The Antikythera Mechanism

It’s no secret that a great deal of Western civilization was informed by the ancient Greeks. They revolutionized mathematics and geometry, developing astronomy along the way. They built ornate statues, beautiful temples to the gods, and amphitheaters for live entertainment with astonishing acoustics. The influence of the ancient Greeks shaped almost every field of human knowledge, from the arts and architecture to politics, philosophy, science, and technology.

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Like the Babylonians, the Greeks paid close attention to the night sky. Our nearest celestial neighbor, the Moon, was particularly important to them from a planning perspective. For instance, debts might be due on the new Moon. By heeding the Moon’s phases and taking note of eclipse cycles, they found that their harvests were more fruitful, and they had fewer incidents at sea.

As savvy and well-rounded as ancient Hellenistic culture appears to have been, it’s not unreasonable to imagine that the Greeks could have created some kind of computing machine to make their Moon-centered scheduling easier. Based on fragments from in a shipwreck that was discovered in 1900, it seems they did exactly this. Based on scientific dating of the coins and pottery found in the wreck and inscriptions on the bronze remnants, historians and scientists believe the Greeks created a mechanical computer capable of calculating the positions of the Sun and the Moon on any given day. This marvelous device is known as the Antikythera mechanism.

The mechanism was housed in a wooden box and controlled with a knob on one side. It is believed that the front of the box was a display made up of a set of concentric rings with graduations, and that each ring corresponded with one celestial body. Pointers attached perpendicularly to output gears moved around the rings as the knob was turned, showing the paths and positions of these celestial bodies over time. This Earth-centric planetarium also displayed the phase of the Moon as well as the positions of the five major planets known to the ancient Greeks—Mercury, Venus, Mars, Jupiter, and Saturn.

Gearing // Composite Plan

Provided the scientific dating of the coins and pottery found among the shipwreck is correct, the Antikythera mechanism also marks the earliest appearance of the differential gear. It is believed that the designer used a pin and slot arrangement to join two gears of differing tooth counts in order to model and compensate for the irregular, elliptical orbit of the Moon. Through a complex series of gearing ratios, this ancient computer could predict solar and lunar eclipses, displaying models of them at the user’s fingertips just as they would happen in the sky.

Storms and Shipwrecks

It’s a wonder the Antikythera mechanism was discovered at all. In 1900, a group of Greek sponge divers were sailing back to Symi, an island in the Rhodes region of Southern Greece. Their ship was in a channel north of Crete, near the small island of Antikythera. They became caught in a storm and were forced take shelter around the island’s main port of Potamós. Once the storm passed, they decided to scout the area for sponges before returning home.

The divers didn’t find any sponges off the coast of Antikythera, but they did find treasure. Among the steep rock shelf below laid the remains of a large ship. Scattered among the ancient timbers, partially obscured by rock and silt, the divers could see the disembodied heads, arms, and legs of large bronze and marble statuary. After recovering what they were able to haul, the captain took note of their bearings and the two ships set sail for Symi.

At eight miles square, Antikythera is a fraction the size of Kythera, the island it opposes in the Sea of Crete. Because of its dimensions, location, and low levels of human activity, the island has long been a major stop for migratory birds. Antikythera has seen a lot of fluctuation in usage over the last few thousand years, and the current population is around fifty inhabitants. Because of its staggering cliff faces and craggy shoreline, the tiny island has been a big hazard for all of maritime history.

The sponge divers and crew spent the next six months figuring out what to do about the treasures they had found. Rather than loot the wreckage site, they decided to notify the standing authorities about their discovery. The ship’s captain went to Athens with a bronze arm that his crew had found in the wreck. Almost immediately, the government sanctioned an official recovery mission.

It was agreed that the crew of sponge divers who made the discovery would revisit the site and turn whatever they found over to the Greek government. They ended up recovering the largest collection to date of artifacts from classical antiquity. They brought back scores of treasure from the ancient Hellenistic period, including corroded bronze fragments of something they couldn’t identify. All of the artifacts went to the National Archaeological Museum in Athens.

Believe it or not, the bronze fragments that comprised the Antikythera Mechanism more or less sat around unnoticed at the museum for eight months after the exploration. This was due to the sheer volume of bronze brought into the museum from the wreck. It required a lot of sorting and re-sorting as statues and other pieces were catalogued and reconstructed by the staff. During one of these re-shufflings, someone noticed inscriptions and graduation markings on one of the fragments, and they began to receive attention befitting the oldest known mechanical computer.

Shortly after the exploration of the shipwreck in 1901, it was reported that the fragments of the mysterious object comprised some sort of astrolabe, a type of inclinometer used to locate the positions of celestial bodies. A naval historian named Konstantin Rados contested this theory, arguing that it was too complex of an instrument to be a mere astrolabe. Albert Rehm, a scholar of ancient language and textual interpretation, loosely compared it to the Sphere of Archimedes, a device the ancient Greek mathematician used for computing the volume and surface area of a sphere with relation to those of a cylinder.

Gears from the Greeks

The first in-depth analysis of the Antikythera mechanism was performed by a British science historian and Yale professor named Derek de Solla Price. He began his study of the fragments in the 1950s, using still photographs and radiographs to make sense of the gear ratios. Price’s examination continued unabated into the 1970s. In June of 1974, he published his findings with the American Philosophical Society in a monograph called Gears from the Greeks: The Antikythera Mechanism: A Calendar Computer from Ca. 80 B.C. The 72-page labor of love is Price’s full inquiry into the matter, ranging from the happenstance of the shipwreck’s discovery and early explorations of the mechanism to all that he finds conclusive and inconclusive about its origins, inner workings, meaning, and the shortlist of possible creators.

Gearing // Back of Main Plate
Gearing // Back of Main Plate

Price leaves no fragment unexamined, but he was limited by the technologies available at the time. In Gears from the Greeks, he writes that every visible cog was so corroded that not a single one could yield an accurate tooth count. He nevertheless took the task on, working with artist Beverly Pope to create the intricate line drawings you see reprinted here.

Through extensive use of radiography, Price came to the conclusion that the mechanism contained at least 27 gears. It’s now believed that the complete mechanism contained at least 30 gears.

