History Hunters International

In my opinion, this story describes the single most illuminating and original find ever. View animation:
http://historyhunters.coolasmustard.com/images/analogue_computer.swf

The article continues here. (https://historyhuntersinternational.org/index.php?page=31)

What an awsome thing this is! I had never run across this information before. Truly astounding and a great read,
thanks,
Doc

Let's hope that when, later this year, the full report is published (and, I assume, broadcast), we are given the full, translated text of the inscriptions.

We are told that after the collapse of the Roman Empire, the world did not recover its technical development until the 19th century (after about a century of the Industrial Revolution). Looking at this Greek computer - made half a millennium before that collapse - it makes me realise just how much of antiquity has been lost to us.

For anyone identifying treasure hunting with gold and silver, this artefact is a stark reminder of how the greatest treasures sometimes are made of more mundane materials. Wouldn't it be fun to get a valuation on this artefact?

Sol

A detail of the mechanism.
(http://historyhunters.coolasmustard.com/images/cogs.jpg)

Just to think that they were accurately cutting gears is, by itself, enough to boggle the mind. I wonder what kind of fine measurement devices they had?

Doc

If somebody had shown me these images and said that it was a Victorian mechanical device, I would have believed it. This is truly mind-blowing. I hope the documentary on this demonstrates how the device was made.

A fascinating object, and long overdue for closer scrutiny. I am curious about any possible historical mention of this or similar devices of the same era, that anyone here may recall.  Have any tools, drawings or possibly related items ever been found? I can think of nothing along these lines of anything related as far as arcaeological finds.  Da Vinci drawings come to mind as being somewhat related to this onject.. how can they be sure it is from this wreck/ era, and not something that wasn't dropped there later? Hopefully this new analysis will help to answer some of the questions.

Bart

Bart
Yes, you are right to question whether or not this is really a device of ancient Greece.

First, even before the computer was found, we knew that at least similar devices probably existed. Cicero, writing in the 1st century BC, mentions an instrument "recently constructed by our friend Posidonius, which at each revolution reproduces the same motions of the sun, the moon and the five planets."

No matter how amazed we are by seeing this computer, or how much it stretches our imagination and credulity, it's a fact that Greeks of that period had both the understanding of the maths and the technology to design and built it.

Similar devices are mentioned in other ancient sources. It also adds support to the idea that there was an ancient Greek tradition of complex mechanical technology which was later transmitted to the Arab 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 ancient cranes.

The advanced geometry needed for the Antikythera mechanism's construction was developed by Archimedes.

When the device was recovered, it took quite a while before anyone realised. It appeared to be just a rock, until it was noticed that a gear wheel was visible. The encrustation, being organic, can be dated by the c-14 method.

The Book of Ingenious Devices (Kitab al-Hiyal) was a large illustrated work on mechanical devices including automata published in AD 850 by the three Persian brothers Ahmad, Muhammad and Hasan bin Musa ibn Shakir (the three together known as Banu Musa), working in the House of Wisdom (Bayt al-Hikma) in Baghdad. [1] The book described about one hundred devices and how to use them. It was based partly on the work of Heron of Alexandria, other ancient texts and orignal work by the brothers.[2]

The book was commissioned by the Abassid Caliph of Baghdad Abu Jafar al-Ma'mun ibn Harun (786-833), who instructed the Banu Musa to acquire all of the Greek texts that had been preserved by monasteries and by scholars during the decline and fall of western civilization.[3]

1. Dimarogonas, 2000, p. 15.
2. Bunch, 2004, p. 107.
3. Rosheim, 1994, p. 9.

See also:
Islamic Automation: A Reading of al-Jazari?s The Book Of Knowledge Of Ingenious Mechanical Devices (1206) (http://www.banffcentre.ca/bnmi/programs/archives/2005/refresh/docs/conferences/Gunalan_Nadarajan.pdf#search=%22%22Book%20of%20Ingenious%20Devices%22%22)

A review of Early Muslim Control Engineering

(http://www.muslimheritage.com/uploads/clock.jpg)

During the period of Islamic-Arabic extraordinary activity in Science and Technology (9th-13th century) there are some recorded contributions to the area of Automatic Control mainly in the development of water clocks using float valve regulators, different level controls using float valves or combination of syphons and the development of On-Off control.

The Islamic Arabic Automatic Control Technology had as a basis the Greek Technology of two scientists namely Philon of Byzantium (Rhodes and Alexandria) of the second half of the third century BC (his book "pneumatica" was translated from Arabic into French and German in 1902 and 1899 respectively) and Heron of Alexandria of the first century AD (his book "pneumatica" was translated from Greek into English and German in 1851 and 1899 respectively).

It is noted in Greek technology the language is Greek but the scientists need not be Greek as in the case with Islamic-Arabic technology.

It is known that there are hundreds of thousands of manuscripts dealing with Islamic Science and Technology to be edited and it is assumed that some of them deal with technology. This report is based on references [1-6] (see resources below).

PART I - AUTOMATIC CONTROL IN WATER CLOCKS

1. "The work of Archimedes on the Building of Clocks"

This is an Arabic book whose arabic author is called pseudo-Archimedes with the earliest reference to it in "The Fihrist "of Al-Nadim (died 955 AD). From the literary style and the technique of its drawings this clock book seems to be an Islamic work based on Greek-Roman technology as mentioned ini. This clock used a float level regulator, which makes it a feedback device. A large float drove the whole apparatus. The description of the complicated clock is so thorough that it could be reconstructed almost completely. This book did have considerable influence on the two great horological books of Al-Jazari and Ibn Al-Saati and other Arabic authors like Ibn Al-Akfani.

2. "Al-Jami bain Al-Ilm..." by Al-Jazari [5]

This book was written in 1206.Al-Jazari is from Al-Jazira the area between Tigris and Euphrates. Sarton [6] mentions "This treatise is the most elaborate of its kind and may be considered the climax of this line of Muslim achievement "The distinctive feature of the book is its practical aspect. The book is rich in minute discription of various kinds of devices.

Hill [3] maintains "It is impossible to over-emphasize the importance of Al-Jazari`s work in the history of engineering. Until modern times there is no other document from any cultural area that provides a comparable wealth of instructions for the design, manufacture and assembly of machines" "Al-Jazari did not only assimilate the techniques of his non-Arab and Arab predecessors, he was also creative. He added several mechanical and hydraulic devices. The impact of these inventions can be seen in the later designing of steam engines and internal combustion engines, paving the way for automatic control and other modern machinery. The impact of Al-Jazari`s inventions is still felt in modern contemporary mechanical engineering." Hill [4] translated the book to English in 1974. A German translation was made in 1915.The chapter on water clocks describes 10 water clocks, the first two of them use float valve regulators. The various time-indicating mechanisms are propelled by a float. The other clocks are regulated differently. Al-Jazari mentions an old machine, which he inspected, in which a musical automaton was powered by a vertical water wheel. In his comments on this machine he clearly implies that he knew how to control the speed of such a wheel by means of an escapement.

3. "Book on the Construction of Clocks and their Use", Ridwan b.Muhammad Al-Saati Al-Khurasani (1203)

This book describes the monumental water clock built by Ridwan`s father at the Jayrun gate in Damascus. A German translation was made in 1915. A large float drives the clock, float valve regulator and the device for varying the length of the hours are incorporated.

4. "The Book of Secrets about the Resulte of Thoughts", Al-Muradi of Andalusia(11th century)

This is the earliest description in Arabic of water clocks. This book deals with water clocks and other devices using automata. The treatise consists of 31 models of which 5 are essentially very large toys similar to clocks in that automata are caused to move at intervals, but without precise timing. The prime movers are water wheels that can be overshot or undershot depending on the intensity of flow. There are nineteen clocks, all of which record the passage of the temporal hours by the movements of automata. The power came from large outflow clepsydras provided with concentric siphons. This power was transmitted to automata by very sophisticated mechanisms, which included segmental and epicyclic gears and the use of mercury. These are highly significant features; they provide the first known examples of complex gearing used to transmit high torque while the adoption of mercury reappears in European clocks from the thirteenth century onwards. Unfortunately, the only known manuscript of this work is badly defaced and it is not possible to understand exactly how the clocks worked. A weight driven clock with a mercury escapement appears in "Libros del Saber" a work written in Spanish at the court of Alfonsos of Castille about 1277 and consisting of translations and paraphrases of Arabic works A novel feature in this treatise is the use of mercury in balances. Al-Zarquali built two large water clocks on the banks of the river Tagus at Toledo in 11th century.

5. "Kitab Mizan Al-Hikma (The Book on the Balance of Wisdom)", Al-Khazini (1121-1122) [2]

The eighth treatise of this work described two steelyard clebsydras. The main one, called the Universal Balance, was designed for 24-hour operation, and consisted of an iron beam divided into unequal arms by a fulcrum. An outflow clepsydra equipped with a syphon was suspended on the end of the short arm, and two movable weights, one large and one small, were suspended from the long arm, which was graduated into scales. As water discharged from the clepsydra, the weights were moved along the scale to keep the beam in balance. At any moment the hour of the day could be told from the position of the large weight, its minutes from the position of the small one."

Part II - Automatic Control of Banu Musa

"Kitab Al-Hiyal" (The Book of Ingenious Devices) by Banu Musa bin Shakir (9th century). The three sons of Musa organized translation and did original work in "Bayt Al-Hikma"(House of Wisdom) which is the science academy in Baghdad the greatest scientific institution since the Museum and Library of Alexandria. Banu Musa were the main supporters of the translation movement which gathered momentum as that important epoch of the Islamic scientific awakening reached fruition in the 9th century. They extended their patronage to Thabit Ibn Qurra, to Hunain Ibn Ishaq and to many other translators and scholars. They have more than 20 works which are known including the seminal engineering book "Kitab Al-Hiyal" translated into English by Donald Hill in 1979 and parts of it into German by Wiedemann and Hauser in 1918 and Hauser in 1922.The book was edited in Arabic by Ahmad Al-Hassan in 1981.

The written Arabic heritage in mechanical technology begins with the Banu Musa book. It is possible they knew Hero`s mechanics written in Alexandria in the first century and translated by Qusta Ibn Luqa at the time of Banu Musa.Hero's other books may have been known to the brothers for he enjoyed great fame among Arabic scholars in the 10th century. Banu Musa describe hundred ingenious devices. Hill identified twenty five devices resembling the ones of Hero and Philo(3rd century BC)books. There exist also other parts of the Banu Musa machines which resemble certain elements in Hero and Philo work. There are Banu Musa machines which bear no resemblance to either Hero or Philo. These include the fountains and dredging machine designed to salvage submerged objects from the bottom of rivers and seas and so on. Banu Musa made use primarily of the principles of the science of hydrostatics and aerostatics. Banu Musa use of automatic valves, delayed-action systems and their application of the principles of automatic control testify of creative mentality. Hill notes the use of crankshafts for the first time in the history of technology.

In two models, they used a mechanism similar to the modern crankshaft, thus outstripping by 500 years the first description of the crankshaft in Europe. Mayr [1] mentions that they use syphons, float valves, Philon`s oil lamp, water wheels, etc. Some control systems work with nonmoving parts combining the principle of Philon`s oil lamp with some cleverly arranged syphons. They have contributions in technological refinements and new applications. They install throttling valves directly in the pipe requiring no constant force to keep them closed. These appear first in the book of Banu Musa. Also they introduce improvements on Philon`s oil lamp by ingenious combination of syphons added to the original system. Most important is the use of On-Off control with upper and lower limit for the controlled variable. Systems of this class are widely used in modern technology. The float valve used by Banu Musa, Al-Jazari and other Arabic engineers emerges again in the middle of the 18th century in Europe and in England.

by: Professor Dr Mohamed Mansour, Fri 22 March, 2002

Very good piece Sol, always nice to learn a bit more.  Soon I will know everythning... well, I can dream, can't I?  I don't think we have come close to understanding the ancient's reasons for so much focus on the cosmos, it seems to permeate every ancient culture. It is more than a case of time on their hands and idle curiosity methinks.

Just out today...

Revealed: world's oldest computer - Antikythera mechanism

Helena Smith
Sunday August 20, 2006
The Observer


It looks like a heap of rubbish, feels like flaky pastry and has been linked to aliens. For decades, scientists have puzzled over the complex collection of cogs, wheels and dials seen as the most sophisticated object from antiquity, writes Helena Smith. But 102 years after the discovery of the calcium-encrusted bronze mechanism on the ocean floor, hidden inscriptions show that it is the world's oldest computer, used to map the motions of the sun, moon and planets.

'We're very close to unlocking the secrets,' says Xenophon Moussas,an astrophysicist with a Anglo-Greek team researching the device. 'It's like a puzzle concerning astronomical and mathematical knowledge.'

Known as the Antikythera mechanism and made before the birth of Christ, the instrument was found by sponge divers amid the wreckage of a cargo ship that sunk off the tiny island of Antikythera in 80BC. To date, no other appears to have survived.

'Bronze objects like these would have been recycled, but being in deep water it was out of reach of the scrap-man and we had the luck to discover it,' said Michael Wright, a former curator at London's Science Museum. He said the apparatus was the best proof yet of how technologically advanced the ancients were. 'The skill with which it was made shows a level of instrument-making not surpassed until the Renaissance. It really is the first hard evidence of their interest in mechanical gadgets, ability to make them and the preparedness of somebody to pay for them.'

For years scholars had surmised that the object was an astronomical showpiece, navigational instrument or rich man's toy. The Roman Cicero described the device as being for 'after-dinner entertainment'.

But many experts say it could change how the history of science is written. 'In many ways, it was the first analogue computer,' said Professor Theodosios Tassios of the National Technical University of Athens. 'It will change the way we look at the ancients' technological achievements.'

http://observer.guardian.co.uk/world/story/0,,1854232,00.html

They actually had engineers that good? And machine shops?
I'm amazed.
Dave

I think it's quite natural, Bart, for people to look up and wonder. In the case of the heavens, it must have occured to the brighter among them that there was a direct correlation between the world they inhabited and celetsial bodies. The seasons, "moonths" (the 4-week lunar cycle), tides and so on impinged on them directly.

Mesopotamia seems to have the source for the much of the development within the region and reappeared later in Egypt, and later on still, in Ancient and Classical Greece.

(http://www.physics.unr.edu/grad/welser/astro/pictures/meso_map.jpg)

Sumeria, Babylon and the Assyrians led the world in astronomy.
Internet Links on Mesopotamian Astronomy and Astrology:
http://www.phys.uu.nl/~vgent/babylon/babybibl_links.htm (http://www.phys.uu.nl/~vgent/babylon/babybibl_links.htm)

I think it's true to say that astrology began as an early form of science, in a primitive attempt to have some control over one's life. The oldest records I know of) are astrological omens preserved from the reign of king Ammi-saduqa (1683-47 BC). However Sumerians a 1000 years earlier had some understanding of the subject.

Our modern science and technology clearly owes a great debt to these peoples.

Sol

(http://www.matrixofcreation.co.uk/greece/Antikythera-clock-reconstruction.jpg)
A clockwork mechanism recovered in 60 metres of water from the wreck that went down in 82 BC (http://www.matrixofcreation.co.uk/ancient-clocks.htm)
It was not clear initially what the device was, except that it was clearly a sophisticated mechanism. X-ray analysis was subsequently used to probe the inner structure of the device, the details of the gears. Finally in 1974, a full analysis was published by Professor D. De Solla Price. While some of the original gearing was missing, there was enough to work out that the device was intended to show the motion of the Moon, Sun, and most likely the Planets through the years, when the handle was turned.

(http://www.matrixofcreation.co.uk/greece/Antikythera-Mechanism-sun-moon.gif)
The sun gear has 64 teeth. It meshes with the smaller of a 38,48 gear pair. The 48 meshes with the smaller of a 24,127 gear pair. The 127 meshes with the 32 teeth of the moon gear. The ratio of angular speeds can then be calculated as
64       48       127       254    
   x       x       =       
38       24       32       19    
               =    13.36842..

which is an excellent approximation of the astronomical ratio 13.368267...

The mathematical application to the progression and the mechanical skill necessary to cut the gears is truly astounding.
Doc

OHIO:  I am trying to remember where I saw or read that  a modern watchmaker duplicated the gesrs with files.  He also constructed a mechanism which gave him the ratio and spacing of the teeth, making it fairly simple -- yeah?

Tropical Tramp

The watchmaking aspect of this would appear to be fairly simple for an experienced watchmaker. The mathematical/ theoretical aspect seems to be likewise fairly simple for an experienced/ trained mathemetician. It would be extraordinary for one person to posess both skills, as I see it. While the math capabilities of that era are well known, the mechanical creation of the device in that era is the surprising factor. It appears to me that the idea of the device could have come from recording astronomical observations, specifically orbits.

- Bart

Jose,
It's all about mathematics, but foretelling the movement of the planets is a bit more difficult than a watch, wouldn't you say? Accuracy to the fourth decimal place?
Doc

Gentlemen:  Apparantly I am being taken slightly out of context.  I am simply referring to the ability to re-construct this fantastic Device with "hand tools only".  This includes the spacing of the teeth and size of the wheels to achive whatever ratio one would wish.

