Posted by on Jul 11, 2017 in Library | Comments Off on GREEK ASTRONOMY AND ITS DEBT TO THE BABYLONIANS* By LEONARD W.CLARKE


‘Recent studies of Babylonian sources have shown that we must revise former estimates of the extent to which the Greeks were indebted for the details of their astronomy to the Babylonians; the debt proves to have been much greater than had been imagined, and further researches may prove it to have been greater still.’ So wrote Sir Thomas Heath in 1932; in the previous year, Professor Filon had written, ‘It is gradually beginning to be realized that many of the achievements of Greek culture in the fields of astronomy and mathematics did not spring, fully armed, from the Hellenic brain, but had their more remote origins in the civilizations of the ancient East.’

There is available now sufficient evidence to show that a great deal of the astronomical knowledge which has come down to us from the Hellenistic period (c. 500 B.C. to A.D. I50) was not initially discovered during that period; and such new empiric discoveries as were made in that time were not all due to Greeks, for important contributions were still being made by Babylonians during the Seleucid Era.

To a large extent it seems that the Greeks kept very closely, even in astronomy, to the mode of research advocated by Plato, who said in The Republic,’Which things (i.e. “the variegated bodies in the heavens”) truly are to be comprehended by reason and intellect, but not by sight’. The Greeks founded a ‘school’ of theoretical astronomy and, with their highly developed mathematics, were able to go far with it; but their source-

material was in very many cases not Greek. The author of Epinomisstates, ‘We may assume that whatever the Greeks

take from the barbarians, they bring it to a finer perfection’. Adrastus (second century A.D.)wrote that the methods used by the Chaldeans and Egyptians in astronomy were imperfect because these people lacked physiologia; no doubt this was true, but it was people of these races who had done, and continued to do, most of the equivalent of modern observatory routine work.

IT would be very difficult to give any account of the Greek contribution to astronomy without making early mention of Thales of Miletus. Thales (c. 630-550 B.C.) is the first Greek, of whom any record exists, who can be regarded as a philosopher and a scientist. He was an engineer (at least for military purposes), a geometer, to some extent an astronomer, but above all, he was a logician, being one of the earliest persons known who could take a set of facts and deduce from them an inevitable con- sequence.

Wherever the name of Thales is mentioned, some reference to eclipses of the sun is bound to follow. For at least a hundred years past it has been fashionable to contend that Thales could not possibly have forecast the eclipse of the sun which is reputed to have stopped the battle between the Medes under King Cyaxares and the Lydians whose king

* Read at a meeting of the Society held at the London Planetarium on 6 February I96I, the President in the Chair.

Mr. Clarke, the Senior Narrator at the London Planetarium, used the Planetarium Instrument throughout the reading of his paper. This meeting was held in the Planetarium by courtesy of the Directors of the London Planetarium Company.


was Alyattes. Great trouble has been taken to identify this particular eclipse, despite the doubts about Thales’ ability; it was almost certainly that of 25 May 585 B.C. Yet why should we go to such pains to detract from what Thales is widely reputed, by a number of writers very much nearer to his own date than we are, to have done? We have the evidence of Herodotus (I. 74), a little more than 100 years after the event, that he did so; Eudemus, in his History of Astronomy, refers to it, though we have to accept a mention of this by Clement of Alexandria (second century A.D.), and another by Theon of Smyrna, also a contemporary of Ptolemy (the compiler of the Almagest), since only a fragment of Eudemus, and not the appropriate one, now exists; and Pliny (first century A.D.) also gives an account of it. All that is claimed by Herodotus is that Thales ‘fixed it for the very year in which it actually took place’. It may be that Thales had visited Babylon; he had certainly been in Egypt. We have no direct evidence whatever against Thales having forecast this eclipse, and in the case of most people who doubt his reported achievement it is almost certainly unwillingness to believe that he could possibly have done so which brings forth the doubting comments. To forecast a total eclipse visible in a particular part of the world requires a very detailed knowledge, certainly far more than Thales is likely to have had; and there is no extant record that even the Babylonians had this knowledge at that time, though there is every likelihood that Thales was familiar with Babylonian astronomical work. It should be kept in mind that none of the writers claims that Thales forecast it in order to stop the battle; that was pure chance. If, however, he knew that there had been an eclipse, perhaps seen in Scythia, or in southern Persia, eighteen years previously, then he was quite safe, though perhaps unsure of his totality band.

