Communications of the ACM

Review articles

The Antikythera Mechanism

By Herbert Bruderer
Communications of the ACM, April 2020, Vol. 63 No. 4, Pages 108-115
10.1145/3368855
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Until the discovery of the Antikythera Mechanism, astrolabes were often considered the earliest analog mathematical devices. Such complex gearwork as in this astronomical calculator, however, only appeared (again) much later, especially in medieval clockworks. Leonardo da Vinci (1452–1519) knew gears, as his drawings show. Heron of Alexandria (1^st century) used cogwheels for his pantograph. The construction of analog measuring and drawing instruments (for example, sectors, proportional dividers, compasses) and logarithmic circular and cylindrical slide rules was comparatively simple. Planimeters and (mechanical) differential analyzers were sophisticated. The first mechanical calculating machines were invented in the 17^th century (Wilhelm Schickard, Blaise Pascal, Gottfried Leibniz). These digital devices required stepped drums, pinwheels, and accumulators. In the second half of the 20^th century there was a competition between electronic analog computers and electronic digital computers.

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Key Insights

This article is not about new groundbreaking insights. Rather, it presents an overview of decades of effort and different views. The review is not aimed at experts, but at computer scientists who are interested in the history of technology.

Some consider the Antikythera Mechanism (see Figures 1,2,3,4,5,6,7,8,9,10,11,12,13,14)—an astronomical calculator—as the world's first analog calculator. This article is based on an international survey among the leading specialists for the Antikythera Mechanism and an adaptation of a chapter of the book on the history of computing by the author and its English translation.^3,4,5 For more explanation, see the sidebar "Structure of the Antikythera Mechanism."

Figure 1. The complex astronomical calculator, over 2,000 years old, was discovered in 1901 in the sea off the Greek island of Antikythera. The discovery of the mysterious technological marvel was a big surprise. It is still unknown where the device was manufactured and who invented it. The opinions about its age vary by about 120 years. There are numerous physical and virtual replicas. Research groups from Greece, the U.K. and the U.S. are trying to elicit the last secrets from the device. The Antikythera mechanism and the astrolabes are considered to be the first analogue calculators (courtesy of National Archaeological Museum, Athens/Costas Xenikakis).

Figure 2. The front of the Antikythera Mechanism shows seven hands (sun, moon, five planets) and a double ring scale (outside: Egyptian calendar, inside: zodiac). At the top and bottom of the digital model is the Parapegma inscription (courtesy of Hublot, with data from the Antikythera Mechanism Research Project).

Figure 3. The rear side of the mechanism (digital reconstruction) has two spiral scales. Above: Metonic cycle with display of the Callippic cycle (restored) and the Panhellenic games; below: Saros cycle for eclipses and Exeligmos cycle (courtesy of Hublot, with data from the Antikythera Mechanism Research Project).

Figure 4. Computer-aided simulation of the front side by Tony Freeth (courtesy of Tony Freeth, Images First Ltd., London).

Figure 5. The Swiss clockmaker Ludwig Oechslin built a replica with sun and moon pointers, but without the presumed planetary hands (courtesy of Ochs und junior AG, Lucerne).

Figure 6. Digital reconstruction by Tony Freeth: on the left the front side with the two concentric scales and seven pointers, on the right the back side with the spiral scales, among others for the display of solar and lunar eclipses (courtesy of Tony Freeth, Images First Ltd., London).

Figure 7. The replica from Thessaloniki is equipped with a cover on both sides in contrast to other real and digital replicas (courtesy of 3D Solidforms, Thessaloniki).

Figure 8. A view into the complex gearing of the replica of Thessaloniki (courtesy of 3D Solidforms, Thessaloniki).

Figure 9. This illustration shows the front side of the reconstruction by Markos Skoulatos and is fully functional (courtesy of Markos Skoulatos).

Figure 10. The illustration shows the rear side of Skoulatos' model. The transparent model allows one to follow the functioning of the mechanism (courtesy of Markos Skoulatos).

Figure 11. Markos Skoulatos and Georg Brandl also created a digital model, operated via a portable computer or a smartphone (courtesy of Markos Skoulatos and Georg Brandl).

Figure 12. This picture shows the help menu for the front side (courtesy of Markos Skoulatos and Georg Brandl).