As to the knowlege behind it, one only has to turn to some of our latest scientific devices,  Nuclear fision bombs or generators for example.    The mechanical part of it is easily handled by technicians but the knowledge behind it is restricted to only  few.

Tropical Tramp

Jose,
Then you understand that the study of astronomy and geometry was very far advanced in Ancient times. This is now only becoming knowledge. That is what makes this device so extraordinary.
Cheers,
Doc

[attachimg=#]
In search of lost time (http://www.nature.com/nature/journal/v444/n7119/full/444534a.html)
Jo Marchant- News Editor, Nature
Abstract

The ancient Antikythera Mechanism doesn't just challenge our assumptions about technology transfer over the ages ? it gives us fresh insights into history itself.

It looks like something from another world ? nothing like the classical statues and vases that fill the rest of the echoing hall. Three flat pieces of what looks like green, flaky pastry are supported in perspex cradles. Within each fragment, layers of something that was once metal have been squashed together, and are now covered in calcareous accretions and various corrosions, from the whitish tin oxide to the dark bluish green of copper chloride. This thing spent 2,000 years at the bottom of the sea before making it to the National Archaeological Museum in Athens, and it shows.

(http://news.bbc.co.uk/nol/shared/spl/hi/pop_ups/06/technology_enl_1164817474/img/1.jpg)
There are 82 remaining fragments of the mechanism that contain a total of 30 gears. The largest piece contains 27 of the gears. (Image copyright of the Antikythera Mechanism Research Project)

But it is the details that take my breath away. Beneath the powdery deposits, tiny cramped writing is visible along with a spiral scale; there are traces of gear-wheels edged with jagged teeth. Next to the fragments an X-ray shows some of the object's internal workings. It looks just like the inside of a wristwatch.

This is the Antikythera Mechanism. These fragments contain at least 30 interlocking gear-wheels, along with copious astronomical inscriptions. Before its sojourn on the sea bed, it computed and displayed the movement of the Sun, the Moon and possibly the planets around Earth, and predicted the dates of future eclipses. It's one of the most stunning artefacts we have from classical antiquity.

No earlier geared mechanism of any sort has ever been found. Nothing close to its technological sophistication appears again for well over a millennium, when astronomical clocks appear in medieval Europe. It stands as a strange exception, stripped of context, of ancestry, of descendants.

Considering how remarkable it is, the Antikythera Mechanism has received comparatively scant attention from archaeologists or historians of science and technology, and is largely unappreciated in the wider world. A virtual reconstruction of the device, published by Mike Edmunds and his colleagues in this week's Nature (page 587), may help to change that. With the help of pioneering three-dimensional images of the fragments' innards, the authors present something close to a complete picture of how the device worked, which in turn hints at who might have been responsible for building it.

But I'm also interested in finding the answer to a more perplexing question ? once the technology arose, where did it go to? The fact that such a sophisticated technology appears seemingly out of the blue is perhaps not that surprising ? records and artefacts from 2,000 years ago are, after all, scarce. More surprising, to an observer from the progress-obsessed twenty-first century, is the apparent lack of a subsequent tradition based on the same technology ? of ever better clockworks spreading out round the world. How can the capacity to build a machine so magnificent have passed through history with no obvious effects?

Astronomic leaps
In search of lost time

A. WRIGHT

Model success: Michael Wright devoted his life to decoding and replicating the Antikythera Mechanism.

To get an idea of what the mechanism looked like before it had the misfortune to find itself on a sinking ship, I went to see Michael Wright, a curator at the Science Museum in London for more than 20 years and now retired. Stepping into Wright's workshop in Hammersmith is a little like stepping into the workshop where H. G. Wells' time machine was made. Every inch of floor, wall, shelf and bench space is covered with models of old metal gadgets and devices, from ancient Arabic astrolabes to twentieth-century trombones. Over a cup of tea he shows me his model of the Antikythera Mechanism as it might have been in his pomp. The model and the scholarship it embodies have consumed much of his life (see 'Raised from the depths').

The mechanism is contained in a squarish wooden case a little smaller than a shoebox. On the front are two metal dials (brass, although the original was bronze), one inside the other, showing the zodiac and the days of the year. Metal pointers show the positions of the Sun, the Moon and five planets visible to the naked eye. I turn the wooden knob on the side of the box and time passes before my eyes: the Moon makes a full revolution as the Sun inches just a twelfth of the way around the dial. Through a window near the centre of the dial peeks a ball painted half black and half white, spinning to show the Moon's changing phase.

On the back of the box are two spiral dials, one above the other. A pointer at the centre of each traces its way slowly around the spiral groove like a record stylus. The top dial, Wright explains, shows the Metonic cycle ? 235 months fitting quite precisely into 19 years. The lower spiral, according to the research by Edmunds and his colleagues, was divided into 223, reflecting the 223-month period of the Saros cycle, which is used to predict eclipses.

To show me what happens inside, Wright opens the case and starts pulling out the wheels. There are 30 known gear-wheels in the Antikythera Mechanism, the biggest taking up nearly the entire width of the box, the smallest less than a centimetre across. They all have triangular teeth, anything from 15 to 223 of them, and each would have been hand cut from a single sheet of bronze. Turning the side knob engages the big gear-wheel, which goes around once for every year, carrying the date hand. The other gears drive the Moon, Sun and planets and the pointers on the Metonic and Saros spirals.

To see the model in action is to want to find out who had the ingenuity to design the original. Unfortunately, none of the copious inscriptions is a signature. But there are other clues. Coins found at the site by Jacques Cousteau in the 1970s have allowed the shipwreck to be dated sometime shortly after 85 BC. The inscriptions on the device itself suggest it might have been in use for at least 15 or 20 years before that, according to the Edmunds paper.

The ship was carrying a rich cargo of luxury goods, including statues and silver coins from Pergamon on the coast of Asia Minor and vases in the style of Rhodes, a rich trading port at the time. It went down in the middle of a busy shipping route from the eastern to western Aegean, and it seems a fair bet that it was heading west for Rome, which had by that time become the dominant power in the Mediterranean and had a ruling class that loved Greek art, philosophy and technology.

The Rhodian vases are telling clues, because Rhodes was the place to be for astronomy in the first and second centuries BC. Hipparchus, arguably the greatest Greek astronomer, is thought to have worked on the island from around 140 BC until his death in around 120 BC. Later the philosopher Posidonius set up an astronomy school there that continued Hipparchus' tradition; it is within this tradition that Edmunds and his colleagues think the mechanism originated. Circumstantial evidence is provided by Cicero, the first-century BC Roman lawyer and consul. Cicero studied on Rhodes and wrote later that Posidonius had made an instrument "which at each revolution reproduces the same motions of the Sun, the Moon and the five planets that take place in the heavens every day and night". The discovery of the Antikythera Mechanism makes it tempting to believe the story is true.

And Edmunds now has another reason to think the device was made by Hipparchus or his followers on Rhodes. His team's three-dimensional reconstructions of the fragments have turned up a new aspect of the mechanism that is both stunningly clever and directly linked to work by Hipparchus.

One of the wheels connected to the main drive wheel moves around once every nine years. Fixed on to it is a pair of small wheels, one of which sits almost ? but not exactly ? on top of the other. The bottom wheel has a pin sticking up from it, which engages with a slot in the wheel above. As the bottom wheel turns, this pin pushes the top wheel round. But because the two wheels aren't centred in the same place, the pin moves back and forth within the upper slot. As a result, the movement of the upper wheel speeds up and slows down, depending on whether the pin is a little farther in towards the centre or a little farther out towards the tips of the teeth (see illustration on page 551).

The researchers realized that the ratios of the gear-wheels involved produce a motion that closely mimics the varying motion of the Moon around Earth, as described by Hipparchus. When the Moon is close to us it seems to move faster. And the closest part of the Moon's orbit itself makes a full rotation around the Earth about every nine years. Hipparchus was the first to describe this motion mathematically, working on the idea that the Moon's orbit, although circular, was centred on a point offset from the centre of Earth that described a nine-year circle. In the Antikythera Mechanism, this theory is beautifully translated into mechanical form. "It's an unbelievably sophisticated idea," says Tony Freeth, a mathematician who worked out most of the mechanics for Edmunds' team. "I don't know how they thought of it."

"I'm very surprised to find a mechanical representation of this," adds Alexander Jones, a historian of astronomy at the University of Toronto, Canada. He says the Antikythera Mechanism has had little impact on the history of science so far. "But I think that's about to change. This was absolutely state of the art in astronomy at the time."

Wright believes that similar mechanisms modelled the motions of the five known planets, as well as of the Sun, although this part of the device has been lost. As he cranks the gears of his model to demonstrate, and the days, months and years pass, each pointer alternately lags behind and picks up speed to mimic the astronomical wanderings of the appropriate sphere.
Greek tragedy

Almost everyone who has studied the mechanism agrees it couldn't have been a one-off ? it would have taken practice, perhaps over several generations, to achieve such expertise. Indeed, Cicero wrote of a similar mechanism that was said to have been built by Archimedes. That one was purportedly stolen in 212 BC by the Roman general Marcellus when Archimedes was killed in the sacking of the Sicilian city of Syracuse. The device was kept as an heirloom in Marcellus' family: as a friend of the family, Cicero may indeed have seen it.

So where are the other examples? A model of the workings of the heavens might have had value to a cultivated mind. Bronze had value for everyone. Most bronze artefacts were eventually melted down: the Athens museum has just ten major bronze statues from ancient Greece, of which nine are from shipwrecks. So in terms of the mechanism, "we're lucky we have one", points out Wright. "We only have this because it was out of reach of the scrap-metal man."

But ideas cannot be melted down, and although there are few examples, there is some evidence that techniques for modelling the cycles in the sky with geared mechanisms persisted in the eastern Mediterranean. A sixth-century AD Byzantine sundial brought to Wright at the Science Museum has four surviving gears and would probably have used at least eight to model the positions of the Sun and Moon in the sky. The rise of Islam saw much Greek work being translated into Arabic in the eighth and ninth centuries AD, and it seems quite possible that a tradition of geared mechanisms continued in the caliphate. Around AD 1000, the Persian scholar al-Biruni described a "box of the Moon" very similar to the sixth-century device. There's an Arabic-inscribed astrolabe dating from 1221?22 currently in the Museum of the History of Science in Oxford, UK, which used seven gears to model the motion of the Sun and Moon.

But to get anything close to the Antikythera Mechanism's sophistication you have to wait until the fourteenth century, when mechanical clockwork appeared all over western Europe. "You start to get a rash of clocks," says Wright. "And as soon as you get clocks, they are being used to drive astronomical displays." Early examples included the St Albans clock made by Richard Wallingford in around 1330 and a clock built by Giovanni de'Dondi a little later in Padua, Italy, both of which were huge astronomical display pieces with elaborate gearing behind the main dial to show the position of the Sun, Moon, planets and (in the case of the Padua clock) the timing of eclipses. The time-telling function seems almost incidental.

It could be argued that the similarities between the medieval technology and that of classical Greece represent separate discoveries of the same thing ? a sort of convergent clockwork evolution. Wright, though, favours the idea that they are linked by an unbroken tradition: "I find it as easy to believe that this technology survived unrecorded, as to believe that it was reinvented in so similar a form." The timing of the shift to the West might well have been driven by the fall of Baghdad to the Mongols in the thirteenth century, after which much of the caliphate's knowledge spread to Europe. Shortly after that, mechanical clocks appeared in the West, although nobody knows exactly where or how. It's tempting to think that some mechanisms, or at least the ability to build them, came west at the same time. As Fran?ois Charette, a historian of science at Ludwig Maximilians University in Munich, Germany, points out, "for the translation of technology, you can't rely solely on texts". Most texts leave out vital technical details, so you need skills to be transmitted directly.

But if the tradition of geared mechanisms to show astronomical phenomena really survived for well over a millennium, the level of achievement within that tradition was at best static. The clockwork of medieval Europe became more sophisticated and more widely applied fairly quickly; in the classical Mediterranean, with the same technology available, nothing remotely similar happened. Why didn't anyone do anything more useful with it in all that time? More specifically, why didn't anyone work out earlier what the gift of hindsight seems to make obvious ? that clockwork would be a good thing to make clocks with?

Serafina Cuomo, a historian of science at Imperial College, London, thinks that it all depends on what you see as 'useful'. The Greeks weren't that interested in accurate timekeeping, she says. It was enough to tell the hour of the day, which the water-driven clocks of the time could already do fairly well. But they did value knowledge, power and prestige. She points out that there are various descriptions of mechanisms driven by hot air or water ? and gears. But instead of developing a steam engine, say, the devices were used to demonstrate philosophical principles. The machines offered a deeper understanding of cosmic order, says David Sedley, a classicist at the University of Cambridge, UK. "There's nothing surprising about the fact that their best technology was used for demonstrating the laws of astronomy. It was deep-rooted in their culture."

Another, not mutually exclusive, theory is that devices such as the Antikythera Mechanism were signifiers of social status. Cuomo points out that demonstrating wondrous devices brought social advancement. "They were trying to impress their peers," she says. "For them, that was worth doing." And the Greek ?lite was not the only potential market. Rich Romans were eager for all sorts of Greek sophistication ? they imported philosophers for centuries.

Seen in this light, the idea that the Antikythera Mechanism might be expected to lead to other sorts of mechanism seems less obvious. If it already embodied the best astronomy of the time, what more was there to do with it? And status symbols do not follow any clearly defined arc of progress. What's more, the idea that machines might do work may have been quite alien to slave-owning societies such as those of Ancient Greece and Rome. "Perhaps the realization that you could use technology for labour-saving devices took a while to dawn," says Sedley.

There is also the problem of power. Water clocks are thought to have been used on occasion to drive geared mechanisms that displayed astronomical phenomena. But dripping water only provides enough pressure to drive a small number of gears, limiting any such display to a much narrower scope than that of the Antikythera Mechanism, which is assumed to have been handcranked. To make the leap to mechanical clocks, a geared mechanism needs to be powered by something other than a person; it was not until medieval Europe that clockwork driven by falling weights makes an appearance.
Invention's evolution

Bert Hall, a science historian at the University of Toronto in Canada, believes a final breakthrough towards a mechanical weight drive might have come about almost by accident, by adapting a bell-ringing device. A water clock could have driven a hammer or weight mechanism swinging between two bells as an alarm system, until someone realized that the weight mechanism would be a more regular way of driving the clock in the first place. When the new way to drive clocks was discovered, says Hall, "the [clockwork] technology came rushing out of the wings into the new tradition".

Researchers would now love further mechanisms to be unearthed in the historical record. "We hope that if we can bring this to people's attention, maybe someone poking around in their museum might find something, or at least a reference to something," says Edmunds. Early Arabic manuscripts, only a fraction of which have so far been studied, are promising to be fertile ground for such discoveries.

Charette also hopes the new Antikythera reconstruction will encourage scholars to take the device more seriously, and serve as a reminder of the messy nature of history. "It's still a popular notion among the public, and among scientists thinking about the history of their disciplines, that technological development is a simple progression," he says. "But history is full of surprises."

In the meantime, Edmunds' Antikythera team plans to keep working on the mechanism ? there are further inscriptions to be deciphered and the possibility that more fragments could be found. This week the researchers are hosting a conference in Athens that they hope will yield fresh leads. A few minutes' walk from the National Archaeological Museum, Edmunds' colleagues from the University of Athens, Yanis Bitsakis and Xenophon Moussas, treat me to a dinner of aubergine and fried octopus, and explain why they would one day like to devote an entire museum to the story of the fragments.

"It's the same way that we would do things today, it's like modern technology," says Bitsakis. "That's why it fascinates people." What fascinates me is that where we see the potential of that technology to measure time accurately and make machines do work, the Greeks saw a way to demonstrate the beauty of the heavens and get closer to the gods.

The Antikythera Mechanism will be explored in an episode of Unearthing Mysteries on BBC Radio 4 on 12 December.

Interactive Relighting of the Antikythera Mechanism (http://www.hpl.hp.com/research/ptm/antikythera_mechanism/index.html)

                        Mystery of ancient astronomical calculator unveiled

Public release date: 29-Nov-2006

Contact: Stephen Rouse


Cardiff University

     An international team has unravelled the secrets of a 2,000-year-old computer which could transform the way we think about the ancient world.

     Professor Mike Edmunds and Dr Tony Freeth, of Cardiff University led the team who believe they have finally cracked the workings of the Antikythera Mechanism, a clock-like astronomical calculator dating from the second century BC.

     Remnants of a broken wooden and bronze case containing more than 30 gears was found by divers exploring a shipwreck off the island of Antikythera at the turn of the 20th century. Scientists have been trying to reconstruct it ever since. The new research suggests it is more sophisticated than anyone previously thought.

     Detailed work on the gears in the mechanism show that it was able to track astronomical movements with remarkable precision. The calculator was able to follow the movements of the moon and the sun through the Zodiac, predict eclipses and even recreate the irregular orbit of the moon. The team believe it may also have predicted the positions of some or all of the planets.