Though the account of the eclipse forecast is the best known of the associations of Thales with astronomy, it is not his only one. Diogenes Laertius (second century A.D.)tells us of his work to establish the interval between solstices, and that he recommended using the little Bear instead of the Wain for navigation. Aristotle cites him as the first of the philoso- phers who sought for an apX’4,a first material cause for all things, and to Thales, that first cause was water. His contemporary and friend, Anaximander, also of Miletus, disagreed. To him, the first cause was ‘the Infinite’, and his thought was surprisingly up to date, even considered in modern terms. He associated with the Infinite a ‘principle of eternal motion’ so that always there are some things coming into being and some being destroyed. Simplicius (early sixth century A.D.) says of Anaximander, coupling him with Leucippus, Democritus and Epicurus, that ‘they assume that the worlds are infinite in number, and that they also came into being and passed away, ad infinitum, there being always some worlds coming into being and some passing away; and they maintained that

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motion is eternal; for without motion there is no coming into being or passing away’. Eusebius (third century A.D.)tells us that Anaximander was the first to construct gnomons for the purpose of distinguishing the turnings-back of the sun (solstices), times, seasons, and the equinoxes; but Herodotus (II. IO9) tells us that the Greeks learned from the Baby- lonians the use of the gnomon and the polos, and the division of the day into I2 parts. This is at least a strong hint that the Greek philosophers at Miletus in the early part of the sixth century B.c.had either travelled in Babylonia or had some knowledge of the work of the Babylonians.

Anaximenes, another Milesian, son of an associate of Anaximander, maintained that the apXn4was Air; Xenophanes, of Colophon, also in Ionia, contemporary of Anaximenes, speaks of it as ‘the One’. Heraclitus of Ephesus chose Fire as his first cause at about the same period.

All these early Ionian philosophers-andwith them we may include Parmenides, who across in the heel of Italy made ‘It is’ his first cause- were seeking for a ‘field equation’ before they had collected the preliminary data of the problem before them. Most of them made pronouncements about the heavenly bodies-thesun, the moon, and the stars. Anaximan- der stated that the earth was cylinder-shaped, Anaximenes that it was flat, like a table, and that the moon was formed of fire. Xenophanes held that the sun and the stars were clouds set on fire, and that there were many suns and moons to serve the various regions of the earth. Heraclitus believed that the heavenly bodies were bowls with the concave sides turned towards the earth, which collected more or less of the exhala- tions from the earth, and so varied in brightness. Parmenides even had some ideas on the nature of the Milky Way.

Almost all of their arguments and their statements were on quali- tative matters; Anaximander ventured on dimensions for the sun and the moon-27and I9 times as large as the earth, respectively. These early Greek astronomers were not long-term observers, and it is very unlikely that they kept or prepared any tables arising from, or for, observation. The building up of material for argument by conducting an experiment and recording results was not a method which recommended itself to them at that time; not even the ‘experiment’ provided gratis by the changing panoply of the skies. It may be that they thought that pure human thought would solve all problems eventually; it may be that they considered that such work could be left to less keen intellects than their own, and that in any case, this work would not contribute to the solution of the problems which engaged them.

Nevertheless, observational work and quantitative work had been going on for centuries elsewhere. It was not undertaken by Greeks, and not for a true scientific purpose, at least in its early and middle stages. Yet without this work, much of the contribution to astronomy made by the later Greeks would have been seriously reduced.


