Antikythera mechanism

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The Antikythera mechanism (Greek: O μηχανισμός των Αντικυθήρων transliterated as O mēchanismós tōn Antikythērōn) is believed by many to be an ancient mechanical analog computer (as opposed to most computers today which are digital computers) designed to calculate astronomical positions. It was discovered in the Antikythera wreck off the Greek island of Antikythera, between Kythera and Crete, and has been dated to about 150-100 BC.

Contents 1 Discovery 2 Origins 3 Function 4 Purpose 5 Similar devices in ancient literature 6 Investigations and reconstructions 6.1 Derek J. de Solla Price 6.2 Allan George Bromley 6.3 Michael Wright 6.4 Antikythera Mechanism Research Project 7 New discoveries 8 See also 9 References 10 Further reading 11 External links

[edit] Discovery

Sometime before Easter 1900, Elias Stadiatis, a Greek sponge diver, discovered the wreck of an ancient cargo ship off Antikythera island at a depth of 42 m (138 ft). Sponge divers retrieved several statues and other artifacts from the site. The mechanism itself was discovered on 17 May 1902, when archaeologist Valerios Stais^[1] noticed that a piece of rock recovered from the site had a gear wheel embedded in it. Examination revealed that the "rock" was in fact a heavily encrusted and corroded mechanism that had survived the shipwreck in three main parts and dozens of smaller fragments. The device itself was surprisingly thin, about 33 cm (13 in) high, 17 cm (6.7 in) wide, and 9 cm (3.5 in) thick, made of bronze and originally mounted in a wooden frame. It was inscribed with a text of over 2,000 characters, many of which have been deciphered.

Jacques-Yves Cousteau visited the wreck for the last time in 1978^[2], but found no more remains of the Antikythera Mechanism.

Professor Edmunds said: "This device is just extraordinary, the only thing of its kind. The design is beautiful, the astronomy is exactly right. The way the mechanics are designed just makes your jaw drop. Whoever has done this has done it extremely carefully."

The device is displayed in the Bronze Collection of the National Archaeological Museum of Athens, accompanied by a reconstruction made and offered to the museum by Derek de Solla Price. Another reconstruction is on display at the American Computer Museum in Bozeman, Montana.

[edit] Origins

The origins of the mechanism are unclear, as are the circumstances by which it came to be on the cargo ship. The ship was Roman, but there is no doubt that the mechanism itself was made in Greece.

One hypothesis is that the device was constructed at an academy founded by the ancient Stoic philosopher Posidonius on the Greek island of Rhodes, which at the time was known as a centre of astronomy and mechanical engineering. Investigators have suggested that the ship could have been carrying it to Rome, together with other treasure looted from the island to support a triumphal parade being staged by Julius Caesar. ^[3]

[edit] Function

The device is remarkable for the level of miniaturization and complexity of its parts, which is comparable to that of 18th century clocks. It has over 30 gears, although some have suggested as many as 70 gears, with teeth formed through equilateral triangles. When past or future dates were entered via a crank (now lost), the mechanism calculated the position of the Sun, Moon or other astronomical information such as the location of other planets. It is possible that the mechanism is based on heliocentric principles, rather than the then-dominant geocentric view espoused by Aristotle and others. The heliocentric view proposed by Aristarchus of Samos (310 BC - c. 230 BC) did not receive widespread recognition, but provides for the possibility of the existence of such a system at this time.^{[citation needed]}

The mechanism has 3 main dials, one on the front, and two on the back.

The front dial is marked with the divisions of the Egyptian calendar, or the Sothic year, based on the Sothic cycle. Inside this there is a second dial marked with the Greek signs of the Zodiac. This second dial can be moved to adjust, with respect to the Sothic dial, to compensate for leap years.

The front dial probably carried at least three hands, one showing the date, and two others showing the positions of the Sun and the Moon. The Moon indicator is ingeniously adjusted to show the first anomaly of the Moon's orbit. It is reasonable to suppose the Sun indicator had a similar adjustment, but any gearing for this mechanism (if it existed) has been lost. The front dial also includes a second mechanism with a spherical model of the Moon that displays the Lunar phase.

There is reference in the inscriptions for the planets Mars and Venus, and it would have certainly been within the capabilities of the maker of this mechanism to include gearing to show their positions. There is some speculation that the mechanism may have had indicators for the 5 planets known to the Greeks. None of the gearing, except for one unaccounted gear, for such planetary mechanisms survives.

