Babylon hands Greek astronomy its numbers (~500 BCE–150 CE)

What Greek astronomers knew before Babylon

In the sixth century BCE, when the Babylonian scribes of the Esagil temple were already two hundred years deep into a continuous archive of dated celestial observations, the cosmological writers of the Ionian Greek world were doing something fundamentally different. Thales of Miletus, the figure later Greek tradition would credit with predicting an eclipse in 585 BCE, has left no genuine astronomical text behind; the eclipse prediction story is most likely a retrospective construction, and recent scholarship doubts that any Greek before the late fifth century BCE could have predicted an eclipse on the basis of indigenous Greek knowledge.¹ Anaximander, his successor, built a cosmological model — concentric rings of fire visible through holes in dark celestial mist — that was a philosophical proposal, not a predictive instrument. Anaximenes, Xenophanes, Heraclitus: their accounts of the heavens belong to the genre of natural philosophy, the discursive search for a single principle behind appearances. They produced no tables, no almanacs, no computational procedures for finding the position of a planet on a future date.

The early Greek calendrical tradition was a regional patchwork. Each polis ran its own civil calendar, with intercalary months added by magistrates on an ad hoc basis to keep the festivals from drifting through the seasons. The Athenian calendar of the fifth century BCE was so erratic that Aristophanes mocked the moon for not knowing what day it was, and Thucydides dated events by Spartan ephor years and Athenian archonships rather than by any common reckoning. Greek astronomy in this period had no concept of a fixed era — no equivalent to the Babylonian count of years from Nabonassar (747 BCE) that Ptolemy would later inherit as the chronological backbone of the Almagest.²

The instruments that didn't exist yet

The Greek astronomical instruments later associated with the great mathematical astronomers — the armillary sphere, the dioptra, the parallactic ruler, and what Hipparchus would call an astrolabe (in a sense different from the medieval planispheric instrument) — are inventions of the fourth century BCE and after. No surviving evidence places systematic instrumental observation in Greek hands before Eudoxus of Cnidus (~390–337 BCE), and even Eudoxus's homocentric-sphere model, brilliant in its geometric ambition, predicted planetary positions with errors of tens of degrees because it had no empirical numerical basis to calibrate against.

What Eudoxus and his pupil Callippus produced were geometric pictures of the heavens — beautiful, mathematically rigorous, and unpredictive in any practical sense. To know when Mars would be in opposition, when Venus would be at maximum eastern elongation, when the next lunar eclipse would occur, a fifth-century Greek would have to wait and watch. He had nothing equivalent to the Babylonian Goal-Year texts, which from the late fourth century BCE forward listed all the predicted planetary phenomena for a given year in advance.

The gap matters because it is structural, not incidental. A culture without standing observational instruments, without a continuous dated archive, without a place-value numerical notation, and without sustained institutional patronage of a scribal class trained in those instruments and archives cannot do mathematical astronomy in the sense that Hipparchus and Ptolemy would later practice it. The Greek world before the Hellenistic period had none of these. It had brilliant philosophers, geometers of the first rank, and a literary tradition that would carry every later development; what it did not have was a tradition of empirical celestial measurement of the sort that the Babylonian temple schools had been conducting since the eighth century BCE.

What Babylon already had

The contrast in 500 BCE was stark. The Babylonian astronomers had been keeping a continuous astronomical record — the Astronomical Diaries, recording night-by-night observations of the moon's position, the visible planets, eclipses, weather, river levels, and commodity prices — since at least 652 BCE; some scholars place the start a generation earlier.³ By 500 BCE the archive ran four or five generations deep. The scribes had identified the eighteen-year, eleven-day Saros cycle for eclipse recurrence; they had inferred the nineteen-year Metonic relationship between solar years and lunar months and were using it to regulate intercalation in the civil calendar; they were producing standardized lists of fixed-star positions and constellation boundaries.⁴

Greek astronomers had none of this. What they had was a tradition of cosmological speculation — extraordinary in its philosophical reach, useless for predicting where a planet would be next Wednesday.

