The Astrophysics of Berossos the Chaldean

The Astrophysics of Berossos the Chaldean Stephen Toulmin Isis, Vol. 58, No. 1. (Spring, 1967), pp. 65-76. Stable URL: http://links.jstor.org/sici?sici=0021-1753%28196721%2958%3A1%3C65%3ATAOBTC%3E2.0.CO%3B2-0 Isis is currently published by The University of Chicago Press.

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The Astrophysics of

Berossos the Chaldean

By Stephen Toulmin*

B

Y N O W WE possess a solid body of evidence about the computational astronomy of the Babylonians, and the nature of their arithmetical procedures is fairly well underst0od.l Yet we know scarcely anything about their astrophysical conceptions. T h e cuneiform tablets deciphered in the years since 1880 comprise almost entirely tables of ephemerides, procedure texts, and similar computational material. We cannot infer from these what the Babylonians considered the heavenly bodies to be; we know only that they gaJe them divine names. otherwise, we have little but mytholbgical traditions to fall back om2 and these are too poetical to provide a substantial indication of Babylonian astrophysical beliefs. In this situation, even thirdhand evidence may be better than nothing. T h e starting point of this discussion3 is a passage in the treatise De architectura of Vitruvius, in which he sets out the astronomical backuound needed in order to understand the principles governing the design of sundials. In this passage Vitruvius refers to ; ~ a b ~ l o n i called an Berossos, or Berosus, who is kn&n to have migrated to the Greek island of Cos around 300-270 B.c., and attributes to him an explanation of the phases of the moon different from any put forward by the Greek natural philosophers. T h e passage in question reads as follows: u

"Brandeis University. outstanding general account is 0.Neugebauer, T h e Exact Sciences in Antiquity (2nd ed. Providence: Brown Univ. Press, 1957). For details, see Neugebauer's Astronomical Cuneiform Texts (London: Lund Humphries for the Princeton Institute for Advanced Study, 1955). 2 See, for instance, A. Heidel, T h e Babylonian Genesis (Chicago: Chicago Univ. Press, 1942); H. Frankfort et al., T h e Intellectual Adventure of Ancient Man (Chicago: Chicago Univ. Press, 1945), reprinted also as Before Philosophy (London: Penguin Books, 1951); and S. H . Hooke, Babylonian and Assyrian Relzgion (London: Hutchinson, 1953). Since Babylonia was ruled by Greek kings from 325 B.C. and formed part of the Hellenistic civilization, some exchange of cosmological and astrophysical ideas between Greeks and Babylonians was already taking place before 290-270 B.C.(the date traditionally associated with the 1T h e

name of Berossos). This is confirmed by the tradition (reported, e.g., by Plutarch, Quaestiones Platonicae, Ques. 8) that the rotation of the earth was discussed around this time by both Aristarchos of Samos and Seleukos of SeleukiaSeleukia being located near the ruins of Babylon. For the earlier period, the most significant indication of the cosmological scheme underlying Mesopotamian astronomical skills is the set of texts dating from the Sargonid period (c. 700 B.c.) presented by J. Schaumberger in Zeitschrift fur Assyriologie, 50 (N.S. 16), pp. 214 ff.; these are discussed below. I owe these last references to the referee who commented on a n earlier version of this paper. 3 T h e present paper is a revised version of one written in 1959-1960 but never published. T h e conclusions were referred to briefly in S. Toulmin and J. Goodfield, T h e Fabric of the Heavens (London: Hutchinson; New York:

STEPHEN T O U L M I N

Berosus, qui a b Chaldaeorum civitate sive nation?

progressus in Asia etiam disciplinam Chaldaicam

patefecit, ita est professus:

Pilam esse ex dimidia parte candentem, reliqua

habere caeruleo colore. Cum autem cursum itineris

sui peragens subiret sub orbem solis, tunc eam

radiis et impetu caloris corripi convertique

candentem propter eius proprietatem luminis

ad lumen. Cum autem ea vocata ad solis orbem

superiora spectent, tunc inferiorem partem

eius, quod candens non sit, propter aeris

similitudinem obscuram videri. Cum ad perpendiculum

esset ad eius radios, totum lumen ad

superiorem speciem retineri, et tunc eam vocari

primam.

