Antikythera Mechanism

Anticitera mechanism (Figure A – reverse)

Anticitera Mechanism (French A – reverse)

The Antikythera mechanism is an ancient analog (or mechanical) computer. Supposedly built by Greek scientists, the instrument is dated to between 150 B.C. C. and 100 B.C. C., or, according to a recent observation, around the year 200 B.C. The component was recovered in the Aegean Sea, between 1900 and 1901, from an ancient shipwreck near the Greek island of Antikythera. This artifact was apparently designed to predict astronomical positions and eclipses of up to nineteen years with astrological and calendrical purposes, and also predict the exact date of six ancient Greek contests, including the four major Panhellenic games and two more minor games.

It must have been housed in a wooden box whose dimensions were 340 by 180 by 90 millimeters; the device is a complex clockwork mechanism made up of at least 30 bronze gears. The remains were found as 82 separate fragments, only seven of which contained significant inscriptions or gears. The largest gear (clearly visible in fragment A on the right) is approximately 140 mm in diameter and originally had 223 teeth.

It is likely that the Antikythera mechanism was not the only one, as Cicero's references to these mechanisms show. This supports the idea that there was a tradition in ancient Greece of complex mechanical technology. All the recovered fragments of the Antikythera mechanism are kept in the National Archaeological Museum of Athens.

In De re publica, Cicero mentions two machines designed and built by Archimedes, which contemporary analysts consider to be planetary-type mechanisms, predictors of the movements of the Moon, the Sun, the major known planets and eclipses. These machines passed into the hands of the Roman consul Marco Claudio Marcelo after the siege of Syracuse, which occurred in 212 a. C.

The spread of this technology was interrupted at some point in antiquity, and technological artifacts approaching the complexity and skill of construction of this instrument did not appear again until 1,600 years later, when clock development began. astronomical in Europe, around the 14th century.

History

Discovery

The Antikythera Mechanism was discovered 45 meters underwater near Glyfadia, on the Greek island of Antikythera. The remains of the old shipwreck were found in April 1900 by a group of sponge-gathering divers; they recovered numerous artifacts, including bronze and marble statues, pottery, glassware, jewelry, coins, and the mechanism. The finds were sent to the National Archaeological Museum in Athens for analysis and storage. The mechanism lay unnoticed for two years as a lump of corroded bronze and wood until the museum team began to piece together the more obvious pieces of the mechanism.

On May 17, 1902, when archaeologist Valerios Stais was examining the remains, he noticed that one of the pieces of rock had an embedded gear. Stais initially believed that it was an astronomical clock, but most of the team believed that the instrument was too technologically advanced and complex to have been built at the same time as the rest of the pieces found. Research was abandoned until the instrument came to the attention of Derek John de Solla Price in 1951. In 1971, Price and a nuclear physicist named Charalampos Karakalos analyzed the 82 fragments with X-rays and gamma rays. Price published a lengthy 70-page essay on the results in 1974.

How the mechanism got on the ship is unknown, but it has been proposed that the instrument was planned to be brought to Rome with the rest of the loot for Julius Caesar's triumph celebration.

Research on its chronology and origin

The island of Anticitera is located between the peninsula of the Peloponnese and the island of Crete.

Although generally referred to as the first analog computer, the quality and complexity of the mechanism's manufacture suggest that it has as yet undiscovered predecessors made in the Hellenistic period. Its construction is based on theories of astronomy and mathematics developed by Greek astronomers. The estimate on the date of manufacture made by the museum of Athens is that it must belong to the second half of the 2nd century BC. C, mainly based on the epigraphic analysis of the preserved texts.

In 1974, British science historian and Yale University professor Derek John de Solla Price concluded, from gear settings and inscriptions on the mechanism faces, that the instrument was made around 87 B.C. and lost a few years later Jacques Cousteau and his associates visited the wreck in 1976 and recovered coins dating between 76 and 67 BC. Although the advanced state of corrosion has made analysis of its composition impossible, the device is believed to be made of an alloy of copper and tin (approximately 95% copper and 5% tin). The instructions for use are written in Koine with Corinthian dialectal features and the prevailing belief among professionals is that the mechanism was created in the Greek-speaking world.

The results of the studies carried out from 2005 by the Antikythera Mechanism Research Project suggest that the concept of the mechanism originated in the Corinthian colonies, since the dialect of the inscriptions so determines. More specifically, Syracuse was a very prosperous former Corinthian colony and home to the great engineer Archimedes, which could imply a connection to the Archimedean school. Another theory suggests that coins found by Jacques Cousteau in the 1970s in the wreck date back to the time the mechanism was built and its origin is the Greek city of Pergamon, home of the famous Pergamon Library. Thanks to the number of manuscripts on science and art, it is the second most important library, after the Library of Alexandria, from the Hellenistic period.