Finally, the front dial includes a parapegma (a precursor to the modern day Almanac) used to mark the rising and setting of specific stars. Each star is thought to be identified by Greek characters which cross reference details inscribed on the mechanism.

The upper back dial, is in the form of a spiral, with 47 divisions per turn, displaying the 235 months of the 19 year Metonic cycle. This dial contains a smaller subsidiary dial which displays the 76 year Callippic cycle. (There are 4 Metonic cycles within 1 Callippic cycle.) Both of these cycles are important in fixing calendars.

The lower back dial is also in the form of a spiral, with 223 divisions showing the Saros cycle. It also has a smaller subsidiary dial which displays the 54 year Exeligmos cycle. (There are 3 Saros cycles within 1 Exeligmos cycle.)

[edit] Purpose

While a century of research is finally answering the question of what the mechanism did, we are actually no nearer to answering the question what it was for. There are numerous suggestions, any of which could be right.

Practical uses of this device may have included the following:

• Astrology was commonly practiced in the ancient world. In order to create an astrological chart, the configuration of the heavens at a particular point of time is needed. It can be very difficult and time-consuming to work this out by hand, and a mechanism such as this would have made an astrologer's work very much easier.
• Calculating solar and lunar eclipses. However, the device would probably only have indicated days when eclipses might occur, and a more accurate calculation of the time of day would have to be done by hand.
• Setting the dates of religious festivals connected with astronomical events.
• Adjusting calendars, which were based on lunar cycles as well as the solar year.

Price suggested that it might have been on public display, possibly in a museum or public hall in Rhodes. The island was known for its displays of mechanical engineering, particularly automata, which apparently were a specialty of the Rhodians. Pindar, one of the nine lyric poets of ancient Greece, said this of Rhodes in his seventh Olympic Ode:

"The animated figures stand

Adorning every public street

And seem to breathe in stone, or

move their marble feet."

[edit] Similar devices in ancient literature

Cicero mentions two machines similar to the Antikythera mechanism:

The first was built by Archimedes and brought to Rome by the Roman general Marcus Claudius Marcellus after Archimedes' death at the siege of Syracuse in 212 BC. Marcellus had a high respect for Archimedes and this was the only item he kept from the siege. The device was kept as a family heirloom, and Cicero was shown it by Gallus about 150 years later. The motions of the sun, moon and five planets were shown by the device. Gallus gave a 'learned explanation' of it and demonstrated it for Cicero.

hanc sphaeram Gallus cum moveret, fiebat ut soli luna totidem conversionibus in aere illo quot diebus in ipso caelo succederet, ex quo et in [caelo] sphaera solis fieret eadem illa defectio, et incideret luna tum in eam metam quae esset umbra terrae, cum sol e regione

When Gallus moved the globe, it happened that the moon followed the sun by as many turns on that bronze [contrivance] as in the sky itself, from which also in the sky the sun's globe became [to have] that same eclipse, and the moon came then to that position which was [its] shadow [on] the earth, when the sun was in line.^[4] If Cicero's account is correct (and there is no reason to doubt it) then this technology existed as early as the 3rd century BC.

Archimedes' device is also mentioned by later Roman writers Lactantius, Claudian, and Proclus in the 4th and 5th centuries.

Cicero also says that another such device was built 'recently' by his friend Posidonius, "... each one of the revolutions of which brings about the same movement in the sun and moon and five wandering stars [planets] as is brought about each day and night in the heavens..."^[5]

It is unlikely that either of these machines were the Antikythera mechanism found in the shipwreck, because both the devices mentioned by Cicero were located in Rome at least 50 years later than the estimated date of the shipwreck. So we know of three such devices. The modern scientists who have reconstructed the Antikythera mechanism also agree that it was too sophisticated to have been a one-off device.

It is probable that the Antikythera mechanism was not unique, as shown by Cicero's references to such mechanisms. This adds support to the idea that there was an ancient Greek tradition of complex mechanical technology that was later transmitted to the Muslim world, where similar but simpler devices were built during the medieval period. The early 9th century Kitab al-Hiyal ("Book of Ingenious Devices"), commissioned by the Caliph of Baghdad, records over a hundred mechanical devices described in Greek texts that had been preserved in monasteries. Such knowledge could have yielded to or been integrated with European clockmaking and medieval cranes.