Price was sure that if he could get an accurate count of any of the gears’ teeth, he could begin to unlock the mysteries of the mechanism. This was quite a difficult task to undertake, given that he was working with two-dimensional x-rays of gears that meshed here and overlapped there in a very tight configuration. Undaunted, he literally traced around the gears to count the teeth. Price believed the largest gear was made with 223 or 225 teeth and represented the Sun. He wasn’t sure of this gear’s exact significance, and proposed that a gear representing the eclipse cycle would have 223 teeth, while a gear standing for the Metonic cycle would have 235 teeth.

Price also counted a gear with 127 teeth, and supposed that it could have been used to follow the moon’s movement around the Earth. This number is significant as it is equal to half the number of Moon orbits in a 19-year solar cycle. Scientists believe that the mechanism’s creator did this to simplify the operation, and that a multiplier gear converted the number to 254.

No one had visited the site of the wreck since the initial dredging in 1901. In 1976, an expedition led by Jacques Cousteau recovered many more objects that helped provide clues to the age of the Antikythera mechanism. Among the ship timbers and bronze figures, Cousteau and his team found bronze and silver coins from the Asia Minor colonies of Pergamon and Ephesus, which are now part of Turkey. A coin expert named Panagiotis Tselekas was able to date these coins as having been struck between 70 and 60 BC. Cousteau’s team had also recovered pieces of pottery and many large wine jugs, which experts were able to date to 65-50BC.

All of the available evidence points to the likelihood that the ship was an immense trading vessel belonging to the Roman Empire. At the time, only a few ports in the Mediterranean such as these three were big enough to handle a ship of its enormity, and it was probably sailing from Asia Minor back to Rome. The ship was heavily laden with objects, which many researchers believe that the Romans had looted from Pergamon, Ephesus, and Rhodes.

New Technology, New Findings

Several years later, a mechanical engineer and former curator of London’s Science museum named Michael Wright performed his own extensive study of the Antikythera mechanism over a period of twenty-five years. Wright studied Derek de Solla Price’s monograph and ultimately concluded that Price’s reconstruction of the mechanism was fundamentally incorrect. In fact, Wright went so far as to call it bizarre and incomplete, suggesting that Price took some creative liberties to fill in the gaps, and to make the astronomical calculations work out against his gear tooth counts.

But Michael Wright didn’t just throw stones. In addition to writing numerous papers about the mechanism, he collaborated with Australian computer historian Allan Bromley to create a complete reconstruction of the device in bronze and wood, drawing upon his mechanical knowledge and the history of craft techniques. Wright also took his own photographs of the fragments and performed radiography with a device he created to adapt X-ray equipment for this purpose. Together, they created plans for the model by compiling data from hands-on examination and from their own measurements of the delicate fragments.

Gearing // Front of the Main Plate
Gearing // Front of the Main Plate

The front display of Wright’s model was an Earth-centric planetarium with indicators for the Sun, Moon, and the five major planets of ancient Greek astronomy. In creating his reconstruction, Wright attempted to stay as true to the original as the radiographs would prove. He machined gears from thin bronze that measured between one and two millimeters thick, which he proposed was the kind of stock that all of the metallic parts of the mechanism were made from.

A few years later, an international team of scientists with access to much better imaging technology confirmed that the largest gear did indeed bear 223 teeth. This particular gear was crucial to reconciling the 12-month solar year with the 29.5-day lunar month—a cycle of 19 solar years exactly equals 235 lunar months. This number 235, which indicates what the Greeks referred to as the Metonic cycle, is repeated in a series of individual graduations on the back of the mechanism. In Michael Wright’s model, a spiral groove with a resettable arm predicted the dates of solar and lunar eclipses as an output function of the internal gearing.

One of Wright’s most insightful suppositions about the device was that the gearing that drove the display on the back side, where eclipse prediction takes place, appeared to have a pin and slot mechanism. His adapted x-rays revealed a slot and the ghost of a circular piece inside of it. Wright ultimately determined that the pin gear and the slot gear pivot on slightly offset axes. Both are connected to the 223-tooth gear, which keeps track of the Moon’s orbit. This meant that the pin and slot mechanism was a differential gearing solution designed to compensate for the irregular, elliptical orbit of the Moon around the Earth.

Another of Wright’s contributions was his discovery of a fixed boss in the main fragment. This suggests that the Antikythera mechanism was designed to show epicyclical motion with subsystems that moved about a central gear. Wright believed that the Antikythera mechanism had likely been altered, or hacked, if you will at one or more points after it was made. Primarily, he supposes the two spiral output displays on the rear of the device were repurposed from some other piece of equipment and added later, citing the appearance of the enclosure’s remains.

Around the time that Michael Wright was studying the mechanism and creating his reconstruction, a team of scientists, astronomers, and mathematicians had come together in Athens to further research the ancient calendar computer. They worked in conjunction with the Antikythera Mechanism Research Project (AMRP) to continue investigation into the mechanism and published an article in 2006 detailing their findings about the machine.

Shortly after publication, British mathematician and filmmaker Tony Freeth of the AMRP collaborated with Alexander Jones, a professor of the History of Exact Sciences in Antiquity at New York University’s Institute for the Study of the Ancient World. Together, they came up with a computer model of the Antikythera mechanism that incorporates newer knowledge about the device.

In 2005, Tony Freeth engaged scientists from Hewlett-Packard who had created a special technique for creating enhanced images of the surfaces and details of paintings. A dome covered with lamps flashes light on the object in question from various angles while a series of still photos are taken. Freeth convinced them to go to Athens and use this equipment to photograph the tiny inscriptions on the mechanism. The images did wonders for furthering the team’s understanding. They were able to confirm once and for all that the largest gear definitely had 223 teeth. Another inscription directly mentions the number ‘235’ as well as the spiral display on the back with reference to the Metonic cycle.

Freeth and Jones were able to use the month inscriptions to help determine where the Antikythera Mechanism was made. At the time of the shipwreck, each of the Greek states used its own calendar scheme. The month inscriptions on the fragments pointed to Corinth, or a colony of Corinth such as Syracuse on the island of Sicily.