The Babylonian observational practice was institutional. The Esagil temple in Babylon and the Reš temple in Uruk maintained a scribal class — the ṭupšarrū Enūma Anu Enlil, scribes of the celestial omen series — whose work was supported by temple revenues and whose training extended over decades. The texts they produced fall into several distinct genres: the night-by-night Diaries; the Goal-Year texts (assembling all the predicted phenomena for a single forthcoming year); the Almanacs (year-by-year ephemerides of lunar and planetary positions); the System A and System B procedure texts (the mathematical algorithms for computing those ephemerides); and the celestial omen series itself, the seventy-tablet Enūma Anu Enlil compendium that linked observed phenomena to predicted political and meteorological outcomes. The corpus is one of the largest and longest-running scientific archives in human history. By 500 BCE it was already older than the entire Greek philosophical tradition would be at its closing.

How the transmission ran

The Babylonian astronomical archive did not move into the Greek world in a single act. It moved in a continuous flow, over roughly four centuries, through three overlapping channels: the Achaemenid-period scholarly contacts beginning around 500 BCE, the Hellenistic post-conquest contact zone after 331 BCE, and the Roman-imperial scholarly tradition culminating in Ptolemy in the second century CE.

Before Alexander: the Achaemenid contact

The Achaemenid Persian empire (550–330 BCE) governed both Babylonia and the Greek-speaking cities of Asia Minor for two centuries. Persian satraps held Sardis and Daskyleion; Greek mercenaries, exiles, and traders moved through Persepolis and Susa; Babylonian scribes calculated for the Achaemenid administration in cuneiform. The contact zone was continuous and dense, and at least one specific astronomical transmission datable to this period is firmly attested: the nineteen-year intercalation cycle that Meton of Athens introduced to the Athenian calendar in 432 BCE was almost certainly of Babylonian origin. The Babylonian state calendar had been regulated by a similar lunisolar scheme from the late sixth century BCE; Meton's coincidence of date and method with the established Babylonian practice is too close to be independent invention.⁵

The contact in this period was largely informal and largely uncredited. The Babylonian astronomical tradition was lodged in the temple schools of Babylon and Borsippa, in a scribal Akkadian written in cuneiform on clay tablets; the Greek tradition was a small philosophical school culture conducted in the Greek alphabet on papyrus. The two scribal systems did not mix easily, and what crossed in the Achaemenid period was probably a thin slice of numerical methods and observational results carried by individual travelers, not a wholesale transmission of the corpus.

Alexander's conquest and the Babyloniaca

The decisive opening came in October 331 BCE, when Alexander's army defeated Darius III at Gaugamela and entered Babylon. The Babylonian astronomers, far from being disrupted, recorded the event in their continuing diary; the tablet that mentions Alexander's entry into Babylon is now BM 36761 in the British Museum's Babylonian collection.⁶ The Achaemenid administration had patronized the Esagil scribes; the Macedonian successor state under Seleucus I continued to do so. The diaries continue without a break across the change of empires.

Within a generation of the conquest, the formal Greek-language transmission began. Berossus, a priest of Bel-Marduk at the Esagil temple, composed his Babyloniaca — a three-volume work on Babylonian history, cosmology, and astronomy written in Koine Greek — around 290–278 BCE, under the patronage of the Seleucid king Antiochus I Soter.⁷ Berossus's original work is lost, but enough fragments survive in later Greek writers (Polyhistor, Abydenus, Eusebius) to establish that his astronomical sections transmitted the Babylonian doctrine of celestial omens, the lunar and planetary periodicities, and the calendrical apparatus. He later moved to the Greek island of Cos, where he is reported to have taught Chaldean astronomy and astrology directly to a Greek-speaking student body. Cos is across a narrow channel from Rhodes; the geographic proximity to where Hipparchus would later work is suggestive even if no direct line of teaching can be drawn.

