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On the Origin of the Rotas-Sator Square1

Published online by Cambridge University Press:  23 August 2011

Duncan Fishwick
Affiliation:
St. Michael's College, University of Toronto

Extract

Since the discovery at Pompeii of specimens of the ROTAS-SATOR rebus scholarly investigation into the origin of the “magic square” has been bedevilled by a fundamental problem. Is it or is it not sheer chance that the letters of the square can be rearranged in two intersecting PATER NOSTER's with two A's and two O's remaining to be positioned at will?

Type
Research Article
Copyright
Copyright © President and Fellows of Harvard College 1964

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References

2 Atti Pont. Ace. Rom. Arch. 3:12 (1936), 397–400; cf. Not. d. Scavi 6:5 (1929), 449, no. 112; 15(1939), 263, no. 139. The discoveries at Pompeii, the earliest examples of the square to have been so far recovered, confirm that the original version began with ROTAS rather than SATOR. For subsequent discussion see Fuchs, op. cit., 31, note 4.

3 This discovery seems to have been made independently by three individual scholars. Chr. Frank, Deutsche Gaue 25(1924), 76; Grosser, F., “Ein neuer Versuch zur Deutung der Sator-Formel,” Z.N.W. 24 (1926), 165ff.Google Scholar; Agrell, S., “Runornas talmystik och dess antika förebild,” Skrifter utgivna av Vetenskaps-Societeten i Lund 6 (1927), 3132Google Scholar. It goes without saying that the intrinsic probability of this rearrangement led to its general acceptance by the majority of reputable scholars. Earlier attempts to pierce the secret of the square had either divided the individual words more or less arbitrarily or had rearranged the individual letters in anagrams ranging from pious prayers to diabolic incantations. For inventories of these see Jerphanion, G. de, “La formule magique SATOR AREPO ou ROTAS OPERA, vieilles théories et faits nouveaux,” Rec. Sci. Rel. 25(1935), 188225Google Scholar; Carcopino, M. J., “Le christianisme secret du carré magique,” Mus. Helv. 5(1948), 1659Google Scholar. The most astonishing feature of these solutions is the number of purportedly meaningful texts which can be wrung from this extraordinary word-square. More than thirty such anagrams are listed by Fuchs, op. cit., 35–37, notes 13–15.

4 Sundwall, J., “L'enigmatica inscrizione ROTAS in Pompei,” Acta Academiae Aboensis, Humaniora 15, 5(1945), 1617Google Scholar.

5 Omodeo, A., “La croce d'Ercolano e il culto precostantiniano della croce,” La Critica 38(1940), 4561Google Scholar.

6 Eitrem, S., “The SATOR AREPO formula once more,” Eranos 48(1950), 7374Google Scholar. For a detailed list of scholars who reject the cruciform PATER NOSTER anagram see Fuchs, op. cit., 39, note 18.

7 See the useful discussions of H. Last, J.R.S. 44(1954), 112–15; cf. J.T.S. 3(1952), 92–97; D. Atkinson, “The Origin and Date of the ‘Sator' Word-Square,” J.E.H. 2(1951), 1–18. The interpretation suggested above differs in several important details.

8 For example in a twenty-five letter square quoted by S. Seligmann (“Die Satorformel,” Hessische Blätter f. Volkskunde 13 [1914], 154 ff.) only one word is comprehensible:

With a sixteen-letter square the problem is rather less complicated, e.g.:

See below, note 52.

9 It has been argued that the mathematical odds against this rearrangement being possible by coincidence are astronomical; cf. D. Atkinson, “The Sator Formula and the Beginnings of Christianity,” Bull. J. Ryl. Libr. 22(1938), 419 ff. I am not certain that this point is entirely valid. Given the conditions that two words of the square must make sense when read in either direction and the third in at least one direction, the number of squares of this kind which can be made with Latin words must be very few. The effect of this would surely be to shorten the odds. What is difficult to believe is that the letters of the square should accidentally make such meaningful symbols as the PATER NOSTER invocation and the A/O sign and that these should accidentally appear twice over and in combination.