It is well to consider what was the world background against which Thales and the long line of Greek philosophers who followed him carried on their work and their thought. Greece itself was a group of small states, sometimes co-operating, sometimes at bitter enmity. The Near and Middle East, where civilizations reaching a very high level had been growing up for several thousand years, was reaching a period where domination by one or another was inevitable. Among the Egyptians, Babylonians and Greeks, the organization of society had long before reached a stage where there were plenty of people who need not concern themselves entirely with the elementary chores of a community-farming and soldiering. Of the three races, the Greeks were the last to reach this stage. Greek civilization had begun at about the beginning of the second millennium B.C. around Mycenae in the north of the Peloponnese. Com- pared with other nations surrounding the eastern end of the Mediter- ranean, Greek power was not strong in its early existence. During the first i,500 years of Helladism, natural calamities-earthquakes,volcanic eruptions, tidal waves-often destroyed great cities and whole areas.’ Yet in parts of the widespread and politically divided Greek nation, intellects were developing of a kind which do not appear to have existed previously.

We often tend to look upon the world before our own era as con- sisting of a number of isolated countries, each having their own pecu- liarities, each contributing some interesting items, some examples of art, or scraps of mythology, in an unrelated pattern. Yet what was the known world at the middle of the first millennium B.C.; that is, known to the people living in it then? It was more extensive than is generally realized, and there was far more contact between the various parts of it than is usually accepted. Besides the three nations already mentioned, Persia was a vast and strong power. Further east, a considerable civiliza- tion had developed in the Indus Valley. In China, beyond the Himalayas, a highly complex society had already grown up.2

How much contact was there between these various countries, and between any of them and the less developed peoples? There is a great deal of evidence available to show that it was very considerable. Travel was not easy, but it was far from impossible; whole nations sometimes trekked over long distances, taking their flocks, herds, and household goods. The Jewish Exodus through the Sinai Desert in the thirteenth century B.C. is by no means the only known instance. Sir Leonard Woolley found at Ur and at Al’ Ubaid treasures of an advanced civilization of about 2500 B.C., and also evidence to show that the original owners of the treasures were of a race which had come from elsewhere and planted

I S. Marinakatos, Creteand Mycenae,London, 1960, pp. 20, 22.

2For the scientific aspects of this complex society, see especially J. Needham, Scienceand Civilisationin China,Cambridge, I959,vol. iii.

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its way of life upon (perhaps) the ruins of a less advanced culture.3 About I900B.C.we know that Abraham trekkedfrom Ur to Canaan; the route from Canaan to Egypt was a well-trodden one in the time of Joseph (c. i6oo B.C.).About I000B.C.a great improvement was made in the means of world communication (comparable, relative to world development, to the change made in the present century by air travel) by the domestication of the camel;4 and certainly, by the same date, the Phoenicians were sailing-evenif coasting only-thewhole length of

the Mediterranean. In the ninth century B.C.,the Queen of Sheba, from Southern Arabia, visited Solomon, with a great retinue; and as she had already heard of his wisdom, many others must have travelled the same route before her. Solomon also received gifts from Ophir; not yet traced, but probably somewhere in Africa south of Egypt. As early as I500B.C., Queen Hephsi-put, of Egypt, had sent an expedition to Punt, again most probably far south in Africa.

By the end of the eighth century B.C.,the Medes, an Indo-European race who had probably come from further north to overthrow the Elamite regime in Iran, were beginning to be mentioned in Assyrian records. About a century later, under Cyaxares, they captured and destroyedNineveh and overthrewthe Assyrians.Persianpower continued to grow. Under Cyrus, the Lydians, who controlled the western half of Asia Minor were subdued, and this brought the Ionians into close contact with Persia. Many Jonians emigrated; Miletus alone of all its cities enteredinto an agreementwith Cyrus,who in 539 B.C.went on to conquer Babylon. Egypt fell to Cyrus’sson Cambyses a few years later; and after the brief reign of Gaumata, Darius extended the Persian Empire far into Europe, subduing Thrace, and then sent a military expedition to explore the Indus Valley from Afghanistan to the mouth of the river. Greece proper was the next obvious prize, but it involved a long, and never completely successful,struggle. Miletus was destroyed after a revolt; then came the continual struggles between individual Greek states, and with the Persians. In the middle of the fourth century B.C.began the threat to Greece-whicheventually proved to be a unifying influence- from the north. Philip of Macedonia became master of Greece following the battle of Chaeronea (338 B.C.).He was followed by Alexander the Great, who in 334 B.C.crossed the Hellespont and annihilated a Persian army in Asia Minor; the following year he beat Darius III himself at Issus. Egypt submitted to, and welcomed, Alexander. Late in 331B.C. he decisively defeated Darius at Gaugamela. Babylon and Susa submitted to him, and he was very soon plundering Persepolisitself.