How it Works – the Current Model

Years of study, measurement, photographs, and educated guesswork by several people have provided an increasingly clear picture of the mechanism’s structure. Essentially, it is a collection of gear wheels that was likely contained in a wooden box and operated with a hand crank on the side. As the crank was turned, the indicators on the front would spin around, each modeling the path of one of the major celestial bodies known to the ancient Greeks. There were separate indicators for the Sun, Moon, and five major planets known at the time. The device’s smallest indicator was a tiny sphere, colored half black and half white by those who would later model it. This little ball spun independently of its indicator arm, showing the phases of the Moon as it moved through each day of the solar calendar.

Gearing // Side View
Gearing // Side View

According to Michael Wright, the inner workings contain multiple gear trains for the calendar year, including the true Sun and mean Sun. Two subsystems emerge from this train, one based on the Sun and one on the Moon. The Sun side contains gearing that computes the four-year cycle of the Pan-Hellenic Olympic Games as well as the nineteen-year Metonic cycle, which is a common multiple of both the solar year and the lunar month. It also computes the seventy six-year Callippic cycle, which is four times the length of the Metonic cycle and was proposed by Greek astronomer Callippus around 330BC as an improvement over the Metonic cycle.

The ancient Babylonian astronomers had discovered what Edmund Halley would come to call the Saros cycle, which describes the full cycle of eclipse activity between the Sun and the Moon. The Babylonians found that every 223 synodic (lunar) months, the Sun, Moon, and Earth return to the same relative geometry, resulting in the same type of eclipse.

The lunar gear train connects to a lunar anomaly platform and on to an eclipse gear train that shows the 223-month Saros cycle and its proposed improvement, the 669-month Exeligmos cycle. There are additional epicyclical gearing mechanisms for the five major planetary bodies known to the ancient Greeks: Venus, Mercury, Mars, Jupiter, and Saturn.

These internal gearing systems output their calculations on the back of the device through two spiral grooves. One is divided to show the calendar cycles for the Olympic Games, the Metonic cycle, and the Callippic cycle. The other acts as an eclipse predictor, operating on the 223-month Saros cycle to show the dates of both solar and lunar eclipses. A pointer spans the radius of each ring of the groove, while an attached needle rides in the slot. This design made it possible to reset the output by lifting the pointer as one would lift the arm of a record player.

Who Made the Antikythera Mechanism?

Derek de Solla Price believed there were a few people who could have created this technological wonder. One of them was Andronicus Kyrrhestes, a Macedonian who had built a kind of ancient weather station called the Tower of Winds. His octagonal structure featured a wind vane and a complex sundial on each of its faces. A frieze around the exterior of the tower paid homage to each of the eight prevailing wind gods. Inside the tower was a clepsydra, or water clock, which was driven by water from the Acropolis.

If not Kyrrhestes, Price supposes the Antikythera mechanism was conceived by some Rhodes engineer studying under Posidonios, a renowned philosopher and meteorologist who took a great interest in measuring the distances to the Moon and stars. If the Antikythera mechanism had been the work of Archimedes, Price believes that his name would certainly have been attached to it in historical records, followed closely by a great deal of praise for having invented the differential gear. In his book, De Republica, Cicero described a device he had seen while studying at Rhodes. This was a planetarium constructed by Posidonios. In his writing, Cicero wrote of some novel differences between this new planetarium and an earlier astronomical device he greatly admired, the sphere of Archimedes.

The Future of the Antikythera Mechanism

Until recently, there had only been two officially sanctioned recovery missions of the Antikythera shipwreck: the original dredging, and Jacques Cousteau’s expedition in 1976. But in September and October of 2014, a group of divers, archaeologists, and scientists returned to the site in partnership with the Hellenic navy. With the help of some cutting-edge diving gear, they were able to recover even more objects, ranging from common tableware to treasures of antiquity, such as the giant bronze spear belonging to a life-sized warrior statue.

Enclosure Theory
Enclosure Theory

The group had many goals for this expedition. One of these was to map the full extent of the shipwreck with a 3D digital blueprint. A bright yellow autonomous underwater vehicle (UAV) named Sirius took care of that by providing high-resolution stereo images. Sirius was built by the marine robotics arm of the Australian Centre of Field Robotics at the University of Sydney.

Because the ship’s remains are so far underwater, diving to the site and staying for more than a few minutes is terribly dangerous. The group’s other main goal was testing a new diving suit technology called the Exosuit, which allows for dives down to 1,000 feet. With these suits, the divers could safely stay down at the wreck for over 30 minutes a day.

Antikythera Admiration

Both Michael Wright’s physical bronze model and Tony Freeth’s computer model of the mechanism greatly moved the needle of understanding with regard to its inner workings and reason for creation. Wright is not the only craftsman who is moved by the mechanism’s mechanical marvels. In 2010, an Apple engineer named Andrew Carol completed a working replica of the mechanism which he constructed entirely from LEGO Technic pieces.

Carol’s model is much larger than the original device, mostly due to the difference between custom-machining brass gears and modeling the same oddly-numbered cogs with pre-formed ABS gears. It also uses about twice as many gears as the original, mostly because Carol had to reckon with the way the calendar has changed over the last 2,000+ years.

In early 2014, a USC mechanical engineering student modeled the Antikythera mechanism using Solidworks. He based his files on Tony Freeth’s and Alexander Jones’ gearing proposal. He has shared the CAD files through his site, theshamblog.com, noting that they are not quite fit for 3D printing in their current state. In December 2014, he made comment about his plan to release a version intended for lasers and wood.

A Mystery Wrapped in an Enigma

There are many layers to the mystery of the Antikythera mechanism. For instance, it could have been one of a kind, or it may be the only one of many such computers to survive from antiquity.

And what was the Antikythera mechanism doing at the bottom of the Sea of Crete? Was it looted from a Greek colony along with hundreds of works of art and pieces of jewelry, or was it among the Roman shipwreck’s remains by coincidence? In his monograph, Derek de Solla Price discusses the Antikythera mechanism as a historical document, offering the point that much of what remains from ancient Greek society are the sturdier pieces of evidence like architecture, jewelry, and pottery. No Hellenistic artifact had yet been found that was anywhere near as complex as the Antikythera mechanism. Prior to its discovery, the earliest-surviving object of similar complexity dates from 1000A.D—an astrolabe created by a Persian scholar named al-Bīrūnī.