10 For example, Simon, M., Verus Israël (Paris, 1948), p. 411Google Scholar, has suggested that as the initial letter of the word nomen N might also serve as the Latin equivalent of the Hebraic šem, the unique Divine Name, fount of Divine Power and centre and origin of all things. With this may be compared the fanciful theory of H. Wehling-Schücking, “Zum Deutproblem der Sator-Inschrift,” Album philologicum voor Th. Baader (Tilburg, 1939), pp. 197ff., who treats the central N as an abbreviation for Nazarenus.

11 Jerphanion, op. cit., 225, note 102, records the observation of an anonymous correspondent that the T's in the square are in every case flanked by A and O, the three letters being regarded as unmistakably Christian symbols (cf. Rev. 1:8; 21: 6; 22: 12).

12 Perhaps these quarrels helped to focus official attention on the Christians: cf. an imperial edict of the period, found possibly at Nazareth, decreeing the death penalty for anyone who destroys a tomb or casts out the buried or “with evil intent removes them to some other spot.” Charlesworth, M. P., Documents Illustrating the Reigns of Claudius and Nero (Cambridge, 1939), p. 15, no. 17Google Scholar.

13 For evidence of communication between the two towns see CIL, IV, 2152, from Pompeii, recording greetings to the colony of Puteoli.

14 For a summary of the detailed description by Maiuri (Atti Pont. Ace. Rom. Arch. 3:15 [1939], 193–218) see Atkinson (above, note 7), 16–17.

15 Les Ruines de Pompei (Paris, 1824), II, 84–5.

16 The consensus of opinion nowadays seems to be that, far from having any sacred character, the imprint is simply that of some trivial object, such as a wall-bracket; cf. L. de Bruyne, “La ‘crux interpretum’ di Ercolano,” Riv. Arch. Crist. 21(1945), 281ff. This explanation, however, does not account for the projection of the vertical stave above the transverse nor for the symmetrical increase in the width of the transverse groove towards both ends. Cf. Atkinson, op. cit., 17.

17 .hristian.., .hristiani., .hristianos, Christianos

18 It should be noted in this connection that Tertullian, Ap. 40.8, which is usually held to show that Tertullian denied the existence of Christians at Pompeii before its destruction might on the contrary be interpreted as actually implying their presence. See the discussion of Last (above, note 7), 113–14.

19 CRAI (1937), 84–93.

20 Lexicon für Theologie und Kirche (Freiburg, 1961), s.v. Kreuz, 606–18. An early example from the third century is probably heretical; cf. C. Cecchelli, Monumenti Cristiano-Eretici di Roma (Rome, 1944), pp. 86, 119. On the general development of the cross in Christian symbolism see A. Grillmeier, Der Logos am Kreuz. Zur christologischen Symbolik des älteren Kreuzigungsbildes (Munich, 1956), pp. xii and 151; J. Fink, “Grundlagen des Kreuzigungsbildes,” Th. Rev. 51 (1957), 241–248; E. Peterson, Frühkirche, Judentum und Gnosis (Freiburg, 1959), pp. 15ff.

21 Cf. St. Justin, I Apol. 55; Dialog. 90. 4—5, 91. 2–4.

22 The earliest epigraphical examples of the A/O sign date from the end of the third century A.D.: Cabrol, Dictionnaire, I(1924), 1–26, s.v. A/Ω; E. Lohmeyer, Reallexikon f. Antike u. Christentum, I(1941), 2, s.v. A und O. For the general significance of this sign see the documentation of Fuchs, op. cit., p. 50, note 45.

