which they appear.

Another possibility suggested for the rendering of the words of the square was that it could be read boustrophedon (zigzag or literally in Greek “as the ox ploughs “), starting with the ‘S’ to give a complete sentence Sator opera tenet (arepo rotas). Many have proposed this approach and have construed its meaning either “as you sow, so you shall reap”or “the creator maintains his works.”4

Hildebrecht Hommel, Schopfer und Erhalter, Studien zum Problem Christentum und Antike, Berlin: Lettner Verlag, 1956.

See pages 32-79. Following an anonymous French suggestion from the Magazin Pittoresque 22 (1854), 348 he assumes that the sator square was written boustrephedon and that the middle word tenet should be read twice – – Sator opera tenet: (tenet) opera Sator, which he translates, “Der Schopfer (Samann, Vater) erhalt seine Werke ” or “The Creator preserves his works. “He believes the sator square derives from a StoicPythagorean setting.

The boustrophedon approach accentuates the agricultural aspects of the square.

In this study I have broken down the investigation into three separate questions. I will treat each of these questions in order.

1. Who composed the square and why? The question of the origin of the square is quite different than what people have read into it ever since. Later interpretations may range far afield from the original author’s intent. A given explanation or interpretation of the square may not offer the most plausible account of the process by which the square came to be discovered.

2. What can the square be interpreted to mean? This is the largest segment of the literature on the square, and even in this article there is no room to include all of the possible solutions, but merely to group some of the more notable guesses into categories.

3. What was the charm used for in later era when knowledge of its original composition and use had long been forgotten?

ORIGIN AND DATING

Part of the answer to the origin question is its date of composition. Archaeological evidence can be used to shed light on the square’s antiquity. A British example had already been found in 1868 scratched on a wall plaster from a Romano-British building near Victoria Road in Cirencester, Gloucestershire. Although the scholar who published it considered it to be the first Roman example of the charm to be found, his theory was discounted because scholars are notoriously skeptical, and no other instances of the square were known at that time that could be dated before the 8th or 9th century A.D. Haverfield based his interpretation on the forms of the letters and the general Romano-British character of the find spot. In fact, he was later proven correct.

Francis John Haverfield, “A Roman Charm from Cirencester,” Archaeological Journal 56 (1889), 319-23.

The article contains a full-size photo of the inscription.

Francis John Haverfield, “Addidamenta quinta ad corporis vol. VII,” Ephemeris Epigraphica. Corpus Inscriptionum Latinarum Supplementum, Vol. IX, fasciculus quartus, 509-690, Berlin 1913.

On p. 519 Haverfield gives inscription number 1001 from Cirencester which is the rotas square. His other two articles discuss the discovery of the inscription in more detail.

Francis John Haverfield, “Notes on the Roman Origin of a Medieval Charm,” Journal of the Anthropological Institute of Great Britain and Ireland 22 (1899), 306ff.

More Roman examples were unearthed in the 1931-32 excavations at Dura-Europas on the Euphrates in Syria under the direction of Professor Michael Rostovtzeff of Yale University and the French Academy of Inscriptions and Letters:

Michael I. Rostovtzeff, The Excavations at Dura-Europus: Preliminary Report of the Fifth Season of Work (1931-1932), New Haven, 1934, pp. 159-161; and op. cit. Sixth Season, New Haven, 1936, 482-6.

In light of the newly discovered Dura rotas squares reported here, Rostovtzeff accepts Grosser’s origin theory as correct. (See below).

Michael I. Rostovtzeff, “Il rebus Sator,” Annali della Reale Scuola Normale Superiore di Pisa, Lettere, Storia e Filosofia, Ser. II, Vol. 3, fasc. 1 (1934), 103-105.

This article has an excellent photograph of the Latin rotas square opposite page 104.

Three specimens of the square were found on the walls of a military office in a building that had originally been the temple of Artemis Azzanathkona. A fourth example was discovered at Dura the following year. For the last years of its existence (ca. A.D. 165-256) Dura was an important fortress in the Roman military defenses against Parthia and then Sassanian Persia. The camp of the Romans was located in the section of the city in which the formula inscriptions were found. It is apparent that the rooms of the temple were taken over by the military, probably at the beginning of the third century when the garrison was considerably increased by local Semitic recruits. A number of the inscriptions are of cabbalistic character: alphabets, magic signs and symbols, pentagrams, evil eyes, a magic animal, and several hermetic texts in mystic alphabets. The room in which the sator formulae were found also contained a large number of graffiti relating to military affairs and indicate that it was a clerical office for the garrison. Many of the inscriptions are Latin written in the Greek alphabet. Two of the three sator formulae substitute Greek letters for the Latin, the earliest known example of this common practice. The formula generally appears in the two forms shown at the beginning of this article. All of these must have been inscribed before the Persians destroyed Dura-Europas soon after A.D. 256. They massacred or carried away its inhabitants into slavery. The terminus ante quem of the Dura examples seems then to be fixed. The terminus post quem is harder to establish, but if the sator formulae are associated with the military inscriptions, which seems plausible, then the date would be around A.D. 200. Rostovtzeff assumed that the inscriber or inscribers of the Dura formulae were members of the Roman military more familiar with Greek than Latin, probably local recruits.

Another Roman example was found at Aquincum on a roof tile from the villa publica, i.e. the residence of the imperial governor of the province of Pannonia Inferior. At the time of its discovery, it was the second oldest example of the formula found. The inscription contains two Latin palindromes: Roma tibi sub(ito motibus ibit amor), and the sator square in the Rotas, Opera, Tenet, Arepo, Sator version.

Janos Szilagi, “Ein Ziegelstein mit Zauberformel aus dem Palast des Statthalters in Aquincum,” Acta Antiqua Academiae Scientiarum Hungaricae 2 (1954), pp. 305-310 = Annee Epigraphique (1956) no. 63.

Primary publication of the rotas square find in Aquincum. Commentary in German and Russian.

K. Karner, “Die Sator-Inschrift von Aquincum,” Theologische Literaturzeitung 82 (1957), 391-394.

Karner discusses the sator inscription found at Aquincum (Szilagi, q.v.). At the time of its discovery, it was the second oldest example of the formula found. Karner feels that Grosser’s theory (q.v.) is not shaken by the find.

Jerome Carcopino, “Encore le carre magique,” CRAI (1955), 500-507. Carcopino criticizes Szilagi’s dating of the Aquincum square and holds it to his own second century dating.

Medieval examples abound. One was found in the monastery of St. Germain de Pres. Twelfth century examples are inscribed in the masonry of the Church of St. Laurent near the Ardeche and in the keep of Loches. A thirteenth century parchment from Aurillac contains the formula; and fifteenth century examples were found in the Chateaux of Chinon and of Jarnac and in the courthouse of Valbonnais. Later examples of the square used as a charm date anywhere from the sixth to the nineteenth century and have been found in Europe, Africa and even America. In most cases, these examples were used as charms, inscribed on amulets or magical figures for diverse religious or magical purposes. The square has been used to avert evil, for curing illnesses, for thwarting calamities, curing snake bites, dog bites, for casting out devils, extinguishing fires and helping women in childbirth. Christian tradition at various times borrowed it to name the five nails of Christ’s cross, the three wise men, and the shepherds of the nativity.

The earliest examples are thus Roman, and the best guess is that some Roman in the first century A.D. composed it as a word game. Alphabetic letter and word magic in antiquity is a subject worthy of a book-length study in and of itself. Franz Dornseiff’s Das Alphabet in Mystik und Magic, (Leipzig/Berlin: B. G. Teubner, 1925) is still one of the best treatments of the subject. Is the square just an example of an ancient word game?

CHRISTIAN SOLUTIONS -“CHRIST THE SOWER”

The combination of a first-century A.D. origin and the rendering of the sentence as having a sower/reaper aspect, led to Christian suggestions in which Christ was identified as the sower. On this theme, see Jean Daneliou, “The Plough and the Axe” in his Primitive Christian Symbols, Baltimore: Helicon Press, 1964 (translated from the 1961 French edition), pp. 99-101.

A. Schmoger, Katholische Kirchenzeitung (Salzburg) no. 21 of May 24, 1917, 173.

This is the earliest attempt to interpret Sator as Jesus the Sower (Matthew 13:3; Mark 4:3; Luke 8:5), or as God the Creator.

Francesco Babudri, “Il Criptogramma Pompeiano in una Leggenda Plutonica del Salento,” Iapigia 17, no. 1 (1946), 105-116.

Babudri discusses an Italian magic phrase: SATREPO TENOPRA ROTAS, a corruption of the famous square, and relates the square to local legends in Greece from Salento of spells to ward off the devil.

Jean Danielou, Primitive Christian Symbols, trans. by Donald Attwater, Baltimore: Helicon Press, 1964, 99-101. (Translation of Les Symboles cretiens primitifs. Paris: Editions du Seuil, 1961).

Daneliou suggests that Bishop Irenaeus of Lyons (c A.D. 200) knew of the cryptogram and spoke of Him “who joined the beginning with the end, and is the Lord of both, and has shown forth the plough at the end,” (Adv. haer. 4.34.4). Irenaeus was refuting the Gnostics who interpreted John 4.37, “one sows, another reaps,” as an opposition between the Demiurge, who created, and Christ, who redeemed. He maintained that the creator and the redeemer are one, and the passage refers to the cross, symbolized by the plow (as in Irenaeus), which was shown forth at the beginning or seed time, and in the end at the final weeding.

Ernst Darmstadter, “Die Sator-Arepo-Formel und ihre Erklarung,” Isis – Quarterly Organ of the History of Science Society 18(1932), 322-329.

Darmstadter also attributes a religious meaning to the famous palindrome. He provides an ingenious series of translations relating the square to the veneration of the macrocosmos.

G. Letonnelier,”Une interpretation du carre magique SATOR AREPO,” Bulletin Archeologique du Comite des Travaux Historiques (1951-1952), 168-69.

Letonnelier suggests some of the words are abbreviations. His reading: Sat Orare Poten(tia) et Oper(a) A Rota S(ervant). Prayer is our strength and will save us from the wheel (of fate?). The formula is thus a Christian call to prayer.

Jean Orcibal, “‘Dei agricultura’: Le carre magique Sator Arepo, sa valeur et son origine,” Revue d’Histoire des Religions 146 (1954), 51-66.

Orcibal concentrates on the concept of Christ as the Sower and the meaning of Sator. He takes examples from the Gospels and Christian writers. He believes it was used for its magical powers long before it was Christian. He discusses the mathematical possibilities of the pater noster solution being just chance. He feels that the magic which pagans saw in the square rested purely on the symmetry of the words. He suggests we might have found the formula in a collection of pagan magical papyri had Diocletian not had such documents burned.

Remigio Sabbadini, Rivista di Filologia 47 (1919), 34.

Interprets Jesus as sower or Sator as God the creator.

Erich Dinkler, “Alteste Christliche Denkmaler,” in his Signum Crucis: Aufsatze zum Neuen Testament und zur Christlichen Archaologie. Tubingen: J. C. B. Mohr (Paul Siebeck), 1967, 134-178.

See pp. 160-173 which deal specifically with the sator-rotas square and the plausibility of its being a Christian production. He was one of the first authors to comment that upon the adoption of the square by Christians it was reversed with sator at the top possibly because that word suggested the Greek word soter or saviour often applied to Christ. This interpretation was suggested earlier by Jerphanion, La Voix des Monuments, pp. 88-89.

C. W. King, Early Christian Numismatics and Other Antiquarian Tracts, London, 1873, p. 187.

King reports a version of the square in a Greek manuscript in the Bibliotheque Nationale in Paris (ms. 2411, f. 60). His translation is: “the laborer holds the plough wheels and I the sower creep after him.”

Giuseppe Gagov, “La soluzione di un antico Crittogramma,” Miscellanea Francescana 61 (April-September, 1961), 276-282.

Gagov believes the message embedded in the square consists of only three words: Sator opera tenet. He interprets this to mean “The Creator, the author of all things, maintains his works.”

Once the square came to be identified with Christianity, people came to believe it concealed a meaning other than the simple translation of the words. In many contexts, the five words were used to symbolize Christian objects or people. In Cappadocia, in the time of the Byzantine emperor Constantine Porphyogenitus (A.D. 913-959), the shepherds of the Nativity story are shown in church decorations called Sator, Arepon, and Teneton:

Guillaume de Jerphanion, Une Nouvelle Province de l’Art Byzantin: Les Eglises Rupestres de Cappadoce, Haut Commissariat de la Republique Francaise en Syrie et au Liban. Services des Antiquites et des Beaux Arts. Bibliotheque Archeologique et Historique. Tome VI. Paris: Librairie Orientaliste Paul Geunthner, 1934.

