Annus Platonicus: A Study of World Cycles in Greek, Latin and Arabic Sources 9068318764, 9789068318760

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Annus Platonicus: A Study of World Cycles in Greek, Latin and Arabic Sources
 9068318764, 9789068318760

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Godefroid DE CALLATA Y





© lnstitut Orientaliste de l'Universite Catholique de Louvain

College Erasme Place Blaise Pascal. I B-1348 Louvain-la-Neuve © Peeters Press Louvain-Paris

Orders should be sent to: Peeters Press, P.O.B. 41. B-3000 Louvain ISSN 0076-1265 ISBN 90-6831-876-4 (Peeters Leuven) ISBN 2-87723-303-0 (Peeters France)

TABLE OF CONTENTS Prologue: Instruments of Time........................................................


The Foundation Stones from Classical Antiquity .... A. The Perfect Year of Plato .......................................................... I. The Manifold Meaning of the teA.eout h,~\,\, the em,neou, , 1e,, that the: Sun " tht' .:t'ntn: ,,i Plat,,·, ,~ ,1c:m. Hi, .:-,,n,·lu'1,,n 1, that · ,~n ne , 0it pa_,ct·adkur- d · 3pri.-, yuelk, d,,nnt'e, a,m,n,,m1yue, Pl.11c,n3Ur31I ru ,ktt'nn1 n.:r ce, nomhre,·. :• Pl.-\TO. T1n1.. :\fx'-.,-a.



harmony is never said to belong to the sensible world - a point that Aristotle clearly missed in his rejection of the theory of celestial harmony 16• Moreover, Plato seems to deny explicitly such a possibility when speaking of the cognitive activity of the world soul17• It is nevertheless worthwhile recalling the importance of the Pythagorean theory of the harmony of the spheres in Plato's writings, as we find it unambiguously expounded, for instance, in the myth of Er at the end of the Republic 18• Considering, on the other hand, the constant parallels between astronomy and music in Plato's classification of sciences 19 , it would be surprising if the most perfect of all achievements in astronomy and music should not coincide. In other words, would it be possible to imagine a better completion for the harmony of the spheres than at the end of the Great Year, when all eight notes are perfectly joined together, so as to produce the best accord possible? But, however essential the link between these two meanings might be, it is primarily in its metaphysical expression that the concept of the Great Year reveals its real importance. Between the Same, 'indivisible Existence that is ever in the same state', and the Other, 'divisible Existence that becomes in bodies', the intermediate Being must be interpreted as a system in which the division of the Primeval Unity has been realized. Indeed, when the god split into two halves the harmonic structure of the world soul, the Same and the Other were separated from each other, and this operation was the division of the Primeval Unity (the Same), giving birth to Duality (the Other) 20• The division of the circle of the Other into six different parts, so as to produce seven unequal circles, 16

Cf. ARISTOTLE, De cael., II. 9, 290b-29la. Cf. PLATO, Tim., 37b. 18 Cf. PLATO, Rsp., X. 617b. 19 On this see above all PLATO, Rsp., VII, 529c-530d, where music and a~tronomy are called •sisters of one another·. 20 One notes, moreover. that this Duality is expressed by the very computation of the seven basic elements. Indeed, while the circle of the Other is I + 2 + 3 + 4 + 8 + 9 + 27 = 54, the circle of the Same is only 27, so that the two circles are in the exact ratio of 2 to I. It is interesting to compare our pa~sage with a brief note from N1coMACHUS OF GERASA, lntrod. arithm., II. I 8, 4, in a section precisely devoted to the Same, the Other, and the birth of numbers according to Plato: '(Since oblong numbers admit of alterity, infinity, and boundlessness,) whatever is of the nature of number and everything in the world that has been created with respect to this nature stands apart, and is divided, and appears to be contradictory. Thus, when the ancients started to speculate about nature, they rightly made the first distinction relating to the creation of the world in this way: Plato referred to "the nature of the Same" and "that of the Other". and again to "that of the indivisible Existence that is ever in the same state" and to "that of the Existence which becomes'". 17



is the expression of a further separation from Unity: Duality is the foundation of all numbers 21• But this separation is neither infinite nor everlasting. At great intervals of time, the movement of the Other comes back to its original position (the conjunction of the seven planets), so as to restore the fundamental Duality. When, furthermore, this renewed Duality comes back into conjunction with the circle of the Same (the conjunction of the seven planets with the starry sphere), then Duality returns to the Primeval Unity. The period of time required for this return to Unity to be fulfilled is called, in Plato's philosophy, the Perfect Year.

II. The Number of Divine Begettings Plato does not assign any explicit measure to the Great Year. Indeed, he seems to be reluctant even to explain the way one might compute its length. We have already seen how Plato restricts to a chosen few the number of those who are concerned with the general problem of planetary revolutions. Plato is sparing of his words in other passages that deal with the same matter. An example is the statement in which he cautiously avoids speaking of the movements of Mars, Jupiter and Satum 22 • This apparent reluctance to treat the problem of astronomical periods mathematically has led several scholars to believe that trying to discover the length of Plato's Great Year is a meaningless and useless task23• This, it should be remembered, despite the fact that Plato's statement about the Great Year begins with the explicit assumption that the problem is not out of human reach ("Ecrn 6' oµroc;ou6ev ~nov ... ). Plato's writings are full of riddles and, to Katavoitcrm 6uvatov chc; say the least, the difficulty in solving them has rarely proved to be due to some inconsistency in the text itself. On the contrary, as Ficino would 21

For an introduction to the Pythagorean theory of numbers see above all the still valuable T. TAYLOR,Arithmetic. Among ancient sources. one should first refer to: N1coTheo/. MACHUSOF GERASA,lntrod. arithm.; PLOTINUS,Enn., VI, 6, 34; IAMBLICHUS, arithm.; THEOSMYRNAEUS, Expos .• I. 22 Cf. PLATO,Tim., 38d-e. 23 Thus, while A.E. TAYLOR, Commentary, p. 216, may well be right to say: 'Timaeus need not be supposed to have any theory about the actual number of days in the period. He does not profess that he knows the length of the "complete year", but only that it is possible to determine it', it is less pardonable to conclude, as does C. MUGLER,Dew: Themes, p. 106: 'La question de la duree de la Grande Annee platonicienne n'a done pas trouve de reponse et n ·en trouvera probablement pas. Mais la decouverte de la valeur attribuee par Platon a cette constante n'aurait fail qu'ajouter a notre connaissance des idees astronomiques du penseur une note pittoresque a laquelle nous pouvons facilement renoncer'.



say, it appears very often that 'Plato himself did not wish certain enigmas to be unfolded' 24 • Experience shows that readers are well advised to pay close attention to such problems, especially when Plato presents them as trifling matters. Since Proclus's time, a celebrated passage from Republic VIII has often been cited by those who are willing to believe in Plato's admonition concerning the possibility of reckoning the measure of the Perfect Year. The text I refer to here is none other than that in which Plato defines the Nuptial Number (or Geometric Number) - in fact, the riddle par excellence of Plato's whole corpus and, as Adam notes in his detailed commentary on this issue, 'notoriously the most difficult passage in his writings' 25 • The mathematical puzzle as Plato playfully put it into the mouth of the Muses reads: Now for divine begettings (0Eicp µi:v yi:vvrit)there is a period comprehended by a Perfect Number (dpt0µoc; tEAEtoc;). and for mortal (dv0pro1tEicpOE) by the first in which augmentations dominating and dominated when they have attained to three distances and four limits of the assimilating and the dissimilating, the waxing and the waning, render all things conversable and commensurable with one another (mivta 1tpocriJyopa Kai {>T]tix1tpoc; a1..1..ri1..a),whereof a basal four-thirds wedded to the pempad yields two harmonies (Ouo apµoviac;) at the third augmentation, the one the product of equal factors taken one hundred times. the other of equal length one way but oblong, - one dimension of a hundred numbers determined by the rational diameters of the pempad lacking one in each case, or of the irrational lacking two; the other dimension of a hundred cubes of the triad. And this entire Geometric Number (3.uµnac; 6i: o6toc; dpt0µoc; yi:roµi:tp11C6c;) is determinative of this thing, of better and inferior births26 • (transl. Shorey)

It is not necessary for us, fortunately, to take up once again a stepby-step analysis of all the intricacies that are contained in those lines, let alone to explain in detail how the mathematical solution of the riddle can be arrived at. For this has been done through the patient and brilliant achievement of many scholars from the past, culminating with the decisive works by Adam and Dies, to which I primarily refer for further exegesis 27• What I should like to retain as major results from this impressive effort of modem scholarship is, above all, the two following points: 24

F1c1No.De num.fat., Expns. (*). J. ADAM,Republic. II, p. 264. 2 " PLATO,Rsp., VIII. 546b-d. 27 See: J. ADAM,Republic, II, pp. 265-312 ('The Number'): A. D1ts. Nombre. with an account of nearly all previous attempts as well as a personal interpretation in which Adam's explanation is slightly improved. For scholarship since Dies's dissertation see: A. AHLVERS,'Zahl'. pp. 11-20; F. von EHRE1'rELs. 'Hochzeitszahl", p. 240; M. ~~



(i) Plato's Geometric Number is 25,920,000, since its two harmonies correspond to the value of 12,960,000, itself equal to the product (3x4x5) raised to the fourth power: 1st (square) harmony= (36 x 36) x (100 x 100) = 12,960,000 2nd (oblong) harmony= (48 x 100) x (27 x 100) = 12,960,000 (ii) It is now clear that both harmonies apply to the period of mortal begettings and not to that of divine begettings, which is the only one Plato refers to as a period measured by a Perfect Number. But if we may assert with confidence that the mathematical solution of Plato's riddle has now been found, there still remains some controversy regarding the philosophical interpretation of the text. Thus while some scholars, as has already been seen, have rejected any link between the Geometric Number of the Republic and the Perfect Number of the Great Year in the Timaeus 28, many others have been inclined to confuse these two notions29 • It is regrettable that the reason for this misleading amalgamation appears to come from Adam's commentary itself otherwise a remarkably argued interpretation; he imagined that the number 12,960,000 was designed to express a period numbered in days, so as to correspond to a 36,000-year cycle. Finding that this cycle, presumably of Babylonian origin, was indeed sometimes referred to as the Annus Platonicus in texts from the Late Middle Ages and even from the Renaissance, Adam was led to conclude, on rather insecure grounds, that Plato had some pre-Hipparchian knowledge of equinoctial precession 30 • DESKINGER,'Enigme', pp. 39-76; K. GAISER.Lehre, pp. 406-16: A.-J. FESTUGIERE, Republique, II, pp. 143-53. On Ficino's interpretation - neglected by Dies - see the recent M.J.B. ALLEN,Nuptial Arithmetic. 28 See, for example, A.E. TAYLOR,Commentary, p. 218 (on the Nuptial Number): 'There is no sufficient evidence, so far as I know. that Plato attaches any astronomical significance to this period·. Similarly, C. MUGLER,Deux Themes, p. 106: 'C'est pour avoir meconnu la qualite purement arithmetique du nombre nuptial, ou ii n'entre pas un seul element susceptible d'une interpretation a~tronomique, qu'on a pu identifier la periode qu'il mesure a la Grande Annee'. 29 See for instance: K. GAISER,Lehre, p. 407; R. VAN DENBROEK,Phoenix, p. 99. 30 Cf. J. ADAM,Republic, II, pp. 304-5. The weakness of Adam's argument has already been underlined by J.D. NORTH,'Chronology'. p. 314: 'Even a modem editor of Plato's Republic, J. Adam, has suggested that when Hipparchus found a figure of one degree per century for the movement of the eighth sphere, thus implying that the stars circuit the sky in 36,000 years, he was influenced by Plato's Perfect Number of the Republic, which he interpreted as the square of 3600. Quite apart from the fact that Hipparchus merely set one degree per century as a lower limit lo the phenomenon he had discovered, the empirical character of his result is nol in doubt. It would also be surprising if Hipparchus had understood the Republic pa5sage in question, since it seems to have been beyond the resources of most of Plato's editors to do so·.



And yet Plato himself had clearly distinguished between the Perfect Number, which embraces the period of divine generation, and the Geometric Number itself, which measures the cycles of human generation. It is, I repeat, essential to note that the whole computation of Republic VIII is only concerned with the second of these periods, and that this latter period is not the one measured by the Perfect Number. While summarizing his own interpretation of the passage, Dies is thus absolutely right to say: 'Or Platon distingue expressement (546b) entre "la periode pour la generation divine, qu'embrasse un nombre parfait", et la periode pour la generation des hommes, et c 'est cette periode de generation humaine qui se traduit par 12.960.000, ou, plutot, par (3x4x5) (3x4x5) (3x4x5) (3x4x5), puisque Platon ne formule pas le produit. Le nombre parfait de la generation divine, c'est quelque chose comme celui de Timee, 39d' 31• Strangely enough, nearly all modem scholars seem to have overlooked the idea that these two numbers could still be regarded as related to one another by some mathematical proportion. This will certainly appear as a serious omission when we discover that Proclus, at least in this respect, proves to be much more inspired than any of the later commentators. Proclus concludes his commentary on the Great Year as defined in the Timaeus in this way: It must be added to what has just been said that this Perfect Number should be thought of as different from the one mentioned in the Republic, which 'encompasses the period of the divine begettings'. This Perfect Number is more partial (µEptKCOtEpov) and brings about the return (d.1toKatacrtattK6v) of the eight periods only, while the other one comprehends both the specific movements on the starry sphere and the movements of absolutely everything in the heavens (tv tot~ d.1tAav&mKtVT]~ toi~ tv oupav Ktvouµ&vot~). whether it is moved invisibly or visibly, whether it is moved amongst divine generations or after the gods, and it also comprehends longer and shorter periods of fertility and Therefore, infertility in the realm under the Moon (tv tot~ u1to 6e XlAlOO'tq>) year both come to draw lots and choose their second life, each choosing whatever it wishes. Then a human soul may pass into the life of a beast, and a soul which was once human, may pass again from a beast into a man 34 • (transl. Fowler)

The same value of 1,000 years is given twice in the myth of Er, with which Plato concludes his Republic. At the beginning of his narrative the messenger reports: And they (the souls) told their stories to one another, the ones lamenting and wailing as they recalled how many and how dreadful things they had suffered and seen in their journey beneath the earth - it lasted a thousand years (dvm 6etllV 1topsiav XlAl&tTI)- while those from heaven related their delights and visions of a beauty beyond words 35• (transl. Shorey)

In the very last line of the same myth - Er remarks again:

and thus of the entire work too

And thus both here and in that journey of a thousand years (Sv tfi XlA.l&tst 1top£ivliµa Kai 1tpo ,TJ~ £1ti AeuKtlirovo~ q,0opa~ tpi-rou 1tp6tepov ui>ato~ e~auriou yevoµtvou)60.(transl. Bury)

This chronological precision is very meaningful, for it confirms, in itself, that Plato had in mind a kind of list in which the major floods were numbered according to their respective antiquity. There is, of course, no need to say to what extent this statement is consistent with the idea of a flood-system, namely, a sort of chronological scheme in which the floods mark the transition between one period and the next. Now, since we know from the same myth that the deluge of Deucalion was the only one which Solon and the other Greeks could remember - while the Egyptian priests asserted that there had been many others before I think we may assume with confidence that it was also the last one of the series referred to in the present statement, so that we are now entitled to confirm that Plato's system contains four floods in all61• The connection with the four ages of Plato's Great Year seems quite natural, and the localization of the four floods inside the whole cycle causes no difficulty. Since the deluge of Deucalion and Pyrrha is the last one of the cycle and since it immediately precedes the present age, we should thus regard it as marking the transition between the Bronze Age and the Iron Age62, and we have, of course, the certainty that the current age is the worst according to Plato. It then follows that the third great flood, the one in which all the soil was washed away from the Acropolis of Athens by a night of exceptional rains, should coincide with the transition between the Silver Age and the Bronze Age. As for the two other floods, they should correspond to the two remaining transitions of the cycle: the second flood should be placed between the Golden Age and the Silver Age; and the first one, at the very beginning of the Great Year. A further logical inference from this is that the most important transition of the whole cycle, namely, that which separates two successive Great Years from one another, is marked at the same time by a flood and a conflagration - a fact which also gives sense to this reconstruction. Next I should like to show how many other indications there are inside Plato's narrative which have led me to conclude that the Atlantis r,o 61

PLATO,Criti .• l l le-112a.

The same conclusion is found in A. RIVAUD,Timee I Critias, p. 261, n. I: 'II y aurait done eu. en comptant le deluge de Deucalion, quatre deluges, avant l'epoque actuelle'. 62 That the deluge of Deucalion separates the Bronze Age from the Iron Age is further Bihl .. '· 7, 2. confirmed by APOLLODORUS,



myth itself was designed to illustrate a carefully determined period in Plato's great cycle. First of all, the Atlantis myth is the story of a former race of powerful military men, once the inhabitants of an extremely wealthy island, but who later disappeared from the world when an immense flood ravaged their country and made their island suddenly sink into the Atlantic Ocean. Even if Plato's text is abruptly interrupted in its development and was probably never completed, the ethical purport of the myth is obvious: the people of Atlantis were, like the Athenians, a formerly righteous race of men, but their state was devastated because Zeus, the god of gods, decided to punish them for their ever-increasing insolence. The whole myth is concerned with the significant metamorphosis of one of the two countries involved; but, to make things clear, I cannot do better here than to quote the very last lines of the story as it has come down to us: For many generations, so long as the inherited nature of the god remained strong in them, they (the people of Atlantis) were submissive to the laws and kindly disposed to their divine kindred. ( ... ) But when the portion of divinity within them was now becoming faint and weak through being ofttimes blended with a large measure of mortality ('E1td o' ft toii 0&oii µi:v µoipa e~itT)AOc;eyiyv&to ev autoic; 1tOA/,(fltq:>0VT)tq:>Kill 1tOAA.llKlc; dvaK&pavvuµ&VT)),whereas the human temper was becoming dominant dv0promvov ~0oc; E7t&KpO:tEl), then at length they lost their come(to liness, through being unable to bear the burden of their possessions, and became ugly to look upon, in the eyes of him who has the gift of sight: for they had lost the fairest of their goods from the most precious of their parts; but in the eyes of those who have no gift of perceiving what is the truly happy life, it was then above all that they appeared to be superlatively fair and blessed, filled as they were with lawless ambition and power. And Zeus, the god of gods, who reigns by law. inasmuch as he has the gift of perceiving such things, marked how this righteous race was in evil plight (ytvoc; em&tKEc;d01.iroc;Otatt0&µ&vov). and desired to inflict punishment upon them, to the end that when chastised they might strike a truer note. Wherefore he assembled together all the gods into that abode which they honour most, standing as it does at the centre of all the universe. and beholding all things that partake of generation; and when he had assembled them, he spake thus .. Y (transl. Bury)


By far the most conspicuous feature of Plato's narrative is the extremely abundant use he makes of all sorts of numeric values in his description of Atlantis and its people, whereas nothing similar appears in what he says of the rival Athens and its inhabitants. A detailed analysis of these values may be found in Brumbaugh's innovative essay on h.,


Criti., 120e-12lc.



Plato's mathematics, where the author notes: 'In his description of Atlantis in the Critias, Plato gives the exact numbers and measures of almost every phase of its geography, public works, and political institutions. In the description of ancient Athens, in the same dialogue, there is only one numerical detail given (the total fighting strength of the state). This suggests that the use of such specific figures is a device peculiarly appropriate to a description of the Atlantean state and that the specific figures which Plato invents have some characteristics intended to reflect peculiarly Atlantean principles of legislation and technology' 64• More recently, a similar conclusion was arrived at by Vidal-Naquet, who in his study of the present myth rightly compared its structure to Plato's cosmological conception as developed in the Timaeus (with the two fundamental principles, the Same and the Other) and in the myth of the Politicus (with the two opposed revolutions of the world). VidalNaquet's interpretation was mainly concerned with what he called 'la dualite que Platon s'amuse atous moments asouligner et qui montre que la structure de I' Atlantide est celle du deploiement de I' ape iron, de l'alterite' 65 • This perhaps needs some further explanation. One of Plato's main intentions in writing the myth was to illustrate the fundamental difference between two kinds of behaviour: the moderate attitude (primitive Athens), when people stay obedient to the rules originally established for them by the gods, and the insolent attitude (Atlantis), when people are no longer satisfied with their present condition so that they always want to have more66• It is also very clear that this fundamental difference ultimately corresponds to the two basic principles of Plato's philosophical system: the Same, as long as the soul continues to contemplate Unity; and the Other, as soon as the soul starts to become concerned with Duality. In this context, the comparison of our myth with the Timaeus and the Politicus makes a good deal of sense indeed, for we have already seen that the same essential difference underlies the opposition between the two half-cycles of the Great Year: in A, which includes the Golden Age (phase I) as well as the immediate prolongation of it (phase 2), the world is forced by the god to go forward, and Unity is dominant (the Same); in B (phase 3), the world is left to move backwards, and Duality is now in command, leading to Multiplicity (the Other).