     The findings suggest that Greek technology was far more advanced than previously thought. No other civilisation is known to have created anything as complicated for another thousand years.

     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 well."

     The team was made up of researchers from Cardiff, the National Archaeological Museum of Athens and the Universities of Athens and Thessaloniki, supported by a substantial grant from the Leverhulme Trust. They were greatly aided by Hertfordshire X-Tek, who developed powerful X-Ray computer technology to help them study the corroded fragments of the machine. Computer giant Hewlett-Packard provided imaging technology to enhance the surface details of the machine.

     The mechanism is in over 80 pieces and stored in precisely controlled conditions in Athens where it cannot be touched. Recreating its workings was a difficult, painstaking process, involving astronomers, mathematicians, computer experts, script analysts and conservation experts.

     The team is unveiling its full findings at a two-day international conference in Athens from November 30 to December 1 and publishing the research in the journal Nature . The researchers are now hoping to create a computer model of how the machine worked, and, in time, a full working replica. It is still uncertain what the ancient Greeks used the mechanism for, or how widespread this technology was.

     Professor Edmunds said: "It does raise the question what else were they making at the time. In terms of historic and scarcity value, I have to regard this mechanism as being more valuable than the Mona Lisa."

http://www.eurekalert.org/pub_releases/2006-11/cu-moa112806.php

Decoding the ancient Greek astronomical calculator known as the Antikythera Mechanism (http://www.nature.com/nature/journal/v444/n7119/abs/nature05357.html)
Letter

Nature 444, 587-591 (30 November 2006) | doi:10.1038/nature05357; Received 10 August 2006; Accepted 17 October 2006
Decoding the ancient Greek astronomical calculator known as the Antikythera Mechanism

T. Freeth1,2, Y. Bitsakis3,5, X. Moussas3, J. H. Seiradakis4, A. Tselikas5, H. Mangou6, M. Zafeiropoulou6, R. Hadland7, D. Bate7, A. Ramsey7, M. Allen7, A. Crawley7, P. Hockley7, T. Malzbender8, D. Gelb8, W. Ambrisco9 and M. G. Edmunds1

   1. Cardiff University, School of Physics and Astronomy, Queens Buildings, The Parade, Cardiff CF24 3AA, UK
   2. Images First Ltd, 10 Hereford Road, South Ealing, London W5 4SE, UK
   3. National and Kapodistrian University of Athens, Department of Astrophysics, Astronomy and Mechanics, Panepistimiopolis, GR-15783, Zographos, Greece
   4. Aristotle University of Thessaloniki, Department of Physics, Section of Astrophysics, Astronomy and Mechanics, GR-54124 Thessaloniki, Greece
   5. Centre for History and Palaeography, National Bank of Greece Cultural Foundation, P. Skouze 3, GR-10560 Athens, Greece
   6. National Archaeological Museum of Athens, 1 Tositsa Str., GR-10682 Athens, Greece
   7. X-Tek Systems Ltd, Tring Business Centre, Icknield Way, Tring, Hertfordshire HP23 4JX, UK
   8. Hewlett-Packard Laboratories, 1501 Page Mill Road, Palo Alto, California 94304, USA
   9. Foxhollow Technologies Inc., 740 Bay Road, Redwood City, California 94063, USA

Correspondence to: M. G. Edmunds1 Correspondence and requests for materials should be addressed to M.G.E. (Email: [email protected]).
Top of page

The Antikythera Mechanism is a unique Greek geared device, constructed around the end of the second century bc. It is known1, 2, 3, 4, 5, 6, 7, 8, 9 that it calculated and displayed celestial information, particularly cycles such as the phases of the moon and a luni-solar calendar. Calendars were important to ancient societies10 for timing agricultural activity and fixing religious festivals. Eclipses and planetary motions were often interpreted as omens, while the calm regularity of the astronomical cycles must have been philosophically attractive in an uncertain and violent world. Named after its place of discovery in 1901 in a Roman shipwreck, the Antikythera Mechanism is technically more complex than any known device for at least a millennium afterwards. Its specific functions have remained controversial11, 12, 13, 14 because its gears and the inscriptions upon its faces are only fragmentary. Here we report surface imaging and high-resolution X-ray tomography of the surviving fragments, enabling us to reconstruct the gear function and double the number of deciphered inscriptions. The mechanism predicted lunar and solar eclipses on the basis of Babylonian arithmetic-progression cycles. The inscriptions support suggestions of mechanical display of planetary positions9, 14, 15, now lost. In the second century bc, Hipparchos developed a theory to explain the irregularities of the Moon's motion across the sky caused by its elliptic orbit. We find a mechanical realization of this theory in the gearing of the mechanism, revealing an unexpected degree of technical sophistication for the period.

In search of lost time (http://www.nature.com/nature/journal/v444/n7119/full/444534a.html)
Nature 444, 534-538 (30 November 2006)

Hear the sound of the Antikythera Mechanism recreated on the 30 November (http://www.nature.com/nature/podcast/v444/n7119/nature-2006-11-30.mp3)
Nature Podcast. (http://www.nature.com/nature/podcast/index.html)

Googling the phrase " Babylonian arithmetic-progression cycles " found within your article, resulted in the following treatise. - Bart

               Geminos's Introduction to the Phenomena:
     A Translation and Study of a Hellenistic Survey of Astronomy

James Evans & J. Lennart Berggren

Part 1 of 6

Introduction

     Geminos, a Greek scientific writer of wide-ranging interests, has been assigned dates ranging from the first century b.c. to the first century a.d., with, we believe, the first century b.c. the more likely. We know nothing of the circumstances of his life. Of three works he is believed to have written, only one, the Introduction to the Phenomena, has come down to us. (This work is also frequently referred to as the Isagoge, from the first word of its Greek title, Eisagoge eis ta phainomena.) The translation of his Introduction to the Phenomena here presented is the first complete English version ever published.

     For the modern reader, Geminos provides a vivid impression of an educated Greek?s view of the cosmos and of astronomy around the beginning of our era. Moreover, he is frequently a graceful and charming writer, constantly aware of his audience, and his book remains quite readable today. Indeed, it is one of a very small number of works of ancient astronomy that can be read right through with appreciation and understanding by a nonspecialist. Because Geminos covers most of the central topics of ancient Greek astronomy, his text provides an excellent general survey of those parts of that astronomy not dependent on sophisticated mathematical models. An English translation of the Introduction to the Phenomena should thus be useful not only to historians of astronomy but also to historians of science more generally, to those interested in classical civilization, and to astronomers who would like to know more about the history of their discipline.

     We have furnished our translation with a commentary, printed at the foot of the page and signaled in the text by superscript numerals. The purpose of the commentary is not to summarize all that is known on the topics at hand, but to open up Geminos?s text, to make it more comprehensible, and to reveal its connections with other ancient sources? philosophical and literary, as well as scientific. It should serve, as well, to direct readers to the specialized scholarly literature. Textual notes, signaled in Geminos?s text by superscript roman letters, are grouped together in appendix 1.

1. SIGNIFICANCE OF GEMINOS?S INTRODUCTION TO THE PHENOMENA

     Geminos?s Introduction to the Phenomena, a competent and engaging introduction to astronomy, was probably written in conjunction with teaching. Geminos discusses all of the important branches of Greek astronomy, except planetary theory. This he promises to take up ?elsewhere.? Perhaps he did discuss planetary theory in another work, but if so, it has not survived. Topics covered in Geminos?s Introduction include the zodiac, solar theory, the constellations, the theory of the celestial sphere, the variation in the length of the day, lunisolar cycles, phases of the Moon, eclipses, helical risings and settings of the fixed stars, terrestrial zones, and an introduction to Babylonian lunar theory. Because the work was written for beginners, it does not often get into technical detail?except in the discussion of lunisolar cycles, where Geminos does indulge in a bit of arithmetic.

     Geminos?s book is important to the task of filling gaps in the history of Greek astronomy in several ways. In general terms, Geminos provides an overview of most of astronomy in the period between Hipparchus (second century b.c.) and Ptolemy (second century a.d.), and thereby provides a good deal of insight into what was current and common knowledge in Geminos?s own day. One of the more charming aspects of his work, frequently in evidence, is his desire to set straight common misconceptions about astronomical matters. In this way, he offers us valuable information about the beliefs of his own audience.

     More specifically, Geminos provides detailed discussions of several topics not very well treated by other ancient sources. (1) His discussion of Babylonian lunar theory is an important piece of the story of the adaptation of Babylonian methods by Greek astronomers. (2) His discussion of the 8- and 19-year lunisolar cycles is the most detailed by any extant Greek source. (3) His discussion of Hipparchos?s rendering of the constellations provides information not found in other sources. (4) His refutation of the then-common view that changes in the weather are caused by the helical risings and settings of the stars is the most patient and detailed such argument that has come down to us.

     In the extant manuscripts, Geminos?s book concludes with a parapegma (star calendar) that permits one to know the time of year by observation of the stars. Many scholars believe that this compilation is older than Geminos by a century or more. Whether by Geminos or not, this parapegma is one of our most important sources for the early history of the genre. The Geminos parapegma was based substantially upon three earlier parapegmata?those by Euktemon (fifth century b.c.), Eudoxos (early fourth century b.c.), and Kallippos (late fourth century b.c.). Because the Geminos parapegma scrupulously cites its sources, it permits us to trace the stages in the evolution of the parapegma between the time of Euktemon and the time of Kallippos. Our book includes a translation of the Geminos parapegma, as well as a synoptic table of its contents (appendix 2), which should be useful in the study of this important historical document.

     Although ancient and medieval Greek readers would have recognized Geminos?s book as belonging to a class of ?phenomena? literature (see sections 3 and 4 below), we cannot be sure that Introduction to the Phenomena is the title that Geminos himself gave it. This is a common difficulty with ancient scientific texts, the conventional titles of which are not always authorial. The Greek manuscripts of Geminos?s text do provide good evidence for the commonly accepted title, although there are several variants. Indeed, the three best and oldest Greek manuscripts present a bit of a puzzle: one gives as its title Geminos?s Introduction to the Phenomena; another gives Geminos?s Introduction to the Things on High (meteora); and still another gives neither title nor author?s name, since the copyist never filled in this information. Some later Greek manuscripts simply have ?The Phenomena? of Geminos.1 As we shall see below (sec. 14), the Latin and Hebrew translations made in the twelfth and thirteenth centuries (from an Arabic intermediary) also show that there was considerable confusion about the title and author of the text. For the sake of simplicity, we shall always refer to Geminos?s book by the title commonly used today, and best supported by the Greek manuscripts, Introduction to the Phenomena.

http://press.princeton.edu/chapters/i8330.html

Geminos's Introduction to the Phenomena:
A Translation and Study of a Hellenistic Survey of Astronomy

James Evans & J. Lennart Berggren


Part 2 of 6

                                                       2. GEMINOS?S OTHER WORKS

     Geminos was the author of two other works that have not come down to us. One was a mathematical work of considerable length that discussed, among other things, the philosophical foundations of geometry. Fortunately, a large number of passages from this work (whether in quotation or in paraphrase) are preserved by Proklos2 in his Commentary on the First Book of Euclid?s Elements. The exact title of Geminos?s book is uncertain, but in one passage Proklos remarks, ?so much have I selected from the Philokalia of Geminos.?3 (Philokalia means ?Love of the Beautiful.?) In one passage of considerable interest, Geminos discussed the branches of mathematical science and their relationships to one another. This is the most detailed such discussion that has come down to us from the Greeks. Moreover, it is clear that Geminos was discussing, not merely abstract divisions of mathematics, but actual genres of mathematical writing. Because several of Geminos?s branches of mathematics pertain to astronomy (e.g., sphairopoi?a, dioptrics, and gnomonics), his discussion sheds light on the relationship of astronomy to other mathematical endeavors. Because of its interest for the history of astronomy, we have included a translation of this passage from Geminos?s Philokalia as fragment 1.

     Geminos was also the author of a meteorological work, which was perhaps a commentary on, or an abridgement of, a now lost Meteorology of Poseidonios.4 A fragment of some length is preserved by Simplikios5 in his Commentary on Aristotle?s Physics. Apparently, by Simplikios?s time, Geminos?s meteorological book had been lost, for Simplikios makes it clear that he is quoting Geminos, not from Geminos?s own work, but from some work by Alexander of Aphrodisias.6 In the course of his citation, Simplikios says that Alexander drew these remarks from Geminos?s ?Concise Exposition of the Meteorology of Poseidonios.?7 The fragment from Geminos preserved by Simplikios is of considerable interest, for it is devoted to the limits of astronomical knowledge. In this passage, Geminos discusses the relationship of astronomy to physics (or natural philosophy), arguing that astronomy is, of itself, unable to decide between competing hypotheses and must rely on physics for guidance about first principles. We include a translation of this passage from Geminos?s lost meteorological work as fragment 2.

http://press.princeton.edu/chapters/i8330.html

                               Geminos's Introduction to the Phenomena:
            A Translation and Study of a Hellenistic Survey of Astronomy

James Evans & J. Lennart Berggren


Part 3 of 6

       3. ON ?THE PHENOMENA? IN GREEK ASTRONOMY

      Geminos?s Introduction to the Phenomena had its roots in a well-established genre. In order to explain what the writers and readers of this genre considered to be relevant, we must say a little about what Greek astronomical writers mean by the phenomena. The word ?phenomena? is a participle of the passive verb phainomai, which carries the meanings of ?to come to light, come to sight, be seen, appear.? The last two are definitive for the astronomical sense of the word, which is ?things that are seen/appear in the heavens.?

     A late source, Simplikios, quotes Sosigenes as having attributed to Plato the statement that the task of astronomy was to show how, by a combination of uniform circular motions, one could ?save (i.e., account for) the phenomena.? The ascription to Plato is controversial (see sec. 10 below), but in any case the word Phenomena appears as the title of a work by an associate of Plato, Eudoxos of Knidos (early fourth century b.c.). Eudoxos?s work has not survived, but its essence is preserved in a poem of the same name by Aratos (early third century b.c.). The poetic Phenomena of Aratos was the subject of a commentary by the great astronomer Hipparchos of Rhodes (second century b.c.), who was able to compare it with the text of Eudoxos and demonstrate that Aratos had indeed relied upon Eudoxos. It appears from these sources that Eudoxos?s work was devoted to a detailed description of the placement of the fixed stars and the constellations, relative to some standard reference circles on the celestial sphere. The following passages give a sense of the character of Eudoxos?s book, and also an idea of what sort of ?phenomena? it was occupied with. We quote directly from Hipparchos?s Commentary, and in each case Hipparchos has made it clear that he is himself directly reporting on Eudoxos?s text:

     There is a certain star that remains always in the same spot; this star is the pole of the universe.8

     Between the Bears is the tail of the Dragon, the end-star of which is above the head of the Great Bear.9

     Aratos, following Eudoxos, says that it [the Dragon?s head] moves on the always-visible circle, using these words: ?Its head moves where the limits of rising and setting are confounded.?10

     Because Aratos includes in his poem a discussion of the principal circles of the celestial sphere (ecliptic, equator, tropics, arctic circle, as well as the Milky Way), we may surmise that the same material was treated, in more detail, by Eudoxos. So, by the early fourth century, the basic theory of the celestial sphere had been established, and a detailed description of the constellations given. Such were the phenomena of Eudoxos.11

     The oldest extant work named The Phenomena is that of Euclid (c. 300 b.c.).12 Unlike the work of Eudoxos, Euclid?s book has no place for uranography. Rather, a short (and possibly spurious) preface introduces the north celestial pole13 and the principal circles on the celestial sphere (including the parallel circles, the ecliptic, the horizon, and the Milky Way). The author also introduces the arctic and antarctic circles relative to a given locality and the consequent division of stars into those that never rise, those that rise and set, and those that never set. Thus Eudoxos?s descriptions of the constellations have been eliminated in favor of a geometrical exploration of the sphere.

     After this beginning, Euclid?s treatise proceeds by a series of propositions with proofs and accompanying diagrams, in the style of his more famous Elements. These begin with proposition 1 on the central position of the Earth in the cosmos, and then progress through three propositions on the risings and settings of stars. Propositions 8?13 deal with the risings and settings of arcs of the ecliptic, particularly the zodiacal signs, and the work concludes with five propositions on how long it takes equal arcs of the ecliptic to cross the visible and invisible hemispheres. The very format of the work illustrates what had become a commonplace among Greek thinkers, namely that celestial phenomena can be explained rationally.

     Other extant early Greek texts for which the celestial phenomena form the subject matter include two works of Euclid?s contemporary, Autolykos of Pitane, both of them written in the theorem-proof style one finds in Euclid?s book. In On the Moving Sphere, Autolykos treats some of the phenomena arising from the uniform rotation of a sphere around its axis relative to a horizon that separates the visible from the invisible portions of the sphere. It is striking that in On the Moving Sphere, the descriptions of all circles other than the horizon are as abstract and geometrical as possible, and there is no explicit mention of the astronomical applications of the theorems. As an example we quote proposition 8: Great circles tangent to the same [parallel circles] to which the horizon is tangent will, as the sphere rotates, fit exactly onto the horizon. The abstract character of many of these propositions illustrates how far the Greek geometrization of astronomy had been carried by the time of Euclid and Autolykos. Many of the propositions are hard to prove, but are easy to illustrate on a celestial globe.