After the fall of the ancient Greek civilization, it is believed that the kind of craftsmanship and technology the mechanism represents moved east through the Byzantine Empire and on to the Arabs after the fall of Constantinople. Complex mechanical clockwork on a smaller scale began to appear in Central Europe around the end of the Middle Ages, and the automata that much of modern technology emerged from in the Victorian Era.

Diagrams Reprinted by Permission

Diagrams reprinted by permission
Gears from the Greeks: The Antikythera Mechanism–A Calendar Computer from ca. 80 B.C.
by Derek De Solla Price (ISBN 9780871696472, published November, 1974)
http://www.amphilsoc.org/node/191


This article was specifically written for the Hackaday Omnibus vol #02. Order your copy of this limited edition print version of Hackaday.

72 thoughts on “The Antikythera Mechanism

  1. I believe this to be a typo: “Price believed the largest gear was made with 223 or 225 teeth and represented the Sun. He wasn’t sure of this gear’s exact significance, and proposed that a gear representing the eclipse cycle would have 223 teeth, while a gear standing for the Metonic cycle would have 235 teeth.”

    225 vs 235 in the two sets of potential teeth counts…

    1. I contacted the guy who built this to see if he might post the plans for this. Unfortunately his busy schedule didn’t permit it. If anyone else does recreate the Lego version please please please post the plans.

  2. This is probably stupid, but maybe someone would be so kind as to explain why it’s stupid? Is it possible that the effort to explain the mechanism suffers from confusing the input and the output? Could it be that careful astronomical observations were fed into the device in order to derive either a local time or an offset from some reference position, in order to determine longitude?

    1. I think that’s a really cool idea. Maybe we can figure it out based on the torque required to turn the gears? It should be possible to calculate whether it would be really annoying to try to backdrive the mechanism.

      1. they could have used a simpler device called an astrolabe to determine local time, latitude and longitude.

        If what I remember is true from the aforementioned Nova special on this device it was used to schedule events, festivals and ceremonies.

        I can’t say with any authority that this is a unique device or a common one but it does seem specialized enough to be in the hands of only royalty or the religious leaders.

        1. Sgt Sandbox – It was probably being smuggled from the island to Rome to Julius Caesar. The Romans had already stolen a similar device by Archimedes after the siege of Syracuse where he was summarily murdered by a Roman soldier. The ship sank at Point Glyphadia probably due to bad weather. It was in a hidden wooden box. It was made of bronze. There was no inscription-name on it which was common of most of Archimedes’ inventions. Since it was dated recently to around 205 BCE that would be AFTER Archimedes’ murder in 212 BCE. And a little before Hipparchus’ and Posidonius’ birth. So I think the new dating is wrong and defer back to the original dating of 150-100 BCE putting that in both Hipparchus’ and Posidonius’ middle-ages or the prime of their lives. They were both on that island too.

          Andronicus Kyrrhestes (actually spelled in English: Andronicus Cyrrhestes) probably did not build this thing for a number of obvious reasons. He was around in 100 BCE though. He was into architecture of buildings versus actual gadgets like the 3 men above who may be the actual designers (all being actually built by a lesser-known unsung metalworker). Look for my posting below about Tatjana who built a working model in 2007!

          1. Seems plausible. Like I said, something only the king or the high priest would be allowed to own. Just imagine being able to accurately predict the movements of the planets and moon. You’d know the secrets of the gods themselves! That kind of knowledge can go to a man’s head.

            I do remember the bit about Archimedes being murdered by a Roman grunt.

  3. You mention the “Current Model” but show gear pictures from the 1970’s understanding of the device. The Current Model is a device that (from the 2012 documentary) “- on its rear face, Greek scientists of 2000 years ago fashioned a computer mechanism that displayed a calendar that followed the moon, that predicted eclipses. While on the front they reproduced the Universe as they understood it. With the five planets, the sun, and the moon – performing their complicated steps of their dance through the heavens.”

    Are there layouts and gear pictures of this 2012+ currently understood model?
    Check out: http://www.antikythera-mechanism.gr/data/models/solid-models
    – Kris

  4. I really love this subject matter. If you would like to pick the brain of the later-day Hipparchus (or Posidonius as Cicero claims invented this thing), go to this Amsterdam Netherlands (aka Holland ) enigmatic woman’s website (Ms. Tatjana Joelle van Vark): http://www.tatjavanvark.nl

    Once there click on “(Click here for) INDEX “. Find the 7th icon on the extreme right called “The Antikythera Mechanism (2007)” and click on it. She ACTUALLY made this thing in 2007 and it works too! You can see a YouTube video in action of it here: http://youtu(dot)be/ULUvxf_Bm8A?t=11m45s (change the (dot) to a period no spaces).

    This PLANETARIUM OF POSIDONIUS is nothing more than a astrolab. It is way ahead of it’s time in BCE (before common era or BC before Christ). Hipparchus was into this type of thing but Posidonius , who really was into Hipparchus, may have had it built just as Cicero claims. Cicero claims it is like Archimedes’ earlier device which was stolen and sent to Rome. However the A.M. is obviously not that device as his name would have been on it and it would not have been on a boat at sea.