Cf. R.S. BRUMBAUGH. /ma>?ination.p. 47. P. VIDAL-NAQUET. 'Athenes', p. 353. Compare, for example. PLATO, Criti .. 113c (Athens) with ibid .. 115d (Atlantis).



Here lies, in my opinion, the key to the interpretation of the myth as a whole. While the former race of Athenians is constantly presented as a sort of remnant of the Golden Age, a period of remarkable fertility and divine justice67, the contemporaneous Atlantean race is one in which a very particular metamorphosis operates: from divinity to humanity, from permanence to change, from Unity to Duality and then Multiplicity. This explains, I think, the moral degeneration in the lines I have just quoted above68, the constant opposition between the stable and terrestrial Athens and the instable, maritime Atlantis 69 , and, of course, the lavish use of all sorts of numbers and mathematical precisions in the account of Atlantis only 70• Now the precise moment of the Great Year at which one passes from Unity to Duality is the world reversal which takes place between A and B, that is, exactly in the middle of the whole cycle. This reversal is, as we have seen, accompanied by a major conflagration, but we should also remember that such a conflagration has no devastating effect on people living near the sea, so that we must admit the possibility of a period in which the same race of men would start before and end after this reversal without being affected by it. In other words, since only floods act as real transitions between one race and the next, we should now consider a system in which the second age, or Silver Age, starts in A with the second flood of the Great Year and does not end before it reaches a certain point in B with the third flood of the cycle. As a matter of fact, there are several elements inside the myth itself which, I believe, allow us to regard the race of Atlantis as the mythical expression of Plato's Silver Age. To begin with, two of these elements appear to fix unambiguously the respective terminus a quo and terminus ad quem of such an epoch: 67

Such a Golden Age, when the gods peacefully shared the regions of the world. is explicitly described in PLATO,Criti., l09b-d (for Athens, with Hephaestus and Athena) and 113b-c (for Atlantis. with Poseidon). 68 Compare, for instance, PLATO,Criti., 12 la-b with the lines following the passage on the Nuptial Number (PLATO,Rsp., VIII. 547a): •And the intennixture of the iron with the silver and the bronze with the gold will engender unlikeness and an unhannonious unevenness, things that always beget war and enmity wherever they arise'. (transl. Shorey) lfl See, above all. PLATO,Tim., 25c-d: •Afterwards there was a time of inordinate earthquakes and floods; there came one terrible day and night, in which all your men of war were swallowed bodily by the earth, and the island Atlantis also sank beneath the sea and vanished'. (transl. Bury) 70 The strangest of all is probably the one concerning the periodic meetings of the kings within the temple of Poseidon in the centre of the island; see PLATO,Criti., I I 9d: ·and thither they assembled every fifth year, and then alternately every sixth year - giving equal honour to both the even and the odd'. (transl. Bury)



(i) From the explicit reference to Evenor - father of Cleito and so the mortal ancestor of the whole race of Atlantis - as one of the few surviving earth-born people, we may assume that the second flood of the cycle, namely, the one between the Golden Age and the Silver Age, had just occurred before the rise of Atlantis71 • (ii) From the necessary identification of the flood mentioned in the Critias - by which the city of Athens is said to have been devastated with the one referred to in the Timaeus - by which both countries are reported to have been ravaged at the same time - we must infer that the end of both races was caused by the third flood of the cycle, namely, the flood between the Silver Age and the Bronze Age72 • In addition to this, we may also note the following indications: (iii) The first king of Atlantis, who gave his name to the island, was Atlas73• One only needs to mention here the obvious connection with the story of the Titan who was forced, as a punishment, to support the world on his shoulders. The comparison is certainly worthwhile, for the story of the unfortunate Titan clearly expresses the end of the Golden Age (Kronos and the Titans) and the beginning of the next Age (Zeus and the Olympians), when mankind is left, like the world in the Politicus, to its natural inclination. (iv) We are told that the Atlantis island was full of all sorts of valuable metals, but that the famous orichalcum (literally 'mountaincopper'), so characteristic of the place, was regarded as 'the most precious of the metals then known, except gold' 74 • Thus, once again, a probable indication that the period considered immediately follows the Golden Age. (v) Between the facts narrated in the myth and Solon's time, the period elapsed is said to have consisted of 9,000 years75 • If we remember that Plato's Great Year consists of 25,920 years in all, and that, according to our hypothesis, the Age of Bronze must be intercalated before the last event, a span of 9,000 years will certainly not appear to be an improbable antiquity for an event belonging to the Silver Age. 71 See PLATO, Criti., I I 3c-d: •And moreover, near the plain, over against its centre, at a distance of about 50 stades, there stood a mountain that was low on all sides. Thereon dwelt one of the natives originally sprung from the earth, Evenor by name, with his wife Leucippe; and they had for offspring an only-begotten daughter, Cleito'. (transl. Bury) 72 Compare PLATO, Criti., 112a with Id., Tim., 25c. 73 Cf. PLATO, Criti., 114a. 74 PLATO, Criti., I 14e. On the orichalcum see R. HALLEUX, 'Orichalque', pp. 64-81. 75 The same value appears on three occasions: PLATO, Tim., 23e; Id., Criti.. I08e and I I la.



Is it possible to determine the respective length of each one of the four Ages? There is, of course, no numeric value of this kind mentioned in any of Plato's works, but this does not prevent us from comparing our present results with other age systems that are known to have been used in classical Greece or elsewhere 76 • A very basic system is the one assuming that the four succeeding Ages, just as the seasons of the solar year, are equal in length, but this does not seem to agree with certain indications in the Platonic myths. In particular, this system would prove hard to reconcile with the myth of the Politicus, in which the Golden Age appears to occupy almost half the entire cycle. We would be better advised, I think, to look for a system in which a general shortening of the ages inside the whole period is assumed. This is unambiguously the system underpinning many classical age theories, and first of all the one expounded by Hesiod in his famous myth of the races. This has already been noticed, among others scholars, by West, who retains this feature as one of the 'striking Oriental parallels' of Hesiod's myth 77 • Although it is certainly not sufficient to validate my attempt at reconstructing Plato's system, the most fruitful comparison of my results is with the Indian system of yugas as it first appears in astronomical treatises in the 5th c. AD. This is one of the four systems that were used in India and later transmitted to the Arabic world, as Pingree notes in his work on Abu Ma'shar's Kitab al-uluf I reproduce here the lines devoted to the particular system of yugas (= System II in Pingree's brief recapitulation): 'The Mahayuga of 4,320,000 years was used in the arddharatrika (midnight) system of Aryabha!a I (c. 500). In this work Aryabha!a follows the orthodox division of the Mahayuga into four unequal yugas whose ratios to each other are 4:3, 3:2, and 2: 1: Krtayuga = 1,728,000 years; Tretiiyuga = 1,296,000 years; Dvaparayuga = 864,000 years; Kaliyuga = 432,000 years. A Grand Conjunction of the mean 76 For a comparison of age systems in many different literatures see the article 'Ages of the World" (several contributors), in J. HASTINGS, ed., Encyclopaedia of Religion and Ethics, l, pp. 183-210. A good summary of most classical representations may be found in F. SEELIGER, 'Weltalter'. cols 375-430. More recently see B. GATZ,Weltalter. For some useful remarks on the doctrine in the esoteric tradition see R. GUE.NON. Formes, esp. pp. I 3-24 ('Quelques Remarques sur la doctrine des cycles cosmiques'); G. GEORGEL, Quatre Ages. is not reliable. 77 Cf. M.L. WEST,Works and Days, p. 174. Parallels are made with Iranian. Biblical. Indian and Babylonian traditions respectively. For the specific comparison of the Indian data with Hesiod's myth sec R. Rom, 'Mythus·. pp. 9-33.



planets only at Aries 0° is assumed for -3,891,101, and another at the end of Kaliyuga in 428,899; since Kaliyuga itself is supposed to begin with a Grand Conjunction of the mean planets only at Aries 0° at midnight of Thursday-Friday, 17-18 February-3101, the mean planets must make an integer number of revolutions every 432,000 years. The Arabs knew this system under the name of al-Arkand' 78 • It is quite remarkable to see how much this doctrine parallels the classical conception, even if we do not have a clear idea of the way the doctrine was actually transmitted. Many elements of the four-age system are probably very old. A good example is the period of 432,000 years assigned to the Kaliyuga, a value which turns out to come from the Babylonian tradition, where it measures the period of the ten antediluvian kings79 • Another, often noted analogy with the classical world particularly relevant in Plato's case - is that the yuga-system coincides exactly with the progression of the Pythagorean Tetraktys, since the four subdividing periods follow the sequence 4 + 3 + 2 + l = l 0. The most conspicuous parallel remains, however, the presence of a general conjunction of the planets which, in exactly the same way as in Plato's definition, marks the transition between a great cycle and the next. All these similarities have prompted scholars - e.g. van der Waerden - to draw some straightforward conclusions about the necessity of a common source for these different traditions80 ; but the problem is far more complicated than he assumed. It is certain that such a yuga-system existed in India before the 2nd c. AD, but its first application to astronomy does not seem to appear in literature until the early 5th c. AD, when Indian astronomers start to combine it with the Ptolemaic doctrine of epicycles as well as with the Platonic assumption of conjunctiona] Great Year. In other words - as David Pingree kindly pointed out to me -, it would not be legitimate to use the Indian system of yugas in the proportion 4:3:2: 1 to explain Plato, since Plato's influence on Indian speculations proves to postdate the existence of this system itself. I must leave aside the vexing but quite unanswerable question of whether a system based on exactly the same ratios was used independently by Greek and Indian thinkers, let alone the possibility that both 78

Cf. D. PINGREE, Thousands, p. 28; see also: G. IFRAH,Histoire, II, pp. 184-9. On the influence of the doctrine in Islam, see D. PINGREE, 'India and Iran', pp. 229-46. For a general account of Indian astronomy, see R. BILLARD, Astronomie indienne. 79 On the Babylonian origin of the number 432,000 see D. PINGREE, 'India and Iran'. p. 238; see also CHAPTER V, SECTION A p. 135. For the use of this number in Babylonian Berossos, pp. 261-3. chronology see P. SCHNABEL. w See B.-L. van der WAERDEN, 'Gro8e Jahr', p. 150.



systems go back to a common source which predates by far the written evidence of the doctrine as we know it from extant literature. When taken for itself - and this is the point I wish to emphasize -, it remains that the inner coherence of Plato's myths is best interpreted when one assumes for the Great Year a subdivision into four periods that follow the proportion 4:3:2: I, which gives the following values: 10,368 years (Golden Age) + 7,776 years (Silver Age) + 5,184 years (Bronze Age) + 2,592 years (Iron Age) = 25,920 years. Let us consider the place of the Silver Age of such a system: it appears at once to be the only period which extends across both half-cycles of the Great Year. This peculiarity, I think, fits remarkably well with the interpretation of the Atlantis myth I have proposed. For it helps us to understand why Plato proves so eager to distinguish between the two sub-periods of that age: on the one hand, the period of the cycle which no longer belongs to the Golden Age but still sees the dominion of the divine principle(= phase 2 of A); on the other hand, the beginning of the period in which the human principle is dominant (= first part of phase 3). The two sub-periods of the Silver Age, it should be noted, are themselves in the ratio I :2, thus expressing once again the critical transition from Unity to Multiplicity. As for the general conjunctions of the planets that is the main feature of Plato's Great Year, common sense would suggest making them correspond to each one of the world reversals, thus every 12,960 years. The two 12,960-year periods of Plato's Perfect Year, based on the two respective principles of Unity and Duality, would thus reproduce exactly, in the ratio I: 1000, the two harmonies of the Nuptial Number.

B. In Search of Aristotle's Greatest Year Paradoxically enough, the best evidence for assuming the existence of an Aristotelian Great Year is not to be drawn from Aristotle (384-322 BC) himself, nor even from any of his commentators. This evidence appears instead in Censorinus's De die natali, an important Stoic treatise about chronology that was written in 238 AD81• The relevant lines are those with which Censorious concludes his remarkable report on magni anni - a text which I shall study in detail later82• Thus, having recalled all sorts of

81 On the De die natali see the following recent works: G. ROCCA-SERRA. Censorin; K. SAU.MANN.Censorinus; C.A. RAPISARDA, De Die Natali. K,See CHAPTERII, SECTIONB pp. 68-72.



cycles that are of greater length than the solar year, Censorious at last comes to the genuine, conjunctional Great Years. The text runs as follows: We find. moreover, the Year which Aristotle calls 'the Greatest' (maximum) rather than 'Great' (magnum), and which is completed by the revolutions of the Sun, the Moon and the five planets, when these stars come back once again to the same sign in which they once were together (cum ad idem signum, ubi quondam simul fuerunt, una referuntur). The supreme winter (hiemps summa) of this Great Year is the KataKAucrµ6r;,that we Latins call 'flood' (diluvionem). and its summer is the £K1t6procrtr;, i.e. the conflagration (incendium) of the universe. Indeed, the universe seems to be resolved now into fire and now into water, alternately. As for the length of this Great Year, Aristarchus assigned 2,484 solar years, Aretes of Dyrrachion 5,552 years. Heraclitus and Linus 10,800 years, Dio 10,884 years, Orpheus I 20,000 years, and Cassandrus 3,600,000 years; but other authors have thought that its duration is infinite and that it never comes back83.

Censorinus's statement raises some problems. Such a definition of the Great Year is nowhere to be found in Aristotle's extant works, although the matter itself is not incompatible with some well-known Aristotelian tenets such as the doctrine of recurrent cycles of knowledge 84 • The alleged incompatibility of sources has prompted some scholars to doubt Censorious' s own reliability85• On the other hand, the Latin chronographer has generally been proved to be trustworthy in what he says and, above all, the reference to Aristotle is here much too explicit to be disregarded without a closer investigation. l. The Lost Protrepticus Modern scholarship has long looked among Aristotle's lost works for the possible origin of this assertion. In his edition of Aristotle's fragments, Rose included it in the De philosophia 86 , while Usener strongly defended the idea that Censorious could only be referring here to the Protrepticus 81 • Subsequent scholars have largely followed the latter of 83

CENSORINUS, De die nal., 18, 11. See, for instance, ARISTOTI.E, Meteor., I, 3, 339b: 'For we maintain that the same opinions recur in rotation among men, not once or twice or occasionally, but infinitely Po/ii., VII. 9, 1329b. often' (transl. Lee); similarly, ARIST0TI.E, 85 Cf., for instance, G. ROCCA-SERRA, Censorinus, p. 63; C.A. RAPISARDA, De Die Natali, p. 228. 86 Cf. V. ROSE,Fragmenta, p. 39 [= ARISTOTI.E, De phi/., fr. 25] and, before him, J. BERNAYS, Theophrastos, p. 170. 87 Cf. H. USENER,'Vergessenes, II', pp. 392-403. Among recent editions or. more exactly, reconstructions of Aristotle's Protrepticus see: I. DORING,Protrepticus; A.-H. CHROUST, Protrepticus; G. SCHNEEWEISS, Protreptikos. 8-1



these views, so that it is now generally agreed that the Protrepticus is the most probable source of Censorinus's statement 88 • Rightly so, it seems. For among the texts which are known to have been widely influenced by Aristotle's treatise, one must particularly mention, along with lamblichus's Protrepticus 89 , a work by Cicero, the Hortensius, which in Antiquity was already regarded as a treatise written ad exemplum protreptici 90 • Cicero's work is lost too, unfortunately, but so many fragments have survived that it has been possible to produce reconstructions of the Hortensius 91 • These reconstructions confirm that Cicero's treatise was a kind of Latin Protrepticus, in which Aristotle's main ideas were put into dialogue form 92• One of these significant ideas is that glory, wealth and pleasures should be considered futile matters, and that the practice of philosophy is the best way to get rid of vanity and superficiality. This is an important element in our investigation, for we know that in the Dream of Scipio - a work written a few years before the Hortensius -, Cicero had developed his views on the Great Year in exactly the same perspective. Here I quote the most relevant lines from that text: But even if future generations should wish to hand down to those yet unborn the eulogies of every one of us which they received from their fathers, nevertheless the floods and conflagrations (eluviones exustionesque) which necessarily happen on the earth at stated intervals (tempore certo) would prevent us from gaining a glory which could even be long-enduring, much less eternal. But of what importance is it to you to be talked of by those who are born after you. when you were never mentioned by those who lived before you, who were no less numerous and were certainly better men; especially as not one of those who may hear our names can retain any recollection for the space of a single year? For people commonly measure the year by the circuit of the Sun, that is, of a single star alone; but when all stars return to the place from which they at first set forth, and, at long intervals (/ongis inte111allis), restore the original

88 See: R. WALZER,Fragmenta. p. 65 [= ARISTOTLE, Protr., fr. 19); D. Ross, ed., Works, p. 55 [= ARISTOTLE. Protr .• fr. 19). The fragment is. however. not taken up in I. DORING. Protreptirns (see the discussion, pp. 167-8). See also W. JAEGER, Fundamentals. pp. 154-6. 89 On lamblichus·s Protreptirns see the recent edition by E.des PLACES. Jamhlique. 90 See TREBELLIUS POLLIO,Vita Gallien., 20, I. 91 For references to these reconstructions see CHAPTER I, SECTION C p. 50. 9 ! See W. JAEGER. Fundamentals, p. 55: 'When Cicero in his Hortensius put the ideas of Aristotle's Protrepticus into dialogue fonn, he thought it necessary to announce the alteration even in the title'. On a fonnal comparison between both works, cf. M. RucH. Hortensius. pp. 20-5 (= Chapter 111,'La fonne du Protreptique chez Aristote et chez Ciceron").



configuration of the whole heaven (eandem totius caeli descriptionem), then that can truly be called a Revolving Year (vertens annus). I hardly dare to say how many generations of men are contained within such a Year93 • (transl. Keyes)

Now there is some evidence that Cicero took up this view again in his Hortensius, and we have good reason to believe that in this treatise the author provided his readers with an even more detailed exposition of the Great Year doctrine. First, both Tacitus and Servius mention the Hortensius as the source in which the length of the Ciceronian Great Year namely 12,954 solar years - can be found 94. Above all, we learn from Augustine that Cicero dealt, also in the Hortensius, with that famous eclipse which was supposed, according to the Somnium 95 , to have coincided with Romulus's death - a significant indication indeed, for we know the important role that the same eclipse played in the computation of Cicero's Great Year 96 • The passage from Augustine's De civitate Dei reads: In the dialogue Hortensius, moreover, speaking of the regular eclipses of the Sun (so/is canonicis defectionibus). he (Cicero) says: •... in order to produce the same darkness that was produced at the time of Romulus's passing, which took place when the Sun was obscured 97 .' (transl. McCracken) What does Augustine mean by 'regular eclipses•, if not that these eclipses are mathematically predictable, as opposed, for instance, to the truly miraculous eclipse which took place at the time of Jesus's crucifixion98? And what would be the point of Cicero mentioning these regular eclipses, if not to stress, as Grilli has already noted, that they are to be taken as partial elements of a mathematical computation 99 ? This is exactly what Cicero invited his readers to do in the Dream of Scipio, and I think I have correctly inferred, mainly from the De natura deorum, the values to be taken into account for the computation of Cicero's Great Year, namely: 30 (Saturn) x 12 (Jupiter) x 2 (Mars) x l (Venus and Mercury) x 18 (Sun and Moon according to the Soros-cycle,

93 94

95 96

97 98 99

CICERO, De rep., VI, 23-4. Cf. TACJTUS, Dial., 16; SERVIUS, in Aen., I. 269 and Ill. 284. Cf. CICERO,De rep., VI, 24. On all this see CHAPTER I, SECTION C p. 49. CICERO,Hort., ed. Ruch, fr. 68 [= AUGUSTINE, De civ., Ill, 15]. Cf. AUGUSTINE, De civ., Ill, 15. Cf. A. GRILLI, Hortensius, pp. 164-5.



or cycle of solar eclipses)= 12,960 years, which I assume to be the real length for the Ciceronian cycle 100 • Since th~ Hortensius is precisely the dialogue in which a very close variant of this length was explicitly stated, and since this dialogue also made reference to the periodicity of solar eclipses, it is probable that it included a computation of the same kind. If we remember, moreover, that Cicero's thought in the Hortensius is thoroughly permeated with what Aristotle had written in the Protrepticus, are we not justified in assuming that the Great Year doctrine might have been discussed in the Aristotelian model as well? This hypothesis has already been proposed by Usener, who even suggested, with uncharacteristic confidence, that the famous eclipse predicted by Thales could have played a role in the Protrepticus comparable to that of Romulus in Cicero's Somnium, but this was probably going too far 101 • Yet one should certainly not reject the idea that a proper definition of the conjunctional Great Year, together with a method of computing its length, might have been part of Aristotle's original writings. After all, the different figures belonging to the computation I conjecture in Cicero's case were all well-known values by Aristotle's time. Moreover, Censorinus's definition of the Aristotelian Great Year - namely, the return into conjunction of the Sun, the Moon, and the five remaining planets in the same (zodiacal) constellation in which they once were together - is not inconsistent with the conception we find in Cicero's works. In the De natura deorum we find a definition which is, indeed, very similar, although not identical, to the one just quoted. Cicero says the following: On the diverse motions of the planets, the mathematicians (mathematici) have based what they call the Great Year, which is completed when the Sun, Moon and five planets, having all finished their courses, have returned to the same positions relative to one another (ad eandem inter se comparationem ). The length of this period is hotly debated (ma,:na quaestio est), but it must necessarily be a fixed and definite time 102• (transl. Rackham)

Similarly for the lines that follow in Censorinus's statement, namely that Aristotle's Great Year has a supreme winter and summer which correspond respectively to a great flood and a great conflagration; all this is in accordance with, if not absolutely indistinguishable from, what we read in the passage from Cicero's Somnium quoted above. 100

IOI 101

For this computation see CHAPTER I, SECTION C pp. 54-58. 'Vergessenes, II'. p. 400. CICERO, De nat .. II, 51.

er. H. USENER.