     Autolykos?s other book, On Risings and Settings, is devoted to heliacal risings and settings?the annual cycle of appearances and disappearances of the fixed stars. This had been a part of Greek popular astronomy from the earliest days, as illustrated by Hesiod?s use of the heliacal risings and settings of the Pleiades, Arcturus, and Sirius to tell the time of year in his poem, Works and Days (c. 650 b.c.). Clearly, the sidereal events in the annual cycle were a part of what the Greeks considered ?phenomena.? Autolykos?s goal in On Risings and Settings is to provide a mathematical foundation, in the form of theorems, for a field that had previously been in the domain of popular lore. Geminos devotes chapter xiii of his Introduction to the Phenomena to the same subject. Indeed, Geminos?s heading for chapter xviii is the same as the title of Autolykos?s book. As we point out in our commentary on that chapter, Geminos follows Autolykos in all significant details, but eliminates the proofs.

     The other major writer on the phenomena was Theodosios of Bithynia (c. 100 b.c.), whose On Habitations and On Days and Nights are the earliest extant works devoted to a discussion of how the phenomena change from one locality to another: as an observer moves north or south, the stars that are visible will become different and the lengths of the day and night may change. An example of a proposition from the first of these is:

     For those living under the north pole14 the same hemisphere of the cosmos is always visible and the same hemisphere of the cosmos is always invisible, and none of the stars either sets or rises for them, but those in the visible hemisphere are always visible and those in the invisible [hemisphere] are always invisible.15
Geminos?s use of Theodosios is quite clear, for the Greek heading of Geminos?s chapter xvi is the same as that of Theodosios?s On Habitations,16 and the heading of chapter vi is only trivially different (singular nouns instead of plurals) from that of Theodosios?s On Days and Nights.

      Many of the founding works on the phenomena, such as those by Euclid, Autolykos, and Theodosios, survived because they were short enough and elementary enough for use in teaching. They became staples of the curriculum for mathematics and astronomy, and so survived through late Antiquity and into the Middle Ages, in both the Arabic and Latin worlds.

     The motions of the Sun, Moon, and planets around the zodiac are also part of what the Greeks considered ?phenomena.? Several features of planetary motion posed challenges for explanation: the Sun appears to move more slowly at some times of year, and more rapidly at others. The planets are even more puzzling, since they occasionally stop and reverse direction in what is known as retrograde motion. Most scholars believe that the earliest Greek effort to explain the complex motions of the planets was the book On Speeds by Eudoxos. It is lost, but we have two rather lengthy discussions of it, one by Aristotle, who was a contemporary of Eudoxos, and one by Simplikios, who lived 900 years later, and whose account must therefore be used with caution. Probably by the time of Apollonios of Perge (late third century b.c.) and certainly by the time of Hipparchos, Eudoxos?s approach of modeling the planetary phenomena by the gyrations of nested, homocentric spheres had given way to eccentric circles and epicycles lying in a plane. But this was daunting material to address in an elementary work.17

http://press.princeton.edu/chapters/i8330.html

                                 Geminos's Introduction to the Phenomena:
            A Translation and Study of a Hellenistic Survey of Astronomy

James Evans & J. Lennart Berggren


Part 4 of 6

4. THE GREEK GENRE OF ASTRONOMICAL SURVEYS

     In the Hellenistic period, there emerged a demand for popular surveys? works that would take students through the celestial phenomena without forcing them through theorems and proofs. The poetic Phenomena of Aratos can be considered one of the first such popularizations. The new popular surveys eschewed the austere geometrical demonstrations of Euclid, Autolykos, and Theodosios tended simply to summarize mathematical results in plain language. They also tended to include a greater variety of subjects of interest to the broad public?phases of the Moon, eclipses, and elements of astronomical geography, such as the theory of terrestrial zones. Of course, all of these topics had deep roots in the history of Greek science. What was new was the attempt to produce comprehensive astronomy textbooks written at an elementary level.

     The popular surveys of astronomy could be read for their own sake, but some were clearly intended to form part of the curriculum of studies expected of a well-born student. The geographical writer Strabo (c. 64 b.c. to c. a.d. 25) mentions that students can learn in the elementary mathematics courses all the astronomy they will need for the study of geography. He mentions as an example of the standard astronomical curriculum the theory of the celestial sphere?tropics, equator, zodiac, arctic circle, and horizon.18 The sort of elementary astronomy course that Strabo had in mind is well represented by Geminos?s Introduction to the Phenomena. Diogenes Laertios tells us that instruction in basic astronomy was part of the curriculum of Stoic teachers.19 And, of course, astronomy had long been part of the quadrivium of mathematical studies in the Platonist school.20 Whether for the sake of popular reading, or for liberal education, or as part of the preparation for more advanced studies, introductions to the astronomical phenomena permeated Greek culture from about 200 b.c. to the end of Antiquity.

     It is quite appropriate, then, that Geminos?s work is named Introduction to the Phenomena, for eisagoge (?introduction?) carries two meanings. On one hand, this is a regular word for an elementary treatise on a subject; on the other, it can denote a conduit, or channel, into a harbor. Thus an eisagoge could serve either as a liberal arts survey of astronomy, complete in itself, or as the preparatory course for higher studies in the subject.

     Geminos occasionally employs demonstrative mathematical arguments (e.g., in his treatment of lunisolar cycles in chapter viii), and he did not write his book for those who were afraid of numbers or geometry. However, his motto seems to have been ?mathematics if necessary, but not necessarily mathematics??and in any case he makes no use of formal mathematical proofs. Nor does Geminos?s work smell of the mathematics classroom. There is none of the graded progression from the easy to the complicated that one finds in, for example, Euclid?s Phenomena. Had Geminos intended to write a textbook of mathematics he would surely have put chapters iv (the axis and the poles) and v (circles on the sphere) at the beginning, and in any case before chapter i (on the zodiac). A third feature of his work is its blending of the topics of the two earlier genres of phenomena literature (the descriptive uranography of Eudoxos and the mathematical topics of Euclid and his successors) with topics outside of these traditions, namely those he treats in chapters viii?xii, xvii, and xviii. Geminos even stretches the definition of the phenomena to include the astrological aspects of the zodiac signs, in chapter i. In summary, Geminos, in his account of the celestial phenomena, extended the tradition of topics treated to include virtually anything having to do with the fixed stars, the Sun, and the Moon. And he did so in a way that was not simply systematic or mathematical, but discursive and, in a broad sense of the word, scientific.

     Geminos?s Introduction to the Phenomena is but one of several Greek elementary textbooks of astronomy that survive from Antiquity. The two most nearly comparable examples are Theon of Smyrna?s Mathematical Knowledge Useful for Reading Plato21 (second century a.d.) and Kleomedes? Meteora22 (probably early third to mid-fourth century a.d.). These three surveys have a fair amount of overlap?for example, they all discuss the eccentric-circle theory of the motion of the Sun. But each of the three also treats subjects not covered by the other two. For example, Theon of Smyrna gives an introduction to the deferent-and-epicycle theory of planetary motion, a subject avoided by Kleomedes and Geminos. Kleomedes, for his part, is our most detailed source for the famous measurement of the Earth by Eratosthenes. And Geminos gives a detailed discussion of lunisolar cycles, a subject avoided by Theon and Kleomedes.

     These three textbooks of astronomy also differ markedly in tone. While Theon?s book is pervaded by Platonism, Kleomedes? book is steeped in Stoic physics and concludes with a savage attack on the Epicureans. Theon and Kleomedes, then, give us nice examples of how an introduction to astronomy could be incorporated into a general course in philosophy?and we have examples in two flavors, Platonist and Stoic. By contrast, Geminos?s Introduction to the Phenomena is remarkable for its comparative freedom from philosophy, for he is very much a straightforward astronomer. Geminos does, however, display a certain literary bent, and is fond of quoting poets, such as Aratos or Homer, in illustration of astronomical points. His Introduction to the Phenomena is also considerably earlier than the textbooks of Theon and Kleomedes, and sheds light on the Greeks? reactions to Babylonian astronomy and astrology, which, in Geminos?s day, were in the process of being absorbed and adapted.

     An earlier, though shorter and much less polished, survey of astronomy is the Celestial Teaching (Ouranios Didascalea) of Leptines.23 See fig. I.1. This famous papyrus, conserved in the Louvre, is the oldest existing Greek astronomical document with illustrations. It was composed in the decades before 165 b.c. by a certain Leptines as an introduction to astronomy for members of the Ptolemaic court. (So it seems that, despite what Euclid is supposed to have said about geometry, there was a royal road to astronomy.) Modern writers sometimes refer to this tract as the ?Art of Eudoxos,? a name that comes from an acrostic poem on the verso of the papyrus, in which the initial letters of the twelve lines of verse spell out Eudoxou Techne. But the colophon on the recto clearly gives the title as the Ouranios Didascalea of Leptines. In any case, the contents of the treatise are certainly not by Eudoxos. Rather, the tract is a brief and rather choppy account of standard astronomical matters. The text includes a short parapegma, an account of the progress of the Sun and Moon around the zodiac, descriptions of the circles on the celestial sphere, a discussion of eclipses, and values for the lengths of the four seasons according to various authorities. This fare overlaps considerably with the material treated more gracefully by Geminos in the next century.

     Finally, numerous commentaries on Aratos?s poem Phenomena often served as introductions to astronomy. One of the most complete is that of Achilleus (often called Achilles Tatius, probably third century a.d.), whose Introduction to the ?Phenomena? of Aratos formed a part of his On the All (Peri tou Pantos).24 In our commentary on Geminos, we shall occasionally make comparisons to these other works, which can be thought of as constituting a genre of elementary astronomy textbooks.

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                          Geminos's Introduction to the Phenomena:
        A Translation and Study of a Hellenistic Survey of Astronomy

James Evans & J. Lennart Berggren


Part 5 of 6

     5. GEMINOS?S SOURCES FOR HIS INTRODUCTION

     Appendix 4 lists the writers that Geminos cites in his Introduction to the Phenomena.    He enjoys quoting the poets Homer, Hesiod, and Aratos in illustration of scientific points. This reflects not only his own tastes but also his concession to the literary training of his students and readers. He is not, however, one to ascribe too much scientific knowledge to Homer, and feels that critics such as Krates have sometimes gone overboard in this regard. (The occasional use of poetry occurs in other elementary surveys as well, e.g., those of Kleomedes, Theon of Smyrna, and Leptines.)

    Of the astronomical writers, Geminos names Euktemon, Kallippos, Philippos, Eratosthenes, and Hipparchos, though he may not have known the works of all these people firsthand. Geminos was quite well-informed about lunisolar cycles, but we cannot tell from his remarks on those matters whose works he really had access to. He seems to have used some work of Hipparchos on the constellations that was different from Hipparchos?s Commentary on The Phenomena of Eudoxos and Aratos. For, in chapter iii, he mentions three decisions of Hipparchos regarding the constellations that have no counterpart in the Commentary. The clearest and most significant of these is the attribution of the constellation Equuleus (Protome hippou) to Hipparchos. Geminos?s is the first mention of this constellation in the Greek tradition. Perhaps it comes from Hipparchos?s star catalogue. In any case, Ptolemy adopted this constellation name in the Almagest. Among writers on such geographical questions as mountain heights, the extent of Ocean, and the arrangement and habitability of the zones, Geminos cites Dikaiarchos, Pytheas, Kleanthes, and Polybios.

     Geminos was clearly influenced by the Stoic Poseidonios in his philosophical musings and in his work on meteorology. (See fragment 2.) In sec. 7 we address the controversial question of whether Geminos, in writing the Introduction to the Phenomena, might have used a lost textbook of Stoic astronomy and physics written by Poseidonios. Here, it suffices to point out that he does not mention Poseidonios a single time in the Introduction to the Phenomena. The material of Geminos?s Introduction consists largely of notions that were the common property of all astronomers. His contribution was in the selection and shaping of material, in his graceful prose, and in the tasteful incorporation of literary examples.25 He would have needed no help from Poseidonios for this.

     But Geminos does leave some of his most important sources unnamed. For as we have seen, and though he does not cite them by name, Geminos clearly knows the material in Euclid?s Phenomena, Autolykos?s On the Moving Sphere and On Risings and Settings, and Theodosios?s On Habitations and On Days and Nights. We shall see below that he probably knew also Hypsikles of Alexandria?s Anaphorikos. Geminos?s merit as a teacher is to absorb all this rather dry mathematical material and transform it into graceful prose?though often at the expense of the original mathematical rigor.

     Highly significant are Geminos?s citations of the ?Chaldeans,? by which he means Babylonian astronomers. We should say a few words about this term. The Chaldeans were a group of tribes who moved into southern Mesopotamia by about 1000 b.c. They assumed a growing importance, and in the eighth century succeeded in putting a king on the throne of Babylonia. Within a few decades, the Chaldean kings lost control to the Assyrian kings, who intervened repeatedly in Babylonian affairs. But under Nabopolassar a new Chaldean dynasty was established, which ruled Babylonia from 625 b.c. until the Persian conquest in 539.26 Ancient Greek writers often used the term ?Chaldeans? (Chaldaioi) simply to mean Babylonians. But because Babylon had a reputation for arcane knowledge, ?Chaldean? also came to mean an astronomer or astrologer of Babylon. Here are a few examples that span the range of meanings from ?Babylonian? to ?astronomer of Babylon? to ?astrologer or magus?: In the Almagest, Ptolemy refers to the ?Chaldean? (i.e., Babylonian) calendar. Vitruvius says that Berossus came from the ?Chaldean city or nation? to spread the learning of this people. Theon of Smyrna says that the Chaldeans save the phenomena by using arithmetic procedures. For Herodotos, the Chaldeans are priests of Bel (i.e., Marduk). This is quite reasonable, since astronomy and astrology were concentrated in the temples, and many of the practitioners were priestly scribes. In Daniel 2.2?4, the Chaldeans are interpreters of dreams and are associated with magicians and sorcerers. For Sextus Empiricus, Chaldeans are astrologers.27

     By about 300 b.c. the Babylonians had developed very successful theories for the motions of the planets, Sun, and Moon. These theories were based upon arithmetic rules, rather than on the geometrical models that characterized the Greek approach. When the Greeks began to deal quantitatively with planetary theory, they were able to base their geometrical models on numerical parameters borrowed from the Babylonians. This process was well under way in the second century b.c. In the Almagest (second century a.d.), Ptolemy begins with planetary periods that he ascribes to Hipparchos (second century b.c).28 But in fact these parameters were of Babylonian origin and turn up on cuneiform tablets. In his discussion of the Moon?s mean motions, Ptolemy again starts with Hipparchos?s values, but in this case says explicitly that Hipparchos had made use of Chaldean observations.29 Hipparchos?s works on lunar and planetary theory have not come down to us, so we do not know exactly how he came into contact with the Babylonian parameters.

     In the period between Hipparchos and Ptolemy, the Greek geometrical planetary theories had not yet reached maturity, and were not capable of yielding accurate numerical values for planet positions. But the rise of astrology (which entered the Greek world from Babylonia in the second or first century b.c.) imposed a need for quick, reliable methods of calculating planetary phenomena. Greek astronomers and astrologers adopted the Babylonian planetary theories with enthusiasm. Astronomical papyri from Egypt show Greeks of the first century a.d. using Babylonian planetary theories with complete facility. Ptolemy?s publication of his planetary theories and tables in the Almagest and the Handy Tables produced a major change in the way practical astronomy was done. But calculating methods based on Babylonian procedures still existed side by side with methods based on Ptolemy?s tables in the fourth century a.d.

     In chapter ii of the Introduction to the Phenomena, Geminos shows that he is familiar with some features of Chaldean astrology, though he mentions only a few doctrines in passing, and does not seem intensely interested in the subject. In any case, nothing about the level of his familiarity with Chaldean astrology is surprising for a writer of his time. Far more detailed and more historically significant is Geminos?s discussion of the Babylonian lunar theory in chapter xviii. His discussion there is important because his is the oldest extant classical text to display familiarity with the technical details of a Babylonian planetary theory based on an arithmetic progression. In particular, Geminos explains a scheme for the motion of the Moon, according to which the daily displacement increases by equal intervals from day to day, until it reaches a maximum, then falls by equal increments from one day to the next. The numerical parameters of Geminos?s theory are in exact agreement with cuneiform sources. Geminos?s treatment of the Babylonian lunar theory is discussed below in sec. 13, below, where we also address the question of the form that his source for the Babylonian lunar theory might have taken. In chapter xi, Geminos mentions that eclipses of the Moon take place in an eclipse zone (ekleiptikon) that is 2 degrees wide. Though he does not mention the Chaldeans in this passage, the 2-degree eclipse zone also comes from Babylonian astronomy. In total, Geminos?s remarks provide important information about the adoption and adaptation of Babylonian knowledge by the Greeks of his time. By contrast, Geminos cites the ?Egyptians? simply for the general structure of the Egyptian calendar and the circumstances of a festival of Isis.