The Seleucid contact zone

The deeper transmission happened not through Berossus's literary work but through the Seleucid-period contact zone itself. Greek-speaking administrators, soldiers, and traders lived in Babylonia for two and a half centuries after 311 BCE; Babylonian scribes worked under Greek-speaking patrons; the astronomical archives at Babylon and the Reš temple at Uruk continued to be maintained in Akkadian cuneiform while parallel Greek-language scholarly traditions developed in Alexandria, Pergamon, and the Aegean cities.⁸ The transmission ran through the bilingual zone of late Babylonian temple scholarship, where the technical procedures of the ACT (Astronomical Cuneiform Texts) — System A and System B planetary models, the lunar System A and System B procedures, the goal-year texts — were available to anyone with the linguistic and mathematical preparation to follow them.

Mathieu Ossendrijver, whose 2012 Babylonian Mathematical Astronomy: Procedure Texts is the standard modern edition, has argued that the System A and System B traditions reached a mature form between roughly 400 and 250 BCE — exactly the period when the Seleucid contact zone was at its densest.⁹ The transmission was not a single act of translation. It was a long bilingual scholarly conversation in which Greek-speaking astronomers absorbed Babylonian numerical methods over generations.

The contact zone was geographically continuous. Greek-speaking soldiers and administrators were settled at Seleucia-on-the-Tigris, founded around 305 BCE roughly forty kilometres north of Babylon, where the Seleucid administrative capital became one of the largest cities in the Hellenistic world. Babylon itself continued under a parallel administration as a religious and scholarly centre with privileged temple status. Greek inscriptions appear in Babylonia alongside Akkadian-cuneiform tablets; the Seleucid era — the year-count beginning in 312 BCE — was used both in cuneiform tablets and in Greek documents. The administrative bilingualism of the Seleucid state was the practical condition of possibility for the scholarly transmission, and the dual-language receipts and contracts that survive show that the bilingual zone was not a thin scholarly elite but a functioning administrative ecosystem.

Hipparchus on Rhodes

The Greek astronomer who pulled the Babylonian inheritance together into a Greek synthesis was Hipparchus of Nicaea (active ~162–127 BCE), working primarily at Rhodes. Hipparchus's lost astronomical writings are known only through Ptolemy's Almagest and a handful of fragments, but enough survives to establish that he had direct access to Babylonian eclipse records spanning roughly eight centuries — back at least to the eighth century BCE — and to Babylonian numerical parameters for the moon's motion.¹⁰ G. J. Toomer's 1988 essay "Hipparchus and Babylonian Astronomy" remains the standard analysis: Hipparchus, Toomer argued, was the figure who carried out the direct synthesis of Babylonian observational and parametric data with Greek geometric models, and Ptolemy's apparent direct use of Babylonian records is largely mediated through a list compiled by Hipparchus.¹¹

William Cuningham, The Cosmographical Glasse, London, 1559. CC BY 4.0 via Wikimedia Commons. · CC BY 4.0

Hipparchus's most famous discovery — the precession of the equinoxes, a slow westward drift of the celestial coordinate frame at about 1° per 72 years — depended on Babylonian data. To detect a phenomenon that small, he had to compare his own observations of stellar positions in the second century BCE against earlier observations made by Greek astronomers (Timocharis and Aristyllus at Alexandria, ~280 BCE) and against observations preserved in the Babylonian tradition reaching far further back. The discovery is, in a precise sense, only possible because the Babylonian observational archive had been kept for centuries before any Greek astronomer began making comparable observations.

Ptolemy in the Almagest

The culminating Greek work, Claudius Ptolemy's Almagest (composed at Alexandria around 150 CE), names its Babylonian sources explicitly. Ptolemy uses the Nabonassar era (beginning 26 February 747 BCE) as his chronological backbone — the Babylonian era from which, in his own words, "the ancient observations are, on the whole, preserved down to our own time."¹² He cites individual Babylonian eclipse observations by date: the lunar eclipse of 23 December 383 BCE (a date confirmed by an independent Babylonian tablet now identified as such), the lunar eclipse of 16 July 523 BCE (preserved on tablet BM 33066), and a number of others, all of which give modern recovered times within about ±0.04 hours of Ptolemy's reported figures. The accuracy is the surviving signature of an unbroken observational tradition that had been running for nearly a millennium when Ptolemy used it.

