Scientists have a new understanding of the mysterious Antikythera mechanism, challenging the assumptions of ancient technology
Tony Freeth is a member of the anti-kythera research team at University College London. As a mathematician and award-winning film producer, Fries has been researching the mechanism of Antikythera since 2000 and promoting it through films and presentations. Image Credit: Nick Higgins
Tony Freeth is a member of the anti-kythera research team at University College London. As a mathematician and award-winning film producer, Fries has been researching the mechanism of Antikythera since 2000 and promoting it through films and presentations. Image Credit: Nick Higgins
In 1900, diver Elias Stadiatis, wearing a copper and brass helmet and a heavy canvas suit, emerged from the sea in horror, muttering "One A pile of dead naked people". He is one of a group of Greek divers from Symi Island in the Eastern Mediterranean, who are looking for natural sponges. They took refuge from a violent storm near the small island of Antikythera between Crete and the Greek mainland. After the storm subsided, they dived in search of sponges and stumbled upon a shipwreck full of Greek treasures-the most important shipwreck in the ancient world discovered so far. "Dead naked people" are marble sculptures scattered on the bottom of the sea, as well as many other cultural relics. Soon after, their discovery led to the first major underwater archaeological excavation in history.
An object found at the scene, a bump the size of a large dictionary, initially escaped attention in a more exciting discovery. However, a few months later, in the National Archaeological Museum of Athens, the lump broke open, revealing a coin-sized bronze precision gear. According to the historical knowledge of the time, such gears should not appear in ancient Greece or anywhere else in the world until many centuries after the shipwreck occurred. This discovery caused great controversy.
This mass is called the Antikythera device, which is an extraordinary object that has puzzled historians and scientists for more than 120 years. For decades, the original material split into 82 pieces, leaving an extremely difficult jigsaw puzzle game for researchers to reassemble. The device appears to be an extremely complex gear astronomical calculator. Today we have a reasonable understanding of some of its operations, but there are still unsolved mysteries. We know it is at least as old as the shipwreck where it was found. Its history can be traced back to 60 to 70 BC, but other evidence suggests that it may have been made around 200 BC
In March 2021, my group at University College London, the UCL Antikythera research team, published a new analysis of the machine. The team includes me (mathematician and filmmaker); Adam Wojcik (materials scientist); Lindsay MacDonald (imaging scientist); Myrto Georgakopoulou (archaeological metallurgist); and two graduate students David Higgon (watchmaker) and Aris Dacanalis ( physicist). Our paper proposes a new explanation for the transmission at the front of the mechanism, and the previous evidence has not been resolved. We now have a better understanding of the complexity of equipment-this understanding challenges many of our preconceptions about the technological capabilities of the ancient Greeks.
We know that the Greeks of that era were accomplished naked-eyed astronomers. They observe the night sky from the perspective of the center of the earth—every night, when the earth rotates, they will see the dome of the star rotating. The relative positions of the stars remain the same, so the Greeks called them "fixed stars". These early astronomers also observed celestial bodies moving against the background of stars: the moon rotates against the star every 27.3 days; the sun takes a year.
Other moving objects are planets, which the Greeks named "wanderers" due to their unstable motion. They were the deepest problems in astronomy at the time. Scientists want to know what they are, and noticed that sometimes wanderers move in the same direction as the sun-"forward" motion-and then stop and reverse the direction to "retrograde". After a while, they reached another static point and resumed their forward movement again. These rotations are called the planet's rendezvous cycle—their cycle relative to the sun. The seemingly strange reversal occurred because, as we now know, the planets orbit the sun instead of the earth as the ancient Greeks thought.
In modern terms, the orbits of all moving celestial bodies are close to the plane of the earth's motion around the sun—the so-called ecliptic—meaning that they all follow almost the same path through the star. Early astronomers had difficulty predicting the position of planets along the ecliptic. It turns out that this task is one of the main functions of the Antikythera mechanism. Another function is to track the position of the sun and moon, which also have variable motions relative to the stars.
