Scientists have long believed inroads in elementary calculus were developed in the 14th century. At that time in history, new concepts were developed to investigate a wide range of problems, one of them being the mathematics of a body’s motion.
In the 1350s, a group of scholars known as the Oxford Calculators, while lacking differential calculus, formulated the “mean speed theorem: a body moving with constant velocity travels the same distance as an accelerated body in the same time if its velocity is half the final speed of the accelerated body.”
But astroarchaeologist Matthieu Ossendrijver of Humboldt University in Berlin has uncovered something quite extraordinary. While studying some ancient Babylonian clay tablets dating from 350 to 50 BC, he found that astronomers had figured out how to track the motion of heavenly bodies almost 1,400 years before Europeans, reports the Washington Post.
Professor Ossendrijver believes his discovery will redefine the history books, showing that Babylonians were using geometry 1,700 years earlier. He says the astronomers used a surprisingly sophisticated geometry to calculate the orbit of what they called the White Star, the planet Jupiter.
For several years, Ossendrijver had puzzled over four particular tablets at the British Museum in London. The tiny scratched marks on the clay tablets were almost incomprehensible to the untrained eye. In a telephone interview from Germany with the Washington Post earlier this week, he said: “I couldn’t understand what they were about. I couldn’t understand anything about them, neither did anyone else. I could only see that they dealt with geometrical stuff.”
In 2014, Ossendrijver was given some black-and-white photographs of tablets stored at the museum. While studying them, one stood out. Officially known as BM 40054 by the museum, and dubbed Text A by Ossendrijver, the markings on the tablet appeared to be an abbreviation of a longer calculation that was familiar to him.
Using the Text A tablet and comparing it to four previous tablets, he was able to figure out that the calculation was all about Jupiter. The five tablets computed the predicted motion of Jupiter in relation to the other planets and distant stars. The markings depicted the planet’s trajectory as it moved along the horizon, calculating its position at 60 and 120-day intervals.
It became evident the ancient astronomers used geometrical calculations based on a trapezoid, a four-sided shape in which the top and bottom lines are parallel, working out the area of the shape, along with its “long” and “short” sides. The technique the ancient astronomers used to calculate the orbit of the gas planet is a cornerstone of modern calculus known as the “trapezoid procedure,” explains Gizmodo.
Until now, the trapezoid procedure was thought to have been developed in the 14th century. “This shows just how highly developed this ancient culture was,” Ossendrijver told Gizmodo. “I don’t think anybody expected something like this would be discovered in a Babylonian text.”
The text is just one of thousands of clay tablets covered in cuneiform and excavated in Iraq during the 19th century. By transcribing and studying the tablets, archaeologists have learned a lot about the Babylonians, including their advanced knowledge of astronomy.
Ossendrijver explains in his study, published in the journal Science, there are about 340 Babylonian astronomy tablets filled with data on planetary and lunar positions, arranged in rows and columns like a spreadsheet. An additional 110 tablets are like a book of procedures, detailing the mathematical operations that were used to compute the positions of celestial objects.
Ossendrijver believes the trapezoid procedure developed by the Babylonians was more than likely lost in the vast gulf of time, and never used again until it reemerged in medieval Europe. “I think it’s more likely they [Europeans] developed it independently,” he said.
“Who knows what else is hidden in the thousands of tablets lying in museums around the world?” Ossendrijver continued. “This is part of the history of science, and I hope it raises awareness of the value of protecting that heritage.”
This very interesting study, “Ancient Babylonian astronomers calculated Jupiter’s position from the area under a time-velocity graph,” was published in the online journal Science on January 29, 2016.