Cum praeteriens vadat ad orientis caeli partes,

relaxari ab impetu solis extremamque eius

partem candentiae oppido quam tenui linia ad

terram mittere splendorem, et ita ex eo eam

secundam vocari. Cotidiana autem versationis

remissione tertiam, quartam in dies numerari.

Septimo die, sol sit ad occidentem, luna autem

inter orientem et occidentem medias caeli

teneat regiones, quod dimidia parte caeli

spatio distaret a sole, item dimidiam candentiae

conversam habere ad terram. Inter solem vero

et lunam cum distet totum mundi spatium et

lunae orienti sol trans contra sit ad occidentem,

eam, quo longius arsit, a radiis remissa XI111

die plena rota totius orbis mittere splendorem,

reliquosque dies decrescentia cotidiana ad

perfectionem lunaris mensis versationibus et

cursu a sole revocationibus subire sub rotam

radiosque eius, et iam menstruas dierum efficere

rati~nes.~

T h i s passage can be translated as follows: Berosus, who came from the city or nation of the Chaldeans

and expounded Babylonian science in Asia Minor,

taught as follows:

T h e globe of the moon is luminous on one hemisphere, the other

being dark blue in color. When in the course of its journey

it comes below the disk of the sun,

the rays of the sun and the violence of its heat take hold

of the shining half and turn it, on account of its

luminosity, toward the light. But while those

Harper & Bros., 1961), but the argument has not hitherto been fully documented. 4 Vitruvius, De architectura, ed. Frank Gran-

ger (Loeb Classical Library) (London: W. Heinemann; New York: G. P. Putnam's Sons, 1934), Vol. 2, pp. 226-228.

BEKOSSOS THE CHALDEAN

upper parts face the sun, the lower part of the moon, which is not luminous, is indistinguishable from the surrounding atmosphere and so appears dark. When it is quite perpendicular to the rays, all its light is retained on the upper face, and then it is known as the first [or new] moon. When moving on, the moon goes toward the eastern parts of the sky, the sun's force on it is weakened, and the very edge of its luminous hemisphere casts its splendor on the earth in the form of a very thin arc, from which it is called the second moon. As the twisting abates, day by day, it is called the third moon, fourth moon, and so on. On the seventh day, the sun being in the west, the moon occupies the middle of the visible sky and, being halfway across the sky from the sun, turns half of its shining face toward the earth. But, when the whole breadth of the world separates the sun and the moon-the moon rising in the east just as the sun sets in the west-then the moon, being at that distance freed from the effects of the sun's rays, displays on the fourteenth day the full glory of its whole sphere as a complete disk. During the remaining days until the completion of the lunar month it diminishes daily, twisting back as it comes once more under the influence of the sun's disk and rays, and so effecting the days of the month in due order. What does this passage mean? How are we to interpret the account here offered to explain the phases of the moon? If we compare the theory attributed by Vitruvius to "Berosus" with the explanations generally accepted by Greek natural philosophers around 300 B.c., we shall be struck by one obvious idiosyncrasy; yet there is a graver difficulty about the theory, which lies deeper. What catches the eye immediately is this: whereas, from the middle of the fifth century B.C.on, Greek natural philosophers were generally agreed that the moon borrowed its light from the sun,5 Berossos still credits the moon with being self-luminous, at any rate on one hemisphere. Indeed, Vitruvius immediately goes on to contrast the theory of Berossos with another theory, which he credits to Aristarchos, who realized "that the moon does not have a light of its own, and that it is like a mirror that receives its splendor from the power [impetus] of the sun." This feature of Berossos' theory is archaic enough, though we might try to help him out-mistakenly, as it will appear-by translating candens as "shining" instead of "self-luminous." Yet this particular feature is only a pointer toward another, more profound difference between Berossos and his Greek contemporaries. This comes to light if we attempt a complete reconstruction of the theory offered. T h e difficulty is this: so long as one 5 C f . J. Burnet, Early Greek Philosophy (4th ed. London: A. & C. Black, 1930), especially

pp. 177, 271. svitruvius, op. cit., p. 228.