[edit] Investigations and reconstructions

The Antikythera mechanism is one of the world's oldest known geared devices. It has puzzled and intrigued historians of science and technology since its discovery.

A number of individuals and groups have been instrumental in advancing our knowledge and understanding of the mechanism:

1) Derek J. de Solla Price (with Charalampos Karakalos)
2) Allan George Bromley (with Frank Percival,Michael Wright and Bernard Gardner)
3) Michael Wright
4) Antikythera Mechanism Research Project

[edit] Derek J. de Solla Price

Following decades of work cleaning the device, in 1951 British science historian Derek J. de Solla Price undertook systematic investigation of the mechanism.

Price published several papers on "Clockwork before the Clock".^[6][7] and "On the Origin of Clockwork",^[8] before the first major publication in June 1959 on the mechanism: "An Ancient Greek Computer".^[9] This was the lead article in Scientific American and appears to have been initially published at the prompting of Arthur C. Clarke, according to the book Arthur C. Clarke's Mysterious World (see end of chapter 3). In "An Ancient Greek Computer" Price advanced the theory that the Antikythera mechanism was a device for calculating the motions of stars and planets, which would make the device the first known analog computer. Until that time, the Antikythera mechanism's function was largely unknown, though it had been correctly identified as an astronomical device, perhaps being an astrolabe.

In 1971, Price, by then the first Avalon Professor of the History of Science at Yale University, teamed up with Charalampos Karakalos, professor of nuclear physics at the Greek National Centre of Scientific Research "DEMOKRITOS". Karakalos took both gamma- and X-ray radiographs of the mechanism, which revealed critical information about the device's interior configuration.

In 1974, Price wrote "Gears from the Greeks: the Antikythera mechanism — a calendar computer from ca. 80 B.C.",^[10] where he presented a model of how the mechanism could have functioned.

Price's model, as presented in his "Gears from the Greeks", was the first theoretical attempt at reconstructing the device. According to that model, the front dial shows the annual progress of the Sun and Moon through the zodiac against the Egyptian calendar. The upper rear dial displays a four-year period and has associated dials showing the Metonic cycle of 235 synodic months, which approximately equals 19 solar years. The lower rear dial plots the cycle of a single synodic month, with a secondary dial showing the lunar year of 12 synodic months.

One of the remarkable proposals made by Price was that the mechanism employed differential gears, which enabled the mechanism to add or subtract angular velocities. The differential was used to compute the synodic lunar cycle by subtracting the effects of the sun's movement from those of the sidereal lunar movement.

[edit] Allan George Bromley

An ingenious variant on Price's reconstruction was built by Australian computer scientist Allan George Bromley of the University of Sydney and Sydney clockmaker Frank Percival. Bromley went on to make new, more accurate X-ray images in collaboration with Michael Wright. Some of these were studied by Bromley's student, Bernard Gardner, in 1993.

[edit] Michael Wright

Michael Wright, formerly Curator of Mechanical Engineering at The London Science Museum, and now of Imperial College, London, made a completely new study of the original fragments together with Allan George Bromley. They used a technique called linear X-Ray tomography which was suggested by retired consultant radiologist, Alan Partridge. For this, Wright designed and made apparatus for linear tomography, allowing the generation of sectional 2D radiographic images.^[11] Early results of this survey were presented in 1997, which showed that Price's reconstruction was fundamentally flawed.^[12] However, at the time Bromley was already suffering from Hodgkin's disease and died in 2002.

Further study of the new imagery allowed Wright to advance a number of proposals. Firstly he developed the idea, suggested by Price in "Gears from the Greeks", that the mechanism could have served as a planetarium. Wright's planetarium not only modelled the motion of the Sun and Moon, but also the Inferior Planets; Mercury and Venus, and the Superior Planets; Mars, Jupiter and Saturn^[13][14]

Wright proposed that the Sun and Moon could have moved in accordance with the theories of Hipparchos, and the five known planets moved according to the simple epicyclic theory suggested by the theorem of Apollonios. In order to prove that this was possible using the level of technology apparent in the mechanism, Wright produced a working model of such a planetarium.^[15][16]

Wright also increased upon Price's gear count of 27 to 31^[14] including 1 in Fragment C that was eventually identified as part of a Moon phase display^[17]. He suggested that this is a mechanism that shows the phase of the Moon by means of a rotating semi-silvered ball, realized by the differential rotation of the sidereal cycle of the moon and the sun's yearly cycle. This precedes previously known mechanism of this sort by a millennium and a half.