A very important element in this discussion is, of course, the use of the expression 'Greatest Year' (maximus annus) instead of 'Great Year' (magnus annus), a rare designation that Censorious explicitly ascribes to Aristotle himself. In any case, one may assert with confidence that Censorious did not invent the designation of Greatest Year, for the Greek expression µtyuno~ eviaut6~ already appears in a passage from Arius Didymus, a Stoic philosopher of the epoch of Augustus. This text, which has been preserved by Eusebius, reads: When common reason has come to this point and when common nature, by increasing and multiplying, has ended up absorbing all things, bringing all things back to itself, they form the whole substance, by going back to this first reason that has been described and to this order that produces the Greatest Year (lvtautov tov µ&ytcrtov), according to which the restoration (d1to1Cat6.0taotLINY THE ELDER, Nat. hist., x. 3-5. SJ FIRMrcus 54



between 500 and 1,461 years56 , and Solinus - who adapts Pliny's statement - leaves his readers undecided between the figures of 540 and 12,954 years57 • Whereas the figures of 500 and 540 years do not seem to correspond to the measure of any astronomical cycle, one has no trouble to recognize those Great Years of 1,461 and 12,954 years - two cycles which, from the strictly astronomical point of view, have nothing whatever to do with one another. II. The Vain Demonstrations of the Greeks

A number of astrological texts refer to an immense Great Year of 1,753,200 years, in which the general conjunction of the planets takes place either in the last degree of Cancer or in the first degree of Leo. According to these sources, the first of these conjunctions is accompanied by a deluge while the latter is marked by a major conflagration, so that the two calamities are separated from one another by only one degree of the Zodiac. First I quote a passage from the De mensibus of Lydus (5th/6th c. AD): Saturn completes its return to the same point (a.xoKatacrmow) after 265 years, Jupiter after 427 years, Mars after 284 [corr. ex: 294) years. the Sun after 1,461 years, Venus after I. 151 years, Mercury after 480 years, the Moon after 25 years. The universal return (TJSi: tou xavtoc; a.1to1Catacnamc;) talces place after 1,753,200 years, and this is when the conjunction of all planets (cruvo6oc; xavtwv to>Va.crt&pwv) talces place at Cancer 30° or at Leo I 0 • A deluge should occur in Cancer and a conflagration in Leo. Yet this (conflagration) would not be universal (Ka0oA.lKTJ),as the Stoics believe it, but wholly partial (µEptKiJ) 58 •

This statement is taken up by the Byzantine Platonist Michael Psellus ( 11th c. AD) in a paragraph of his De omnifaria doctrina entitled 'Whence one may know the end of the world through the demonstrations of the Greeks'. Psellus's paraphrase provides us with some elements of interpretation: Of the last day and hour, no one knows, according to the word of the Gospel, except for the Father and his co-eternal Son, and the Spirit who proceeds from the Father. But the Greeks strive hard to know this too by way of vain demonstrations (EA.A.TJVEva.xo6Ei~ewv). Saturn completes its greatest return to the same point in 265 years, Jupiter in 427 years. Mars in 284 years, the Sun in 56



Sow,us. Collect., 33, 13 (* ). LYDIIS, De me11J., III, 16.

.v £tO)V Kai C1ttaKOCJlO)V t~aoµriKovta Kai t1tta). How then, I ask, will human observation for one birth be able to harmonize with so many ages; and this not once, but oftentimes ... [the rest is lost] 19• (transl. MacMahon) IK SEXTUS EMPIRICUS, 19

Adv. math.,



103-6. Rtfur., IV, 7 (*).



The validity of the correction is further confirmed by the fact that in his Placita philosophorum the Pseudo-Plutarch (2nd c. AD) concludes his list of Great Years with a cycle of precisely the same length20 • The number 7,777 has a clear Apollonian resonance, as has been convincingly demonstrated by Burkert in a recent article devoted to an oracular text that was found in the city of Olbia (on the Russian coastline of the Black Sea)21 • This oracle text, dated from the 6th c. BC, links the numbers 7, 70, 700,. and 7000 to Apollonian symbols in a progession that expresses, according to the author, the number of years that the new city was expected to survive. It goes without saying, on the other hand, that the connection of the number 7,777 with the problem of the conjunctional Great Year is a much later invention.

C. The Growing Hostility of the Christians As Duhem noted in his inquiry on the Fathers of the Church and the Great Year, we have abundant evidence that the Christians did not oppose, at first, the idea of recurring world cycles; rather they viewed the theory as a sort of confirmation of Biblical material22• I. The Pagan Distortion of the Bible

A good example of this attitude is Clement of Alexandria (2nd-3rd c. AD), who in his Stromateis considers the theories of floods and conflagrations of ancient Greek philosophy as little more than plagiarism of Moses's teaching. Heraclitus and the Stoics are mentioned in this context, but it is Plato's Timaeus which mostly engages his attention: Plato also states in like manner that the Earth is purified at certain times by fire and water: 'There have been many destructions, in many ways, which have struck men and which will strike them again; the biggest ones by fire and water, smaller ones in countless different ways' [= PLATO, Tim., 22c]. And a little later he adds: 'The truth is that a reversal takes place in the heavenly bodies which revolve around the Earth, and that, at large intervals of time, a destruction occurs of earthy things, by the abundance of fire' [= PLATO, Tim., 22d]. Then, speaking of the flood: 'But when the gods


2 Cf. Pl.UTARCH (PSEUOO-), Placit., II. 32. For a detailed examination of this text see CHAPTER IV, SECllONA pp. 103-106. 21 Cf. W. BURKERT, 'Olbia', pp. 49-60 (for the article) and 145-9 (for the notes and bibliography). Burkert refers to the Placita philosophorum of the Pseudo-Plutarch. but does not mention either Sextus or Hippolytus. 22 Cf. P. DuHEM,Systeme, II, p. 447.



purify the Earth in submerging it, those who are in the mountains, cattlemen and shepherds, are saved, while the inhabitants of our cities are carried away to the sea by the rivers' [= PLATO,Tim., 22d-e]. I have shown in the First l:tproµmi:uc; that the Greek philosophers deserve to be called thieves, for they have taken their main tenets from Moses and the prophets, without any acknowledgement of debt 23.

Clement uses and briefly defines the expression 'Great Year' in one passage of his Stromateis, but there does not seem to be much to say about a vaguely christianized statement in which the Great Year only finds itself related to the general symbolism of number eight on account of the fact that there are eight celestial spheres: And they (the Pythagoreans) call the ogdoad a cube, counting the fixed sphere in addition to the seven wandering spheres, by which the Great Year (µtyac; tviaut6c;) is produced, as a kind of period for the repayment of what has been promised (ofov 1ti:pioo6c; nc; tiic; tci>v £7tTJYYEA.µtvrov dvta1too6cri:roc;)24•

Minucius Felix (c. 200 AD) is another of those Early Christian thinkers who believed that the theory of catastrophes belonged in fact to the Biblical tradition. In the Octavius, for instance, this defender of Christianity goes as far as to pretend that the pagan philosophers of Greece did nothing more than to disfigure the pure and divine predictions of the Christian prophets: As for the destruction of the world by fire, it is a vulgar error to regard a sudden conflagration, or a failure of moisture as incredible. What philosopher doubts, or does not know, that all things which have come into being die, that all things created perish, that heaven and all things therein cease as they began. So too the universe, if Sun, Moon and stars are deprived of the fountains of fresh water and the water of the seas, will disappear in a blaze of fire. The Stoics firmly maintain that when the moisture is dried out, the universe must all take fire. And Epicureans hold the same about the conflagration of the elements and the destruction of the universe. Plato speaks of parts of the world as subject alternately to floods and to fire; and while maintaining that the universe itself was created eternal and indissoluble, adds that only God himself, who created it, can make it dissoluble and mortal. What wonder then if it should be destroyed in its entirety by him who built it up! The philosophers, you observe, use the same arguments as we; not that we have followed their footsteps, but that they, from the divine predictions of the prophets, have borrowed the shadow of a garbled truth 25 • (transl. Kerr) 23 CLEMENT OF ALEXANDRIA, 24 CLEMENT OF ALEXANDRIA,


Strom., V. I. 9-10 (*). Strom., VI, 16, 140 (*). Octav., 34, 1-5.



A clearer attempt at reconciling pagan and Christian tenets on the question of periodic purgations of the universe may be seen in the Adversus nationes of Amobius (c. 300 AD). The main purpose of this work was to show that the Christians could not be held responsible for the numerous catastrophes which had occurred in the recent troubled days, and Amobius naturally argues that similar calamities, of which he will then proceed to give famous historical examples, had already taken place long before the Christians: When was the human kind devastated by inundating waters? Was it not before us? When was the universe burnt and dissolved into dust and ashes? Was it not before us26?

Now, one may wonder, if the Christians are not reponsible for them, where do these great misfortunes to mankind come from? Amobius does his best to answer this question, and his argumentation has the air of a rather curious mixture of pagan physics, astrology and philosophy: Who knows, indeed, whether the primeval matter which is dispersed among the four elements does not contain the causes of all misfortunes rolled in its own irritations? Who knows whether the movements of the stars do not generate these diseases through certain signs, places, times, or rays, and if they do not bring to those whom they influence the necessity of undergoing various critical experiences. ( ... ) Plato, the apex and summit among philosophers, stated in his writings that those harsh floods and conflagrations are a purgation of the earth (purgationem terrarum), and this wise man was not afraid to call renewal of things (rerum innovationem) the overthrow, the destruction, the ruin, the annihilation and the death of mankind, and that a certain rejuvenation (iuventutem quandam) was produced from the restoration of its strength 27 •

Duhem was right to compare this text with the end of the passage that Calcidius (4th/5th c. AD), another Christian, later devoted to Plato's Great Year in his influential commentary on the Timaeus: I

Yet one should not believe that this motion and configuration will bring ruin and dissolution to the world, but rather that some restoration (recreationem) and. as it were, some new vigour (novel/am viriditatem) will be placed under the auspices of a new motion. I do not know whether any harm would originate from this renewal (innovatione) in some parts of the world 28 •

Whereas Amobius believes that universal catastrophes are likely to take place in our world - still stressing that they only act as a purgation 2b ARNOBIUS. 27



Adv. nat., I, 4, I. Adv. nat., I. 8, 2-7. in Tim., 39d (*). On

lhis see





B pp. 106-108.



of it -, Calciclius simply denies the possibility of their existing. Both writers agree, however, in stating that some sort of general and periodic rejuvenation of the world is generated, at long intervals of time, by the recurrence of certain astronomical cycles.

II. The Attack on Astrology The attitude of Early Christian authors towards the pagan theory of world cycles with recurrent floods and conflagrations was generally not so conciliatory. In particular, the astrological postulate that historical events could be influenced by the regular movements of the stars was to be strongly criticized in many Christian works, and we have already seen that Hippolytus of Rome did not hesitate to take up again the argumentation of the Sceptic Sextus Empiricus in order to refute the Great Year of the astrologers 29• Among those who adopted a very hard-line position on this matter, one must in the first place mention the name of Origen (185-253/4 AD), Clement's successor as head of the Christian School of Alexandria. I should first like to single out the passage from Origen's De principiis in which one finds probably the three most frequent objections to the Great Year doctrine raised by the defenders of Christianity until the end of the Middle Ages and the beginning of the Renaissance. Following a procedure very typical of those polemical treatises, Origen begins with a reductio ad absurdum of the doctrine he wishes to castigate. Origen does not name any partisan of the theory he condemns, but it is clear from what he says that the Stoics are quite central on the target: As for those who assert that worlds are without any dissimilarities and that they succeed one another, being perfectly similar to each other, I do not know on which sources they can base their assertion. For if a world is said to be similar, in every respect, to another world, it will follow that, once again, Adam and Eve will do the very things they have done; that there will be another flood; that the same Moses will, once again, lead out from Egypt a people of 600,000; that Judas himself will betray his lord a second time; that Paul will, once again, guard the clothes of those who stoned Stephen to death, and everything which took place in this life is said to take place once again 30• 29 HIPPOLYTUS OF ROME,

Refut., IV, 7 (*). ORJGEN,De princ., II, 3, 4. Origen, it should be noted, takes his examples from the two testaments. This is in fact a Christian adaptation of a story where examples are usually taken from ancient Greek philosophy; cf. also ORIGEN,Contra Cels., IV, 68 (where he mixes both kinds of examples) and V, 20 (where he gives the more common example of Socrates's life and deeds). 30



Origen next proceeds to develop his three fundamental objections: (i) The first is the absolute incompatibility of so determinist a view with

the free will of human souls: I cannot think of any reason why this could be asserted. since souls are guided by free will (arbitrii libertate), and since they go through progressions or recessions by virtue of the strength of their will (pro voluntatis suae potestate). Indeed, souls are not guided to do or to desire this or that by virtue of some course which comes back to itself, after many centuries, according to the same revolutions, but, on the contrary, they guide the course of their deeds to where the freedom of their own minds (proprii ingenii libertas) has led them31•

(ii) The second objection, perhaps a little less expected here, is that the

theory of endless recurrences turns out to be a mathematical impossibility. Origen's point is an appeal to common sense rather than to a proper mathematical demonstration. The very curious thing about Origen's statement is his avowed ignorance in regard to the number of possible coexisting worlds32 , which makes the Christian Father closer to Epicurus than to anyone else: We can compare the assertions of those people with the situation of someone who would like this to be possible: namely that, for a measure of corn poured out deep into earth, the same grains should fall a second time in exactly the same way, so that every single grain should be poured out next to the one which had been poured out with it on the previous occasion, and that they should be spread out according to the same order and the same pattern as those according to which they had been first dispersed. Now, since there is a countless number of grains in a measure, it is absolutely impossible that this should take place, even if the grains should be poured out unceasingly and indefinitely, during a boundless number of ages (etiamsi per immensa saecula indesinentur ac iugiter effundantur). In the same way, it looks impossible to me that a world should be renewed a second time, according to the same order and to the same conditions in regard to those who are born, who die, and who live. On the contrary, worlds may exist, which diverge from one another by not so minimal changes, so that for obvious reasons the state of a world should be better or, as the cases may be, inferior or equivalent. As for the number and the situation of these 31

De princ.·.,II, 3, 4. Origen's hesitancy on the number of worlds leaves him in a vulnerable position; see R. SORABJI, Time, p. 186: 'Origen's solution is not quite satisfactory. He confesses himself ignorant how many worlds there may have been. But there seems to be a dilemma: if there was a first one with a beginning, the question remains what God was doing before that. If, however, there was an infinity of differing successive worlds, or a first one without a beginning, the question remains how on Origen's view God can comprehend an infinity of worlds or of days'. 32




worlds, I confess my ignorance: should someone make this clear for me, I would learn it with great pleasure 33 •

(iii) The last objection is the one most concerned with the preservation of the Christian message, since it deals with the uniqueness of Christ's incarnation and the very sense of His mission: As a matter of fact, this world is said to be the end of many ages, and is itself called an age. Yet the saint and apostle teaches that Christ did not suffer in the age which came before this one, nor even in the age which was before that one, and I do not know whether I could enumerate all the previous ages in which He did not suffer. In order to understand this, I should rather like to quote some words of St Paul; for he said: 'Now only once, at the consummation of the ages, has He revealed Himself, so as to repel the sin by becoming Himself a victim' [= Hebrews, 9, 26]34 •

The other important work in which Origen condemns the pagan doctrine of endless recurrences is his Contra Celsum, a violent diatribe against the Platonic philosopher of the 2nd c. AD famous for his many attacks on the Christian dogma. In several passages of this work, Origen accuses Celsus of having taken up Plato's view on periodic deluges and conflagrations while he would have been better inspired to follow Moses instead: But let this man who attacks the faith of the Christians tell us by what sort of arguments he was forced to accept the doctrine that there have been many conflagrations and many floods, and that more recent than all others is the flood in the time of Deucalion and the conflagration in the time of Phaethon. If he adduces the dialogues of Plato as authority for these, we would say to him that we can also believe that in the pure and pious soul of Moses, who rose above all that is created, and united himself to the Creator of the universe, there dwelt a divine spirit which showed the truth about God far clearer than Plato and the wise men among the Greeks and barbarians 35 • (transl. Chadwick)

Further on in the same work, Origen comes back to the anteriority and superiority of the Christian faith over the vain beliefs on world cycles that the heathen seemed to accept so widely. On this occasion we find him quoting some words from the Bible that were to enjoy a remarkable success among the Christian authors who later dealt with the hypothesis of recurrent world cycles:



De princ .. II. 3, 4. De prim·., II. 3, 5. Contra Cels .. I, 19.



It is not the right time to say whether or not there are cycles, and floods or conflagrations in each cycle, and whether this doctrine is mentioned in the Bible, as in these words of Solomon among many others: 'What is it that has been? That very thing which shall be. And what is that which has been made? That very thing which shall be made' [= Ecclesiastes, I, 9], and so on. It is enough merely to remark that Moses and some of the prophets, being men of great antiquity, did not receive from others the idea of the world conflagration. The truth is rather, if we may pay regard to the matter of their dates, that others misunderstood them and failed to reproduce accurately what they said, and invented the notion that identical occurrences happen periodically, which are indistinguishable from one another in both their essential and their incidental characteristics (Kata 1t&p16001> autcp ;cpoicp tcp tat'.>pcp yey6vaow ol €1tta 1tA.avcoµevot),if not all to the same degree, so that they all are likely to come back to the same sign51 •

Modem calculations confirm, indeed, the truth of Philoponus's assertion: in May 529 AD, all seven planets were gathered together in the constellation of Taurus 52• 49 Reference to the Protrepticus is made in ALEXANDER OF APHR0DISIAS, in Top .• p. 149, II. 9-17. De opif., IV, 14: 'Each one of the planets completes its own year, of so PHILOPONUS, which the slowest one is concluded after 30 solar years. The Great Year is said (to occur) when the restoration of the seven (planets) takes place, from one sign to the same (dm.'> tOUautoii t:lc;to auto CTT]µt:iov d1to1mtacrtaitthan 'apex', which I use in the sense of turning-point (for a planet) or solstice (for the Sun). 56 Cf., for instance, GEMINUS, lntrod., I, 9-13; HYGINUS, Astron., IV, 5; PHIL0PONl'S. De opif., IV, 14. 54



Olympiodorus, as we can see, was perfectly right to mention the zodiacal signs in the way he did; only his text would have been a little clearer had he named them in a more symmetrical manner. That Olympiodorus believed this theory to be that of Aristotle himself is apparent from a passage a little further on, when the commentator states: He (Aristotle) wants to explain why, according to the arrangement of the Great Year (01' ftv tv tfi tal;et tou µeyaA.ou tvmutou), it happens that, during the summer, the sea becomes a mainland, while the opposite occurs during the winter. This is, he says, because the parts of the earth flourish and decline in the same way as living beings do. For they flourish when they receive moisture and decline when they become dry. They become wet when it is cold, i.e. when the winter talces place. They become dry when it is warm, i.e. when the summer arises 57 .

As for the exact meaning of the expression 1tavtrovtrov 1tAavrrcrov ta~1i:;,there can be no doubt that it refers to the general conjunction of the planets, for a few lines later and in the same context Olympiodorus uses an expression that is not at all equivocal: Aristotle says that parts of the earth, such as perhaps the mountains, fall apart by becoming dry and burnt by the Sun. And if the Sun alone is not strong enough to do this, still the conjunction of all the planets (cruvoooc; 1tavtrov tci>V1tAavfitrov) or the typhoons, the hurricanes and the thunderbolts are. For these are strong enough to inflame and destroy the mountains58.

