Ancient Babylonian astronomers were ahead of their time
Inscriptions on clay tablets reveal pre-calculus math in tracking Jupiter’s motion
For people living in the ancient city of Babylon, Marduk was their patron god, and thus it is not a surprise that Babylonian astronomers took an interest in tracking the comings and goings of the planet Jupiter, which they regarded as a celestial manifestation of Marduk.
What is perhaps more surprising is the sophistication with which they tracked the planet, judging from inscriptions on a small clay tablet dating to between 350 B.C. and 50 B.C. The tablet, a couple of inches wide and a couple of inches tall, reveals that the Babylonian astronomers employed a sort of pre-calculus in describing Jupiter’s motion across the night sky relative to the distant background stars. Until now, credit for this kind of mathematical technique had gone to Europeans who lived some 15 centuries later.
“That is a truly astonishing find,” said Mathieu Ossendrijver, a professor at Humboldt University in Berlin, who described his archeological discovery in an article published Thursday by the journal Science.
“It’s a figure that describes a graph of velocity against time,” he said. “That is a highly modern concept.”
Mathematical calculations on four other tablets show that the Babylonians realized that the area under the curve on such a graph represented the distance travelled.
“I think it’s quite a remarkable discovery,” said Alexander Jones, a professor at the Institute for the Study of the Ancient World at New York University, who was not involved with the research.
Ancient Babylon, situated in what is now Iraq, south of Baghdad, was a thriving metropolis, a centre of trade and science for more than a millennium. Early Babylonian mathematicians who lived between1800 BC and 1600 BC had figured out, for example, how to calculate the area of a trapezoid, and even how to divide a trapezoid into two smaller trapezoids of equal area.
For the most part, Babylonians used their mathematical skills for mundane calculations, such as figuring out the size of a plot of land. But on some tablets from the later Babylonian period, there appear to be some trapezoid calculations related to astronomical observations.
In the 1950s, an Austrian-American mathematician and science historian, Otto E. Neugebauer, described two of them. Ossendrijver, in his new research, turned up two more. But it wasn’t clear what the Babylonian astronomers were calculating.
A year ago, a visitor showed Ossendrijver a stack of photos of Babylonian tablets now held by the British Museum in London. He saw a tablet he had not seen before. This tablet did not mention trapezoids, but it recorded the motion of Jupiter, and the numbers matched those on the tablets with the trapezoid calculations. “I was certain now it was Jupiter,” Ossendrijver said.
In September, Ossendrijver went to the British Museum, where the tablets were taken in the late 19th century. A close-up look of the new tablet confirmed it: the Babylonians were calculating the distance Jupiter travelled in the sky from its appearance to its position 60 days later. Using the technique of splitting a trapezoid into two smaller ones of equal area, they figured out how long it took Jupiter to travel half that distance.
Ossendrijver said he did not know the astronomical or astrological motivation for these calculations.
But, he said, “it shows a level of abstraction and insight into how you deal with motion.”
It was an abstract concept not known elsewhere at the time. “Ancient Greek astronomers and mathematicians didn’t make plots of something against time,” he said.