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# Ancient Babylonians Tracked Jupiter With Calculus

## Clay tablets reveal that Babylonian astronomers employed a sort of precalculus to describe Jupiter’s motion across the night sky. Continue reading →

The earliest known examples of mathematical and geometric astronomy have been identified in a series of ancient Babylonian cuneiform tablets.

An analysis of the tablets, reported in the journal Science, reveals ancient Babylonians were able to calculate the position of Jupiter using geometric techniques previously believed to have been first used some 1,400 years later in 14th century Europe.

"These texts are the earliest evidence we have from antiquity of mathematical astronomy," said the study's author Dr Mathieu Ossendrijver, a historian on Babylonian astronomy with the Humboldt University in Berlin.

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"It describes Jupiter's velocity across the sky and how that changes with time."

The tablets, which are housed at the British Museum, are believed to have been unearthed from an archaeological dig in what is now modern day Iraq sometime in the 1800s.

The almost completely intact tablets are thought to have been written in Babylon between 350 and 50 BCE.

The tablets are part of a larger collection of 450 astronomy tablets from Babylon and Uruk containing celestial data arranged in rows and columns, together with instructions.

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Dr Ossendrijver examined five tablets numbered as trapezoid text A to trapezoid text E, four of which deal with geometrical trapezoid shapes, but nobody understood what they were about.

## One tablet key to puzzle

However, one of the tablets - trapezoid text A - provided Dr Ossendrijver with the key to understanding the other four tablets.

"I discovered that they describe the motion of Jupiter as a velocity, the number of degrees it moves across the sky in a day," Dr Ossendrijver said.

"If you plot the velocity of Jupiter against time, you get a creeping curve which looks like a rectangle with a slanted top - that's the trapezoid."

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The tablets show two intervals from when Jupiter first appears along the horizon at night, to the planet's position in the sky after 60 and 120 days.

The tablets also computed the time when Jupiter covers half of this 60-day distance by partitioning the trapezoid into two smaller ones of equal area.

"We're not really sure why the Babylonians were so interested in the motion of the planet Jupiter, but one possible explanation is that Jupiter was associated with Marduk the supreme god of Babylon," Dr Ossendrijver said.

"These astronomers or priests were employed by Babylon's main temple where Marduk was venerated. Each god had a star and Marduk's was Jupiter."

Babylonian writing is thought to have originally developed as an accounting system for keeping track of property such as sheep, grain, or the size of a field.

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"That's what most of the cuneiform tablets we have from Mesopotamia deal with," Dr Ossendrijver said.

"But by about 2000 BCE they began to develop a form of mathematics with sophisticated field computations and methods for solving what we call quadratic equations that go beyond these practical things. It's a way of describing and computing motion, similar to what we today call integral calculus."

These tablets redefine our history books as the origins of calculus are generally traced back to the Middle Ages when people began using geometry to calculate velocity by plotting the position of an object against time.

"This is highly surprising. No-one expected to find something like this in antiquity," Dr Ossendrijver said.

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

This originally appeared on ABC Science Online.

Ancient Babylonian cuneiform tablet text A provided essential clues to understanding four other tablets numbered text B to text E.

Egypt will likely offer promising finds in 2016. King Tutankhamun's tomb will be under the spotlight as

recent investigation

suggests the western and northern walls of the 3,300-year-old burial may hide two secret chambers. According to Egypt's Minister of Antiquity Mamdouh al-Damaty there is a 90 percent chance the tomb of King Tut contains such chambers. Damaty made the announcement last November at the end of a radar-based investigation. The non-invasive search followed a claim by Nicholas Reeves, a British Egyptologist at the University of Arizona, who first speculated the existence of the chambers, arguing that one contains the remains, and possibly the intact grave goods, from queen Nefertiti. She was the wife of the "heretic" monotheistic pharaoh Akhenaten, Tutankhamun's father. Will archaeologists try to access the hidden chambers? Their attempt may lead to what Damaty called "one of the most important finds of the century."

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The noninvasive technologies applied to King Tut's tomb will be widely used this year in another ambitious project. Called Scan Pyramid, the investigation is carried out by a team from Cairo University's Faculty of Engineering and the Paris-based organization Heritage, Innovation and Preservation under the authority of the Egyptian Ministry of Antiquities. The project aims to scan the largest pyramids of Egypt in order to detect the presence of any unknown internal structures and cavities. The technique could lead to a better understanding of the pyramids' structure and how they were built. The project uses a mix of technologies such as infrared thermography, muon radiography, and 3D reconstruction to look at the inside of four pyramids, which are more than 4,500 years old. They include Khufu, or Cheops, Khafre or Chephren at Giza, the Bent pyramid and the Red pyramid at Dahshur. One

particularly remarkable anomaly

has been already detected on the eastern side of the Great Pyramid, also known as Khufu or Cheops, at the ground level. Much more is to come -- the first results are expected in the first months of the year.

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Last year a study made an

extraordinary and controversial claim

: Stonehenge was basically a second-hand monument from Wales. It would have stood there hundreds of years before it was dismantled and transported to Salisbury Plain in Wiltshire. The research indicates that two quarries in the Preseli Hills of Pembrokeshire, in southwest Wales, are the source of Stonehenge's bluestones. Carbon dating revealed such stones were dug out at least 500 years before Stonehenge was built -- suggesting they were first used in a local monument that was later dismantled and dragged off to England. "Stonehenge was a Welsh monument from its very beginning. If we can find the original monument in Wales from which it was built, we will finally be able to solve the mystery," Mike Parker Pearson, director of the project and professor of British later prehistory at University College London said. Researchers have been using geophysical surveys, trial excavations and aerial photographic analysis to identify the ruins of a lost, dismantled monument. The results of such research promise to make the headlines this year. "We think we have the most likely spot. We may find something big in 2016," Kate Welham, of Bournemouth University, said.

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In early December,

the Colombian government announced

they had found the holy grail of treasure shipwrecks -- an 18th-century Spanish galleon that went down off the country's coast with a treasure of gold, coins and precious stones now valued between \$4 billion and \$17 billion. The multibillion-dollar ship, called the San Jose, was found off the island of Baru, near Cartagena. The vessel was part of Spain's only royal convoy to bring colonial coins and bullion home to King Philip V during the War of Spanish Succession from 1701 to 1714. The San Jose was trying to outrun a fleet of British warships off the island of Baru on June 8, 1708, when an explosion sent it to the bottom of the Caribbean Sea. She was reportedly carrying 600 people, chests of emeralds and tons of silver, gold and platinum. The shipwreck has been at a center of a decades-long search that also involved a legal battle with the Seattle-based Sea Search Armada, or SSA, a commercial salvage company that claims it first discovered the wreck's location in 1981. Moreover, Peru has argued that any treasure recovered from the San Jose should be considered a Peruvian national patrimony. As more legal fights will likely occur, new expeditions to the wreck in 2016 are expected to recover the much disputed treasure of gold and emeralds.

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One of the most promising discoveries last year was

an oval-shaped structure

unearthed in the Tuscan town of Volterra. Archaeologists believe it represents the most important Roman amphitheater finding over the last century. The foundations of the colosseum, which is oval-shaped like the much larger arena in the heart of Rome, might date back to the 1st century A.D. Amphitheaters like these were used during Roman times to feature events including gladiator combats and wild animal fights. The archaeologists estimate the structure, which mostly lies at a depth of 20 to 32 feet, measured some 262 by 196 feet. Only a small part of it has been unearthed during a small dig survey. New finds are expected this year as a full-scale dig is launched.