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CENSORINUS, THE SOTHIC CYCLE, AND C ALENDAR YEAR ONE IN ANCIENT EGYPT: THE EPIST EMOLOGIC AL PROBLEM*
PATRICK F. O'MARA, Los Angeles City College

I. INTRODUCTION ENSORINUS and other early writers on the subject inform us that since the Eg yptian calendar prescribed a year of 365 days, whereas the natural solar year is of 365!/4 days, Sirius moved upward on the calendar one day every four years (the tetraeteris). The star would appear again on I Иht 1, New Year 's Day, after 1,460 years (the Sothic cycle). Whether oversimplistic or not, this progression of Sirius o^ers the promise of astronomical dating. If, for instance, an annual heliacal rising of Sirius is recorded for the 101st day of the year, then 100 days--i.e., 400 to 403 years--have passed since Calendar Year One (hereafter CY 1). Near-lying lunar appearances of the New and Full Moon that would be otherwise unplaceable within half a millennium can be pinpointed by astronomical calculation.1 The key question in all this is, of course, just when is CY 1? The answer is not simple because the problem itself is far more complex than our brief introductory remarks might indicate. Firstly, which Sirius are we dealing with? Like the nymph Thetis, the goddess Isis-Sopdet assumed many forms to elude easy capture, and the "Sothic cycle" varies accordingly. The cycle of 1,460 Julian years discussed by Greco-Roman and early modern writers was not the same as that of the Eg yptians themselves, with a cycle of 1,460 Egyptian years (only 1,459 Julian years). Nor did either of these cycles involve the same star as the physical Sirius of the heavens as observed by modern astronomers. The ~rst two were mental concepts--calendrical constructs--whose cycle did not correspond to the actual progress of the star. The di^erence between the Sirius of the mind and the Sirius of the sky was so small (1 to 2 minutes over a year) that some have wondered whether the ancients ever noticed it (or cared). Which form of Sirius, then, is relevant for the study of Eg yptian chronolog y, the schematic or the physical? The di^erence amounts to 8 to 12 years and is critical for establishing CY 1 and all Sothic dates deriving from it.2 A second complexity concerns the de~nition of the Eg yptian day. Both the annual rising of Sirius and the last appearance of the Old Crescent moon, which determines all lunar

C

* I am grateful to Stanford Miller of Los Angeles City College for his help with certain problems in Latin phraseolog y. [Patrick F. O'Mara (2 October 191430 January 2001), after his retirement from teaching at Los An[JNES 62 no. 1 (2003)] Г 2003 by The University of Chicago. All rights reserved. 00222968/2003/6201-0002$10.00.

geles City College, continued his scholarly research, especially in matters dealing with ancient Eg yptian chronolog y. He published a number of brief papers on this subject. This, his last paper, had been accepted and was awaiting publication at the time of his death. Eds.] 1 By a uke of the Eg yptian 365-day calendar, any lunar date will usually repeat itself after 25 years with an error of no more than 1 day, this over a period of 50 years. 2 See n. 19 below.

