Editing Antikythera mechanism (section)

===Faces===
[[File:Computer graphic for front of Antikythera mechanism.jpg|thumb|right|Computer-generated front panel of the Freeth model]]

====Front face====
The front dial has two concentric circular scales. The inner scale marks the Greek signs of the zodiac, with division in degrees. The outer scale, which is a movable ring that sits flush with the surface and runs in a channel, is marked off with what appear to be days and has a series of corresponding holes beneath the ring in the channel.

Since the discovery of the mechanism more than a century ago, this outer ring has been presumed to represent a 365-day Egyptian solar calendar, but research (Budiselic, et al., 2020) challenged this presumption and provided direct statistical evidence there are 354 intervals, suggesting a lunar calendar.<ref name="budiselic"/> Since this initial discovery, two research teams, using different methods, independently calculated the interval count. Woan and Bayley calculate 354–355 intervals using two different methods, confirming with higher accuracy the Budiselic et al. findings and noting that "365 holes is not plausible".<ref name="Auto82-31"/> Malin and Dickens' best estimate is 352.3±1.5 and concluded that the number of holes (N) "has to be integral and the SE ([[standard error]]) of 1.5 indicates that there is less than a 5% probability that N is not one of the six values in the range 350 to 355. The chances of N being as high as 365 are less than 1 in 10,000. While other contenders cannot be ruled out, of the two values that have been proposed for N on astronomical grounds, that of Budiselic et al. (354) is by far the more likely."<ref name=budiselic /><ref name="Auto82-32"/><ref name="Auto82-33"/>

If one supports the 365&nbsp;day presumption, it is recognized the mechanism predates the [[Julian calendar]] reform, but the [[Sothic cycle|Sothic]] and [[Callippus|Callippic]] cycles had already pointed to a {{sfrac|365|1|4}}&nbsp;day solar year, as seen in [[Ptolemy III Euergetes|Ptolemy&nbsp;III]]'s attempted calendar reform of 238&nbsp;BC. The dials are not believed to reflect his proposed leap day ([[Epag.]]&nbsp;6), but the outer calendar dial may be moved against the inner dial to compensate for the effect of the extra quarter-day in the solar year by turning the scale backward one day every four years.

If one is in favour of the 354&nbsp;day evidence, the most likely interpretation is that the ring is a manifestation of a 354-day lunar calendar. Given the era of the mechanism's presumed construction and the presence of Egyptian month names, it is possibly the first example of the Egyptian civil-based [[lunar calendar]] proposed by [[Richard Anthony Parker]] in 1950.<ref name="Auto82-34"/> The lunar calendar's purpose was to serve as a day-to-day indicator of successive lunations, and would also have assisted with the interpretation of the lunar phase pointer, and the [[Metonic]] and [[Saros (astronomy)|Saros]] dials. Undiscovered gearing, synchronous with the rest of the Metonic gearing of the mechanism, is implied to drive a pointer around this scale. Movement and registration of the ring relative to the underlying holes served to facilitate both a 1-in-76-year [[Callippic cycle]] correction, as well as convenient lunisolar intercalation.

The dial also marks the position of the Sun on the ecliptic, corresponding to the current date in the year. The orbits of the Moon and the five planets known to the Greeks are close enough to the ecliptic to make it a convenient reference for defining their positions as well.

The following three [[Egyptian calendar#Months|Egyptian months]] are inscribed in [[History of the Greek alphabet|Greek letters]] on the surviving pieces of the outer ring:{{sfn|Jones|2017|page=97}}
* {{lang|grc-EG|ΠΑΧΩΝ}} ([[Pachon]])
* {{lang|grc-EG|ΠΑΥΝΙ}} ([[Payni]])
* {{lang|grc-EG|ΕΠΙΦΙ}} ([[Epiphi]])