Figure 13. This picture shows the help menu for the rear side (courtesy of Markos Skoulatos and Georg Brandl).

Figure 14. One of the 48 models designed by two Chinese researchers for the design of the Antikythera Mechanism. Above are shown the hands for sun, moon and five planets, below four astronomical cycles and the course of the Panhellenic games (courtesy of Jian-Liang Lin and Hong-Sen Yan).

It is not easy for most laypeople to understand the movements of the celestial bodies. The structure of the Metonic dial "was very unusual, having two distinct centers. We will call one of them the axial center because this was the location of the axle or arbor bearing the dial's pointer ... On the right side of the plate, a series of five concentric semicircular slots ... were cut through the plate. On the left side was another series of five concentric semicircular slots, centered on the secondary center.¹⁷ (To learn more about the structure, the astronomical functions, and the details of the gearing, see Seiradakis,¹⁹ Edmunds,⁹ and Freeth.¹⁴)

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Astrolabe, Planetarium, or Calendar Calculator?

For a long time, the purpose of the Antikythera Mechanism—a bronze gearwork in a wooden case—was unknown. Was the approximately 32cm-33cm high, 17cm-18cm wide, and at least 8cm deep, shoe-box sized device an astrolabe, a planetarium, or a calculator?

This question has been resolved today, unlike many others. It is an astronomical calculating machine. The device determines the approximate position of the sun, the moon and—as can be inferred from the texts on the device—possibly the (five then known) planets and serves as a calendar. It predicted or described solar and lunar eclipse possibilities based on the Saros cycle and calculated the phases of the moon. The machine also showed the data for the four Panhellenic games (the Isthmia, Olympia, Nemea, and Pyhtia) as well as the minor Naa of Dodona and Halieia of Rhodes. The scales are concentric on the front. The major cycles of the back (Metonic and Saros dials) were spiral-shaped. Greek (astronomical and technical) texts were found on the covers of both sides of the device. Almost certainly the machine contains over 40 individual gears (including any plausible reconstruction of the lost planetary gearwork). The fixed programmed calculator was presumably operated by a lateral knob or a crank. The development of such astronomical instruments apparently began in the 3^rd century B.C. The mechanism is so mature that it can hardly be a unique device. In the history of culture, technology, and science, gear-works are of outstanding importance. Such complex constructions only reappear in Europe with the astronomical tower clocks in the 14^th century, more than 1,000 years later. The Antikythera Mechanism is probably the world's the first analog calculator. Alexander Jones of New York University believes the device was designed primarily for educational and philosophical purposes. It certainly was good for demonstrations. For astronomers it was probably too imprecise, and unsuitable for navigation.

Why astronomical calculators have rarely survived? The bronze gears of the Antikythera Mechanism were only 2mm thin. This fine, fragile construction may explain why hardly any devices have survived. Metal was precious and was therefore recycled. These devices were not gold-plated artifacts with precious stones.

The Antikythera Mechanism Research Project. In 2005, an international research community called Antikythera Mechanism Research Project was founded. It is mainly made up of experts from the fields of astronomy, physics, astrophysics, mathematics, engineering, history of technology and science, archaeology, and classicists. For further information, see http://antikythera-mechanism.gr.

When was the astronomical calculator found? The Ionian island of Antikythera, originally called Aigila, is located between the Peloponnese peninsula and Crete, opposite Kythera (hence Antikythera). The shipwreck was found by sponge divers in 1900. The Antikythera Mechanism came to light in the summer of 1901 (probably July). Dives were also carried out in 1953, 1972, and several since 2012 up to the present year. The mechanism is only partially preserved and consists of 82 damaged fragments. Fundamental investigations have only been carried since the 1950s. Tomographic methods were also used for this purpose.

When did the ship go down? As can be seen from the finds of coins and amphorae, the ship sank between 70 B.C. and 50 B.C. This date period is generally accepted. "Around 60 B.C., a ship was wrecked of the northeast coast of a small island called Aigila in the straits between Crete and the Peloponnese ... The exact character of the ship is not known, but it was probably a large merchant vessel, perhaps about 40 meters long."¹⁷ The vessel may have been on its way from Asia Minor to the western Mediterranean. Perhaps the sail freighter was about 10m wide and could load 250 tons. The cargo included silver and bronze coins dating between 85 B.C. and 60 B.C.