More accurate tooth counts were also obtained,^[18] allowing a new gearing scheme to be advanced^[19] This more accurate information allowed Wright to confirm Price's perceptive suggestion that the upper back dial displays the Metonic cycle with 235 lunar months divisions over a five-turn scale. In addition to this Wright proposed the remarkable idea that the main back dials are in the form of spirals, with the upper back dial out as a five-turn spiral containing 47 divisions in each turn. It therefore presented a visual display of the 235 months of the Metonic cycle (19 years = 235 Synodic Months). Wright also observed that fragmentary inscriptions suggested that the pointer on the subsidiary dial showed a count of four cycles of the 19-year period, equal to the 76-year Callippic cycle.^[20]

Based on more tentative observations, Wright also came to the conclusion that the lower back dial counted Draconic Months and could perhaps been used for eclipse prediction.^[21]

All these findings have been incorporated into Wright's working model,^[20] demonstrating that a single mechanism with all these functions could not only be built, but would also work.

Despite the improved imagery provided by the linear tomography Wright could not reconcile all the known gears into a single coherent mechanism, and this led him to advance the theory that the mechanism had been altered, or modified, with some astronomical functions removed, and others added^[20].

Finally, as an outcome of his considerable research ^{[22] [23][24][25][26][11][20]}, Wright also conclusively demonstrated that Price's assumption of the existence of a differential gearing arrangement was incorrect,^[20][17]

Michael Wright's research on the Mechanism is continuing in parallel with the efforts of the Antikythera Mechanism Research Project, and recently Wright has modified his model of the mechanism to incorporate the latest findings of the Project. On the 6th of March 2007 he presented his model in the National Hellenic Research Foundation in Athens, Greece.

[edit] Antikythera Mechanism Research Project

The Antikythera mechanism is now being studied by the Antikythera Mechanism Research Project,^[27] a joint program between Cardiff University, the National and Kapodistrian University of Athens, the Aristotle University of Thessaloniki, the National Archaeological Museum of Athens, X-Tek Systems UK^[28] and Hewlett-Packard USA, funded by the Leverhulme Trust and supported by the Cultural Foundation of the National Bank of Greece.^[29]

The mechanism's fragility precluded its removal from the museum, so the Hewlett-Packard research team^[30] and X-Tek systems had to bring their devices to Greece. HP built a 3-D surface imaging device, known as the "PTM Dome," that surrounds the object under examination. X-Tek systems developed especially for the Antikythera Mechanism a 12 ton 450kV microfocus computerised tomographer.

It was announced in Athens on 21 October 2005 that new pieces of the Antikythera mechanism had been found. There are now 82 fragments. Most of the new pieces had been stabilized but were awaiting conservation.

On 30 May 2006, it was announced that the imaging system had enabled much more of the Greek inscription to be viewed and translated, from about 1,000 characters that were visible previously, to about 2,000 characters, representing about 95% of the non-lost text. The team's findings shed new light concerning the function and purpose of the Antikythera mechanism. Research is ongoing. The first results were announced at an international conference in Athens (Greece), November 30 and December 1 2006. ^[31]

[edit] New discoveries

On 30 November 2006, the science journal Nature published a new reconstruction of the mechanism based on the high resolution X-ray tomography described above. ^[32] This work doubled the amount of readable text, corrected prior transcriptions, and provided a new translation. The new discoveries confirm that the mechanism is an astronomical computer or orrery used to predict the positions of heavenly bodies in the sky. This work proposes that the mechanism possessed 37 gears, of which 30 survive, and was used for prediction of the position of the sun, moon, and probably planets.

On the front face were graduations for the solar cycle and the zodiac together with pointers that indicated the position of the sun and the moon, and the lunar phase. Based on the inscriptions, which mention the stationary points of the planets, the authors speculate that planetary motions may also have been indicated here. The inscription lead to a new dating of the Mechanism, as they have been written between 150 to 100 BC. It is evident that they contain a manual with an astronomichal, mechanical and geographical section. The name of ISPANIA (Spain) in these texts is the oldest reference to this country.