The vessel carrying the mechanism also carried vessels in a Rhodian style; this leads to the belief that the mechanism was built at an academy founded by the stoic philosopher Posidonius on that Greek island. Rhodes was a busy trading port and was also a center of astronomical and mechanical engineering, home to Hipparchus of Nicaea, who was active from 140 B.C. C. until the year 120 a. The fact that the mechanism draws on Hipparchus's theory of the motion of the Moon indicates that he may have designed it or contributed to its construction.

In 2014, a study conducted by Carman and Evans argued that the origin of the mechanism was actually 200 B.C. According to Carman and Evans, the Babylonian style of predictive arithmetic fits the predictive model of the mechanism better than the traditional Greek trigonometric style.

In a study published in 2017, Paul Iversen argues that the Antikythera mechanism was a device created for an Epirus client from a prototype that had originally been made for use on the island of Rhodes.

Description

Apparently, the original mechanism left the Mediterranean as a single encrusted piece; soon after it fractured into three main pieces. Various small pieces of the interior have broken off while the mechanism was being handled or cleaned, and others were found on the sea floor by Cousteau's expedition. There is a possibility that there are more fragments stored since the discovery of the mechanism and have yet to be discovered; fragment F came to light in this way in the year 2005. Of the 82 fragments, 7 are mechanically significant and contain most of the mechanism inscriptions; there are another 16 fragments that contain partial and incomplete inscriptions.

Major Fragments

Minor Fragments

Many of the smaller fragments that have been found contain nothing of value; however, sixteen of them have inscriptions. Some of them, which were previously thought to describe instructions on the function of the rear discs, actually only contain descriptions of the rear discs. The absence of instructions suggests that the person for whom the mechanism was intended was well educated. in astronomy.

Mechanism

Operation

Modern reconstruction of the mechanism by Mogi Vicentini in 2007.

On the front face of the mechanism (see reproduction here:) there is a ring-shaped disc, fixed to the structure, which represents the ecliptic and the 12 zodiac signs marked in 30-degree sectors. This agrees with the Babylonian custom of assigning one twelfth of the ecliptic to each zodiac sign equally, although the constellation boundaries were variable. Outside the disk is another ring that is rotating; this is marked with the months and days of the Egyptian calendar: 12 months of 30 days plus 5 epagomenal days. The months are marked with their respective Egyptian names transcribed into the Greek alphabet. The first task is to rotate the Egyptian calendar to match the zodiac signs on the artifact with current ones. The Egyptian calendar ignored the 5 epagomenal days, so it advanced completely by one zodiacal symbol in approximately 120 years.

The mechanism was operated by rotating a crank (now lost) that was connected by a crown-shaped gear to the larger gear, the gear with four teeth at the front of the fragment has been called B1. This moved the cursor on the front disk which would select the correct day on the Egyptian calendar. The year was not selectable, so it was necessary to know the currently selected year or look up the cycles with the help of the various calendar cycle indicators on the back of the Babylonian ephemeris tables for the selected day of the year, since the cycles of the calendar are not synchronous with the year. The crank moved the date cursor for 78 days each full rotation; this made it easier to select a particular day if the mechanism was in good condition. The action of turning the handle of the crank would cause the interconnected gears within the mechanism to rotate; this resulted in the simultaneous calculation of the position of the Sun and the Moon, the lunar phase, eclipse, calendar cycles and possibly the position of planets.

The operator also had to be aware of the position of the spiral selector cursors on the two discs on the back of the mechanism. The slider had a “follower” that would track the spiral incisions in the metal as the discs entered 4 or 5 full rotations of the slider. When a cursor reached a terminal month position at the end of the spiral, the cursor follower had to be manually moved to the other end of the spiral before operation could continue.

Faces

Front face

The front disc has two concentric circular scales that represent the path through the heavens. The outer ring is marked with the 365 days of the Egyptian calendar or the Sothian year based on the Sothian cycle. In the inner ring there is a second disk marked with the Greek zodiac signs and divided into degrees. The outer calendar was not fully fixed to the inner disk, but to compensate for the effect of the extra quarter day in the solar year, the operator of the mechanism could move it back relative to the inner one by one day every 4 years.

Scheme of the known mechanism of the artifact.