I would summarize this investigation of Aristotelian commentaries in the following way. The Stoic Censorinus speaks of a Great Year that he ascribes to Aristotle. As in Plato's Timaeus, this cycle is defined as the period required for all planets to come back into conjunction in a certain place in the heavens. But the main feature of this Greatest Year, unlike Plato's Perfect Year, is that it is modelled on the image of the solar year, with its recurrent cycle of alternate seasons: a great flood is said to take place in the winter of the Great Year, while a major conflagration is believed to occur during its summer. This conception is very close to the Babylonian Great Year, which was transmitted to the classical world, notably through Berosus, and which was especially favoured by the Stoics. Although we must admit that some adaptation had to be made in order to reconcile both systems, especially in relation to the proper scale 57


OLYMPI0DORUS, in Meteor., l, 14, 35 la 26, p. I 14. II. 26-31. OLYMPIOOORUS,inMeteor.,l.14,351a31,p.115,ll.18-22.



to be assigned to the great floods and conflagrations, there is strong evidence, from the extant works of Aristotle and his commentators, to surmise that Censorinus's attribution should not be dismissed altogether.

E. A Foretaste of the Precessional Great Year in Macrobius

In passing I mention two brief statements on the Great Year that seem to be connected with Cicero's reflections. The first is a definition that was to be found in the De verborum significatu of Verrius Flaccus (1st c. BC - 1st c. AD), a lost encyclopaedic treatise that has been preserved in part in an abridgment by Sextus Pompeius Festus (2nd c. AD), itself abridged, much later on, in the Epitome of Paulus Diaconus (c. 720 - c. 799 AD). The article "Magnum annum" reads: Astrologers (mathematici) call a Great Year (magnum annum) the period required for the seven planets to reach a common accord (sibimet concordant) after having completed their own courses 59•

This text has a possible link with Cicero's De natura deorum, the only earlier source I know that refers so explicitly to the Great Year as a problem dealt with by the mathematic,-oo.The other passage I should like to quote is extracted from the Uber explanationum in rhetoricam M. Tu/Iii Ciceronis by a certain Fabius Laurentius Victorinus. It is quite safe to assume that Victorinus knew at least some of Cicero's loci on the Great Year, although it would be difficult to single out the one he may have used in particular. What is clear, however, is that the annus magnus referred to by Victorinus in this passage has an astrological undertone which is not at all Ciceronian: Seven stars, on seven circles, revolve backwards around the heaven, and each one of them requ,ires a certain period of time to come back to the same sign where it started its motion from. But when they all come back together to those signs from which they started (quae cum singulae ad idem signum, unde profectae sunt, revertantur), then is produced that period of time which one calls the Great Year (tune fit illud tempus, quod annus magnus dicitur), and it is necessary that every thing should be born again in its proper order (et necesse est omnia rursus per ordinem suum, quae ante nata sunt, renasci). Thus a Great Year occurs when all stars come back together to their own starting-points 61 • sq Verrius Flaccus in FESTUS, De l'erh., p. 131, art. Magnum a1111um. 611 Cf. CICERO, De nat., II. 51-2. See also CHAPTER I. SECTION C p. 36. 61 VICTORINUS, Uber exp/.• I, 26.



The relevance of these two statements is only trifling, anyway, when compared with the section on the annus magnus that is contained in the famous commentary on Cicero's Somnium by Macrobius (c. 400 AD), one of the most influential texts ever written on the Great Year. Cicero stated in the Somnium that the true 'Revolving Year' (vertens annus) was the one completed when all the planets came back to the places which they held previously, in such a way that the original configuration of the whole heaven is finally restored. In that passage, as we may remember62, Cicero did not mention the length of the Great Year as explicitly as he is reported to have done in the Hortensius, but he proved nevertheless eager to specify that a twentieth part of the cycle had not elapsed between the eclipse at the moment of Romulus's death and the time of Scipio's dream itself. Macrobius's interpretation of those lines starts with his distinction between the solar year and those other years that designate the individual periods of revolution of the other planets. This explanation - for which Macrobius refers to the Virgilian verse containing the expression magnus annus - shows some striking similarities to the one made by Servius in his comment on that verse63 • I shall not quote here that part of Macrobius's interpretation 64, since the rest of the passage deserves to be examined in much greater detail. It runs as follows: But the so-called World Year (Annus vero qui mundanus vocatur), which is the True Year's round (qui vere vertens est), since it is measured by a revolution of the whole universe (quia conversione plenae universitatis efficitur), is accomplished in very long ages (largissimis saeculis), the explanation for which is here presented. All stars and constellations (stellae omnes et sidera) which seem fixed in the sky and whose peculiar motions no human can ever discern, nevertheless do move, and in addition to the rotation of the celestial sphere (et praeter caeli volubitatem) by which they are pulled along, they proceed at a pace of their own which is so slow (suo quoque accessu tarn sero) that no mortal's life span is sufficiently long to detect by continuous observation any movement away from the position in which he first saw them. A World Year will therefore be completed when all stars and constellations in the celestial sphere have gone from a definite place and returned to it (cum stellae omnes omniaque sidera quae d.1tA.aVJic; habet a certo loco ad eundem locum ita remeaverint), so that not a single star is out of the position it previously held at the beginning of the World Year, and when the Sun and the Moon and the five other planets are in the same positions and quarters that they held at the start of the World Year. 62 63 64

De rep .• VI, 23-4. See CHAPTER I, SECTION C p. 49. Cf. SERv1us. in Aen., III, 284 (*); see CHAPTER I, SECfION C pp. 51-52. Cf. MACROBIUS, in Somn., II, 11, 5-8. Cf. CICERO,



This, natural philosophers tell us, occurs every 15,000 years (Hoe autem, Ill physici volunt, post annorum quindecim milia peracta contingit). Thus the lunar year is a month, the solar year twelve months. and the years of the other planets are as mentioned above: similarly, the World Year is estimated to be 15,000 of the years we reckon by at the present. That must truly be called the Revolving Year (Ille vero annus vertens vocandus est) which we measure not by the return of a single star, the Sun, but by the return of all stars in every quarter of the sky to their original positions, with the same configurations over all the sky (ad eundem locum reditus sub eadem caeli totius descriptione); hence it is called the World Year (mundanus). for it is proper to refer to the sky as the world65.(transl. Stahl)

The interpretation of Macrobius is remarkable in several respects. To begin with, the value of 15,000 years - which, thanks to Macrobius's authority, was to enjoy great success in the Middle Ages and in the Renaissance66- appears to be a unicum in the literature of Antiquity. Not much is known of those 'natural philosophers', but the identification of these physici with the Stoics is made probable from another passage, earlier in the text, in which Macrobius deals with a theory of deluges and conflagrations that most probably derives from Posidonius (c. 135-51 BC)67 • By far the most arresting point of this interpretation is that the commentator proves in this place to be confusing two great periods of time that have nothing to do with one another from the strictly astronomical point of view. Let us thus have a closer look at the lines which we have just quoted. The passage ends with the expected Ciceronian definition of the conjunctional Great Year as a cycle whose completion is reached when the two luminaries (the Sun and the Moon) and the five other wandering stars (the planets) have come back to the respective places that each one of them had held at the beginning of the cycle. The rest of the passage is not at all related to this general conjunction of the planets, however, but quite unambiguously alludes to the movement of the starry sphere that is now usually referred to as the movement of equinoctial precession. This phenomenon, whose effects are believed to have been first noted by Hipparchus in the second half of the 2nd c. BC, is described at length in the Almagest of Ptolemy (2nd c. AD) 68 • The reality is that the axis of the Earth is not absolutely fixed in space, but rotates slowly like a spinning-top around the pole of ecliptic at a rate of 6

II. 11. 8-12. VI. SECTION B pp. 168-17:1. 7 ' Cf. MACROBIL'S. in So11111 .• II. 10. "" Cf. PTOLEMY. Synt. math., VII, 2. For an introduction to the Ptolemaic system see 0. NEllGEBAt:FR, Exact Sciences. pp. 191-207. '

MACROBIUS, ill S011111.•

"" See particularly




36" a year, according to Ptolemy's value, which gives 360° or one complete revolution in 36,000 years 69 • Similarly, the vernal point, i.e. the point of intersection between the celestial equator and the ecliptic, moves at the same speed along the ecliptic with a retrograde motion. This movement, which has immense implications, since it affects the coordinates of all stars, was called equinoctial precession because it brings, every year, an advancing of the vernal equinox, from East to West, through the stars of the zodiacal signs 7°. It is only since the recent Macrobe et le Neoplatonisme romain by Flamant that we are in position to appraise the importance of Macrobius's arnalgarnation71• Strangely enough, Duhem did not even mention it, although it did not escape his notice that Macrobius had made in the present passage 'une breve et vague allusion' to the precessional movement 72 • Macrobius had already dealt briefly with the movement of precession earlier in his Commentary, and Flarnant provides us with an interesting comparison of both statements from the formal point of view 73 • On that first occasion, however, there was no reason to introduce any allusion to the general conjunction of the planets, for Macrobius's only purpose there was to recall that the starry sphere was believed by some to have a proper movement: Attention must be called to this fact, too, that some authorities maintain that, with the exception of the two brilliant luminaries and of the five errant planets, the stars move only with the celestial sphere, being fixed in it. Other authorities maintain - a position closer to the truth - that these stars have their own motions in addition to their revolutions in the celestial sphere, but that, because of the vast dimensions of the celestial sphere (a/ii quorum adsertio vero proprior est has quoque di.xerunt suo motu praeter quod cum caeli conversione feruntur accedere), ages past belief are consumed in a star's completion of its individual orbit. So these movements are imperceptible to us because our brief moment of time is not sufficient to detect them. Hence Cicero, acquainted with all the better schools of thought, made allowance for either opinion (utramque sententiam) when he said, 'In it are fixed the eternally revolving movements of the stars' [= OCERO, Rep., VI, 17), calling the stars 'fixed' and yet not denying that they have their own movements (nam et infi.xos dixit et cursus habere non tacuit) 74 • (transl. Stahl) 69

Modem values give 25,765 years, which correspond to a shift of about 50" per year. For a comprehensive history of this movement see P. DuHEM,Systeme, II, pp. 180'Discovery', pp. 1-8; Id., HAMA, I, pp. 292-8; 266. More recently see: 0. NEUGEBAUER, R. MERCIER, 'Studies', pp. 197-220 (part I [1976]) and pp. 33-71 (part II [1977]). 71 Cf. J. FLAMANT, Macrohe, pp. 408-9. 72 Cf. P. DUHEM, Systeme, II. p. 196. 73 Cf. J. FLAMANT, Macrohe, pp. 409-10. 74 MACROBIUS, in Somn., I. 17, 16-17. 70



These last lines would suffice to reveal how little Macrobius knows of the astronomical theory he is trying to explain. For either the starry sphere is fixed or it is not, but claiming that Cicero managed to reconcile both views looks very much like a pretty desperate attempt. In fact, Cicero never endowed the starry sphere with a movement other than the diurnal motion by which all celestial spheres are driven from East to West indiscriminately, and it is likely that he did not even suspect the existence of the precessional movement. On the other hand, the commentator is right to assume that the reality of precession was not admitted by all scientists in Antiquity. The phenomenon remained largely ignored during the first centuries after Hipparchus, and this despite the fact that Ptolemy had treated the question in great detail in the Almagest. So much so, for example, that, if one excepts an extremely vague and inconsistant reference to Hipparchus's achievement by Pliny75, Macro bius appears to be one of the very first Latin writers to have alluded to the precession with some awareness of what this movement was. Flamant also mentions a certain number of reasons that may explain why so crucial a theory did not enjoy for many centuries the general recognition it deserved 76 • In the first place, the movement of precession, by slowly affecting the equatorial coordinates of the stars, constrained the observer to base himself on abstact concepts instead of visible objects. Secondly, the idea that the eighth sphere might have two movements, one of which being in the retrograde direction, did not fit with one of the most fundamental principles of Greek cosmology, namely, that the sphere of the 'fixed' stars only moves in the direct sense (the 'Same', according to Plato's terminology). Thirdly, the proper motion of the starry sphere was seen as a powerful argument against the validity of astrology, since it inevitably brings a shift of the abstract zodiacal signs with respect to the visible constellations. To these objections we may add that the movement of precession is incommensurably too slow to be visually apprehended by any individual observer, a point stressed by Macrobius in the two passages we have quoted. In short, the new theory not only offended all the admirers of Plato as well as all those who believed in astrology; it also went deeply against people's common sense.

75 Cf. PLJNY TIJE ELDER, Nat. hist .. ll, 95, where the great astronomer of Bithynia is praised, in fact, for having discovered a 110,·astella. 76 Cf. J. FLAMANT, Macrohe, p. 405.



Where then did Macrobius take the theory from? No definitive answer may be given to this question. The most plausible source seems to be the lost commentary on the Timaeus by Porphyry (c. 234 - 301/5 AD), a work of which Macrobius is known to have made plentiful use. Porphyry's Commentary in tum is believed to be permeated with ideas that ultimately derive from Posidonius. Should Posidonius be one of those physici referred to by Macrobius on several occasions, it would then be reasonable to count him as one of those who assigned this uncommon period of 15,000 years to the Great Year. It is not possible, unfortunately, to know whether Posidonius had some awareness of precession, although it may be interesting to recall that he spent most of his life at Rhodes, i.e. in the city where Hipparchus is reported to have made his brilliant discovery. Supposing that Posidonius knew the phenomenon, there would still remain to investigate the way in which the theory was then transmitted to Macrobius. Of course we may think of Porphyry's Commentary as the most probable way of transmission, in this case as in so many others. But how could we explain, then, that Calcidius and Augustine did not write anything about this theory, either to adopt or to refute it, although they both are known to have made an extensive use of Porphyry's Commentary? One may also consider, as Flamant does 77 , another of Porphyry's works, namely the Sententiae, where on one occasion the Great Year is related to the world soul in Plotinus (c. 205-271 AD)78• Porphyry's statement reads: There is a difference between the duration of the course of the Sun, and that of the Moon, as well as that of Venus, and so on. There is a difference between the solar year, and the year of each stars. Different, further, is the Year that embraces all the other years, and which conforms to the movement of the soul, according to which the stars regulate their movements 79 • (transl. Guthrie)

Not much can be inferred from the comparison of this statement of Porphyry to Macrobius's report on the annus mundanus. The context, moreover, makes it unlikely that this is the source of Macrobius's comment. The figure of 15,000 years is of no help here, unfortunately, for it n


Macrobe, p. 413. Nowhere in Plotinus is the movement of the world soul explicitly connected to the doctrine of conjunctional Great Years, but the theory of periodic world recurrences is mentioned in Pt.OTINUS, Enn., V, 7, 1-3 ("On the question whether there are ideas of particulars"); on this, see also R. SORABJI, Time, p. 186. 79 PORPHYRY, Sent., 44. 78



has no equivalent at all among the values assigned to the World Year in Antiquity. Particularly puzzling is the fact that this value, which is obviously too big to correspond to Cicero's own estimate of the Great Year, is also much too small to correspond to the figure traditionally assigned, since Ptolemy at least, to the movement of equinoctial precession. As we shall see later, the amalgamation of the precessional movement and the Great Year will prove a rather common feature of Arabic astronomy in the Middle Ages, but in the case of those Arabic astronomers the value assigned to both periods will be, more often than not, the Ptolemaic estimate of 36,000 years itself-11°. Scarpa is of the opinion that Macrobius found his source in an astronomical work written by someone who believed in precession 81 • This is fair enough, but Scarpa does not even suggest a single name. We might also think of Pliny the Elder, since this encyclopaedist pretended to have some notions of both cycles. Pliny's allusion to the discovery of equinoctial precession is, as we have seen, a model of vagueness. What he says of the Great Year is, in fact, hardly more valuable. In a section of Book II of his Natural History where he deals with the movements of the superior and inferior planets, Pliny merely concludes: Consequently the course of these stars (i.e. the inferior planets) also is peculiar, and not shared by those above-mentioned: those are often observed to be a quarter or a third of the heaven away from the Sun and travelling against the Sun, and they all have other larger circuits of full revolution, the specification of which belongs to the theory of the Great Year (maioresque alios hahent cuncta plenae conversionis ambitus in maini anni ratione dicendos)82• (transl. Rackham)

But Pliny nowhere develops that theory, except for the brief allusion in Book X, where the measure of the Great Year is said to coincide with the 540-year life span of the phoenix 83 • There seems to be a certain disappointment waiting for those who try to discover the sources that could have led Macrobius to confuse the conjunctional Great Year with equinoctial precession. Anyway, I should rather like to conclude this investigation by agreeing with Aamant that the amalgamation of both theories is part, so to speak, of a natural process whose origin cannot be precisely determined 84 • 80



L. SCARPA, Commentariorum Libri Duo, p. 486. PLtNY THE ELDER, Nat. hist., II. 39-40. Cf. PLtNY THE ELDER, Nat. hist., X, 4-5, On Lhissee also CHAPTER II, SECTION C p. 75. Cf. J. FLAMANT, Macrohe. p. 411.



81 · H4

pp. 149-162.



However different these two astronomical cycles are in fact, both ultimately express but one fundamental meaning, namely that at very long intervals the arrangement of our universe reaches its most perfect accomplishment. As far as the philosophical approach is concerned, what essential difference can we make between two cycles in which the. complete return of all celestial bodies to their original positions is assumed? Even to astrologers, it appears that the influences of these long periods are exactly the same, whether all the spheres or only the highest one are ultimately taken into account. Both cycles are similarly believed to involve the deepest changes upon earth, and no-one could discriminate between the great flood coinciding with a general conjunction and the inundation of entire regions entailed by the precession of equinoxes. As to the purely metaphysical meaning of all this, it is plain that both periods may be equally understood as cycles of Multiplicity, ending in both cases with a return to the original principle, i.e. the Primeval Unity. All this would tend to prove that the combination of both periods could have been realized 'dans des systemes de pensee eloignes dans le temps et dans l'espace, sans qu'il soit necessaire de supposer une influence des uns sur les autres' 85 • Hence, the question of whether Macrobius might have invented the amalgamation of these two periods proves truly a hazardous hypothesis, as Regali points out in his recent edition of the Commentary, for it is well-known how reluctant Macrobius is to use astronomical arguments which are not clearly distinguishable from astrology86 • As we have already noted, it looks rather as though the commentator had not clearly understood what he was trying to explain, so that in any case a deliberate amalgamation should be excluded.

85 R6

fLAMANT. Macrohe. p. 413. M. REGAL!. Macrohio, p. 186.