In this historical period, and before Alexander the Great, Herodotus was writing. He was born at Halicarnassus,on the Ionian coast of Asia

3 Sir L. Woolley, Ur of theChaldees,London, I929,Pelican ed., pp. i6, I7. 4 W. Keller, The Bible as History, London, 1956,p. I67.


Minor, about 484 B.C.He travelled extensively himself, in Thrace and Scythia (into South Russia), in Egypt, Babylonia, and Persia; but he was aware also, and gives descriptions so far as he knew them, of the Indian Ocean, the steppes of Central Russia, the Cassiterides (there is little doubt that these were the Scilly Isles), and he also knew that the best amber came from the Baltic. He tells of a voyage made in the time of King Necos of Egypt, some i30 years before his own time, circum- navigating Africa (IV. 42).It may not be a true account; but it is given interesting credibility by Herodotus’s own unwillingness to believe that the reported voyagers ‘had the sun on their right hand (i.e. to the north of them) for part of the voyage’. Certainly by 470 B.C. the west coast of Africa, probably as far south as Sierra Leone, had been visited via the Pillars of Hercules (the Straits of Gibraltar).

It is not at all surprising that at least as early as the fifth century B.C. we find objects-boundary stones, vases, stone slabs and pillars- inscribed in several languages. A fragment of an alabaster vase from Persia, of the reign of Xerxes, 485-465 B.C., bears the same inscription in Persian, Elamite, Babylonian and Egyptian.5 During this first millenium B.C. there were always foreigners in any of the countries of this Middle East cradle of civilization. Some of them were ambassadors, or members of trade missions; some of them, like Herodotus, were simply visitors, or tourists. Many of them, certainly the majority, were slaves. The custom of the time was such that anything taken by force of arms became the property of the conqueror-whetherit were men, or goods, or knowledge. Not only the hewers of wood and drawers of water were made slaves in the country of the victors, but also the men of culture; and from the time of conquest, their abilities and their knowledge were at the service of the overlords. Did Aristotle actually instruct his nephew

Callisthenes, when the latter was military commander in Babylon, to send back the astronomical records kept (reputedly for tens of thousands of years, but certainly for many centuries) by the Babylonians? The statement that he did so (by Simplicius, quoting Porphyry) is usually regarded as a pretty fable. Whether they acquired them in this particular way or not, it is certain that they were fully available to the Greeks. A conquering nation took everything, though they might allow the conquered people to continue their own practices. In fact, the conquerors might need them to do so, not being able to do it themselves; but all the results, and all the credit, accrued to the victors.

It is now quite certain that a very considerable amount of the astronomical knowledge used, analysed, and to some extent better interpreted by the Greeks, was taken from the Babylonians. With admitted exceptions, the Greek philosophers were not observers. Aristarchus of Samos (active about 260-280 B.C.) certainly was; he was so successful,

5 British Museum, Item No. I32114.

GreekAstronomyand its Debt to the Babylonians7′

that besides discovering some correct quantitative properties (e.g. angular diameter of the moon), he believed in a heliocentric universe, with the stars at vast distances away from the earth, and, in fact, put forward practically the Copernican system some 2,000years before Copernicus. Hipparchus (mid-second century B.C.) was an observer, and a very important one, assisting as he did in laying the foundations for Ptolemy’s work some 300 years later; but Hipparchus was not highly regarded by his philosopher-contemporaries. There were some eminently practical astronomers among the Greeks; but into the astronomical field there entered also a large number whose main preoccupation was simply ‘philosophizing’-takingthe observed data, or initial axioms, or accepted conclusions, from a large number of subjects; in fact, from the whole of human knowledge, so far as they could, and arguing on them, recon- sidering them. Babylonian observation, Babylonian records, of astro- nomical events and of periodic recurrences, had reached a stage which provided a very well-sown, and in some cases, fruitful, field for this kind of research.

