Babylonians discovered astronomical geometry 1400 years before Europeans

“The crucial new insight provided by the new tablet without the geometrical figure is that Jupiter’s velocity decreases linearly within the 60 days”.

A Babylonian clay tablet would appear to show that geometry was developed by humans 1,400 years before than thought.

By examining and translating cuneiform tablets used by ancient Babylonian mathematical astronomers, he was able to reveal that they used a geometric technique considered a modern-day emergence in calculus. Although geometry was often used in Babylonian mathematics, historians thought their astronomy relied only on arithmetic – so the trapezoid didn’t make sense.

After cuneiform died out around 100 C.E., Babylonian astronomy was thought to have been virtually forgotten, he notes. 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.

“It’s geometry, which is itself old, but it’s applied in a completely new way, not to fields, or something that lives in real space, but to something that exists in completely abstract space”, Ossendrijver said.

What astonished the scientific community is that the method that Babylonians used to calculate the location of Jupiter looked similar to the astronomical geometry techniques that were elaborated in the 14th century in Oxford. To track the gas giant’s path across the sky, the Babylonians used a geometric technique – the so-called trapezoid procedure – that’s a cornerstone of modern calculus.

However, Mathieu Ossendrijver of Berlin’s Humboldt University managed to comprehend many of them.

It was this ability to compute the movements of an object moving with a changing velocity using geometric principles that was unheard of before the 14th Century AD, Professor Ossendriver said.

“It’s not an actual trapezoid that describes the shape of a field, or some configuration of the planets in space”, Ossendrijver told Live Science. “It’s a highly abbreviated version of a more complete computation that I already knew from five, six, seven other tablets”, he said. “I found, so to speak, the key to understanding these weird texts that deal with trapezoids”, he says. In particular there was Jupiter, known as the White Star and connected to the Babylonian god Marduk. 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 four tablets, excavated around 1880, were stored at the British Museum in London. By translating and studying them over the past century, archaeologists have learned a great deal about Babylonians, including their advanced system of astronomy, which grew out of the development of the zodiac around 400 BCE.

Armed with this Babylonian “Rosetta stone”, Ossendrijver determined that Babylonian astronomers used trapezoid-shaped graphs to determine Jupiter’s movements.

Ossendrijver will continue to work with these other Babylonian astronomical tablets. “Their presence … testifies to the revolutionary brilliance of the unknown Mesopotamian scholars who constructed Babylonian mathematical astronomy”.

“And they did this over a very long period of time, over centuries”. The list includes four tablets that refer to a trapezoid shape while discussing Jupiter, which had always been confusing.