What changed and what was replaced

The Babylonian transmission did not modify Greek astronomy. It built it.

Numbers in base sixty

The first and most pervasive change was the adoption of the sexagesimal computational system. Greek arithmetic, before the contact, had been performed in a decimal system with alphabetic numerals — clumsy for fractional computation and entirely inadequate for the astronomical work that lay ahead. The Babylonian sexagesimal system, with its sixty divisors and its place-value structure, was perfectly suited to angular and temporal measurement. Hipparchus adopted it; Ptolemy made it the standard of Greek mathematical astronomy; through Ptolemy, it became the standard of the medieval Islamic zīj tradition, the Latin Toledan and Alfonsine tables, and modern Western timekeeping.¹³

The modern hour of sixty minutes, the minute of sixty seconds, the degree subdivided into sixty arcminutes and the arcminute into sixty arcseconds, the circle of 360 degrees — all of these descend, through a continuous textual lineage, from the sexagesimal practice of the late Babylonian scribal schools.

The place-value structure of the sexagesimal system was essential, not incidental. Greek alphabetic numerals were not place-value: writing 47,259 in classical Greek required a string of distinct alphabetic symbols, with no positional regularity, and computation with such numerals was correspondingly awkward. Babylonian sexagesimal, by contrast, used only two basic signs (a vertical wedge for one, a corner wedge for ten) and built every number out of them through positional notation. The economy of computation that this enabled is what made the Babylonian astronomical procedures feasible in the first place; Greek astronomers who absorbed those procedures had to absorb the notation along with them. Ptolemy in the Almagest writes ordinary integers in Greek alphabetic form but switches to sexagesimal for every astronomical quantity — angles, times, ratios — because the procedures he is computing require it. The medieval Latin tradition transliterates this faithfully, and the modern conventions for degrees-minutes-seconds and hours-minutes-seconds are its direct descendants.

Eclipse prediction as a procedure

The second change was the replacement of Greek qualitative astronomy with Babylonian quantitative procedure. The Saros — the cycle of approximately 6,585.3 days (18 years, 11 days, 8 hours) over which lunar eclipses recur in a recognizable pattern — was a Babylonian discovery datable to the seventh or eighth century BCE.¹⁴ It is the simplest predictive procedure in mathematical astronomy: given a list of past eclipses, the next eclipse can be located in time without any geometric model whatsoever. The Babylonian astronomers had been doing this for centuries; the Greeks acquired it as a finished product.

The Saros allowed Hipparchus to verify his lunar theory by predicting eclipses backward into the Babylonian record and matching the predictions against the observed dates. The Babylonian numerical parameters for the moon's mean motion, anomalistic period, and nodical period (the rate at which the moon crosses the ecliptic) all entered Greek lunar theory through Hipparchus and survived essentially unchanged in Ptolemy's work three centuries later.

Planetary theory

The Babylonian planetary models known as System A (using zigzag and step-function descriptions of synodic phenomena) and System B (using linear zigzag functions) were the world's first quantitative procedures for predicting planetary positions in advance.¹⁵ Greek astronomy before the contact had no equivalent. The geometric epicycle-and-deferent model that Hipparchus pioneered and Ptolemy completed in the Almagest is structurally Greek — geometrical, intuitive, visualizable — but its empirical content, the numerical periods that calibrate it against the real sky, came directly out of the Babylonian System A and System B parameters. The most striking sign of the inheritance is that Ptolemy's reported lengths for the synodic periods of the visible planets agree with the Babylonian values to within rounding error; the agreement cannot be coincidence, and the direction of borrowing — given the older Babylonian observational base — is unambiguous.¹⁶

James Evans and J. Lennart Berggren, in their 2006 study and translation of Geminos's Introduction to the Phenomena (a Hellenistic astronomy textbook of the first century BCE), have shown that Geminos transmits Babylonian lunar System A and System B parameters with great technical accuracy — direct evidence that the Babylonian numerical traditions were circulating in Greek scholarly hands at least a century before Ptolemy.¹⁷ Geminos is the earliest extant Greek text to display intimate familiarity with the technical details of Babylonian planetary theory.