68

STEPHEN TOULMIN

attempts to interpret Berossos' theory in terms of the sort of cosmological picture common to all the Greek philosophers from 500 B.C. on, it remains confused and incoherent. For the problem the theory is intended to account for arises as a problem only if one assumes a more primitive picture of the layout of the heavens. We must begin by asking what exactly Berossos was trying to explain. T h e basic facts about the phases of the moon have always been clear enough. When the sun and moon rise and set at the same time, the moon is invisible from the earth; when they rise and set twelve hours apart, the moon is visible as a full disk; when six hours apart, the moon appears as a half disk; and so on for intermediate cases. Only when an attempt is made to explain these facts do precise theoretical questions arise, and these in turn depend on the general cosmological picture by which the particular astronomer interprets the facts. What, then, is Berossos' precise question? Evidently, on his account, the moon is nearer to the earth than the sun is (sub orbem solis). At the beginning and end of the month, the moon turns its bright face toward the sun, so as to be invisible from the earth; halfway through the month, on the other hand, its bright face is entirely visible from the earth, and so once again for intermediate cases. This "twisting" of the moon's globe away from and back toward the earth-the word versatio has forcible overtones-is the phenomenon Berossos sets himself to explain. His theory is that when the sun and moon come close together in the sky, the force (impetus) exerted by the sun's "rays and heat" causes the moon's bright half to turn away from the nonluminous earth and to face-on the general principle that like attracts liketoward the luminous sun. At the middle of the month, by contrast, the two bodies are so far apart that the sun's light and heat lose their power to act on the moon (a radiis remissa), with the result that it is free to turn its shining face back toward the earth. For Berossos, accordingly, the phases of the moon involve a "twisting" of its globe, caused by a force from the sun whose strength diminishes as the two bodies get further apart. In half a dozen places, the language of Vitruvius' account implies the exercise of an active power by the sun on the moon: not only such words and phrases as impetus, versatio, and a radiis remissa, but even more the use of such verbs as corripere ("to seize upon"), convertere ("to make to turn completely round"), and relaxare ("to slacken, or release"). Yet what necessity is there for this hypothesis? Cannot the observed phases of the moon be explained quite simply, without invoking any such forcible interaction? At this point, we are approaching the heart of our problem. As always, the physics of this celestial process is bound up with, and dependent on, its geometry. If we construe Berossos' problem in terms of those geometrical relationships which come naturally to us today-or even those which the Greek natural philosophers took for granted-we can dispense entirely with his solar impetus; and, at the same time, we can dispense also with his other

BEROSSOS THE CHALDEAN

69

fundamental assumption, that the moon is, over one hemisphere at least, self-luminous. For, as we shall see shortly, these two hypotheses are connected.

First, then, let us depict the relative positions of the sun and moon as seen from the earth around sunset, making our normal assumptions (1) that the sun is much more distant than the moon, and (2) that the moon's track is effectively circular. T h e result will be as shown in Figures 1 and 2. (Notice

FIGURE 1. Aspect of the moon as seen from the earth at sunset: at new moon (right), first quarter (middle), and full moon (left).

2. Relative positions of the FIGURE earth and moon with respect to the sun's light (arrows): at new moon (right), first quarter (middle), and full moon (left).

that in Fig. 2 the earth is represented as a sphere. This is not essential: so long as the moon's track is circular, one can combine the doctrine that the moon's light is borrowed-as Anaxagoras seems to have done7-with a belief that the figure of the earth is that of a flat disk rather than a sphere.) In terms of such a picture, what are we to make of Vitruvius' text? In particular, what role can a "force" from the sun's rays play in this situation? T h e Loeb editor's interpretation is fanciful. He presents a diagram similar to Figure 2 and comments on it: Berosus' optical theory of the conflict between the rays from the moon and the more powerful rays of the sun anticipated Young's discovery of the absorption of light by interference. This gloss is quite without foundation. Vitruvius is explicit; there is no mention at all of the sun's light destroying or absorbing the moon's light "by interference." T h e whole theory starts from the supposition that proximity to the sun forces the moon to turn its bright face away from the earth and toward the sun. 7

Cf. Burnet, op. cit., p. 270.