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calculations, occurred in the hour of morning twilight just before sunrise. We do not know for certain whether Eg yptians considered their day to begin at ~rst light (dawn) or at ~rst ash (sunrise),3 that is, in the ~rst hour of the morning or in the last hour of the previous day 's night. This slight di^erence of a brief hour produces a stellar displacement of 4 years and a lunar displacement of 11 to 14 years. Given the complexities of star and moon, how do we go about calculating the proper year for CY 1? The answer is that we cannot calculate it, not by astronomical means, at any rate. Mathematics can approximate the varying length of the physical cycle but cannot determine with certainty the year or the day of either the beginning or the end of a cycle (the Apokatastasis).4 We need some sort of reliable historical datum as a point of departure. One such ~xed datum is a recorded heliacal rising of Sirius on II smw 1 of 239 B.C. under the reign of Ptolemy III Euergetes I. This would yield a raw Sothic distance of 1,080 + 1,460 Julian years, for a placement of CY 1 at ca. 2779 B.C. Unfortunately, for the technical reasons just described, this date can only represent a range of at least 16 years. For a century and a half, chronologers have perforce relied upon a recorded rising of Sirius on I Иht 1 in A.D. 139 (the last historical Apokatastasis), according to the Roman writer Censorinus in his little book De die natali. Some dozen other ancient writers have made mention of Sothis and/or its cycle and have o^ered us the day of its annual rising but, unfortunately, not the year. The overwhelming majority give its day as 19 July,5 implying an Apokatastasis somewhere in the quadrennium A.D. 140 43. It is Censorinus alone who tells us with seeming great precision that the cycle had ended a century before his time on 20 July of the speci~c year A.D. 139. Using this indispensable ~xed point as the axis of all Eg yptian chronolog y, early modern advocates of a calendrical Sirius reck3 U. Luft, "Tagesbeginn in дg ypten," Altorientalische Forschungen 14 (1987): 111; C. Leitz, Studien zur Дgyptischen Astronomie, дg yptische Abhandlungen, vol. 49 (Wiesbaden, 1989), pp. 15, and "Der Mondkalender und der Beginn des Дg yptischen Kalendertages," Bulletin de la Soc iИte d 'иgyptologie, GenХve (BSEG) 18 (1994): 4960. For critical discussion, see R. A. Wells's review of Leitz, Studien, in Bibliotheca Orientalis 49 (1992): 72328; R. Krauss, "VorlДu~ge Bemerkungen zu Seth und Horus/Horusauge im Kairener TagewДhlkalender nebst Notizen zum Anfang des Kalendertages," BSEG 14 (1990): 54 f., and "Was wДre, wenn der altДg yptische Kalendertag mit Sonnenaufgang begonnen hДtte?," BSEG 17 (1993): 6371; see J. von Beckerath's review of Luft's Die chronologische Fixierung des Дgyptischen Mittleren Reiches nach dem Tempelarchiv von Illahun (Vienna, 1992), in Orientalia, n.s., 62 (1993): 43638. 4 "In welches Jahr der ersten Tetraeteris der drei ersten Perioden der Beginn einer Periode wirklich gefallen ist, weiъ man natЭrlich nicht" (K. Schoch, Die LДnge der Sothisperiode betrДgt 1456 Jahre [Berlin, 1927], B 10, col. 2). The day, too, is relative. M. F. Ingham indi^erently used a model that, ending in A.D. 136, implies the day 20 July, while his second model, ending in A.D. 141, implies the day 19 July (see Ingham, "The Length of the Sothic Cycle," Journal of Egyptian Archaeology 55 [1969]: 36 40, tables 2 and

3). Foerster, Meyer, and Ginzel had an initial rising holding ~rm on 19 July until deep into the ~nal cycle (see E. Meyer, Aegyptische Chronologie [Berlin, 1904], p. 14; F. K. Ginzel, Handbuch der mathematischen und technischen Chronologie: Das Zeitrechnungswesen der VЖlker [Leipzig, 1906], vol. 1, p. 186, table). L. Borchardt considered that there was no need to discuss the matter, but it is clear from his cycles of 1458 and 1456 years that he would have held for 18 July (see Borchardt, Die Annalen und die zeitliche Festlegung des Alten Reiches der Дgyptischen Geschichte, Quellen und Forschungen zur Zeitbestimmung der Д g yptischen Geschichte, vol. 1 [Berlin, 1917], pp. 56 ^.). 5 Among ancient astronomers and writers citing 18 July are Dositheos (. 239 B.C., probably the source of the Sothic date in the Canopic Decree); Hephaistos of Thebes; Aetios (. A.D. 540); Salmasius (. A.D. 325); Zoroaster, Palladius (. A.D. 350). The day 20 July was cited by Solinus (. A.D. 25080); 21 July was cited by the famous Meton (. 425 B.C.) and (the unemended) Censorinus; 22 July was cited by the great Ptolemy (. A.D. 139). Theon of Alexandria (. A.D. 325), Geminos of Rhodes (. 70 B.C.), and Olympiodoros (. A.D. 565) have discussed Sirius and/or the Sothic cycle (see Ginzel, Handbuch, pp. 18891, and Meyer, Chronologie, pp. 22 f.).

