A new paper for PLOS ONE, “Eclipse Prediction on the Antikythera Mechanism”, transforms our understanding of eclipse prediction on this amazing geared calculating machine from ancient Greece:
“The Antikythera Mechanism is an astounding landmark in the history of science and technology—one of the true wonders of the ancient world. Understanding how it worked has been a fascinating detective story over more than a hundred years.”
A simple and ingenious design
Not only did the Antikythera Mechanism predict eclipses over many decades, but also a whole range of their characteristics. Dr Tony Freeth is a London-based researcher on the Antikythera Mechanism, who uncovers for the first time the simple and ingenious arithmetic design for the remarkable eclipse prediction scheme on the Antikythera Mechanism.
Recovery by sponge divers
The Antikythera Mechanism is a highly sophisticated geared astronomical calculating machine from ancient Greece, recovered in 1901 by Greek sponge divers from a first century BC wreck just off the tiny Mediterranean island of Antikythera. Eclipse prediction on the Antikythera Mechanism was discovered in 2005 by Dr Tony Freeth, working with the Antikythera Mechanism Research Project and the National Archaeological Museum in Athens. It was published in a key paper in Nature in 2006, which analyzed new scientific investigations of the Antikythera Mechanism. The Antikythera Mechanism is now split into 82 fragments. Each fragment was investigated using two innovative techniques: high-tech surface imaging from Hewlett-Packard (USA) and high resolution 3D X-rays by X-Tek Systems (UK). X-Tek Systems developed a new prototype X-ray machine incorporating a uniquely powerful 450kV microfocus source, with sufficient power to penetrate all the bronze fragments. Using this X-ray Computed Tomography technology , the inner details of the Antikythera Mechanism were reconstructed in 3D volumes.
Babylonian eclipse prediction
By the 7th century BC, Babylonian astronomers had discovered a remarkable repeating cycle of the Earth-Sun-Moon system, called the Saros Cycle, which is the basis of eclipse prediction on the Antikythera Mechanism. This is a cycle of 223 lunar months—just over 18 years—which predicts the repetition of similar eclipses: a process that can be mechanized. The repetition is so accurate that it lasts for 12 – 15 centuries. Dr Tony Freeth:
“This research publication reveals the richness and variety of a key aspect of the Antikythera Mechanism: its ability to predict eclipses and many of their characteristics, such as time-of-day, colour, magnitude, direction of shadow obscuration, angular diameter of the Moon and distance North or South of the lunar node. It may not have been very accurate but its ambition was breathtaking.”
The Eclipse Prediction Scheme on the Antikythera Mechanism
The lower back dial of the Antikythera Mechanism is a four-turn spiral, divided into the 223 lunar months of the Saros cycle. The eclipse predictions are distributed in the appropriate months as “glyphs”, groups of Greek characters and symbols that describe the type of eclipse (lunar or solar) as well as the time-of-day of the eclipse. In addition, each glyph includes an index letter, which refers to inscriptions round the Saros Dial describing characteristics of groups of eclipses. To discover whether there will be an eclipse in a future month, a user turns the Mechanism to that month on the Saros Dial and checks for a glyph. Finding a glyph, the user then looks up its index letter in the eclipse inscriptions to discover the eclipse’s characteristics. The paper includes a new reading of the eclipse inscriptions by a leading expert on ancient Greek inscriptions, Dr Charles Crowther (Oxford University).
Arithmetic models are the basis of eclipse prediction
How was the eclipse prediction scheme devised? This research reveals a simple arithmetical basis for predicting eclipses and their characteristics. This scheme depends critically on the lunar nodes: the points where the inclined orbit of the Moon crosses the plane of the Earth’s orbit round the Sun. A numerical measure of how far the eclipse is North or South of the node is the organising principle that solves the design of the prediction scheme.
The times of eclipses are also shown in the glyphs. The paper shows that these eclipse times can be well modelled by another arithmetic scheme, based on a linear “zigzag” system from Babylonian astronomy. This implies that each quarter of the four turns of the Saros Dial represented a Full Moon Cycle—the nearly-14-month cycle of the diameter of the Moon when seen from Earth—which is one of the determinants of the appearance and duration of an eclipse. This is the reason that the Saros Dial was designed with four turns.