It has long been fashionable to speak of the ‘Chaldaean astrologers’ and, without bothering about the true facts, to regard what they had done-overseveral millennia past-ascontributing only to divination and forecasting. It is quite true that they were astrologers; so, in exactly the same sense of the word were all the Greeks who contributed to astronomy up to the beginning of our era. The necessity for discriminating between astrology and astronomy did not arise until the first century A.D.,after the fantastic rise of genethliacal astrology (the casting of personal horoscopes) among the Greeks themselves in the last two centuries B.C. The word ‘astrologos’ meant until that time ‘the study of the stars’-and that is what the Babylonians had been engaged in for many centuries past. Certainly they used it in forecasting; but some of it was correct and useful forecasting. They were able, well before 500 B.C., to produce ephemerides for the moon and some of the planets for several years ahead. It was used in arranging ‘elections’, the kind of elections which in mediaeval times occupied so much of an astrologer’s attention- favourable times for undertaking particular ventures. Most particularly it was used in respect of all royal and state affairs, for the whole under- lying method of the Babylonian system of government had grown up with its development, and had sprung from it. Very little of the Babylonian ‘astrology’ before the country came under Greek control was concerned with personal horoscopes, and not much of it within the country even after that time. Of the considerable number of astronomical cuneiform texts which have now been translated, most of which date from the Seleucid era-after Alexander the Great-only a very few contain horoscopes.6 Divination was certainly practised in Babylon; largely, as

6 0. Neugebauer, The Exact Sciencesin Antiquity,Rhode Island, p. i68.


among the Greeks and the Romans, by the ‘auspices’-by observing the entrails of slaughtered animals and birds.

In Babylonia we have the only available example of the progress of a nation from complete fear of natural events to at least a beginning of scientificanalysisof them; and as this processtook place, so the religion and the public administration of the country developed in accordance with it and inextricably associated with it. Relics of Babylonian civiliza- tion dating back to at least 3000 B.C. have been found. The gods, through- out, were personificationsof natural phenomena, although changes in the way they were regarded became evident with the progress of time. These changes themselves show a greater awareness of the ‘nature’ of things-theessential preliminary to a scientific understanding. In the later period it is more correct to say that the natural phenomena were regarded as observable manifestationsof the gods.

As long ago as 2630 B.C., King Sargon’s daughter made offerings at the temple of the Moon goddess at Ur.7 Some three centuries later, Ur-Nammu began to build the great Ziggurat at Ur-oneof the temples (rather than observatories) at which homage was paid to the natural deities. In Sumer, Nannar, the moon-god was the principal god; some- times the moon-god is called Sin. Shamash, the sun-god, was also of high importance, as were Enlil, the storm-god, and Anu, the heaven (sky). Observation of them, and all natural happenings, went on con- tinuously, for the gods could be angry, and then man suffered. In Lower Mesopotamia he suffered mainly from the devastation of floods, and in a slightly more advanced form of the religious belief, Ti’amat (some- times male, sometimes female) was the Flood-theFlood which might devastate at any time, or the bitter waters of the sea, the very powerful deity which must be placated. It is not surprising that Ti’amat was regarded as the mother of the gods which appeared later; gods who were not new, but rather revised versions of the earlier gods. Ideas changed in accordancewiththeincreasedknowledgeofnaturalthingsgainedover the centuries. It is, of course, mythology, not science; in many particulars

it is very similar to the Greek mythology. Oceanus was the god whom Homer regarded as inferior only to Zeus, just as Ti’amat could only be over-ruledby Anu.