CENSORINUS, THE SOTHIC CYCLE, AND CALENDAR ONE

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oned back to the years 27822780 B.C., advocates of a physical Sirius to the years 2773 2766, as the approximate date of Calendar Year One.6 It is diЇcult to overestimate the huge importance of Censorinus for all of ancient Near Eastern chronolog y. Yet there are serious problems with Censorinus and his datum. For four centuries now, it has been felt necessary to emend his given date from 21 July to 20 July. Nevertheless, a case can be made (I am not sure it is a winning one) for refusing to emend by citing Meton as the authority for 21 July. More seriously, all ancient writers thought Sirius's heliacal rising remained stable on the same ~xed day. Even Censorinus himself thought so; he states that Sirius rose "customarily" on 20 July (canicula solet facere exortum).7 But on the Julian/Eg yptian conversion table, 20 July is 1 Иht 1 in ever y year of the quadrennium 13639. Brandes, a century ago, and Ulrich Luft, today, have accordingly set the Apokatastasis at A.D. 136 rather than 139. Eduard Meyer disregarded Censorinus entirely, placing the end of the cycle at 140, preferring to follow the astronomer Foerster 's erroneous determination of an almost ~xed Sirius of 19 July.8 M. F. Ingham, too, disregarded Censorinus, placing the cycle's end at 136 in one model, at 141 in another. P. V. Neugebauer used both 141 and 139.9 The most serious de~ciency of Censorinus is that he neglects to tell us how he arrived at his information, nor does he name his source or sources. The ~rst step in using any historical authority is to raise the epistemological questions: what did he know (or think he knew), and how did he know it? Was he competent to speak of and judge the matter at hand? Perhaps because Censorinus's information was deemed too indispensable to question, perhaps because his datum 20 July 139 had become a dogma taken on faith and its author something of a cult icon, in any case, as far as I can see, the epistemological question has never been raised about the author of De die natali. Should we not now broach the subject of Censorinus's competence? How well quali~ed was he in the ~eld of astronomy and the calendar? How well did he know Eg ypt, the scienti~c community of Alexandria, and the indigenous community of Heliopolis? In short, did he know what he was talking about? II. CENSORINUS AND HIS BOOK Censorinus, a somewhat obscure grammarian of the third century A.D., wrote De die natali to honor the birthday of his rich patron, Quintus Caerellius. It is a short study about time, the passing of days, months, years, and cycles of all kinds, from the period of human gestation and the origins of man to the ~nal cataclysm--all this in order to place his patron's anniversary in the framework of cosmic time and to assure him of a long life. The extensive materials are drawn overwhelmingly from Varro, the Roman encyclopedist (d. 27 B.C.). Dozens of other Greco-Roman authors are cited, giving an aura of deep scholarship to the little work, but almost all of these are taken from Varro. Only Suetonius, Livy, and Fenestella are cited as writers from among those living later than Varro. A
6 27822780: calculated from cycles of 1460 and 1459 Julian years, respectively, with no trieterides; 27732766: 9 trieterides (P. V. Neugebauer) and 14 trieterides (Ingham), respectively (see also n. 19, below). 7 Censorinus, De die natali, par. 18: 10 and par. 21: 10 and 11. 8 Meyer, Chronologie, pp. 24 and 28; Ingham, "Length," n. 4. 9 P. V. Negebauer in Astronomische Nachrichten 261 (193637): 23 f. and table 21; Schoch, Die LДnge, B-13 (annex by Neugebauer).

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brief exposition of the contents of his essay, his sources, and his methods of inquiry may be useful in judging his competence.10 Time and the Individual Censorinus's ~rst topic is the length of the period of human gestation. He cites with great respect the view of the "Chaldaeans" (astrologers) that the period of gestation is of 7, 9, or 10 months. This is determined by the sun's position along the great circle of the zodiac at the moment of conception (De die natali, par. 8: 113). The points corresponding to conception form at the 7th month a diagonal cutting the semicircle, a period of maximum illumination. The points corresponding to the 9th and 10th months form a triangle and a square, respectively. He then considers the views of the Pythagoreans as presented by Varro in his treatise Tibero, a view he considers to be "nearer the truth and for this reason should be given preference" (De die natali, pars. 911). The numerical basis of gestation is analogous to the principles of music. Pythagoras had shown that two utes (or strings) whose lengths are in a ratio of 3:4 will sound the fourth (the "Amen" chord); in a ratio of 2:3 they sound the ~fth (the dominant); in a ratio of 1:2, the octave. Moreover, the number 6 is preeminent in human gestation. During the ~rst 6 days the embryo is in the form of seed uid, which changes to blood for the next 8 days. This ratio of 6:8 marks the fourth tone. There follows a 9-day period of unshaped esh; here the ratio of 6:9 is that of the ~fth note, to be succeeded by a period of 12 days when the body and its limbs assume positive form. The ratio is that of the octave. To conclude: the total of these four stages is 35 days and 6 x 35 = 210, the period of a short gestation. The normal length of human life is relative to certain numbers, 7 and 9, particularly in the form of their squares. Thus the 49th and 81st years are critical years that may end the lifespan, the one of the soul, the other of the body. A third age, 7 x 9, is also critical but less so, and Censorinus assures his patron that having passed this barrier he may anticipate many more years. Yet Censorinus notes that some authors feel that the human lifespan is greater--100 years or perhaps 110. For this he cites reliable (!) evidence from Eg ypt. The astronomer Dioscorides, according to Varro, asserts that the embalmers of Alexandria, who carefully weighed parts of the body at all stages of life, agreed that the maximum span of life was 100 years for this reason: the heart of an infant of one year weighed 6 (grams); at the age of two, 12 (grams), and its weight increased successively at that rate until the age of 50. At this point, the heart began to lose 6 (grams) every year, so that death must follow at the century mark (par. 17: 14). It is relative to our question about the nature of his sources of information that Censorinus picked up this bit of Eg yptian lore not from a visit to Alexandria but from the pages of a Latin writer quoting a distant Greek writer.

