We have long known that ancient Babylonians were superior mathematicians and astronomers: They understood the Pythagorean theorem some 1,000 years before Pythagoras himself was born and maintained detailed records of the heavens, including the passage of what is now known as Halley’s Comet, in their efforts to predict the future through observation of the stars and planets. But the newly decoded markings on a small clay tablet provide evidence that Babylon’s mathematical prowess went beyond what we imagined. In fact, early astronomers in Babylon (an ancient city located in what is now Iraq, south of Baghdad) circa 350 B.C. to 50 B.C. used sophisticated geometrical principles to track the path of the planet Jupiter, anticipating similar methods developed in medieval Europe by nearly 15 centuries.
At a time when attacks by extremist groups such as ISIS are destroying much of Iraq’s rich cultural heritage, new findings highlighting the mathematical and astronomical accomplishments of Babylon gives researchers hope that all might not be lost. Mathieu Ossendrijver of Berlin’s Humboldt University has spent years studying a few hundred clay tablets, most containing understandable numbers and arithmetic that represent the mathematics behind ancient Babylonian astronomy. Four tablets, however, appeared very different, and indecipherable. On one of them, the cuneiform text described a trapezoid (a rectangle with a slanted top) along with notations about its sides and its area, and the process of dividing that area into parts.
A year ago, Ossendrijver found the key to understanding such strange markings after a visitor showed him photographs of Babylonian tablets held by the British Museum in London since the 1880s. On one of them, the German researcher recognized, a Babylonian astronomer-scribe had recorded the motion of the planet Jupiter across the sky—and the numbers on that tablet matched the ones on the tablet with the trapezoid calculations. After traveling to London to examine the British Museum tablets in person, Ossendrijver confirmed the relationship between them. His translations of the clay tablets, published last week in the journal Science, show that the Babylonians were using sophisticated geometry—an early form of integral calculus—to deal with the abstract concept of how Jupiter’s velocity changes over time.
Because Jupiter and Earth are constantly moving in their orbits, observers on Earth see Jupiter as slowing down from when it first appears in the night sky. Some 120 days after it first becomes visible, the planet appears to come to standstill before reversing its course. As recorded on the tablets, Babylonian astronomers calculated how far Jupiter traveled from the time it appeared in the sky to the position it reached 60 days later, using trapezoids to symbolize the planet’s motion. By splitting a trapezoid into two smaller trapezoids of equal area, they calculated how long it took Jupiter to travel half that distance. As Ossendrijver told the New York Times of the markings he translated: “It’s a figure that describes a graph of velocity against time….That is a highly modern concept.”
As far back as 1800 B.C.-1600 B.C., Babylonian mathematicians had figured out how to calculate the area of a trapezoid, and even how to divide it into two smaller trapezoids of equal area. After applying these techniques to relatively mundane calculations, such as land use, they seem to have realized they could use the same math to the motion of celestial objects. To them, Jupiter was a celestial manifestation of their patron god, Marduk. They wanted to track the planet’s movement in order to understand his divine will, as well as to predict future grain harvests and other important events.
Such sophisticated math put the Babylonians ahead of their contemporaries in both ancient Greece and Egypt, and is strikingly similar to methods developed in 14th- century Europe. In the mid-1300s, a group at Merton University in England, known as the “Oxford Calculators,” came up with what they called the mean speed theorem, a pioneering idea that—as it turns out—was a reinvention of a technique used at least 1,400 years earlier in ancient Babylon.