How Modern Math Solved a Mystery About an Ancient Greek Computer

Andrei Mihai

In 1901, a group of sponge divers exploring the waters near the Greek island of Antikythera came across an impressive shipwreck site. Among the treasures aboard the sunken Roman vessel – statues, jewelry, and coins – was an unassuming, corroded lump of bronze. At first, it seemed insignificant, but closer examination revealed something extraordinary: a complex, gear-driven device unlike anything else from antiquity.

The Antikythera Mechanism, as it is now called, resembles an orrery (model of the Solar System), consisting of numerous interlocking gears. Encased in a wooden box, it was part of a larger, now-lost instrument; yet, even in its fragmented state, the mechanism is remarkable. It contains over 30 interlocking gears, dials, and inscriptions that suggest it was used for astronomical purposes.

Thought to be the world’s oldest known analog computer, the Antikythera Mechanism predates comparable mechanical devices by more than a thousand years. Nothing of similar complexity appeared until the 14th century. But all this raises the question: Who built the mechanism, and why?

Several studies have suggested potential uses for the Antikythera mechanism, but the latest one draws from an unexpected field of mathematics: Bayesian inference. In fact, it was a similar approach to what researchers used at LIGO: an observatory that uses laser interferometry to detect gravitational waves from cosmic events.

“It’s a neat symmetry that we’ve adapted techniques we use to study the universe today to understand more about a mechanism that helped people keep track of the heavens nearly two millennia ago,” said Professor Graham Woan, of the University of Glasgow’s School of Physics & Astronomy, who authored the research, in a press release. “We hope that our findings about the Antikythera mechanism, although less supernaturally spectacular than those made by Indiana Jones, will help deepen our understanding of how this remarkable device was made and used by the Greeks.”

An Ancient Puzzle

There are almost no clues as to who built the mechanism. It was most likely constructed around the year 100 BC, possibly in nearby Rhodes, but despite some plausible speculation, we have no real indication as to who built this mechanism. The why, however, is much more intriguing.

The first steps to understanding the Antikythera Mechanism came from a careful analysis of its individual components. In 2005, researchers from Cardiff University used computer X-ray tomography and high-resolution scanning to peer inside the corroded fragments, uncovering hidden details of its intricate design. These scans revealed 37 interlocking bronze gears, which allowed the mechanism to track the movements of the Sun and Moon, predict eclipses, and even model the Moon’s irregular orbit – a concept studied by the ancient Greek astronomer Hipparchus of Rhodes.

Further analysis suggests that a missing section may have been used to calculate the positions of the known planets. In 2016, additional inscriptions were deciphered, linking the mechanism to the cycles of Venus and Saturn, further reinforcing its role as a sophisticated astronomical tool. But this approach only goes so far, because there are parts of the mechanism that were never discovered, and have probably been lost to the waves.

The latest research focuses on the mechanism’s calendar ring, a key component in tracking time. Found in “Fragment C,” this ring is incomplete, with only partial sections surviving. This ring contained between 346 and 367 holes arranged in a circular pattern. But how many holes exactly did it have?

The question is not trivial, it could be the key to understanding what the entire mechanism was used for.

Statistics for Christmas

Professor Graham Woan, of the University of Glasgow’s School of Physics & Astronomy, is known for his work on gravitational waves. In late 2023, the Antikythera mechanism drew his attention.

“It struck me as an interesting problem, and one that I thought I might be able to solve in a different way during the Christmas holidays, so I set about using some statistical techniques to answer the question,” said Woan.

The researcher used an approach that allows for a nuanced probability assessment. He was joined by Joseph Bayley, who had also heard about the problem and adapted techniques used by their research group to analyse the signals picked up by the LIGO gravitational wave detectors. These detectors confirmed one of Einstein’s key predictions: that there could be ripples in space-time in the form of gravitational waves. Because the signal for these waves is so weak, physicists use Bayesian inference to sift through noisy data, statistically estimate the properties of these faint signals, and confidently distinguish them from background noise.

Bayesian inference is a statistical method that updates the probability of a hypothesis as more evidence becomes available. It is based on Bayes’ theorem, which describes how prior beliefs (existing knowledge) are adjusted when new data is introduced. Unlike traditional (frequentist) statistics, which rely on fixed probabilities and significance tests, Bayesian inference treats probability as a measure of belief or certainty that changes with new information. It is especially useful in cases with uncertainty or incomplete data, allowing for more flexible and intuitive conclusions.

The study considered precise X-ray measurements of the surviving holes, the likely errors in hole placement due to ancient manufacturing techniques, the spatial arrangement of broken fragments, and plausible deformations. The approach managed to narrow the likely number of holes to somewhere between 352 and 356. It might not seem like a significance difference compared to the previous estimate (346-367), but it is.

It essentially rules out the 365-day calendar as a plausible explanation for the holes. Furthermore it suggests a correlation to the 354-day lunar calendar, which aligns more closely with Greek astronomical traditions.

The Greeks used several types of calendars, but they were all lunar calendars. As opposed to the solar calendars (like the one we use today), a lunar calendar consists of 12 lunar months about 29.5 days each, totaling approximately 354 days per year.

What Does This Mean for the Antikythera Mechanism?

This latest research essentially confirms that the Antikythera mechanism was used for astronomy, and suggests that it was somehow connected to the lunar calendar. However, it is not yet clear what exactly it was used for.

Was it used for calculating? For teaching? Did it have any religious significance, or was it just an extremely special decorative object? Given the level of detail and sophistication, it seems likely that it served a practical role and was a high-grade instrument at the time, but otherwise, it is hard to say.

The artifact itself is unlikely to answer that all by itself. Bronze itself would have been a valuable metal and if other similar mechanisms existed, their materials would have likely been recycled in time. Divers are still exploring the Antikythera site looking for more clues, and there is always a chance of something similar appearing at a different archaeological site.

Was this the only mechanism of this sort ever made, or were there several? Did they come from a specific craftsman with a unique ability, or was this knowledge more widely available? These are tantalizing questions that Bayesian inference cannot answer; or at least, not yet.

But in the meantime, we have mathematics to thank for a better understanding of this remarkable artifact.

The post How Modern Math Solved a Mystery About an Ancient Greek Computer originally appeared on the HLFF SciLogs blog.