An illustration in a Byzantine bible of an earlier period conjures out of the square the baptismal names of the three Magi: Ator, Sator, and Peratoras.

Guillaume de Jerphanion, “La formule magique: Sator Arepo ou Rotas Opera. Vieilles theories et faits nouveaux,” Recherches de science religieuse 25 (1935), 188-225.

Reviewed in Analecta Bollandiana 53 3/4 (1935), 382-385 by H. D.

Gabriel Germain, “Contemplation et Interpretation du ‘carre magique’,” Bulletin de l’Association Guillaume Bude, 4th series, No. 1, (1966), 124-132.

Written in response to the publication of Jerome Carcopino’s Etudes d’histoires chretiennes. Le christianisme secret du carre magique; les fouilles de Saint Pierre et la tradition. Paris, 1953. (q.v.)

In the Staatliche Museum in Berlin is a bronze amulet from Asia Minor. On the obverse are two fish turned toward one another and several mysterious characters. On the reverse is a sator-square in Greek characters. Each letter of the square is enclosed in one section of a checkerboard pattern. Over the square are the letters “ICHTHUS” which stands for Jesus Christ. The amulet has been dated to the sixth century. If this dating is correct, then this is the earliest known example of the sator form of the square, and it is also the earliest known square which, from its context, is undeniably Christian. See:

Franz Joseph Dolger, “Ein Amulett mit Oxyrhynosfischen und der SATOR-Formel,” IXTHUS. Die Fisch-Denkmaler in der fruhchristlichen Plastik Malerei und Kleinkunst, Vol. 5 (1943) Munster in Westfalen: Aschendorffsche Verlagsbuchhandlung, 1943, 57-64.

Knowledge of the charm and attempts to explain it were not confined to Europe. In his Arithmologia sive de abitis numerorum mysteriis, (Rome, 1655) the Jesuit Athanasius Kircher related that on a voyage to Abyssinia he had discovered that local inhabitants invoke Christ by naming the five nails of the Cross which they call: Sador, Alador, Danet, Adera, Rodas – clearly the five words of the square in a corrupt form.5 A similar usage appears in a version from a tomb near Faras in Nubia where the five words follow a Coptic phrase that has been interpreted to mean the names of the nails of Christ’s Cross. For these Egyptian, Nubian, and Ethiopian examples, see:

Rene Basset, Les Apochryphes Ethiopiens, Paris: Librairie de l’Art Independent, 1895, Vol. 5, p. 16.

On the nails of the cross theory.

Walter Ewing Crum, “Coptic Studies,” Egypt Exploration Fund (1897-98), 63.

Walter Ewing Crum, Coptic Monuments. Catalogue generale des Antiquites Egyptiennes du Musee du Caire, No. 8001-8741, Cairo: Imprimerie de L’Institut francais d’archeologie orientale, 1902, 42.

Walter Ewing Crum, Catalogue of the Coptic MSS in the British Museum, London: British Museum, 1905, No. 524, p. 254, col. 2, vii.

Richard Pietschmann, “Les inscriptions coptes de Faras,” Recueil de travaux relatifs a la philologie et a l’archeologie egyptienne et assyriennes 21 (1899), 133-136.

Supplements reports by A. H. Sayce in Recueil de Travaux XX. Pietschmann’s discussion of the names inscribed around the sator square found at Faras indicates its Christian associations.

Archibald Henry Sayce, “Gleanings from the Land of Egypt,” Recueil de Travaux relatifs a la philologie et a l’archeologie egyptiennes et assyriennes 20 (1898), 169-176.

See pp. 175ff for the sator charm in Coptic found at Faras.

Sebastian Euringer, “Das SATOR-AREPO-Quadrat: Aberglaube oder Arkandisziplin?,” Historisches Jahrbuch 71 (1952), 334-353.

J. Schwartz, “A propos du carre SATOR chez les Ethiopiens,” Annales d’Ethiopie 2 (1957), 219-223.

Schwartz discusses a graffito found at Touna el-Gebel on the wall of a funerary monument from Hermopolis. It is the sator rebus but in Coptic with a few changes in consonants due to the language difference. He relates the words to the names of the five nails of the cross and the use of these names and symbols in Coptic amulets.

In Abyssinia, during the sixteenth century, the five words appear as the names of the five wounds of Christ:

Hiob Ludof, Ad Historiam Aethiopicam Commentarius, Osnabruck: Biblio Verlag, 1982 reprint of the 1694 edition, 351.

Adolph Erman, “Die Sator Arepo Formel,” Zeitschrift fur Ethnologie 13 (1881), 35-36. Erman describes a Coptic ostrakon in the Berlin Museum, No. 7821 bearing the sator acrostic and refers to Hiob Ludolf, Ad historiam Aethiopicam commentarius, (Osnabruck: Biblio Verlag, 1982 reproduction of the 1691 edition) p. 351 who discovered these five words in an Ethiopian manuscript. The five words are identified as names of the five wounds of Christ: sador, aroda danad adera rodas. Budge (q.v.) Zeitschrift fur Ethnologie. Verhandlungen der Berliner Gesellschaft fur Anthropologie, Ethnologie und Urgeschichte, 13 (1881), p. 35.

He mentions the formula again in Aegypten und Aegyptisches Leben in Altertum, Tubingen: Mohr, 1923, 486.

E. Wallis Budge, (ed.and trans.), The Bandlet of Righteousness, an Ethiopian Book of the Dead, London, 1929, 37, 75, 101.

The phrase descriptive of the nails of the cross in association with the sator formula occurs in an Ethiopic work, the Lefafa Sedek or “Bandlet of Righteousness, “where the formula is repeated four times in garbled but identifiable form and preceded once by the sentence: “in the five nails of the Cross of Our Lord Jesus Christ, I thy Servant Stephen have taken refuge.” Another introduction to the formula in the same work is “I demand this by the five nails that were driven into Thy Body on the Glorious Cross, being … [sator formula].” The garbled form of the formula is Sador, Alador, Danat, Adera, Rodos. It is clear that the Ethiopians borrowed it from the Copts and that neither people knew what the words really meant.

Jean Marques-Riviere, Amulettes, Talismans et Pentacles dans les Traditions Orientales et Occidentales, Paris: Payot, 1938, 167-70.

See pages 167-170 on the sator formula. He cites examples from Cappadocia where the words of the formula are connected with the names of the shepherds who worshipped the infant Jesus at the Nativity.

See also Maurice Bouisson, Magic: Its History and Principal Rites, New York: E.P. Dutton & Co., 1961 (translated from the French edition of 1958), pp. 148-150 whose discussion seems to be based on Marques-Riviere.

THE ANAGRAM SOLUTIONS

The widespread appearances of the formula from the Euphrates to France and from Ethiopia to Britain, had long ago raised suspicions among scholars that it must have once conveyed to those who knew its secret more than the words themselves seem to say. Accordingly attempts were made by various authors to discover the hidden meaning by the anagrammatic method of rearranging the letters of which the square is composed. Here are a selection of their results ranging from pious prayers to diabolic incantations:

G. Fritsch, “Die Bedeutung des Sator-Spruches,” Zeitschrift fur Ethnologie (Organ der Berliner Gesellschaft fur Anthropologie, Ethnologic und Urgeschichte), (1883), 535.

Fritsche rearranges the letters and finds in them an invocation to Satan: Satan oro te pro arte a te spero.

G. Fritsch, “Sator Tenet Opera Rotas,” Zeitschrift fur Ethnologie (Organ der Berliner Gesellschaft fur Anthropologie, Ethnologie und Urgeschichte) (1917), 144-145.

He reviews an article by Alexander Moskowski in the Vossische Zeitung about ‘Buchstabenspiele’ and uses it to give to the sator square a numerical value that translates to an invocation of Satan.

Anonymous, “A proposito della formula medioevale ‘Sator arepo’,” Bibliofilia 25 1/2 (1923/1924), 42-43.

The anonymous author notes several medieval examples of the square and notes that the solutions may contain the names of the authors. For example: Augusto Gaudenzi suggested arepo was really aretro and related it to alepe in Dante’s verse: Pape Satan pape Satan aleppe.

Other credible examples yield a formula for an exorcism: Retro Satana, tot opere asper, and the prayers:

Oro te pater, oro te pater, sanas

O Pater ores pro aetate nostra

Ora, operare ostenta te pastor

Kuno von Hardenberg, Damstadter Tageblatt, 1935 no. 69.

Another ingenious anagram. Hardenberg believed he had found in the square a reference to the comfort the Rose of Sharon is said to have brought to St. Peter for his sin in denying Christ. Petro et Reo Patet Rosa Sarona. i.e. “For Peter even [sic] guilty the Rose of Sharon is open.” The interpretation is dubious since the authority given for this incident (Acts 9.35) is dubious, and there is no reference to the Rose of Sharon, at least in the Vulgate. The incident is probably apocryphal and merely a poetic tradition. Both the incident and the Latinity of von Hardenberg’s solution have been questioned. (q.v. Fishwick, CCHA 1 (1959), p. 34 ).

Theodor Valentiner, “Arepo,” Romische Mitteilungen. Deutsches Archaologischen Instituts, Rom 57(1942), 250.

Proposes new explanation of the word arepo with the argument that it might be an acrostic, that is a summary of the first letters of a line of words “A r(erum) e(xtremarum) p(rincipio) o(mni).” The meaning of the rotas formula would be: “The Creator from the very beginning to the last moment of eternity holds (in his hand) the celestial movement (of the stars) and events.” Rejected by Wendell (q.v.)

Ed. von Welz, “Sator Arepo,” Societas Latina 5 (1937), 55ff.

Discusses anagrams that can be made from the letters of the sator square.

Kolberg, Verhandlung der Berliner Gesellschaft fur Anthropologie, 1887, 69.

He regards the letters of the sator acrostic as abbreviations of Latin words. He refers to the Nuremberg plate described in Verhandlung der Berliner Gesellschaft fur Anthropologie, 1883 p. 354 and interprets it as a paten or communion plate. On the outer circle are the words: + Deo Honorem + Et Patria + Liberationem + Mentem Sanctam + Spontaneam, and the sator acrostic, which he arranges arbitrarily as follows:

SAT ORARE

POTENter ET OPERAre

RatiO (oder auch ReligiO) TuA Sit.

He interprets:

Viel beten

Und kraftig arbeiten

Das sei Deine Lebensweise (oder Religion)

He believes it is an ancient rule of the Benedictines.

THE PATER NOSTER SOLUTION

The Christian solution which really sent scholars reeling, and which for a very long time was accepted as the ultimate solution by a large number of reputable scholars was discovered by three people independently. They suggested that the letters of the square could be arranged to produce the first two words of the oratio dominica (the “our Father” prayer). Felix Grosser, a German priest, caused a furor when he published an article in 1926 where he demonstrated that by rearranging the letters of the sator rebus, he created a Christian cryptogram of two pater nosters crossing on the common N and with A and O at the ends of the cross. This referred to the Apocalypse’s symbolism of God as the Beginning and the End. He believed the sator rebus was invented during the persecutions of the Christians.

Felix Grosser, “Ein neuer Vorschlag zur Deutung der Sator-Formel,” Archiv fur Religionswissenschaft 24 (1926), 165-169.

Unbeknownst to him, a Swedish scholar working simultaneously and independently, came to the same conclusion:

Sigurd Agrell, “Runornas talmystik och dess antika Forebild,” Skrifter utgivna av Vetenskaps-Societeten i Lund 6 (1927), 31ff.

Agrell introduced the theory in a lecture in 1925. Only page 30-32 are on the sator square. It forms a sidelight in a book about runic numerical magic.

Indeed, a third scholar had stumbled upon the pater noster solution two years earlier: Christian Frank, Deutsche Gaue 25 (1924), 76.

Grosser’s remained the best known and most influential of the three independent explanations of the pater noster theory. Since all the known examples of the square found in the 1920s had dated to the fourth century or later, authors felt secure in giving the formula a Christian context. When Jerphanion published an extensive treatment of the problem along these lines in 1935, the matter seemed closed. Many reputable scholars accepted the pater noster solution:

Guillaume de Jerphanion, “La formule magique: Sator Arepo ou Rotas Opera. Vieilles theories et faits nouveaux,” Recherches de science religieuse 25 (1935), 188-225.

