A new insight into Babylonian mathematics

It has long been known that the ancient Babylonians were great astronomers and mathematicians. Already in Hellenistic times Greek authors like Strabo credited the Babylonians with inventing mathematics and astronomy and the discovery of cuneiform clay tablets from the nineteenth century onward has confirmed this notion. Babylonian priests meticulously kept track of the movements of heavenly bodies, since they believed that the paths of the stars and planets had been established by the gods and thus influenced the events on earth. By using advanced mathematics they were able to calculate the paths of the planets and the stars across the night sky and predict lunar eclipses. Up until now it had been believed that these Babylonian astronomers only used simple arithmetics to calculate planetary movements, but a new discovery by Mathieu Ossendrijver, professor of history at Berlin’s Humboldt University, implies that they had knowledge of complex geometry that foreshadowed the development of calculus.

Mathieu Ossendrijver, Science/AAAS
Mathieu Ossendrijver, Science/AAAS

Babylonian cosmology
Despite their great understanding of mathematics and astronomy, the Babylonians had a geocentric world view. They believed the heaven and the earth to be two rotating disks situated above each other and they believed that the heavenly bodies followed fixed, circular paths across the heavenly disk. Some of these heavenly bodies, however, known as ‘wandering stars’ or ‘planets’, did not follow this rule. These planets seemed to make smaller ‘epicycles’ whilst traveling across the night sky. This idea, made famous by Ptolemy the astronomer, continued to dominate astronomy up to the sixteenth century. Because these planets appeared to travel in epicycles, it seemed that the velocity at which the planets traveled changed regularly. For this reason, a more complex form of mathematics was required.

Ossendrijver’s discovery
Ossendrijver’s new insights are based on four cuneiform clay tablets of uncertain dating, although they fall within the range of 350 to 50 BC. The tablets contain tables with calculations on how to trace the movement of the planet Jupiter across the sky. Because the Babylonians identified Jupiter with their supreme god Marduk, great importance was attached to the movements of this planet. The calculations were based on the area of a trapezoid, a complex geometrical shape, and allowed the astronomers to not only calculate the distance and the speed at which a planet traveled, but also the changes in velocity. This way, they could accurately predict the seemingly illogical movements of the planets. Before this discovery it had been thought that such complex geometrical insights weren’t know until the 14th century, when Oxford scholars rediscovered this method. These advanced geometrical insights would pave the way for the development of calculus by Newton and Leibniz during the late seventeenth century. The Babylonian astronomical tradition died out around AD 100, but who knows what could have happened if their concepts had been developed further?

Epicycle and deferent . Under the licence pf CC BY 1.0 via Wikimedia Commons.
Epicycle and deferent . Under the licence pf CC BY 1.0 via Wikimedia Commons.

More on Babylonian astronomy
Ever since the time of the Sumerians, the peoples of Mesopotamia had held the belief that the whole universe was held together by a predetermined divine order. Everything, from the movement of the stars to natural disasters and geopolitical events, was thought to be interconnected. For this reason the priests, whose task it was to discover the will of the gods, tried to find causal relations between them. Since at least the early second millennium BC the Babylonians have recorded the movements of heavenly bodies along with diverse anomalous phenomena. The heavenly bodies were thought to have a special importance, since their fixed paths appeared to be a clear sign of the divine order. The planets, who moved in a more unpredictable way, were even identified with the gods themselves.

Astronomical Diaries
During the reign of the Babylonian king Nabonasir (747-734 BC) Babylonian astronomers started a new project to systematically record the movements of the heavenly bodies, along with all kinds of phenomena – from natural disasters, weather patterns and water levels to grain prices, wars and the death of kings – in so-called Astronomical Diaries. These Astronomical Diaries would serve as a catalogue and a reference for anyone interested in finding patterns between these events. Although the assumption that heavenly bodies directly infuence the events on earth has now been proven wrong, the methodology of the Babylonian astronomers was mostly scientific and did lead to great astronomical and mathematical insights, as we have seen above.

The decline of Babylonian astronomy
The Astronomical Diaries project continued for centuries. By the time that the calculations discovered by Ossendrijver were recorded, somewhere between 350 and 50 BC, Babylonia was ruled over by the Hellenistic Seleucids (312-144 BC) and the Iranian Parthians (144 BC onward), after having been ruled by the Achaemenid Persians between 539 and 330 BC. Babylonia had lost its independence long ago and the Akkadian language and culture had given way to Aramaic. Only these priests, with their astronomical and mathematical pursuits, preserved their ancient Akkadian heritage. Because of this, these priests were increasingly seen as mysterious oriental ‘Magi’ by the Greeks. Unfortunately, this enclave of Akkadian culture died out around AD 100 and the dominant Aramaic culture of Mesopotamia did not display as great an interest in astronomy as the Akkadians. For this reason, the astronomical and mathematical insights of the Babylonians were mostly lost, although some of it was preserved by the Greeks and the Arabs.

Further reading
You can find the most recent work by Mathieu Ossendrijver here. If you want to read the Astronomical Diaries yourself: you can find them here.

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