Most of the design of this mechanism relies on the wisdom of early Middle Eastern scientists. In particular, astronomy underwent a transformation in Babylon and Uruk (both in modern Iraq) during the first millennium BC. The Babylonians recorded the daily positions of the celestial bodies on a clay tablet, which showed that the sun, moon, and planets were repetitively moving in cycles—a fact that was essential for making predictions. For example, the moon goes through 254 cycles in the background of the stars every 19 years-this is an example of the so-called cycle relationship. The design of the Antikythera mechanism used several Babylonian relationships.
One of the early center researchers in Antikythera's research was the German linguist Albert Rehm, who was the first to understand this mechanism as a computer. Between 1905 and 1906, he made important discoveries, which were recorded in his unpublished research notes. For example, he found the number 19 engraved on a surviving fragment of Antikythera. This number refers to the 19-year cycle of the moon, called the Metonic cycle, named after the Greek astronomer Meyton, but was discovered earlier by the Babylonians. In the same segment, Rem found the number 76, which is a Greek improvement over the 19-year cycle, and 223, which is used to represent the number of lunar months in the Babylonian eclipse forecast cycle (called the Salo cycle). These repetitive astronomical cycles are the driving force behind Babylonian predictive astronomy.
The second key figure in the history of Antikythera research was a British physicist who later became the historian of science Derek J. de Solla Price (Derek J. de Solla Price). In 1974, after 20 years of research, he published an important paper "Greek's Gear". It mentions wonderful quotes from the Roman lawyer, orator, and politician Cicero (106-43 BC). One of them described a machine made by the mathematician and inventor Archimedes (approximately 287-212 BC), "On this machine the movement of the sun and moon and five stars called Wanderers are depicted. ..... (five planets)... Archimedes... came up with a way to use a device to accurately represent the various motions of the earth rotating at different speeds." This machine sounds like an Antikythera mechanism. This passage shows that although Archimedes lived before we believe the device was made, he may have established the tradition that led to the Antikythera mechanical device. The Antikythera device is probably based on Archimedes' design.
For decades, researchers have been trying to decipher the working principle of the device by observing the surface of its disintegrating fragments. In the early 1970s, they finally got a peek inside. Price worked with the Greek radiologist Charalambos Karakalos to perform X-ray scans of the fragments. To their surprise, the researchers found 30 different gears: 27 of the largest fragments, one for each of the other three. Karakalos and his wife Emily were able to estimate the number of teeth of a gear for the first time, which is a key step in understanding the calculations of the mechanism. This machine looks more complicated than anyone thought.
X-ray scans are two-dimensional, which means that the structure of the gears looks flat, and they only show partial pictures of most gears. Scientists can only infer the number of teeth in many gears. Despite these shortcomings, Price determined a gear train-a set of interconnected gears-to calculate the average position of the moon on any given date by using its periodic relationship of 254 star revolutions in 19 years. The gear train is driven by a distinctive feature of the front of the mechanism called the main drive wheel, starting with a 38-tooth gear (twice as much as 19 because a gear with only 19 teeth is a bit too small). This 38-tooth gear drives (through some other gears) a 127-tooth gear (half of 254; all require too large gears).
The device appears to be used to predict the position of the sun, moon, and planets on any particular date in the past or future. The manufacturer of the machine must calibrate these objects with their known positions. Then, the user only needs to turn the crank to the desired time range to view the astronomical forecast. For example, the device displays its position on the "Zodiac Disk" on its front. The ecliptic is divided into dozens of 30-degree sections, representing the zodiac. Based on the X-ray data, Price developed a complete model of all transmissions on the equipment.
Price's model is my introduction to the mechanism of Antikythera. In fact, my first paper "Challenge the Classical Research" was a complete dismantling of most of the gear structure that Price proposed for the machine. Nevertheless, Price correctly determined the relative position of the main fragments and defined the overall architecture of the machine, with the date and zodiac dials on the front and the two large dial systems on the back. Price's achievement is an important step in solving the mystery of Antikythera.
The third key figure in the history of Antikythera research is Michael Wright, who is the former curator of mechanical engineering at the Science Museum in London. In 1990, Wright collaborated with Australian computer science professor Alan G. Bromley to conduct a second X-ray study of the mechanism using an early 3-DX ray technique called linear tomography. Bromley died before the results of this work, but Wright persevered and made important progress, for example, in identifying the key number of teeth in gears and understanding the upper dial on the back of the device.