Franz Dornseiff, Das Alphabet und Mystic und Magie, Leipzig/Berlin: B. G. Teubner, 2nd ed. 1925, 79 & 179.

Discusses the Satorformel along with other acrostics and magic formulas from antiquity. He accepts the pater noster arrangement.

Franz Dornseiff, “Das Rotas-Opera-Quadrat,” Zeitscrift fur neuetestamentlische Wissenschaft 36 (1937), 222-238.

Dornseiff accepts Cumont’s explanation of the rotas formula being based on Ezekiel, but believes that the prophecy of Ezekiel is a secondary influence, and that the primary root of the square is the pater noster. This makes it primarily a Christian-Judaic manifestation in Pompeii. He suggests that the rotas figure was conceived in Judaic or Christian-Judaic circles in Pompeii for the purpose of condemning Rome by practicing black magic. Dornseiff also proposes that the formula had a prophylactic sense, and indicates the four T’s that can be explained like the sign tav in the vision of Ezekiel (IX 4-6). Not convincing. For the counter argument, see Sundwall, p. 13.

Millar Burrows, What Mean These Stones? New Haven: American School of Oriental Research, 1941.

Burrows points out on pp. 33-34 that the pater noster theory, if accepted, supports the text of the Lord’s Prayer as found in Matthew rather than the version found in Luke. No one else seems to have followed up on this text-critical observation.

However, when della Corte (see below) produced two specimens from Pompeii in a context that dated to earlier than A.D. 79 and was probably not Christian, the effect was disturbing. Jerphanion, for one, recanted completely:

Guillaume de Jerphanion, Rendiconti della Pontificia Accademia Romana di Archeologia 12 (1936), 401-404.

Guillaume de Jerphanion, “A propos des nouveaux exemplaires trouves a Pompeii, du carre magique ‘Sator,’ par le R. P. Jerphanion,” CRAI (1937), 84-94.

A notice written on the occasion of the finds at Dura. He summarizes the problems of origins and use. At the end he discusses Cumont’s suggestion of a Jewish origin.

Guillaume de Jerphanion, “Du nouveau sur la Formule magique: Rotas Opera (et non SATOR AREPO),” Recherches de science religieuse 27 (1937), 326-35.

Guillaume de Jerphanion, La Voix des Monuments: Etudes d’archeologie. nouvelle serie. Paris: les Editions d’Art et d’Histoire, 1938, 38-94.

In this work he substantially reprints the three articles above but restates his opinion on the square which actually changed between 1935 and 1938. He gives his revised opinion in the full context of his historical research. He was one of the first to suggest that when the Christians adopted the square, it was reversed with sator now at the top. This is one of the best two collections of data and bibliography on the subject of the sator square.

Many others, however, would not give up a Christian interpretation. Jerome Carcopino insisted that the Pompeian examples were written by Christian treasure-hunters among the ruins many years after the eruption in A. D. 79, perhaps even as late as the third century, thereby saving the Christian interpretation.

Jerome,Carcopino, “Le Christianisme secret du carre magique,” Museum Helveticum 5 (1948), 28ff.

See also his earlier article on Christian numerology:

Jerome Carcopino, “El lenguaje cifrado de los primeros cristianos,” Boletin de la Academia Nacional de la Historia, Buenos Aires 9 (1936), 261-271.

Franz Cumont still believed the square to be Christian on account of the prominent and regular positions of the T’s and of their being always set between A (alpha) and O (omega). He believed its inwardness was not be found in any anagram but in the plain meanings of the words when interpreted as referring to various passages in the visions at the beginning of Ezekiel.

Franz Cumont, Rendiconti Pontificia Accademia di Archeologia 13 (1937), 7-8.

Floyd V. Filson, “Were There Christians in Pompeii?” Biblical Archaeologist 2 (1939), 13-16.

Filson argues for a conflation of the Cumont/Jerphanion interpretation.

However, both the sealed contexts of the Pompeian discoveries discussed by della Corte and cogent arguments raised by Atkinson show that Carcopino and Cumont were wrong and the square was known by the late seventies of the first century in Pompeii long before any Christian presence there:

Matteo Della Corte, “Reale Istituto di Archeologia e Storia dell’Arte. Atti della Reale Accademia Nazionale dei Lincei,” Notizie degli Scavi di antichite 6, 5 (1929) 449, no. 112; 447, fig. 2-112; 15(1939), 263, no. 139.

These are the earliest examples so far discovered and confirm that the original version began with rotas rather than sator. One fragment was found in a private home, and the other is a complete version of the square scratched in a column in the palaestra, both of them beginning with the word rotas. They may be dated between 50 and 79 A.D. because the decoration of the house is in a style generally agreed to have been developed after A.D. 50, and Pompeii was destroyed in A.D. 79.

Matteo Della Corte, Rendiconti Accademia di Archeologia, Lettere e belle arti di Napoli 19 (1939), 28-30.

Discusses of the pater noster theory of the rotas-opera square, its earliest appearance, whether the formula is Christian (he believes it is), and whether there were Christians at Pompeii (he believes there were).

Matteo Della Corte, “I Cristiani a Pompei,” Rendiconti Accademia di Archeologia, Lettere e belle arti di Napoli 19 (1936), 5-30.

Basing his conclusions on a thorough study of the Pompeii graffiti, Della Corte is certain that Christians were present at Pompeii, although probably not in great numbers. He defend’s Grosser’s pater noster solution against the criticism of Jerphanion. Among his proofs he offers the epigraph [C]ristiani found in the atrium of the Hospitium and a cross in a bas relief over a corner shrine in the house of Pansa. (p. 6). Both Della Corte and Atkinson believe that the Lord’s Prayer was recited immediately by all Christians and was translated into Latin at an early date.

Matteo Della Corte, Rendiconti Accademia di Archeologia, Lettere e belle arti di Napoli 12 (1936), 394-400.

In 1936 a version of the sator arepo square was found on the column of a building cleared near the amphitheatre at Pompeii, and this led Della Corte to recognize that in 1929 he had already published fragments of a similar text from the house of P. Paquius Proculus in the same city (see below, JRS). The examples found in the palaestra may have been done by military personnel because the palaestra was used as a barracks. The examples at Cirencester (Haverfield, q.v.) and Dura Europas (Rostovtzeff, q.v.) were also found in military contexts.

See Notizie delle Scavi, Ser. 6, vol 5 (1929), p. 449, no. 112.

See also, “Il crittogramma del Pater Noster,” Rendiconti Accademia di Archeologia, Lettere e belle arti di Napoli 17 (1937), 96ff.

Matteo Della Corte, “Publicius Paquius Proculus,” Journal of Roman Studies 16 (1926), 136-154.

This article discusses the house where a partial rotas square was discovered, but the square is not mentioned since its identity as a sator square was not yet realized.

Donald Atkinson, “The Origin and Date of the ‘Sator’ Word-Square,” Journal of Ecclesiastical History 2 (1951), 1-18.

Hans Lietzmann, “Die Sator-Rebus in Pompeji,” Archaeolgischer Anzeiger. Beiblatt zum Jahrbuch des Deutschen Archaeoligischen Instituts, Berlin, 1937, 478-482.

Another article by Atkinson provided a good discussion of the state of research and argued that the pater noster theory was unproveable. He believed the strength of the pater noster argument lay in its intrinsic “probability “and the fact that the mathematical odds against such a combination occurring by chance were astronomical. Mathematical theories will be discussed further below.

Donald Atkinson, “The Sator-Formula and the Beginnings of Christianity,” Bulletin of the John Rylands Library 22 (1938), 419-434.

Jerphanion best summarized the reasons why the square could not have been Christian if it were found in a pagan context at Pompeii. 1) It would have been surprising if there had been Christians at Pompeii before the destruction of the city; 2) If the square had originated among the Christians of the first century, one would have expected the inscription to be in Greek, not Latin; 3) The Alpha and Omega as a description of God passed into Christian terminology from the Apocalypse which had not yet been written in A.D. 79. 4) The intersecting arrangement of the double pater noster would require the Cross to have become a Christian symbol by A.D. 79. In no other place is it found earlier than the Epistle of Barnabas for which Jerphanion accepted a later, Hadrianic date (A.D. 117-138).6 The use of the cross as an esoteric sign of Christianity is, again, a practice not known before the second century.

Others, nevertheless, continued to accept the pater noster solution or cite Christian examples:

Clifford A Pickover, The Zen of Magic Squares, Circles, and Stars, Princeton and Oxford: Princeton University Press, 2002, 23-25.

Pickover states that “most of the authors discussing the square “have not noticed the pater noster solution. The works in this section would suggest otherwise.

Carl Wendel, “Das Rotas-Quadrat in Pompeji,” Zeitschrift fur neuetestamentlische Wissenschaft 40 (1941), 138-51.

Wendel tries to substantiate the theory of the pater noster, stating that the magic formula of the Pompeian square is explained as an expression of faith of the masses in spirits and also of the faith of the new Christian community, faith of a different nature from that of the Apologists and the Apostolic Fathers. He suggests the shift from the rotas version to the square with sator on top was due to a desire to have the nominative subject of the sentence come first in the square. Decisively refutes Valentiner’s acrostic theory. Detailed bibliography.

Oscar Wulff, and W. F. Volbach, (eds.), “Die Altchristlische und Mittelalterlischen Byzantinischen und Italienischen Bildwerke (Koniglische Museen zu Berlin,” Beschreibung der Bildwerke der Christlischen Epoche, 3 Band; Berlin: Walter de Gruyter & Co., 1909. Vol. I, 317 no. 1669.

Discusses an example of the sator square from Cappadocia dated by the author to the fourth or fifth century A.D. The square is shown with definite Christian associations: the fish and the Greek word ichthus.

Werner Kilian, “Gedanken zum Grossen Palindrome,” Forschungen und Fortschritte 32 (1958), 272-277.

Kilian is not interested in translating the five words of the square. Rather he is interested in the use of the letters to form the pater noster anagram. He rearranges the pater nosters in endless forms, proving nothing, but is convinced of the genius of the author in creating this palindrome that bonded together the cognoscenti (the Christians) while warding off their enemies (the Romans).

REJECTION OF THE PATER NOSTER SOLUTION

Slowly but surely rejection of the pater noster solution set in:

Hugh Last, Review of: Jerome Carcopino, Etudes d’Histoire Chretienne. Le Christianisme Secret du carre Magique: Les Fouilles de Saint-Pierre et la Tradition, Paris: Albin Michel, 1953, in Journal of Roman Studies 44 (1954), 112-115.

Pages 112-114 deal with the section of the book which discusses the sator square.

Carl Hermann Kraeling, “The Sator Acrostic,” Crozer Quarterly 22 (1945), 28-38.

He disputes Grosser’s pater noster solution in favor of a reversible, four-way acrostic. He believes the square originated as a word game, but once it was established as a magic formula, its perpetuation in Christian circles is readily explicable without the hypothesis of Christian origin. He believes the square might have originated among gladiators or army men because of the find at Dura, and denies that this is evidence of Christianity at Dura. Regardless of whether one accepts his theory, this is one of the most sensible evaluations of the whole problem. Kraeling takes into consideration both the Religionsgeschichte and the problem of constructing palindromes.

Carl Hermann Kraeling, The Christian Building. The Excavations at Dura Europos. Final Report VII, Part II. New Haven: Dura-Europos Publications, 1967, 111-112.

Kraeling gives his final estimation of the sator square in relationship to Christianity at Dura: it is not Christian, and he rejects the Grosser theory.

Emile Suys, “La formule SATOR est-elle chretienne?,” Etudes classiques 4 (1935), 291-294.

Suys discusses the formula and debates whether it is Christian or pagan, and whether its origin is Gallic and whether it was used by Christians during a Roman persecution. He was one of the first writers to reject the widely-accepted pater noster solution to the square. He offers no better solution.

NON-CHRISTIAN SOLUTIONS

If the square was not Christian, then what was it? Was it pre-Christian? Was it religious at all? If so, to what religion did it belong? Below are some of the possibilities listed by religion/philosophy:

Pre-Christian:

Henri Leclerq, “SATOR-AREPO . . .” Dictionnaire d’archeologie chretienne et de liturgie 167, col. 913-915).

Leclerq is critical of all Jewish-Christian origin theories.