23 One notable attempt to overcome these problems is that of M. J. Carcopino (above, note 3), who argues that the Pompeian squares were, in fact, inscribed after the destruction of the town by treasure-seekers burrowing among the ruins. This theory seems to have been dissipated on the whole by Atkinson's article (above, note 7). Clandestine scavengers, he points out, would have been more likely to dig in the vicinity of the better-class houses, away from the building that housed the more complete of the Pompeian squares. In any case, crude digging would be particularly easy to detect at Pompeii, and there is no trace of this in the neighborhood where the undamaged rebus was found.

24 The only other notable attempt to explain the square in terms of Grosser's discovery (above, note 3) is that of H. Hommel (Schöpfer und Erhalter [Berlin, 1956], pp. 32–80), who traces the pater noster invocation, A/O symbol etc. through Cicero and Posidonius to a Stoic and before that a Platonic origin. Even if the texts he adduces provide real parallels, however, there remains the very great difficulty that cryptic writing of this kind does not seem to have been a basic characteristic of Stoicism, nor do we have other evidence for Stoic influences at Pompeii.

25 An earlier interpretation of Cumont subsequently developed by Jerphanion (CRAI [1937], 93; cf. Rend. Pont. Acc. 13 [1937], 7ff; Rech. Sci. Rel. 27 [1937], 326ff.), while abandoning the PATER NOSTER-A/O anagram, had supposed a Jewish origin in tracing the imagery of the square to Ez. 1:15ff., where in the Vulgate text both ROTAS and OPERA occur in close proximity during the account of the prophet's vision. As the remaining words of the square are not discernibly relevant, however, the point of connection is very tenuous, and it is in any case difficult to believe that a Jewish inventor of the rebus would have been inspired by a Latin version of the Ezekiel passage, which he would surely have read in Hebrew or Greek. If the square is derived mechanically from the PATER NOSTER-A/O sign, as I have suggested, this derivation would, of course, lose all force. For a detailed review of Cumont's interpretation see Atkinson (above, note 7), 3–6.

26 The best discussion of Jewish influences at Pompeii is by Frey, J. P., “Les Juifs à Pompei,” R. Bibl. 42(1933), 365–84Google Scholar.

27 Origen, contra Celsum 1.26. Cf. Th. Reinach, Textes d'auteurs grecs et romains relatifs au judaïsme (Paris, 1895), p. 165Google Scholar. The origin of this is probably to be found in the episode of the six plagues of Egypt, Ex. 7–11.

28 For recent discussion of superstition and magic among the Jews see M. Simon (above, note 10), pp. 394–431; Goodenough, E. R., Jewish Symbols in the Greco-Roman Period, II (New York, 1953), pp. 153295Google Scholar.

29 Marcus, R., “Alphabetic Acrostics in the Hellenistic and Roman Periods,” J.N.E.S. 6 (1947), 109–15Google Scholar.

30 A famous example of word-play occurs in the Talmud: “… R. Aqiba expounded: When husband and wife are worthy, the Shechinah abides with them; when they are not worthy, fire consumes them. Raba said: [The fire which results] from the woman is severer than that from the man. What is the reason? In the case of the former [the letters aleph and shin] are consecutive but not in the case of a man.” I. Epstein, ed., The Babylonian Talmud (London, 1938), Sotah 17a, 89. Aqiba is also credited with a meditation on the individual letters of the alphabet. Strack, H. L., An Introduction to the Talmud and Midrasch (Philadelphia, 1931), pp. 229, 347, n.4Google Scholar. The only known example of a magic square in Hebrew is that attributed at a much later period to Abraham Ben Meir Ibn Ezra (1092–167 C.E.); cf. A.G. Eschkol, Encyclopaedia Iudaica, II (Berlin, 1928), 49.