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Geminos's Introduction to the Phenomena:
A Translation and Study of a Hellenistic Survey of Astronomy

James Evans & J. Lennart Berggren


Part 6 of 6

                                          6. GEMINOS?S COUNTRY AND DATE

     Modern scholars sometimes refer to our astronomer as ?Geminos of Rhodes,?30 but there is no ancient mention of his native land or city. The few ancient writers who cite him refer to him simply as Geminos, or as ?Geminos the mathematician.? The evidence for placing him in Rhodes is suggestive, but not conclusive. In several passages in the Introduction to the Phenomena, Geminos uses Rhodes as an example in making some astronomical point?involving the length of the longest day, or the portion of the summer tropic cut off above the horizon, or the meridian altitude of the star Canopus, or the date of the morning rising of the Dog Star.31 But although he does use Rhodes most frequently for such examples, he also gives examples for Alexandria, Greece, Rome, and the Propontis.32 Does his proclivity for using Rhodes suggest a fondness for his native city, or merely reflect Rhodes?s usefulness in astronomical examples, owing to its roughly central location in the Greek world? Geminos remarks (xiv 12) that celestial globes and armillary spheres were commonly constructed for this klima, or band of latitude. And it is noteworthy that in the second century a.d., Ptolemy, who lived at Alexandria, still found it natural to construct examples for the parallel through Rhodes, ?where the elevation of the pole is 36 degrees and the longest day 141⁄2 hours.?33 Or perhaps, as Dicks suggests,34 Geminos?s use of the klima of Rhodes reflects examples he found in his sources, which may have included the geographical or astronomical works of Hipparchos. Blass makes an interesting point about Geminos?s use of two geographical examples. Geminos (xvii 3) refers to Mt. Kyllene, and immediately specifies that it is ?the highest mountain in the Peloponnesos?; but in the very next sentence he refers to Mt. Atabyrion without making any similar specification that it is on the island of Rhodes.35 Does this suggest that he expected his readers to be familiar with Rhodian geography?

     Finally, we know that Geminos wrote some sort of abridgment of, or commentary on, the Meteorology of Poseidonios, whose native land was Rhodes. And a likely dating of Geminos?s Introduction to the Phenomena would make Geminos a younger contemporary of Poseidonios, and thus potentially his student. (Geminos?s possible debts to Poseidonios will be discussed below.) Near the end of her own discussion of this issue, Aujac concludes, ?Let us allow, then, since no other better hypothesis presents itself, that Geminos was born at Rhodes and that he there received his first instruction.?36 This is not an unreasonable position to take, since no convincing evidence exists for placing him elsewhere.37 But we simply do not know. In any case, as Tannery has pointed out,38 all the writers who cited Geminos were associated with Alexandria or with Athens, which suggests that his works circulated mainly in the Greek world of the eastern Mediterranean.

     Whether Geminos is a Greek name or a Hellenization of a Latin name (Geminus) has been the subject of dispute. As Aujac remarks, ?Petau made it a Latin name, Manitius a Greek name, Tittel again a Latin name (!)?39 A crucial point in the argument is the length of the central vowel? a long vowel favoring the Greek. Whatever the origin of his name, Geminos was thoroughly Greek in education, intellectual interests, and manner of expression.

     But when did Geminos write? There are two ways to narrow the possibilities. Appendix 4 lists the writers that Geminos mentions. The latest datable writers cited in the Introduction to the Phenomena are Hipparchos, Polybios, and Krates of Mallos, who all flourished in the middle of the second century b.c. Conversely, Geminos was quoted by Alexander of Aphrodisias, the Aristotelian commentator, who flourished at the end of the second century a.d. Thus we may place Geminos between 150 b.c. and a.d. 200.

     It appears possible to date Geminos more closely by his remark (viii 20?22) concerning the wandering year of the Egyptians:

. . . most of the Greeks suppose the winter solstice according to Eudoxos to be at the same time as the feasts of Isis [reckoned] according to the Egyptians, which is completely false. For the feasts of Isis miss the winter solstice by an entire month. . . . 120 years ago the feasts of Isis happened to be celebrated at the winter solstice itself. But in 4 years a shift of one day arose; this of course did not involve a perceptible difference with respect to the seasons of the year. . . . But now, when the difference is a month in 120 years, those who take the winter solstice according to Eudoxos to be during the feasts of Isis [reckoned] according to the Egyptians are not lacking an excess of ignorance.
The feasts of Isis (ta Isia) were celebrated at a fixed date in the Egyptian year. But as the Egyptian year consists of 365 days (with no leap day), the feast days shift with respect to the solstice by 1 day every 4 years. Because the Egyptian year is too short, the feast days gradually fall earlier and earlier in the natural, or solar, year. If we knew the Egyptian calendar date on which this Isis festival was observed, it would be easy to calculate the year in which the festival coincided with the winter solstice. We would then place Geminos 120 years after that year.

     Most writers on the subject have tried to date Geminos by the use of a remark by Plutarch (late first to early second century a.d.):

. . . they say that the disappearance of Osiris occurred in the month of Athyr. . . . Then, among the gloomy rites which the priests perform, they shroud the gilded image of a cow with a black linen vestment, and display her as a sign of mourning for the goddess, inasmuch as they regard both the cow and the Earth as the image of Isis; and this is kept up for four days consecutively, beginning with the seventeenth of the month.40
Denis Petau, in his Uranologion of 1630,41 used Plutarch?s remark to date Geminos?s composition, with the following result:

year 4537 of the Julian period,
fourth year of Olympiad 175,
year 677 after the founding of Rome,

or, as we would say, 77 b.c. Petau was followed by most later writers on the subject, with only minor adjustments. Thus, most writers who have accepted this evidence put Geminos?s composition of the Introduction to the Phenomena in the 60s or 70s b.c.42 But as we shall see, the margin of error should be taken quite a bit wider.

     The reasoning is straightforward. Let us work with 19 Athyr, the 3rd day of the 4-day festival. Athyr is the 3rd month of the Egyptian calendar, so 19 Athyr is the 79th day of the Egyptian year.43 In Table I.1, the first column lists years of the Julian calendar. In the second column, we have written the date of 1 Thoth, the 1st day of the Egyptian year that began in the course of the given Julian calendar year.44 Thus, in −200, a new Egyptian year began on 12 October.45 To obtain column 3, we add 78 days to the dates in column 2. In this way, we move from the 1st day of the Egyptian year (1 Thoth) to the 79th day (19 Athyr). Thus, in the Julian year −200, the 19th of Athyr fell on 29 December. The 4th column gives the date of the winter solstice46 for each of the given Julian calendar years. Comparing the 3rd and 4th columns, we see that the winter solstice fell on 19 Athyr sometime between −200 and −150. Interpolation gives −179. Geminos wrote 120 years later, or around the year −59.

     An error of 3 days in the date of the solstice could shift the date by ?12 years.47 Again, Geminos speaks in rough fashion of a whole month, as the difference by which the Isis festival missed the solstice in his own day. He might have spoken in this same way if the actual difference were, say, as small as 28 days or as great as 32, which introduces another ?8 years of uncertainty. Finally, the festival itself stretched over a period of 4 days, which gives us 4 more years of uncertainty after 60 b.c. and 8 more years before. Putting all this together, we find the period 88?36 b.c. as the most likely for the composition of the Introduction to the Phenomena, or, to speak in round numbers, 90?35 b.c.

     In 1975, Otto Neugebauer proposed a date for Geminos about a century later, around a.d. 50.48 Although Neugebauer?s dating was influential for a while, we shall see that it can no longer be sustained. The argument that follows will be somewhat intricate. But at the end we shall not abandon the dating of 90?35 b.c. that we have just explained. Thus, readers with little enthusiasm for details of ancient chronology should feel no guilt in skipping ahead to the next section.

     The key question that Neugebauer posed is whether Petau?s argument, based on Plutarch?s remark, involved a confusion between the Egyptian and the Alexandrian calendars. After Egypt became a province of the Roman empire, Augustus reformed the Egyptian calendar by introducing a leap day once every four years, the first such day being inserted at the end of the Egyptian year 23/22 b.c. In the reformed calendar, now usually called ?Alexandrian? to distinguish it from the original Egyptian calendar, three years of 365 days were followed by a year of 366 days. The reformed calendar thus was very similar to the Julian calendar, which had been used at Rome since 45 b.c. Of course, the Alexandrian calendar continued to use the old Egyptian months of 30 days each, as well as the original Egyptian month names. For dates near 23 b.c., a given day has nearly the same date in both the Egyptian and the Alexandrian calendars. But gradually, at the rate of 1 day in 4 years, the calendars diverge. Moreover, the two calendars continued to be used side by side. For example, Ptolemy, in the Almagest, used the old calendar for astronomical calculation, because of its simpler structure, nearly two centuries after it had been abandoned for civil use. In his parapegma, however, Ptolemy adopted the Alexandrian calendar, because the heliacal risings and settings of a given star have more nearly fixed dates in this calendar. When an ancient writer, writing after Augustus?s reform, says ?the 17th of Athyr,? it is not immediately clear whether he is expressing the date in terms of the Egyptian calendar or the Alexandrian calendar. One must examine the context carefully.

     Neugebauer was troubled by a second reference in Plutarch to what was apparently the same Isis festival:

. . . then Osiris got into [the chest] and lay down, and those who were in the plot ran to it and slammed down the lid, which they fastened by nails from the outside and also by using molten lead. They say also that the date on which this deed was done was the seventeenth of Athyr, when the Sun passes through Scorpio. . . . 49
We have again the date Athyr 17, but now with the added information that the Sun passes through Scorpio during the month of Athyr. As Neugebauer pointed out, this was true in the Alexandrian, but not in the Egyptian calendar, for Plutarch?s time. The Alexandrian month of Athyr runs from 28 October to 26 November (Julian), which corresponds rather closely to the sign of Scorpio. In Plutarch?s time, say a.d. 118, the Egyptian and Alexandrian calendars were out of phase by 35 days: 1 Athyr (Egyptian) then fell on September 23 (Julian), corresponding to the Sun?s entry into Libra, not Scorpio. Neugebauer concluded that Plutarch was using the Alexandrian, and not the Egyptian, calendar. Moreover, he surmised that Plutarch (or his source) took the original date of the Isis festival, as expressed in the Egyptian calendar, and converted it to an Alexandrian equivalent. The Alexandrian calendar was, after all, the one in official use, and the one more likely to be understood by Plutarch?s readers in the wider Roman world.

     Neugebauer found the Egyptian date for what he took to be the same festival in a hieroglyphic text in the East Osiris Chapel on the roof of the Temple of Hathor in Dendera.50 The text describes the rituals of an Osiris festival that lasted from 12 to 30 Choiak. The text is not later than 30 b.c. and thus predates the reform of the calendar. Moreover, as Neugebauer also pointed out, the papyrus Hibeh 27 (c. 300 b.c.) mentions an Osiris festival on 26 Choiak.51 Now in Plutarch?s time (a.d. 118), the date 26 Choiak (Egyptian) = 21 Athyr (Alexandrian), which appeared to confirm Plutarch?s use of the Alexandrian calendar when he placed the rites on 17?20 Athyr. Neugebauer then computed the year when the winter solstice fell on 15 Choiak (Egyptian). (This date is within the span of rituals mentioned by the text in the East Osiris Chapel.) The answer is the year −70; Geminos wrote 120 years later, or around a.d. 50, according to Neugebauer. The new dating by Neugebauer, pushing Geminos forward into the first century a.d., was gradually adopted by historians of ancient astronomy.

     Alexander Jones reexamined the question in 1999.52 As Jones points out, Neugebauer deserved credit for being the first to use papyrological evidence for the date of the Isis festival. The advantage of such evidence is that it comes from a time when the Isis festival was a living custom, that it comes directly from Egypt without having passed through the hands of other writers, and that some of it comes from a date before the reform of the Egyptian calendar, thus removing any possibility of confusion between the calendars. But there was much more such evidence (in both the Greek and Egyptian languages) available than Neugebauer had realized.

     Jones adduces a good deal of evidence showing that Neugebauer had wrongly taken the Osiris festival of 12 to 30 Choiak (Egyptian) to be the same festival as the Isia that Plutarch mentions. Jones also points out that Geminos refers to the festival simply as ta Isia, without any further specification. This implies that the festival was so well known that Geminos had no fear that it would be confused by his readers with other festivals associated with Isis or Osiris. Now, as Jones points out, there are at least nineteen references in Greek papyri to a festival called the Isia (also spelled Iseia or Isieia). Only a few of these provide calendrical information. But enough do that it is possible to confirm Plutarch?s dates of

50 For a bibliography pertaining to this text, see Porter and Moss 1927, vol. 6, 97.
51 Grenfell and Hunt 1906, 144, 148.
52 Jones 1999a. 17?20 Athyr, and to be sure that these dates indeed apply to the old (Egyptian) calendar. For example, several papyri from before the calendar reform are private letters or records, with dates in Athyr, concerned with ordering or issuing supplies (logs and lamp oil) for the Isia. One papyrus gives the dates of the Isia in terms of the Macedonian calendar. These dates can be converted to the Egyptian calendar (with an uncertainty of 1 day) and indeed correspond to 17?20 Athyr. Slightly altering the chronological assumptions and broadening the error bars, Jones concludes that it is very probable that Geminos wrote his Introduction to the Phenomena ?between 90 and 25 b.c., and definitely not during the first century of our era.?53 There is an irony in the fact, confirmed by the papyri, that after the calendar reform, the Isia continued to be celebrated on days called 17?20 Athyr, but in the new calendar. Thus, Plutarch?s dates turn out to refer to the reformed calendar after all! (But they should not be converted back into the old calendar to obtain the dates that Geminos would have been familiar with.)

     One minor problem with dating Geminos to the first century b.c. involves his mention of Hero of Alexandria in fragment 1. The dating of Hero has been controversial, with suggested dates from the middle of the second century b.c. to the middle of the third century a.d.54 In Dioptra 35, however, Hero mentions a lunar eclipse observed simultaneously in Alexandria and Rome. Although Hero does not mention the year of the eclipse, he is detailed about its other circumstances: 10 days before the vernal equinox, 5th seasonal hour of the night at Alexandria. Neugebauer55 has shown that these circumstances were satisfied by only one lunar eclipse between about −200 and +300, namely that of March 13, a.d. 62. If Hero used an eclipse of recent memory, we must place him in the second half of the first century a.d. Thus, if the dating of Geminos to the first century b.c. is correct, we must suppose that Proklos or a later copyist interpolated the name of Hero in fragment 1.

     Finally, we note that Geminos writes about Babylonian astronomy and astrology as if they were still new to his Greek readers. This well suits a dating to the first century b.c., when this material was still being absorbed and adapted by the Greeks.56

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Many thanks, Bart: a most useful addition to our knowledge of the instrument.

Posidonius (http://en.wikipedia.org/wiki/Posidonius)
Posidonius (Greek: Ποσειδώνιος / Poseidonios) "of Rhodes" (ο Ρόδιος) or, alternatively, "of Apameia" (ο Απαμεύς) (ca. 135 BCE - 51 BCE), was a Greek Stoic philosopher, politician, astronomer, geographer, historian, and teacher. He was acclaimed as the greatest polymath of his age. None of his vast body of work can be read in its entirety today as it exists only in fragments.

Life
Posidonius (also spelled Poseidonius), nicknamed "the Athlete", was born to a Greek family in Apamea, a Roman city on the river Orontes in northern Syria, and probably died in Rome or Rhodes.

Posidonius completed his higher education in Athens, where he was a student of the aged Panaetius, the head of the Stoic school.

He settled around 95 BCE in Rhodes, a maritime state which had a reputation for scientific research, and became a citizen.

Political offices
In Rhodes, Posidonius actively took part in political life, and his high standing is apparent from the offices he held. He attained the highest public office as one of the prytaneis (presidents, having a six months tenure) of Rhodes. He served as an ambassador to Rome in 87 - 86 BCE, during the Marian and Sullan era.

Along with other Greek intellectuals, Posidonius favored Rome as the stabilizing power in a turbulent world. His connections to the Roman ruling class was for him not only politically important and sensible but was also important to his scientific researches. His entry into the highest government circles enabled Posidonius to undertake his travels into the west beyond the borders of Roman control, which, for a Greek traveler, would have been impossible without such Roman support.

Travels
After he had established himself in Rhodes, Posidonius made one or more journeys traveling throughout the Roman world and even beyond its boundaries to conduct scientific research. He traveled in Greece, Hispania, Africa, Italy, Sicily, Dalmatia, Gaul, Liguria, North Africa, and on the eastern shores of the Adriatic.

In Hispania, on the Atlantic coast at Gades (the modern Cadiz), Posidonius studied the tides. He observed that the daily tides were connected with the orbit and the monthly tides with the cycles of the Moon, and he hypothesized about the connections of the yearly cycles of the tides with the equinoxes and solstices.