The position of the Sun on the ecliptic is equivalent to the current date in the year. The Moon and the five planets known to the Greeks travel along the ecliptic closely to each other, so close that it made sense to define their position on the ecliptic.

The following Egyptian months are inscribed on the outer ring:

• 
• (Phaophi)
• (Athyr, Hathor)
• (Choiak)
• Τhib
• MORSE:
• (Phamenoth)
• (Pharmouthi)
• ・1⁄4⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄2⁄
• (Payni)
• ̄{pos(Epiphi)}
• (Mesore)
• (Ep[agomene)

The zodiac disc contained Greek inscriptions of the members of the zodiac; this is supposed to be to accommodate the tropical month version instead of the sidereal month version:

• Κ)IOσ (Krios [Carnero], Aries)
• ΤYHYPHEN (Tauros [Toro], Taurus)
• (Didymoi, Gemini)
• ΚÍ)ΚINOKOσ (Karkinos [Crab], Cancer)
• (Leon [Leon], Leo)
• (Parthenos [Virgen], Virgo)
• (Chelai, Scorpion or Zygos, Libra)
• σΚMILITARY FORM (Skorpios [Scorpion], Scorpio)
• Τοrοngοnοn οn οn οn οn οn οnοng οn οnοng οn οn οn οn οn οn οn οn οr οnοng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οng οr
• ÍI orderOΚΕ)Ω (Aigokeros [cabra], Capricorn)
• And Δ deπκεκσ (Hydrokoos [Water Charger], Aquarium)
• I isolationist (Ichtheis [Pez], Piscis)

On zodiac discs, unique characters are also found at certain points (see reconstruction here:). They are related to a Greek almanac, a forerunner of the modern almanac inscribed on the front face behind the discs. These mark the locations and longitudes of the ecliptic for specific stars. Parts of the Greek almanac read (brackets indicate inferred text):

• {Κ} Night
• { Scores} The setting of the Híades at night
• {Mm} Taurus begins to rise
• {N} Vega rises in the night
• (sighs) The Pleiades rise in the morning.
• {cHFFFF} The Hydes rise in the morning
• {cHFFFF} Gemini begins to rise
• {cHFFFF} Altair rises in the morning
• {cHFFFF} Arturo's set up in the morning

At least two cursors indicate the position of bodies on the ecliptic. A lunar cursor indicates the position of the Moon and an approximate solar cursor is also observed. The lunar position was not simply approximate, since the indicator did not describe a uniform movement but took into account the typical acceleration and deceleration of what is known today as an elliptical orbit, all this through the first known use of a planetary gear.

It also tracked the precession of the elliptical orbit around the ecliptic in a cycle of 8.88 years. The approximate position of the Sun is, by definition, the current date. It is speculated that, with all the effort put into representing the actual position of the Moon, there would be a similar accuracy for the Sun; no evidence of this has been found to date. Similarly, no evidence of planetary orbit cursors, for the five planets known to the Greeks, is found among the remains.

Lastly, mechanical engineer Michael Wright demonstrated that there is a mechanism for displaying the moon phase as well as its position. The indicator is a small sphere embedded in the moon cursor, half black and half white, which rotates to represent the moon cursor. moon phase (new moon, first quarter, half, third quarter, full moon and black moon) graphically. The information to display this feature is available given the positions of the Sun and Moon as angular rotations; in essence it is the angle between the two, translated into the rotation of the sphere. A differential is required, a gear arrangement that accumulates or differentiates two angular inputs. The Antikythera mechanism is historically the first known deliberate construction of a differential.

Back side

On the back of the mechanism are at least four discs: the two large ones calculate the metonic and Saros cycle, while the two small ones are for sports games, and exeligmos. It is possible that there were two more discs as well, one for the callipic cycle, symmetrical to that of the games and another symmetrical to that of exeligmos, but neither of these last two has been able to be confirmed by research.

The metonic disc is located on the upper side of the mechanism. The Metonic cycle, defined in various physical units, is 235 synodic months, which is very close (less than 13 millionths) to 19 tropical years. This is why this is a convenient interval to which to convert between the lunar or solar calendar. The Metonic disk covers 235 months in five disk rotations; it does this by following a spiral track with a tracker on the cursor that tracks the layer of the spiral. The cursor indicates the synodic month, counted from new moon to new moon, and the cell contains the names of the months in the Corinthian calendar or in another calendar derived from it, which could be the Epirote.