In 2000, I proposed the third X-ray study, which was conducted in 2005 by a group of scholars from England and Greece in cooperation with the National Archaeological Museum of Athens. X-Tek Systems (now owned by Nikon) has developed a prototype X-ray machine that can use microfocus X-ray computed tomography (X-ray CT) to take high-resolution 3-DX-ray images. Hewlett-Packard uses an excellent digital imaging technique called polynomial texture mapping to enhance surface detail.
The new data surprised us. The first major breakthrough was that I discovered that this mechanism can predict solar eclipses in addition to the motion of celestial bodies. This discovery is related to the inscription discovered by Rehm, which mentions the 223-month cycle of the Saros solar eclipse. The new X-ray film shows that there is a 223-tooth large gear at the back of the mechanism, which can make the pointer circling out, a total of four revolutions, divided into 223 parts, which lasted 223 months. Named after the customary name of the Babylonian eclipse cycle, the Salo dial predicts which months there will be solar eclipses, and the characteristics of each eclipse, as described in the inscription in the mechanism. The discovery revealed an impressive new feature of the device, but it left a big problem: a set of four gears located within the circumference of the large gear does not seem to have any function.
It took months to understand these gears. When I did this, the results were surprising. It turns out that these gears calculate the variable motion of the moon in a very beautiful way. In modern terms, the motion of the moon is variable because its orbit is elliptical: when it is farther away from the earth, it moves more slowly towards the stars; when it gets closer, it moves more. quick. However, the moon’s orbit is not fixed in space: the entire orbit rotates in less than nine years. The ancient Greeks did not know about elliptical orbits, but they explained the subtle motion of the moon by combining two circular motions in the so-called planetary theory.
Based on an extraordinary observation by Wright, I figured out how the mechanism calculates the turnover theory. He studied two of the four mysterious gears on the back of the mechanism. He saw a pin on the surface of one of the gears that meshed with the groove on the other gear. This seems to be a useless arrangement, because the gears will definitely rotate together at the same speed. But Wright noticed that the gears were rotating on different axes a little more than a millimeter apart, which meant that the system would produce variable motion. All these details appear in the X-ray CT scan. The shafts of the gears are not fixed-they are revolvingly mounted on the 223-tooth large gear.
Wright rejected the idea of these gears to calculate the variable motion of the moon, because in his model, the 223-tooth gear turned too fast to make sense. But in my model, the 223-tooth gear rotates very slowly to turn the hands of the Salo dial. The planetary theory of calculating the moon with planetary pin-grooved gears in this subtle and indirect way is an extraordinary idea of the ancient Greeks. This ingenuity reinforces the idea that the machine was designed by Archimedes. This study of the rear dial and gear mechanism completes our understanding of the mechanical rear and harmonizes all the evidence so far. My colleagues and I published our research results in the journal Nature in 2006. However, the other side of the device remains a mystery.
The most prominent feature in the front of the largest debris is the main drive wheel, which is designed to rotate once a year. It is not a flat plate like most other gears; this one has four spokes and is covered with puzzling features. The spokes indicate that they are equipped with bearings: they have round holes for rotating shafts. The outer edge of the gear contains a circle of pillars-the little fingers stand upright, and the shoulders and perforated ends are obviously used to carry the plates. Four short pillars hold a rectangular plate, and four long pillars hold a disc.
Following Price, Wright proposed to install an extensive planetary system on the main drive wheels—the idea of two circles that the Greeks used to explain the strange reverse motion of planets. Wright even built an actual model gear system out of brass to show how it works. In 2002, he published a groundbreaking planetarium model for the Antikythera installation, which showed all five known planets in the ancient world. (The discovery of Uranus and Neptune in the 18th and 19th centuries, respectively, required the appearance of a telescope.) Wright showed that the planetary wheel theory can be transformed into a planetary wheel system with a pin and groove mechanism to show the variable motion of the planets.