10 The standard edition of Censorinus's De die natali is F. Hultsch, ed., De die natali liber (Leipzig, 1867). An excellently annotated modern French translation is available in G. Rocca-Serra, Censorinus: Le jour natale (Paris, 1980). For standard bibliographical

sketches, see A. F. von Pauly, Paulys Realenc yclopДdie der classischen Altertumswissenschaft, ed. G. Wissowa et al. (Stuttgart, 18941972), cols. 190810; C. C. Gillispie, ed., Dictionar y of Sc ienti~c Biography (New York, 1971), vol. 3, pp. 175 f.

CENSORINUS, THE SOTHIC CYCLE, AND CALENDAR ONE

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Moving on to the core of his paper, Censorinus considers at great length the period of the saeculum (par. 17: 513). Pursuing the idea that the saeculum, originally de~ned as a generation, ~nally came to mean a century, he studies in great detail the secular games of Rome. This is his best work; he cites numerous authors, many via Varro, but also many independently of the encyclopedist: Livy, Suetonius, Piso, Antias, G. Gellius, and Cassius Hemina, as well as oЇcial records of the decemvirs and the quindecemvirs. The purpose of this excessively long exposition is to place both Caerellius's birth and his current anniversary in the tenth century of the founding of Rome (A.D. 147246). The Great Epochs For us the next sections are the most important. He passes through the Greek tetraeterides and octaeterides as well as the 19-year ~xed lunar cycles of Meton, Calippus (76 years), and Hipparchus (304 years - 19 x 16), to arrive at the great calendrical cycles of the Mediterranean peoples. He relates the current year in which he was writing to the Greek Olympiads (1,014th year), the foundation of Rome (991st year), the Julian era (the 265th), the Babylonian era of Nabonassar (the 986th), and the Macedonian era of Phillip Arrhideus (the 562d). Finally, either as a culmination or as an afterthought, he arrives at the greatest of all the ancient epochs, the Eg yptian Sothic cycle of 1,460 years that by chance had commenced on 20 July exactly one century, he states, before the birthday of his rich patron. He informs us that he obtained his era datings (except that of the Eg yptians) by extrapolating from Varro, who apparently had drawn up canon tables similar to those of the astronomer Ptolemy. He does not tell us, or event hint at, his sources of information for the Sothic cycle. Caerellius's life had now been located with detailed precision in a rational moment of epochal history. After a gestation of 9 months ~xed by the sun's position in the heavenly zodiac and by the numbers-morpholog y of fetus development, he was born in the tenth century of great Rome; his birth is now to be celebrated at the centenary of the culmination of the Eg yptian 1,460-year cycle, itself associated as we know with Aeternitas, the Aion, the Phoenix, and rebirth. The primary purpose of this lengthy and scrupulous investigation of time, indeed its sole raison d 'Йtre, was not truly to determine the day and year of the Apokatastasis itself but, rather, to situate his current year A.D. 238, and his patron's birthday, at a culminating moment of universal time. Unfortunately, Censorinus seems to have counted inclusively, as Romans were wont to do. Starting with A.D. 238 and ticking o^ 100 paired names from his consular list, it would appear, he arrived back at the year 130 and stopped. III. SOME UNRESOLVED QUESTIONS The central question, of course, is this: is it simply fortuitous that Censorinus happens to cite a year for the Apokatastasis that made of his patron's birthday a centenary celebration of the Great Epoch? Or was it simply a manipulated result? There are inherent diЇculties in his datum 20 July, A.D. 139 that every modern scholar has had to deal with. First of all, his 20 July is an emended date: the text reads "21 July," which would be appropriate for a cycle ending in A.D. 13235. Secondly, there is that troublesome word "solet," with its implication that the cycle might have ended in any year of the quadrennium 13639.