In Gaul, he studied the Celts. He left vivid descriptions of things he saw with his own eyes while among them: men who were paid to allow their throats to be slit for public amusement and the nailing of skulls as trophies to the doorways. But he noted that the Celts honored the Druids, whom Posidonius saw as philosophers, and concluded that even among the barbaric 'pride and passion give way to wisdom, and Ares stands in awe of the Muses'. Posidonius wrote a geographic treatise on the lands of the Celts which has since been lost, but which has been assumed to be one of the sources for Tacitus Germania.

School
Posidonius's extensive writings and lectures gave him authority as a scholar and made him famous everywhere in the Graeco-Roman world, and a school grew around him in Rhodes. His grandson Jason, who was the son of his daughter and Menekrates of Nysa, followed in his footsteps and continued Posidonius's school in Rhodes. Although little is known of the organization of his school, it is clear that Posidonius had a steady stream of Greek and Roman students.

Partial scope of writings
Posidonius was celebrated as a polymath throughout the Greco-Roman world because he came near to mastering all the knowledge of his time, similar to Aristotle and Eratosthenes. He attempted to create a unified system for understanding the human intellect and the universe which would provide an explanation of and a guide for human behavior.

Posidonius wrote on physics (including, meteorology and physical geography), astronomy, astrology and divination, seismology, geology and mineralogy, hydrology, botany, ethics, logic, mathematics, history, natural history, anthropology, and tactics. His studies were major investigations into their subjects, although not without errors.

None of his works survive intact. All that we have found are fragments, although the titles and subjects of many of his books are known.[1]

Philosophy
For Posidonius, philosophy was the dominant master art and all the individual sciences were subordinate to philosophy, which alone could explain the cosmos. All his works, from scientific to historical, were inseparably philosophical.

He accepted the Stoic categorization of philosophy into physics (natural philosophy, including metaphysics and theology), logic (including dialectic), and ethics. These three categories for him were, in Stoic fashion, inseparable and interdependent parts of an organic, natural whole. He compared them to a living being, with physics the meat and blood, logic the bones and tendons which held the organism together, and ethics ? the most important part ? the soul. His philosophical grand vision was that the universe itself was similarly interconnected, as if an organism, through cosmic "sympathy", in all respects from the development of the physical world to the history of humanity.

Although a firm Stoic, Posidonius was, like Panaetius and other Stoics of the middle period, eclectic. He followed not only the older Stoics, but Plato and Aristotle. Although it is not certain, Posidonius may have written a commentary on Plato's Timaeus.

He was the first Stoic to depart from the orthodox doctrine that passions were faulty judgments and posit that Plato's view of the soul had been correct, namely that passions were inherent in human nature. In addition to the rational faculties, Posidonius taught that the human soul had faculties that were spirited (anger, desires for power, possessions, etc.) and desiderative (desires for sex and food). Ethics was the problem of how to deal with these passions and restore reason as the dominant faculty.

Posidonius upheld the Stoic doctrine of Logos, which ultimately passed into Judeo-Christian belief. Posidonius also affirmed the Stoic doctrine of the future conflagration.

Physics
In Stoic physics, Posidonius advocated a theory of cosmic "sympathy", the organic interrelation of all appearances in the world, from the sky to the earth, as part of a rational design uniting humanity and all things in the universe, even those that were temporally and spatially separate. Although his teacher Panaetius had doubted divination, Posidonius used the theory of cosmic sympathy to support his belief in divination - whether through astrology or prophetic dreams - as a kind of scientific prediction.

Astronomy
Some fragments of his writings on astronomy survive through the treatise by Cleomedes, On the Circular Motions of the Celestial Bodies, the first chapter of the second book appearing to have been mostly copied from Posidonius.

Posidonius advanced the theory that the Sun emanated a vital force which permeated the world.

He attempted to measure the distance and size of the Sun. In about 90 BCE Posidonius estimated the astronomical unit to be a0/rE = 9893, which was still too small by half. In measuring the size of the Sun, however, he reached a figure larger and more accurate than those proposed by other Greek astronomers and Aristarchus of Samos.

Posidonius also calculated the size and distance of the Moon.

Posidonius constructed an orrery, possibly similar to the Antikythera mechanism. Posidonius's orrery, according to Cicero, exhibited the diurnal motions of the sun, moon, and the five known planets.

Geography, ethnology and geology
Poseidonios?s fame beyond specialized philosophical circles had begun, at the latest, in the eighties with the publication of the work "about the ocean and the adjacent areas". This work was not only an overall representation of geographical questions according to current scientific knowledge, but it served to popularize his theories about the internal connections of the world, to show how all the forces had an effect on each other and how the interconnectedness applied also to human life, to the political just as to the personal spheres. In this work, Posidonius detailed his theory of the effect on a people?s character by the climate, which included his representation of the "geography of the races". This theory was not solely scientific, but also had political implications -- his Roman readers were informed that the climatic central position of Italy was an essential condition of the Roman destiny to dominate the world. As a Stoic he did not, however, make a fundamental distinction between the civilized Romans as masters of the world and the less civilized peoples.

Posidonius measured Earth's circumference from the position of the star Canopus. As explained by Cleomedes, Posidonius used the elevation of Canopus, to determine the difference in latitude between Rhodes and Alexandria. Due to observational errors, his result was about 24,000 miles. This was 1,000 miles less than the distance calculated by Eratosthenes but still very close to the correct distance of 24,901 miles. See history of geodesy and Greek distances.

Like Pytheas, he believed the tide is caused by the Moon. Posidonius was, however, wrong about the cause. Thinking that the Moon was a mixture of air and fire, he attributed the cause of the tides to the heat of the Moon, hot enough to cause the water to swell but not hot enough to evaporate it.

He recorded observations on both earthquakes and volcanoes, including accounts of the eruptions of the volcanoes in the Aeolian Islands, north of Sicily.

Meteorology
Posidonius in his writings on meteorology followed Aristotle. He theorized on the causes of clouds, mist, wind, and rain as well as frost, hail, lightning, and rainbows.

Mathematics
In addition to his writings on geometry, Posidonius was credited for creating some mathematical definitions, or for articulating views on technical terms, for example 'theorem' and 'problem'.

History and tactics
In his Histories, Posidonius continued the World History of Polybius. His history of the period 146 - 88 BCE is said to have filled 52 volumes. His Histories continue the account of the rise and expansion of Roman dominance, which he appears to have supported. Posidonius did not follow Polybius's more detached and factual style, for Posidonius saw events as caused by human psychology; while he understood human passions and follies, he did not pardon or excuse them in his historical writing, using his narrative skill in fact to enlist the readers' approval or condemnation.

For Posidonius "history" extended beyond the earth into the sky; humanity was not isolated each in its own political history, but was a part of the cosmos. His Histories were not, therefore, concerned with isolated political history of peoples and individuals, but they included discussions of all forces and factors (geographical factors, mineral resources, climate, nutrition), which let humans act and be a part of their environment. For example, Posidonius considered the climate of Arabia and the life-giving strength of the sun, tides (taken from his book on the oceans), and climatic theory to explain people?s ethnic or national characters.

Of Posidonius's work on tactics, The Art of War, the Roman historian Arrian complained that it was written 'for experts', which suggests that Posidonius may have had first hand experience of military leadership or, perhaps, utilized knowledge he gained from his acquaintance with Pompey.

Reputation and influence
In his own era, his writings on almost all the principal divisions of philosophy made Posidonius a renowned international figure throughout the Graeco-Roman world and he was widely cited by writers of his era, including Cicero, Livy, Plutarch, Strabo (who called Posidonius "the most learned of all philosophers of my time"), Cleomedes, Seneca the Younger, Diodorus Siculus (who used Posidonius as a source for his Bibliotheca historia ("Historical Library"), and others. Although his ornate and rhetorical style of writing passed out of fashion soon after his death, Posidonius was acclaimed during his life for his literary ability and as a stylist.

Posidonius appears to have moved with ease among the upper echelons of Roman society as an ambassador from Rhodes. He associated with some of the leading figures of late republican Rome, including Cicero and Pompey, both of whom visited him in Rhodes. In his twenties, Cicero attended his lectures (77 BCE) and they continued to correspond. Cicero in his De Finibus closely followed Posidonius's presentation of Panaetius's ethical teachings. Posidonius met Pompey when he was Rhodes's ambassador in Rome and Pompey visited him in Rhodes twice, once in 66 BCE during his campaign against the pirates and again in 62 BCE during his eastern campaigns, and asked Posidonius to write his biography. As a gesture of respect and great honor, Pompey lowered his fasces before Posidonius's door. Other Romans who visited Posidonius in Rhodes were Velleius, Cotta, and Lucilius.

Ptolemy was impressed by the sophistication of Posidonius's methods, which included correcting for the refraction of light passing through denser air near the horizon. Ptolemy's approval of Posidonius's result, rather than Eratosthenes's earlier and more correct figure, caused it to become the accepted value for the Earth's circumference for the next 1,500 years.

Posidonius fortified the Stoicism of the middle period with contemporary learning. Next to his teacher Panaetius, he did most, by writings and personal contacts, to spread Stoicism in the Roman world. A century later, Seneca referred to Posidonius as one of those who had made the largest contribution to philosophy.

His influence on philosophical thinking lasted until the Middle Ages, as is shown by citation in the Suda, the massive medieval lexicon.

At one time, scholars perceived Posidonius's influence in almost every subsequent writer, whether warranted or not. Today, Posidonius seems to be recognized as having had an inquiring and wide-ranging mind, not entirely original, but with a breadth of view that connected, in accordance with his underlying Stoic philosophy, all things and their causes and all knowledge into an overarching, unified world view.

The Posidonius crater on the Moon is named for him.

Cleomedes (http://en.wikipedia.org/wiki/Cleomedes)
Cleomedes was a Greek astronomer who is known chiefly for his book On the Circular Motions of the Celestial Bodies.

Placing his work chronologically
His birth and death dates are not known--historians have suggested that he wrote his work sometime between the mid-1st Century B.C. and 400 C.E. The earlier estimates rely on the fact that Cleomedes refers extensively in his writing to the work of mathematician and astronomer Posidonius of Rhodes (135 BC-51 BC), and yet seemingly not at all to the work of Ptolemy (85-165 C.E.). These conclusions have been challenged on the grounds that Cleomedes' work was in relatively elementary astronomy, and that reference to Ptolemy would not necessarily be expected. The 20th Century mathematician Otto Neugebauer, however, looked closely at the astronomical observations made by Cleomedes, and concluded that a date of 371 C.E. (?50 years) better explains what is found there. Neugebauer's estimate has been challenged on the grounds that Cleomedes makes observational errors with enough frequency that there is difficulty in deciding which observations to trust for the purpose of dating his work.

On the Circular Motions of the Celestial Bodies
The book for which Cleomedes is known is a fairly basic astronomy textbook in two volumes. His purpose in writing seems to have been as philosophical as it was scientific--he spends an extensive amount of time criticizing the (admittedly fallacious) scientific ideas of the Epicureans (Cleomedes appears to have been a dedicated Stoic).

Cleomedes' book is criticized by most modern astronomers as being poorly written--it is valued primarily for preserving, apparently verbatim, much of Posidonius' writings on astronomy (none of Posidonius' books have survived to the modern day). Cleomedes is accurate in some of his remarks on lunar eclipses, especially his conjecture that the shadow on the Moon suggests a spherical Earth. He also remarks presciently that the absolute size of many stars may exceed that of the Sun (and that the Earth might appear as a very small star, if viewed from the surface of the Sun).

This book is the original source for the well-known story of how Eratosthenes measured the Earth's circumference. Although the story is now believed by some to be purely legendary, many modern mathematicians and astronomers believe the description to be reasonable (and believe Eratosthenes' achievement to be one of the more impressive accomplishments of ancient astronomy).

Fragmentary Knowledge

Was the Antikythera Mechanism the world?s first computer?

by John Seabrook - May 14, 2007

   -In October, 2005, a truck pulled up outside the National Archeological Museum in Athens, and workers began unloading an eight-ton X-ray machine that its designer, X-Tek Systems of Great Britain, had dubbed the Bladerunner. Standing just inside the National Museum?s basement was Tony Freeth, a sixty-year-old British mathematician and filmmaker, watching as workers in white T-shirts wrestled the Range Rover-size machine through the door and up the ramp into the museum.

   Freeth was a member of the Antikythera Mechanism Research Project?a multidisciplinary investigation into some fragments of an ancient mechanical device that were found at the turn of the last century after two thousand years in the Aegean Sea, and have long been one of the great mysteries of science.

   Freeth, a tall, taciturn man with a deep, rumbling voice, had been a mathematician at Bristol University, taking a Ph.D. in set theory, a branch of mathematical logic. He had drifted away from the academy, however, and spent most of his career making films, many of them with scientific themes. The Antikythera Mechanism, which he had first heard about some five years earlier, had rekindled his undergraduate love of math and logic and problem-solving, and he had all but abandoned his film career in the course of investigating it.

   He was the latest in a long line of men who have made solving the mystery of the Mechanism their life?s work. Another British researcher, Michael Wright, who has studied the Mechanism for more than twenty years, was coincidentally due to arrive in Athens before the Bladerunner had finished its work. But Wright wasn?t part of the research project, and his arrival was anticipated with some trepidation.

   It had been Freeth?s idea to contact X-Tek in the hope of finding a high-resolution, three-dimensional X-ray technology to see inside the fragments of the Mechanism. As it happened, the company was working on a prototype of a CAT-scan machine that would use computer tomography to make 3-D X-rays of the blades inside airplane turbines, for safety inspections. Roger Hadland, X-Tek?s owner and chief engineer, was interested in Freeth?s proposal, and he and his staff developed new technology for the project.

   After the lead-lined machine was installed inside the museum, technicians spent another day attaching the peripheral equipment. At last, everything was ready. The first piece to be examined, Fragment D, was placed on the Bladerunner?s turntable. It was only about an inch and a half around?much smaller than Fragment A, the largest piece, which measures about six and a half inches across?and it looked like just a small greenish rock, or possibly a lump of coral.

   It was heavily corroded and calcified?the parts of the Mechanism almost indistinguishable from the petrified sea slime that surrounded them. Conservationists couldn?t clean off any more of the corroded material without damaging the artifact, and it was hoped that the latest in modern technology would reveal the ancient technology inside.

   The Bladerunner began to whirr. As the turntable rotated, an electron gun fired at a tungsten target, which emitted an X-ray beam that passed through the fragment, so that an image was recorded every time the turntable moved a tenth of a degree. A complete three-hundred-and-sixty-degree rotation, resulting in three thousand images or so, required about an hour. Then the computer required another hour to assemble all the images into a 3-D representation of what the fragment looked like on the inside.

   As Freeth waited impatiently for the first images to appear on the Bladerunner?s monitor, he was trying not to hope for too much, and to place his trust in the skills of the group of academics and technicians who were there with him. Among them, waiting with equal anticipation, were John Seiradakis, a professor of astronomy at the Aristotle University of Thessaloniki; Xenophon Moussas, the director of the Astrophysics Laboratory at the University of Athens; and Yanis Bitsakis, a Ph.D. student in physics. (Mike Edmunds, an astrophysicist at Cardiff University, who was the academic leader of the research project, remained in Wales.) ?I was just focussed on my relief that this was happening at all, with all the delays of the past four years,? Freeth told me. ?Honestly, there were times when I thought it would never happen.?

   One day in the spring of 1900, a party of Greek sponge divers returning from North Africa was forced by a storm to take shelter in the lee of the small island of Antikythera, which lies between Crete and Kythera. After the storm passed, one of the divers, Elias Stadiatis, put on a weighted suit and an airtight helmet that was connected by an air hose to a compressor on the boat, and went looking for giant clams, with which to make a feast that evening.

   The bottom of the sea dropped sharply, and the diver followed the underwater cliff to a shelf that was about a hundred and forty feet below the surface. On the other side of the shelf, an abyss fell away into total darkness. Looking around, Stadiatis saw the remains of an ancient shipwreck. Then he had a terrible shock. There were piles of bodies, all in pieces, covering the ledge. He grabbed one of the pieces before surfacing in order to have proof of what he had seen. It turned out to be a bronze arm.

   The following autumn, the sponge divers, now working for the Greek government, returned to the site, and over the next ten months they brought up many more pieces of sculpture, both marble and bronze, from the wreck, all of which were taken to the National Museum to be cleaned and reassembled.

   It was the world?s first large-scale underwater archeological excavation. Evidence derived from coins, amphorae, and other items of the cargo eventually allowed researchers to fix a date for the shipwreck: around the first half of the first century B.C., a time when the glorious civilization of ancient Greece was on the wane, following the Roman conquest of the Greek cities. Coins from Pergamum, a Hellenistic city in what is now Turkey, indicated that the ship had made port nearby.

   The style of the amphorae strongly suggested that the ship had called at the island of Rhodes, also on the eastern edge of the Hellenistic world, and known for its wealth and its industry. Given the reputed corruption of officials in the provinces of the Roman Empire, it is possible that the ship?s cargo had been plundered from Greek temples and villas, and was on its way to adorn the houses of aristocrats in Rome. The sheer weight of the cargo probably contributed to the ship?s destruction.