When was the ship built? According to the 2010 radiocarbon analyses by Andrew Wilson (University of Oxford), the wood used for shipbuilding is estimated (with a probability of 84.8%) to have been cut between 211 B.C. and 40 B.C. This can be seen from the new calibration curves of radiocarbon dating (C-14 method, 14C method).⁷ Since wooden ships do not last indefinitely long and are not permanently seaworthy, the boat is likely to have been manufactured at the earliest a few decades before the shipwreck.

When was the astronomical calculator built? Opinions on the year of manufacture of the astronomical calculator vary widely. The estimates range from 205 B.C. to 50 B.C. Christián Carman, James Evans, and Tony Freeth assume a production approximately 205 B.C. Michael Edmunds, Paul Iversen, Alexander Jones, and Michael Wright however believe in a much later production at a time when the ship was much closer to sinking.

Michael Edmunds from the University of Cardiff writes: "The present best estimate of its construction date is around the middle of the range 150 B.C.—60 B.C.—although a date as early as early as 220 B.C. is not completely ruled out."⁷ The astrophysicist adds: "My preferred period is 140 B.C.-70 B.C. But there must have been earlier, probably simpler versions. So, one would guess that similar mechanical devices might date from 200 B.C. or maybe 250 B.C."⁷ According to Edmunds, there are references in the literature mentioning that astronomical devices were made or at least known from 250 B.C. to at least 500 A.D.

The historian of science and classicist Alexander Jones writes in this context: "We are obviously a long way from being able to put together a coherent story of the evolution and eventual degeneration of the ancient tradition of astronomical mechanisms, but there is enough evidence to suggest that complex and scientifically ambitious mechanisms were being made at least through the three centuries from about 100 B.C. to A.D. 200, and that the people who were most likely to encounter them were mechanicians, philosophers, and scientists."¹⁷

Paul Iversen from Case Western University, Cleveland, believes in a late production of the Mechanism: "I would say the Mechanism was manufactured soon before the shipwreck of about 70 BCE-50 BCE, but in any case, probably not more than one generation, or about 100 BCE at the earliest."¹⁶

Jones shares a similar opinion: "A far simpler hypothesis, however, is that the Mechanism was made somewhere around the Aegean not long before the shipwreck and was on its way to its intended home by a route that would next have proceeded up the Adriatic toward, say, Brundisium, stopping somewhere along the way to deliver part of the cargo. Occam's razor thus makes it probable that the Mechanism was commissioned by someone who lived in or near Epirus in the first half of the first century B.C."¹⁷

Jones adds: "I argued that the archeological context favors the hypothesis that the Mechanism was new when it was lost in the wreck, because otherwise it becomes difficult to account for the presence of an antique object that was manifestly made for a locality west of the Aegean in a cargo originating in the Aegean and destined for points west."¹⁷

Michael Wright (formerly of the Science Museum, London): "There is, however, no good argument for suggesting that the instrument was designed that early [205 B.C.] and there is a counterargument that the several displays were adjusted to mutual agreement in a way that could not have been done before the latter half of the second century B.C. The most likely explanation is that the designer of these displays drew on old information."²⁰

The physicist Wright, however, rejects the assumption the instrument was new when the ship sank. Part of the device was mechanically confused. He writes: "I think it very unlikely that the instrument was very old at the time because I think it simply would not have lasted very long without being destroyed by use and handling. I suggest that it was probably built with a generation or so of its loss; that is, within a few decades of 100 B.C.²⁰

The physicist James Evans from the University of Puget Sound, Tacoma, WA, tends to assume an early production: "The eclipse predictor best fits an 18-year Saros cycle that started in 205 B.C. One or two Saros cycles later would also work, though with somewhat larger errors. Of course, we cannot rule out the possibilty that it was built considerably later but using an out-of-date eclipse cycle."¹¹

London-based Tony Freeth, on the other hand, assumes a construction around 205 B.C.: The prediction of the solar and lunar eclipses is based on the Saros cycle. The display on the back of the mechanism is intended to allow the determination of its age.¹³

According to Christián Carman and James Evans, the eclipse dial works best when the full moon of the first month of the Saros cycle reaches May 12, 205 B.C.⁶

If the astronomical calculator had been manufactured by Archimedes during his lifetime, it would have been approximately 150 years old when the ship sank. Such an early production does not seem very plausible.

