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Previous research on the Antikythera Mechanism established a highly complex ancient Greek geared mechanism with front and back output dials. The upper back dial is a 19-year calendar, based on the Metonic cycle, arranged as a five-turn spiral. The lower back dial is a Saros eclipse-prediction dial, arranged as a four-turn spiral of 223 lunar months, with glyphs indicating eclipse predictions. Here we add surprising findings concerning these back dials. Though no month names on the Metonic calendar were previously known, we have now identified all 12 months, which are unexpectedly of Corinthian origin. The Corinthian colonies of northwestern Greece or Syracuse in Sicily are leading contenders-the latter suggesting a heritage going back to Archimedes. Calendars with excluded days to regulate month lengths, described in a first century bc source, have hitherto been dismissed as implausible. We demonstrate their existence in the Antikythera calendar, and in the process establish why the Metonic dial has five turns. The upper subsidiary dial is not a 76-year Callippic dial as previously thought, but follows the four-year cycle of the Olympiad and its associated Panhellenic Games. Newly identified index letters in each glyph on the Saros dial show that a previous reconstruction needs modification. We explore models for generating the unusual glyph distribution, and show how the eclipse times appear to be contradictory. We explain the four turns of the Saros dial in terms of the full moon cycle and the Exeligmos dial as indicating a necessary correction to the predicted eclipse times. The new results on the Metonic calendar, Olympiad dial and eclipse prediction link the cycles of human institutions with the celestial cycles embedded in the Mechanism's gearwork.

The ancient Greek astronomical calculating machine, known as the Antikythera Mechanism, predicted eclipses, based on the 223-lunar month Saros cycle. Eclipses are indicated on a four-turn spiral Saros Dial by glyphs, which describe type and time of eclipse and include alphabetical index letters, referring to solar eclipse inscriptions. These include Index Letter Groups, describing shared eclipse characteristics. The grouping and ordering of the index letters, the organization of the inscriptions and the eclipse times have previously been unsolved. A new reading and interpretation of data from the back plate of the Antikythera Mechanism, including the glyphs, the index letters and the eclipse inscriptions, has resulted in substantial changes to previously published work. Based on these new readings, two arithmetical models are presented here that explain the complete eclipse prediction scheme. The first model solves the glyph distribution, the grouping and anomalous ordering of the index letters and the structure of the inscriptions. It also implies the existence of lost lunar eclipse inscriptions. The second model closely matches the glyph times and explains the four-turn spiral of the Saros Dial. Together, these models imply a surprisingly early epoch for the Antikythera Mechanism. The ancient Greeks built a machine that can predict, for many years ahead, not only eclipses but also a remarkable array of their characteristics, such as directions of obscuration, magnitude, colour, angular diameter of the Moon, relationship with the Moon’s node and eclipse time. It was not entirely accurate, but it was an astonishing achievement for its era.

Ever since its discovery by Greek sponge divers in 1901, the Antikythera Mechanism has inspired fascination and fierce debate. In the early years no-one knew what it was. As a result of a hundred years of research, particularly by Albert Rehm, Derek de Solla Price, Michael Wright and, most recently, by members of the Antikythera Mechanism Research Project, there has been huge progress in understanding this geared astronomical calculating machine. With its astonishing lunar anomaly mechanism, it emerges as a landmark in the history of technology and one of the true wonders of the ancient world. The latest model includes a mechanical representation of the Cosmos that exactly matches an inscription on the back cover of the instrument. We believe that we are now close to the complete machine.