The trigonometric apparatus through which Hipparchus and Ptolemy made the Babylonian numbers visualizable was itself a Greek development on a Babylonian computational substrate. Hipparchus's chord table — the first systematic table of trigonometric values in the Western tradition, computed in sexagesimal fractions of the chord-of-a-degree — was the technical instrument that allowed Babylonian numerical periods to be converted into Greek geometric predictions.¹⁸ G. J. Toomer's 1973 Centaurus essay on Hipparchus's chord table remains the standard analysis of the construction, which proceeds by sexagesimal subdivision and uses the Babylonian computational notation throughout. Ptolemy refined the chord table in Almagest Book I, and through Indian and Arabic translation it became the medieval Islamic sine table, the parent of every later trigonometric table down to modern computation.

Coordinates, latitudes, and the round earth's geometry

The Babylonian astronomical archive had organized the heavens through the path of the ecliptic, divided into twelve thirty-degree segments — the Babylonian zodiac, datable in its standardized form to the fifth century BCE. Greek astronomy inherited this division wholesale. The names of the constellations, the boundaries of the zodiacal segments, and the choice of the ecliptic as the principal reference circle for the planetary motions are all Babylonian-derived. When Hipparchus computed the ecliptic coordinates of stars for what was likely the first systematic Greek star catalog (the catalog incorporated into Ptolemy's Almagest with disputed modifications), he was working in a coordinate system that Babylonia had supplied.¹⁸

The Babylonian unit of celestial-arc measurement, UŠ (1° = 4 minutes of time, a unit that ties degree to rotation), passed into Greek time-reckoning. The Almagest uses sexagesimal fractions of a degree for every star position, every planetary mean motion, every angular separation it records.

The count of 360 degrees in a full circle is itself probably Babylonian. The number is not arbitrary: 360 is six times sixty (matching the sexagesimal base) and is also approximately the number of days the sun spends traversing the ecliptic — a coincidence that the Babylonian scribes exploited by dividing the ecliptic into 360 degrees, each corresponding to roughly one day of solar mean motion. By the late fifth century BCE the convention was standard in the Babylonian observational record; by the time Hipparchus inherited the framework, the 360-degree circle was a finished tool, and it has remained the standard unit of angular measure in the Western tradition ever since.

What was displaced

The Greek tradition that this transmission displaced was the Eudoxan-Callippan tradition of geometric, non-numerical celestial modeling — beautiful as philosophy, useless as prediction. Eudoxus's twenty-seven concentric spheres, Callippus's expansion to thirty-three, Aristotle's still-larger system in Metaphysics Λ — these were taught in late fourth- and third-century BCE Greek philosophical schools and were the dominant cosmological framework before Hipparchus. The geometric ambition survived (the epicycle-and-deferent model of Hipparchus and Ptolemy is also a geometric system, after all), but the unpredictive purism was replaced by a hybrid: Greek geometric structure calibrated by Babylonian numerical parameters. The result was the world's first quantitative astronomy on something like the modern model, and it was Babylonian numbers that made it so.

What was also displaced was the older Greek calendrical chaos. The Nabonassar era that Ptolemy adopted gave Greek astronomy a continuous fixed chronological frame for the first time, and the Metonic intercalation regularized the lunisolar calendar in a way that Athenian magistrates had never managed unaided.

Through Islamic, Latin, and modern hands

The Babylonian-derived apparatus of Greek mathematical astronomy moved, in the centuries after Ptolemy, through the Sasanian Persian and early Islamic translation movements. Ptolemy's Almagest was rendered into Arabic in the late eighth and ninth centuries CE under the Abbasid translation program; the title al-Majisṭī ("the greatest") is itself the Arabic transliteration that gave the work its modern name. The Arabic zīj tables of al-Khwārizmī, al-Battānī, al-Ṭūsī, and Ulugh Beg are descendants of Ptolemaic and ultimately Babylonian computational practice.¹⁹ From Toledo in the twelfth century, the Almagest re-entered Latin Europe through Gerard of Cremona's translation from Arabic; the medieval Alfonsine tables of the thirteenth century are a direct continuation. Copernicus, working in the early sixteenth century, structured De revolutionibus (1543) on Ptolemy's model and inherited the Babylonian numerical parameters through it; Kepler, Brahe, and Newton built on the empirical apparatus that had now been refining itself for nearly two and a half thousand years.