31 Notably Fuchs, op. cit., 50–51. Cf. also Simon (above, note 10), p. 412. For the possible derivation of the Lord's Prayer from the Jewish Amidah see Guignebert, Ch., “Le Pater,” Mélanges G. Glotz (Paris, 1932), I, pp. 417–30Google Scholar; H. L. Strack and P. Billerbeck, Kommentar zum Neuen Testament aus Talmud und Midrasch 2 (Munich, 1954), I, 392–96 (on Mt. 6:4) and 406–16 (on Mt. 6:9).

32 E.g., in the Babylonian recension, petition 5: Lead us back, Our Father, to thy Torah .…; petition 6: Forgive us, Our Father, for we have sinned; in the Palestinian recension, petition 4: Grant us, Our Father, knowledge of Thee and comprehension and understanding from Thy Torah; petition 6: Forgive us, Our Father, when we have sinned against Thee.

33 For full documentation see Fuchs, op. cit., 50, note 43.

34 Strack and Billerbeck (above, note 31), III, 789 (on Rev. 1:8). The idea also occurs in Martial, Epig. 9.95.

35 “Zur Geschichte des Kreuz-symbols,” Z.Th.K. 48(1951), 148–72.

36 In palaeo-Hebrew script tau was regularly × from the eighth century B.C. to the second century A.D. As a mark on ossuaries, however, + and × seem interchangeable: for example, a group from No. 79 of the Dominus Flevit on the Mount of Olives includes ossuaries inscribed with rectangular (+) and diagonal (×) crosses: ossuary number 12 bears both forms; B. Bagatti and J. T. Milik, Gli Scavi del “Dominus Flevit,” I, La Necropoli del Periodo Romano (Jerusalem, 1958): R. Bibl. 66(1959), 299–301; Antonianum 34(1939), 345–47; Th.L.Z. 84(1959), 569–97.

37 See the discussion in N.T.St. 10(1963).

38 It is most unlikely that the cross-sign always represents the “sign of Jahweh,” since crosses appear regularly on eastern charms and amulets, being by no means restricted to Jewish use; cf. Goodenough (above, note 28), I, p. 132. That it served generally as a magical mark of protection, however, seems certain.

39 Frey, CIJ, nos. 149, 173, 203 (in Greek); no. 229(Greek transliterated into Latin).

40 Haverfield, F., Arch. J. 56(1899), 319323Google Scholar. Eph. Ep. 9, 1001; cf. Collingwood, R. G., The Archaeology of the Roman Empire (London, 1930), p. 176Google Scholar. For similar examples see Fuchs, op. cit., 33, note 8.

41 arripere, rapere, apparere and parere have all been thought etymologically connected with arepo. For documentation and discussion see Fuchs, ibid., 34, note 12.

42 E.g., SA(LVA)TOR A RE(GE) P(ONTIFICI)O or SATOR A R(ERUM) E(XTREMARUM) P(RINCIPIO) O(MNI). See the inventories of Jerphanion (above, note 3), 221, and Fuchs, op. cit., 35, note 13.

43 Carcopino (above, note 3), 28–29, believes that AREPO is Celtic in derivation and means plough; cf. F. Dölger, ICHTHYS 5(1932), 57–64, for a similar suggestion. D. Daube sees in AREPO a Hebrew or Aramaic rendering of Alpha O, Exp. T. 62(1951), 316.

44 See, e.g., the collections of K. Preisendantz, Papyri Graecae Magicae, Vols. I and II (Leipzig, 1928–31), and S. Eitrem, Papyri Osloenses, Fasc. 1 and 2 (Oslo, 1925–1931).

45 Simon (above, note 28), pp. 399–400.

46 Cf. CIJ, I, 562 (from Pompeii), where incomprehensible words accompany a magical figure closely resembling those found in the magical papyri. The relevance of this inscription to the ROTAS rebus or at least to the mentality that produced it does not seem to have been noticed before.

47 E.g., “The Sower, Arepo, guides the wheels carefully”: Collingwood (above, note 40); or, “The sower intentionally holds the wheels firmly on the plough-field (on his plough)”: Jerphanion (above, note 3), 196; Carcopino (above, note 3), 29.