    What’s amazing is that Tatjana is more skilled than ALL of these ancient Greeks as she not only philosophizes (thinker) about really heady stuff she ACTUALLY builds these gadgets (gets her hands dirty) unlike how they used metalworkers to build stuff. That includes Archimedes who probably never got his nails dirty like Tatjana does daily (when she’s not wearing gloves) 8-)

  5. ——————————————————————————————————————
    I hate this!!! : “Your comment is awaiting moderation.” – Why is it activated???!!!
    Sorry for the duplicate posting coming up…
    ——————————————————————————————————————
    I really love this subject matter. If you would like to pick the brain of the later-day Hipparchus (or Posidonius as Cicero claims invented this thing), go to this Amsterdam Netherlands (aka Holland ) enigmatic woman’s website (Ms. Tatjana Joelle van Vark): tatjavanvark (dot) nl
    (Change (dot) to period and remove all spaces)

    Once there click on “(Click here for) INDEX “. Find the 7th icon on the extreme right called “The Antikythera Mechanism (2007)” and click on it. She ACTUALLY made this thing in 2007 and it works too! You can see a Dutch YouTube video in action of it here (add the YouTube URL before it): /watch?v=ULUvxf_Bm8A&feature=youtu.be&t=11m45s

    This PLANETARIUM OF POSIDONIUS is nothing more than a astrolab. It is way ahead of it’s time in BCE (before common era or BC before Christ). Hipparchus was into this type of thing but Posidonius , who really was into Hipparchus, may have had it built just as Cicero claims. Cicero claims it is like Archimedes’ earlier device which was stolen and sent to Rome. However the A.M. is obviously not that device as his name would have been on it and it would not have been on a boat at sea.

    What’s amazing is that Tatjana is more skilled than ALL of these ancient Greeks as she not only philosophizes (thinker) about really heady stuff she ACTUALLY builds these gadgets (gets her hands dirty) unlike how they used metalworkers to build stuff. That includes Archimedes who probably never got his nails dirty like Tatjana does daily (when she’s not wearing gloves) 8-)

    1. All units of measurement are arbitrary. Have you ever looked up the definition of a Kilogram?

      It’s funny how people from SI countries complain about non-SI measurements. I guess we stupid Americans benefited from being taught both systems and how to effortlessly convert between them.

      1. many SI definitions are bound by physical constants today and not the entirely arbitrary logical statements or even worse bespoke reference that is used in most systems (including the SI system until recently)

        i do agree that as long as conversions can be accurately made there shouldnt be an issue.

  6. Chris – CUBITS were much worse!!! How long is your forearm compared to mine? Who knows? Cubits had to be the worst standard of measurement ever! I like inches as I am a dumb-old-American. I know I need to adopt the metric system and I am trying hard but my neural plasticity is fighting me, 0.0254 meters to an inch… Jeez that’s hard to remember!

    1. The only reliable observable CONSTANT was the speed the earth spins (sun’s apparent movement?). A rudimentary sun dial could have been constructed that marked where the sun shadow was at zero length (aim ground-mounted stick directly at sun until there is no shadow) then where it was 60 seconds later. That could have been the entire planet’s standard of measurement. You could measure time with an hour glass, water clock, sun dial, or just saying one-thousand-one to one-thousand-sixty out loud (that’s roughly 60 seconds). The Greeks could have called it: μέτρο ήλιο (pronounced metros ilio).

      CUBITS where just stupid! Everybody’s forearms are different.

    2. Apologetic American silliness. 12 is commensurate with 2, 3, 4, and 6 and is far superior to 10, which is commensurate with only 2 and 5. Rulers of 12’s can be made by folding.

  7. I wonder how much of this was known to the writers of the Avatar: the Last Airbender episode where Aang and his party travel to the lost library in the desert and use a mechanical device much like this one to discover the date of the next solar eclipse.

  8. I really don’t get this, perhaps someone can correct me.

    The first beliefs were ‘earth centric’ or it was believed that everything revolved around the earth and not the sun.

    Through the discover of various items excluding this one – it appeared that this belief persisted for a very long time perhaps to the 1800’s

    I though it *was this* discovery that lead us to see that the Ancient Greeks did in fact have a sun centric perception long before other civilisations did.

    Or in other words – I though the greatest significance of this item (apart from analog computing) was that it showed the earliest sun centric perception of our solar system.

    Here I read that this device is earth centric which is completely at odds with what I expected.

    When I look at the gearing, it appears to be sun centric in it’s calculations even if it is earth centric in it’s display.

    1. Well as far as I know the Greeks proved the earth was round and there was some debate about geocentric vs. solarcentric (word?) but the geocentric view was the most popular, and as you can tell from the Antikythera mechanism the mathematics did work for a geocentric world view.

      1. The word you’re looking for meaning sun centric is heliocentric,.

        Aristarchus did not prove the world was round with his “sticks and shadows and wells” experiment where he managed to very accurately measure a degree of the Earth’s circumference. That is a common misunderstanding of the results. What it allowed him to do was estimate the circumference of the Earth if it were indeed a sphere. It also allowed him to estimate the diameter of the sun and how far away it might be. He came up with two possible answered, one being wildly wrong with the sun being less than 50 miles in diameter and only about 300 miles away and then the mind bogglingly huge numbers we know today. They were only estimates and still wrong, but very close to what our measurements are today. I think it was about a 1% error?
        Don’t quote me though, I’m too busy now to Google it and my kids want a snack ASAP.

        1. awww crap. It wasn’t Aristarchus it was Eratosthenes of Cyrene who did the experiment, measurement and estimate of the Earth’s possible diameter.

          Well, at least the kids aren’t hungry anymore.

          1. Sgt Sandbox – Eratosthenes also helped us today with strong encryption using non-prime number (or composites) factoring. I think it was called The Sieve of Eratosthenes circa 240 BCE – it would find prime numbers up to a limit – composites where a byproduct. However, Herodotus in 440 BCE was the true father of encryption we call today as Steganography.

          1. The “circle of the Earth” was known as far back as the 14th century BCE (circa 1473 BCE) by Moses (that includes the Egyptians). It can be found in The Book of Job at Job 26:10. And in the 8th century BCE by Isaiah at Isaiah 40:22. So flat-earthers have always been misinformed even today.

      2. I recall that there were many attempts to make the mathematics work for a geocentric universe, epicycles, for instance.
        Almost everything made more sense when the universe went heliocentric.

        1. There were still problems with the early heliocentric models, though, as they still assumed that the orbits were circular. Tycho went to his grave believing this, and his student Keplar was making measurements of orbits to prove this, but ended up proving that they were elliptical instead.

        2. For “epicycles”, read it as “Fourier series”.

          They were not wrong, they were just doing it the hard way! 8-)

          Where they were wrong was in the belief that the universe had to be “Perfect”.

