Geometry helped ancient Babylonians track planets

“When I looked at the text, I was immediately convinced”, said Jens Høyrup, an expert in Babylonian mathematics at Roskilde Universityin Denmark, who was not involved in the new study. After careful scrutiny, Ossendrijver found that together these five tablets computed the predictable motion of Jupiter relative to the other planets and the distant stars.

A newly discovered tablet written in Babylonia’s cuneiform script discusses calculating the position of Jupiter. But the Jupiter link was tentative. The four tablets, excavated around 1880, were stored at the British Museum in London. Alone in his office a few months later, Ossendrijver perused the photos. “I think it’s more likely they [Europeans] developed it independently”, he said. He says the astronomers used a surprisingly sophisticated geometry to calculate the orbit of what they called the White Star, the planet Jupiter.

Although the tablet did not reveal any pictures, or even associations with Jupiter, the technique perfectly aligned with Osserndrijver’s suspicions: that the Babylonians used a trapezoid graph to draw lines connecting the planet’s positions on the first and last day of measurement, and then lines that would connect to the “ground” below.

The procedure Ossendrijver translated from the Babylonian tablets appears to show how to calculate the distance that Jupiter has traveled over a long stretch of time, by using measurements of how fast it was moving across the sky on given days. The trapezoid was formed by plotting the two main variables, Jupiter’s velocity over time.

Ossendrijver will continue to work with these other Babylonian astronomical tablets.

Although elated, Ossendrijver wasn’t ready to publish, because a second part of the trapezoid prescription remained unclear.

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 BC and 50 BC.

“No one expected this”, said Mathieu Ossendrijver, a professor of history of ancient science at Humboldt University in Berlin, noting that the methods delineated in the tablets were so advanced that they foreshadowed the development of calculus. The mathematicians could divide the trapezoid in half to determine the distance traveled in 30 days. There are about 4,000 to 5,000 other astronomical texts among the Babylonian tablets at the British Museum, and so far none of them have mentioned using geometry or graphs to do astronomical computation, but many other tablets still haven’t been translated.

An historian of science has discovered evidence that Babylonian priests living between 350BC and 50BC invented and used an abstract form of geometry that until now was thought to have been invented in the 14th Century, eventually evolving into calculus, the mathematical study of how something changes over time.

Noel Swerdlow, a researcher at Caltech who studies the history of astronomy, says the analysis of these tablets appears to be correct.

Astronomical phenomena were important to the Babylonians. It’s a bit like a geometry textbook with the actual figures missing, but the method described would be familiar to any 21 century physicist.

“They’re in a way like modern scientists and in a way they’re very different”, says Jones.