Where was the mechanism made? The origin of the mechanism is unknown. Sicily was once thought to be the place of production, current thinking puts Rhodes as the likely location.

Possibilities include Alexandria, Pergamon, Syracuse and Rhodes. Syracuse had the advantage of any heritage left by Archimedes, but the problem that it was sacked in at the time of his death in 211 B.C., although something may have remained. The best candidate must be Rhodes, a port at which the Antikythera ship had called (judged by some of its cargo) not long before its wreck. Rhodes was a highly technological naval center around 100 B.C. with a fine bronze industry and an astronomical tradition. It is also one place where we know that a similar contemporary device was reputedly made and seen."¹⁶

Edmunds adds that the star calendar (Parapegma) on the wheels corresponds to the geographical latitude of Rhodes and that Cicero had seen a comparable device on Rhodes in the first century B.C.⁸

The classicist and epigrapher Iversen contends the computer was most likely to be manufactured in Rhodes for several reasons:¹⁶

• The games of Halieia, played in honor of the sun god, appear beside the Panhellenic games on the back of the device. The Halieia are mostly attested only on Rhodes or the territory it controlled on the mainland opposite the island known as the Rhodian Peraia. They are mentioned in the Doric not Attic-Ionic dialect, the latter of which is customary on the rest of the Mechanism. Dorian halios means sun.
• We know from writings that such devices were manufactured in Rhodes at the time of the shipwreck. This is evidenced by writings written during this period. Cicero describes such a machine built by his teacher, Poseidonios. This scholar lived on Rhodes. At this time, Geminos, who in his treatise explains the astronomical theory underlying the gearwork, probably also worked on this island.
• In the 1^st century B.C., around the time of its demise, the island of Rhodes was a center for astronomy.
• The astronomers of Rhodes used the Attic-Ionic dialect in the 1^st century. On the island, a single inscription written in this scientific language was found.
• The alphabetical lists of the annual astronomical events (for example, solstice, equinox) for the sun and the fixed stars (Parapegma) contained on the front of the Mechanism are best for the northern latitudes 33.3 to 37.0 and thus for Rhodes. However, they do not apply to Epirus (Western Greece) or Alexandria.

Iversen considers it unlikely that Archimedes built the device, because it makes use of certain findings on the movement of the sun and moon, which are attributed to Hipparchos (around 150 B.C.). For example, Poseidonios or an employee of his school could be considered as the creator. The customer is likely to be from Epirus due to the epirotic calendar (Metonic spiral).¹⁶

Cicero mentions in De Natura Deorum, book 2, (45 B.C.), the "sphaera" of Posidonius. The word "sphaera" (Greek sphaira) has several meanings: "We need to be careful to distinguish mechanized planetaria from certain other concepts and categories of objects that may be described in similar language. The Greek word sphaira (or Latin sphaera) may refer to an astronomical mechanism but was also appropriate for a simple globe."¹⁷

The star calendar is also associated with the Greek author Geminos, who presumably lived in the 1^st century.

The mathematician Freeth, on the other hand, assumes the original form of the astronomical computer originated from Archimedes. This famous scholar, who died in 211 B.C., lived in the Corinthian colony in Syracuse. According to Cicero, the great Greek scholar is said to have made such an instrument. The sophisticated state of the mechanism was a surprise. Until the discovery of Price, nothing comparable was known in ancient Greek technology. Freeth writes: "I personally think it is likely that the original design came from Archimedes and he started the tradition of making these devices. The Antikythera Mechanism is simply a later version of the Archimedes design. But there is little hard evidence. ... The sophistication of the mechanism, when uncovered by Price, was astonishing, given what had previously been known about ancient Greek technology."¹³

According to Wright, however, the mechanism of Archimedes was a completely different device, namely a mechanical celestial globe. The English man, who also works as a mechanic, has reconstructed it. Cicero, who reported in De Re Publica (book 1, 54 B.C-51 B.C.) and in Tusculanae Disputations (book 1, 45 B.C.) on the "sphaera" of Archimedes, has lived, however, over 100 years later than the outstanding Sicilian researcher.