1. хрорики рания (Fenish)
2. Κ)нанининь (Cranium)
3. Урориники рики (Lanotropio)
4. MILITARY ISLAND (Macaneo)
5. ΔΩΔΕΚYΤYσ (Dodecateo)
6. Τhereinafter:
7. )Τheym apostolate (Artemisio)
8. )ndiΔ)ннния (Psydreo)
9. Уарики старики (Gamily)
10. ) He did not want to (Agrini)
11. (Panamo)
12. ∙ ∙ Русский

Therefore, the correct solar date setting on the front panel indicates the current lunar month on the reverse panel with approximately one week resolution.

It was previously believed that the callipic disk—a 76-year cycle thus comprising four metonic cycles—was the secondary upper disk within the metonic disk, but research published in 2008 established that this disk was actually Secondary top was the one that indicated the Panhellenic games. However, the inscription 76 years on fragment 19 is an indication that there could be another hypothetical disk indicating the callipic cycle and that it would be symmetrical to the game disk.

The games disc is the upper right secondary disc; it is the only cursor on the instrument that travels counterclockwise with the passage of time. The disk is divided into four sectors; each has a year indicator and the name of two Panhellenic Games. These were the Isthmian Games, the Olympic Games, the Nemean Games and the Pythian Games and also include minor games such as the quadrennial Games of the Naia (based in Dodona and in honor of Dione Naia) and another event that could be the festival of the Halieia, of Rhodes. The inscriptions in each of the four divisions are:

The Saros disk is the main lower spiral disk on the reverse of the mechanism. The Saros cycle consists of 18 years and 11 ¹⁄₃ days (6585.333… days), which is very close to 223 synodic months (6585.3211 days). It is defined as the repetition cycle of the positions needed to form the solar and lunar eclipses; therefore, it could be used to predict eclipses not at the month or day level but at the time of day. Note that a cycle is approximately 8 hours longer than an integer number of days. Translating this into global rotation, it means that the eclipse will occur not only 8 hours later but also a third of a rotation further east. Glyphs found in 51 of the disk's 223 synodic month cells specify the occurrence of 38 lunar eclipses and 27 solar eclipses. Some of the abbreviations on the glyphs say:

• σ = σιίånΗ (Luna)
• Η = Τhereafter (Sol)
• HM = ΗMiss train (day)
• ωρ = ωρα (hour)
• NY = NOYCKING FORM (night)

The glyphs indicate whether the designated eclipse is lunar or solar, giving the date of the day of the month and the time, since solar eclipses are not visible at any time, and lunar eclipses are only visible if the Moon is above the horizon at the indicated time.

The exeligmus disc is the lower right secondary disc on the reverse of the mechanism. The exeligmus cycle consists of three Saros cycles with a total of 54 years; this means that it lasts 19,756 days. Since the Saros cycle duration is 8 hours, a complete cycle of exeligmos shows the count in whole days. This is why it has inscriptions like:

• Empty (represents zero)
• H (number 8)
• I) (number 16)

As a result, the disk indicates how many hours must be added to the times of the glyphs on Saros's disk in order to calculate exact eclipse times.

Doors

The mechanism has a casing made of wood with a front and a rear door; both contain inscriptions. The back door appears to be the "Instruction Manual". In one of the fragments —the so-called fragment 19— it reads “76 years, 19 years”, which refer to the callypic and metonic cycles. The inscription "223" for the cycles of Saros can also be appreciated. In another of the fragments it is written, in the spiral subdivisions, "235" for the metonic disk.

Gear

The mechanism is extraordinary in terms of its level of miniaturization and complexity of its parts; it is comparable to the astronomical clocks of the 14th century. It has at least 30 gears, although scholar Michael T. Wright suggests that the Greeks at the time were capable of implementing more.

There is much controversy about the ability of the mechanism to predict the positions of the planets known to the Greeks at that time. No gear set dedicated to such a task has been found except for a 63-tooth gear (g1) in fragment D for which no other function has been found.

The purpose of the front face was to position astronomical bodies relative to the celestial sphere along the ecliptic from the point of view of an observer on Earth. That is irrelevant to asking whether the position was calculated using a heliocentric or geocentric view of the Solar System; whichever was used would result in the same position (ignoring ellipticity) within the error range of the mechanism.

Ptolemy's epicyclic solar system (300 years in the future of the apparent date of the mechanism) worked with more epicycles; was more accurate in predicting the positions of the planets than Copernicus until Kepler introduced the possibility that the orbits were ellipses.

Evans proposed that in order to show the approximate positions of the planets he would require 17 additional gears to be positioned in front of the main gear and using individual circular disks on the same face.