Paul Louis Couchoud, and Amable Audin, “Le carre magique. Une interpretation graphique,” Latomus 17 (1958), 518-27.

An ingenious, if fanciful, interpretation which sees in the square a device for determining the wind directions.

Gnostic:

The word Gnostic comes from the Greek term gnosis which means knowledge. In the ancient world gnosticism was a complex religious movement based on a myth of redemption. It may have been pre-Christian in origin, and grew out of a fusion of ideas from pagan religion, Judaism, and Christianity. It came to prominence in the second century A.D. in both Christian and pagan forms and spread throughout the Roman empire and as far east as China.

Jean Doignon, “Le carre magique et Sainte Irenee,” Bulletin de la Faculte des Lettres de Strasbourg 34 (1955-1956), 232-234.

Doignon focuses on the translation of arepo and relates it to a passage in Saint Irenaeus, Adv. haer. 4.34.4 as did Carcopino. He feels that the number five is privileged in the text, and that the Gnostics played around with the symbolism of the number five. This square may have been Gnostic propaganda later turned into a Christian symbol by St. Irenaeus. Duplicated in Revue des Etudes Latines 33 (1955), 82ff.

J. Gwyn Griffiths, “‘Arepo in the Magic ‘Sator’ Square,” Classical Review 80 (1971), 6-8.

Gives a plausible explanation of the word arepo as a personal name derived from the Egyptian Hr-Hp. He proposes an Egyptian, specifically an Alexandrine origin where there was a Gnostic tradition that used acrostics.

Gustav Maresch, “Zur Sator-Formel,” Commentationes Vindobonenses, Vienna 1, (1935), 94-97.

Rather than the pater noster solution, he prefers an early version with Pater-Soter and a gnostic interpretation. In support of his Gnostic interpretation he sees N as a symbol of the Holy Ghost as possibly as suggestive (to a gnostic) of an M for the Mother.

Adolfo Omodeo, “La croce d’Ercolane e il culto preconstantiniano della croce,” La Critica 38 (1940), 45-61.

See note 3, pp. 46-47 which deal with the rotas version of the square. He believes the origin is military because of the find in Dura which suports a Mithraic interpretation. The cult of Mithras was only open to men and was thus popular with the Roman army.

Hildebrecht Hommel, Schopfer und Erhalter, Studien zum Problem Christentum und Antike, Berlin: Lettner Verlag, 1956.

See above.

Orphic:

From about the 6th century BC or possibly earlier, there are indications of a mystery cult associated with Orpheus. It was the first Greek religion to have a founder, and it spread to southern Italy. The Greek myth has as its central doctrine the punishment of individuals after death in the underworld. The Orphic cult also recognized reincarnation after death.

John Sundwall, “L’enigmatica inscriziones ROTAS in Pompeii,” Acta Academiae Aboensis Humaniora XV, 5 Abo, (1945 ), 3-17.

Sundwall connects the “sower” and “the plow” to the Eleusinian mysteries where the sower is a predominant figure in the Orphic movement in southern Italy.

Milan Budimir, “Quadratum magicum retractatur,” Ziva Antika 8 (1958), 301-304.

In German. The author connects the Greek form of arepo with Orpheus.

Mithraic:

The cult of Mithra was a mystery religion which spread from Persia and reached Rome in the second half of the first century B.C. It had secret rites and stages of initiation. In the first century A.D. it began to spread in the Roman empire reaching its peak in the third century A.D. before being suppressed along with other pagan religions at the end of the fourth century. Mithraism was confined exclusively to men and appealed particularly to merchants, soldiers and treasury officials so that the cult barely affected the civilian popular. It is an offshoot of Zoroastrianism.

Adolpho Omedeo, “La croce d’Ercolano e il culto preconstantiniano della croce,” La Critica 38 (1940) 46, n. 3.

A Mithraic interpretation of the square. He bases his interpretation on a graffito containing the square found in the Pompeian palaestra which he believes suggests a Mithraic origin because the area was used for military exercises for the iuvenes. For a Mithraic interpretation based on other grounds, see Moeller below.

Walter O. Moeller, The Mithraic Origin and Meanings of the Rotas-Sator Square, Leiden: E. J. Brill, 1973, 53 pp., plates.

Not convincing, but contains an excellent bibliography.

Local Italian:

Samson Eitrem, “The SATOR AREPO-fomula once more,” Eranos 48 (1950), 73-74.

He offers an interpretation based on an unusual reading of the square. Reading only the last half of the sator square beginning with the central letter N, he gets net opera rotans ( “She spins her works “). The meaning is that some feminine being, a goddess like Hecate, demon or maybe the square itself rotating on its own TENET spokes, spins or revolves. Citing several folkloristic motifs involving spinning, he posits an Italian/ pagan origin and the square as wind indicator.

Jewish:

Duncan Fishwick, “On the Origins of the Rotas-Sator Square,” Harvard Theological Review 57 (1964), 39-54.

He believes the form we now have originated with Latin-speaking Jews in the period immediately preceding the Christian era. It fell out of use, only to be revived as a Christian symbol at Dura Europas, Aquincum, and Cirencester.

See also his earlier work:

Duncan Fishwick, “An Early Christian Cryptogram?,” Report – Canadian Catholic Historical Association 1 (1959), 29-41.

A good summary of the state of research in 1959. Fishwick believes that the square consists of five words ingeniously evolved from the pater noster charm which, when properly combined, form a square that can be read in four different directions. The ‘magic’ of the square is basically the perfect symmetry of its component letters. These also contain cryptic Jewish symbols to those who know their origin and secret. Constructing such a square from the pater noster is, according to the author, “a technical achievement of the highest order.” He believes those who require that the individual words, (including the palindrome for opera that is not even a Latin word) also be meaningful when read concurrently, is to ask the impossible. Any superficial meaning that can be wrung from them is, therefore, purely superficial. The final verdict on the origin of the Rotas-Sator square is clearly dependent on future archaeological discoveries. In the form we have it now, Fishwick believes it should be described as a charm that originated with Latin-speaking Jews settled in Italy in the period immediately prior to the Christian era.

M. Harald Fuchs, “Die Herkunft der Satorformel,” Schweizerisches Archiv fur Volkskunde 47 (1951), 28-54.

The most astonishing feature of the solutions to the mystery are the number of purportedly meaningful texts that can be wrung from this extraordinary word square. Fuchs lists over thirty anagrams. The article also contains an excellent bibliography. Fuchs sides with a Jewish interpretation of the square.

Paul Grosjean, “Sat orare poten?” Journal of Theological Studies n.s. 3 (1952), 97-98.

This article (in French) begins by reading the rotas square boustrophedon. Beginning from the right-hand side instead of the left. The message he gets is Sat orare poten? which is taken to stand for the question “are you able to pray enough?” The message is a Jewish injunction to perpetual prayer.

John M. McBryde, Jr., “The Sator-Acrostic,” Modern Language Notes 22 (1907), 245-249.

McBryde discusses much of the earlier German literature on the magical and curative powers of the formula, and concludes that the sator square is related to the Jewish Kabbalah, but at the same time is also related to magic squares where letters and words are reduced to numbers with definite fixed values. These are older than the Kabbalah and may be traced back through the Pythagorean philosophy to ancient Babylon.

He adds many examples that he found in manuscripts but had been previously unpublished. He does not discuss the origin question.

H. Wehling-Schucking, Zum Deutproblem der Sator-Inschrift, album philologicum voor Th. Baader, Tilburg, 1939, pp. 197ff.

A fanciful explanation that treats the central N as the abbreviation for Nazarenus. He follows Cumont and Jerphanion in thinking the Pompeian squares are Jewish.

Word magic, alphabetic acrostics, and gematria, by which a numerical value was ascribed to individual letters of a word, were very important in Jewish exorcism, cosmogonic theories, and the symbolic representation of divine powers. On this, see M. Simon, “Versus Israel,” Bibl. des Ecoles francaises d’Athenes et de Rome, fasc 166, Paris, 1948, pp. 394-431.

David Daube, “‘Arepo’ in the ‘Sator’ Square,” Expository Times 62, 10 (July, 1951), 316.

Daube discussed the mysterious and unexplained word AREPO in the square. He believes it is Hebrew or Aramaic for alpha omega (aleph o), and thus gives a Jewish-Christian origin to the square.

David Daube, “Two Symbols: A. A Symbol of Ezekiel in Revelation, B. ‘Arepo’ in the Sator Square,” The New Testament and Rabbinic Judaism. London: University of London, Athlone Press, 1956, 401-405.

The second part of this study is a reprint of the previous article.

Pythagorean:

Rolland Boris, and Louis Philippe May, “Le Pythagorisme Secret du Sator Arepo. Lettres et nombres,” Recueil des Notices et Memoires de la Societe; Archeologique, Historique, et Geographique du Departement de Gonstantine, 69 (1955-1956), 95-117.

Miroslav Markovich, “Sator Arepo = Georgos Harpon (Knoyphi) Harpos, [Greek Arpo(cra), Harpo(crates),” Zeitschrift fur Papyrologie und Epigraphik 50 (1983), 155-171.

Markovich attacks the interpretation advanced by Hommel and defended by Huffman in Pauly-Wissowa that interprets the square as eminating from a Stoic-Pythagorean setting. Marcovich gives one of the best clues to the meaning of the word arepo. He believes it is a Latinized nickname for the god of good luck in Graeco-Roman Egypt – – Harpon (Knuphi). The translation of the charm would be: “The sower Horus/Harpocrates checks, toils, and tortures.”

Stoic:

Johannes B. Bauer, “Die SATOR-Formel und ihr Sitz im Leben,” ADEVA Mitteilungen 31 (1972), 7-14.

Heinz Hoffman, Pauly-Wissowa, Realencyclopadie der Classischen Altertums Wissenschaft, Supplementband XV, (Munich, 1978), col. 477-565.

Hoffman provides historians of Graeco-Roman religion with an exhaustive, 87 column account of the attempts to solve the puzzle since 1823. He adopts and strongly defends the position taken by Hildebrecht Hommel in 1952, that the square has a Stoic-Pythagorean origin.

Hildebrecht Hommel, “Die Satorformel und ihr Ursprung. Studien zum problem Christentum und Antike,” Theologia viatorum 4 (1952), pp. 108-180; 5 (1953/54), 322-378.

These two articles are combined in his book, Schopfer und Erhalter. See above. On pages 32-79 he discusses the sator formula, augmenting his Stoic origin theory.

Wolfgang Christian Schneider, “Sator Opera Tenet – Poros Aras. Der Samann erhalt die Werke – Du aber pflugst Eine Deutung des Sator-Quadrats,” Castrum Peregrini 189/90 ( (1989), 101-124.

Schneider believes the sator square is the key to an important philosophical concept that joins the tradition of Etruscan/Roman religion and philosophy to the Stoic and Academic Greek traditions of philosophy.

Satanic:

V. Zatzman, “Die Sator-formel und ihre Losung,” Hessische Blatter fur Volkskunde 24 (1925), 98-105.

Sees the square as an apotropaic formula against the devil. The acrostic should read Satan Adama Tabat Amada Natas. He believes the original formula was Hebraic/Aramaic.

The Numerological Solutions

Some have suggested the magic square is actually a number-square.

Waldemar Deonna, “Talismans Magiques trouves dans l’Ile de Thasos,” Revue des etudes Grecques 20 (1907), 364-382.

Page 365 illustrates an example of the sator square on a bronze disk from, Thasos. Deonna suggests that the formula should be read boustrephedon. This solution supposes a transitional phase in writing between cultures with writings in opposite directions. Although this condition existed between Semitic languages and Latin, it would imply that the formula was evolved in a Semitic culture. There is no evidence at this point to suggest that this was the case. This is the earliest example of a numerical square in conjunction with the sator square. Deonna dates the amulett to the 16th-17th century.

One of the problems with this approach is that the words of the square are Latin, and that the Romans did not have a ciphered number system as did the Greeks and the Semites. But if the letters are transliterated to the Greek, and one assigns numbers to the square, one finds that a very significant number can be derived from the central word Tenet. The most notable is the system which renders it as 666, the number of the mark of the beast in Revelation 13.18. Walter O. Moeller discusses many of the possible combinations one can derive from such a system in his book on The Mithraic Origin and Meanings of the Rotas-Sator Square (Leiden: Brill, 1973). He believes the origin of the square is Mithraic numerologists who were familiar with the Saturn square and the square of the Sun as well as other number squares that are thought to have originated with the Kabbala. He believed the square originated in Gaul, Egypt or Italy.