On the back, two spiral pointers indicated the state of two further important astronomical cycles: the Saros cycle, the period of approximately 18 years separating the return of the sun, moon and earth to the same relative positions (essential in eclipse prediction); and the Callippic cycle that proposed 940 cycles in approximately 76 years.

The Moon mechanism shows the position and phase of the Moon during the month. The velocity of the Moon is variable following the theory of Hipparchus following to first approxiamtion Keplers law for the angular velocity.

[edit] See also

• Armillary sphere
• Astrarium
• Astrolabe
• Astronomical clock
• Classical planets
• Equatorium
• Horoscopic astrology
• Orrery, a free-standing solar system model
• Planetarium
• Prague Orloj
• Reverse engineering
• Torquetum
• Uriel's machine

[edit] References

[edit] Further reading

• Yalouris, N. (1990). "Ceramic and Iconographic Studies in Honour of Alexander Cambitoglou". Eumousia: 135. *Zeeman, E. C., (1986). "Gears From The Ancient Greeks". Proc. Roy. Inst. GB 58: 137-156.  (See also the slides from a lecture here [1], slide 22 is a view of how the mechanism for a model comes to replace actual reality).
• Weinberg, G. D.; Grace, V. R., Edwards, G. R., Robinson, H. S;, Throckmorton, P., & Ralph, E. K. (1965). "The Antikythera Shipwreck Reconsidered". Trans Am Philos. Soc. 55 (New Series) (3): 3-48. 
• Toomer, G. J. (1998). Ptolemy's Almagest (trans. Toomer, G. J.). Princeton, New Jersey: Princeton Univ. Press. 
• Steele, J. M. (2000). "Eclipse prediction in Mesopotamia". Arch. Hist. Exact Sci. 54: 421-454. 
• Steele, J. M. (2000). Observations and Predictions of Eclipse Times by Early Astronomers. Dordrecht: Kluwer Academic. 
• Stephenson, F. R. (1997). Historical Eclipses and the Earth's Rotation. Cambridge, UK: Cambridge Univ. Press. 
• Charette, François (2006). "High tech from Ancient Greece". Nature 444: 551-552. DOI:10.1038/444551a. 
• Britton. (1985). "The Design of Astronomical Gear Trains". Horological Journal 128 (6): 19-23. 
• Bromley, J. P. (1993). in Die Rolle der Astronomie in den Kulturen Mesopotamiens (ed. Galter, H. D.). Graz: rm-Druck & Vergansgesellschaft, 61-67. 
• Price, D. de S. (1959). "An Ancient Greek Computer". Scientific American 200 (6): 60-67.  see "An Ancient Greek Computer
• Price, D. de S. (1975). "Gears from the Greeks: The Antkythera Mechanism – A Calendar Computer from ca 80BC". Trans Am Philos. Soc., New Series 64 (7). 
• Price, Derek J. de Solla (1975). Gears from the Greeks: The Antikythera Mechanism — A Calendar Computer from ca. 80 BC. New York: Science History Publications. ISBN 0-87169-647-9. 
• Rice R. S. (4 – 7 September 1997). "Physical and Intellectual Salvage from the 1st Century BC". USNA Eleventh Naval History Symposium: 19–25.  see The Antikythera Mechanism
• Rosheim, Mark E. (1994). Robot Evolution: The Development of Anthrobotics. John Wiley & Sons. ISBN 0-471-02622-0.. 
• Steele (1994). Robot Evolution: The Development of Anthrobotics. John Wiley & Sons. ISBN 0-471-02622-0.. 
• Russell, Rupert, The Antikythera Mechanism
• Jones, A. (1991). "The adaption of Babylonian methods in Greek numerical astronomy". Isis 82: 440-453. 
• Jacques Cousteau. The Cousteau Odyssey: Diving for Roman Plunder [Tape]. Warner Home Video/KCET, Los Angeles.
• Edmunds, Mike & Morgan, Philip (2000). "The Antikythera Mechanism: Still a Mystery of Greek Astronomy". Astronomy & Geophysics 41: 6-10. DOI:10.1046/j.1468-4004.2000.41610.x.  (The authors mention that an "extended account" of their researches titled "Computing Aphrodite" is forthcoming in 2001, but it does not seem to have appeared as of yet.)
• Freeth, T. (2002). "The Antikythera Mechanism: 1. Challenging the Classic Research". Mediterranean Archeology and Archeaometry 2 (1): 21-35. 
• Freeth, T. (2002). "The Antikyhera Mechanism: 2. Is it Posidonius’ Orrery?". Mediterranean Archeology and Archeaometry 2 (2). 
• Freeth, T.; Bitsakis, Y., Moussas, X., Seiradakis, J. H., Tselikas, A., Mankou, E., Zafeiropulou, M., Hadland, R., Bate, D., Ramsey, A., Allen, M., Crawley, A., Hockley, P., Malzbender, T., Gelb, D., Ambrisco, W., & Edmunds, M. G. (2006). "Decoding the ancient Greek astronomical calculator known as the Antikythera Mechanism". Nature 444: 587-591. DOI:10.1038/nature05357. 
• James, Peter; Thorpe, Nick (1995). Ancient Inventions. New York: Ballantine. ISBN 0-345-40102-6. 
• Bromley, A. G. (1986). "The Design of Astronomical Gear Trains (b)". Horological Journal 128 (9): 10-11. 
• Bromley, A. G. (1986). "Notes on the Antikythera Mechanism". Centaurus 29: 5. 
• Bromley, A. G. (1990). "The Antikythera Mechanism". Horological Journal 132: 412-415. 
• Bromley, A. G. (1990). "The Antikythera Mechanism: A Reconstruction". Horological Journal 133 (1): 28-31. 
• Bromley, A. G. (1990). "Observations of the Antikythera Mechanism". Antiquarian Horology 18 (6): 641-652. 
• Cary, M. A. (1970). History of Rome. London: Macmillan, 334. 