    2. RÖB – The A.M. gear is part of a gadget called a “planetarium” by Cicero of Rome. It is evidently geocentric (earth centric) and not heliocentric (sun centric). Aristarchos of Samos proposed a heliocentric viewpoint long before this gear was even invented. Even Archimedes wrote about it in his paper “The Sand Reckoner”. However, it is alleged that people were being persecuted in Ancient Greece for propagating the heliocentric model. So the inventor of the A.M. was probably playing it safe but knew what was the correct model (i.e., heliocentric). In any event the Romans were in the process of stealing it when the ship sank. They had stolen Archimedes planetarium years before after murdering him at Syracuse. They say it was an accidental killing but I think Marcus Claudius Marcellus was really pissed off about Archimedes’ fancy boat burning idea by focusing sun’s rays on their opaque colored attack fleet sails at the Siege of Syracuse. And Archimedes had OTHER less noted innovated gadgets he used to thwart the Italian siege of his city too. He was murdered shortly after that by an angry Roman soldier bitter about the Archimedes’ use of smarts to defeat his comrades. The soldier was disobeying direct orders from Marcellus NOT to bother Archimedes. But didn’t help that Archimedes was so rude to that soldier too.

      SOTB

      1. Hi, I hope you can have the patience for an armature like myself.

        Now first off. I don’t know what you mean by A.M. gear. I though you may have meant the drive (gear A) to M (one of the time domain shafts). This relationship can only be Sun centric as it’s purely time domain (days, Sun).

        From what I understand, at the time, supporting a Sun centric perspective would have been akin to volunteering for your head to be lopped off. And this device (if perceived to be Sun centric) would have been seen as the ‘work of the devil’ or an ‘Anti-Christ’ or what ever the equivalent of that time was.

        You said “It is evidently geocentric”. Well yes it is. It’s hard to imaging that the Greeks needed something to help them know accurate time and the seasons while they’re traversing the surface of the Sun. So obviously the output or the display if you like has to be Earth centric. It would be meaningless otherwise.

        My point was that the maths that it does certainly appears to be Sun centric. The driven wheel is the SUN and everything else is derived from that by that.

        All the time domain things are also driven directly by the Sun and the position of the other planets are driven by the Sun.

        The differentiator may look confusing as it’s inputs are are the Sun and the Moon but look carefully and you see that the Moon itself is driven by the Sun. Or in other words this is NOT doing any sort of perspective transference (from the Sun to Earth or vies versa) as you may expect. The reason it is done this way is simply that they want to avoid a large prime number that would require a very large cog. So they are stating with a calculation that has already been done. The most complex output of *this* sub-chain of calculations is the moon phase because it relates to the position of the Earth, Sun AND Moon. This is also the calculation that has the largest prime number. The other Moon calculations are simple from there.

        So while this thing lack’s in position accuracy to some degree – it has a very high degree of periodic accuracy and certainly – to me – the maths represented by the gears is done in with the central reference point being the Sun rather than the Earth.

        Some of it seems to be missing. One calculation path doesn’t complete in an output.

        1. RÖB (I replied in CAPS LOCK to you)
          “Hi, I hope you can have the patience for an armature like myself.”

          I DON’T KNOW WHAT YOU MEAN BY “ARMATURE”.

          “Now first off. I don’t know what you mean by A.M. gear. ”

          I MEANT A.M. FOR Antikythera Mechanism

          “From what I understand, at the time, supporting a Sun centric perspective would have been akin to volunteering for your head to be lopped off. And this device (if perceived to be Sun centric) would have been seen as the ‘work of the devil’ or an ‘Anti-Christ’ or what ever the equivalent of that time was.”

          WELL MAYBE, BUT ANCIENT GREEKS LIKED TO POISON PEOPLE. REMEMBER SOCRATES? HE HAD TO TAKE THE POISON HIMSELF FOR HIS EXECUTION. NO ANCIENT GREEKS WERE NOT PRO-CHRISTIANS HENCE DID NOT ACCEPT OUR DEVIL NOR CHRIST. THE APOSTLE PAUL TRIED TO CHANGE ALL THAT. YOU CAN READ ABOUT IT IN HIS MANY BOOKS AND LETTERS IN NEW TESTAMANT.

          “You said “It is evidently geocentric”. Well yes it is. It’s hard to imaging that the Greeks needed something to help them know accurate time and the seasons while they’re traversing the surface of the Sun. So obviously the output or the display if you like has to be Earth centric. It would be meaningless otherwise.”

          I MEANT THAT THE INVENTER SECRETLY BELIEVED THAT THE EARTH REVOLVED AROUND THE SUN (HELIOCENTRIC) BUT DISPLAYED THE RESULTS ON THE PLANETARIUM AS IF IT WERE THE OTHER WAY AROUND. HOWEVER, AN ASTUTE OBSERVER COULD SEE THE DECEPTION AND HOPEFULLY NOT “OUT” THE INVENTER AS A HERETIC AND GET HIM KILLED.

          I'm not understanding what prime number maths has to do with this. Can you please explain?

          I agree with the rest of the stuff you said in your posting... SOTB

          1. Quote: I’m not understanding what prime number maths has to do with this. Can you please explain?

            Three parts –

            1) Digital math for comparison
            Base 10 math allow the number 0 to 9 before an increase in digits – that is – the first digit is modulus of the base. The second digit is then raised by first exponent of the base ie 10 = 1 * 10^1 and the second digit likewise the second exponent ie 100 = 1 * 10^2
            Digital math can be used for devices like the Curta but the Curta is only capable of one calculation per cycle.
            If you were to use base 10 for the Antikythera Mechanism or digital math it would probably be the size of a small building. Just not practical at all.

            2) Fixed period non-synchronous planetary maths
            The mathematicians that designed this could move around in many different number system just as just as easily as we move around only one.
            They knew that it is pointless (to them) to be restricted to number bases that are an integer in some other arbitrary number base system. Ie why listen to the argument that you can’t have – say – 1 to the base 0.5 (which would be 20 in base 10) because 0.5 is not an integer in base 10. You could simply argue well 0.5 to the base 0.25 is an integer in base 10 so – that perspective it irrelevant and the base is completely arbitrary even to the extent that a non-integer base is valid.
            Phew
            So they used bases that derived from planetary periods. So you get this sort of thing –
            x * time (an input) to the base of the planetary period of one planet (which this calculation relates to) will yield unity when x is equal to the planetary period of the planet – simple. Unity being one rotation of a gear that represents a position. Now do the same for another planet and you can create a ratio between the bases the represents the relationship (time wise) between the planets.