THE WORLD YEAR IN ISLAM I. Abu Ma'shar and the Cycle of the Persians The study of great astronomical cycles in the Islamic world is a complicated one. In his fundamental article 'Ramifications of the WorldYear Doctrine in Islamic Astrology' Kennedy defined the situation facing the scholar in the following terms: 'The matter', he wrote, 'is so diffuse, the elements so contradictorily compounded of religion, magic, and myth, and the sources so numerous that one often feels, as Biruni would say, that the only reason for studying the subject is to be able to warn the reasonable man away from it' 1• Kennedy's own contribution to this titanic undertaking is considerable: his works are indispensable companions of all those who would like to venture into this selva oscura without risk of losing their bearings at all times. The question of World Years in Islam is also frequently dealt with by Pingree, the other major pioneer in this particular field of the history of ideas, to whose impressive set of writings I shall refer here almost continually. Abu Ma'shar of Balkh (787-886 AD), the most famous of all astrologers in the Middle Ages, played a unique role in the extremely entangled process by which ideas and methods belonging to what we may call the Graeco-lndo-lranian tradition eventually reached the Arabic civilization 2• What is known of his long and highly productive life has been gathered by Pingree3 and Sezgin4 so that there is no need to take up here this matter again. Among Abu Ma'shar's many works, one should nevertheless mention his Kitdb al-madkhal a/-kabir 'aid 'ilm a~kdm a/nujum (or Great Introduction to the Science of Astrology), whose immense reputation extended to the West via the double translation into Latin by John of Seville (in 1133 AD) and Hermann of Carinthia (in 1140 AD). Yet the works of his that are most concerned with the 1

2 3 4

E.S. KENNEDY, 'Ramifications", p. 23. See for instance D. PINGREE, 'AbQ Ma'shar", p. 33. D. PINGREE, 'AbQ Ma'shar', pp. 32-9. F. SF.ZGIN, GAS, VII, pp. 139-51.



theories of world cycles appear to have been the Kitab al-uluf (or Book of the Thousands), the Zij al-hazarat (or Tables of the Thousands) and the Kitab ikhtilaf al-zijat (or Book of the Differences Between Tables), all written between 840 and 860 AD. Unfortunately the two former works are completely lost in their original form while the latter treatise has only survived in fragments. However there are later summaries of the Book of the Thousands and, by carefully gathering together this material, Pingree has been able to reconstruct and to discuss a substantial part of Abu Ma'shar's system in his book The Thousands of Abu Ma'shar5. This system is based on an overriding assumption. Indeed Abu Ma'shar seems to have exercised his wits to demonstrate, with the greatest care, that the three great traditions that had influenced the astronomers of his own time - namely the Greek (with Ptolemy's Almagest), the Iranian (with the Zfj al-Shah) and the Indian (with the Zij al-Sindhind) - all derived from a unique revelation that had occurred before the great flood and the general conjunction of the planets in the year 3,101 BC. In his Kitab al-ulfif he even claimed that he himself had found, in I~fahan, the manuscript of that revelation that had been buried there by the legendary Tahmurath 6 • Among the few extant summaries of the Book of the Thousands, we have the Muntakhab Kitab al-uluf composed by al-Sijzi (10th c. AD) and included in his Jami' al-Shahi, as well as a summary of this Muntakhab, entitled the Dastfir al-Munajjimfn, by an anonymous member of the Ismaili movement7. These sources have visibly suffered the bias of independant transmissions and the latter contains important additions, but both suggest that Abu Ma'shar had treated the subject of World Years and epochs at the very beginning of his Kitab al-uUif. In a joint article, Kennedy and van der Waerden have given a valuable translation of the section devoted by each summary to Abu Ma'shar's theory of world cycles 8 • The version of the Dastur (= "A") reads: ~ D. PINGREE, Thousands. On the Kitab al-uluf before Pingree see: J. LIPPERT,•Abu Ma'shar', pp. 351-8; M. PLESSNER, 'Hermes Trismegistus', pp. 45-59: E.S. KE1'NEDY, 'Ramifications·, pp. 23-43. On specific points of discussion since then see: C. BURNETT, 'Three Hermes', pp. 231-4; A. STROBEL, 'Weltenjahr', pp. 1128-44. 6 Cf. D. PINGREE, Thousands, pp. 1-13. On the influence of those three main traditions on Islamic astronomy see above all: D. PINGREE. 'India and Iran·. pp. 229-46: Id., 'Greek Influence·. pp. 32-43. 7 For a list of the manuscript sources for the Book of the Thousands see D. PINGREE, Thousands. pp. 21-7. x E.S. KENNEDY - B.-L. van der WAERDEN, 'The World-Year', pp. 315-27. For the Dast11r al-M1111ajji111i11 (= ..A .. ) lhe scholars have used the unique manuscript of the Bibliotheque



A World Year, according to the generality of the astrologers, is from the time of arrival of the planets at the first of Aries until the time of their return to the end of Pisces, without there being a difference in their amounts (i.e .• longitudes). As for those in a region of India and their adherents, they say that the seven planets and their apogees and nodes begin the motion from the first of Aries, and they conjoin at the end of Pisces in 4,320,000,000 years. As for the partisans of the year of Arjabhar (Aryabhata), they differ from them and make the World Year 4,320,000 years. The partisans of the years of the Arkand said differently from this. The Persians (ah/ Fars) and some of the Babylonians said that the World Years are 36(0),000 solar years, of which there are 365 days. 15 minutes, 3(2] seconds, (and) 24 thirds, without requiring their apogees and nodes (to be at Aries 0°). If we divide the years of the Sindhind by a thousand there come out the Arjabhar years. If we divide by twelve thousand there comes out the Year of the Persians. It is necessary to know that if the motions of the apogees and nodes are the same it prevents their conjunction in one degree because they are scanered 9 • (transl. Kennedy)

The comparable passage in al-Sizji's Jami' a/-Shahi (= "B ") runs as follows: "Statement concerning World Years and the chronology used in this book". Verily. the generality of the learned among the people of India, and China, and Rum (the Byzantines). and Fars, and the people of Babylon, and those who follow them among the peoples are agreed (on the fact) that the seven planets were in conjunction at the first minute of Aries and that they conjoin at the end of Pisces at the end of the world. As for the Hindus, they claim that the planets, their apogees and nodes, were in conjunction in the first minute of Aries, and that they conjoin at the last (point) of Pisces at the end of the world, and the years of the world are from the time of the conjunction of the planets at the first minute of Aries until the time of their conjunction at the end of Pisces, it being one and the same place. except that they differ among themselves as to the travel of the planets in the heaven. As for those of one of the regions in India, they claim that the years of the world are 4,320,000,000, they being the partisans (a$~fib) of the Sindhind. However, the other group of them, they being the partisans of the years of Arjabhar. they claim that the years of the world are 4,32[0],000. But the author ($fi~ib) of the Book of the Thousands used the Years of the Persians for the cycles and tasyirfit. However, some of the modems used the world years according to the way the partisans of the Sindhind explained them, but we now, in this book, will utilize what the Nationale, Paris, MS Arabe 5968; for the Jami' al-Sha/ii(= "B") they have chosen the manuscript of the British Museum, London, MS Or. 1346. 9 Dastur a/-Munajjimin, MS BN Arabe 5968, fol. 236', II. 1-12. For the correction of "Arjabha:" (as in Kennedy) by "Arjabhar", cf. C.A. NALLIN0,Racco/ta, vol. V, Rome. 'Dustur a/-Munajjimin", 1944, p. 206, n. 4. On the Dastur, see also F.W. ZIMMERMANN, vol. II, Aleppo, pp. 184-92.



author of the Book of the Thousands used. So if you want to extract the World Years and their days, look at the (number of) days and their fractions in which one of the planets rotates once around the heavens in the mean rriotion, and multiply it by the days and fractions thereof in which another of the planets rotates once. Then what results is the number of days in which the two will conjoin at the same position from which they started moving. Then multiply what resulted of those days and fractions by the days and fractions in which another planet rotates (back) to the position in which it was at the beginning of the motion, and thus according to this manner. Then multiply what you obtain for all seven of the planets and the nodes and apogees, and it will be the days of the world 10. (transl. Kennedy)

The interpretation of these lines is not without problems, but of the questions that are raised by these statements none has proven as controversial as that of the real origin of AbO Ma'shar's 'Cycle of the Persians'. Finding that in his Chronology al-BirOni also assigns the discovery of the 360,000-year period to 'the observations of the Persians' 11 , van der Waerden was led to conclude that 'the Persians' in those texts were to be identified with the authors of the Zfj-i Shah, namely a series of astronomical tables composed in Sassanian Persia and later revised under Khusrau I (6th c. AD). But Kennedy has demonstrated that the Zfj-i Shah was itself largely indebted to Indian sources12 , and Pingree has pointed out the almost complete lack of innovation of Sassanian astronomy13• In all, this matter has given rise to a series of very polemical discussions between van der Waerden, who supports a truly Iranian origin 14, and Pingree, who, I think, demonstrates much more convincingly that AbO Ma'shar had merely tried to conceal a direct borrowing from Indian cosmology 15• The essential proof of the demonstration is that nearly all planetary parameters used by AbO Ma'shar - and preserved in like manner by al-Hashimi, al-TanOkhi and al-BirOni - derive directly from the Sindhind 16• Perhaps the best way to clarify our two passages is to list, reproducing Pingree's own classification 17, the four Indian systems that are known to have existed: 10

AL-SIZJI,J/Jmi', MS BM Or. 1346, fols 80V,I. 22-81', I. 14. Cf. AL-BIRONf, Athlir, transl. Sachau, p. 29. 12 On this work see E.S. KENNEDY, 'Zfj-i Sh/Jh',pp. 246-62. 13 Cf. D. PINGREE, 'India and Iran', pp. 229-46. 14 Cf. for instance B.-L. van der WAERDEN, 'Great Year', pp. 364-7. 1 ' In addition to Pingree's works already mentioned see also: D. PINGREE, 'Review', pp. 258-60. 16 Cf. D. PINGREE, Thousands, pp. 30-3. 17 D. PINGREE, Thousands, pp. 28-9. 11



I. The Ka/pa of 4,320,000,000 years was first used, so far as we know at present, in the Paitiimahasiddhiinta (c. 400-450) of the Vi~,:,udharmottarapurii,:,a. It assumed a Grand Conjunction of the mean planets, their apogees, and their nodes at Aries 0° at the vernal equinox of 1,972,947,101, and another in 2,347,052,899; the day begins at dawn. This system was known to the Arabs as that of the Sindhind. II. The Mahiiyuga of 4,320,000 years, which was used in the iirddhariitrika (midnight) system of Aryabhata I (c. 500). In this work Aryabhata follows the orthodox division of the Mahayuga into four unequal yugas whose ratios to each other are 4:3, 3:2; and 2: 1: Krtayuga = 1,728,000 years; Tretiiyuga = 1,296,000 years; Dviiparayuga = 864,000 years; Kaliyuga = 432,000 years. A Grand Conjunction of the mean planets only at Aries 0° is assumed for -3,891, 101, and another at the end of Kaliyuga in 428,899; since Kaliyuga itself is suposed to begin with a Grand Conjunction of the mean planets only at Aries 0° at midnight of Thursday-Friday, 17-18 February -3101, the mean planets must make an integer number of revolutions every 432,000 years. The Arabs knew this system under the name of al-Arkand. III. The Mahiiyuga of 4,320,000 years was also used in the audayaka (sunrise) system of the Aryabha[fya of Aryabhata I. In this work the same assumption regarding a Grand Conjunction of the mean planets only at Aries 0° at the beginning· of Kaliyuga was made, but this was now dated at dawn of Friday, 18 February -3101. Furthermore, the lengths of the four yugas were equalized: Krtayuga = 1,080,000 years; Tretiiyuga = 1,080,000 years; Dviiparayuga = 1,080,000 years; Kaliyuga = 1,080,000 years. This means that the Grand Conjunctions of the mean planets only at Aries 0° which mark the beginning and the end of the Mahiiyuga must be dated respectively -3,243,101 and 1,076,899. This system the Arabs knew as that of a/-Arjabhar. IV. A Yuga of 180,000 years is attested for the original Old Suryasiddhiinta (c. 450), which was converted to system II by Lltadeva in c. 505, and which displays system I in its modem version. This assumed a conjunction of the mean Sun and mean Moon - and probably of the mean planets - at Aries 0° in -3101 and another in 176,899. Immediately after this classification Pingree notes: 'Abu Ma'shar's system is very close to this system IV. He assumes a Grand Conjunction of the mean planets only at Aries 0° in -183, I 0 1; at midnight of ThursdayFriday, 17/18 February -3101 (the epoch of the flood); and in 176,899. This yuga of 360,000 years occurs not only in Isma'ili sources, but in the Sanskrit Vi~,:,upura1Ja(fourth cent.?) as well. Al-Bin1ni recognized that



this system of Abu Ma'shar was derived from an Indian source; and Abu Ma'shar himself, by comparing its characteristics with the Sindhind, alArjabhar, and al-Arkand, emphasizes this relationship' 18• These four systems, as may be noted, are those referred to in the two passages compared above. Indeed, while the Dastur (= "A") mentions the Sindhind (System I), al-Arjabhar (System III), al-Arkand (System II), and the 'Cycle of the Persians' (variant of System IV) successively, al-Sijzt's Jami' a/-Shahf (= "B") mentions the Sindhind, al-Arjabhar and Abu Ma'shar's 'Cycle of the Persians', thus only omitting System II. The omission is probably due to the fact that both System II and System Ill use as their fundamental unit the same mahayuga of 4,320,000 years. The correct proportions between the three fundamental units are explicitly given by the Dastur: one thousandth of a kalpa of 4,320,000,000 years (= Sindhind) gives a mahayuga of 4,320,000 years (= al-Arkand and a/-Arjabhar), and this latter number, when divided by 12,000 years, gives a yuga of 360,000 years(= 'Cycle of the Persians'). For our purposes, what is worth noting is mainly that the Grand Conjunction is said to coincide, in Abu Ma'shar's system, with the universal deluge, and that this event is dated 17/18 February -310 I, according to the computations referred to in our passages themselves. This date, which is confirmed by al-Khwarizmi and al-Birfini, is precisely the date assigned to the beginning of a kaliyuga in Systems II, III and IV, so that its Indian origin cannot be missed. As for the expression 'Cycle of the Persians'. there cannot be any doubt that it refers, not to this allegedly flourishing period in the development of Sassanian astronomy, but to the kings and heroes, like Hushank or Tahmurath, whose mythical lives had been related to the story of the famous flood: in his introduction to The Thousands of Abu Ma'shar, Pingree cites texts from lbn al-Nadim, al-Hashimi and al-Birfini that are clear confirmations of this 19 • It is now time to have a closer look at some of the elements most characteristic of Abu Ma'shar's eclectic theory. I should like to focus the investigation on the three following components of his 'Cycle of the 18 D. PINGREE, Thousands,pp. 29-30; see AL-BIRONl, Hind: 'The context of these passages makes it clear that this destruction of the world takes place at the end of a kalpa, and hence is derived the theory of AbO Ma'shar that a deluge takes place at the conjunction of the planets, because, in fact, they stand in conjunction at the end of each i;aturyuga [= maMyuga] and at the beginning of each kaliyuga'. (transl. Sachau, I, p. 325) 19 Cf. IBNAL-NADtM, Fihrist, Cairo, pp. 348-50; AL-HASHIM!, Kitab 'ilal al-zfjdt, MS Bodleian Arch. Seid. A. 11, fol. 107v (cf. D. PINGREE - E.S. KENNEDY - F.1. HADDAD, Book of the Reasons, pp. 124-5); AL-BIRONt, Athdr, transl. Sachau, pp. 27-8.



Persians': (i) the universal flood; (ii) the general conjunction of the planets at Aries 0° in 3, 10 I BC; (iii) the period of 360,000 years. (i) The notion of a universal flood, with its corollary of antediluvian

kings, ultimately derives from the Babylonians, and we have already seen that this theory formed a significant part of Berosus's Babyloniaka 20• The precarious transmission of this book to the Hellenistic world has been summarized by Lambert and Millard in these terms: 'Despite the considerable interest in that kind of material in the Hellenistic world, incredibly few people read the book, and it is now lost. For the flood (and most other things) we have to depend on Alexander Polyhistor, a Greek of the first century BC, who quoted Berosus extensively. This work too is lost, but was in tum quoted by Eusebius, especially in his Chronicles, which survives in an Armenian translation. However, the passage relating to the flood is quoted in Greek by the Byzantine chronicler Syncellus. Another writer who gives a briefer account of the flood ultimately derived from Berosus is Abydenus' 21• We may assert with confidence that at least a part of the theory was known to Indians as well, for 432,000 years, i.e. the period of the ten antediluvian kings, is also the measure of one kaliyuga in Indian chronology: 'It seems likely', Pingree writes, 'that it (the number 432,000, sexagesimally writt~., 2,0,0,0) should have become known as a significant number in India the time when other Babylonian influences were being felt, that is, during the Achemenid occupation of the Indus Valley' 22 • On the other hand, one should note that the legendary flood does not appear in any of the four originally Indian systems. (ii) The idea of a conjunction of all the planets at Aries 0° in the year 3, 10I BC is, undoubtedly, Indian. Its invention should probably be ascribed to .A.ryabhafa23 • Furthermore, the choice of Aries seems in itself to be in contradiction with what Seneca tells us of the Babylonian Great Year, where the general conjunction is said to occur in the solsticial signs of Cancer (conflagration) and Capricorn (flood). As Pingree remarks, 'the choice of Cancer and Capricorn is clearly due to a desire to connect the world-year with the summer and winter solstices. In this tradition the Aries conjunction of -3101 is meaningless. But it is also contrary to astrological theory. The zodiac is divided into four 20



W.G. LAMBERT - A.R. MILLARD. Atra-ljusis. p. 134. D. PINGREE. 'India and Iran', p. 238. Cf. R. BILLARD. Astronomie indienne. pp. 27-8.



II, SECTION A p. 72.



triplicities, which are connected with the four elements. The first consists of Aries, Leo, and Sagittarius, and is fiery; the second of Taurus, Virgo, and Capricorn, and is earthy; the third of Gemini, Libra, and Aquarius, and is airy: and the last of Cancer, Scorpio, and Pisces, and is watery. The conjunction of -3101 occurs in a fiery triplicity and astrologically must indicate, if anything, a conflagration, not a flood. The latter can take place only when there is a conjunction in a watery triplicity. This was recognized by Abu Ma'shar's predecessor, Masha'allah, who dated the flood in -3300 because in that year occurred a Saturn-Jupiter conjlll1ction in Cancer, the first sign of the watery triplicity; and Masha'allah expressly states that he is using the Zij-i Shah. Cancer is also connected with the Flood in the Pahlavi Buruiahishn' 24• It is not easy to say who was responsible for the amalgamation of the Babylonian flood-theory with the Indian traditional date of 310 l BC. Pingree, following a suggestion made by Sachs, proposes this explanation: 'In his Book of Conjunctions Abu Ma'shar says that this date (= 3101 BC) was proposed by someone whose name, corruptly preserved in Arabic, may be Abydenus. Abydenus (2nd c. AD?), it may remembered, was one of those Greek historians who placed the Babylonian kingdom of 432,000 years' duration before the flood; and this 432,000 years is the length of the kaliyuga which begins in -3101. Someone aware of both Abydenus's flood story and the astronomical date of the beginning of kaliyuga has rather sloppily combined the two traditions. As Biruni remarks, the Persians did not usually believe in the flood; but there were some who did accept it, confining its effectiveness to western Asia. It is surely these Persians whom one must suspect of dating the flood in -3101, for they occupied the ground, quite literally, between the two ideas which were synthesized. This interpretation agrees with Biruni's statement in the India that Abu Ma'shar's date for the flood was derived from the Hindu kalpa-theory' 25• (iii) The period of 360,000 (or 2 x 180,000) years may be found in the Old Suryasiddhanta, and three different sources, as we have seen, confirm that Abu Ma'shar used Indian parameters for the numbers of revolutions of the mean planets in 360,000 years. Now could this period have been used before the Indians? This question, I think, cannot be answered in a decisive and conclusive way. Only one should recognize that the number 360,000, as any multiple of 360, is so naturally suitable for this 24


D. D.


'India and Iran', p. 244. 'India and Iran', p. 243.



kind of computation that it may well have been adopted by different civilizations, even independently. In the Qur'an - as well as in the Bible 26 - is to be found the statement that a day of God equals 1000 years of men, so that a Year of God must be considered as measuring 360 x 1,000 years= 360,000 years. Indeed, SuraXXII has a verse that reads: Yet they ask thee to hasten on the Punishment! But Allah will not fail in His promise. Verily a Day in the sight of the Lord is like a thousand years of your reckoning (wa-inna yawman 'inda rabbi-ka ka-a/ft sanatin mim-mii ta'udduna) 21 •

Similarly, one finds in SuraXXXII: He directs the affairs from the heavens to the Earth: then it ac;cends unto Him, on a Day the measure of which is a thousand years of your reckoning (Ji yawmin kana miqddru-hu a/fa sanatin mim-nui ta'udduna) 28•

This probably explains why the number 360,000 frequently appears in the cosmological speculations of the Ismailis, as has been shown by Corbin 29• Last but not least, it is perhaps worthwhile recalling that Ptolemy's authoritative value for the precessional period, i.e. 36,000 years, was later often confused with the real Great Year in which a general conjunction of all planets is assumed. This relationship between world cycles of 36,000 and 360,000 years will be the subject of the next section.