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Thirdly, the overwhelming bulk of ancient authors from as early as 239 B.C. to as late as A.D. 540 cite 19 July as the normal day of Sirius's rising,11 which would be appropriate for a schematic Sirius rising in A.D. 140 43 or a physical Sirius with a somewhat greater arcus visionis--a possibility seriously considered by Meyer, Schoch, Neugbebauer, and Ingham.12 Lastly, a blind faith in Censorinus loads the dice in a question that ought not to be settled a priori: was Sirius physical or schematic for the ancient Eg yptians? Since the cycle of a physical Sirius is 8 to 14 years shorter than that of a schematic Sirius, any retrocalculation from the end of a cycle would have schematic Sirius rising some years before astronomical Sirius. This is manifestly impossible, as Borchardt pointed out long ago in quashing the then popular notion of a schematic Sirius.13 The two concepts of Sirius must start together. Reliance upon Censorinus alone has bound us to a predetermined result in favor of a proposition that would appear to many to be absurd.14 It has inhibited us from searching for the only point of departure that allows us to view the problem pragmatically and with an open mind: the start of both concepts at CY 1. Censorinus's Knowledge of Egypt and of Sirius It would not appear that the author of De die natali was ever in Eg ypt. His only Eg yptian topic, apart from the two paragraphs on Sirius, is the tale of the Eg yptian embalmers, and this is taken from Dioscorides via Varro (par. 17: 14). He does not seem to know the Greek language. He cites dozens of Greek authors, but all such references are taken from Varro. Whenever he cites authors directly, the sources are all in Latin. He does not know that Eg ypt had six time zones; for him Sirius rises on 20 July "in Eg ypt." For us, his blissful failure to indicate whether Sirius was observed (by Greek astronomers) in Alexandria or in Memphis is of critical importance.15 He displays ignorance of when the Eg yptian day commenced under circumstances where, if he had ever been in Eg ypt, he would have mentioned it (see next section, below). His one error in locating the year 238 with respect to the great cycles is with the Alexandrian calendar of Augustus, where he gives the erroneous 267th day (rather than the 268th), perhaps because Varro, from whom he had extrapolated all his other cyclic dates, had died in 27 B.C. and had probably not included the new calendar in his Canon. From this perspective, Censorinus's failure to give the customary double dates required by the diЇcult relationship between the Alexandrian year and the "archaic" Eg yptian year reaЇrms the notion that he had never been in Eg ypt.

11 For the many references to 19 July, see n. 5, above. 12 Meyer, Chronologie, pp. 14, 18, and 28; Schoch, "Die LДnge," B 10 and tables C and D; Neugebauer in Schoch, "Die LДnge," B 13, annex; Ingham, "Length," table 2. 13 Borchardt, Die Annalen. 14 One of se veral absurdities is that in Neugebauer 's model, the most widely accepted model from 1939 to 1969, there is only one departure from absolute regularity (i.e., only one trieteris) in the 939 years from the First to the Ninth Dynasties (Astronomische Nachrichten, table 21, years 3145, 2638, and 2199).

What in the world were Sirius-watchers looking for in the other 938 years? But, of course, one can follow Cardinal Newman: "Credo quia absurdum est," or one may point to modern quantum physics to show that reality may indeed appear absurd. 15 The Christian writer Olympiodorus (. A.D. 565) is often cited to show that Ptolemaic astronomers made their observations at Memphis. Neugebauer, however, considered Alexandria to have been their site (see Borchardt and Neugebauer, "Beobachtung des FrЭhaufgangs des Sirius in дg ypten," Orientalistische Literaturzeitung [OLZ] 29 [1926]: 316).

CENSORINUS, THE SOTHIC CYCLE, AND CALENDAR ONE Playing at "Pick-and-Choose" Two statements of Censorinus ought to have raised eyebrows to the very hairline:

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1. Rather than telling us what we need to know, whether the heliacal rising was observed in Memphis or in Alexandria, he merely remarks that it rose "in Eg ypt" (par. 20: 10). Does he not know that "in Eg ypt" the star rose successively in seven time zones between 15 and 21 July? Or--and is this what he meant--that there was in operation a single schematic Sirius for all of Eg ypt? This is awkward for us. If we have trusted him implicitly for the datum "Sirius - 139," should we not have trusted his statement implying that the star was calendrical and not regularly observed? And if we have rejected the latter paradigm--as most scholars have--ought we not to have rejected as well his remarks on the ending of the Sothic cycle? 2. He discusses elsewhere in his book the de~nition of the day held by di^erent nations: for the Babylonians the day ran from sunrise to sunrise; for the Umbrians, from midday to midday; for the Athenians, from sunset to sunset; and for Romans, from midnight to midnight (par. 23: 3). Astounding! He does not mention what the great majority of modern chronologers have taken for granted: that there was a ~fth option, an Eg yptian day of dawn to dawn. Or are we to deduce from his silence what has recently become a more acceptable idea: that the Eg yptian day indeed did not run from dawn to dawn but from sunrise to sunrise? Here again, for those who hold the dawn-to-dawn assumption, is it reasonable to reject Censorinus's apparent sunrise-day, while giving full faith and credit to his pronouncement on the Apokatastasis? Can we continue to pick and choose from the assorted menu Censorinus serves up?16 It is not suЇcient to explain that he may have been speaking in general terms and need not have been aware of the subtle di^erence between "~rst light" (dawn) and "~rst ash" (sunrise). On the contrary, he possessed a most precise awareness of these things when he distinguished among the following stages of the early day: (1) midnight; (2) continued darkness following midnight; (3) cockcrow; (4) the silence following cockcrow; (5) dawn, when the light of the sun, which has not yet arisen, becomes apparent; (6) the aurora, when the light shines once the sun has risen (par. 24: 2). In his listing of nations, why did he not mention Eg ypt at all, instead of--or at least alongside of--Babylon, not elsewhere mentioned? I fear Censorinus simply did not know when the Eg yptian day began, and I cite this as further evidence that he had never been in Eg ypt. Sources and Discussion The reluctance of some to concede full authority to Censorinus is warranted by the unusual absence of source citations and discussion of the basic data. Everywhere else in his essay, he is careful to bring forward diverse opinions and to cite sources, even though these might be secondhand via Varro and often to a point of su^ocating excess. In the
16 For supporters of the sunrise-day thesis, see Luft, "Tagesbeginn"; Leitz, Studien; and von Beckerath's review of Luft's Die chronologische Fixierung. For supporters of the dawn-day hypothesis, see Wells, review of Leitz, Studien; Krauss, "VorlДu~ge Bemer-

kungen"; and, implicitly, L. E. Rose, "The Astronomical Evidence for Dating the End of the Middle Kingdom of Ancient Eg ypt to the Early Second Millennium: A Reassessment," JNES 53 (1994): 23761.

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obscure matter of the embryo, he cites no fewer than a dozen authors (par. 7: 57). His discussion of the saeculum requires two and a half pages, with a detailed analysis of eight authors as well as oЇcial public records--merely to arrive at the conclusion that a saeculum was 100 years. His establishment of the year 139 can be compacted within one brief sentence: "In this year 238 the ~rst day of Thoth (1 Иht t) fell on 25 June, while 100 years ago it fell on 20 July (emended), at which time Sirius customarily rose in Eg ypt." He says nothing else. We may surmise that his date, 139, does not come from a document of that year but that it is a retrocalculation made in his own day and possibly by himself. All one needed in order to make the statement just cited was a "customary" day of rising--several choices were available and all were stable over perhaps a century and a quarter at that time--and a copy of the Julian/Eg yptian conversion table. One did not need the year. There were at the time four possible dates for the heliacal rising of Sirius: (1) 19 July, the day most widely cited among ancient authors, ~rst of all by Diosthenes, a contemporary of the Canopus Decree and possibly the observer of the crucial heliacal rising of II smw 1 of 239 B.C.; (2) 20 July, mentioned by Solinus, who drew his materials largely from Pliny (d. A.D. 29) and undoubtedly known to Censorinus; (3) 21 July, advanced by Meton, whose astronomical work is cited by Censorinus via Varro (par. 18: 8); and (4) 22 July (probably dubious), by the well-known astronomer Ptolemy, a contemporary of the Apokatastasis; his work would probably not have been known to Censorinus unless he had been a resident of Alexandria. A rising on 19 July would have placed the Apokatastasis in the quadrennium 140 43; a rising on the 20th, in 13639; and one on the 21st, in 13235. If I were writing in the year 241, say, and wished to establish it as the centenary of the Apokatastasis, I would ~nd out from the Julian/Eg yptian conversion table that the required Eg yptian date 26 Thoth (I Иht 26) was 24 June. Subtracting 25 days from the Julian day, I would ~x the Apokatastasis on 19 July, con~rmed on the table as indeed the 19th, and corroborated by Diosthenes and others.17 If I were writing in the year 233, the conversion table would show the date I Thoth to be 16 June and a century earlier to have fallen on 21 July, corroborated in this case by Meton. An Apokatastasis in A.D. 141 or 133--or for that matter any year between 132 and 143--would be as convincing as Censorinus's actual fortuitous choice, 139. As far as I can see, there is nothing in De die natali that would rebut the notion that his datum was deduced from wish-ful~lling manipulation, nothing that would be inconsistent with the conclusion that Censorinus's paragraphs on Sirius might well have been written in the newly established Imperial Library in Rome or among the scrolls of some rich collector in a villa in Latium. Any clari~cation he might have needed regarding the sequence of Eg yptian month names might easily have been secured from a priest of Isis, whose cult had been established in Rome for centuries. A Julian/Eg yptian conversion table was probably more likely to be found among the Eg yptian community in Rome than in Alexandria. Censorinus's Competence How competent was Censorinus to judge astronomical and calendrical problems in Eg ypt? He was primarily a grammarian and a pop philosopher, with a dabbling interest in
17

