Stone tablets (pictured) used by Babylonians reveal how they tracked the movements of Jupiter

ishtartv.com- grandjee.com

January 28, 2016

Ancient Babylonians used geometry to track planets in the solar system more than 1,400 years before Europeans were believed to have devised the mathematical technique. 

The findings come from analysis of four stone tablets, which reveal how the ancient civilisation tracked the movements of Jupiter.

Scientists had believed the mathematical method had been developed by scholars in Europe in the 14th century, but the tablets date to between 350 to 50 BC.

This could mean Babylonians were using geometrical methods as much as 1,700 years earlier.

Professor Mathieu Ossendrijver, a researcher in the history of ancient science at the Humboldt-Universität zu Berlin who deciphered the markings, said the tablets have redefined the history books. 

Translation of the cuneiform tablets revealed they described a mathematical technique to calculate the positions of large bodies in space and time.

The markings depict measurements made to track Jupiter as it moved along the horizon, calculating the planet’s position at 60 days and then at 120 days.

From this, it appears the Babylonians used geometrical calculations based on a trapezoid – a four-sided shape in which the top and bottom lines are parallel – working out the area of the shape, along with its ‘long’ and ‘short’ sides.

The ancient astronomers also computed the time when Jupiter covered half of the 60-day distance by partitioning the trapezoid into two smaller shapes of equal area.

What makes the findings surprising is that it had previously been thought that Babylonian astronomers only used arithmetical concepts, and not geometry.

While ancient Greeks used geometrical figures to describe configurations in physical space, these Babylonian tablets use geometry in an abstract sense to define time and velocity.

The markings depict measurements made to track Jupiter as it moved along the horizon, calculating the planet’s position at 60 days and then at 120 days. From this, it appears the Babylonians used geometrical calculations based on a trapezoid (right) working out the area of the shape

The ancient astronomers also computed the time when Jupiter (pictured) covered half of the 60-day distance by partitioning the trapezoid into two smaller shapes of equal area. What makes the findings surprising is that it had previously been thought that Babylonian astronomers only used arithmetical concepts, and not geometry 

The discovery of these calculations had historically been credited to scholars in Europe during the 14th century, at Merton College, Oxford as well as in Paris.

GEOMETRY AND ASTRONOMY 

Analysis of four stone tablets has revealed that Babylonian astronomers used geometry to track the movement of Jupiter.

Translation of the cuneiform tablets revealed they described a mathematical technique to calculate the positions of large bodies in space and time. 

The markings depict measurements made to track Jupiter as it moved along the horizon, calculating the planet’s position at 60 days and then at 120 days. 

From this, it appears the Babylonians used geometrical calculations based on a trapezoid – a four-sided shape in which the top and bottom lines are parallel – working out the area of the shape, along with its ‘long’ and ‘short’ sides. 

When the measurements were made, Jupiter would have first been seen rising at dawn and would have been visible for a number of days. 

The astronomers would have then captured the ‘daily displacement’ of the gas giant as it moved across the sky, measured as degrees per day.

Scientists had believed that the mathematical method had been developed by scholars in Europe in the 14th century, but the tablets date to between 350 to 50BC, which could mean Babylonians were using geometrical methods as much as 1,700 years earlier.

Professor Ossendrijver explained: ‘The Babylonian trapezoid procedures can be viewed as a concrete example of the same computation. 

‘They also show that Babylonian astronomers did, at least occasionally, use geometrical methods for computing planetary positions.’

The translations were prompted by a newly discovered tablet, approximately 4cm across, which shed new light on how the Babylonian astronomers used the trapezoid method.

When the measurements were made, Jupiter would have first been seen rising at dawn and would have been visible for a number of days. 

The astronomers would have then captured the ‘daily displacement’ of the gas giant as it moved across the sky, measured as degrees per day.

Professor Ossendrijver wrote: ‘The idea of computing a body’s displacement as an area in time-velocity space is usually traced back to 14th-century Europe.

‘I show that in four ancient Babylonian cuneiform tablets, Jupiter’s displacement along the ecliptic is computed as the area of a trapezoidal figure obtained by drawing its daily displacement against time.