With the continuousobservationthat was essentialto the propitiation of Nannar, the moon-god, the Babylonians could not fail, eventually, to become aware of certain periodic recurrences.The position of the moon against the star-backgroundwas important for religious observances; and so, the star-backgroundbecame familiar. The step from that to recognizing the five wandering stars, the naked-eye planets, is not a great one, and the candidates for deification increased. The planet we now call Jupiter became at first the night-manifestation of Shamash;

7 Op. cit. (3), pp. 78, 79.

GreekAstronomyand its Debt to the Babylonians73

but Shamash later diminished greatly in importance (the night skies have far more of interest than those of the day), and Jupiter became Marduk, son of Ti’amat, and constantly warring with her. Marduk (Merodach) was the principal god of later Babylon8; but the other planets were known. Venus was Nin-dar-anna (sometimes a deputy for the moon- goddess), Mars was Sag. Kud, and Saturn Kaimanu or Kaiwanu. Mercury served as an alternative manifestation of Marduk; for so great was the insistence on the importance of this ‘god-star’ that public functions could not be held in Babylonia ifJupiter was not visible. It was the royal ‘star’; many Babylonian kings had ‘Merodach’ hyphened to their own names. To allow public and royal business to proceed during those two months or so in any year when Jupiter was not visible in the night skies, Mercury, also named Marduk, could sometimes serve as a ‘stand-in’.

In Enuma Elish, the Babylonian Epic of Creation, we are told some of the tasks that Marduk accomplished after he had vanquished Ti’amat. He organized the calendar; and the responsibility for continuing this always remained a duty of the king of Babylon until the time of Nabonidus, whom Cyrus overthrew. At each New Year festival, the great annual festivals of Babylon (and held at the Spring Equinox, when the new year began), the king, in ritual, assumed the identity of Marduk, and re-enacted the vanquishing of Kingu, the leader of Ti’amat’s host. To assist the king in arranging the calendar, the Epic tells us that Marduk had set up in the sky constellations of stars, to determine, by their rising and setting, the years, months, and days. The station of the planet Jupiter was established to give orders regarding the duties of the days:

‘To make known their obligations that none might do wrong or be remiss.’9

He also set on the heaven two bands-theWay of Enlil and the Way of Ea. He made entrance- and exit-gates for the sun. He fixed the zenith in the midst of the sky, and he gave orders to the moon:

‘He bade the moon come forth; entrusted night to her; Made her a creature of the dark, to measure time; And every month, unfailingly, adorned her with a crown. At the beginning of the month, when rising over the land, Thy shining horns six days shall measure;

On the seventh day let half (thy) crown (appear) At full moon thou shalt face the sun.

(But) when the sun gains on thee in the depth of heaven Decrease thy radiance, reverse all growth.’

This is not yet science, but it is advancing towards it. In the early days of Sumer, Nannar, the moon-god, was supreme. Now, the observers

8 See author’s ‘Science in The Bible’. Nature,vol. I93,no. 4810.

9 H. Frankfort, Mrs. H. A. Frankfort, J. A. Wilson, T. Jacobsen, Before Philosophy, Pelican ed., p. I96.


have discovered something about the moon; they give back that know- ledge to the god Marduk (often depicted in human form). Marduk has provided a scientificallyarrangedbackgroundin the sky. He has provided the Way of Enlil (the zodiac), along which he, the other planets, the moon and the sun, always move; and the Way of Ea, the band of constellations below the zodiac, the assumedreturn-pathof the sun below the horizon of a flat earth.

There is a tablet in the Hilprecht collection at Jena dating from the Cassite period in Babylonia (1500 B.C.),inscribed with a statement which has been translatedas: ‘I9 from the moon to the Pleiades; I7 from the Pleiades to Orion; I4 from Orion to Sirius; . . .’ and so on. It ends with the question: ‘How much is one god (star) beyond the other god?’Io Another text of about the same date gives a method of zone-division of the -sky; it contains the names of constellations and planets, and numbers in arithmetical progression. Numbers, an arithmetic-atool which the Greeksnever really had at all; at least, not of their own. The method was being used to assistin plotting positionsfor religious purposes as early as this. These same arithmetic progressionslater developed into the zig-zag functions of the Seleucid-period Babylonians. A scientific method was beginning even if those who used it had no conception whatever of the nature or meaning of science. We can see clearly here how a primitive mythology, if based on natural happenings, must inevitably lead to the emergence of science; and perhaps also it is true that science could not begin withoutmythology as a nurse.

