For millenia upon millenia, humans knew that certain objects in the sky moved while other stars stood still. These are the objects we now know as planets. But precise calculations on their movements remains a fuzzy area of history. But a new clay tablet from ancient Babylonia shows that they may have used advanced geometrical techniques somewhere between 350 BCE or 50 BCE, pushing back the "discovery" of these principles back as far as 1750 years.

While the use of geometry stretches back at least to 3000 BCE, previous evidence suggested the use of the technique to track movements in space and time was not in wide use until the 1400s. The tablets specifically trace the movements of Jupiter across the night sky, helping pinpoint its position year after year.

"t's a completely new application of geometrical techniques which they had developed by 1800-1600 BC," Mathieu Ossendrijver, author of the paper and a professor at Humboldt University in Berlin, said in an email. "On these astronomical tablets the geometrical figure describes how Jupiter's velocity changes with time, so the figure is defined in time-velocity space, not in real space, the space in which we live. This kind of geometrical computation was thought to have been invented in 1350 in Europe, but we nowhave it on Babylonian tablets."

In particular, it demonstrates the use of what we now know as Mertonian mean speed theorem, a 1330s CE discovery that essentially was used to calculate the motions of an object across space and time to determine their velocity. As Ossendrijver points out, this may be one of the earliest times that geometry was used in abstract (rather than physical) senses. That is, rather than being used for construction, it was instead used to measure some other value. That value was, in this case, velocity.

The paper was published today in Science and adds on to the body of evidence that Babylonians used advanced mathematics centuries before their purported "discovery" in the western world. Along with plotting the position of Jupiter, the clay tablets also traced the path of the Moon, and some tablets contained instructions to reading those charts.

"With this method, distance traveled by a planet that travels at a linearly decreasing velocity is computed from the area of the velocity figure," Ossendrijver said. "There is no comparable computation in antiquity, not even in ancient Greek astronomy,which used a lot of geometry. "





Note: This post has been updated with comments from the paper's lead author.



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