See n. 5 above.

CENSORINUS, THE SOTHIC CYCLE, AND CALENDAR ONE

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many ~elds. Nowhere in his little volume does he express any interest in astronomy. He shows no awareness of the complexities involved in the interplay of three calendars to reach the simple date "XIII Kal. Aug." (20 July). His discussion of the various calendrical epochs is well done, but his knowledge of this topic and of everything else is secondhand and in bits and pieces. His work illustrates completely Weill's description many years ago with respect to Sothic dates when he commented: "La surprenante inaptitude des Anciens Ю confИrer un tИmoignage documentaire avec un fait rИel, ou deux tИmoignages documentaires ensemble; l'Иcrivain ancien copie de vieux livres, dИcoupe des extraits, et fait un livre cousant bout Ю bout ses notes."18 Rembrandt could not have sketched more incisively the soul of Censorinus! He never deserved to be the arbiter of the Sothic cycle. How ironic it would be if it should turn out that the ~xed starting point for all calculations of Eg yptian chronolog y has been not the second Apokatastasis of Sirius but merely an anniversary celebration of the obscure Councillor Quintus Caerellius, minus 100 years . . . and miscounted! IV. SEARCHING FOR CALENDAR YEAR ONE The comfortable dogma that Censorinus, by proper retrocalculation, could lead us back to an exact placement of CY 1 was always misplaced. At best, this writer might furnish a choice within the quadrennium 13639. But his lack of demonstrable competence and the strong suspicion that his selected date 139 was a product of manipulation ought to deprive him of any special authority above other ancient sources, some of them quali~ed astronomers whose dates 19 and 21 July were pointing to the quadrennia 13235 and 140 43. Moreover, we face a greater quandary than just Censorinus's de~ciencies. Even if his year A.D. 139--or for that matter, any year between 132 and 143 cited by any other ancient author--might be proven true, we would still have the uncertainty inherent in any attempt to retrocalculate the cycle of a physical Sirius. With three recent choices to consider-- Schoch's double cycle of 2,912 years, Neugebauer 's 2,911 years, and Ingham's range of 2,9062,911 years19--we would arrive at a minimum zone of six years for CY 1. Nor can we ever make a certain choice a priori among these because we can never know the everchanging visibility factor for epochs three and ~ve thousand years ago. Calculation of the Sothic cycle is not merely a matter of the geometric relationship among sun, star, and horizon; it involves atmospheric conditions and the quality of the horizon.20 We know that
18 Raymond Weill, Bases, mИthodes, et rИsultats de la chronologie Иgyptienne: ComplИments (Paris, 1928), p. 43. 19 Schoch, "Die LДnge"; Neugebauer, Astronomische Nachrichten, pp. 23 f. and table 2; Ingham, "Length," tables 2 and 3. Schott, using an arcus visionis of 9.0o, calculated two historical cycles of 1,456 years; Neugebauer, re~ning the methodolog y, prescribed cycles of 1,456 and 1,455 years; Ingham, using Schoch's arc of 9.0o, but a somewhat di^erent methodolog y, calculated cycles of 1,456 and 1,453 years. Knowing, however, that Sirius moved with respect to the ecliptic, he extended Schoch's 9.0o to 8.0o, producing cycles of 1,454 and 1,452 years. Since his arc-range was arbitrary, he could easily have used,

say, the Neugebauer/Borchardt observation of 9.2o and extended it downward to 8.2o or 8.4o. Since he made little or no allowance for greater humidity in early antiquity, his mobile cycles might well be considered as exible; i.e., of 1114 trieterides. 20 Weather cycles varied back and forth over millennia--even from year to year. Whether the quality of the horizon was determined by water vapor or by sand and dust particles, the arc of vision in Heliopolis and Memphis was di^erent in a year when an early June Nile rose before Sirius than in a year when a late August inundation followed after the star. The e^ect of clouds and mist upon the observation of Sirius is illustrated by the problems encountered by Borchardt and his team in their e^orts to observe heliacial risings