B. The lkhwan al-~afa' on Precession and General Conjunctions It has long been recognized that the Ikhwan al-~afa' - or Brethren of Purity, as they are more commonly known in English - had some important connections with the Isma'ili movement 30 • I shall not take up once more the much debated discussion about the exact identity of the Ikhwan, nor shall I summarize the arguments adduced to date the fifty or so Rasa'il (or Epistles) that have come down to us under the name of this Muslim brotherhood 31• Suffice it to recall what seems to be agreed See, for instance, Psalms, 90, 4. Qur'dn, XXII,47 (*). 28 Qur'dn, XXXII.5 (*). 29 See: H. CORBIN, Histoire, p. 129; Id., Temps, pp. 52-3. JO See for example: I.R. NETTON, 'Foreign Influences', pp. 49-67; Y. MARQUET, 'lsmaelisme', pp. 69-76; Id., 'evmutcj> µiJ EA.acrcrovii tKatocrtov µiac; µoipm;}, then it follows that in 300 years they must have shifted not less than three degrees (µiJ fMcrcrov ii y µoipac;)' 37•

This is the erroneous rate of l O every l 00 years - or one complete revolution in 36,000 years - that was to prevail, almost unrivalled, among astronomers around the world for about one millennium after Ptolemy. Arabic translations of the Almagest, from the original Greek as well as from a Syriac version, appeared at the beginning of the 9th century. These translations - by al-l;laijaj and, later on, by IsJ:iaq ibn l;lunayn - form part of the extraordinary activity that took place in Islam during the 'Abbasid period and which was to establish Ptolemy as the undisputable model for all later astronomers in the Arabic world 38 • As for the value of I O per I 00 years, the Ikhwan may have taken it directly from the famous Jawiimi' (or Elements) of al-Farghani (9th c. AD), a sort of very simplified summary of the Almagest that the Brethren are known to have read39 • Here I quote the passage from al-Farghani's Elements that deals with the precessional movement. As one may already observe, the movement is not restricted to the starry sphere alone: We say that it (the starry sphere) moves from West to East and carries with itself the spheres of all seven planets around the poles of the zodiacal sphere one degree every 100 years (Ji kull mi'a sana juz'an wiiQidan) according to Ptolemy's measurements ('a/a qiyasat ha{limus). For this reason, the apogees and nodes of the seven planets (awjat al-kawiikih al-sab'a wa jawzahrati-ha) are moved, following the order of the zodiacal signs, at the same rate of 1° in 100 years (Ji ku/1 mi'a sana hadha al-miqdar), and their revolution on the zodiacal sphere takes place in 36,000 years (wa yakiinu dawr-ha li-falak a/-buruj ft sitta wa thalathina a/f sana) 40 • (ii) The other long cycle considered by the Ikhwan al-~afa' in Epistle

XXXVI is the 360,000-year period, which they assume to be indicated by the great conjunction of all the planets at Aries 0°. That the Ikhwan were 7 ~



.ix On the introduction and influence of Ptolemaic astronomy in Islam see above all: D. PINGREE, 'Greek Influence·, pp. 32-43; Id .. "Ilm al-hay'a', pp. 1135-8. _IQ Al-Farghani's name appears in Epistle XXX/X of the Ikhwan; cf. S. DIWALD. Arahische Philosophie, p. 382. 40 AL-FARGHANi, Ja1n1mi'. XIII. pp. 49-50 ( *).



perfectly alive to the Indian origin of this cycle is proved from their explicit reference to a certain Zfj a/-Sindhind in which this great conjunction is called a day of the days of the Macrocosm. There are several works bearing this name in Arabic literature. But the one referred to here is most likely to be the Mahdsiddhdnta, a treatise derived from the celebrated Brdhmasphu{asiddhdnta that was composed by the astronomer Brahmagupta in 628 AD41 • From al-Binlni, among other testimonies, we know that this Brdhmasphu{asiddhdnta was brought to Baghdad on the occasion of an embassy sent to the court of al-Man~ur (reign: 754-775 AD) and that al-Fazari was put in charge of the translation. In his India, al-Binlni notes: It is one of the conditions of a kalpa that in it the planets (al-kawakib alsayyara), with their apogees and nodes (ma'a awjati-ha wa jawzahrati-ha), must unite in the first degree of Aries (Ji awwal burj al-l_uimal),i.e. in the point of the vernal equinox (nuq{at al-i'tida/ al-rabi'iyya). Therefore. each planet makes within a kalpa a certain number of complete revolutions of cycles. These revolutions of the planets, as known through the :ij-s of alFazari and Ya'qub ibn Tariq. were derived from an Indian who came to Baghdad as a member of the political mission which Sind sent to the Caliph, al-Man1?0r,in A.H. 154 [= 11on11 AD]. If we compare these secondary statements with the primary statements of the Indians, we discover discrepancies, the cause of which is not known to me. Is their origin due to the translation of al-Fazari and Ya'qub? or to the dictation of that Indian? or to the fact that afterwards these computations have been corrected by Brahmagupta, or someone else42 ? (transl. Sachau, 11,p. 15)

The story of the Zfj al-Sindhind is, indeed, not an easy one. I cannot do better here than to quote a part of Pingree's summary of it: 'Though some Indian astronomical texts related to the Aryabha{iya written by Aryabha~ (whose epoch is 499) and to the Ka,:,4akhddyaka written by Brahmagupta (whose epoch is 655) had influenced Arabic astronomy in the first half of the eighth century, the primary direct infusion of Indian material into Islam occurred when an embassy from Sind to the court of al-Man~ur in Baghdad in 771 or 773 included an Indian who had the text of a siddhdnta, probably entitled Mahdsiddhdnta, which belonged to the Brahmapak~a of Indian astronomy. This was rendered into Arabic with additions from other sources by al-Fazari as the Zfj al-Sindhind al-kabfr. Al-Fazari wrote several other astronomical works related to the Sindhind, as did also Ya'qOb ibn Tmq'43• 41

On this story see C.A. NALLINO, Raccolta, pp. 203-8; D. PrsGREE,'Ya'q0b ibn Tliriq', pp. 97-125; Id., 'al-FazAri', pp. 103-23. 42 AL-BIRONt,Hind, Hyderabad, pp. 351-2 ("'). 43 Cf. D. PINGREE, 'Indian Passages', pp. 151-2.



Now the system which the Arabs normally referred to as that of the Sindhind is, as one may remember, System I, which indeed assumes a great conjunction of all planets, with their apogees and nodes, after a kalpa of 4,320,000,000 years. This obviously does not correspond to the 360,000-year cycle mentioned by the lkhwan, which is 12,000 times shorter. In other words, the great conjunction alluded to by the Brethren in the present Epistle is, just like Abu Ma'shar's 'Cycle of the Persians', to be connected with System IV, of which we know that it 'displays System I in its modern version ' 44 • What is clear, anyway, is that the Ikhwan did not identify with one another the periods of 36,000 and 360,000 years. They were even plainly aware, as we may infer from this statement on extreme revolutions and conjunctions alone, that these two periods have a very different geographical provenance. It is worthwhile insisting on this fact, for it has been a customary mistake of modern scholarship, at least since Duhem, to think of the Ikhwan as probably those who first amalgamated the Ptolemaic precession with this Indian conjunctional World Year. There are, indeed, a few manuscripts which have the same value of 36,000 years for both the longest revolution and the longest conjunction, but a closer look at the apparatus criticus in Diwald's edition reveals how much these manuscripts are in the minority45• By only reading the Epistles of the Ikhwan through the old German translation of Dieterici46 , Duhem thought it a good idea to 'correct' Dieterici whenever his translation preserved the trace of the 360,000 years. This regrettable confusion led him to comment on our passage in the following way: 'Ils (the Brethren of Purity) en avaient conclu l'identite de deux periodes astronomiques celebres, qu'ils faisaient toutes deux egales a 36.000 ans' 47 • Unfortunately, Duhem's misjudgement later prompted Diwald herself to choose the wrong reading at this point in her edition of this text48• In addition to what has been said thus far, one finds in another Risa/a of their corpus the quite unambiguous proof that the Brethren did not themselves make the confusion imputed to them by Duhem and those who have blindly followed his view on this matter. I refer to a passage 44


D. PINGREE. Thousands, p. 29. See S. DIWALD. Arabische Philosophie,

p. 214: seven manuscripts have 360.000 years for the conjunctional cycle from India, whereas only three have 36,000 years. Let us mention, on the other hand, that all manuscripts have 36.000 years in the case of equinoctial precession. 46 F. DIETERICI, We/tsee/e, p. 53. 47 Cf. P. DUHEM. Sysreme, p. 216. 4 x Cf. S. DIWAW. Arabische Philosophie, p. 214. This mistake is repeated on p. 253.



from Epistle XXII where the two periods of 36,000 years and 360,000 years are mentioned side by side. Epistle XXJ/ is the one that contains the well-known "Fable of the Animals versus Man", but this celebrity apparently did not prevent our passage from being overlooked by modem scholarship: The days of this nether world run in cycles allocated among its inhabitants, turning at the behest of God and by His foreknowledge and the action of His almighty will, through the influences of the conjunctions and the revolutions (of the stars) every 1,000 years, or 12,000 years, or 36,000 years (Ji ku/1 sitta wa rhaMthina a/f sana marra /wii!Jidaj), or 360,000 years (Ji ku/1 rhaliirhami'a a/f wa sittina a/f sana marra /wii!Jida]), or each day of 50,000 years49 • (transl. Goodman).

II. Precession and the Periodic Interchanges on Earth

The theory of periodic interchanges between seas and mainlands has, undoubtedly, a strongly Aristotelian undertone. Aristotle himself, as we have seen, believed this alternation of dryness and moisture to be linked to the never-ending succession, at fixed intervals, of great summers and winters, but at the same time he categorically denied the possibility for alternations to have universal implications50• Under the probable influence of the Stoics, Aristotle's later commentators did not hesitate to establish a precise relationship between, on the one hand, the interchanges of seas and mainlands, and, on the other hand, the general conjunctions of the planets in the zodiacal signs that mark the solstices of this Aristotelian Greatest Year'i1• With the Ikhwan we now find the same original theory adapted in yet another way. At the end of Epistle XXXVI, while speaking of the effects that the 36,000-year cycle produces on earth, the Brethren state: Among the slow movements, of long duration and far-reached recurrence, there are the movements of the fixed stars on the zodiacal sphere, taking place once in every 36,000 years (Ji sitta wa rhalathina a/f sana marra and wii!Jida). as well as those of the apogees (awjat), the perigees (l}ar.j,ief,) the nodes (jawzahrat) of the planets. What follows these movements during that period - in this world of coming-to-be and passing-away (Ji 'ii/am a/-kawn wa l1asiid). is that civilization is shifted on the surface of the earth from one quarter to the next (min rub' ilii rub'). Mainlands (mawatji' a/-bariiri) become seas (bi/Jar), and seas (mawar.j,i' al-bi!Jar) 9 ~

50 51

IKHWAN AL-SAFA'. Rasii'i/, XXII. vol. 11, p. 233, II. 19-24 (*). See CHAPTER I. SECTION B pp. 38-39. See CHAPTER IV. SECTIO~ D pp. 116-120.



become mountains (jihal), the mode of which we have explained in the Epistle on Minerals52•

In other words, Aristotle's theory of periodic interchanges finds itself systematized to a degree that was probably never reached in classical Antiquity. Yet the clearest innovation of all is certainly that the original doctrine is now framed on Ptolemy's precessional cycle. The innovation is likely to belong to Indian speculations in astronomy. This is, at least, what a similar passage in the contemporary Muruj al-dhahab (or Golden Meadows) of al-Mas•udi (10th c. AD) would seem to indicate in spite of the many historical errors it contains. The passage deals with the greatest achievements of a certain Brahman, allegedly the first king of India but in fact none other than the astronomer Brahmagupta: In his days some wise men joined together to produce the book of the Simlhind, that is to say 'the Age of Ages' (dahr al-duhur). From it derive the book of the Arjabhad and the Almagest. From the Arjabhad derives the Arkand and from the Almagest, the book of Ptolemy. Then derive, from these works, the ::fj-s. They invented the nine numerals that form Indian arithmetic. He (Brahman) was first to define the apogee of the Sun (awj al-shams), asserting that the Sun stays in each sign for 3,000 years and that it completes the revolution of the sphere in 36,000 years (yaqfa' al-falakft sitta wa thalathfna alf sana). At the present time, i.e. A.H. 332 [i.e. 943 AD], the apogee is, according to Brahman, in the sign of Gemini (Ji burj altaw 'am). But when it will be transferred to the Southern signs (ila al-buruj al-janllbiyya), the inhabited region will be transferred: the inhabited region will be covered with sea and the region covered with sea will be inhabited (~ara al- 'amir ghamr wa al-ghamr 'amir); the North will become the South and the South will become the North (/ ~ara] al-shamal janub wa al-janub shamal) 53•

In this text and in some other Arabic sources already quoted we notice that the movements of the seven planets are all considered in exactly the same way. Ptolemy would never have contemplated such a possibility, for in his writings he was convinced that the Sun's apogee, unlike those of the other planets, was not involved in the movement of precession 54 • 52

IKHWANAL-$AFA'. Rasd'il. XXXVI, vol. III, pp. 265, I. 21-266, I. 2 (*); see also p. 267, II. 1-11. For the Epistle "On Minerals" see IKHWAN AL-$AFA',Rasd'il, XIX, vol. II, p. 92, where one finds, indeed, a little more detailed exposition of the same theory; the general idea is that an analogical correspondence exists between the four quarters of the earth and the four types of regions found on its surface, i.e. seas, mainlands, mountains and inhabited regions. 53 AL-MAs'0ol. Muruj, VII, vol. I, p. 85, § 153, II. 2-9 (*). 5-4 See for instance ProLEMY, Synt. math., III, 4 and the note in G.J. TOOMER, Almagest. p. 153: 'According to Ptolemy the Sun's apogee (unlike those of the five planets, as it later



To assume that the solar apogee has no motion with respect to the fixed stars is an Indian invention which belongs to the system of the Mahayuga (Systems II and III) and which also appears in Abu Ma•shar's 'Cycle of the Persians ' 55• This non-Ptolemaic component was to be taken over - and even extended to the Moon's apogee - by alFarghani and most astronomers of Islam. As to the reason why Indians themselves held this more unified theory, one can only make conjectures, but Duhem was probably right to advocate a kind of common sense: 'Mais ii est plus probable qu'ils [the Indians] avaient simplement etendu a I' apogee du Soleil la loi que Ptolemee avait acceptee pour les apogees des cinq planetes' 56 • III. Two Allegories on the Conjunctional Great Year I should like to conclude the present investigation with two little tales that one may find in Epistle XVI ("On the Heaven and the World"). Both have been conceived, the Ikhwan tell us, with the intention of explaining how the general conjunction of the planets should be understood. In spite of a redundant style quite typical of the Brethren, I have chosen to quote both stories in full: (i) "The allegory of the pilgrims". The origin of this story is not specified, but it is quite clear from its content that it belongs to the Muslim world in its own right. It runs as follows: turns out, IX, 7) does not share in the motion of precession. The reproaches that have been cast on Ptolemy (e.g. by Manitius I 428-9) for failing to discover that the Sun's apogee too has a motion through the ecliptic are unjustified. To do that he would have needed observations of the time of equinox and solstice far more accurate than those available (to the nearest ¼-day), and not only for his own time but also for an earlier time'. Compare with AL-BiRDNi,Athar, transl. Sachau, p. JO: •According to Ptolemy these revolutions (of the Sun) are equal, because he did not find that the apogee of the Sun moves; whilst they are unequal according to the authors of the Sindhind and the modem astronomers. because their observations led them to think that the apogee of the Sun moves'. 55 See D. PINGREE, Thousands, p. 33: 'He (al-Hashimi) does not realize that the apsidal motion in Ptolemaic astronomy is due to the precession of the equinoxes; in other words, all the planetary apogees (excluding again those of the two luminaries) are fixed with respect to the fixed stars. In the Indian system of the Mah/iyuga and in Abu Ma'shar's "Persian" system, where the year is sidereal, the motionless apogees (including that of the Sun, but not that of the Moon) are also fixed with respect to the fixed stars. The system of the Ka/pa. however, which is that of the Sindhind, in insisting on a true conjunction of the planets at the beginning and end of 4,320,000,000 years, must include the apogees and nodes in these two Grand Conjunctions, and then endow them with a sufficiently slow motion that they will have the proper sidereal longitudes for the time during which the system is intended to be employed'. 56 P. DUHEM, Systeme, II, p. 213.



In the same way as the House (al-bayt) [i.e. the Ka'ba] is the centre of the Forbidden Mosque (al-masjid al-lJardm), and the Mosque is the centre of the Forbidden Place (al-baram) [i.e. Mecca], and the Forbidden Place is the centre of Hejaz (al-bijdz), and Hejaz is the centre of the Countries of Islam (buldon al-isldm), so the Earth is the centre of the orb of Air (kurrat alhawd '), and the orb of Air is the centre of the orb of the Moon (kurrat a/qamar), and the orb of the Moon is the centre of the spheres (al-aflok). In the same way as those who pray from the horizons tum their faces to the House, so do the stars in the spheres and the projections of their rays to the centre of the Earth. In the same way as the spheres revolve, with their stars, around the Earth, so do revolve those who circumambulate ({o'ijin) around the House. In the same way as their revolutions around the Earth differ from one another, so do differ the revolutions the courses (ashwot) of those who circumambulate around the House. For we see that among those who circumambulate around the House, there are some who walk at a gentle pace, some who hasten, some who rush, and some who run; for this reason their courses are different from one another, but all of them in their circumambulations tum their faces to a unique direction and have a unique goal. No doubt, when the one who walks has reached the 'Iraqi Comer (i.e. the Northern Comer), the one who hastens will have reached the Syrian Comer (i.e. the Western Comer), and the one who rushes (will have reached) the Yemenite Comer (i.e. the Southern Comer), and the one who runs (will have reached) the Black Stone (i.e. the Eastern Comer); for this reason, when the one who walks has completed one circumambulation, the one who runs will have completed (several) circumambulations. Yet, while the courses of these circumambulating people are different from one another because of the speed and the slowness of their movements, their goal is nothing but a unique goal, towards a unique direction. In like manner also the spheres and their stars are in their revolutions around the Earth. In the same way as those who circumambulate around the House start from the Door of the House (bah al-bayt) and join together after the seven courses they complete around the House, so it is said that all stars start their movements from the point in alignment with the first minute of Aries (min muwozot awwal daqiqatin min burj al-bamal), as if it was the Door of the Sphere (ka-anna bah a/-falak). Then they revolve around the Earth and, after a while, their alignments differ from one another on the degrees of the zodiac according to their speed and their slowness, as has been said. When all these (stars), after a great number of revolutions (ba'da dawrat kathira), have join together in alignment on this minute from which they started, then is completed the Great Resurrection (qawma a/-kubrd) and the revolution is renewed 57•

(ii) "The Indian allegory of the circular city". The second story, which immediately follows the first, is said to be of Indian origin and we have no reason to doubt the report of the Ikhwan on this point. The text contains 7 ~

IKHWAN AL-~AFA .. Rasa 'ii, XVI. vol. II, pp. 39. I. 15-40. I. 12 ( *).



a certain number of mathematical values which have not been faithfully preserved in the Beirut edition, but the general computation to which these figures belong is so simple that correct values can be supplied in every place. The beginning of the tale reads as follows: Know further, my brother, that the wise men of India have fonnulated an allegory (mathal) of the revolutions of these stars around the Earth, so that the comprehension of this may be brought closer to those who learn and that its representation may be made easier to those who meditate. According to their report, a king among kings built a city with a circumference of 60 parasangs and sent seven individuals to revolve around it at different paces: one of them l parasang every day, another one 2 parasangs every day, the third 3 parasangs every day, the fourth 4 parasangs every day, the fifth 5 parasangs every day, the sixth 6 parasangs every day, and the seventh 7 parasangs every day. And the king told them: 'Revolve around this city, starting from this door; when, by the number of your revolutions (bi- 'adad dawrati-kum), you join together at the same door, come (to me) and announce to me how many revolutions each one you will have completed'. Whoever has understood the computation of the revolutions of these individuals around the city and succeeded to figure it by imagination is likely to understand the revolutions of these stars around the Earth, and to figure out how many revolutions it will take them to join together in the first (minute) of Aries (ba'da kam dawra yajtami'una ft awwal burj alJ:,amal), in the same way as they were when they started (kama kana ibtida 'u-hum) 58•

The Ikhwan have always been very keen on mathematical demonstrations. However laborious it may seem, the following attempt at explaining the present story in mathematical terms comes thus as no surprise in itself. What is more puzzling in this case is that the demonstration they embark on is wrong. The simple reading of the following lines reveals this at once: As for the computation (IJisab) (concerning) these individuals, it is as follows. After 60 days, 6 individuals join together at the door of the city. The first one has completed l revolution, the second 2 revolutions, the third 3 revolutions, the fourth 4 revolutions, the fifth 5 revolutions, the sixth 6 revolutions. As for the one who completes, every day, 7 (parasangs), he has completed 8 revolutions plus 4nof the parasangs of a revolution, so that these individuals must renew the revolution. After 120 days, they join together once again at the door and each one has completed his first count once again, but the seventh has completed 17 (revolutions) plus l)n of the parasangs of a revolution), so that they must renew the revolution. After 180 days, the six join together for the third time [corr. ex: the second time] and each one has completed, for the third time, his first count, but the 58

IKHWAN AL-SAFA',Rasii"i/, XVI, vol. II, pp. 40.1. 18-41, I. 5 (*).



seventh companion has completed 25 revolutions plus 5n, so that they must renew the revolution. After 240 days, they join together for the fourth time and each one of them has completed his first count, but the seventh companion has completed 34 revolutions plus 2n, so that they must renew the revolution. After 300 days, they join together for the fifth time, but the seventh companion has completed 42 revolutions plus 6n, so that they must renew the revolution. After 360 days, they join together for the sixth time and each one of them has completed his first count for the sixth time, but the seventh companion has completed 51 revolutions plus 3(n) of the parasangs (of the revolution), so that they must renew the revolution. After 420 days, all of them join together at the door of the city: the first one has completed 7 revolutions, the second 14 revolutions, the third 21 revolutions, the fourth 28 revolutions, the fifth 35 revolutions, the sixth 42 revolutions, and the seventh has completed 60 revolutions. This is the allegory (mathal) that the wise men of India have invented in order to account for the revolutions of the spheres and the stars around the Earth. Thus, the Earth is like this city that was built with a circumference of 60 parasangs. The seven planets and their revolutions around the Earth are like these seven individuals. The difference in speed and slowness between their movements are like the differences between the courses of these individuals. As for the king, he is the God, the Creator, the Founder - Blessed be the God, Lord of the Worlds 59 •

It was quite an obvious mistake from the start to say that the seventh companion completes 7 parasangs a day. The sequence of values that follows show that the Ikhwan - or the source they used - should have spoken, not of 7 parasangs a day, but of Y-,of a revolution a day (whether expressed in parasangs or not), which is far from being the same. Once this value has been corrected, the computation does not cause any further problem. For Y-,of 60 parasangs is 8 and 41-, parasangs. which means that after 60 days the seventh companion will have completed 8 revolutions+ 41-, (of a revolution), as stated in the allegory. Then we find, as expected, the values of 17 + Y-,(after I 20 days), 25 + 5/2 (after 180 days), 34 +½(after 240 days), 42 + 6/2 (after 300 days), and 51 + 3/ 7 (after 360 days). According to this progression, the first number without fraction is, indeed, 60, which is thus reached after 420 days. Had the seventh companion completed 7 parasangs a day - as stated twice at the beginning of the fable -, he would have completed, after 420 days, 49 revolutions exactly, thus an integer number less than 60. As a matter of fact, even 60 days would have sufficed, in that case, for all individuals to come back to a perfect conjunction at the door of the city: the seventh individual would have completed 7 revolutions exactly, ~Q


0 ,

Rasc1"if,XVI, vol. II, pp. 41. I. 5-42. I. 9 (*).



making the rest of the story completely meaningless. It is true that 420 is the least common multiple of 1, 2, 3, 4, 5, 6, and 7, and this is what the Ikhwan intended to explain. But it was wrong of them to consider the present problem in terms of days where they should have dealt only with parasangs.