            3) Now forget most of the above as it’s not the practicably solution.
            If you have a gear that has 400 teeth because it represents (time to base 400) a planet that rotates every 400 time units AND another gear that it drives that has 50 teeth because it represents a planet that rotates every (time to base 50) where the relationship is 4:1.
            This is not a practical solution because it requires a large gear.

            You could instead 50 tooth cog that drives a 50 tooth and a 8 tooth. A much small gear size.

            The process for working this out is simply factorising the ratios into there prime number factors. And that’s where the primes come from.

            4) Practical limitations.
            This device does not represent the limits of their math or observations. As well as the limitation of gears size (and hence largest prime number base) they are also limited to integer numbers only for teeth (obviously).

            This is demonstrated by the part (cog) designated “K2” in the second diagram on this page. It is one of the two inputs to the differencing stage and has two teeth missing. The differential stage itself is not a device that subtracts, rather it takes the difference between two rotation rates. The missing two teeth subtract 1 (or perhaps 2) from one of the inputs. This is an “error” correction to get the device closer to the results they get with their *actual* math because it’s not mechanically practical to include the largest prime used in their normal math.

            One note: If someone wants to evaluate this themselves they will find a error ratio of 2:1 in the Moon gears. This is because the Moon hand (an axil) actually holds a small sphere that rotate between a black side and a white side representing Moon phase. To rotate, the Moon axil has a pinion gear that meshes at 45 degrees with a flat gear that concentric on the face. Obviously the face gear has twice as many teeth as the axil gear.

  9. It was the first of its kind. They said it would allow you to navigate your vessel with only minor knowledge of constellations. They never mentioned you had to be good at math. Those poor sailors never found their way home.

    1. Ross Reed – Where did you read that the AM gear was used in a device used for NAVIGATION? First a boat’s pitching and yawing would throw off any semblance of accuracy. That was an age old problem with clocks and stuff used for marine navigation. Then MARCELLUS (Roman commander that stole Archimedes gadget) only used the device as psyops (psychological operations). He could use it to predict Lunar Eclipses which was a big thing with some of his enemies. He used it as a force multiplier and really fricked out his superstitious enemies by either knowing when it was going to happen or making it look like he was causing a lunar eclipse on queue. I’ve seen this tactic in many a movie about fricking out superstitious natives.

  10. OK, I am still hoping for some clarification. This article describes this device as geocentric when it certainly appears to me to be sun-centric.

    The crank turns two cogs the same size but in opposite direction. One is labelled Sun so the movement other is not only directly (counter) proportional to the sun it has exactly the same rotation speed. Every other gear is driven by this which means everything is derived from the Sun.

    The only body that is directly driven by the Sun is the Moon and this is because the Earth has a complementary rotational periodic relationship with both of these. Other things like units of time are also directly driven as these are independent of your view perspective.

    Everything else is driven by a differentiator that serves the propose of transferring the mathematical point of reference for other bodies from the Earth to the Sun.

    Don’t be confused by the fact that the gear for a synodic (Lunar) month is driven by the differentiator. While it is true that the phase of the moon is an observation from Earth, what you are actually looking at is a relationship to the Sun’s shadow caused by the Earth so it’s a complex relationship of all three. If you have already creates gears (math) for that relationship then it’s easier to use that as a starting point for the next step.

      1. I spent some time looking at this and I well understand the confusion now.

        The machines was made from just as much observation as it was calculation.

        I maintain that the math appears heliocentric but that is of little consequence when the only two direct visual outputs are the Sun and the Moon both of which have a one to one rotational relationship with the Earth so it’s irrelevant weather the math is done heliocentric or geocentric as they’re both one to one relationships anyway. By one to one I mean that one rotates around the other so it matters not what your perspective is – one is simply the inverse of the other. By direct visual display, I mean that it displayed *as it would appear* rather than in a table or indexed format where other calculations or observations can be included (hidden) in the format.

        I was hoping to find some 3D model as there is a “subtract 2” gear that intrigues me. I suspect it was used in conjunction with a geared ration instead of a very large prime number in much the same way we use 22/7 instead of PI. Knowing what the largest projected prime *approximation* was would tell the accuracy if the planetary calendar.

        Anyway I learnt something.

        Thanks, for the help along the way.

        And as for the heliocentric believers – off with their heads. lol

  11. I’m rather surprised there is no mention of the work done at the Univ. of Puget Sound in Tacoma, WA. At least two faculty have been deeply involved in this for ages. I think there is some of the work on display – not sure though since I have not been there in many years. IIRC they made a working model some time ago.

    1. TheRegnirps – I understand Evans and Carman arriving at the 205 B.C.E. which puts the A.M. in Archimedes lifetime. However, he already had one of his own according to Cicero, and the Italians (i.e. Romans) stole it after murdering him. Also what would a Archimedes Planetarium be doing off the coast of Island of Antikythera? He was in Syracuse. Island of Antikythera is 700+ Km in the WRONG direction from Rome via Syracuse. Also 100 to 150 BCE would fit better for Hipparchus and Posidonius who are better candidates as the creators of the A.M. And Cicero claims it was Posidonius’ planetarium that was stolen by the Romans at Antikythera for some sort of parade in Rome for Julius Caesar.

      Evans and Carman could be right that the A.M. is designed to start in 205 BCE. Haven’t you used a astronomical prediction software to go back in time to see what was visible in the heavens at an ancient time? Maybe Hipparchus and/or Posidonius designed it to go back to Archimedes days to see what he saw. Maybe they had access to the first unit and the same Babylonian tables too. I’m not sure but I think the wood remnants from the box it was in was Carbon dated to 100-150 BCE. 205 BCE is not based on radiometrics.

