In 1881, Epping announced that the numbers represent steps in a calculation of the dates and times of a series of new moons, covering the years 104–101 BC. Another text included a similar table for the positions of Venus and Jupiter. The calculations were impressively accurate, even taking account of subtle variations in the apparent speed of the moon and planets through the sky (caused by their elliptical orbits). Although Greek and Roman writers often refer to the Babylonians’ astral wisdom, no one had expected that alongside their magical omens and prayers, the scribes of Marduk developed a new type of mathematical knowledge about the cosmos. Epping called his discovery a ‘precious historical treasure’. The priests really could foretell the future, using accurate formulas to predict celestial events decades in advance.
As more tablets have been catalogued and read, historians can now trace a gradual progression in the priests’ abilities. Enuma Anu Enlil, the handbook found in Ashurbanipal’s library, contains a series of omens that list risings and settings of Venus,4 dated to the second millennium BC. Some of the numbers seem to be based on observations but others have been corrected to fit a pattern. The scheme isn’t very accurate, but shows that the Babylonians were already trying to describe the heavens using mathematical rules. The later tablets from Babylon (and also some written by temple priests in the city of Uruk) show that from around the eighth century BC, the priests started keeping more systematic records, watching the sky each night and writing down everything they saw. These ‘astronomical diaries’ also include notable terrestrial events, from the level of the Euphrates river or prices of wool, barley and sesame, to reports of monstrous births.
Within a few generations, the scribes started to notice ‘great cycles’: periods after which particular types of event roughly repeat. Ishtar repeats her wandering path after 8 years, for example, and Marduk after 71 years, while eclipses follow an 18-year cycle. By checking what had happened during previous great cycles they could monitor signs in the sky without even needing to watch.
Then, around 400 BC, came another jump in sophistication. The priests invented the zodiac by dividing the ecliptic (the path through the sky followed by the sun, moon and planets) into 12 equal segments of 30 degrees, naming each one after a nearby constellation, such as ‘Bull of Heaven’ (now Taurus) and ‘Great Twins’ (Gemini). This gave them an accurate system for recording and computing events in the sky. Shortly afterwards, they came up with arithmetic methods to describe the repeating cycles recorded in their diaries.
These were based on finding ‘period relations’, which express different astronomical cycles in terms of one another. For example, each planet moves around the zodiac at a characteristic speed (its ‘tropical cycle’), but superimposed on this is a zigzag pattern in which it sometimes stops or temporarily reverses direction (its ‘synodic cycle’).5 Venus can be described pretty well by a very simple relation – in eight years, it goes through eight tropical cycles and (almost exactly) five synodic cycles – while others are far more complex. The final step was to incorporate the subtle variations in speed that occur throughout these cycles, by adding or subtracting different values over time according to set rules.6
It’s very clever maths, says historian of astronomy James Evans. The scribes no longer needed to rely on long lists of past observations, just a small set of numerical parameters to define the behaviour of each celestial event.7 Epping had uncovered the moment when humanity transitioned from simply experiencing phenomena in the sky to explaining them.
And that wasn’t the only surprise hidden in the crumbling clay.
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In 336 BC, more than 1,600 kilometres northwest of Babylonia, a young prince called Alexander ascended the Macedonian throne. Over the next five years he carved out a huge empire, winning Greek states, then Asia Minor, then Egypt. And in October 331 BC, after a decisive battle against Persian forces on the plains near Nineveh, he marched his armies to Babylon.
According to the later Roman historian Quintus Curtius Rufus, while many of the inhabitants climbed the city walls to watch Alexander the Great arrive, most went out to meet him as he approached the blue-glazed gate. Officials carpeted the ceremonial road with flowers, and lined it with silver altars, heaped with perfume. They sent out gifts – herds of cattle and horses; lions and leopards in cages – and showed off their cultural treasures with a procession of musicians, wise men and the scribes of Enuma Anu Enlil. Surrounded by his armed guard, Alexander entered the gate by chariot and went straight to the royal palace. Taken by the city’s beauty and antiquity, he made it his new capital. His victory ushered Babylon into the Greek world – and brought the scribes into contact with the astronomers and philosophers of the west. Their two views of the cosmos could not have been more different.
Whereas the temple priests saw celestial events as written on a flat tablet, Greek scholars were interested in three dimensions; they wanted to know how the solar system was arranged. And while the Babylonian belief in omens meant precision mattered above all else, the Greeks had little tradition of accurately observing the sky. They based their models on lofty, philosophical ideals.
In the fourth century BC, the dominant figure in Greek thinking was Alexander’s tutor, Aristotle. His fundamental assumption was that since the heavens are divine, they must be structured in the appropriately perfect and efficient way: a series of spheres. He proposed a spherical Earth at the centre of the cosmos, surrounded by concentric circles or spheres that carried the orbits of the sun, moon, five known planets and fixed stars. The only imaginable heavenly motion was constant speed in a perfect circle, but that couldn’t explain why the planets sometimes stop and change direction. In the third century BC, western astronomers came up with an elegant solution: the planets move in small circles, called epicycles, at the same time as tracing a larger loop around the Earth. Off-centre orbits were suggested to explain the varying speed of the moon and sun. These geometric theories included no accurate numbers; the principle was what mattered. Until the second century BC, that is, when an astronomer named Hipparchus changed everything.
Born around 190 BC, Hipparchus worked on the island of Rhodes and seems to have conducted a one-man revolution of Greek astronomy, essentially transforming this philosophical art into a practical science. He made extensive astronomical observations, and is credited with compiling the first star catalogue. He also slated his peers for their sloppiness, arguing that their models of the cosmos were useless if they didn’t accurately match what happened in the sky. His attitude, according to James Evans, ‘represented a radically new way of regarding the world – at least among the Greeks’. Hardly any of Hipparchus’s work survives directly, but the later mathematician and astronomer Ptolemy reports that Hipparchus used astronomical observations to derive accurate numbers – period relations – to describe the cyclic behaviour of the sun, moon and planets. Then he used the new maths of trigonometry (and possibly even invented it; Hipparchus was the first we know of to use such techniques) to plug these numbers into the existing geometric models.
‘Hipparchus turned a broadly explanatory geometric model into a real theory,’ says Evans. He wasn’t able to fully explain the motions of the planets using Aristotle’s perfect circles. But for the first time, the Greeks could calculate the position of the sun or moon in the zodiac for any given date.
The next great astronomer of the ancient Greek world was Ptolemy. Working in Alexandria in the second century AD, he built on Hipparchus’s work in a monumental text, the Almagest, in which he set out a logical, mathematical explanation for all the movements seen in the sky, derived step by step from observations. It included the planetary theory that eluded Hipparchus: Ptolemy suggested that epicycles move through the sky at a constant speed not as seen from Earth or from the centre of their orbit but from a third point, which he called ‘the equant’. Though complicated, this scheme was impressively accurate, and the Almagest proved to be one of the most influential science books ever written, defining a view of the cosmos that lasted for 1,500 years.
For much of recent history, then, this chain of events was thought to explain the origin not just of western astronomy but of scientific thinking in general, part of the so-called ‘Greek miracle’, as Evans puts it, ‘as if the Greeks had