To the ancient Babylonians, the planet Jupiter was more than a bright light in the Mesopotamian night sky: It was the celestial manifestation of their god, Marduk. Jupiter’s location told of Marduk’s plans for them, such as if they would be blessed with a good harvest. It was so important to know Marduk’s plans that Babylonian astronomers developed a sophisticated, surprisingly modern mathematical technique for predicting Jupiter’s location, according to a new study published in the journal Science.
This new study changes our current thoughts on where and when humans first figured out this mathematical technique, which we now call calculating the integral of two points. This technique involves solving for a single value—such as time or location—by calculating the area under a curve on a graph. A precursor to calculus, it was thought to have been first developed in medieval Europe. However, this new finding by historian Mathieu Ossendrijver relocates the technique’s origins to Iraq more than 1,400 years ago.
Ossendrijver’s original goal wasn’t to upend historian’s beliefs: He just wanted to figure out what two Babylonian tablets were describing. Like many historians interested in ancient Mesopotamia, Ossendrijver was well-acquainted with the British Museum’s hundreds of fragile, hand-sized clay tablets. The tablets’ spiky cuneiform writing discussed mathematics and calculations used for astronomy. But the purpose of two tablets had long perplexed historians.
“Nobody understood what they are about, including me,” Ossendrijver told reporter Nell Greenfieldboyce at National Public Radio. The tablets described how to construct a trapezoid to use for calculations, but they didn’t explain what the calculations were for. For 14 years, Ossendrijver trekked weekly to the British Museum to research these tablets. But his lucky break came when he examined two other tablets outside the museum.
These other tablets recorded Jupiter’s motion. Surprisingly, the recorded numbers were very similar to those used in the puzzling calculations. By comparing the numbers, Ossendrijver realized that the tablets described how to calculate and predict Jupiter’s movement. As they tracked Jupiter’s location in the night sky over a 60-day period, the ancient Babylonians were graphing the gas giant’s velocity against time. “That is a highly modern concept,” Ossendrijver told reporter Kenneth Chang at the New York Times.
Because of how we perceive Jupiter’s orbit from our planet’s own orbit about the sun, the gas giant appears to slow down after about 30 days into its period. This gives its velocity-time graph a trapezoidal shape. The puzzling tablets in the British Museum had been describing how to use this trapezoid to calculate how far Jupiter had moved over its 60-day period, and how long the planet would take to reach the halfway point of its journey.
While the Babylonians’ astrological reasons for tracking Jupiter might seem strange to modern scientists, the technique they used is anything but strange. As Ossendrijver told the New York Times, “This is utterly familiar to any modern physicist or mathematician.”
To learn more about how modern scientists graph scientific data such as Jupiter’s velocity against time, please check out our module on using graphs and visual data in science.
Written by Megan Cartwright
Megan Cartwright is a freelance science/medical writer near Seattle. Before becoming a full-time writer, she worked as a scientist studying infectious diseases and vaccines, and earned her Ph.D. in Toxicology from the University of Washington. Megan has written for Slate and Bitesize Bio, and helps write blog posts and learning modules on chemistry for Visionlearning.