C. Arabic Material in Latin Translation In the Arabic world, as we have seen, many different theories had been put forward concerning the World Year, and even more different values had been attached to the cycles considered in those theories. One needs only to remember the four Indian systems that were known to Abu Ma'shar or the numerous cycles of 'Thousands' we find listed in the Rasa 'ii of the Ikhwan al-Safa' and in so many other sources. Among this heterogeneous material, the precessional cycle, with its traditional value of 36,000 years (or 1° in 100 years), became increasingly important. Yet the incomparable authority of Ptolemy on this point proved to be insufficient to prevent his Muslim successors from reconsidering his estimate: al-Battani (c. 858-929 AD) and some of his contemporaries assigned to the equinoctial precession the value of 23,760 years (or 1° in 66 years), while Ibn Yunus (10th c. AD) came even closer to the exact value with 25,200 years (or 1° in 70 years). And I do not even mention the many values involved in the computations of the so-called trepidation theory, a strange supposition first mentioned by Theon of Alexandria (4th c. AD) which was to enjoy a considerable fortune with the Arabs after Thabit ibn Qurra (836-901 AD)60 • One would expect the situation to have become even more complex in the course of the 12th century, when so many astronomical and astrological works came to be translated, mainly from Arabic into Latin, as part of the whole process by which Islamic science was transmitted to the Christian Medieval West61 • Moreover, since numeric values were likely to be unfaithfully transmitted from one language to the other, one

60 On the movement of trepidation see: P. DuHEM, Systeme, II. pp. 238-46; H. MICHEL,'Origine', pp. 1-8; B.R. GOLDSTEIN, 'Trepidation', pp. 232-47; R. MERCIER, Studies, pp. 47-66 (part II [ 1977]). 61 0n this period of transmission see: L. THORNDIKE, History. vol. II; C.H. HASKINS, Studies; L. THORNDIKE - P. KIBRE, Catalof?ue; F.J. CARMODY, Bibliof?raphy; R. LEMAY, Abu Ma'shar; D.C. LINDBERG, 'Transmission', pp. 52-90; J. VERNET.Cultura; M.-T. d'ALVERNY,'Translations', pp. 421-62; C. BURNlc.TT, 'Comments', pp. 161-71.



would presume that innumerable estimates were circulating, from this period onwards, that were designed to measure all sorts of astronomical and astrological cycles. But this was not the case, as we may surmise from a large number of texts, of which those presented hereafter are but a selection. In this section I should like to underline the way in which the World Year doctrine, far from becoming the expected chaos from such an intense period of translation, was instead lowered to a level of simplification that had probably never been reached before. In the previous sections I tried to show that the Ikhwan al-~afa' did not confuse the cycle of the World Year - for which they mentioned the Indian value of 360,000 years -, and the period of precession, with its Ptolemaic value of 36,000 years. Similarly Abu Ma·shar, who had also derived from the Indian yuga the value of 360,000 years for his 'Cycle of the Persians', was aware of Ptolemy's estimate for the equinoctial precession, as one may infer, for instance, from John of Seville's Latin translation of his Book on Conjunctions, where Ptolemy's value appears twice62• It should be added here that Abu Ma'shar in his Kitab al-uluf actually used a cycle of 36,000 years for his predictions, but this period, technically named a big world-tasyfr, is part of an astrological system that has nothing to do with Ptolemy63 • Even before Abu Ma'shar, we find that Masha'allah (fl. 762-815 AD) already mentioned the precessional shift of I O per I 00 years for the sphere of the fixed stars64 , but still considered a completely different theory of cycles for the division of world history65 • If we now tum to Abraham lbn Ezra (c. 1090 - c. l t64n AD), the Jewish scientist who was himself an important translator of Arabic works, we see that the distinction between precession and the World Year is, once again, very clear. In his treatise on the "Foundations of the 62 Cf. ABO MA'SHAR[ALBUMASAR), De magnis coniunct .• sig. a 4. 1st p .• I. 35 and 2nd p., I. 2. 63 This is the system of the world-tasyirat, as it is usually known. in which the four following cycles are taken into account: small world-tasyfr (360 years); middle worldtasyfr (3,600 years); big world-tasyir (36,000 years); mighty world-tasyir (360,000 years); on this system and related matters see E.S. KENNEDY.'Ramifications•. pp. 26-30; D. PINGREE,Thousands, pp. 57-68. 64 See for instance MAsHA'ALLAH[MESSAHALA], De elem. et orb., Cap. XIX, sig. Hii' (*). The Arabic original of this treatise is lost. 65 For this system as used by Masha'allah in his Ff 1-qirdndt wa 1-adylin wa I-mi/al (On Conjunctions and Peoples and Religions) see E.S. KENNEDY- D. PINGREE,Astrological History. especially pp. 69- 75. Masha'allah 's system is in fact a combination of (i) the old Zoroastrian division of the world into cycles of 12,000 years, and of (ii) the conjunctions of Jupiter and Saturn.



Astronomical Tables", apparently a Latin text in its original form, lbn Ezra indicates the three values assigned to the equinoctial precession by Ptolemy, al-Battani and, as he wrongly states, al-~ufi66; this account has obviously no connection with what the author says, a few pages later, of the Indian theories on world cycles. This last passage I quote here in full, for it gives a good idea of how the Indian speculations on great cycles, once blindly accepted by the astronomers of Islam, turned out to be received by their successors in the 12th century: The mean course of all the planets is computed, according to the Indians, by the days Acintdeindi. They maintained that God created all the planets at the beginning of Aries (in capite Arietis), and they maintained that the days of the world were I ,000,000,000,000 and also 77,000,000,000 and also 215,000,000 and also 450,000. According to them, every planet comes back to its original position without the addition of any fraction (sine fraccionis superadiectione); for example the Sun in 1,461 years, which is named the greatest year (annus maximus), while Jupiter's greatest year is 429. I say, however, that human sense does not understand how anyone, in a fallible art (falibili arte), could be so learned as to fabricate an instrument which would not be misleading regarding the seconds. For if we were to say that it is possible to construe an instrument that would not be misleading except in decimal fractions, we would then say that, in such a great number of years (tanto numero annorum), even a fallacy in the decimals, by recurring many times, would expand to entire years. We thus say that this subject cannot be known. save by the Prophet; but such a thing - i.e. the Prophet - these selfsame Indians deny. Moreover, the days of the world according to Archend contradict (the opinions of) the Indians and do not agree with them 67 •

Acintdeindi and Archend are evidently corruptions for Sindhind and Arkand, i.e. Systems I and II according to Pingree's classification of Indian World Years. All the enormous figures given in this passage appear questionable 68 ; at any rate, none of them seems to correspond to the measures ascribed in the Sindhind and in the Arkand to the Ka/pa (4,320,000,000 years) and to the Mahayuga (4,320,000 years) respectively, although Abraham ibn Ezra must have known them both69 • Now it is still possible to recognize in the values quoted in this passage some elements of the kalpa-period when this cycle is expressed in days, 61> See ABRAHAM IBN EZRA[AVENEZRA), Cognit11m est corpus ... [first words of the treatise], p. 78, II. 8-10 (*). lbn Ezra has probably confused al-~0fi with lbn Y0nus. 67 ABRAHAM IBNEZRA[AVENEZRA). Cognitum est corpus ... , pp. 88, I. 33-89. I. 14 (*). 68 See also the apparat11s criticus in Millas Vallicrosa's edition, p. 89. 69 See the Hebrew text in ABRAHAM IBNEzRA,"Preface" to lbn al-Muthannii, p. 148; transl. in D. PINGREE, 'Ya'qub ibn Tariq', p. 101.



namely l,577,916,450,000 days 70 , so that we should regard the curious succession of values appearing in our text as a corruption of this unique value. The other values to be considered here are 1,461 and 429 - or rather 427 -, which are indeed the numbers of years in which the Sun (Sothic period) and Jupiter are said to complete an integral number of their revolutions. Yet the multiplication of these numbers with those of the five remaining planets would give, as we have already seen71, the value of 648,483,416,738,640,000 years, which we do not find in our passage. Anyway, such a value would have certainly not alleviated Ibn Ezra's suspicion as to the scientific capabilities of the Indians. To sum up, the majority of the Arabic texts dealing with great astronomical cycles present us with a clear differentiation between the equinoctial precession and what we have become accustomed to call the real, conjunctional Great Year: on the one hand, the slow movement of the sphere of the fixed stars, with the Ptolemaic estimate of 36,000 years or a value close to it; on the other hand, the great conjunction of this starry sphere with all the planets, their apogees and nodes, a period usually measured by much higher values deriving from India. As we have already seen, another important reference to the theory of precession could be found in the Jawami' 'ilm al-nujum (or Elements of astronomy) that had been composed shortly after the death of the great 'Abbasid caliph al-Ma'mun (reign: 813-833 AD) by al-Farghani. One cannot overestimate the enormous popularity that this book, which al-Farghani wrote as a summary of the Almagest, was to enjoy in the Muslim world and then, even more, in the medieval West, thanks to the two Latin translations by John of Seville (1135 AD) and Gerard of Cremona (before 1175 AD). As Sabra mentioned in his notice on al-Farghani's [Alfraganus] life and works: 'The influence of the Elements on medieval Europe is clearly attested by the existence of numerous Latin manuscripts in European libraries. References to it in medieval writers are many, and there is no doubt that it was greatly responsible for spreading knowledge of Ptolemaic astronomy, at least until this role was taken over by Sacrobosco's Sphere. But even then, the Elements of alFarghani continued to be used, and Sacrobosco's Sphere was clearly indebted to it. It was from the Elements (in Gerard's translation) that Dante derived the astronomical knowledge displayed in the Vita nuova and in the Convivio' 72• 70

See D. PINGREE,'Ya'qOb ibn Tariq', p. 99. See CHAPTERIV, SECTIONC p. 115. n A.I. SABRA, 'AI-Farghani', p. 542. 71



I quote here the passage - from Gerard of Cremona's translation in which al-Farghani deals with the planets and with the starry sphere at one time: Let us say that it (the starry sphere) is moved from West to East and that it carries together with itself the spheres of the seven planets, around the poles of the zodiacal sphere, at a rate of 1° in I 00 years according to Ptolemy's estimate (secundum considerationem Pto/omaei). Owing to this movement, the apogees (auges) and the nodes (genzahar) of the seven planets are carried forward, following the order of the signs, at the same rate of I O in 100 years (in omnibus JOOannis hac quantitate), and their revolution around the whole zodiacal sphere is completed in every 36,000 years (et fit revolutio earum in orbe signorum 1010 in 36000 annis) 13.

We have emphasized above in which respect al-Farghani's text and other Arabic sources departed from Ptolemy's view on precession. I should like to quote here one more passage in which it is confirmed that the movement of precession applies to all the planets without exception. This passage is taken from the Sententiae de diversis libris attributed to John of Seville: Yet perhaps someone will say that I have raised this matter foolishly, for the apogees of the planets are carried forward from their places. Indeed, many astronomers (astro/ogi) believe that all the planets and their apogees as well as the other stars which are fixed (omnes planetas et auges eorum ac ceteras stellas fixas), are carried forward by the movement of the zodiac (per motum circuli signorum moveri), that they recede from their previous places and wander (ambulare) thus in the order of the signs at a rate of one degree in l 00 years, so that in 36,000 years the revolution is completed once. And this was, according to the Ancients, the motion of the eighth circle, namely the circle of the signs (motus octavi circuli, circuli scilicet signorum)14.

One does not know clearly from the Sententiae whether the astronomical phenomenon mentioned by the author was only meant to involve the movements of the planetary apogees - with presumably the perigees and nodes too -, or those of the planetary apogees and of the planets themselves as well. The distinction is essential, for if it would be wrong to see anything more than the mere extension of the theory of equinoctial precession in the first case, following the alternative possibility we could not help regarding this text as a reference to the conjunctional Great Year. 73 74

AL-FARGHANi [ALFRAGANUS], Elem., Xlll, p. 116 (*). JOHN OF SEVILLE, Sent .. p. 281 ( * ).



It would probably be impossible to single out the original text in which the exposition of the precessional theory had become so penneated with elements belonging to the doctrine of conjunctional Great Years that the confusion of both theories would have become inevitable. As we could already infer from the study of Macrobius's Commentary on Cicero's Somnium 75 , the amalgamation of these two major cycles was, so to speak, fated to be realized by people who, like Macrobius in his time, were not too aware of the fundamental distinction to be made, from the purely astronomical standpoint, between the two periods. The process was certainly facilitated by the fact that the two values most usually ascribed to these cycles after the time of al-Farghani and Abu Ma'shar showed a particularly striking family likeness, being of 36,000 years and 360,000 years respectively. There is, I suppose, no need to insist on the risks of confusion that such a similarity could have prompted in the manuscript tradition. That both figures further correspond to cycles involved in the computations of world-tasyirat may well have made matters even worse. What follows now is an attempt at appraising to what extent those first glimpses of confusion later turned out to reverberate and be amplified in the Latin medieval West. In I 143, thus at about the time of John's translation of the Jawami', Hennann of Carinthia wrote his De essentiis, a philosophical treatise based on an extremely wide range of sources 76 • The influence of al-Farghani's work on a series of astronomical notions exposed by Hennann, although less conspicuous than that of his famous contemporary Abu Ma'shar, is nevertheless indisputable. In a passage devoted to the measures assigned to the distances between the celestial spheres, Hennann states: And by this method the measurement of the distances of the planets lying in between can also be readily calculated by comparing the ratios of their orbits. until finally from Saturn to the eighth sphere the distance would stand at 366 times as much as the distance of Saturn from the centre of the Earth's orb that is, according to those who bring the eighth sphere through one degree every 66 years; but the distance will be much greater if one follows those who bring the eighth sphere through one degree every I00 years - i.e. those people who measure the Great Year at 36.000 solar years (qui videlicet annum vertentem annis so/arihus .xxxn. metiuntur). which is the third of the four circuits of the universe which Abu Ma'shar measures for the purpose of predicting mundane events in the Kitah al-uli1.f1.(transl. Burnett) 7

IV. SECTIOI\ Epp. 120-127. For a precise an:ount of these sources sec HER~IANN OF CARINTHIA, De essenr .. ed. Burnett, pp. 370-9. 71 HERMA'-N OF CARINTHI.-\, De es.H'III., I, fols 66' H - 67' A. p. 141 (*). ~





The reference to the Kitab al-uluf is doubtless an element of high significance for the history of Abu Ma•shar's treatise in the Latin West 78 , but it should not mislead us: Hermann only points out here that one of Abu Ma•shar's tasyfrat happens to have the same period as the precessional shift when Ptolemy 's estimate of the latter is used. The primary relevance of the passage for our purposes is, of course, that Hermann plainly names as a Great Year - or Revolving Year (annus vertens) a cycle in which the general conjunction of the planets is not even suggested. This is especially worth noting, for we know that the expression annus vertens had always been used, so far, to designate the Great Year in the genuine sense of a conjunction of all planets. This designation already appeared in Cicero's Somnium 19 , but it owed its fortune to Macrobius, who in his commentary on the same work considered it necessary to add: But the so-called World Year (Annus vero qui mundanus vocatur), which is truly the Revolving Year (qui vere vertens est), since it is measured by the revolution of the whole universe (quia conversione plenae universitatis efficitur). ( ... ) That must truly be called the Revolving Year, which we measure not by the return of a single star, the Sun, but by the return of all stars in every quarter of the sky to their original positions, with the same configurations over all the skyw. (transl. Stahl)

That Hermann of Carinthia is here implicitly referring to the conjunctional Great Year at the same time as he defines the revolution of the eighth sphere is further confirmed, a few pages later, by his second allusion to Abu Ma•shar system of world-tasyfrat. There, once again, the Latin writer pretends to base himself on the Kitab a/-uluf so as to justify his own strange theory on time, with three 'differences' (differentie) which he calls respectively the 'well-known' (ce/ebris), the 'probable' (probabilis), and the 'necessary' (necessaria). His reference to the Book of the Thousands reads: Abu Ma'shar, in his Uher Millenarius, divides the necessary part into four, multiplying the whole circle by the first four degrees of numbers - in imitation of the four quadrants - and beginning his calculation from the first kind of well-known difference: the first division he calculates at 360 years, the second at 3,600, the third at 36,000, the fourth at 360,000. We, however, take the third division, and wish that it should be to this that the term 'necessity' should properly, and as if by a certain privilege, be applied although (Abu Ma'shar's) other divisions are by no means without effect. 78

On this see C. BURNETT, 'Three Hennes·. pp. 161-71.





De rep., VI. 24. in Som11.• II. 11, 8-12.