Kyriakos Efstathiou (University of Thessaloniki) suggests that at this time one of the most important Greek astronomers, Hipparchos, lived in Rhodes. Many researchers believed he, his disciple Poseidonios, or someone from the astronomy school there could be considered the creator of the mechanism.¹⁰

The most convincing assumption is the Antikythera Mechanism comes from the surroundings of Poseidonios. The stoic philosopher had no astronomical or craft skills himself. There are obviously close relations between the Mechanism and Hipparchos as well as Geminos.

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Rebuilds

There are numerous real replicas (reconstructions) of the Antikythera Mechanism and some virtual models (simulations). Among the best known real (that is, physical) replicas were the devices of Ioannis Theofanidis (Greece, 1934), Derek de Solla Price and Robert Deroski (U.S.), Allan Bromley and Frank Percival (Australia), John Gleave (U.K.), Michael Wright (U.K.) as well as John Seiradakis and Kyriakos Efstathiou (Greece). Further models have been produced by Dionysios Kriaris (Greece), Massimo Vicentini (Italy), and Tatjana van Vark (Netherlands). However, some replicas are not operational and differ from the original design. 3D Solidforms sells the devices developed in cooperation with the Aristotle University of Thessaloniki. Markos Skoulatos and Georg Brandl (Germany) have built new real and virtual replicas.

Digital replicas are available, for example, from Tony Freeth (U.K.). In Switzerland, the Mechanism was also reconstructed, for example by Ludwig Oechslin (formerly International Watch Museum in La Chaux-de-Fonds). Matthias Buttet created for Hublot SA, Nyon VD a watch that incorporates the functions of the Antikythera Mechanism.

The most important (real) replicas are the reconstructions of Michael Wright and the Antikythera Mechanism Research Project (2006). Wright, the leading model maker of Antikythera Mechanism, justly points out that a computer-generated 3D image does not have the same persuasive power as a physical model. In the artificial world there is neither mass, inertia, force, friction, nor elastic or inelastic deflection. Questions of material strength and wear properties are excluded.

The physicist Markos Skoulatos of the University of Technology in Munich designed a real reconstruction and then followed with a digital model, developed together with the physicist Georg Brandl. The mechanical reconstruction exhibits less friction and the virtual model high accuracy.

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Is the Antikythera Mechanism an Analog Device?

The (non-programmable) mechanism of Antikythera is sometimes called the world's oldest analog "computer." The gear trains refer to the orbits of the planets. Due to this similarity, the mechanical calendar computer appears as an analog device. In addition to the input, the output of this machine is also analog: the dials (scales) and the continuously rotating hands.

However, the calendars are calculated digitally. The number of teeth on the gears is always an integer. The ratio between two gears is always a rational number. These relations reflect the celestial movements, for example, in the Metonic cycle (x cycles in y years, where x and y are integers). Rational numbers are numbers that can be represented as a quotient of two integers. In addition to the number zero, this includes all (positive and negative) whole and fractional numbers.

The display is analog, but the gear-work operates digitally. Most researchers regard the astronomical marvel as an analog device. However, it can also be understood as a mixed calculator. Astronomical clocks are also hybrid, as are digital clocks with analog display. A numerical display is more precise than analog pointers but less comfortable to read.

For further explanations see Computation and its Limits by P. Cockshott, L.M. Mackenzie, and G. Michaelson (Oxford Press 2012).

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Conclusion

The current state of research can be summarized as follows: The Antikythera Mechanism, discovered in 1901, was lost about 60 B.C. when a Roman merchant ship sank in the Mediterranean Sea. The complex astronomical calculator was probably built on the island of Rhodes near the Greek philosopher Poseidonios. The client for the teaching material seems to be a person in northwestern Greece.

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Acknowledgment

I am very grateful to Michael G. Edmunds, Kyriakos Efstathiou, James C. Evans, Tony Freeth, Paul A. Iversen, Alexander R. Jones, and Michael T. Wright for their helpful answers in connection with my survey and for the valuable comments of the reviewers. Markos Skoulatos and Georg Brandl provided exciting information on their new project. In addition, I would like to thank all for the permission to reproduce the fascinating images.

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