In 1901, an extraordinary ancient Greek artefact was discovered in a shipwreck just off the tiny island of Antikythera. It was later shown to be a complex astronomical calculating machine and is now known as the Antikythera Mechanism. In 2005, it was established that it predicted eclipses, using a 7th century BC Babylonian eclipse cycle of 223 lunar months, known as the Saros Cycle. Understanding the complex eclipse prediction scheme on the Antikythera Mechanism has resulted from a fascinating series of discoveries. The eclipse prediction scheme is implemented through descriptive glyphs, inscribed round a 223-month Saros Dial at the rear of the Mechanism: a glyph in a particular month indicates a predicted eclipse. A 2008 publication deciphered the meaning of the glyphs: they indicate whether the predicted eclipse is lunar or solar; the possible visibility of the eclipse; and its time of day. The glyphs also include an alphabetical Index Letter, referring to inscriptions round the Saros Dial, which describe eclipse characteristics. In that publication, the full eclipse prediction scheme was not understood but subsequent work in 2014 made substantial progress. The eclipse characteristics, such as the colour and magnitude of the eclipse, are listed together in the inscriptions, together with a group of Index Letters for the eclipses to which they apply. The deeply puzzling grouping and ordering of these Index Letter Groups was solved with a simple mathematical model, which both explained these groups and the distribution of the glyphs round the Saros Dial-revealing an eclipse prediction scheme of extraordinary sophistication and ambition. Later work in 2016 proposed a radical revision of this eclipse prediction scheme, though it did not challenge the mathematical basis of the scheme. The 2016 scheme implied a completely different picture of the whole of the back plate of the Antikythera Mechanism, destroying its essential mathematical symmetry. This revision is comprehensively refuted here, except for the identification of a new text character in one of the Index Letter Groups, which implies an interesting revision of the 2014 scheme but which preserves the elegant 2014 reconstruction of the back plate of the Antikythera Mechanism.

The Antikythera Mechanism, an ancient Greek astronomical calculator, has challenged researchers since its discovery in 1901. Now split into 82 fragments, only a third of the original survives, including 30 corroded bronze gearwheels. Microfocus X-ray Computed Tomography (X-ray CT) in 2005 decoded the structure of the rear of the machine but the front remained largely unresolved. X-ray CT also revealed inscriptions describing the motions of the Sun, Moon and all five planets known in antiquity and how they were displayed at the front as an ancient Greek Cosmos. Inscriptions specifying complex planetary periods forced new thinking on the mechanization of this Cosmos, but no previous reconstruction has come close to matching the data. Our discoveries lead to a new model, satisfying and explaining the evidence. Solving this complex 3D puzzle reveals a creation of genius—combining cycles from Babylonian astronomy, mathematics from Plato’s Academy and ancient Greek astronomical theories.

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In at least 400 European caves such as Lascaux, Chauvet and Altamira, Upper Palaeolithic Homo sapiens groups drew, painted and engraved non-figurative signs from at least ~42,000 bp and figurative images (notably animals) from at least 37,000 bp. Since their discovery ~150 years ago, the purpose or meaning of European Upper Palaeolithic non-figurative signs has eluded researchers. Despite this, specialists assume that they were notational in some way. Using a database of images spanning the European Upper Palaeolithic, we suggest how three of the most frequently occurring signs—the line <|>, the dot <•>, and the <Y>—functioned as units of communication. We demonstrate that when found in close association with images of animals the line <|> and dot <•> constitute numbers denoting months, and form constituent parts of a local phenological/meteorological calendar beginning in spring and recording time from this point in lunar months. We also demonstrate that the <Y> sign, one of the most frequently occurring signs in Palaeolithic non-figurative art, has the meaning <To Give Birth>. The position of the <Y> within a sequence of marks denotes month of parturition, an ordinal representation of number in contrast to the cardinal representation used in tallies. Our data indicate that the purpose of this system of associating animals with calendar information was to record and convey seasonal behavioural information about specific prey taxa in the geographical regions of concern. We suggest a specific way in which the pairing of numbers with animal subjects constituted a complete unit of meaning—a notational system combined with its subject—that provides us with a specific insight into what one set of notational marks means. It gives us our first specific reading of European Upper Palaeolithic communication, the first known writing in the history of Homo sapiens.