Even earlier, in the reign of Ammisaduqua, one of the kings of the Hammurabi dynasty (I800-I600B.C.),observationsof the appearances and disappearancesof the planet Venus were made and recorded; not for any scientific purpose, but because of the supposed influences of the planets on the omina. This was the general purposeof all the astronomical observationsat that time, but nevertheless,the methods used were such as to give much more assistanceto the practical use of astronomicalfacts than did the later contemplative methods of many of the Greeks.Already, by this time (i800 B.C.)the sexagesimal,place-value system of Babylonian arithmetic was well established and its methods were highly developed. Of the mathematical cuneiform texts which have been translated, the majority date from this period. By 700 B.C.the ‘pattern’ of the sky was well organized into three parallel bands; the ‘dividers of the heavens’ had done theirwork.The behaviourof the moon, the seasons,the varying lengths of shadowsin differentlatitudes, had all been studied, and a great deal was known about the periodic recurrence of eclipses and the con- ditions under which eclipses could occur. By the time Thales was living in Miletus a scheme was growing up to ‘level up’ the lunar and solar years by inserting intercalary months, and soon after, the Metonic

Io op. cit. (6), p. 99.

GreekAstronomyand its Debt to the Babylonians


cycle was well recognized. Whether this was a Greek or Babylonian discovery initially cannot be discovered; first references to it in the records of the two nations are separated by only a few years. What is certain is that the Babylonians used it, and the Greeks did not.

By 450 B.C. the Babylonians had a very definite mathematical astronomy. In establishing it they had one overwhelming advantage over the Greeks. Their system of arithmetic, long established, thoroughly developed, and supple, was a powerful tool. The Greek insistence on geometrical methods was to a large extent a handicap to their progress- especially when one considers that Euclidean geometry pre-supposes a flat earth. The methods of the Greeks could, as they were improved, lead to a discovery of whyit all worked, which is what their philosophers were aiming at in seeking the apx’; but it was as late as A.D. 100 when Menelaus first realized that spherical geometry must be based on great circles. Certainly the conics were studied, but the works of Euclid

(about 300 B.C.) and Apollonius of Perga (250 B.C.) contain no hint of any connection between any of the conic sections and astronomy. His later biographers and editors state that Pythagoras attached great importance to arithmetic; but his arithmetic was apt6O1LTtKr5-the theory of numbers-towhich the stiff and unrelaxing ordinal-number system of the Greeks was amenable. For Aoyorw-tKuc,alculations concerning numbers of things, the Babylonian system was far better. It is doubtful whether it ever occurred to the Babylonian priests, or even to the later Seleucid philosophers, to ask themselves the question ‘why’ it all happened; it was so inextricably bound up with their religious beliefs; but they were adept at answering many of the questions beginning ‘how’ or ‘when’. In the fourth century B.C. they ‘regulated’ the division of the zodiac into I2equal parts. This does not mean that the naming of the constellations comprising the zodiac dates only from this time; that happened very much earlier. The accurate plotting of the positions of sun, moon and planets was now easily possible-andthe arithmetic progressions had been developed to a stage at which they approached near to the power of the calculus. The zig-zag functions were not far from becoming a method of dealing with infinitesimals. Even without these, incommensurables, to any required number of sexagesimal places, presented no difficulty, and at least the results arising from Pythagoras’s Theorem were known a thousand years before Pythagoras was born. Instruments were being used for observation, and the Greeks borrowed them.Thegnomon(yvco’pcovw)asinuseinBabylonasearlyas1000B.C. -for measuring the lengths of shadows, from which, besides telling the time, many other results (e.g. solstices, latitudes) were calculated. The ‘polos’ (rOnAos)was similar to the ‘scaphe’ (UrKaJfq)which continued to be used as a time-measurer for many centuries afterwards; a hemi- spherical bowl with a gnomon set radially in the bowl. The Babylonian


polos probably had a gnomon of considerable length so that it could be used as an alidade, by pointing the gnomon at the observed object and reading off the angle of elevation from the angle through which the bowl had turned.