Such number manipulation proves nothing, and the results are no more convincing than the recent best-seller The Bible Code, which found predictions in the Bible based on computer generated combinations.

THE MATHEMATICAL SOLUTION

Is it a mere accident that the word square contains letters which can be arranged as two intersecting pater nosters, together with two A’s and two O’s? Was the square constructed to contain these letters and so serve as a sign which might be recognizable by Christians without arousing the suspicion of pagans much like the fish sign? Or is it mere accident? This second possibility was already raised by a scholar in 1948:

Friedrich Focke, “Sator Arepo: Abenteuer eines magischen Quadrats,” in Wurzburger Jahrbucher fur Altertumswissenschaft 3 (1948), 366-401.

This article is one of the two best works on the subject which collects both the data and a bibliography of secondary works.

To answer this question, it seems necessary to discover the odds against the use of these particular letters being an accident; for the longer the odds the more probable it will be that the choice of these letters was intentional. This brings us to the possibility of a mathematical solution. Hugh Last discussed the possible methods of inquiry in 1952:

Hugh Last, “The Rotas Sator Square: Present Position and Future Prospects,” Journal of Theological Studies n.s. 3 (1952), 92-97.

He believed the odds could not be determined by purely mathematical means. He stated it was useless to calculate in how many ways a square of twenty-five letters could be formed from an alphabet of twenty-three letters because the letters in each line and column are only admissable if they form words. He felt even if one could discover how many pure palindromes of five-letters (such as tenet, solos, malam) there were in Latin, and how many five-letter words there were which had some significance when read backwards, one could not use them to calculate in how many ways one palindrome and two of these five-letter words (both written once in each direction) could be combined to form a twenty-five letter square. That approach would not work because all five words together would still have to make some sort of sense. The only approach he found reasonable was to compose twenty-five letter squares of this sort and see how many could in fact be made with Latin words. He suspected the number would not be large, and the task would certainly be laborious, but it would help determine the probability that Cumont was correct when he identified the square as the earliest Christian inscription.

Polge and Gunn were among the first to use the computer to solve the Satorarepo mystery:

Henri Polge, “La fausse enigme du carre magique,” Revue d’Histoire des Religions 175 (1969), 155-163.

Polge examines the idea the the sator formula is simply a gibberish abracadabra. He was one of the first scholars to use the computer to prove his case. He calls the sator square “une construction phraseomorphe anacyclique a quadruple entrfe.” He has the computer calculate the 625 applicable permutations of the 25 letters of the square and concludes that none of the combinations is linguistically viable. He concludes that arepo is “un anthroponyme imaginaire,” “un artifice lexicale,” “une option irrationelle.” Any attempt to link it to a person or thing in the Graeco-Roman world is fruitless.

Gunn on the other hand came to the conclusion that a Roman origin could be supported and that the words were designed as an attempt to construct the perfect word-square:

Charles Douglas Gunn, The Sator-Arepo Palindrome. A New Inquiry into the Composition of an Ancient Word Square, Yale University, 1969. Unpublished dissertation.

This is my personal favorite as one of the finest studies ever done on the square. Although it does not have a complete bibliography, it does take an extremely sensible approach to solving the problem. He is most concerned with the origin problem. He suggests that a Latin-speaking person in the first century A.D. who was familiar with the Roma-Amor square decided to create a better one. Gunn then describes the steps he believes were followed.

Most useful was his computer study of 5555 five-letter Latin words and their possible combination into word squares. He comes up with 2,264 Latin word squares, printed on pp 82-182. He still considers the sator square the best one.

William Baines also used the computer to dispute the pater noster interpretation of the famous square. He concludes that it is possible to abstract a number of pseudo-Christian formulae from the word square, and that this proves nothing about its original use. There may well be no explanation called for other than the inclination of people to construct word games and the fascination that this partiuclar arrangement of letters held for those people.

William Baines, “The Rotas-Sator Square: A New Investigation,” New Testament Studies 33 (1987), 469-476.

WORD GAMES

The “magic” of the square thus rests surely on the perfect symmetry of its component letters which yield the same combinations in four different directions. The Romans were fond of anagrams and word games.

Arsenio Frugoni, “Sator Arepo Tenet Opera Rotas,” Rivista di Storia e Letteratura Religiosa 1 (1965), 433-439.

Frugoni surveys the literature and then concludes that the square meant different things to different people, but probably originated as a piece of word play and cites its appearance in the Carme delle scolte modenesi where it is written in the margin next to another famous palindrome: Roma muro luceas summus saeculorum amor.

Albrecht Dieterich, “ABC-Denkmaeler,” Rheinisches Museum fur Philologie 56 (1901), 77-105. Reprinted in Dieterich’s Kleine Schriften, Leipzig/Berlin: B. G. Teubner, 1911, 202-228.

The sator square is dealt with on p. 92. The author thinks the rotas rebus is a giuoca di parole i.e. simply a word game.

Franz Joseph Dolger, “Die SATOR-formel: ein richtiger Krebs,” Antike und Christentum 3 (1932), 278-279.

The author chooses the palindrome as the primary explanation for the square to the exclusion of more complex theories or word rearrangements.

Margherita Guarducci, “Il misterioso ‘Quadrato Magico’ L’interpretazione di Jerome Carcopino e documenti nuovi,” Archeologia Classica 17 (1965), 219-270.

An excellent review of recent work up to 1965. Guarducci successfully puts to rest Carcopino’s shaky interpretation. She cites the work of Amedeo Maiuri on the excavations at Pompeii where two examples of the sator rebus were found. This work was overlooked by Carcopino. She concludes the formula is a simple word game.

Margherita Guarducci, “Ancora Sul ‘Quadrato Magico’,” Archaeologica Classica 19 (1967), 9-10.

Guarducci compares the Rotas/Opera/Tenet/Arepo/Sator palilndrome to another which reads Roma/Olim/Milo/Amor. There are examples of this word game from Ostia, Pompeii, and another found at Bolonia (Belo in the province on Cadice) found during the 1917-21 excavations there.

Paul Veyne, “Le carre Sator ou beaucoup de bruit pour rien,” Bulletin de l’Association Guillaume Bude, 4th series, (1968), 426-60.

In a somewhat over-argued but perceptive article, Veyne applies the theory of probablility to prove that the anagrams drawn from the square are posteriori events and are therefore in no way remarkable. The square is purely a palindrome. For discussion see Moeller, p. 37, n. 1.

Hans Weiss, Bella Bulla: Lateinische Sprachspiele. Bonn: Ferd. Dummlers Verlag, 1951.

See pp. 57-62 for much interesting material and numerous solutions and rearrangements of the sator square’s letters such as A Rohi EPiscOpus, A Rex Et Pontifex O, sat orAre Per Omnia, etc.

Dmitri A. Borgmann, Language on Vacation: An Olio of Orthographical Oddities, New York: Charles Scribner’s Sons, 1965.

On page 208 he calls the square “a symbol of imperfection, of failure to achieve a desired goal. “The flaw is the non-word arepo.

Borgman is the editor of: Word Ways: The Journal of Recreational Linguistics. (Vol I/1 – February 1968), New York: Greenwood Periodicals.

LATER SUPERSTITION

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, Iceland and eventually even crossed to North America. We have already mentioned that the shepherds of the nativity came to be called Sator, Arepon, and Teneton, and the three Magi are referred to as Ator, Sator, and Peretoras. Nor was the square confined to Europe alone. In Nubia the words came to represent the names of the nails of Christ’s cross and in the eleventh century, the five words were used in Abyssinia to denote the five wounds of Christ. In Germany it was used to put out fires – the formula was written on a disk that was thrown into the fire to extinguish it. An edict in 1743 by Duke Ernest Auguste of Saxe-Weimar ordered that all towns and villages should manufacture such fire disks to serve as a means of quenching conflagrations that endangered the community. In Bosnia the formula was used as a remedy for headache and for hydrophobia, and in Iceland it was scratched on the fingernails of patients as a cure for jaundice. The most recent examples come from nineteenth century South America where it was in use to cure dog-bites and snake-bites. Also, enclaves of Germans in the Allegheny Mountains in the eastern United States used it to prevent fire, stop fits, and prevent miscarriages. Below are listed numerous examples of medical cures attached to the formula by people who had no idea of the meaning of the words or the origin of the square.

THE MEDICAL USES

A. Alcock, “A Coptic Magical Text,” Bulletin of the American Society of Papyrologists 19 (1982), 97-103.

The formula is found on a Copic amulet believed to cure fevers:

Jerome Cardan, De Rerum Varietate, Milan, 1557.

Here, the square as a cure for fever or insanity.

Jean du Choul, De Varia Quercus Historia, Lyons, 1555.

In the section “De veteribus Gallorum Magis” he discusses the square as a cure for insanity and fever. It was used by the ancient Gauls as a febrifuge, and was used to awaken love or to obtain favor. As one example: A citizen of Lyons recovers from insanity after eating three crusts of bread, each inscribed with the magic square. The meal was punctuated by the recitation of five pater nosters in remembrance of the five wounds of Christ, and of the five nails of the cross: pro quinque vulneribus Christi, quae moriendo accepit, nee non pro clavibus. This local association with the Lord’s Prayer may go back to the second bishop of Lyons, St. Irenaeus, who himself had a devotion to the five summits of the cross: et ipse habitus crucis fines et summitates habet quinque, duas in longitudine et duas in latitudine et unam in medio in quo requiescit qui clavis affigitur. Irenaeus, adv. Haer 2.24.4.

Richard Ernst-Bader “Sator arepo: Magie in der Volksmedizin,” Medizinhistorisches Journal 22 (1987), 115-134.

A discussion of the many forms of the sator formula used as charms to ward off evil or illness, or used as a cure for diseases or animal bites. Brings together much of the 19th century literature by Treichel and colleagues (q.v.) Interesting illustrations of disks containing the sator formula from Nuremberg.

Thomas Rogers Forbes, The Midwife and the Witch, New Haven: Yale University Press, 1966.

Chapter 6 is entitled: “Word Charms and the SATOR Mystery.” Pages 84-93 contain a good modern survey on the history of interpretation of the sator square plus extensive listings of occurrences of the formula. It is especially good on linking the sator square to medieval medicine and superstition. Examples of how the sator square was used as a spell against fire, to prove whether a person was a witch or not, against poisonous air and pestilence and against sorcery.

In his review of this book in Scientific American, February 1967, p. 140, Martin Gardner says: “The five Latin words have meaning, if not clarity.”

Marchese P. Franco, “Sator Arepo Formel,” Zeitschrift fur Ethnologie (Organ der Berliner Gesellschaft fur Anthropologie, Ethnologie und Urgeschichte) 13 (1881), 333-334.

The anagram is solved as: Pater, oro te, pereat Satan roso. Roso comes from rodere, to bite as in dog bite. Thus another example of the charm being used as a preventative or cure for dog bites.

George Gardner, Travels in the Interior of Brazil, principally through the Northern Provinces and the Gold and Diamond Districts during the years 1836-1841, New York: AMS Press, 1970, 562 pp.

On pp. 52-53 Gardner gives the most recent example of the square being used as a cure for dog-bites and snake bites. Each line of the acrostic is to be written separately on a slip of paper and then rolled into the form of a pill. All five are to be given to the patient as soon as possible after the person (or animal) has been bitten.

Francis Llewellyn Griffith, (ed.), Egypt Exploration Fund: Archaeological Report, London, 1897-98, 63.

In the desert west of Faras in Nubia, an inscription in a tomb consists of a prayer dated A.D. 739 for the soul of a certain Theophilus. The sator formula is included in columns of inscriptions among which is a Coptic version of the apocryphal letter from Jesus to Abgar V, King of Edessa, a letter widely employed by the Copts as a prophylactic against illness. Another list records the names of the forty martyrs of Sabaste, also a talisman against disease. The final lists consists of the sator formula in linear form preceded by the phrase: “These are the names of the nails of Christ.” The names are SADOR, DANET, ADERA, RODAS.

See above, A. H. Sayce, “Gleanings from the Land of Egypt,” Recueil et Travaux 20 (1898), 176.

Heinrich Handelmann, “Satorformel,” Zeitschrift fur Ethnologie 18 (1886), 315.

Another dogbite formula.