Tony Freeth and Alexander Jones have modeled and published a version using various gears mechanically similar to the lunar anomaly system allowing the indication of planetary positions as well as the synthesis of the solar anomaly. According to Freeth and Jones, their system is more authentic than Wright's model, since theirs requires skills that the Greeks of that time possessed and does not add additional complexity or internal stress to the machine.

The teeth of the gears were equilateral triangles with an average circular pitch of 1.6 mm; the average wheel thickness was 1.4mm and the average gear spacing was 1.2mm. The teeth were probably made from a bronze disk using hand tools; this is evident since they are not all uniform. Thanks to advances in X-ray technology, it is now possible to determine the number of teeth and gear sizes of the fragments found and as a result the basic operation of the mechanism is known. and it has been able to be replicated precisely. Although the doubt of the existence of planet indicators persists.

A table of gears, their teeth, and the expected number of rotations of major gears is shown below. Gear functions are from Freeth et al. (2008) and those in the second half of the table are from Freeth and Jones (2012). The calculated values start with one revolution of the gear b1 and the rest were calculated from the ratios of the gear teeth. Gears marked with an asterisk (*) have not been found or have lost predecessors; they have been calculated on the basis of what is known about the mechanism with reasonable numbers of teeth.

Table notes:

There are several gear ratios for each planet that result in close values in the calculation of synodic periods of planets and the sun. The ones chosen at the top appear to be of high precision with reasonable tooth numbers, but the specific gears that may have been used probably remain unknown.

Scheme of known gears

Scheme representing the gear of the Anticitera mechanism including the 2012 interpretation of the existing gear, additional gear to perform known functions and additional gear to perform additional functions. Among them is the precise indicator of the sun and indicators for the five known planets, proposed by Freeth and Jones (2012). It is based on a drawing of the Freeth supplement (2006) and on Epicycles Part 2 de Wright (2005). The proposed gear (in contrast to the known gear) is shaded.

The sun gear is operated from the manually driven crank (connected to gear a1 which drives the large average 4-tooth sun gear b1) and drives the rest of the gear sets equally. The sun gear is b1/b2 and b2 has 64 teeth. This directly moves the cursor of the average sun (a more precise gear of the sun may have existed which represented the elliptical anomaly of the sun; this is discussed below in Freeth's reconstruction). In this discussion, the reference are models of rotational periods of various cursors and indicators; all assume that the rotation of b1 is 360 degrees which corresponds to a tropical year, they are calculated based solely on the ratio of the mentioned gears.

The moon gear setr starts with gear b1 and continues through c1, c2, d1, d2, e2, e5, k1, k2, e6, e1 and b3 until it reaches the indicator on the front face of the mechanism. Gears k1 and k2 form a planetary gear, are identical and not connected but operate “face to face” with a pin coming out of k1 and going into a notch of k2. Both gears have different centers of rotation so the bolt moves back and forth within the notch, as the radius at which k2 operates increases and decreases, its angular velocity also varies (assuming the velocity of k1 is uniform). this being faster in certain parts. The average speeds are the same after one complete revolution, but the change in speed represents the effect of the moon's elliptical orbit as a consequence of Kepler's second and third laws. The modeled rotational period of the lunar indicator (averaged over a year) is 27.321 days, very close to the modern value of a sidereal lunar month of 27.312661 days. As mentioned before, the difference in the centers of rotation between k1 and k2 varies the time displacement of the year and mounting these two gears on the e3 gear provides a precessional advance of ellipticity modeling with a period of 8.8826 years., value similar to the current value of the lunar precession period of 8.85 years.

The system also models moon phases. The moon pointer supports a shaft through itself, on which is mounted a small shaft (r) that connects to the sun pointer at B0 (the connection between B0 and the rest of B is not visible in the original mechanism so it is unknown if B0 is the average indicator of the sun or a more accurate indicator). The gear travels through the disk with the moon but it is also oriented to the sun, this effect is to perform a differential operation so the gear rotates in the period of the synodic month, measuring the effect and the angle of difference between the sun indicators and the moon. The gear has a small sphere that is visible through an opening in the face of the moon, it is painted longitudinally with one half white and the other black showing the phases pictorially. It rotates with a period of 29.53 days; the modern value of the synodic month is 29.530589 days.

The metonic gear set is made up of b1, b2, l1, l2, m1, m2 and n1 (the latter is charging the indicator). The modeled rotational period of the indicator is 6939.5 days (through the spiral of 5 rotations) while the modern value for the Metonic cycle is 6939.69 days.