48 By reading only the first three words one would thus get SATOR OPERA TENET in four different directions: Fuchs, op. cit., 43–46. Though this phrase might conceivably recall such passages as Galatians 6:7–10, or even Proverbs 1:31, 18:20, etc., any interpretations along these lines is purely subjective if the rebus is simply a reconstruction of the PATER NOSTER-A/O symbol.

49 The words were never written consecutively until the early Middle Ages and then only in a corrupt form: e.g., SADOR ALADOR DANET ADERA RODAS — “the names of the nails of Christ's cross”: W. E. Crum, E.E.F. (1897/8), 63; Simon, J., Anal. Boll. 49(1931), 165Google Scholar. In Abyssinia these five words were used in the eleventh century to denote the five wounds of Christ: H. Ludolf, Ad Historiam Aethiopicam Commentarius (Frankfurt a./M., 1695), p. 351.

50 For Jewish inscriptions from Pompeii written in Latin see CIJ, I, 564–67. Only a fraction of the Jewish inscriptions from Rome, Pompeii and other sites are written exclusively in Hebrew, but solitary Hebrew words occur occasionally in Greek, Latin, and bilingual inscriptions, thus indicating that some recollection was preserved of the ancient tongue. Leon, H. J., The Jews of Ancient Rome (Philadelphia, 1960), pp. 7678Google Scholar.

51 The graffiti accompanying the undamaged rebus may possibly provide evidence. Above the square is written in three lines SAVTRAN(e) VA(le)/S/Δ and below, again in three lines, ANO/SAVTRAN(e)/VALE. The two farewell greetings to Sautranus or Saturanus appear to be by the same person who wrote the rebus, and the large S is similarly deeply incised, but the triangle and ANO are more lightly scratched in what is clearly a different hand. While the S might reasonably be explained as an abbreviation for s(alutem), it is a matter for conjecture what interpretation should be placed on the remaining graffiti. If, as seems likely, they were inscribed by a later hand, their position immediately above and below the rebus might well indicate that they were intended as a kind of key to its meaning. Several commentators have noted in this connection (Hommel [above, note 24], pp. 65–69) that a, n and o are the first, middle and last letters of the Greek alphabet, that is we have here the A/O symbol combined with the central N of the rebus. Could this be a symbol of the deity who is past, present, and future (cf. Rev. 1:8, 17), and if so, is the triangle likewise a symbol of His Eternity? If such an interpretation of ANO is not, in fact, pure fantasy, we may have evidence here for the association of the A/O symbol with the rebus at a very early date.

52 Composing word-squares may have been a favourite pastime at Pompeii. Cf.

Not. d. Scavi 6:5 (1929), 465, no. 200 = Diehl, Pompejanische Wandinschriften und Verwandtes (1930), no. 856:

With this may be compared the curious alphabet discovered on the column close to the undamaged SATOR inscription (axbvctdserfq etc.): Not. d. Scavi, ibid., 142 = Diehl 56. The popularity of such a pastime, however, sheds no light on the problem of whether the Rotas square was derived from the PATER NOSTER-A/O symbol or invented independently. In later times, Sidonius tells us (9.14. 4–5), the palindrome or versus recurrens provided endless amusement for Roman landed gentry.

53 Rostovtzeff, M. I., The Excavations at Dura Europos: Preliminary Report of the Fifth Season (New Haven, 1934), pp. 159–61Google Scholar; Sixth Season (ibid., 1936), p. 486.

54 Szilagyi, J., Acta Antiqua Academiae Scientiarum Hungaricae 2(1954), 305310Google Scholar = AEpig. (1956), no. 63. Cf. M. J. Carcopino, “Encore le carré magique,” CRAI (1955), 500–07.

55 See above, note 40.

56 E. v. Welz, Societas Latina 5(1937), 57.

57 Fuchs, op. cit., p. 29, note 1.