J. Hampden Porter, “Folklore of the Mountain Whites of the Alleghenies,” Journal of American Folklore 7 (1894), 105-117.

On p. 113 he describes an example of the sator rebus he found that was used as a talisman. It was writtten on parchment, in ink that was “dim with age “and was surmounted by an indistinct device that looked like an equilateral triangle inscribed in a circle. It was used for “almost everything to carry with you to be safe any place or to keep in your house to keep it from burning down or stop fits or prevent miscarriage. If convulsions occur in consequence of injuries, no benefit follows the use of this remedy, but a copy of the formula swallowed or taken in the form of an infusion will certainly prevent a mad dog’s bite from causing hydrophobia, and the same methods of administration prove effectual in cases of continued fever.”

Henri Leclerq, “Amulettes,” Dictionnaire d’archeologie chretienne et de liturgie, I, 2 (cols. 1784-1860).

Much material relevant to interpretation of the square as an amulet. The square itself is discussed in cols. 1809-1816. He quotes from Kircher’s Arithmologia (see above).

Viljo Johannes Mansikka, Litauische Zauberspruche. Helsinki: Academia Scientiarum Fennica 1929.

Items no. 97-101 give four variants of the sator square used against mad dog bites.

Robert L. Ripley, Believe It Or Not, New York; Simon and Schuster, 1929.

See p. 45 of this classic collection of oddities for treatment of the sator square.

Wilibald von Schulenberg, “Formel ‘Sator Arepo’,” Zeitschrift fur Ethnologie, (Organ der Berliner Gesellschaft fur Anthropologie, Ethnologie und Urgeschichte) 13 (1881), 85-86.

Tells the 16th century story of several women with eye maladies who had them cured by wearing a parchment around their neck that had the sator square written on it. The sator square was also found on a lead tablet that was nailed to the oldest house in Posneck to protect it from fire.

Paul Schwartz, “Sator arepo Formel,” Zeitschrift fur Ethnologie, (Organ der Berliner Gesellschaft fur Anthropologie, Ethnologie und Urgeschichte) 13 (1881), 131-132.

Schwartz was the Gymnasiallehrer in Salzwedel and reports on an example of the sator formula being used as a cure for dogbites.

Godfrid Storms, Anglo-Saxon Magic, The Hague, 1948.

See pp. 281-282 for an 11th century Latin formula for childbirth involving the words of the sator square.

Alexander Treichel, “Das Tolltafelchen aus Wahlendorf,” Zeitschrift fur Ethnologie, Verhandlung der Berliner Gesellschaft fur Anthropologie 12 (1880), 42-47.

Brief communication in which the author describes a curious Tolltafel or small wooden tablet containing the sator formula, and used as a charm against the bite of a mad dog or other rabid animal. He can find no translation for Arepo and so treats it as a proper name. The translation is “Der Saemann Arepo halt mit Muhe die Rader.” (the Shaman, with effort, holds the wheels). Later in the same issue (p. 215) he reports the discovery of another little tablet, inscribed with an acrostic containing several letters of the sator formula, but including other letters in different order.

Alexander Treichel, “Tolltafel aus Jeseritz,” Zeitschrift fur Ethnologie. Verhandlung der Berliner Gesellschaft fur Anthropologie 12 (1880), 215-217.

An inscription on a tolltafel (charm against rabid dog bites) with a very garbled version of the sator square found in Jeseritz.

Alexander Treichel, “Nachtrage uber die Tolltafelchen,” Zeitschrift fur Ethnologie. (Organ der Berliner Gesellschaft fur Anthropologie, Ethnologie und Urgeschichte) 12 (1880), 276-284

Treichel suggests another interpretation. Sator = Father, Nourisher, Supporter. Rotas = Wheel of fate. Hence, “Der gutige Vater halt mit Muhe auf das verderbliche Rollen der Schicksalrader. “(With effort, the kind father holds on to the ruinous rolling wheels of fate). He still finds, however, no satisfactory explanation for the word arepo.

He cites examples of the use of the sator acrostic to cure toothaches. The letters are supposed to be written in butter or on a piece of bread and butter that is then to be eaten. The idea is to swallow the magic words so that they may expel the sickness. Instances are given where the acrostic was used to extinguish fires.

Alexander Treichel, “Nachtrage zu den Tolltafeln und zur Satorformel,” Zeitschrift fur Ethnologie. (Organ der Berliner Gesellschaft fur Anthropologie, Ethnologie und Urgeschichte) 13 (1881), 258-260.

Albrecht Durer’s famous “Melancholie” shows a figure holding a tablet with numbers. Some believe the numbers can be related to the sator formula. Treichel also relates stories about tolltafeln as rabies cures. One baked a rye flour “cookie” that contained pieces of the heart, liver, and spleen of the dog that had bitten someone (and was now presumably dead). The sator square was pressed on the outsde of the cookie. The bitten person ate the cookie, but just to be sure, the wound was also cauterized.

Alexander Treichel, “Zur Satorformel und Tolltafel,” Zeitschrift fur Ethnologie, (Organ der Berliner Gesellschaft fur Anthropologie, Ethnologie und Urgeschichte) 13 (1881), 306-307.

Treichel reports examples of the sator formula being used to cure the bite of a rabid dog.

Alexander Treichel, “Beitrage zur Satorformel und zur Tolltafel” Zeitschrift fur Ethnologie 14 (1882), 264.

The sator square was used as a talisman against rabies. Wooden molds were made out of two pieces of pear wood carved like castinets. Dough was squeezed between them and the resultant cookie was baked. One piece was fed to the bitten person and one to the dog as a cure against rabies.

Vincenzo Ussani, “Per un esemplare cassinese di ‘Rotas Opera’,” Studi Medievali n.s. 16 (1943), 237-241.

Ussani discusses three medieval examples of the sator square. One is from Codex 384 from Monte Cassino dating to the 9th or 10th century, one was found inscribed in the church of San Pietro all’Oratorio di Capestrano, and the third is written in the margin of a work entitled Versus de cavenda Venere et vino found in Codex 1.4 of the Capitolare di Modena. There are illustrations of all three.

Alexander Treichel, “Satorformel,” Zeitschrift fur Ethnologie 19 (1887), 69-74. A series of examples of the sator square in different contexts. One use involves taking a copy of the square and adding various herbs and marine plants, then sealing them in a leather bag and wearing them around the neck as a cure for vertigo.

MISCELLANEOUS

Not all articles on the sator square present original material. Many are just short notices giving examples of the square, or announcing the discovery of a new one. Some authors attack the interpretations of others without supplying a new interpretation of their own. The articles listed below do not fit easily into the categories above but provide some far-ranging possible solutions to the problem. I have presented them in alphabetical order.

W. Ahrens, “Studien uber die ‘magischen Quadrate’ der Araber,” Der Islam: Zeitschrift fur Geschichte und Kultur des Islamischen Orients VII (1917), 186-250.

This is one of the best treatments of magical number squares. It does not deal directly with the sator square, but letter-squares are discussed on pp. 240ff under “Nicht-‘magische’ Zahlenquadrate.”

[Albertus Magnus] Approved and Verified, both Sympathetic and Natural Egyptian Secrets, for Man and Beast … translated from the German. Harrisburg, PA: n.p., 1875, 3 volumes in one.

This is a good example of the kind of 19th century popular book which discussed the magic square. It does not contain any of the occult lore of Albertus Magnus, nor does it represent any Egyptian secrets, but references to the sator square appear in Vol. 1, p. 62; Vol. 2, pp. 15, 18, 55,64; Vol. 3, pp. 47, 49.

T. van den Baar, “On the Sator Formula,” In J. J. van Baak (ed.) Signs of Friendship. To Honour A. G. F. van Holk, Slavist, Linguist, Semiotician, Amsterdam, 1984, 307-16.

Discusses the Russian sator squares. See also:

A. I. Sobolevsky, “Perevodnaya literatura Moskovskoi Rusi XIV-XVII vekov,” Sbornik Otdeleniya russkogo yazyka I slovesnosti Akademii nauk, 74/1 (1903), 226.

D. Rovinsky, Russkie narodnye kartinki, Spb. 1881, iii, 87; iv, 581ff and the appended atlas iii, no. 798.

Albert Becker, “Die Sator-Arepo-Formel patentamtlich geschutzt,” Zeitschrift fur Volkskunde 44 (1934), 66.

The sator formula was copyrighted as a business trademark in the imperial patent office in 1921, and was renewed in1931. The company defended its right to the logo in court several times charging copyright infringement. This was one of the first articles to advance the idea that the square could be read boustrophedon. He cites an article by A. Spamer in Die Deutsche Volkskunde II (1935), pp. 6ff.

Walter Beltz, “Noch Zwei Berliner Sator-Amulette,” Archiv fur Papyrusforschung 24/25 (1976), 129-134.

Two examples of the sator square appear on P. 982 and P. 8096, two papyri at the Staatlichen Museum in Berlin. They are examples of Greek versions of the formula dating to the seventh century. Cf. Krall (q.v.)

Hans Biedermann, “SATOR AREPO TENET OPERA ROTAS,” in Handlexicon der magischen Kunste von der Spatantike bis zum 19 Jahrhundert. Graz: Akademische Druck und Verlagsanstalt, 1968, 320-321.

Short encyclopedia entry on the sator square. He gives both Christian and Jewish interpretations. The sator square appears on the cover of the book. It is also illustrated with an example of the square found in the church of Pieve Terzagni in Cremona, Italy.

H. J. Bodman, Jr., “The Sator Formula: an Evaluation,” in Laudatores Temporis Acti: Studies in Memory of Wallace Everett Caldwell. . .” edited by Mary Francis Gyles and Eugene Wood Davis, The James Sprunt Studies in History and Political Science 46 (1964), 131-141.

Bodman believes that no solution embodying a translation of the formula’s words can be accepted without a reasonable interpretation of arepo. Yet it still seems impossible to find one. The author gives a good summary of the state of knowledge in 1964 but adds little to the interpretation except agreeing with Grosser on the pater noster solution. Reviewed by J. Simon, Analecta Bollandiana 49 (1931), 163-168.

Charles Carroll Bombaugh, Oddities and Curiosities of Words and Literature, edited and annotated by Martin Gardner, New York: Dover Publications, 1961. See the chapter on “palindromes. “Martin Gardner’s notes on pp. 347-348 which view the sator square in the context of word puzzles and conundrums.

Jerome Carcopino, “Une note du R. P. Jerphanion sur de nouveaux exemplaires du carre magique SATOR recemment decouverts a Pompeii,” CRAI (1937), 84-93.

Carcopino comments on the four inscriptions found at Dura Europas. He points out that the earlier the Christian community, the more likely they would have had access only to the Greek text of the Gospels and therefore the pater noster should be in Greek. He does not believe the rebus has a Celtic origin. He also believed there were enough examples to suggest the rule that magic cube, when found in the Roman world, was read ROTAS OPERA but when it is found in a Christian context it reads SATOR OPERA. He wants to wait until there are more pre-Christian examples before making a judgment on its ultimate origin.

Madeleine H. Caviness, “Images of Divine Order and the Third Mode of Seeing,” Gesta 22 (1983), 99-120.

A brief discussion of the sator rebus in the context of medieval artistic patterns – i.e. expressing divine order through abstract structures including perfect geometrical forms, symmetrical schemata, palindromes and monograms. Such forms provided the underlying structure for images of heavenly beings, of those who are spiritually enlightened, and of man’s position in an ordered universe.

Carlo Cipolla, “Per la storia della formula Sator Arepo,” Atti della Reale Accademia delle Scienze di Torino 29 (1893-1894), 209-212.

Robert George Collingwood, The Archaeology of Roman Britain, London: Methuen and Co., 1930.

Many interpretations of the square founder on the word arepo which has never been satisfactorily explained. On p. 176. Collingwood (as did Haverfield (q.v.)) treats the word Arepo as a proper noun, though admittedly one of no known connotation.

E. C. Corte, “Le carre magique de Pompeii,” Humanites. Revue d’enseignement secondaire et d’education 27 (1954-55), 5ff.

Margaret Ann Courtney, “Cornish Folk-Lore Part III,” The Folk-Lore Journal 5 (1887), 177-220.

The square as a Cornish charm against witchcraft inscribed on a piece of parchment worn around the neck. The author’s trenchant remark: “many are the charms against ill-wishing worn by the ignorant.”(p. 196).

Leo Crozet, “Credo secret antique dans un carre magique,” Bulletin de l’Association Guillaume Bude, 4th series, No. 2 (June, 1960), 572-578.