   Most of the marble pieces were blackened and pitted from their long immersion in the salt water, but the bronze sculptures, though badly corroded, were salvageable. Although bronze sculptures were common in ancient Greece, only a tiny number have survived (the bronze was often sold as scrap, melted down, and recast, possibly as weaponry), and most of those have been recovered from shipwrecks. Among the works of art that emerged from the waters near Antikythera are the bronze portrait of a bearded philosopher, and the so-called Antikythera Youth, a larger-than-life-size naked young man: a rare specimen of a bronze masterwork, believed to be from the fourth century B.C.

   Other artifacts included bronze fittings for wooden furniture, pottery, an oil lamp, and item 15087?a shoebox-size lump of bronze, which appeared to have a wooden exterior. Inside were what seemed to be fused metal pieces, but the bronze was so encrusted with barnacles and calcium that it was difficult to tell what it was. With so much early excitement focussed on the sculptures, the artifact didn?t receive much attention at first. But one day in May, 1902, a Greek archeologist named Spyridon Sta?s noticed that the wooden exterior had split open, probably as a result of exposure to the air, and that the artifact inside had fallen into several pieces.

   Looking closely, Sta?s saw some inscriptions, in ancient Greek, about two millimetres high, engraved on what looked like a bronze dial. Researchers also noticed precisely cut triangular gear teeth of different sizes. The thing looked like some sort of mechanical clock. But this was impossible, because scientifically precise gearing wasn?t believed to have been widely used until the fourteenth century?fourteen hundred years after the ship went down.

   The first analyses of what became known as the Antikythera Mechanism followed two main approaches. The archeologists, led by J. N. Svoronos, of the National Museum, thought that the artifact must have been ?a kind of astrolabe.? A Hellenistic invention, an astrolabe was an astronomical device that was widely known in the Islamic world by the eighth century and in Europe by the early twelfth century. Astrolabes were used to tell the time, and could also determine latitude with reference to the position of the stars; Muslim sailors often used them, in addition, to calculate prayer times and find the direction of Mecca.

   However, other researchers, led by the German philologist Albert Rehm, thought that the Mechanism appeared much too complex to be an astrolabe. Rehm suggested that it might possibly be the legendary Sphere of Archimedes, which Cicero had described in the first century B.C. as a kind of mechanical planetarium, capable of reproducing the movement of the sun, the moon, and the five planets that could be seen from Earth without a telescope?Mercury, Venus, Mars, Jupiter, and Saturn. Still others, acknowledging the artifact?s complexity, thought that it must have come from a much later shipwreck, which may have settled on top of the ancient ship (even though the Mechanism had plainly been crushed under the weight of the ship?s other cargo). But, in the absence of any overwhelming evidence one way or the other, until the nineteen-fifties the astrolabe theory held sway.

   Looking back over the first fifty years of research on the Mechanism, one is struck by the reluctance of modern investigators to credit the ancients with technological skill. The Greeks are thought to have possessed crude wooden gears, which were used to lift heavy building materials, haul up water, and hoist anchors, but historians do not generally credit them with possessing scientifically precise gears?gears cut from metal and arranged into complex ?gear trains? capable of carrying motion from one driveshaft to another.

   Paul Keyser, a software developer at I.B.M. and the author of ?Greek Science of the Hellenistic Era,? told me recently, ?Those scholars who study the history of science tend to focus on science beginning with Copernicus and Galileo and Harvey, and often go so far as to assert that no such thing existed before.? It?s almost as if we wished to reserve advanced technological accomplishment exclusively for ourselves. Our civilization, while too late to make the fundamental discoveries that the Greeks made in the sciences?Euclidean geometry, trigonometry, and the law of the lever, to name a few?has excelled at using those discoveries to make machines. These are the product and proof of our unique genius, and we?re reluctant to share our glory with previous civilizations.

   In fact, there is evidence that earlier civilizations were much more technically adept than we imagine they were. As Peter James and Nick Thorpe point out in ?Ancient Inventions,? published in 1994, some ancient civilizations were aware of natural electric phenomena and the invisible powers of magnetism (though neither concept was understood). The Greeks had a tradition of great inventors, beginning with Archimedes of Syracuse (c. 287-212 B.C.), who, in addition to his famous planetarium, is believed to have invented a terrible clawed device made up of large hooks, submerged in the sea, and attached by a cable to a terrestrial hoist; the device was capable of lifting the bow of a fully loaded warship into the air and smashing it down on the water?the Greeks reportedly used the weapon during the Roman siege of Syracuse around 212 B.C. Philon of Byzantium (who lived around 200 B.C.) made a spring-driven catapult. Heron of Alexandria (who lived around the first century A.D.) was the most ingenious inventor of all.

   He described the basic principles of steam power, and is said to have invented a steam-powered device in which escaping steam caused a sphere with two nozzles to rotate. He also made a mechanical slot machine, a water-powered organ, and machinery for temples and theatres, including automatic swinging doors. He is perhaps best remembered for his automatons?simulations of animals and men, cleverly engineered to sing, blow trumpets, and dance, among other lifelike actions.

   Although a book by Heron, ?Pneumatica,? detailing various of these inventions, has survived, some scholars have dismissed his descriptions as fantasy. They have pointed to the lack of evidence?no trace of any of these marvellous machines has been found. But, as other scholars have pointed out, the lack of archeological evidence isn?t really surprising. No doubt, the machines eventually broke down, and, as the know-how faded, there was no one around who could fix them, so they were sold as scrap and recycled. Very few technical drawings or writings remained, because, as Paul Keyser observes, ?the texts that survive tend to be the more popular texts?i.e., those that were more often copied?and textbooks, not the research works or the advanced technical ones.? Eventually, following the dissolution of the Roman Empire, the technological knowledge possessed by the Greeks disappeared from the West completely.

   But, if the Greeks did have greater technological sophistication than we think they did, why didn?t they apply it to making more useful things?time- and work-saving machines, for example?instead of elaborate singing automatons? Or is what we consider important about technology?which is, above all, that it is useful?different from what the Greeks considered worthwhile: amusement, enlightenment, delight for its own sake? According to one theory, the Greeks, because they owned slaves, had little incentive to invent labor-saving devices?indeed, they may have found the idea distasteful. Archimedes? claws notwithstanding, there was, as Keyser notes, cultural resistance to making high-tech war machines, because ?both the Greeks and the Romans valued individual bravery in war.? In any case, in the absence of any obvious practical application for Greek technology, it is easy to believe that it never existed at all.

   In 1958, Derek de Solla Price, a fellow at the Institute for Advanced Study, in Princeton, went to Athens to examine the Mechanism. Price?s interests fell between traditionally defined disciplines. Born in Britain, he trained as a physicist but later switched fields and became the Avalon Professor of the History of Science at Yale; he is credited with founding Scientometrics, a method of measuring and analyzing the pursuit of science. The study of the Mechanism, which incorporates elements of archeology, astronomy, mathematics, philology, classical history, and mechanical engineering, was ideally suited to a polymath like Price, and it consumed the rest of his life.

   Price believed that the Mechanism was an ancient ?computer,? which could be used to calculate astronomical events in the near or distant future: the next full moon, for example. He realized that the inscriptions on the large dial were calendrical markings indicating months, days, and the signs of the zodiac, and postulated that there must have been pointers, now missing, that represented the sun and the moon and possibly the planets, and that these pointers moved around the dial, indicating the position of the heavenly bodies at different times.

   Price set about proving these theories, basing his deductions on the fundamental properties of gearing. Gears work by transmitting power through rotational motion, and by realizing mathematical relationships between toothed gear wheels. The Mechanism concentrates on the latter aspect. Price seems to have assumed that the largest gear in the artifact, which is clearly visible in Fragment A, was tied to the movement of the sun?one rotation equalled one solar year. If another gear, representing the moon, was driven by the solar gear, then the ratio of wheels in this gear train must have been designed to match the Greeks? idea of the moon?s movements. By counting the number of teeth in each gear, you could calculate the gear ratios, and, by comparing those ratios to astronomical cycles, you can figure out which gears represented which movements.

   However, because only a few of the gears appear at the surface of the Mechanism, and because many of the gear teeth are missing, Price had to develop methods for estimating total numbers from partial tooth counts. Finally, in 1971, he and a Greek radiographer, Dr. C. Karakalos, were permitted to make the first X-rays of the Mechanism, and these two-dimensional images showed almost all the remaining gear teeth. Price developed a schematic drawing of a hypothetical reconstruction of the internal workings of the Mechanism. In 1974, Price published his research in the form of a seventy-page monograph titled ?Gears from the Greeks.? He had written, ?Nothing like this instrument is preserved elsewhere. Nothing comparable to it is known from any ancient scientific text or literary allusion. On the contrary, from all that we know of science and technology in the Hellenistic Age we should have felt that such a device could not exist.?

   Price expected his work on the Mechanism to change the history of technology. The Mechanism ?requires us to completely rethink our attitudes toward ancient Greek technology,? he wrote, and later added, ?It must surely rank as one of the greatest mechanical inventions of all time.? Price also pointed out that the Mechanism cannot have been the only one of its kind; no technology this sophisticated could have appeared suddenly, fully realized. Not only did the Mechanism demonstrate that our concept of ancient technology was fundamentally incomplete; it also contradicted the neo-Darwinian concept of technical progress in general as a gradual evolution toward ever greater complexity (technological history being the last refuge of the nineteenth-century belief in progress)?an idea firmly embedded in A. P. Usher?s classic 1929 study, ?A History of Mechanical Inventions.? As Price writes, it is ?a bit frightening to know that just before the fall of their great civilization the ancient Greeks had come so close to our age, not only in their thought, but also in their scientific technology.?

   But Price?s work, though widely reviewed in scholarly journals, did not change the way the history of the ancient world is written. Otto Neugebauer?s huge ?A History of Ancient Mathematical Astronomy,? which came out the year after ?Gears,? relegates the Mechanism to a single footnote. Scholars and historians may have been reluctant to rewrite the history of technology to include research that had lingering doubts attached to it. Also, Price?s book was published at the height of the popularity of ?Chariots of the Gods,? a 1968 book by the Swiss writer Erich von D?niken, which argued that advanced aliens had seeded the earth with technology, and Price got associated with U.F.O.s and crop circles and other kinds of fringe thinking.

   Finally, as Paul Keyser told me, ?Classical scholarship is very literary, and focusses on texts?such as the writing of Homer, Sophocles, Virgil, or Horace, or it is old-fashioned and historical, and focusses on leaders and battles, through the texts of Herodotus and Thucydides, or it is anthropological-archeological, and focuses on population distributions and suchlike. So when an archeological discovery about ancient technology arrives, it does not fit, because it?s new, it?s scientific, and it?s not a text.

   Plus, there is only one such device, and unique items tend to worry scholars and scientists, who quite reasonably prefer patterns and larger collections of data.? Whatever the reason, as one scholar, Rob Rice, noted in a paper first presented in 1993, ?It is neither facile nor uninstructive to remark that the Antikythera mechanism dropped and sank?twice??once in the sea and once in scholarship.

The National Museum in Athens took no special pains in displaying the lumps of bronze. Item 15087 wasn?t much to look at. When the physicist Richard Feynman visited, in 1980, there was little information explaining what the Mechanism was. In a letter to his family, later published in the book ?What Do You Care What Other People Think?,? the physicist wrote that he found the museum ?slightly boring because we have seen so much of that stuff before. Except for one thing: among all those art objects there was one thing so entirely different and strange that it is nearly impossible. It was recovered from the sea in 1900 and is some kind of machine with gear trains, very much like the inside of a modern wind-up alarm clock.? When Feynman asked to know more about item 15087, the curators seemed a little disappointed. One said, ?Of all the things in the museum, why does he pick out that particular item, what is so special about it??

For the Greeks, as for other ancient civilizations, astronomy was a vital and practical form of knowledge. The sun and the moon were the basis for calendars by which people marked time. The solar cycle told farmers the best times for sowing and harvesting crops, while the lunar cycle was commonly used as the basis for civic obligations. And, of course, for mariners the stars provided some means of navigating at night.

Xenophon Moussas, one of the two Greek astronomers who are part of the research project, is a compact, soft-spoken man. He grew up in Athens, and as a boy, visiting the museum, he often pondered the Mechanism; now as a professor of astrophysics, he uses it to connect with his undergraduate students, for whom ancient technology is often more compelling than ancient theory.

One evening in January, Moussas led me on a memorable walk around the archeological park in central Athens, which includes both the Greek and the Roman agoras. As a quarter moon shone in the clear night sky, illuminating the ruined temples and markets, Moussas narrated the story of how the ancients slowly learned to recognize patterns and serial events in the movements of the stars, and to use them to tell time and to predict future astronomical events. ?It was a way of keeping track not of time as we think of it,? he told me, ?but of the movement of the stars?a deeper time.?

For the Greeks, like the Babylonians before them, the year consisted of twelve ?lunations,? or new-moon-to-new-moon cycles, each of which lasted an average of twenty-nine and a half days. The problem with a lunar calendar is that twelve lunar cycles takes about eleven days less than one solar cycle. That means that if you don?t make regular adjustments to the calendar the seasons soon slip out of synch with the months, and after eighteen years or so the summer solstice will occur in December. Finding a system that reconciled the lunar year with the solar year was the great challenge of calendar-making.

   Most ancient societies readjusted their calendars by adding a thirteenth, ?intercalary? month every three years or so, although methods of calculating the length of these months, and when they should be added, were never precise. Babylonian astronomers hit upon an improvement. They discovered that there are two hundred and thirty-five lunar months in nineteen years. In other words, if you observe a full moon on April 4th, there will be another full moon in that same place on April 4th nineteen years later. This cycle, which eventually came to be known as the Metonic cycle, after the Greek astronomer Meton of Athens, was an extremely useful tool for keeping the lunar calendar and the solar calendar in synch. (The Metonic cycle is still used by the Christian Churches to calculate the correct day for celebrating Easter.) The Babylonians also established what would come to be known as the saros cycle, which is a way of predicting the likely occurrence of eclipses. Babylonian astronomers observed that eighteen years, eleven days, and eight hours after an eclipse a nearly identical eclipse will occur. Eclipses were believed by many ancient societies to be omens that, depending on how they were interpreted, could foretell the future of a monarch, for example, or the outcome of a military campaign.

   The Greeks, in turn, discovered the Callippic cycle, which consisted of four Metonic cycles minus one day, and was an even more precise way to reconcile the cycles of the sun and the moon. But the Greeks? real genius was to work out theories to explain these cycles. In particular, they brought the concept of geometry to Babylonian astronomy. As Alexander Jones, a professor of classics at the University of Toronto, put it to me recently, ?The Greeks saw the Babylonian formulas in terms of geometry?they saw all these circles all spinning around each other in the sky. And of course this fits in perfectly with the concept of gearworks?the gears are making little orbits.? Some Greek inventor must have realized that it was possible to build a simulation of the movements in the heavens by reproducing the cycles with gears.

   But who? Price called the inventor simply ?some unknown ingenious mechanic.? Others have speculated that the inventor was Hipparchus, the greatest of all ancient Greek astronomers. Hipparchus, who is also believed to have invented trigonometry, lived on the island of Rhodes from about 140 to 120 B.C. He detailed a theory to explain the anomalous movements of the moon, which appears to change speed during its orbit of the Earth. Hipparchus is also thought to have founded a school on Rhodes that was maintained after his death by Posidonius, with whom Cicero studied in 79 B.C. In one of his letters, Cicero mentions a device ?recently constructed by our friend Posidonius,? which sounds very like the Mechanism, and ?which at each revolution reproduces the same motions of the sun, the moon, and the five planets that take place in the heavens every day and night.?

   As Moussas and I headed uphill, toward the Acropolis, he pointed out the spot where Meton?s astronomy school and solar observatory had been. On our way back down, we stopped at the famous Tower of the Winds, the now gutted shell of what was the great central clock of ancient Athens. Designed by the renowned astronomer Andronicus of Cyrrhus, it is thought to have been an elaborate water clock on the inside and a sundial on the outside. ?But, in light of what we know about the Mechanism,? Moussas said, ?I am beginning to wonder whether this was a much more complicated clock than we think.?

   When Derek Price died, of a heart attack, in 1983, his work on the Mechanism was unfinished. Although his fundamental insights about the device were sound, he hadn?t figured out all the details, nor had he succeeded in producing a working model that was correct in all aspects.

   That year, in London, a Lebanese man walked into the Science Museum, on Exhibition Road, with an ancient geared mechanism wrapped in a handkerchief in his pocket. Michael Wright, one of the curators of mechanical engineering, was summoned to examine the artifact, which was in four main fragments. The man said that he?d bought the artifact in a street market in Beirut several weeks earlier. The Science Museum eventually bought it from him, and Wright and a colleague, J. Field, showed that it was a geared sundial calendar that displayed the positions of the sun and the moon in the zodiac. Wright also built a reconstruction of the sundial. The style of lettering on the dial dated the device to the sixth century A.D., making it the second-oldest geared device ever found, after the Antikythera Mechanism.

