Babylonian tablet showcases an early form of ‘calculus’ for tracking Jupiter


A complex computation of geometry done for tracking Jupiter – no, this is not a part of any NASA handbook. Rather it pertains to a more than 2,000-year old tablet that fits in your palm. This clay-made artifact in question is Babylonian in origin, and dates from between 350 BC to 50 BC. As for the scope of mathematics contained within the tablet, it harks back to an abstruse form of geometry that was previously believed to be invented in 14th century AD. This abstract ambit ultimately evolved into what is known as calculus, the study dedicated to the mathematical gauging of change.

Now while there have been evidences that confirm how ancient Greeks also practiced both rudimentary algebra and geometry during the same contemporary time, their scope of mathematics was only limited to real, 3D space – like mapping of planetary orbits in conceivable circles. But the tablet analysed here displays some form of abstract geometry that was used to plot the changeable movements of a planet – which was totally unheard of, until now. As Mathieu Ossendrijer, a professor of the history of ancient science at Humboldt University in Berlin, made it clear –

What is new is that the Babylonians also used geometry in their astronomy. We have evidence that they used geometrical figures to gauge the motion of planets but the really exciting thing is that the kind of geometry they used is very special. What we have found essentially is almost like a modern-day graph – a geometrical figure that represents an abstract mathematical space. That’s really new and exciting as it was thought to have been first invented much later, around 1350 [AD].


Image Credit: Trustees of the British Museum/Mathieu Ossendrijver

As for the etchings on this tablet, the inscriptions pertain to a Babylonian cuneiform text. Expert assessment of this script has revealed that the Babylonian scholars (most likely priests) were observing the movements of Jupiter during the first 60 days it rises above the horizon. The priests computed the planet’s shifting motion by mapping its motional course away from the regular path of the Sun. Now this shifting motion appears to be decreasing because of the planet orbit’s relative movement with that of Earth’s. If represented in a graph, this ‘astronomical’ relationship is best depicted by the shape of two conjoined trapezoids. The area of each of these trapezoids defines Jupiter’s total displacement along the sun’s path – measured in degrees.

Simply put, this probably marks for the first time how the ancients had the ability to compute the movements of a motional object with altering velocity, with the aid of abstract geometry. Interestingly enough, there are no geometrical figures or graphs depicted on the clay tablet itself, while the inscriptions also eschew the mention of Jupiter. But the cuneiform script confirms that the priests indeed used some rudimentary form of abstract geometry (that later paved the way for calculus). Professor Ossendriver said –

It’s like a precursor if you like of what we know today as integral calculus, which allows us to calculate the movements of decelerating or accelerating objects. It’s a concept that was invented twice; once in ancient Babylonia and then re-invented around 1350 in medieval Europe. The ancient Greeks never did this.

He further added –

The tablets were written by priests in the temple. They computed the position of all five planets that they knew about, but Jupiter had the largest number of texts devoted to it. This was probably because Jupiter was associated with the supreme god of Babylon, Marduk.


Image Credit: Trustees of the British Museum/Mathieu Ossendrijver

The study was originally published in the Science journal.

Source: Independent

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About the Author

Dattatreya Mandal
Dattatreya Mandal has a bachelor's degree in Architecture (and associated History of Architecture) and a fervent interest in History. Formerly, one of the co-owners of an online architectural digest, he is currently the founder/editor of The latter is envisaged as an online compendium that mirrors his enthusiasm for ancient history, military, mythology, and historical evolution of architecture.
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