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Babylonians Tracked Jupiter With Advanced Tools: Trapezoids

Ancient tablets describe math that was thought to have been invented over 1,000 years later, rewriting the history books.

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The Babylonians used advanced mathematical skills to follow heavenly movements. Using geometry, they could calculate how far Jupiter (shown here with its moon Ganymede) moved across the night sky.


Newly translated ancient tablets show that ancient Babylonian astronomers used unexpectedly advanced geometry to understand the planets.

The find, described on Thursday in the journal Science, reveals that Babylonians tracked Jupiter by calculating the areas of trapezoids they used to symbolize  the planet’s motion across the sky. This geometrical trick rewrites the history books: The technique was thought to have originated in England more than a millennium later.

The study also fills in crucial gaps, says Niek Veldhuis of the University of California, Berkeley, who wasn’t involved with the study, since it “finally connects Babylonian mathematical astronomy with geometrical mathematics”—a missing link that has eluded scholars for more than a century.

The Right Angle

Researchers have long known that the Babylonians, who lived in what is now Iraq, had considerable mathematical skill: They successfully approximated the square root of 2 and understood the Pythagorean theorem nearly 4,000 years ago—more than a millennium before Pythagoras was born.

They were also talented astronomers, maintaining nightly catalogs detailed enough to record the passage of Halley’s comet. Babylonians regularly used arithmetic to boost their astronomical predictions.

But no one had ever found a Babylonian astronomical calculation that leveraged their impressive knowledge of pure geometry, until Mathieu Ossendrijver of Germany’s Humboldt University of Berlin spent 13 years deciphering what he described as a “small bunch of four weird trapezoid computations” between 2,000 and 2,400 years old.

Ossendrijver was the first to notice that the tablets—stored in the British Museum since the 1880s—had something to do with the planet Jupiter. However, they didn’t make much sense without knowing how the Babylonians encoded aspects of Jupiter’s motion, such as its appearances on the horizon.

Ossendrijver eventually found an undeciphered, remarkably intact tablet in the museum’s vast collections that described a full cycle of Jupiter’s journey through the sky, allowing him to carefully reconstruct what the other tablets actually meant.

His translations reveal that Babylonian astronomers used trapezoids to abstractly represent speed, time, and position. To find how far Jupiter moved between two different sightings, for instance, they would measure its apparent speed across the sky during each sighting, average them, and then multiply the average speed by the time between sightings.

The tablets explicitly link this formula to calculating the area of a trapezoid, with sides representing the speeds and elapsed time.

A Top-Shelf Find

The Babylonians’ techniques outshine those used by contemporary Greek and Egyptian astronomers—and shockingly mirror the mean speed theorem, a mathematical description of motion developed by a 14th-century English group known as the Oxford Calculators.

And the findings probably represent the tip of a mathematical iceberg. “There are thousands of tablets in various museums that were never translated,” says Ossendrijver, “and often we can translate a tablet but don’t understand what is going on until much later.”

Ossendrijver’s newly deciphered tablet also heartens researchers after years of war and the rise of ISIS have damaged or destroyed much of Iraq’s archaeological heritage.

“That such an important, and almost completely preserved, example can now be added to the corpus...speaks volumes about the untold treasures that may still be found in the drawers of the British Museum and other such collections,” says Veldhuis.

Such a find also speaks to the human spirit of discovery—both of the ancient astronomers who gazed at the heavens, and the modern researchers who seek to reconstruct their understanding of the cosmos.

Follow Michael Greshko on Twitter.

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