   In addition to his job as a curator, Wright helped to maintain the old clocks exhibited in the museum. Among them was a replica of the oldest clock that we have a clear account of, constructed in the early fourteenth century by Richard of Wallingford, the Abbot of St. Albans. It was a fantastic astronomical device called the Albion (?All-by-One?). Another reconstruction was of a famous planetarium and clock built by Giovanni de? Dondi, of Padua, in the mid-fourteenth century, known as the Astrarium. Like many students of mechanical history, Wright had noted this odd upwelling of clockwork in Europe, appearing in several places at around the same time. He was familiar with the theory that many of the elements of clockwork were known to the ancients.

   With the decline of the West, goes this theory, technical expertise passed to the Islamic world, just as many of the Greek texts were translated into Arabic and therefore preserved from loss or destruction. In the ninth century, the Banu Musa brothers, in Baghdad, published the ?Book of Ingenious Devices,? which detailed many geared mechanical contrivances, and the tenth-century philosopher and astronomer al-Biruni (973-1048) describes a Box of the Moon?a mechanical lunisolar calendar that used eight gearwheels. The more Wright looked into these old Islamic texts, the more convinced he became that the ancient Greeks? knowledge of gearing had been kept alive in the Islamic world and reintroduced to the West, probably by Arabs in thirteenth-century Spain.

   In the course of this research, Wright became intensely interested in the Antikythera Mechanism. Upon studying Price?s account closely, he realized that Price had made several fundamental errors in the gearing. ?I could see right away that Price?s reconstruction doesn?t explain what we can see,? he told me. ?The man who made the Mechanism made no mistakes. He went straight to what he wanted, in the simplest way possible.? Wright resolved to complete Price?s work, and to build a working model of the Mechanism.

   Whereas Price worked mainly on an academic level, approaching the Mechanism from the perspective of mathematical and astronomical theory, Wright drew on his vast practical knowledge of arbors, crown wheels, and other mechanical techniques used in gear-train design. His experience in repairing old grandfather clocks, many of which also have astronomical displays that show the phases of the moon, led him to one of his key insights into the engineering of the Mechanism. He posited that there must have been a revolving ball built in the front dial that indicated the phases of the moon?one hemisphere was black, the other white, and the ball rotated as the moon waxed or waned. Wright also showed how a pin-and-slot construction could be used to model the movement of the moon.

   Wright, who is fifty-eight, has a British public-school demeanor, which is generally courteous and hearty and seemingly rational. But he is prey to dark moods, wild, impolitic outbursts, and overcomplicated personal entanglements??muddles,? he calls them. Although he told me, ?I really hate confrontation, and antagonism of any kind, even competition,? he consistently finds himself in disastrous confrontations with people who should be his allies. Whereas academic researchers are used to collaboration, and to sharing resources and insights, Wright is temperamentally more like a lone inventor, working away in secrecy and solitude until he has found the solution.

   He did have a collaborator once?Allan Bromley, a lecturer in computer science at the University of Sydney and an expert on Charles Babbage, the nineteenth-century British mathematician who was the first to conceive of the programmable computer. Bromley used to come to the Science Museum to study Babbage?s papers and drawings and Wright would often lunch with him. In 1990, the pair took new X-rays of the Mechanism, the first since Price?s. But Bromley brought the data back to Sydney and would allow Wright to see only small portions of the material. (According to Wright, Bromley confessed ?that he had it fixed in his mind that it would be his name, preferably alone, that would be attached to the ?solution.? ?)

   Meanwhile, Wright got into a muddle with his boss at the Science Museum, an ?out-and-out bully? who would allow Wright to work on the Mechanism only in his free time. (?We don?t do the ancient world,? Wright remembers another colleague saying.) This meant that while Wright?s wife would go on holiday with their children, Wright would go to the museum in Athens. (Eventually, after years of this routine, he and his wife divorced.)

   By the late nineteen-nineties, Bromley was dying of cancer. Wright went to see him in Sydney, and Bromley turned much of the data over to him. Just as Wright was finally able to work up their findings for publication, however, he learned of the research project and the effort to take a new set of X-rays of the Mechanism. Instead of viewing this new investigation as a potential boon, he saw it as an improper encroachment on his own turf. ?There is a long-established unwritten law concerning the study of Greek antiquities, which is that when one researcher has access to the material, any other researcher is denied access until the first has finished,? he wrote to me. ?In my case, this understanding was swept aside through the machinations of the group.? So, when he arrived at the National Museum while the Bladerunner?s X-rays were in progress, he was not excited, like the others; he was ?angry, tired, and depressed.?

   The first images of Fragment D to appear on the Bladerunner?s monitor were stunning??so much better than we dared to hope,? Freeth told me. ?They took your breath way.? Inside the corroded rock was what looked like a geared embryo?the incipient bud of an industrial age that remained unborn for a millennium.

   Then the team spotted an oddlooking inscription. Andrew Ramsey, X-Tek?s computer-tomography specialist, who was operating the viewer, zoomed around inside the 3-D representation until he found the right slice. Written on the side of the gear were the letters ?M? and ?E???ME.? Was this the maker?s mark? Or could ?ME? mean ?Part 45?? (?ME? is the symbol for forty-five in ancient Greek.) Freeth joked that Mike Edmunds had scratched his initials on the fragment. Others suggested that this particular piece of the Mechanism could have been recycled, and that the ?ME? was left over from some earlier device.

   Altogether, the team salvaged about a thousand new letters and inscriptions from the Mechanism?doubling the number available to Price. Together with earlier imaging, the new inscriptions support theories that both Price and Wright had advanced. On Fragment E, for example, the group read ?235 divisions on the spiral.? ?I was amazed,? Freeth said. ?This completely vindicated Price?s idea of the Metonic cycle of two hundred and thirty-five lunar months on the upper back dial.? They also read words explaining that on the extremity of ?the pointer stands a little golden sphere,? which probably refers to a representation of the sun on the sun pointer that went around the zodiac dial at the front of the Mechanism. Wright had proposed that the rings of the back dials were made in the form of spirals; the word eliki, meaning ?spiral,? can be seen on Fragment E. On Fragment 22, the number ?223? has been observed, pointing to the use of the saros dial as an eclipse indicator.

   It was, as Xenophon Moussas put it to me, as if ?we had discovered the user?s manual, right inside the machine.? What had been regarded mainly as an archeological artifact took on a different sort of artifactual status, as an important astronomical text. Very few copies of original astronomical texts remain from the period; most of our knowledge about ancient astronomy comes from other, later astronomers. Little of Hipparchus? writing survives; we rely largely on Ptolemy of Alexandria, who some believe took much of Hipparchus? work and called it his own.

   Many of the inscriptions took months to read. Yanis Bitsakis, the Ph.D. student, collaborated with Freeth and the X-Tek team in rendering the X-ray data as computer images, while Agamemnon Tselikas, a leading Greek paleographer, did all the readings and most of the translations. As Bitsakis explained to me, ?One of the difficulties in reading the texts was that in ancient Greek there were no spaces between the words, and there are many alternative readings. Also, in many cases the edges of the lines are missing, so we don?t know what is continuous text.? He and Tselikas would work on the readings through the night, frequently e-mailing and calling other members of the team about new discoveries. Moussas remembers this period, lasting until the spring of 2006, as ?the most interesting time in my life.? For example, finding the words ?sphere? and ?cosmos? was extremely moving, Moussas told me: ?I felt as though I were communicating with an ancient colleague, through the Mechanism.?

   One day last month, I paid a visit to Michael Wright, in his book-and-clock-cluttered home, in West London. Wright was reading Xenophon, the Greek historian, in ancient Greek. He put the book down and brought out his model of the Mechanism from a cabinet underneath the stairs. In size, it is startlingly similar to a laptop computer, though a bit thicker. On the front dial, in addition to the pointers for the sun and the moon that Price posited, Wright added pointers for the planets and a separate pointer for the day of the year. On the back dial were two hundred and twenty-three divisions, marking months in the saros cycle; a similar dial above that showed months in the Metonic cycle. The gears were hidden inside a wooden casing, which had a large wooden knob on one side.

   Wright was still a little upset about what he considered the sweeping claims that the research group had made when it published its findings, in the November 30, 2006, issue of Nature. He almost stayed home from the two-day conference on the Mechanism that the group put on, in early December. In the end, he decided to go, taking his wife, Anne, whom he married in 1998, ?to stop me from lifting my knee in some chap?s groin.?

   We went upstairs to Wright?s workshop. It was filled with tools and pieces of metal, and the air held the pleasantly acrid scent of machine oil. Scattered across the tables and the floor were clever devices that Wright had fashioned out of gears?clocks, astrolabes, engines of various kinds. I recalled Price?s description of the maker of the Mechanism??some unknown ingenious mechanic??and wondered if this mysterious maker might have been a bit like Wright, with a workshop similarly cluttered with machines.

   Wright took his model apart and showed me how all the gears fitted together. I noticed some writing on a rectangular metal plate in the middle of the mechanism, and Wright told me that it was made of recycled bits of brass left over from some previous incarnation.

   ?So you think that the letters ?ME???

   ?Precisely,? Wright interjected. ?I think they must relate to whatever that bit of metal was used for before.?

   Then Wright put the machine back together and turned the hand knob that drives the solar gear. It engaged with the smaller gears, through the various gear trains, and the pointers began to spin around the dials. The day-of-the-year pointer moved forward at a regular pace, but the lunar and planetary pointers traced eccentric orbits, sometimes reversing course and going backward, just as the planets occasionally appear to do in the night sky. Meanwhile, the pointers on the back dials crept through the months in the saros and Metonic cycles; eclipses came and went. I noticed that as long as he kept turning the knob Wright himself seemed, for once, perfectly unmuddled.

   Until this moment, I had, like many others, continued to puzzle over why, if the Greeks were capable of building such a technically sophisticated device, they used that capacity to construct what is essentially a toy?an intellectual amusement. But as I beheld this whirring, whirling symphony of metal, a perfect simulation of a mechanistic and logical universe, I realized that my notions of practicality were foolish and shortsighted. This machine was much more than a toy; it embodied a whole world view, and it must have been, for the ancients, wonderfully reassuring to behold.

http://www.newyorker.com/reporting/2007/05/14/070514fa_fact_seabrook

(http://www.scienceandsociety.co.uk/pr/16762822/Science_&_Society_Picture_Library_10308322.jpg)
Sundial-calendar, Byzantine, c 400-600. (http://www.scienceandsociety.co.uk/results.asp?image=10308322)

Reconstruction of a Byzantine sundial-calendar based on the remains of a portable sundial with calendrical gearing in the Science Museum's collection. The original sundial is the second oldest survivng example of a such a device with gear wheels. It provides important evidence linking the earliest known geared mechanism, a Hellenistic calendrical instrument, (1st century BCE), with the earliest gearing from the Islamic world (c CE 1000), indicating the path of transmission of such technology. The outer scale names major Greek towns with their latitudes, and these would have been used to set the instrument.

M.T. Wright: Publications to date, August 2006 (http://216.239.59.104/search?q=cache:HWKrJsTtuOkJ:www3.imperial.ac.uk/historyofscience/aboutthecentre/staff/mr%2520michael%2520wright/+geared+sundial+calendar&hl=en&ct=clnk&cd=6)
Papers

?Bergeron on Flute-Making?, Galpin Society Journal , XXIX (1976), pp. 26 ? 34.

?Gears from the Byzantines: a portable sundial with calendrical gearing?, Annals of Science , 42 (1985), pp. 87 ? 138.

(jointly with J.V. Field.)

?Rational and Irrational Reconstruction: the London sundial-calendar and the early history of geared mechanisms?, History of Technology , 12 (1990), pp. 65 ? 102.

?Simple X-ray Tomography and the Antikythera Mechanism?, PACT (R?vue du groupe europ?en d'?tudes pour les techniques physiques, chimiques, biologiques et math?matiques appliqu?es ? l'arch?ologie or Journal of the European Study Group on Physical, Chemical, Biological and Mathematical Techniques Applied to Archaeology) , vol.45 (1995), pp. 531 ? 543.

(jointly with A.G. Bromley and H. Magou.)

?On the Lift Pump?, History of Technology , 18 (1996), pp. 13 ? 37.

?Londra: il Science Museum e sua collezione di macchine tessili (The Science Museum, London, and its collection of textile machinery)?, Museoscienza , no.10, year VI (June 1997), pp.14 ? 19 & 46, 47.

?Current Work on the Antikythera Mechanism?, Proc. Conf. Αρχαια Ελληνικ? τεχνολογια ( Ancient Greek Technology ), Thessaloniki, 4 ? 7 September 1997, pp. 19 ? 25.

?Greek and Roman Portable Sundials: an Ancient Essay in Approximation?, Archive of History of Exact Sciences 55 ( 2000 ), pp. 177 ? 187.

?Moxon's Mechanick Exercises: or Every Man his own Clock-Smith?, Antiquarian Horology , vol. 25 no. 5 (September 2000), pp. 524 ? 531.

?James Watt, Musical Instrument Maker?, Galpin Society Journal , LV (2002), pp.104 ? 129.

?A Planetarium Display for the Antikythera Mechanism?, Horological Journal , vol. 144 no. 5 (May 2002), pp. 169 ? 173, and vol. 144 no. 6 (June 2002), p. 193.

?Towards a New Reconstruction of the Antikythera Mechanism?, ed. S.A. Paipetis, Extraordinary Machines and Structures in Antiquity , Peri Technon, Patras 2003, pp. 81 ? 94.

?In the Steps of the Master Mechanic?, Η Αρχαια Ελλ?δα και ο Σ?γχρονοσ Κ?σμοσ ( Ancient Greece and the Modern World ), University of Patras 2003, pp. 86 ? 97.

?Epicyclic Gearing and the Antikythera Mechanism, part 1?, Antiquarian Horology , vol. 27 no. 3 (March 2003), pp. 270 ? 279.

?The Scholar, the Mechanic and the Antikythera Mechanism?, Bulletin of the Scientific Instrument Society , no. 80 (March 2004), pp. 4 ? 11.

?On Reaming Flutes?, Galpin Society Journal , LVIII (2005), pp. 51 ? 57.

(jointly with R. Bigio.)

?The Antikythera Mechanism: a New Gearing Scheme?, Bulletin of the Scientific Instrument Society , no. 85 (June 2005), pp. 2 ? 7.

?Ο Μηχανισμ?σ των ΑντικυΘ?ρων? (The Antikythera Mechanism), Αρχαιολογια & τεχν?σ 95 (June 2005), pp. 54 ? 60.

?Μηχανισμοι με γραν?ζια απ? την αρχαι?τερα ?ωσ σ?μερα: μια συνεχ?σ παρ?δοση? ( Geared Instruments from Antiquity to the Present Day: a Continuous Tradition), Αρχαιολογια & τεχν?σ 96 (September 2005), pp. 58 ? 63.

?Epicyclic Gearing and the Antikythera Mechanism, part 2?, Antiquarian Horology vol. 29 no. 1 (September 2005), pp. 51 ? 63.

?Counting Months and Years: the Upper Back Dial of the Antikythera Mechanism?, Bulletin of the Scientific Instrument Society , no. 87 (December 2005), pp. 8 ? 13.

?The Antikythera Mechanism and the early history of the Moon Phase Display?, Antiquarian Horology vol. 29 no. 3 (March 2006), pp.319 ? 329.


Contributions to Books

John Joseph Merlin, The Ingenious Mechanick , Greater London Council, 1985.

(jointly with A. French & F. Palmer.)

Early Gearing: Geared Mechanisms in the Ancient and Mediaeval World , The Science Museum, 1985.

(jointly with J.V. Field.)

Byzantine and Arabic mathematical Gearing , The Science Museum, 1985.

(jointly with J.V. Field and D.R. Hill.)

Eds. M. Hunter & S. Schaffer, Robert Hooke: New Studies , The Boydell Press, Woodbridge, 1989.

Chapter 3: ?Robert Hooke's Longitude Timekeeper?.


Πρωιμα Γραv?ζια , a translation into Greek of Early Gearing (vide supra), The Technical Museum, Thessaloniki, 1997.

Eds. N. Cossons et al., Making of the Modern World: milestones of science and technology , John Murray in association with The Science Museum, 1992.

Various entries.

Eds. R. Bud & D. Warner, Encyclopedia of Scientific Instruments. Entries on: ?angular measurement?; ?linear measurement?; and ?surface texture, measurement of?.

Eds. N. Easterbrook et al., Master Seafarers: the Phoenicians and Greeks (vol. 2 of Encyclopaedia of Underwater Archaeology ), Periplus, 2003.

A contribution concerning the Antikythera Mechanism .


Ed. E. Lo Sardo, Eureka! Il genio degli antichi , Electa Napoli 2005.

Chapter: ?Il meccanismo di Anticitera: l'antica tradizione dei meccanismi ad ingranaggio? ( The Antikythera Mechanism: evidence for an ancient tradition of the making of geared instruments), pp. 241 ? 244.