When I first saw Wright's model, I was shocked by its mechanical complexity. It even has eight coaxial outputs—all tubes are concentrated on one axis—to bring information to the front display of the device. Is it really credible that the ancient Greeks could build such an advanced system? I now believe that Tete’s coaxial output concept must be correct, but his gear system does not match the economics and originality of known gear trains. The challenge for our UCL team was to coordinate Wright's coaxial output with our understanding of the rest of the equipment.
A key clue comes from the X-ray CT study in 2005. In addition to displaying gears in three dimensions, these scans also provide an unexpected revelation—thousands of new text characters are hidden in fragments that have not been read for more than 2,000 years. Rem proposed in his research notes from 1905 to 1906 that the positions of the sun and planets are shown in a system of concentric rings. The device initially had two covers-front and back-to protect the display and include a large number of inscriptions. The inscription on the back cover scanned in 2005 is the user manual of the device. In 2016, Alexander Jones, professor of the history of astronomy at New York University, found definitive evidence of Rehm's idea in this inscription: it described in detail how the sun and planets were displayed in the ring, and marked their positions with marker beads.
Any working model of the mechanism should fit this description—an explanation literally engraved on the back cover of the device, describing how the sun and planets are displayed. However, due to technical problems that we cannot solve, the previous model failed to include this ring system. Wright discovered that the device uses a semi-silvered sphere to display the moon phase, which is calculated mechanically by subtracting the solar input from the lunar input. But such a process seems incompatible with the ring system used to display planets, because the output of Mercury and Venus prevents the moon phase device from accessing the input from the sun gear system. In 2018, Higgon, a graduate student of our UCL team, came up with a surprisingly simple idea that cleverly solved this technical problem and explained a mysterious perforated block on the spokes of the main drive wheel. This block can transmit the "average sun" rotation (as opposed to the variable "real sun" rotation) directly to the moon phase device. This setup enabled a ring system for the front of the Antikythera mechanism, which fully reflected the description in the inscription on the back cover.
When trying to decipher the front of the device, the planetary cycles built into the device must be determined, because they define how the gear train calculates the planet's position. Early research hypothesized that they would be based on the planetary cycle relationships derived by the Babylonians. But in 2016, Jones' discovery forced us to abandon this assumption.
The X-ray CT of the inscription on the cover shows that it is divided into five planets each. In the part of Venus, Jones found the number 462; in the part of Saturn, he found the number 442. These numbers are very staggering. No previous research has shown that ancient astronomers knew about them. In fact, the time relations they represent are more accurate than those found by the Babylonians. The manufacturer of the Antikythera device seems to have discovered their own improved cyclic relationship between the two planets: Venus has 289 rendezvous cycles in 462 years, and Saturn has 427 rendezvous cycles in 442 years.
Jones never figured out how the ancient Greeks came to these two periods. We started to try ourselves. Dacanalis, another of our University College London graduate students, collected a comprehensive list of planetary cycle relationships and their estimation errors from Babylonian astronomy. Can the combination of these early relationships be the key to a more accurate Antikythera relationship? In the end, we discovered a process developed by Elia’s philosopher Parmenides (6th to 5th centuries BC) and reported by Plato (5th to 4th centuries BC) to combine known period relations to Get a better relationship.
We recommend that any method used by the creators of Antikythera requires three criteria: accuracy, decomposability, and economy. The method must be accurate to match the known periodic relationship of Venus and Saturn, and it must be decomposable so that gears small enough to calculate planets can be used to fit the mechanism. In order to make the system economical, if the cycle relationship shares the main factors, different planets can share gears, thereby reducing the number of gears required. This economy is a key feature of the surviving gear train. Based on these criteria, our team used Parmenides' ideas to derive the 462 and 442 cycles, and used the same method to find the missing cycles of other planets, the inscriptions of these planets are missing or damaged.
With the periodic relationship of the planets, we can now understand how to install the planetary gear train into the small space available. For Mercury and Venus, we theorized the economical five-gear mechanism and pin-slot device, similar to the mechanism Wright designed for these planets. We found strong supporting evidence in a four-centimeter-diameter fragment to support our reconstruction. In this work, X-ray CT shows a disc connected to a 63-tooth gear that rotates on a D-shaped plate. The numbers 63 and 462 (Venus period) share prime factors 3 and 7. The gear train using 63-tooth gears can be designed to match the bearing on one spoke of the main drive wheel. The Mercury’s similar design matches the features on the opposite spokes. These observations give us full confidence that we are on the right track of Mercury and Venus.
