According to Prof. Mathieu Ossendrijver of Humboldt University in Germany, Babylonian astronomers used geometry to calculate the position of Jupiter — a technique historians of science previously believed humans had not developed until at least 1,400 years later.
Left: BM 34757, one of the Babylonian cuneiform tablets translated by Prof. Ossendrijver. Right: a visualization of trapezoid procedure on the tablet – the distance traveled by Jupiter after 60 days, 10º45′, is computed as the area of the trapezoid; the trapezoid is then divided into two smaller ones in order to find the time (tc) in which Jupiter covers half this distance. Image credit: Mathieu Ossendrijver, Humboldt University / British Museum.
Prof. Ossendrijver translated five Babylonian cuneiform tablets from 350 to 50 BC and found that they contain a sophisticated calculation of the position of Jupiter.
These tablets were unearthed in the 19th century near the temple Esagila in Babylon and are now on display in the Middle Eastern Department of the British Museum, London.
According to Prof. Ossendrijver, they depict two intervals from when Jupiter first appears along the horizon, calculating the planet’s position at 60 and 120 days.
The texts contain geometrical calculations based on a trapezoid’s area, and its ‘long’ and ‘short’ sides. Previously, it was thought that Babylonian astronomers operated exclusively with arithmetical concepts.
The ancient astronomers also computed the time when Jupiter covers half of this 60-day distance by partitioning the trapezoid into two smaller ones of equal area.
“The idea of computing a body’s displacement as an area in time-velocity space is usually traced back to 14th-century Europe,” said Prof. Ossendrijver, who is an author of a new paper in the journal Science.
“I show that in four ancient Babylonian cuneiform tablets, Jupiter’s displacement along the ecliptic is computed as the area of a trapezoidal figure obtained by drawing its daily displacement against time.”
“None of the tablets contains drawings but the texts describe the figure of which the area is computed as a trapezoid. Two of these so-called trapezoid texts had been known since 1955, but their meaning remained unclear, even after two further tablets with these operations were discovered in recent years.”
“While ancient Greeks used geometrical figures to describe configurations in physical space, these Babylonian tablets use geometry in an abstract sense to define time and velocity,” Prof. Ossendrijver said.
The tablets redefine history books, revealing that European scholars in Oxford and Paris in the 14th century, who were previously credited with developing such calculations, were in fact centuries behind their ancient Babylonian counterparts.
“These computations anticipate the use of similar techniques by European scholars, but they were carried out at least 14 centuries earlier,” Prof. Ossendrijver said.
“The so-called Oxford calculators, a group of scholastic mathematicians, who worked at Merton College, Oxford, in the 14th century, are credited with the Mertonian mean speed theorem. This theorem yields the distance traveled by a uniformly decelerating body, corresponding to the modern formula S=t*(u+v)/2, where u and v are the initial and final velocities.”
“In the same century Nicole Oresme, a bishop and scholastic philosopher in Paris, devised graphical methods that enabled him to prove this relation. He computed S as the area of a trapezoid of width t and heights u and v.”
“The Babylonian trapezoid procedures can be viewed as concrete examples of the same computation,” he said.
“This surprising discovery changes our ideas about how Babylonian astronomers worked and may have influenced Western science.”
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Mathieu Ossendrijver. 2016. Ancient Babylonian astronomers calculated Jupiter’s position from the area under a time-velocity graph. Science, vol. 351, no. 6272, pp. 482-484; doi: 10.1126/science.aad8085