70

STEPHEN TOULMIN

Can we ourselves d o any better? If we ignore all the "forcible" idioms in Vitruvius' account of the theory, we can at any rate argue that Berossos' account does justice to the observed facts about the moon's monthly phases, even though it remains to be explained why, on this theory, the "selfluminous" lunar hemisphere is sometimes eclipsed at full moon. For, in Figure 1, the three positions shown for the moon correspond to its position at sunset at new moon, on the seventh day of the month, and at full moon, respectively, and what we shall actually observe in each case closely resembles the aspect which a "parti-colored sphere" would present to the eye. Yet this reading still has shortcomings. I t succeeds only at the price of selecting from Vitruvius just those features of the theory he is reporting which survive into the modern picture; and it leaves unaccounted for just those aspects which are apparently distinctive of Berossos' theory. I n the first place, if one accepts Figures 1and 2 as a correct picture of the celestial layout, then the moon's luminous face will be turned toward the sun at all times, and the hypothesis that one hemisphere is self-luminous is superfluous. I n the second place, since the luminous face of the moon will now be directed toward the sun automatically, no impetus solis will be called for to corripere, convertere, relaxare, or remittere. Now, indeed, there will be no need for the moon even to "rotate" between new moon and full moon, as the text plainly asserts-always supposing that we are prepared to read the words converti and versatio in a weakened, intransitive sense, to mean simply "turn round" and "rotation." What alternative remains? At this point, we could give u p the attempt to make consistent sense of Vitruvius' account, shrugging off the references to, for example, "the effects of the sun's rays" as representing merely a lapsus on the part of Berossos or maybe a misunderstanding on Vitruvius' part, or as having some other meaning which has so far escaped us. But that would be premature. Whatever merits or defects Berossos' theory may have as an account of the best Babylonian views on the subject in 300 B.c., we have at any rate a cross-check on Vitruvius. For Lucretius reports a very similar theory as being the "Babylonian Doctrine" of the "Chaldean sages":

. . . versarique potest, globus ut, si forte, pilai dimidia ex parti candenti lumine tinctus, versandoque globum variantis edere formas, donique eam partem, quae cumque est ignibus aucta, ad speciem vertit nobis oculosque patentis; inde minutatim retro contorquet et aufert luciferam partem glomeraminis atque pilai; ut Babylonica Chaldaeum doctrina refutans astrologorum artem contra convincere tendit, . . .8 8 Lucretius, De rerum natuva, Bk. V.11.720 ff. This passage is translated by R. C. Trevelyan (Cambridge, Eng.: Cambridge Univ. Press, 1937), p p 203-204:

O r perhaps she [the moon] may turn round Like a ball, let us say, whose sphere is tinged With glowing light over one half its surface;

71

BEROSSOS THE CHALDEAN

It is true that this summary does not bring in the sun's forcible action on the moon, but it confirms the central idea, that during the first half of the month the self-luminous hemisphere of the moon gradually rotates to face the earth, and during the succeeding two weeks it progressively turns away again. So let us make one last attempt to salvage Vitruvius' account of Berossos' impetus solis.

Two steps are required. For a start, let us recall that the supposed impetus acts powerfully when sun and moon are close together, but weakens progressively as they separate. If we read Vitruvius carefully, we shall see that (on his account) "Berosus" assumes that the two bodies are very much closer together at new moon than they are at full moon, when "the whole breadth of the world separates them"; indeed, it is this great difference in separation that explains why the solar power ,.-a)--. , ' acts so differently in the two cases. \ / / \ We might try to allow for this, / \ \ within our accepted picture of the 1 geometrical layout, by modifying Figure 2 as shown in Figure 3. But this \ change only highlights our central i difficulty. For the function of the i m 1/ / \ petus solis (according to Vitruvius) is / \ \ convertere candentem [partem] . . . , , ' ad l u m e n : at new moon, being ex3. Amended version of Figactly sub orbem solis-cunz per- ureFIGURE 2, with the sun shown much close, pendiculum esset ad eius radios - to the earth. all the moon's light ., ad superiorem specie,m retinetur. Unfortunately, as will be clear from Figure .3 quite as much as Figure 2, on any radially symmetric picture of the situation the shining face of the moon will be ad perpendiculum ad solis radios not only at new moon but at full m o o n also; and this fact makes seeming nonsense of the whole "Berosus" theory. Let us therefore see whether we can make any better sense of the Vitruvius passage by using a radically different picture 01 the celestial geometry. We can get a hint of what is called for if we notice how much of Vitruvius' language is earth-oriented: the moon "comes below the disk of the sun," its light "is retained on the upper face," and so on. It is accordingly worth experimenting with an earth-oriented picture of the heavens, which has

. \

/

,'

'\

+e

@

..-_/-/

'*

And as she turns her sphere, she may present Varying phases, till she has turned that side Which g l o ~ ~with ~ s fire towards our gazing eyes; Then she twists gradually back once more

And hides the luminous half of her round

ball;

As the Chaldean sages seek to prove,

Refuting with their Babylonian doctrine

T h e opposing science of the astronomers. . .