The Olympic gear set is made up of b1, b2, l1, l2, m1, m², n1, n2 and 01 (the latter is carrying the indicator). Its modeled rotational period is exactly 4 years as expected. Incidentally this is the only cursor in the mechanism that rotates counterclockwise, all others rotate counterclockwise.

The calypic gear set is made up of b1, b2, l1, l2, m1, m2, n1, n3, p1, p2 and q1 (the latter charges the gauge). Its modeled computational period is 27,758 days while the modern value is 27,758.8 days.

Saros's gear set is made up of b1, b2, l1, l2, m1, m3, e3, e4, f1, f2, and g1 (the latter charges the gauge) and has a modeled rotational period of the Saros cycle of 1643.3 days (this in 4 rotations along the track of the spiral); the modern value is 1636.33 days.

The exeligmos gear set is made up of b1, b2, l1, l2, m1, m3, e3, e4, f1, f2, g1, g2, h1, h2 and i1 (this last loads the indicator). The modeled rotational period of exeligmos is 19,756 days and the modern value is 19,755.96 days.

It appears that gears m3, n1-3, p1-2, and q1 did not survive the wreck. The functions of the indicators were deduced from the remains of the discs on the rear face, and a reasonable gear was proposed to satisfy the functions which is generally accepted.

Proposed gear diagrams

Because there is a large gap between the average sun pointer and the front of the cover, and the size of mechanical features such as the sun gear, it is very likely that the mechanism contained more gears that were lost during or after the wreck or that they were removed before being loaded onto the ship. The lack of evidence and the nature of the front of the mechanism have led to various attempts to recreate what the Greeks of that period might have done, resulting in in various proposed solutions.

Wright Proposal

Proposal by Evans et al.

Proposal by Freeth et al.

Michael Wright was the first person to design and build a model that not only contained the known parts of the mechanism, but also a simulation of a potential planetary system. He suggested that further adjustments would have been made, in addition to the lunar anomaly, for the solar anomaly (known as the "first anomaly"). He included indicators for the exact sun, Mercury, Venus, Jupiter, and Saturn, all in addition to the familiar average sun and lunar indicators.

Evans, Carman and Thorndike published a solution with significant differences from Wright's model. Their proposal is based on the spatial irregularity of the inscriptions on the face of the frontal disk that they observed, this irregularity seemed to indicate an off-center solar indicator that simplified the mechanism by eliminating the need to represent the solar anomaly. They also suggested that instead of providing precise planetary indication (proven impossible by misaligned inscriptions) there would be simple disks for each planet showing key events such as the planet's cycle, initial and final appearances in the night sky, and apparent changes in direction. This system would result in a simpler overall gear with reduced forces and complexities compared to Wright's model.

Their proposal used simple connected gears and answered the question of the 63-tooth gear in fragment D. They proposed the use of two-faced plates, one face with evenly spaced discs and another with a gap above the face to respond to criticism for the lack of use of gear b1. They proposed that instead of using pillars and supports for the gears and shafts, weather and weather icons visible through a window should be used.

In a paper published in 2012, Carman, Thorndike, and Evans proposed the use of a planetary gear system with pin-and-groove followers.

Freeth and Jones published their proposal in 2012 after extensive research and work. They proposed a compact and feasible solution to the unknown of the indication of the planets. They also proposed the indication of the solar anomaly (the apparent position of the sun on the zodiacal disk) in a separate indicator from the date indicator, which gives approximate position of the sun, just like the date on the monthly disk, in case the two disks were correctly synchronized. Its front panel was essentially the same as Wright's with the only difference being that this model was not physically built but is a 3-D computer model.

Relations of the internal gear of the Anticitera mechanism based on the proposal of Freeth and Jones.

The system for synthesizing the solar anomaly is very similar to Wright's proposal. There are 3 gears fixed to the center of gear b1 and attached to the sun axis, the second was fixed to one of the rays (in his proposal it is the lower left one) acting as an unoccupied gear and the last gear was positioned next to the previous one and was it was equipped with a bolt on which a notched arm would go, this arm was attached to the sun axis inducing the anomaly as the wheel rotated.