26

JOURNAL OF NEAR EASTERN STUDIES

there was much more humidity and less desiccation in North Africa in the distant past than today. In terms of haze and ground mist, the Nile was more voluminous, the oodplain broader, and the Delta marshier and less tamed.21 Moreover, we cannot tell a priori whether Sirius might be calendrical rather than astronomical, in which case the retrocalculation would be of the order of 2,918 or 2,920 years. In short, it is self-defeating to attempt to deduce the beginning of the Sothic cycle from the date of its end. This has it all backwards. We must somehow devise a scheme that will bring us directly to that ~rst moment when physical Sirius and conceptual Sirius constituted a single cell and before they split apart some decades (or centuries) later at the ~rst trieteris. One untried approach might be to use the two Sothic dates we have ready at hand. The predicted heliacal rising of IV prt 16 in the 7th year of Sesostris III (or II ?) might be pinpointed by a cluster of lunar dates from that reign.22 Unfortunately, lunar dates can only give us a 25-year cyclical line extending over centuries. Besides this, it is still to be determined de~nitely whether the Eg yptian day began at dawn or at sunrise; the di^erence amounts to 11 years. Thus, Sesostris's datum cannot be translated into a Julian year until CY 1 has itself been ~rmly established. A more promising heliacal rising is that of II smw 1 from year 8 of Ptolemy III Euergetes I. This can be pinpointed to a precise day and year: 19 July of 239 B.C. in civil year 240239. Nevertheless, we do not know by inspection, nor can we tell a priori, whether the cycle is to be considered that of a physical or a schematic Sirius. This latter consideration a^ects the distance from CY 1; II smw 1 marks the passage of 270 raw quadrennia (108083 years) by a schematic Sirius, only 268 or 269 quadrennia (107279 years) by a physical Sirius. Thus, neither of our two known Sothic dates can pinpoint the year of CY 1. If neither Censorinus nor our most promising Sothic dates o^er any hope of furnishing a precise and reliable dating for CY 1, it is clear that we must search for a radically new point of departure, a wholly fresh perspective from which to view the problem--perhaps even a complex new paradigm.

of Sirius over the three-year period 192426. Failure in the ~rst two years led to a highly organized expedition in 1926. The summary article of Borchardt/ Neugebauer noted an obvious error of observation by Jameson at Asyut and recognized the possibility of errors at Cairo and Minya. Indeed, analysis of F. S. Richards's report for Cairo (see Borchardt and Neugebauer, "Beobachtungen des FrЭhaufgangs des Sirius in дg ypten im Jahre 1926," OLZ 30 [1927]: 444-- items for 2 August, 5.7 hour, and 3 August, 5.4 hour) makes clear that a thick cloud up to 5o above the horizon had in all probability masked a heliacal rising of 2 August. Borchardt concedes that Richards's conclusion would lower the true arc of vision to "8o3 bis 8o5"; cf. the same problem on 2 August 1925 (Borchardt and Neugebauer, "Beobachtung," in OLZ 29, col. 314). Paradoxically, the unsatisfactory results obtained by the weather-plagued expedition sent out to establish once and for all the modern arcus visionis of Sirius furnishes the strongest argument ever made that, for Eg yptians, Sirius was schematic rather than astro-

nomical/observational. Would Eg yptians have put up with conditions like these for 3,000 years when an easy and "certain" schema beckoned? Is our realistic modern trieterid shift relevant against an ancient Platonic concept of an idealized tetraeteris? There are, of course, strong counter-arguments against a schematic Sirius. My point is merely that the matter is controversial and replete with uncertainty. 21 For weather conditions in northern Eg ypt during the ~rst three dynasties, H. Kees cites the extensive marshs, swamps, and papyrus thickets of the Delta, the presence of water-loving creatures such as hippopotamus and crocodile, and extensive forests in southern Libya and the eastern desert; see idem, Anc ient Egypt: A Cultural Topography (Chicago, 1961), pp. 18, 20, 24, 3234. 22 Thanks to Luft's splendid labors on the Illahun materials, we now have some three dozen utilizable lunar dates from the Twelfth Dynasty; see idem, Die chronologische Fixierung, p. 225.

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