Babylonians tracked Jupiter with a graph 1,400 years early

Babylonian astronomers writing between 350 and 50 BC calculated how far Jupiter moved across the sky by treating its distance as the area of a trapezoid drawn from its speed over time — a method historians had credited to European scholars of the 14th century AD. Mathieu Ossendrijver of Humboldt University in Berlin published the decoding in Science in January 2016.

The numbers are on the clay. One text gives Jupiter’s daily motion as 12 arcminutes on the day it reappears and 9½ arcminutes sixty days later. Average the two, multiply by 60 days, and you get 10°45′ of travel. On four other tablets the same sum appears as a trapezoid, with the two speeds as its parallel sides; the scribes even split it into two equal areas to find when Jupiter had covered half the distance.

Is it really calculus?

Not quite. Headlines called it calculus, but the tablets show one specific case: distance as the area under a velocity–time graph for speed that changes steadily. That matches the Merton mean-speed rule of 14th-century Oxford and Nicole Oresme’s graphs in Paris, not Newton’s general method.

“It’s not unlike what we do in integral calculus when we compute areas under such curves.” — Mathieu Ossendrijver, 2016

What makes it a surprise is the abstraction. Greek astronomers drew figures in real space; this trapezoid lives in a space of speed against time.

Why Jupiter, and why did it take so long to see?

Jupiter was associated with Marduk, Babylon’s chief god, and its position was read for omens about crops and the river. The four trapezoid tablets, excavated in the 19th century and held by the British Museum, made little sense until Ossendrijver, studying museum photographs in January 2015, found a fifth tablet that names Jupiter and spells out the same calculation step by step.

Babylonian astronomy was otherwise thought to be purely arithmetical. The technique, Ossendrijver says, was “reinvented more than a thousand years later” — though other Babylonian cycles, recorded in cuneiform, lived on in the Antikythera mechanism.