.

STEPHEN TOULMIN

FIGURE 4. The effects of the sun's impetus on the moon. (a) At new moon

the effect is at its maximum, and the moon's luminous half is turned completely toward the sun. (Position shown corresponds to midday.) (b) ,4t first quarter the sun's force is weakening, and the moon has partly turned its luminous half back toward the earth. (Position shown approximates 3 P.M.) (c) At full moon the sun's force is completely "relaxed," and the moon's luminous half faces directly toward the earth. (Position shown approximates 8

P.M.)

not a radial but a rectangular symmetry, as shown in Figure 4.The base of this rectangle is the great flat expanse of the earth. T h e sun and moon rise into the sky in the east, then travel sideways above the earth in straight lines at much the same height, shining down vertically onto it, and lastly drop below the horizon in the west. Such a picture would, of course, have had a certain intuitive appeal to early observers whose interests in the heavens were practical rather than theoretical or, still less, geometrical. However, just because it was an intuitive picture rather than a formal theoretical model, one would not look for geometrical accuracy in it. Indeed, the layout shown in Figure 4 is one that was probably taken for granted in thinking about the heavens and need never have been consciously formulated. Against the background of such a scheme, the problem Berossos tackles is a serious one. When the sun and moon enter the heavens close together in time and in distance, the visible part of the moon is reduced to a thin crescent. When the one enters the heavens just as the other leaves, the moon appears from the earth as a complete circle. If the sun's track is only slightly higher above the earth than the moon's, the fundamental question about the phases of the moon will indeed be the one Berossos tries to answer: why at new moon is the bright face of the moon turned toward the sun and away from the earth, whereas at full moon it is turned toward the earth and away from the sun. Berossos' hypothesis is that the partial or complete invisibility of the

BEROSSOS THE CHALDEAN

73

moon when in the neighborhood of the sun results from its being forced to turn its bright face away from the earth. Unless some power were acting forcibly on it, it would remain continuously at the full, its pars candens shining down on the earth and the other half caeruleo colore turned up toward the sky. T o the extent that the sun's impetus has the power to act on the moon, the bright face will tend to turn away from the earth; but, when the moon "is released from the sun's force," it returns to the full. As will be clear from Figure 4, the explanation is elegant and plausible.

If this reconstruction is accepted, the theory reported by Vitruvius preserves traces of a celestial geometry more primitive than any to be found in the Greek natural philosophers. T h e whole Greek debate took for granted a geometrical layout having the radial symmetry of Figures 2 and 3, with the sun and moon moving along circular tracks around the earth. Once such a layout was consciously accepted, it must very soon have been recognized that the bright face of the moon always faces the sun, and from that point it is a short and natural step to the "borrowed light" hypothesis. Berossos' theory apparently antedates all three discoveries. This fact, incidentally, is our best protection against any suggestion that Vitruvius' report is unreliable-on the grounds, for example, that he was quoting the views of a man who taught and wrote more than three centuries earlier, in another country, and about a subject in which Vitruvius was not an expert. If the passage we started from was seriously corrupt, one would not expect it to make clear sense on any interpretation; but if (as is argued here) it represents a kind of intellectual fossil, that very fact may have saved it from corruption. For, when Berossos was teaching in Asia Minor around 290 B.c., his astrophysics was, by Greek standards, already long out of date. There was little the Greeks could do about his teachings but pass them on in the form in which he presented them, for whatever they were worth. If his theories had been more consistent with contemporary Greek ideas, they would have been more likely to be altered and added to in transmission. As things stood, their very unfamiliarity was probably a safeguard against change. Yet the question still has to be faced, whose ideas was Berossos expounding when he presented this account of the phases of the moon. Given the archaic character of his explanation, are we entitled to draw any conclusions from it about the general state of Babylonian astronomy in 300 B.c.? Were Berossos' ideas typical? Was he fully conversant with "the best astronomical opinion" in contemporary Mesopotamia? Faced with these questions, we can only reply that there are grounds for wondering whether Berossos was reporting the views of the professional Babylonian astronomers or, rather, the popular cosmology current in his native city. However, the direct evi-