  12. The mechanism is really interesting, but I have a more basic question. How did they machine gears with over 200 teeth and actually make them mesh? The tooth spacing, tooth width and pitch diameter would have to be very very close or the thing would bind. Too loose and it wouldn’t be an accurate calculator. So, how do you make the gears? THAT’s an article I would love to read.

    1. Willie – Total Wild Arse Guess? Clay mold hand made by a sculptor artisan. That way intricate details could be added. Fire it in kiln oven until super hard. Then pour molten bronze in the finished mold. Let it cool for several days. Maybe the bronze gear will just come right out for sanding with a rasp file or maybe the mold had to be broken off. Possibly coat the mold with paraffin to prevent sticking. Then the metalworker (i.e. blacksmith?) could weld on the center braces and axis spindle. The designer would probably draw it out on papyrus or even rice paper in fine detail, The sculptor would match it up perfectly. The drawings were probably to scale too as the gears needn’t be huge. The planetariums, as they were called, would probably only be as big as a old fashioned floor model color TV. That’s portable in BC times.

      SOTB

  13. Mechanism is Heliocentric, display is Geocentric. The gears convert automatically. It doesn’t mean they thought the sun went around the earth, any more than printing a map on a flat sheet of paper means that we think the earth is flat.

    How did they make the gears? Very Carefully! 8-)

    Probably not cast, because clay molds tend to change size as they dry. But they very well could have used complex jigs and holding mechanisms. Few survive, but they were quite common in use long before modern machinery.

    1. The A.M is geocentric for the same reason astronomy and planetarium apps show is the sky from the Earth. Because the people using them are probably standing on the Earth looking at the sky. The decision to make it geocentric was one of practicality. Knowing how the sky looks from Jupiter, the sun or moon while using the device on Earth would be useless to the people of the time.
      As for making the gears, watch the Nova special on the A.M. A clockmaker manages to make a gear from brass bar stock with little more than a scribe, a compass, a hammer and chisel and a file. He first scribes a circle, decides how many teeth he wants then scribes them out, punches out a rough disk with the hammer and chisel then goes about the long work of carefully filing out the teeth.
      Most of the people reading this site are pretty clever, but man you guys can over-think things AND be so impatient.
      I get the impression the ancients were much more willing to accept that things can take time to make. There are many people today who just can’t conceive of ancient people building the pyramids because they didn’t have modern equipment. They didn’t have jack hammers and cranes but they did have thousands of workers and a couple decades before the pharoh died.
      They had brass and bronze as well as whatever tools they could make. If the A.M. would let them accuratey predict the positions of the planets I can imagine them eagerly awaiting the machine but also wanting it built correctly. I’d bet there was some trial an error and more than a few mistakes but the Greeks had some amazing mathematicians. They did all their work with their brains, pen an paper. No electronic or even mechanical computers!

  14. Carl W. Sumner – It did not have to be clay mold as I said. I was only guessing. A sculptor could use soapstone, marble, alabaster, etc. and coat it with bees wax. They could be very intricate with the details like the teeth. Then poured molten bronze in the mold. Those rocks would not shrink. Getting the finished product out would be a challenge though. Italian scientists found some more parts in Rome that looked like the A.M. They think it was Marcellus’ booty of Archimedes Planetarium. Here’s the YouTube video dated 2013 – it’s in Italian with English subtitles. /watch?v=miiY69hc_lA
    Put Youtube URL in front of that...

  15. Great article, I just need to make a small historical clarification on the last paragraph and how the automata knowledge reached Arabs. The Greek civilisation never fell per se, as it was never represented by a solid state. Instead, it got transformed into the Byzantine civilisation via the christianisation of the Roman empire. The problem with christian Byzantine Greeks is that they didn’t favour science and technology at all, in fact they related them to paganism and did not wish to promote them (though they didn’t ban them either). However, when the Arabs conquered the near East and northern Africa from the Byzantine empire, they also incorporated many significant Greek cities, the most notable being Alexandria (and the famous library). The Arabs found interest in scientific Greek works and translated them from Greek to Arab, and so they eventual produced their own works on the subjects. In the meantime, christian Europe had no interest in those works. In fact, what we know today as western Europe was experiencing dark barbaric ages. With the Roman empire run down by Goths, the link to the classical word was lost and got re-established 800 years later when the Byzantine Greeks fled from Constantinople to Florence and re-translated ancient Greek works to Latin. This started the renaissance and inspired people like Da Vinci to work on Automata.

  16. Brilliant article – I’m amazed I haven’t found this before with the amount of reading I do on this amazing machine.

    I just thought that you might like to know that I’ve actually built one – with all hand cut wooden gearing – and it works beautifully! My version also includes the complex gear train to run the planet position pointers.

    It’s taken the best part of two years to get to this point but the prototype now appears to be working exactly as shold – I’vegot to say that it does look really cool with all gearing spinning. I’m currently working on the MK2 version which will include the spiral dials and all the pointers – the prototype had all the output shafts but it was never meant to be anything other than a proof that the machine could be built with wooden gearing, and it can!
    I’m hoping to get the MK2 version finished in the next few months, I just wish that there were more hours in the day…

    [IMG]http://i1295.photobucket.com/albums/b629/minimoa12/Mobile%20Uploads/20150607_081248_zpsty3yjeun.jpg[/IMG]

    Thanks again for article.
    Cheers,
    Dave.

    Thanks

  17. Hmm… the photo link in my previous post doesn’t seem to be working for some reason, and I managed to report my own post to admin – great start.
    Right, here’s another go at the photo – if this doesn’t work I’ll try something different.

    Dave.

  18. Hi Kristina – thank you!

    After working at it for what seems like forever, it’s nice when somebody notices what you’re up to.
    I’ve been talking about it almost from the start on a web forum called Brass Goggles. It specialises in steampunk culture but also has a reasonably active clock and gear wheel section (which they call Chronoautomata) for the kind of thing that I do – wooden orreries mainly. So although what I build isn’t strictly steampunk, the folk there seem to like what I do.

    Here is a direct link to the start of my Antikythera Mechanism posts – it does drone on for six pages I’m afraid. Hope you enjoy the read.

    http://brassgoggles.co.uk/forum/index.php/topic,43364.125.html

    Thanks again,
    Dave.

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