[edit] External links

• Wilford, John Noble. "An Ancient Computer Surprises Scientists", New York Times, 2006-11-29. Retrieved on 2006-12-06.
• Wilford, John Noble. "Early Astronomical ‘Computer’ Found to Be Technically Complex", New York Times, 2006-11-30. Retrieved on 2006-12-06.
• Lienhard, John H.. Antikythera Mechanism The Engines of Our Ingenuity.. KUHF-FM, Houston.
• Mueller-Maerki, Fortunat F.. Geartrain diagram.
• Decoding an ancient computer.
• Pastore, Giovanni (2006). Antikythera E I Regoli Calcolatori.
• Phillips, Tony.. The Antikythera Mechanism I.
• Phillips, Tony.. The Antikythera Mechanism II.
• Bill Casselman. [Java Animation.
• The Antikythera Calculator (Italian and English versions).
• The Antikythera Mechanism Research Project.
• Recent study of the mechanism. Nature.
• Provisional translation of the text inscribed on the mechanism.
• An emulator of the Antikythera Mechanism, under Squeak EToys].
• Unearthing Mysteries (audio). BBC Radio 4 (2006-12-12).
• Times of London article on results published in "Nature".
• Roumeliotis, Manos. Antikythera Mechanism MOV files.
• Photographs of the mechanism's exhibit at the National Museum of Archaeology in Athens.
• Mr Michael Wright - staff page at Imperial College, London.
• Ancient Greek star calculator finally yields up its secrets.. Irish Independent News.
• BBC News - Ancient Moon 'computer' revisited.
• Preview of research results announced at Athens conference (2006-11-30).
• Report includes six slides, indexed. (2006-11-26).
• Discovery Channel website article (2006-6-8).
• Google Maps satellite image of relevant part of Mediterranean.
• Ancient Calculator Was Ahead of Its Time.
• HP imaging helps scientists figure out world's oldest mechanical calculator. San Francisco Chronicle (2006-11-30).
• Hero of the Industrial Revolution - an alternative history story featuring the Antikythera computer.
• Mysteries of computer of 65BC are solved. The Guardian]] (2006-11-30).
• Compendium article combines an article from the The Economist with a Scientific American article..
• Jay Garmon. Geek Trivia: Ahead of its time(piece) - What ancient shipwreck artifact suggests the ancient Greeks could build complex clockwork devices?. TechRepublic.
• Decoding an ancient computer - Photos of the Antikythera Mechanism. TechRepublic.
• Weijgaert, R. van der, (2005). A Greek Time Machine.
• Rice, R. S. (1993). Gears, Galleys, and Geography - The Antikythera Mechanism's Implications (Text of the 1993 APA Abstract).