For the other known planets-Mars, Jupiter, and Saturn-our team conceived very compact systems to fit the available space. These designs completely deviate from the system Wright designed for these planets. Working independently with Christián C. Carman of the National University of Quermes in Argentina, I have proved that the subtle indirect transmission system for the variable motion of the moon can be applied to these planets. Our UCL team proved that these gear systems can be expanded to incorporate new periodic relationships of planets. This system allows Antikythera manufacturers to mount multiple gears on the same board and design them to precisely match the cycle relationship.
These economical seven-speed trains can be intricately interlaced between the plates on the main drive wheel pillars so that their output conforms to the customary cosmic order of the celestial bodies-Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn-to determine the ring The layout of the system. The size of the space available between the boards fits these systems perfectly, with some spare capacity and some evidence that is still unexplainable.
We have added a sun variable motion mechanism and a planetary mechanism for calculating the "node" of the moon-the point where the moon's orbit crosses the ecliptic plane, making solar eclipses possible. A solar eclipse occurs only when the sun is close to one of these nodes during the full or new moon. Astronomers in the Middle Ages and the Renaissance referred to the double-headed pointer of the moon node as the "dragon hand." The planetary gear transmission of this dragon's hand also accurately explained a protruding bearing on a spoke that did not seem to have any function before. We finally explained all the functions on the main drive wheel; we published our findings in Scientific Reports in March 2021.
We now understand how the front display matches the description in the user manual on the back cover, with the sun and planets displayed by marker beads on concentric rings. The cover also shows the moon phase, location and age (the number of days from the new moon), as well as the dragon's hand showing the year and season of the lunar eclipse.
With the concentric rings of planets, we realized that we can now also understand the inscription on the cover. This article is a formulaic list of the rendezvous events of each planet (such as its rendezvous with the sun and its resting point) and the number of days between them. On the back panel, the inscription of the solar eclipse is indexed to the mark on the Salo dial. On the front panel, inscriptions about the rising and falling of stars are indexed on the dial of the Chinese zodiac. Our opinion is that the previous inscription may refer to the index letters on the planetary rings: if the sun pointer is on one of these letters, then the corresponding inscription entry describes the number of days for the next rendezvous event. Because the left side of the inscription (where we expect these index letters to be) is missing, we cannot prove this hypothesis-but it is a convincing explanation.
The device is unique among the discoveries at the time. It single-handedly rewritten our understanding of ancient Greek technology. We know that they are very capable-they built the Parthenon and Alexandria lighthouse even earlier than the Antikythera mechanism. They have pipes and use steam to operate equipment. But before the discovery of the Antikythera mechanism, ancient Greek gears were thought to be limited to coarse wheels in windmills and watermills. In addition to this discovery, the first known precision gear mechanism was a relatively simple but impressive gear sundial and calendar at the time, which originated in the Byzantine style around 600 AD. It was not until the 14th century that scientists created the first complicated astronomical clock. The Antikythera mechanism has precision gears about one millimeter long, which is completely different from any other device in the ancient world.
Why did scientists spend centuries reinventing something as complex as the Antikythera device, and why didn't archaeologists discover more such mechanisms? We have every reason to believe that this object cannot be the only model of its kind-its development must have an aura. But bronze is a very valuable metal, and when such an object stops working, its material may be melted. Shipwrecks may be the best prospect for finding more shipwrecks. As for why this technology seems to have been lost for so long before being re-developed, who knows? There are many gaps in historical records, and future discoveries are likely to surprise us.
With the Antikythera mechanism, we obviously have not made it to the end. We believe that our work has made significant progress, but there are still many mysteries to be solved. Due to the loss of a large amount of evidence, the UCL Antikythera research team is not sure whether our reconstruction is completely correct. It is difficult to match all the surviving information. In any case, we can now see more clearly than ever what a great achievement this object represents.
This article was originally published in "Scientific American" 326, 1, 24-33 (January 2022), with the title "Miracle of the Ancient World"
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