Early date for the Antikythera Mechanism
When synchronized with the historical record of eclipses, these two arithmetic models imply that the Saros Dial was designed to start in 205 BC. Surprisingly, this early date had been proposed before by Professor James Evans (University of Puget Sound, USA) and Dr Christián Carman (Universidad Nacional de Quilmes, Argentina), based on a different approach (publication forthcoming). It is a much earlier date than previously considered and it brings the Mechanism close to the life of Archimedes (d. 212 BC), who made similar mechanisms, and within the life of Apollonios of Perga (d. c. 190 BC), who initiated epicyclic theories for the variable motions of the Moon and planets, which were built into the Antikythera Mechanism. Previous dates for the Antikythera Mechanism in the range 140 BC – 100 BC were based on stylistic analysis of the inscriptions. The new epigraphic analysis by Dr Charles Crowther (Oxford University) is fully consistent with an earlier date at the end of the 3rd century BC.
The surviving inscriptions surrounding the Saros Dial only describe solar eclipses. Another consequence of the analysis is that the Antikythera Mechanism also included lost lunar eclipse inscriptions. While the prediction of eclipse characteristics was quite good for lunar eclipses, it was not at all accurate for solar eclipses, which seem to have been included for completeness by analogy with lunar eclipses.
A beautiful mathematical design
Dr Tony Freeth sets this new research into context:
“The eclipse prediction scheme on the Antikythera Mechanism was extremely ingenious and truly extraordinary. The results in this paper add significantly to previous research that has revealed the beautiful mathematical design of the Antikythera Mechanism.”
Freeth T (2014) Eclipse Prediction on the ancient Greek astronomical calculating machine known as the Antikthera Mechanism. PLOS ONE, http://dx.plos.org/10.1371/journal.pone.0103275.
The paper includes many images that can be used in press reports, provided the appropriate credit is given. In addition, more images (obligatory credit: Copyright 2013 Tony Freeth) are available on the following link: https://www.hightail.com/download/ZUcyNWNwbWdwcFZwdmNUQw
- Exploded computer model of the Antikythera Mechanism.
- The Saros & Exeligmos Dials of the Antikythera Mechanism, showing glyphs and inscriptions.
- Computer model of the gearing of the Antikythera Mechanism.
- Saros & Exeligmos Dials & eclipse inscriptions.
- X-ray CT of Fragment F, showing a glyph and inscriptions.
- Reconstruction of Greek sponge diver.
- Dr Tony Freeth examining the Antikythera Mechanism in the National Archaeological Museum in Athens.
- Dr Tony Freeth with the Parthenon in the background.
Dr Tony Freeth:
Tony Freeth studied pure mathematics: MA, MMath (Cantab); MSc, PhD (Bristol). He then trained as a film director at the National Film & Television School in the UK. After more than 25 years as a film & TV producer and director, he was introduced to the Antikythera Mechanism in 2000 by Professor Mike Edmunds (Cardiff). Tony Freeth researched, proposed and co-organized new investigations of the Antikythera Mechanism, which were carried out in 2005 by an Anglo-Greek team of scientists in collaboration with the National Archaeological Museum in Athens and two high-tech companies, Hewlett-Packard (USA) and X-Tek Systems (UK). This yielded a rich set of data on the Antikythera Mechanism and led to two papers in the prestigious science journal Nature, Freeth et al., Nature 444 2006, Freeth et al., Nature 454 2008). These included startling revelations about the highly sophisticated functions of the Antikythera Mechanism. Further significant research followed as well as several popular presentations, such as an article in Scientific American; and major contributions to a number of exhibitions. He produced a TV film in 2012, “The 2000 Year-Old Computer”, which had extensive international broadcast and won many awards. He continues to do research on the Antikythera Mechanism and is currently collaborating on new physical models with University College London as well as preparing a book proposal about the Antikythera Mechanism.
Dr Tony Freeth
Tel: +44(0)20 8579 6848
Dr Charles Crowther