For, if the revolutions of certain planets, even when taken individually, measure out definite differences of time, how much more will a necessary radical change to the whole universe follow one complete general revolution of all the planets and stars (integrum et genera/em omnium siderum et ste/larum circuitum necessaria totius mundi novitas consequitur) ! From this, natural scientists (phisici) derive the floods (eluviones) and conflagrations (exustiones) of the universe; from here also are taken the elegant inventions of the poets (poetica figmenta) 81• (transl. Burnett)

In fact, the last lines of the passage do not refer to the Kitiib a/-uluf, nor to any of Abu Ma'shar's works. Rather, they form a faithful recollection of some elements belonging to Macrobius's comment on Cicero's Great Year, where not only the 'floods' and 'conflagrations' 82 , but even the 'natural scientists' and the 'poetical fictions' could already be found, with the use of exactly the same terminology: in Macrobius, these physici were precisely those who assigned the Great Year a period of 15,000 years83, while the poetical fictions referred to Homer's account for the recurrent floods and conflagrations 84 • We could sum up our investigation of Hermann's Great Year by saying that it is the combination of no less than three different notions. One is the big world-tasyfr of Ab0 Ma'shar, which Hermann was alone responsible for having introduced in this context. But the total confusion of the two other notions was not Hermann's own mistake, as appears from the study of the sources he used. For he would never have been able to harmonize the 36,000 years of Ptolemy's precession with the 15,000 years that he could find in Macrobius, clearly his main source on the topic of genuine Great Years. A very authoritative text - one may think of al-Farghani's Elements - must have biased Hermann in favour of an amalgamation so incompatible with these data. Alexander Neckam (1157-1217 AD) was a brilliant English man of science. Although his trust in astrology seems to have been limited 85 , he devoted several chapters of his De naturis rerum to the heavenly bodies and to their influence on the elements of the sublunar world. In this book Alexander admits, not without some hesitation, the controversial theory of the harmony of the spheres86 • He also speaks of the Great Year in a passage which may be translated as follows: HERMANN OF CARINTIUA, De essenr.• I, fol. 70' EF, p. 165 (*). Cf. MACROBIUS, in Somn., II. 10, 14. The terms elul'io and exustio were already those used in Macrobius·s model; cf. CICERO,De rep .. VI, 23. 81 · Cf. MACROBtus. in Somn., II, 11, 10. 114 Cf. MACROBIUS,in Somn., 11, 10, 11. 8~ Cf. L. THORNDIKE,History, II, pp. 202-3. 86 ALEXANDER NECKAM, De nat., I. 15. Kl 81



If what we said before is to be remembered carefully, namely, that the stars, as clearly appears, complete in the finnament one degree of the circuit in 100 years, it will be manifest that the stars will pass through one sign in 3,000 years, since every sign consists of 30 degrees, and every degree of 60 minutes. Now since it is universally agreed that the zodiac is divided into twelve signs, it will follow that the stars will bring their course to completion in 36,000 years. This is the Great Year on which philosophers debate (Hie est magnus annus, de quo phi/osophi disserunt) 81 •

As was the case with Hermann's De essentiis, we find, once again, a text in which the Great Year (magnus annus) is plainly defined as the precessional revolution of the eighth sphere. There is no explicit mention of the general conjunction which used to determine the completion of the real Great Year, but, apart from the expression itself, a hint of the classical definition is still preserved in the reference to these 'philosophers' (philosophi), a term which more likely alludes to Plato, Cicero or Macrobius than to Ptolemy, al-Battani or lbn YOnus. About one generation after Neckam, his fellow-countryman Bartholomew the Englishman wrote a treatise of the same kind entitled De genuinis rerum coelestium, terrestrium et inferarum proprietatibus. Astronomy and astrology are dealt with in Book VIII of the nineteen booksincluded in this encyclopaedia. Book VIII is an amalgam of many different theories, most of them proving to derive from four traditions: Neoplatonic notions with Calcidius, Macrobius and Martianus Capella; Aristotelian physics with the Meteorologica and the De caelo; Ptolemaic astronomy and astrology with the Almagest and the Tetrabiblos; Arabic astronomy and astrology with Masha'allah, Abu Ma'shar and al-Farghani88 • The Great Year is briefly referred to at the end of the chapter on the fixed stars: Indeed, (the fixed stars) are shifted at a rate of one degree in 100 years, so that the great shift is made in 36,000 years. And this is the Great Year, which is the end of all things. So far Aristotle in the same book (i.e. the De proprietatibus elementorum); also what Macrobius says in Cicero's book. The end of this World Year is when all the stars and all the constellations and planets will have come back from a certain position to the same (/stius mundani anni finis est, cum stellae omnes omniaque sidera ac planetae a certo loco ad eundem remeaverunt). And natural scientists (physici) maintain that this (Year) is reached after the completion of 15 [corr. ex: 25] thousands of years, etc ... Whatever philosophers (philosophi) may have said about this, it must not be forgotten that it is not our duty to define when the very end will be. This only the Founder of times knows, who holds in His power the moments and times [= Actus Apostolorum, I, 7]89 . 87 ALEXANDER

NECKAM, De nat., I. 6 (*). this see M.C. SEYMOUR er al., Bartholomaeus, pp. 17-28 and 97-8. BARTHOLOMEW THE ENGLISHMAN. De propriet., VIII, 33. pp. 420-1 (*).

Kl4 On 89



In this case the two theories merge to become even more confused. The explicit resignation of the last lines reveals that Bartholomew is at a loss, as does also his mentioning of two different values for the period considered. As for an accurate definition of the Great Year, it looks as if the author had also left the question open to the Creator, for his explanation of the astronomical phenomenon is not clear at all90 • What is more relevant here is that Bartholomew indicates two sources for his statement. One is Macrobius's Commentary on the Somnium, which was already an important source for Hermann's De essentiis. It is thus no surprise to find here a new reference to those same physici who, according to the commentator, estimated the period of the Great Year at 15,000 years. The other source, which the author refers to as Aristotle's De proprietatibus e/ementorum, is in fact the Pseudo-Aristotle's De causis proprietatum et elementorum, an Arabic treatise which had been translated into Latin by Gerard of Cremona. There is no reason for doubting that Bartholomew used this work, for he appears, indeed, to quote one phrase of it almost word for word. The original phrase was part of a passage in which the Pseudo-Aristotle tried hard to refute the idea that the periodic interchange on earth between seas and mainlands might be due to any astronomical cycle. The PseudoAristotle's argument - which wholly contradicts Aristotle himself was summarized by Vodraska as follows: 'The opponents agree that the change is dependent upon change in the heavenly region; but the change in the heavenly region requiring the longest span of time is the precession of the equinoxes, which requires 36,000 years; but the known circumference of the Earth is 20,400 miles, so that the complete interchange of sea and land would involve a displacement of .285 miles a year; but there are cities on the coast which have existed for a long time, and for which there are continuous records, and neither from present experience nor from past records do we see that the cities now are any farther from or closer to the sea than they were in the past; therefore. there is no interchange of sea and land. What the author has done is to deduce from a theory an observable consequence which can, in this case, be shown to be false. What he proves, of course, is not that there is no 90

Bartholomew is here quoting Macrobius almost literally (cf. MACROBIUS, in Sonm., II, 1 I. 10: Mundani ergo an11ifinis est, cum stel/ae omnes omniaque sidera quae d1t1..uviJ~habet a certo loco ad eundem locum ita remeaverint), but he (or one of the transmitters before him) obviously failed to interpret the Greek word d1t1..uviJ~(fixed) correctly, to the effect that he took it for ac planetae. For the use of the terms stella and sidus see A. LE 8CEUFFLE, Noms, pp. 5-23.



interchange of sea and land, but either (a) that the interchange is not dependent upon changes in the heavens, or (b) that the interchange does not take place in so short a period as 36,000 years, or both (a) and (b)' 91 • Thus, having enumerated a certain number of shorter cycles92, the author finally rules out the hypothesis that the interchange of seas and mainlands may be due to the precessional shift: Or is this (periodic interchange) due to the shift of the sphere of the fixed stars (propter permutationem orbis stellarum fixarum), for this sphere is shifted at a rate of one degree in every I 00 years, so that this shift is made in every 36,000 years? For this is the end of all things (Et hoe est ultimum rerum omnium), and this is also the thing upon which the supporters of the return base themselves, and the opinion they have expressed (et est res super quam innituntur auctores recidivationis, et sententia quam dixerunt)93• (transl. Vodraska)

Now since the Pseudo-Aristotle already called the shift of the eighth sphere 'the end of all things• and 'the thing upon which the supporters of the return base themselves•, we are led to regard this text as yet another evidence of the confusion of both theories. The writing of the Pseudo-Aristotle's treatise is difficult to locate and to date, but we have good reasons for conjecturing that it was written in 'Iraq at about the end of the 9th century94 , which means that this text was possibly one of the very earliest to propagate the amalgam. To stay in the same context of the Aristotelian Arabic Middle Ages, a word should be said of a discussion that we find at the end of the Epitome of the De generatione et corruptione by the famous commentator lbn Rushd [Averroes] (1126-1198 AD). The discussion has its root in the passage in which Aristotle stressed the distinction between the return of things in species and in number95 • The passage from the Epitome is interesting, because it does not only present us with Averroes's view but also with the lost comment on the same locus by another great of Aristotle's commentators, namely, Alexander of Aphrodisias (2nd/3rd c. AD). Averroes first describes the problem itself: But this kind of cyclical generation must return upon itself in species, but it cannot return upon itself in the individuals of the species. For it is impossible for Zaid as an individual to come into being again after having once been in such a way that he will return upon himself cyclically, and it is 91

S.L. VODRASKA. Pseudo-Aristotle. pp. 32-3. 92 Cf. ARISTOTLE (PSEUDO·), De causis propr. et e/em., Sect. 9, pp. 147-52 (*). 9 J ARISTOTLE (PSEUDO·). De causis propr. et elem .• Sect. 9. pp. 152-3 (*). 94


See the discussion in Vodraska's edition, pp. 57-66. gen .• II. 11. 338a-b. See also CHAPTER I. SECTION B pp. 41-42.

Cf. ARISTwAN[HALY ABENRUDIAN], in Pto/emaei Quadripartitum, I, 2 (Venice, 1484, fol. a3'): Nequaquam est possibile nee ab aliquo dici poterit nisi [quam] stulte deridendo perfecte se id scire confiteatur quod a nullo unquam perfecte sciri potuit vet quam se ad id pervenisse dicat ad cuius perventum nullius mortalis vita suffecit. ABRAHAM IBN EZRA,Cognitum est corpus so/are habere magnitudinem ... (ed. J.M. Millas Vallicrosa, El libro de losfundamentos de /as Tablas astr6nomicas, Madrid - Barcelona, 1947, p. 78, II. 8-10): Antiqui vero et Ptholomeus dicunt quod 100 annis unum gradum pretereunt. Albateni vero probavit quod 66 annis uno gradu moventur; Azofi vero 70 annis uno gradu. ABRAHAMIBN EZRA, Cognitum est corpus so/are habere magnitudinem ... (ibid., pp. 88, I. 33-89, l. 14): Et medius cursus omnium planetarum secundum indos sumptus est a diebus Acintdeindi, qui dixerunt Dominum omnes planetas in capite Arietis creasse et dies mundi dixerunt esse I 000000000000 et adhuc 77000000000 et adhuc 215000000 et adhuc 450000, et secundum eos omnis planeta revertitur ad punctum sui loci sine fraccionis superadiectione, ut sol in 1461 annis, qui annus maximus dicitur, et annus lovis maximus dicitur 429. Ego autem dico quod sensus humanus non capit aliquem in falibili arte adeo peritum posse esse qui instrumentum aliquid adeo fabrefaciat quod non in secundis fallacia sit. Quod si dixerimus sic posse componi instrumentum ut nee etiam nisi in decimarum fractionibus fallacia sit, ad hoe dicimus quod in tanto numero annorum etiam in decimis fallacia multociens occurrens usque in annos integros fallacia conflaret, dicimus ergo quod ista res cognosci non potuit nisi per prophetam, quod tamen ipsi indi scilicet prophetam negant, et eis sunt contrarii dies mundi secundum Archend qui eis non consentiunt. ALBERTTHEGREAT,Speculum Astronomiae, Cap. VII (ed. Zambelli, The Speculum Astronomiae and its Enigma, Dordrecht - Boston - London, 1992, p. 228): Prima ergo constitit in coniunctibus duorum planetarum in uno signo, et sunt viginti unum coniunctiones. Et trium planetarum, et sunt triginta quinque coniunctiones. Et quatuor planetarum, quae sunt similiter triginta quinque coniunctiones. Et quinque planetarum, quae sunt iterum viginti unum coniunctiones. Et sex planetarum, quae sunt septem coniunctiones. Et omnium, quae est una. Haec sunt in universo centum viginti, quarum praecipue considerat eas quae trium sunt altiorum.



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ALEXANDER NECKAM,De naturis rerum, I, 6 (ed. T. Wright, The Chronicles and Memorials of Great Britain and Ireland during the Middle Ages, London, 1863, p. 39): Si autem diligenter memoriae commendetur quod supra diximus, videlicet quod stellae in centum annorum curriculis unum gradum in firmamento adquirant, patebit quod stellae in tribus annorum millibus signum unum pertranseant, cum quodlibet signum in se triginta gradus habeat, et quilibet gradus sexaginta minuta. Cum autem vulgo constet duodecim esse signa in quae dividitur zodiacus, proveniet stellas in triginta sex millibus annorum cursum suum perficere. Hie est magnus annus, de quo philosophi disserunt. AL-FARGHANi [ALFRAGANUS], Elementa, XIII [transl. by Gerard of Cremona] (ed. R. Campani, II libro dell'aggrega:zione de/le stelle (Elementa astronomica), Florence, 1910, p. 116): Dicamus ergo quod ipsa movetur ab occidente ad orientem et movet secum spaeras stellarum 7 simul super duos polos orbis signorum in omnibus I00 annis parte una, secundum considerationem Ptolomaei; et propter illud permutantur auges stellarum 7 et genzahar earum secundum continuitatem signorum, vel successione, in omnibus 100 annis hac quantitate et fit revolutio earum in orbe signorum toto in 36,000 annis vel ipsae secant zodiacum et revolvuntur in eo toto. AL-fARGHANt, Jawami' (Elements), XIII, ed. J. Golius, Amsterdam, 1669, p. 49:


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ARISTOTLE (PSEUDO-),De causis proprietatum et elementorum, Sect. 9 (ed. S.L. Vodraska, Ph.D. Dissertation, University of London, 1969 pp. 147-52): (l) Dico ergo quod causa quam dixerunt de permutatione maris super terram non potest esse. Quin sit causa illius ex permutatione lune super signa et ex operatione eius, et est illud in omnibus viginti octo diebus, quare destruitur agricultura a grano? Aut sit causa illius ex permutatione mercurii et veneris, et est illud in omnibus decem mensibus aut minus illo? Aut accidit illud ex permutatione solis, et permutatur mare in omni anno? Aut ex operatione martis et motu eius, et fit permutatio in omnibus decem et octo mensibus? Aut est causa illius propter motum iovis et eius permutationem, et erit accidens quod diximus in omnibus duodecim annis? Aut est causa permutationis satumus, et est illud accidens in omnibus triginta annis? Aut propter coniunctionem duarum stellarum gravium. et est illud in omnibus viginti annis? Aut est illud propter coniunctionem et permutationem ex triplicitate ad triplicitatem. et est illud in omnibus ducentis et quadraginta annis? Aut est illud propter rem quam dixerunt auctores atalasimet quod orbi signorum est accessio octo partium et recessio octo partium in omnibus octaginta annis gradus. quare accidit illud in omnibus sexcentis et quadraginta annis? (2) Aut est illud propter permutationem orbis stellarum fixarum, et ipse permutatur in omnibus centum annis gradu uno, quare accidit ilia permutatio in omnibus triginta sex milibus annis? Et hoe est ultimum rerum omnium, et est res super quam innituntur auctores recidivationis, et sententia quam dixerunt.

Tractatus de tempore adventus Antichristi (ed. H. Finke. Aus den Tagen Bonifaz VIII., Munster. 1902, p. cxxxiv): Astrologi vero, qui probant. quod motus retardationis octave sphere compleri nequit in paucioribus annis quam in XXXVI milibus, debent scire, quod suam potentiam et sapientiam Deus non alligavit naturalibus causis. Set sicut in productione mundi fuit supematuraliter operatus. sic et in consummatione huius seculi supematuraliter operabitur. Et si totius retardationis revolutio necessaria foret, ut asserunt, ad universalem perfectionem, nichilominus Deus est potens motum orbium ARNOLD OF VILLANOVA,



velocitare, quantum placuerit, et revolutionem complere brevissimo tempore. ita ut revolutiones L vel centum annorum compleantur in uno anno vel dimidio. BARTHOLO¥EW THEENGLISHMAN, De genuinis rerum coelestium, terrestrium et inferarum proprietatibus, VIII, 33 (Frankfurt, 160 I ; facs. Frankfurt, I 964, pp. 420-1): Pennutantur enim in I 00. annis uno gradu, quarum accidit pennutatio magna 36. millibus annis. Et hie est annus magnus, quod est ultimum omnium rerum. Hucusque Aristot. in eodem libro. In libro autem Ciceronis dicit Macr. Istius mundani anni finis est, cum stellae omnes omniaque sidera ac planetae a certo loco ad eundem remeaverunt. Hoe autem et physici volunt, post annorum 25. millia peracta contingere, etc. Quicquid autem super hoe dixerunt philosophi, hoe certitudinaliter tenendum est, quod nostrum non est diffinire, quando ultimus finis erit. Hoe enim solus novit temporum conditor, qui momenta et tempora continet in sua potestate.

De temporum ratione, 36 (ed. J.-P. Migne, Paris: PatroloBEDETHEVENERABLE, gia Latina, XC, 1904, coll. 463b - 464a): Annus magnus est, cum omnia simul errantia sidera ad sua quaeque loca quae simul habuere recurrunt. De quo Iosephus in primo Antiquitatum libro cap. 4, cum longaevitatem primorum hominum describeret, ita meminit: "Nullus autem ad vitam modemam, et annorum brevitatem, quibus nunc vivimus, vitam comparans antiquorum, putet falsa quae de illis sunt dicta, et eo quod nunc vita tanto non ducatur tempore. credat neque illos ad vitae illius longitudinem pervenisse. Illi namque cum essent religiosi, et ab ipso Deo facti, cumque eis pabula opportuniora ad maius tempus existerent praeparata. tantorum annorum curriculis rite vivebant; deinde propter virtutes et gloriosas utilitates, quas iugiter perscrutabantur, id est, astrologiam et geometriam, Deus eis amplius vivendi spatia condonavit, quae nunc baud ediscere potuissent, nisi sexcentis viverent annis, per tot enim annorum curricula magnus annus inpletur. BEDE(PSEUDO-),De mundi celestis terrestrisque constitutione, 178 (ed. C. Burnett, London: Warburg Institute Surveys and Texts, X, 1985, p. 34): Quod [eclipsis Lune] vero in eodem signo. mense, parte, revocatis cunctis planetis ad locum suum, non nisi post quindecim milia annorum fit. BEDE (PSEUDO-),De mundi celestis terrestrisque constitutione, 182 (ibid., p. 34): Sed quando [Sol patitur eclipsim) in eodem signo, mense et parte fit, revocatis omnibus stellis ad priorem locum, hoe est post .XV. milia annorum. CALCIDIUS, Timaeus, 38c (ed. J.H. Waszink, London - Leiden: Corpus Platonicum Medii Aevi, IV, 1975. p. 30, II. 19-24): Hae ergo dei ratione consilioque huius modi genituram temporis volentis creari sol et luna et aliae quinque stellae quae vocantur erraticae factae sunt. quo tarn partes temporis notarentur certa dimensione quam reditus anfractusque temporarii sub numeri comprehensionem venirent, corporaque siderea fabricatus assignavit vitalibus diversae naturae motibus numero septem totidem corpora.

Timaeus, 39d (ibid., p. 32, II. 7-10): Est tamen intellectu facile, quod CALCIDIUs, perfectus temporis numerus perfectum annum compleat tune demum. cum omnium



octo circumactionum cursus peracti velut ad originem atque exordium circumactionis alterius revenentur, quam semper idem atque uniformis motus dimetietur. CALCIDIUS, in Tim .• 39d (ibid., pp. 162, I. 13-164, I. 2): Perfectum temporis numerum, qui perfectum complet annum, appellat eum, quo tarn septem planetes quam ceterae stellae quae dicuntur ratae repraesentatae originalibus sedibus eandem, quae fuit initio rerum principioque mundi, constitutionis efficiunt designationem, ita ut et prolixitas prolixitati et intervallorum pristinorum latitudini latitudo et profunditati profunditas quadret. Hoe autem tempus continet annorum innumerabilem seriem, quippe cum stellarum errantium circuitus impares sint necessarioque diversis temporibus cursus suos compleant, praeterea latius aliae a medietate mundi evagentur, angustius vero aliae ad austri septentrionisve convexa, celsiores aliae a terra sint, aliae non adeo longo altitudinis intervallo distent a regione terrae, diversos quoque inter se motus agant, ut citae tardius progredientibus, ultra progredientes retrorsum recedentibus, humilibus excelsae, dextrae sinistris sinisteriores dexterioribus occurrant in unum nihilque omnino sit, quod in designatione differat a ceterorum astrorum habitu specie figuris. Atque ut omnes omnibus aequis diametris distent unumque nutum atque unam efficiant stellarum omnium confonnationem, cum sit necesse, si unus aliquis ex ignibus repraesentatus fuerit in antiquae constellationis statum iuxta rationem fone altitudinis, latitudini tamen non sit repraesentatus antiquae, vel si perfecte per omnia momenta unus revocatus ad antiquum statum fuerit, ceterorum tamen, quorum est diversa condicio, perfecta repraesentatio minime provenerit, necesse sit etiam eius stellae quae una repraesentatione perfecta invenietur rursum fieri aliam mutationem, quoad opponunitas ilia proveniat, quae unam faciem atque eandem repraesentet quae fuit ab initio mundi. Quern quidem motum et quam designationem non est putandum labem dissolutionemque afferre mundo, quin potius recreationem et quasi novellam viriditatem positam in auspicio motus novi; baud sciam an in quibusdam regionibus terrae proventura sit ulla ex innovatione iactura.

Chartularium Universitatis Parisiensis (ed. H. Denifle - A. Chatelain, I, Paris, 1899 [repr. Brussels, 1964, p. 544, an. 61): Quod redeuntibus corporibus celestibus omnibus in idem punctum, quod fit in XXX sex milibus annorum, redibunt idem effectus, qui sunt modo. CLEMENT OF ALEXANDRIA, Stromateis, V, l, 9-10 (ed. 0. Stahlin - L. Frilchtel, Berlin: Die Griechischen Christlichen Schriftste/ler, 1985, p. 332): 'O


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