Crozet is doubtful about Carcopino’s interpretation of the sator square. He interprets it as Christian, the product of a great mind, created to be obscure. He expands arepo into A REP(aratione) O(ptima). His solution: “Le Createur, depuis qu’a eu lieu une Restauration Parfaite, retient l’action du destin.” He proceeds then to show how it fits in perfectly with Catholic doctrine about the early Church.

Alexis Curvers, “Le carre magique,” in: Itineraires Part I: 120 (1968), 33ff; Part II: 121 (1968), 168ff.; Part III: 122 (1968), 329ff.; Part IV: 123 (1968), 876ff.; Part V: 124 (1968), 93ff.; Part I: 125 (1968), 258ff.; Part VII: 126 (1968), 117ff.; Part VIII: 128 (1968), 111ff.

An eight-part overly-labored piece of research that was unedited and was ultimately meant to appear in a book called De La Subversion. A very Catholic interpretation, ultimately unconvincing.

A. Dain, “Au dossier du mot carre ‘Sator’,” Revue des Etudes Latines 29 (1951), 84-85.

Text of a sator square found in the 15th century legal manuscript (Parisinus Suppl. gr. 1238) in Greek characters.

Olafur Davidsson, “Islandische Zauberzeichen und Zauberbucher,” Zeitschrift des Vereins fur Volkskunde 13 (1903), 268, item no. 26.

The sator square appears in Icelandic myth and magical number squares.

Erich Dinkler, “Sator arepo …,” Die Religion in Geschichte und Gegenwart, (3rd. edition) vol. 5, (1961), col. 1373-1374.

A very useful summary article. A translation can be found in appendix IV of C. D. Gunn, The Sator-Arepo Palindrome: A New Inquiry into the Composition of an Ancient Word Square, Ph.D. Dissertation, Yale University, New Haven, 1969.

Armand Delatte, Anecdota atheniensia, Liege-Paris: H. Vaillant-Carmanne, E. Champion, 1927.

The author includes a number of magic spells that contain garbled versions of the sator formula as well as several magic texts attributed to Solomon. These two elements are not found combined. Metal talismans called seals of Solomon are known in Byzantium, but they do not contain the sator square. Ryan (q.v.).

Lewis H. Diuguid, in The Washington Post, October 4, 1964.

He mentions the fact that the square can be read boustrophedon and ascribes it to Ludwig Diehl, but cites no specific references. See. C. G. Gunn, The Sator-Arepo Palindome, p. 61-62.

Franz Dornseiff, “Martialis IX, 95 und das Rotas Opera Quadrat,” Rheinisches Museum fur Philologie 96 (1953), 373-378.

Dornseiff finds in the Alfius-Olfius transformation in Martial’s epigram an echo of the Alpha-Omega in the Rotas-Sator square. This epigram was a parody on the well-known pederast Athenagoras and his male consort Alphius, who after the marriage of Athenagoras was called Olphius. This latter name has a ridiculing connotation because of its reference to the Latin word olfacio.

Franz Dornseiff, “Weiteres zum Rotas-Opera-Quadrat,” Archaeologischer Anzeiger 52 (1937), cols. 527-529.

Dornseiff sees the message as “no puzzle, no childish playing and also no magic, but a political threat i.e., a political threat against Rome. His translation “The Snatcher (Scatterer) o(f God’s fiery coals) holds the (fire-) wheels (and) the works (of vengeance).” The Snatcher is evidently an angel or instrument of God’s wrath.

Johannes H. Emminghaus, “Satorformel,” Lexicon fur Theologie und Kirche, 9 (1964), 343 -344.

A short encyclopedic entry on the sator formula with bibliography divided into Christian, Jewish and other interpretations.

Adolph Erman and Fritz Krebs, Aus den papyrus der Koniglischen Museen, Berlin: W. Spemann, 1899), 262.

The earliest example of the sator square found on a papyrus in Egypt dated to the fourth or fifth century. It shows no evidence of a Christian association. It is merely a formula inscribed in Coptic letters on papyrus. There was a two-century gap in the evidence in this area before several Coptic and Ethiopic examples were be found in strikingly Christian contexts dating to the 6th or 7th centuries.

Antonio Ferrua, ‘no title’ Civilta Cattolica 3 (1937), 127-139.

A brief review of the discussion over the rotas-sator square found at Pompeii. Ferrua considers the question of whether the origins are Christian, pagan or Jewish, considers Grosser’s theory on the pater noster solution, and then comes up with the best explanation for what the cryptogram means: “Esattamente quello che si vuole”(!) E basta di questo argumento. (It means exactly what you want it to mean. And so much for that argument!).

Adolph Franz, Die kirchlichen Benediktionem im Mittelalter. Freiburg im Breisgau: Herdersche Verlagshandlung, 1909, Vol. 2, 94-95.

Cites a fifteenth century formula from Ms. Olm 21 004 which includes the words of the sator square.

H. Handelmann, “Diskussionsbemerkung,” Zeitschrift fur Ethnologie 12 (1880), 216-217.

Richard Heim, “Incantamenta Magica Graeca Latina,” in Jahrbucher fur classische Philologie, 19 Supplementband (1893), 463-576.

See p. 530 of the chapter on Ephesia grammata on the sator square.

Liselotte Hansmann and Lenz Kriss-Rettenbeck. Amulett und Talisman: Erscheinungsform und Geschichte. Munich: Verlag Georg D. W. Callwey, 1966.

A short treatment of the sator square on pp. 140-144 with illustrations. Valuable treatment of magical charms which is one context in which the square often occurs.

Hugo Hepdings, “Die Satorformel,” Hessische Blatter fur Volkskunde 34 (1935), 111-113.

A short notice on the discovery of four new examples of the square found in Dura Europas and a review of the articles by Jerphanion, Zatzmann and Grosser.

Hugo Hepdings, “Die Sator-Formel,” Hessische Blatter fur Volkskunde 36 (1937), 175-176.

Short notice on the discovery of the sator formula in Pompeii and the Grosser hypothesis for the evidence of Christians in that city.

Hildebrecht Hommel, “Satorformel,” Lexicon der Alten Welt, Zurich & Stuttgart: Artemis Verlag, 1965, 2705. 1969, 2706.

Short summary of the formula and its history.

Margaret Ihlenfeldt, “Bread-wrapper Palindrome,” Classical Journal 49 (1953), 100.

A high school student in Springfield, Illinois found the sator-formula on the back of a bread wrapper. The students not only noticed that the sentence reads the same backwards as forwards, but the initial letter of each word spells the first word, the second letter of each word spells the second word, the third letter of each word spells the third word and so for the other two words. It was billed as “The World’s Most Amazing Sentence.” They translated it as “God, the Creator, rules the motion of the Universe,” which will not hold up to scrutiny.

Hr. Jagor, “Die Formel Sator Arepo,” Zeitschrift fur Ethnologie. Verhandlung der Berliner Gesellschaft fur Anthropologie 14 (1882), 415.

A short notice suggesting a plausible translation of the famous formula. An inscription found at the Chateau de Rochemaure on the Rhone: Sator opera tenet … he translates as: le semeur tient son ouvrage, ou comme on seme on recolte.

V. Krall, “Sator Areto Tenet Opera,” Mitteilungen aus der Sammlung der Papyrus Erherzog Rainer, 5 (Wien, 1889), 99-122.

Discusses a Greek version of the sator-arepo square found on a Coptic papyrus (Kopt. Perg. Nr. 2434-2436).

V. Krall, “Koptische Amulette,” Mitteilungen aus der Sammlung der Papyrus Erherzog Rainer 5 (Wien, 1882), 115ff.

Coptic amulette with the sator rebus on it.

H. Leclercq, “Sator Arepo,” Dictionnaire d’Archeologie Chretienne et de Liturgie, Paris: Letouzey et Ane, Vol. 15 (1950), col. 913-915.

After a discussion of some of the more popular interpretations, Leclercq traces the origin of the rebus to folklore and doubts its connection with either Hebraic or Christian symbolism.

G. Letonnelier, “Note sur l’inscription de Valbonnais,” Cahier d’histoire et d’archeologie (Nimes) no. 13, 1932, 291-299.

A medieval French example of the rotas-opera formula. It was inscribed long after anyone comprehended the meaning, but was used as a magical talisman.

Hans Lietzmann, (Review of The Excavations at Dura-Europos … Report V (1931-1932) and Report VI (1932-1933) Gnomon 13 (1937), 225-237.

On pp. 227-228 Lietzmann notes the rotas square found at Dura and its corroboration of Grosser’s theory.

Hans Lietzmann, “Sitzung am 5. Oktober 1937 … uber den Sator-Rebus in Pompeji,” Archaologischer Anzeiger 52(1937), col. 478-481.

Reviews the finds in Pompeii and Jerphanion’s theory and concludes that he still prefers the pater noster hypothesis.

Ernst Lohmeyer, Our Father: An Introduction to the Lord’s Prayer. New York: Harper & Row, 1966. English translation of Das Vater-Unser. Vandenhoeck and Ruprecht, 1952.

See pp. 17-18 and 32 for Lohmeyer’s use of the Christian-origin hypothesis regarding the sator-rotas square to support the early Latin translations of the Lord’s Prayer.

S. Liddell MacGregor-Mathers (translator), The Book of the Sacred Magic of Abra-Melin the Mage As Delivered by Abraham the Jew Unto His Son Lamech: A Grimoire of the Fifteenth Century, Chicago: The de Laurence Co., 1932.

See the introduction, especially xxix-xxx. A variant of the sator square is used to gain the love of a maiden.

S. Liddell MacGregor-Mathers, The Key of Solomon (Clavicula Salomonis) . . . , translated and edited from British Museum MS Lansdowne 1202, London, n.p. 1889, p. 59.

He attributes the square to King Solomon.

Johannes Mestorf, Zeitschrift fur Ethnologie. Verhandlung der Berliner Gesellschaft fur Anthropologie 14 (1882), 555-558.

Mestorf describes a cup of “oriental workmanship” found on the island of Gotland. It has Runic letters engraved upon it which spell out the sator acrostic, together with the five-pointed star or wizard pentagram. The cup is said to date to the fourteenth century.

Bruce M. Metzger, “Rotas-Sator Square,” (supplement), Twentieth Century Encyclopedia of Religious Knowledge, Grand Rapids, Mi, 1955, vol. 2, 983.

A short summary of the theories on the sator square with a bibliography almost as long as the entry.

J. Meysing, “Introduction a la numerologie biblique. Le diagramme Sator Arepo,” Revue des Science Religieuse 40 (1966), 321-52.

A planetary, astrological, cosmological interpretation of the famous square. Rarely has so much been made of so little.

R. Mowat, “Sator Arepo Tenet Opera Rotas,” Memoires de la Societe Nationale des Antiquaires de France, 7 series, 4 volume, Paris (1905), 41-68.

Much material is gathered here on the later squares, particularly medieval manuscripts and inscriptions in both Greek and Latin.

Jules van Ooteghem, “Le Rebus Sator,” Etudes Classiques 3 (1934), 557-558.

A short description of the square, its history and a discussion of other scholars’ work. He accepts the Christian interpretation and rejects Suys (q.v.).

J. Palma, “Une curieuse inscription,” L’Intermediaire des Chercheurs et-Curieux, 3, 57 (1866), 476-477.

The author takes arepo to be a proper name, that of the “sower, “and produced: “an indefatigable sower, the worker Arepo, holds the works, the wheels.” He then interpreted the translation to mean “God, the creator, holds in his hand both his vases of clay known by the name of man and all the force of the round machine.” This solution required the interpolation of additional letters to derive a meaning.

Anne E. Pennington, “South Slavs in Malta,” in Byzance et les Slavs. Etudes de civilisation. Melanges Ivan Dujcev, Paris, 1979, 333-5.

A previously unpublished Serbian version of the square. It was used as the antidote to the bite of a mad dog (p. 334, n. 3).

S. Petrides, “Les ‘Karkinoi’ dans la litterature grecque,” Echos d’Orient 12 (1909), 86-94.

The best single work on the Greek palindrome; deals briefly on pp. 87-88 with the sator square, but offers no new interpretations. See also Karl Preizendanz, “Palindrom,” Pauly-Wissowa R-E 36/2, col. 134. As a magical text, palindromes represent a charm or incantation that, because it may be continually reversed and read again, is eternal and never-ending in its efficacy.