The lower planetary mechanism included the sun (treated as a planet), Mercury and Venus. For each of the three systems there was a planetary gear whose axis was mounted at b1 resulting in the basic frequency being an Earth year (as it is for the sun and all the planets in epicyclical motion, with the exception of the moon). Each connects with a fixed gear to the frame of the mechanism. Each has a bolt mounted, probably in an extension on one side of a gear that extends the gear but does not interfere with the teeth; in some cases a certain distance is needed between the center of the gear and the pin is further than the radius of the gear itself. A bar with a notch through itself extends from the bolt to the appropriate coaxial tube, at the other end of which is located the target indicator in front of the discs. The bars could be full gears although there is no need and it would be a waste of material as the notch is the only functional part. The use of the bars prevents interference between the three mechanisms, each of which goes on the spokes of gear b1. The result is a new fixed gear (one was identified in the ruins and the second is shared by two planets), a gear used to reverse the direction of the solar anomaly, three planetary gears, and three bars/coaxial tubes/indicators that could optionally be used. be gears each. Five gears and three notched bars in total.

The systems of the upper planets (Mars, Jupiter, and Saturn) follow the general principle of the lunar anomaly mechanism. As in the case of the lower systems, each has a gear whose pivot lies to an extent of b1 and which connects with a fixed gear. This features a pin and a pivot center for the planetary gear, which has a notch for the pin, and connects with a gear attached to a coaxial tube and thus to the indicator. Each of the three mechanisms fits in a quadrant of the extension of b1 so that they are all in a single plane parallel to the front disc. Each uses a fixed gear, a driving gear, a driven gear, and a gear/coaxial tube or indicator resulting in a total of 12 gears.

As a result, there are 8 coaxial tubes of various sizes nested to transfer the rotations in the mechanism to the 8 indicators. There are 30 original gears, 7 added gears to complete the calendar functionality, 17 gears and 3 notched bars to support the 6 new gauges, all resulting in 54 gears, 3 bars and 8 gauges in the Freeth and Jones design.

In the visual representation, provided by Freeth in the research, the markers on the frontal zodiacal disc have small round identifying stones. Freeth, interestingly, mentions a quote from an ancient papyrus:

...a voice comes to you talking. Let the stars position on the board according to their nature except for the Sun and Moon. And let the Sun be golden, the silver moon, Cronos [Saturno] of obsidian, Ares [Marte] of red onix, Aphrodite [Venus] lapislázuli veted of gold, Hermes [Mercury] turquoise; let Zeus [Jupiter] be of stone (blancuzca?), crystalline (?)...

New work published by Tony Freeth in March 2021 claims to have devised the first model that fits all the physical evidence and matches the descriptions of the scientific inscriptions engraved on the mechanism itself. The new model has made it possible to minimize the number of gears in the entire system, so that they would fit into the reduced spaces available in the original device. According to writer Adam Wocjk, this is a key theoretical breakthrough into how the mechanism was built, the feasibility of which is intended to be demonstrated by reproducing it using ancient techniques.

Precision

Investigations conducted by Freeth and Jones revealed that their simulated mechanism was not particularly accurate, the pointer on Mars being as much as 38° off. This was not due to errors or inaccuracies in the proportions of the gears, but rather came from the Greek theories of that time. The accuracy could not be improved until Ptolemy published his Planetary Hypothesis in the second half of the II century AD. C. and much later with the introduction of Kepler's Second Law.

"In brief, the Anticitera mechanism was a machine designed to predict sidereal events based on the most recent sophisticated astronomical theories of that time, it is the only witness of a lost history of brilliant engineering, a product of pure genius, one of the wonders of the ancient world but it did not really work very well. "

In addition to theoretical inaccuracy, there is mechanical inaccuracy. Freeth and Jones noted that the inevitable looseness in the mechanism due to hand-made gears, with their triangular teeth and intergear friction, and bearing surfaces would have overwhelmed the delicate mechanisms for solar and lunar correction of the mechanism.

"Although engineering is extraordinary for its time, recent studies conclude that the design exceeded the precision of its manufacturing by a large margin, by means of significant inaccuracies in the gears that accumulated to cancel the subtle anomalies of the design. "

Similar devices in ancient Greece

In The Republic by Marcus Tullius Cicero, a philosophical dialogue from the first century B.C. C., two machines are mentioned that some modern authors consider a type of planetary predictor of the movements of the Sun, the Moon and the five planets known at that time. Both built by Archimedes, they were brought to Rome by General Marco Claudio Marcelo after the assassination by Roman soldiers of the great Greek engineer at the siege of Syracuse (212 BC), the last bastion of Magna Graecia (south of Italy and Sicily). Marcelo, who had great respect for Archimedes, kept one of his machines as the only loot from his siege (the second he offered to the temple of Virtus). The device was kept as a family heirloom and Cicero made Philus (one of the characters in the aforementioned dialogue De republica) affirm that Gaius Sulpicius was a Gallus (consul with Marcellus's nephew in 166 BC and accredited by Pliny the Elder as the first Roman to write a book explaining solar and lunar eclipses) gave "learned explanations" of the mechanism demonstrating its operation. The dialogue takes place in a villa belonging to Publius Cornelius Scipio Emiliano during the year 129 a. C., and the allusive text is as follows:

I have often heard about this heavenly globe or sphere mentioned about the great fame of Archimedes. His appearance, however, did not seem particularly surprising. There is another, more elegant in form and more generally known, shaped by the same Archimedes and deposited by Marcelo himself in the temple of Virtus in Rome. But as soon as Galo has begun to explain, with his sublime science, the composition of this machine, I felt that the Sicilian geometry must have possessed a genius superior to anything we usually conceive from our nature. Galo assured us that the solid and compact balloon was a very old invention and that the first model was presented by Tales de Mileto. That later Eudoxo of Cnido, a disciple of Plato, brought on his surface the stars that appear in the sky and that many years later, borrowing from Eudoxo this beautiful design and representation, Arato illustrated them in his verses, not by any astronomy science but by the ornament of the poetic description. He added that the figure of the sphere, which showed the movements of the Sun and Moon and the five wandering planets or stars, could not be represented by the primitive solid globe. And that in this, the invention of Archimedes was admirable, because it calculated how a simple revolution would maintain unequal and diverse progressions in dissimilar movements.

When Galo moved this balloon he showed the Moon's relationship with the Sun and there was the same number of laps on the bronze device as the number of days on the true balloon of the sky. Thus he showed the same eclipse of the Sun as in the balloon [of heaven], as he showed the Moon entering the shadow area of the Earth when the Sun is online... [laughs]

[p.e. showed both solar and lunar eclipses. ]

So, at least one of Archimedes' machines, probably quite similar to the Antikythera mechanism, given Gallus's interest and that in this part of the dialogue De Republica refers to prodigy and in particular eclipses, was still in operation around 150 B.C. c.

Papo of Alexandria claimed that Archimedes wrote a now-lost manuscript on the construction of these devices entitled On Making Spheres. Surviving texts from the Library of Alexandria describe many of these creations of his and some contain simple sketches. One such device is your odometer, the exact model later used by the Romans to locate their mile marker (described by Marcus Vitruvius, Hero of Alexandria, and in the time of Emperor Commodus). However, although the drawings in the text appear to be functional, attempts to make them look like them have failed, but they did work when the drawn gears (which have square teeth) were replaced by gears of the type used by the mechanism. from Antikythera, which are angled. Whether this is an example of the devices created by Archimedes and described in his texts lost in the Alexandria library fire or a device based on his discoveries or has anything to do with him is debatable..

If Cicero's account is correct, this technology existed as early as the III century BCE. The Archimedean device is also mentioned by later Roman writers such as Lactantius (Divinarum Institutionum Libri VII), Claudian (In sphaeram Archimedes), and Proclus ( Commentary on Euclid's first book, Elements of Geometry) in the 4th and 5th centuries.

Cicero also said that another of these devices was built recently by his friend Posidonius, "... each of the revolutions of which brings about the same motion in the Sun and the Moon and the five wandering stars [planets] like the one that is brought every day and night in the heavens...".

It is unlikely that either of these machines was the Antikythera mechanism found on the wreck as both the devices made by Archimedes and mentioned by Cicero were located in Rome at least 30 years after the estimated date of the wreck and the third it was almost certainly in the hands of Posidonius at that time. So we know that there were at least four such devices. Modern scientists who have reconstructed the Antikythera mechanism also agree that it was too sophisticated to have been a single device.

This technology was later, in part, transmitted to the Byzantines and the Islamic world, where mechanical devices that were complex, though simpler than the Antikythera mechanism, were built during the Middle Ages. Fragments of a mechanical calendar attached to a sundial, from the 5th or 6th century of the Byzantine Empire have been found; the calendar may have been used to help tell time. In the Islamic world, Banū Mūsā's book Kitab al-Hiyal, or Book of Ingenious Mechanisms, was commissioned by the Caliph of Baghdad at the beginning of the 9th century. This text describes over a hundred mechanical devices, some of which date back to ancient Greek texts preserved in monasteries. A mechanical calendar similar to the Byzantine device was described by the scientist al-Biruni around the year 1000, and a surviving 13th-century astrolabe also contains a similar clockwork device. It is possible that this medieval technology was transmitted to Europe. and contributed to the development of mechanical watches.

Further reading

Books