74

STEPHEN T O U L M I N

dence either way is so slender that we are inescapably driven back to indirect evidence and inference. There are two fairly solid grounds for hesitation. One of these is based on the early astronomical cuneiform tables referred to ab0ve.O In the texts preserved on these tablets, which date back to around 700 B.c., the distances between culminating fixed stars are expressed first in units of time (differences in culmination times, measured by water clocks), next in degrees (US), and finally in "miles at the sky" (beru ina sum&) computed according to the equation "1degree = 1,800 miles." This seems to imply that among professional Mesopotamian astronomers the paths of the fixed stars were conceived, even at this early date, as circles having a circumference of 618,000 (i.e., 360 X 1,800) miles. T h e other doubt is founded on what little is known about the background, qualifications, and intentions of Berossos himself. We know, for instance, that he migrated from Babylon to Cos within a dozen years or so of 280 ~ . c . l O We know also that quite apart from any oral teaching he gave, he set himself the task of writing an encyclopedic account in Greek of the history, geography, cosmology, and chronology of the Babylonians, from legendary antediluvian days to the capture of Babylon by Alexander. This treatise was current in antiquity under the title of Babylonika, and it has been reconstructed, so far as is still possible, by P. Schnabel. We do not know whether Vitruvius took his account from some lost fragment of this treatise, or relied on oral tradition. Either way, we must bear in mind Schnabel's comment: Aber Berossos war nur Literat, dazu Astrolog, kein Astronom, kein schopferisches Genie wie sein alterer Zeitgenosse Kidinnu aus Sippar. Die Astronomie erwahnt er in seinem Werke nur beriihrungsweise.ll Although Berossos was writing at a time when men like Kidinnu were bringing Babylonian astronomical computation to its peak, it remains uncertain whether the views he reported represented the latest ideas of professional astronomers or the cosmological ideas current among the "educated public" of the time. Quite possibly-though we lack any positive evidenceKidinnu and his associates understood very well the true explanation of the moon's phases and Berossos' report presents only the popular picture.12 9 Schaumberger, op. cit. 10 Neugebauer ( T h e Exact

Sciences . . . , p. 151) accepts a date o f 270 B.C. Berossos' modern editor, P. Schnabel (Berossos und die babylonisch-hellenistische Literatur, Leipzig: T e u b ner, 1923, pp. 9 ff.), prefers 290 B.C. See also Schnabel's Berosi Babyloniacorum libri tres quae supersunt (Leipzig, 1913). 11 Schnabel, Berossos . . . , p. 238. 12 I f there was such a divergence between t h e professional astronomy o f m e n such as Kidinnu and t h e popular cosmological picture reported

i n t h e Babylonika, t h e n Berossos should probably lose t h e credit which h e has generally been given-in t h e absence o f any other nameas the channel b y which t h e astronomical knowledge o f t h e Babylonians was transmitted to Hipparchos and t h e later Greek astronomers. (See, for instance, t h e judicial discussion i n Neugebauer, T h e Exact Sciences . . . , p. 151.) Quite probably, m u c h o f this knowledge wab carried to Greece and Alexandria b y Greek scholars and scientists w h o visited Babylonia i n t h e footsteps o f Alexander and Callisthenes.

75

BEROSSOS THE CHALDEAN

T h e small amount of additional, indirect evidence we possess is consistent with this assessment. T o begin with, the "monthly prognosticators"13 who were professionally responsible for astronomical and astrological computations in Babylon and Uruk seem to have worked as civil (or religious) servants of the state, and their techniques were apparently "classified" -as witness the recurrent rubric, "The informed may show this tablet to the informed but not to the uninformed."14 There is some indication also that these skills were confined to a closed guild, or even to certain families, being handed down from father to son, as is done to this day among the muezzinastrolabists in the mosques of Islam.15 This being so, it would have been entirely natural for highly conservative-even archaic-ideas about cosmology to remain current among the general populace at Babylon long after the professional astronomers had developed computational techniques which assumed the circular orbits familiar to the Greeks. We can, in fact, find in the traditional Middle Eastern liturgies and religious practices independent signs that they were established at a time when the accepted picture of the heavens had not yet reached a radially symmetric form (as in Figs. 2 and 3), but was still laterally symmetrical (as in Fig. 4). These traces are not only evident in the religious practices of antiquity, as described in the literary tradition, but have survived to affect those of contemporary Islam. T h e philosopher Porphyry, for instance, reproduces a firsthand description of priestly life in Egypt in the first century A.D. by the "sacred scribe" (tcpoypappa.rcds) Cheremon, who later became Nero's tutor.l"mong other things, Cheremon specified the hours of prayer: Divine service comprises, four times [a day], the singing of hymns in honor of the Gods-at dawn, at dusk, when the sun is at the midpoint of the sky, and when it sinks toward setting.17 Islamic tradition, similarly, prescribes not merely the three hours of prayer required in the Quran, but five.18 One of these is known as SalEh-al-'qr: this is roughly two and a half hours before sunset, and is defined as "the 13 This phrase comes from Isaiah 47: 13. 14 See Neugebauer, T h e Exact Sciences