The parallel transmission line into India is equally important and equally Babylonian in origin. David Pingree's lifelong work, summarized in his 1997 From Astral Omens to Astrology: From Babylon to Bīkāner, traced the chain of borrowings by which Babylonian astral science entered Sanskrit scholarly tradition via the Yavanajātaka and related works of the early centuries CE, and from Indian astronomy returned to the Islamic world in modified form in the eighth and ninth centuries. The Babylonian inheritance, in other words, did not travel along a single line through Greek alone — it travelled along multiple branches, recombining in Baghdad and Toledo and Samarkand, and the modern global apparatus of mathematical astronomy is the convergent product of those branches.

The living descendants of the Babylonian transmission are easy to enumerate: the sixty-minute hour, the 360-degree circle, every modern eclipse prediction (which is computed by a method that descends from Babylonian Saros logic and Greek geometric refinement), every astronomical coordinate system based on the ecliptic, every set of tabulated planetary positions in any almanac. The Babylonian inheritance is not visible to a modern reader because it is load-bearing — it is the substrate through which everything else has been computed.

What the cost was

The transmission proper was substantially peaceful. The Babylonian astronomers were not displaced by the arrival of Greek scholars; they continued to maintain the Astronomical Diaries through the Achaemenid, Seleucid, and Parthian periods, and the last datable cuneiform astronomical tablet (an astronomical almanac for the year 75 CE) was inscribed when the corpus had been continuous for some seven and a half centuries.²⁰ Berossus was a willing teacher; the Seleucid kings were willing patrons; Hipparchus and Ptolemy were willing students. There is no recorded violence specifically traceable to the transmission of astronomical knowledge between cultures.

What existed alongside the transmission, and what frames it, were the broader political and imperial systems that the temple-school astronomers served and that the Hellenistic scientific tradition emerged within. Three threads of cost run through the period of transmission, and the record requires that they be named, even if none of them is the transmission's own bill.

Achaemenid suppression of Babylonian revolts

The Achaemenid empire (550–330 BCE), under whose administration the Babylonian astronomical archive was maintained, was an extractive imperial system in the standard ancient sense: tribute was levied on conquered populations, satrapal administrations imposed Persian-language and Aramaic-language documentation on the older Akkadian-cuneiform scribal world, and revolts were suppressed by military force. In 484 BCE, two short-lived Babylonian pretenders — Bel-shimanni and Shamash-eriba — declared themselves king of Babylon and were defeated by Xerxes I within months.²¹

What happened next is contested in current scholarship. Herodotus reported that Xerxes punished Babylon by removing a divine image from the Esagil temple and, in some readings, by levelling parts of the city. Modern scholars including Amélie Kuhrt, Susan Sherwin-White, Caroline Waerzeggers, and Reinhard Pirngruber have argued, on the basis of the cuneiform archives themselves, that there was no general destruction of Babylonian temples and no comprehensive cultic suppression after 484 BCE — but that a significant transition in the elite priestly families of Babylon did occur, with several long-established lineages disappearing from the textual record and replacements appearing in their place. Whatever the precise institutional change, the Esagil temple did continue to operate, and the Astronomical Diaries continue to be compiled there without a visible break. The cost of 484 BCE was political and dynastic at the elite level; the astronomical archive itself was preserved.

The economic apparatus the diaries record

The Astronomical Diaries themselves contain, alongside the celestial observations, monthly records of commodity prices for barley, dates, mustard, cress, sesame, and wool, together with notes on the level of the Euphrates and weather. The economic data is one of the corpus's most distinctive features and has been extensively analyzed by Robartus van der Spek, Bert van Leeuwen, and others. The grain prices spike, sometimes by tenfold or more, during episodes of warfare, plague, drought, and Achaemenid or Seleucid military extraction — and the spikes correlate with documented famines.²² The diaries are, in this sense, also a long-term record of the subject Babylonian population's hunger under successive imperial regimes. The temple-school astronomers were maintained by temple revenues, which were maintained by extraction from the same population whose famine years they were also recording.

