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Techniques developed to analyze the waves in space-time detected by one of the most sensitive pieces of scientific equipment of the 21st century have helped shed new light on the function of the oldest known analog computer.

Astronomers at the University of Glasgow have used statistical modeling techniques developed to analyze gravitational waves to work out the likely number of holes in one of the broken rings of the Antikythera Mechanism, an ancient artifact that was featured in the movie Indiana Jones and the Dial of Destiny. .”

While the film version allowed the intrepid archaeologist to travel through time, the Glasgow team’s results provide new evidence that one of the components of the Antikythera mechanism was most likely used to track the Greek lunar year. They also offer new insight into the remarkable craftsmanship of the ancient Greeks.

The mechanism was discovered in 1901 by divers exploring a sunken ship near the Aegean island of Antikythera. Although the shoebox-sized mechanism had broken into pieces and eroded, it quickly became clear that it contained an intricate series of gears that were unusually complex.

Decades of subsequent research and analysis have established that the mechanism dates back to the second century BC and functioned as a type of hand-operated mechanical computer. External dials connected to internal gears allow users to predict eclipses and calculate the astronomical positions of the planets on any given date with an accuracy unmatched by any other known modern device.

In 2020, new X-ray images of one of the mechanism’s rings, known as the calendar ring, revealed new details of properly spaced holes that lie beneath the ring. Since the ring was broken and incomplete, however, it was not clear exactly how many holes it originally had. Initial analysis by Antikythera researcher Chris Budiselich and colleagues suggested it was probably somewhere between 347 and 367 AD.

Now, in a new paper published in Horological JournalGlasgow researchers describe how they used two statistical analysis techniques to reveal new details about the calendar ring.

They show that it is much more likely that the ring had 354 holes corresponding to the lunar calendar than 365 holes that would follow the Egyptian calendar. The analysis also shows that 354 holes are hundreds of times more likely than a ring with 360 holes, which previous research suggested as a possible number.

Professor Graham Vaughan of the University of Glasgow’s Faculty of Physics and Astronomy is one of the authors of the paper. He said: “Towards the end of last year, a colleague pointed me to data acquired by YouTuber Chris Budiselic, who wanted to make a replica of the calendar ring and was researching ways to determine exactly how many holes it contained.

“This struck me as an interesting problem, and I thought I might be able to solve it in a different way over the Christmas holidays, so I set out to use some statistical techniques to answer the question.”

Professor Woan used a technique called Bayesian analysis, which uses probability to quantify uncertainty based on incomplete data, to calculate the likely number of holes in the mechanism using the positions of the surviving holes and the arrangement of the six surviving ring fragments. His results show strong evidence that the movement’s calendar ring contains either 354 or 355 holes.

At the same time, one of Professor Vaughan’s colleagues at the university’s Institute for Gravitational Studies, Dr Joseph Bailey, had also heard about the problem. He adapted the techniques used by their research group to analyze the signals picked up by the LIGO gravitational wave detectors, which measure the tiny ripples in spacetime caused by massive astronomical events such as colliding black holes as they pass through Earth to examines the calendar ring carefully.

The Markov chain Monte Carlo and nested sampling methods used by Woan and Bayley provide a comprehensive probabilistic set of results, again suggesting that the ring most likely contains 354 or 355 holes in a circle of 77.1 mm radius, with an uncertainty of about 1/3 mm. It also reveals that the holes are precisely positioned with extreme accuracy, with an average radial variation of only 0.028 mm between each hole.

Bailey, a co-author of the paper, is a research associate in the School of Physics and Astronomy. He said: “Previous studies have suggested that the calendar ring probably tracked the lunar calendar, but the dual techniques we have applied in this work greatly increase the likelihood that this is the case.

“It gave me a new appreciation for the Antikythera mechanism and the work and care Greek craftsmen took to make it – the precision of the positioning of the holes would have required extremely precise measuring techniques and an incredibly steady hand to drill them.

Professor Vaughan added: “It is pure symmetry that we have adapted the techniques we use to study the universe today to understand more about a mechanism that helped humans track the heavens almost two millennia ago.

“We hope that our discoveries of the Antikythera mechanism, while less supernaturally spectacular than those made by Indiana Jones, will help to deepen our understanding of how this remarkable device was made and used by the Greeks.”