...,

pp. 136, 144. 15 I owe this information to conversations with al-Hajj Muhammad Ibn al-Hajj Ahmed Lahbsbi, the muezzin and astronomer at the Qarawayin Mosque in Fez (Morocco). Lahbabi learned his craft from his father who preceded him and plans to train his own son (born c. 1955) to succeed him as astrolabist and calendrical computer to the Mosque. 16 See A. J. Festugikre, L a Rdvklation $Hermes Trismkgiste, Vol. 1 (Paris: Gabalda, 1950), pp. 28-30; also F. Cumont, T h e Oriental R e .

ligions i n R o m a n Paganism (New York: Dover, 1956), p. 87. 1 7 Porphyry, D e abstinentia, IV, 8. T h e full passage reads as follows: 61fjp0~v S;V;HTCY C ; S ; H L T & ~ U ~ VO ; ~ C Y V ; W Y , \ , evrore x a i ayiure;*.v TGV Ocijv, xa0';iv T C T ~ & H L S , ~ra.r(n r;tv iw x a i rqv cuaepav pcaovprvo~vr&re rbv $hiov x a ; ~ p b s6b61V x c u r a ~ e p d ~ c v o rohrov v, s I;pvo~vre s. See Porphyrius, Opuscula selecta, ed. A. Nauck (Leipzig: Teubner, 1886), p. 240. 18 See, for instance, Alfred Guillaume, Islam (London: Penguin Books, 1954), p. 66. 3

P

I

,

.

,

76

STEPHEN TOULMIN

moment when the sun begins to decline in the sky and when shadows begin to lengthen." l9 Both these specifications of the time of afternoon prayer raise the same problem. For, if we regard the path of the sun across the sky as an arc of a circle, then there will be no distinction between noon (the moment when the sun is at the midpoint) and al-'asr (the moment when it begins to decline toward setting): on such a view, shadows would have to begin lengthening from midday on-as careful observation shows them to do. Yet, even today, muezzins compute the time of al-'asr according to the traditional formulas, to the exact minute, with the same care and exactitude they give to the times of sunrise and sunset or to the first visibility of the crescent moon.20 Once again, the change from a radially symmetric picture to a rectangular one immediately makes sense of the distinction. Suppose that the sun and moon, once well risen into the sky, travel from east to west along tracks which are roughly horizontal, until the moment comes for sinking toward the horizon: the significance of al'asr will at once become apparent. Here again, we may perhaps detect traces of the same primitive assumption that apparently underlay Berossos' theory of the solar impetus. T o sum up: We began by looking at Vitruvius' report on the Babylonian theory of the moon's phases, in the hope of discovering something about the astrophysical ideas lying behind the computational techniques of Naburi'-annu and Kidinnu. We ended by uncovering a more primitive cosmological scheme, which probably dates well before 1000 B.c., and which is actually inconsistent in certain respects with the ideas of professional astronomers in Mesopotamia from 700 B.C. Whether this older, rectangular scheme retained any conscious hold on men's minds as late as 300 B.c., or whether the theory taught by Berossos was only a confused tradition based on ideas which were by then outgrown, we cannot say. Yet the persistent traces of an archaic celestial geometry which are detectable, both in Berossos' theory and in the liturgical practices of the Middle Eastern religions, are-if nothing else-a tribute to the enduring powers of an intuitive cosmological picture. 1 9 A . Sefrioui, Morocco (Paris: Hachette, 1965), p. 17. 20 I possess, for example, a table of ephemerides prepared at Fez for the month of Ramad8n, 1382 A.H. (27 Jan.-24 Feb. 1963) and pre-

sented to me by the muezzin: in this table, the time of the afternoon prayer (allay) changes in the course of the month from 2:51 to 3:11 p.m., while sunset advances from 5:16 to 5:42 p.m.