This is not a cost of the transmission to Greek astronomy. It is the cost of the imperial system that funded the scholarly enterprise that the transmission ran through. The distinction matters: the borrowing itself was not a violent act, but it was a borrowing from a scholarly tradition that was institutionally embedded in extractive imperial structures.

The end of cuneiform

By the early first century CE, the Akkadian-cuneiform scholarly tradition was running out. The last datable astronomical almanac was compiled in 75 CE; the last datable cuneiform tablet of any kind, an astronomical text, is dated to either 79 CE or, in another reading, slightly later. The cause was not violence but slow displacement: Aramaic, the Achaemenid administrative language, had become the spoken vernacular of Mesopotamia, and Greek had become the language of higher education in the Hellenistic and early Parthian periods. By the time the cuneiform scribal schools wound down, their astronomical procedures and observational records had already been absorbed into the Greek tradition. The Babylonian inheritance survived the death of its parent script.

What did not survive was the indigenous Mesopotamian intellectual continuity. The cuneiform corpus of mathematics, astronomy, medicine, divination, law, and literature became unreadable for nearly two thousand years — until the European decipherment of cuneiform in the mid-nineteenth century by Henry Rawlinson, Edward Hincks, and others reopened it for modern scholarship. The continuity that the Babylonian temple schools had sustained, generation after generation, from the third millennium BCE through the first century CE, was broken at the end of the period that brought the transmission to Greek into its final form. For nearly two thousand years between the late first century CE and the early Victorian period, the Babylonian astronomical corpus existed in the world only as silent earth: tablets in the soil of the mound at Babylon, in the ruins of the Esagil temple platform, awaiting the archaeologists who would eventually dig them up and the philologists who would eventually read them again. When Otto Neugebauer in the mid-twentieth century assembled the procedure texts into a coherent picture of Babylonian mathematical astronomy, he was reading a tradition that had been illegible to the world for sixty generations.

What the bill names

If the cost of this transmission must be named, it is the cost of the imperial systems — Achaemenid, Seleucid, Parthian — within which both the Babylonian and the Greek scholarly traditions were embedded. The astronomical archive was preserved, the procedures were transmitted, the synthesis was accomplished; the populations that paid the tribute that funded the temples that paid the scribes that kept the records were the Mesopotamian agricultural and urban poor of seven centuries. They are unnamed in the Diaries except in the form of grain prices and barley rations, but they were the substrate on which the world's first systematic astronomy was built. The Diaries themselves, in this sense, are a double document: the celestial column records the heavens that the temple schools were paid to watch, and the price column records the cost of the watching, in barley per shekel and dates per quart, year after year, for seven centuries.

Photograph by Madeleine Slierstaart. Openbare Bibliotheek, Bruges (Ms. 519, f. 074r). CC BY-SA 3.0 via Wikimedia Commons. · CC BY-SA 3.0

The Greek inheritance that comes down to us through Ptolemy, the Arabic zīj tradition, the Latin Toledan and Alfonsine tables, and into modern timekeeping is structurally a Babylonian inheritance. The numbers are Babylonian; the eclipse cycles are Babylonian; the planetary periods are Babylonian; the sexagesimal system that puts sixty minutes in our hour is Babylonian. The Greek contribution was to give Babylonian numbers a geometric body — the epicycle-and-deferent apparatus that allowed the numerical periods to be visualized and refined. To tell the history of Western astronomy as a Greek achievement, without the Babylonian foundation, is to mis-tell it. The astronomical archive that Hipparchus consulted on Rhodes in 162 BCE had been kept by people who did not speak his language, in a script he did not write, working at the foot of a ziggurat he never saw. They were the first systematic empirical scientists of antiquity, and the apparatus they bequeathed to the Greek world is, in real measure, still ticking on every clock in every modern timekeeping system.