Charles Picard, “Sur le carre magique a l’eglise odorante, (Kokar Kilise, Cappadoce),” Revue Archeologique 1 (1965), 101ff.

In the region of Hasan Dagi in Cappadocia (Turkey), two French scholars found on the wall of a church a series of musicians next to a figure being baptised. Underneath appears the enigmatic sator formula. The figures are wearing pointed Phrygian caps and oriental dress. Picard, of course, accepts a Christian interpretation of the square.

V. Ricci, “Sator Arepo,” Catholic Encyclopedia New York: The Encyclopedia Press, Inc., 1917, 1098.

Ricci believes a possible transliteration is: sator, the sower; arepo, with his plow, tenet, holds; opera, with purpose; rotas, the wheels. The five words can be read consecutively either horizontally or perpendicularly; and while the disposition of the words varied in both East and West during the Middle Ages, the device was traced to the fourth century A.D. and considered of Christian origin.

W. F. Ryan, “Solomon, Sator, Acrostics, and Leo the Wise in Russia,” Oxford Slavonic Papers, n.s. 19 (1986), 46-61.

Ryan has found Cyrillic examples of the sator formula in Russian manuscripts where it was usually titled “Seal of King Solomon the Wise. “Russian scholars have not discussed the sator square in the context of the more general history of the subject, and there are some aspects of it which Ryan thinks deserve comment. In particular, its possible Jewish connections, its associations with divinatory, conaputistic and ‘Solomonic’ texts, and the acrostic text ascribed to Leo the Wise which goes with some specimens. Ryan lists twenty-nine examples of the Russian sator square known to him. Illustrated.

Pater W. Schooneman, “Het cryptogram van Pompeii,” Hermeneus 21 (1950), 69-70.

A short Dutch article which presents the problem and interprets arepo as an abbreviation of archepiscopo (archbishop).

W. von Schulenberg, Zeitschrift fur Ethnologie, (Organ der Berliner Gesellschaft fur Anthropologie, Ethnologie und Urgeschichte) 1881, 167.

An attempt to translate arepo as”areben.”

Siegfried Seligmann, “Ananisapta und Sator” Hessische Blatter fur Volkskunde, 20 (1921), 1-14.

Relates the magic word ananisapta to the sator square.

Marcel Simon, Versus Israel; Etude sur les relations entre chretiens et juifs dans l’empire romain, 135-425 Paris: E. de Boccard, 1948.

See pp. 410ff for material on the interpretation of the sator square. On p. 411 he suggests that N stands for nomen and thus serves as a Latin equivalent for the Hebrew shem, the Divine Name.

Hermann Sokeland, “Zwei Himmselsbriefe von 1815 und 1915,” Zeitschrift des Vereins fur Volkskunde 25 (1915), 241-259.

There is a picture of an 11th century mosaic floor with symbols of four evangelists on p. 257, Fig. 6 along with other literature cited on page 258, note 1. On the sator square in the Himmelsbriefe. See Thomas R. Forbes, The Midwife and the Witch, New Haven: Yale University Press, 1966, p. 83 who discusses the Himmelsbriefe phenomenon.

Victor Stegemann, “Die Koptischen Zaubertexte der Sammlung Papyrus Erzherzog Rainer in Wien,” Heidelberger Akademie der Wissenschaften. Sitzungsberichte der Heidelberger Akademie der Wissenschaften. Philosophisch-historische klasse 1 (1933-34), 26, 74-75.

An example of the sator square in Coptic of the Sa’idic dialect, dated by its orthography to the sixth of seventh centuries. It is preceded by three crosses.

Alexander Treichel, “Sator Arepo Formel und Tollholz,” Zeitschrift fur Ethnologie, (Organ der Berliner Gesellschaft fur Anthropologie, Ethnologie und Urgeschichte) 13 (1881), 162-167.

Treichel refers to an article by Frischbier on “Hexenspruch und Zauberbann, “(Berlin, 1870) who gives an imperfect acrostic, apparently a corruption of the sator-acrostic, which reads thus:

NATOR

AUTNO

TERUT

AUTHQ

ROTUR

Alexander Treichel, “Nachtrag zur Satorformel,” Zeitschrift fur Ethnologie 15 (1883), 354-55.

An example of the sator rebus that appears in the middle of an elaborate series of concentric circles with Christian inscriptions. It is in the German National Museum in Munich.

Alexander Treichel, Zeitschrift fur Ethnologie. (Organ der Berliner Gesellschaft fur Anthropologie, Ethnologie und Urgeschichte) (1884), 66-70.

The author considers a Celtic interpretation of the formula.

Alexander Treichel, Zeitschrift fur Ethnologie, (Organ der Berliner Gesellschaft fur Anthropologie, Ethnologie und Urgeschichte) (1886), 349.

Treichel suggests the god Saturn for sator and takes rotas to refer to the wheels of the sun chariot, translating: “Saturnus nThevoll die Rader (das Sonnenrad) lenkt.” For arepo he suggests a derivation from the Finnish Aurinko, the sun.

Joseph Vendryes, “Une hypothese sur le carre magique,” CRAI (1953), 198-208.

Vendryes accepts a Christian interpretation of the square. He then goes on to discuss the word arepo which he believes is a Celtic adverb and the square is therefore Gallo-Roman. This would fit with Carcopino’s second-century origin theory.

Carl Watzinger, “Die Christen in Dura (Europos),” in Theologische Blatter, Leipzig 17 (1938), pp. 113-119.

The author uses the sator rebus inscribed on the walls of a military office in a building that had originally been the temple of Artemis Azzanathkona as evidence for Christians in Dura Europos.

Otto Weinreich, “Zweifel an der Richtigkeit der Losung unmoglich,” Gnomon 6(1930), 365-367.

Review of Grosser’s article.

C. Wescher, “Note sur l’Interpretation d’une inscription Provenant de Rochemaure (Ardeche),” Bulletin des Antiquitees de France, 1874, 153.

The sator formula was found in a walled-up section of the chapel of Saint-Laurent in Rochemaure, Ardeche. Wescher uses the Byzantine manuscript’s hypothetical Greek equivalents of the words and comes up with the solution: “The sower is at the plough; the work (of plowing) occupies the wheels.”

Adolph Wuttke, Der deutsche Volksaberglaube der Gegenwort, Berlin: Verlag von Wiegandt & Grieven, 1900 (3rd edition), 180; 401.

Briefly notes the use of the square in German superstition, including its use in the putting out of fires.

My conclusions about the square are concerned not so much with presenting the definitive solution as much as pointing out the correct routes to be followed and pulling together a vast literature to help others do the same. When one looks at all the evidence and the commentary on it, what becomes clear is that there are three separate questions which must be answered, as I suggested in the beginning of this article.

The first question is that of origin: who invented it and why? The best answer so far is that it was invented in the Roman empire in the first century A.D. by someone interested in creating a clever palindrome. This is not such a difficult hypothesis to believe about the Roman world where other examples of such palindromes such as the Roma Amor square are known.7 The sator square certainly qualifies as one of the more clever examples. All it would take to debunk this theory, however, is an earlier example of the square from a nonRoman context. Everyone was convinced the square was medieval until the square from Cirencester was uncovered.

Once the square was created, then the second question arises: what did it mean to people of subsequent generations? The square can mean almost anything to anybody if you play around with it long enough. Many of the articles cited above all give examples of rearrangement of the letters, all which render seemingly meaningful latin sentences. To give just a few examples:

Petro et reo patet rosa Sarona

Ero ante portas, ero ante portas

Orare nostrae oporteat stare

Eros operans portat aere tota

Arte opiate ornare posse orta

A se optat orare; O pater noster

Persona e torto aere parata est

Optatore orante portares aes

oratores se apte orare optant

Ore torta aperta sonare potes.

Tantopere potes orare optant

Ora, Nestor, pro postera aetate.

Ante portas eat o pereat soror.

O apostata, poena retro terres.

Retro Satana totopere asper.

Oro te Pater, oro te Pater, sanas.

O Pater ores pro aetate nostra.

Ora, operare, ostenta te Pastor.

Satan, ter oro te, opera praesto.

Satan, oro te, reo portas patere.

Satan, ter oro te, reparato opes.

Satan, pater, oro stare te pro eo.

Satan, pereo apro, restat, oro te.

Satan, oro te et appare e rostro.

And these are not all. My personal favorite is Apator Nero est, which makes the emperor Nero the result of a virgin birth! Once a rearrangement was made that was meaningful to a certain group like the Christians, they could read into it whatever meaning or power they wished.

The final question is how was the square used by later peoples who may have had no knowledge of its creation, its original meaning or its original use. Once the square took on a Christian meaning it may have been used as a way of identifying Christians to each other secretly during persecutions, and it was certainly used as a charm to guard against evil. Its use as a charm continued even long after people forgot what the original words meant and thus reinterpretation of the words themselves began. They were said to be the names of the wise men, the nails of the cross, or the shepherds of the nativity. By the time it reached non Latin-speaking countries, the words became garbled even though they continued to be copied as a magical charm that would cure snake bites, prevent fires, or help in childbirth.

One thing can be said for certain. As soon as someone announces the search for a solution is finished, someone else publishes another possible solution and the hunt takes a new direction. I have no doubt I will discover a dozen more articles on the square as soon as this article goes to press. If readers are aware of interpretations I have left out, I would be grateful to hear about them. In the meantime, by putting this bibliography before a larger audience, especially those with cryptographic experience, perhaps new interpretations and solutions will be made possible.

* I would like to thank Professor Gordon Williams of the Virginia Military Institute, and Dr. David Kahn for their help on this article. I am grateful to the Dean’s office of the Virginia Military Institute which provided travel funds for my research at Yale University to collect materials. For help on translations I am indebted to Michael Harris, Robert Schonberger, Yvonne Emerson, Inge Hynes, Arend von Heemskerck, Anna Crockett and Roger Crockett, Kathleen Bulger-Barnett, Elena Andre’eva and Natalia Sverdlova. The staff of Preston Library at VMI, especially Mrs. Elizabeth Hostetter, were immensely helpful in identifying and getting materials through inter-library loan. All errors in fact and interpretation remain mine.

1D. Atkinson, “The Sator Formula and the Beginnings of Christianity,” Bulletin of the John Rylands Library 22 (1938), p. 419.

2See, for example Clifford A. Pickover, The Zen of Magic Squares, Circles, and Stars, (Princeton and Oxford: Princeton University Press, 2002), pp. 23-25.

3Rose Mary Sheldon, Espionage in the Ancient World: An Annotated Bibliography, (Jefferson, North Carolina: McFarland, 2002).

4The interpretation seems to have cropped up in several places independently. See entries for Becker, Spamer, Grosjean, and Diuguid.

5He saw the square as a producttion of Kabbalistic magic. This is the same Athanasius Kircher who wrote the Polygraphia nova et universalis (Rome, 1663) which describes processes of encipherment as well as a multi-lingual, cross-indexed code which is one of the earliest attempts to produce a universal language. See David Kahn, The Codebreakers, (New York: Scribner, 1996), 154, 846, 864, 904-05.

6See Epistle of Barnabas 9.8; H. Rahner, Greek Myths and Christian Mysteries, trans. Brian Battershaw, (London, 1957).

7 The Roma-Amor square has been found in Pompeii, Ostia and Bolonia. The Pompeian example was published by Matteo della Corte, Notizie degli Scam (1929), p. 465, No. 200. This is also published as No. 856 in Ernst Diehl, Pompeianische Wandinschriften und Verwandtes, (Berlin: Walter de Gruyter, 1930, p. 65; CIL IV 8297. See above the two articles by Margherita Guarducci in Archeologia Classica.

Rose Mary Sheldon

ADDRESS: Department of History, Virginia Military Institute, Lexington VA 24450 USA.

BIOGRAPHICAL SKETCH

Rose Mary Sheldon received her PhD in ancient history from the University of Michigan. Her dissertation, on intelligence gathering in ancient Rome, won a National Intelligence Book Award in 1987. She is a Professor of History at The Virginia Military Institute, and has published widely in the field of intelligence history Her articles have appeared in The International Journal of Intellligence and Counterintelligence, Intelligence and National Security, The American Intelligence Journal, Studies in Intelligence, and Small Wars and Insurgencies. She is a Fellow of the American Academy of Rome (’80), and is on the editorial boards of The Journal of Military History and The International Journal of Intelligence and Counterintelligence.

Copyright Cryptologia Jul 2003

Provided by ProQuest Information and Learning Company. All rights Reserved