During the Seleucid period-approximately the three centuries immediatelyprecedingourera-progress inBabylonianastronomywas considerable. This is after the time of Alexander the Great, and Greece, or at least Macedon, was the overlordof Babylonia. Lunar and planetary ephemerides were calculated and recorded. The time of first visibility ofthemoon,soimportantfortheBabyloniancalendar,couldbecalculated to a high degree of accuracy. The occurrence of eclipses as incidentals to the motion of the moon was recognized, and certainly during this period (perhaps earlier) the wrongly named ‘Saros’, the period of 223 mean synodic months, was completely understood. The Babylonian historian and philosopher, Berossos,who deserves as much fame as his Greek contemporaries,lived in the island of Cos and translated Baby- lonian history and lore for the benefit of the Greeks in about 270 B.C. Eratosthenesdid his excellent work on finding the dimensionsof the earth a few years later. Naburianus and Kidinnu, and no doubt many others were producing regular ephemerides for the moon and planets, and teaching the art of calculating them to others. By the time of Hipparchus

(about I50 B.C.)much of the Babylonian method was known to the Greeks, for it cannot be questioned that Hipparchus used precisely the Babylonian parameters in his calculations. Somebody, sometime, in the years that followed, made the step from ‘annual’ ephemerides to the idea of relating the calculations to ‘mean motion’. It may well have been a subject Babylonian who did this, but we do not know. Certainly in the Seleucid period and probably long before, the framework of reference that we still use for division of the celestial sphere was well established.The sexagesimalsystem,probablycombinedwith the approxi- mate number of days in the year, led to the division of the horizon into 360 ‘degrees’.The sub-divisioninto minutes and seconds (both for angles and time) is a direct consequence of Babylon’s number-system. The idea of ‘hours of right ascension’ was in being, and the importance of the meridian was recognized. A method of reckoning the latitude of a place, by using the ratio of the longest day to the shortest night, devised by Babylonians,was used by them, by Greeksand by Egyptians.For instance, the latitude of Babylon itself was 3: 2.”

The influence of Greece was diminishing, for Rome was strong; but in Egypt, the centre of culture begun by Alexander still continued. By A.D.I50Babylon was already part of the forgotten past; but Ptolemy, at Alexandria, in compiling the ‘very great syntax’ could not, and did not want to, neglect the tremendoushelp he could get from its learning.

1I Op. cit. (6), p. 159.

GreekAstronomyand its Debt to the Babylonians77

His parameters were still those of the Seleucid-period ephemerides; his whole numerical system was the Babylonian sexagesimal system; his ‘rote’ dates were dates derived from Babylonian eclipse and planetary observations. They were not as accurate as he would have liked, but the observations of ‘first visibility’, heliacal risings, etc., were the impor- tant things for religious purposes at the time when they were made- and there were no better records available.

Far back in the sands of Mesopotamia, the great highway of astro- nomy began at least 4,000 years ago. At first it was merely a track, distinguishable from the surrounding desert only by those who constantly used it. Often it was overgrown with scrub and thorn, but it continued, and all the time it widened and became more firmly trodden down. There came a time when even visitors to the country could recognize it; realized that it led somewhere, and wished to travel by the road. In about 550 B.C. the road divided; the northern track, the geometrical road, led through Greece. The southern track, the linear road, carried on in Mesopotamia, and progress was made along both branches. Often those on the northern track found it necessary to make journeys across to the other section, for servicing facilities were not adequate on the geometrical road. Those who travelled the road were few, and they were pedestrians; the more affluent travellers preferred to amuse them- selves at the fun-fair of astrology, which had become a vast enterprise

between the roads. Often, too, the pedestrian travellers were compelled to replenish their fortunes by becoming stall-holders at the fun-fair. The road by-passed Rome almost completely, but the two tracks came together again in Alexandria, and Ptolemy made an impressive junction there. Some Greeks continued to travel, but the main stream were Arabs, some of them direct descendants of the Babylonians. The Greek manu- scripts were translated into Arabic; Gerard of Cremona and John Sacrobosco resurfaced the road by translating into mediaeval Latin. Still there were travellers on both sides of this one-way road. The right- hand side led on to Copernicus and Kepler; far back along the road Aristarchus was still waving a flag. The left-hand side had its travellers too, perhaps leading to Newton and Leibniz.

When we stand and look back along that road well may we ask ‘How many miles to Babylon?’