He added: ‘The tablets date from 350 to 50 BC. 

‘The trapezoid procedures offer the first evidence for the use of geometrical methods in Babylonian mathematical astronomy, which was thus far viewed as operating exclusively with arithmetical concepts.’

Speaking to MailOnline, Professor Ossendrijve said: ‘The importance of the findings is that these tablets prove that the Babylonians were using geometry in a way that anticipates how we describe and compute motion nowadays. 

‘That is, the construct figures that are actually graphs of the velocity (of a planet) against time, so time on one axis, velocity on the other. This is not found anywhere else in antiquity.

hen the measurements were made, Jupiter would have first been seen rising at dawn and would have been visible for a number of days. The astronomers would have then captured the ‘daily displacement’ of the gas giant as it moved across the sky, measured as degrees per day (stone pictured)

‘Any book on the history of math and physics will tell you this type of graph (velocity against time) was invented around 1350, in the middle ages. We now know the Babylonians already invented it.’ 

A spokesperson for the British Museum, which supplied the tablets, told MailOnline: ‘We always make our objects freely available to scholars and researchers and are truly delighted when one of these valiant workers makes an important breakthrough.

‘It enlarges our appreciation of what the ancient Babylonian astronomers were capable of all those centuries ago.’

The findings are published today in the journal Science. 

The cuneiform stone tablets left behind by the Babylonians, like the ones translated in this study, provide a wealth of information on ancient Mesopotamian civilisation.

Last year an exhibition of ancient
clay tablets discovered in modern-day Iraq shed light on the daily life of Jews exiled to Babylon 2,500 years ago.

The cuneiform stone tablets left behind by the Babylonians, like the ones translated in this study, provide a wealth of information on ancient Mesopotamian civilisation. This stock image of cuneiform inscriptions from Babylonia are written in the Sumerian language. They date from the 15th century

More than 100 cuneiform tablets,
each no bigger than an adult’s palm, detailed transactions
and contracts between Judeans driven from, or convinced to move
from, Jerusalem by King Nebuchadnezzar around 600 BC.

Archaeologists got their first chance to see the tablets – acquired by a wealthy London-based Israeli collector – barely two years ago, and said they were ‘blown away’.

Nebuchadnezzar, a powerful ruler famed for the Hanging
Gardens of Babylon, came to Jerusalem several times as he sought
to spread the reach of his kingdom.

Each time he came – and one visit coincided with the
destruction of Jerusalem’s first temple in 586 BC – he either
forced or encouraged the exile of thousands of Judeans.

One exile in 587 BC saw around 1,500 people make the
perilous journey via modern-day Lebanon and Syria to the fertile
crescent of southern Iraq, where the Judeans traded, ran
businesses and helped the administration of the kingdom.

BABYLON AND ANCIENT MESOPOTAMIA

Mesopotamia is an ancient Greek term meaning ‘the land between rivers.’ 

The region was the name for the Tigris–Euphrates river system, corresponding to modern-day Iraq, northeastern Syria and southeastern Turkey and smaller parts of southwestern Iran and Kuwait.

Mesopotamia has been called the ‘cradle of civilisation’ because agriculture and domestication developed there earlier than anywhere else, around 8,000 years ago.

Bronze Age Mesopotamia included Sumer and the Akkadian, Babylonian, and Assyrian empires. By 3,000 BC, the Mesopotamians had already invented the wheel, developed writing, and created the world’s first cities. 

Babylon was a significant city in the region, which was established in 2,300BC. 

It is thought to have been the largest city on the world during its history, and spawned an advanced civilisation, known for its astronomical observations.

The city of Babylon was famed for its ‘hanging gardens’ but some have suggested they were not in Babylon at all but were in a Assyrian city called Ninevah, which was known as New Babylon. 

Gate to Babylon: Babylon was a significant city in Mesopotamia, established in 2,300BC

The hanging gardens of Babylon were believed to have been built in the city because of its name. However, the gardens may have been found in the Assyrian capital of Nineveh, which was known as New Babylon