The other months have been reconstructed; some reconstructions of the mechanism omit the five days of the Egyptian intercalary month. The Zodiac dial contains Greek inscriptions of the members of the zodiac, which is believed to be adapted to the [[tropical month]] version rather than the [[Sidereal month|sidereal]]:<ref name=freeth-06-1/>{{rp|8}}{{Failed verification|reason=This page mentions neither tropical nor sidereal|date=September 2016}}
[[Image:Antikythera model front panel Mogi Vicentini 2007.JPG|thumb|upright=1.3|Front panel of a 2007 re-creation]]
* {{lang|grc|ΚΡΙΟΣ}} ({{transliteration|grc|Krios}} [Ram], Aries)
* ΤΑΥΡΟΣ (Tauros [Bull], Taurus)
* ΔΙΔΥΜΟΙ (Didymoi [Twins], Gemini)
* ΚΑΡΚΙΝΟΣ (Karkinos [Crab], Cancer)
* ΛΕΩΝ (Leon [Lion], Leo)
* ΠΑΡΘΕΝΟΣ (Parthenos [Maiden], Virgo)
* ΧΗΛΑΙ (Chelai [Scorpio's Claw or Zygos], Libra)
* ΣΚΟΡΠΙΟΣ (Skorpios [Scorpion], Scorpio)
* ΤΟΞΟΤΗΣ (Toxotes [Archer], Sagittarius)
* ΑΙΓΟΚΕΡΩΣ (Aigokeros [Goat-horned], Capricorn)
* ΥΔΡΟΧΟΟΣ (Hydrokhoos [Water carrier], Aquarius)
* ΙΧΘΥΕΣ (Ichthyes [Fish], Pisces)

Also on the zodiac dial are single characters at specific points (see reconstruction at ref<ref name=isaw-1/>). They are keyed to a ''[[parapegma]]'', a precursor of the modern day [[almanac]] inscribed on the front face above and beneath the dials. They mark the locations of longitudes on the ecliptic for specific stars. The ''parapegma'' above the dials reads (square brackets indicate inferred text):

{| class="wikitable"
|-
| Α || {{lang|grc|ΑΙΓΟΚΕΡΩΣ ΑΡΧΕΤΑΙ<br />ΑΝΑΤΕΛΛΕΙΝ [...] Α}} || [[Capricorn (constellation)|Capricorn]] begins to rise
|rowspan="11" style="background:white;"| <!-- blank column to separate separate sides -->
| Ι || ΚΡΙΟΣ ΑΡΧΕΤΑΙ ΕΠΙΤΕΛΛΕΙΝ<br />[...] Α || [[Aries (constellation)|Aries]] begins to rise
|-
| || ΤΡΟΠΑΙ ΧΕΙΜΕΡΙΝΑΙ [...] Α || [[Winter solstice]]
| || ΙΣΗΜΕΡΙΑ ΕΑΡΙΝΗ [...] Α || [[March equinox|Vernal equinox]]
|-
| Β || [...] ΕΙ ΕΣΠΕΡΙ || ... evening
| Κ || [...] ΕΣΠΕΡΙΑ [...] ΙΑ || ... evening
|-
| Γ || [...] ΙΕΣΠΕΡΙ || ... evening
| Λ || ΥΑΔΕΣ ΔΥΝΟΥΣΙΝ<br />ΕΣΠΕΡΙΑΙ [...] ΚΑ || The [[Hyades (star cluster)|Hyades]] set in the evening
|-
| Δ || [...] ΥΔΡΟΧΟΟΣ ΑΡΧΕΤΑΙ<br />ΕΠΙΤΕΛΛΕΙΝΑ || [[Aquarius (constellation)|Aquarius]] begins to rise
| Μ || ΤΑΥΡΟΣ ΑΡΧΕΤΑΙ<br />Ε{Π}ΙΤΕΛΛΕΙΝΑ || [[Taurus (constellation)|Taurus]] begins to rise
|-
| Ε || [...] ΕΣΠΕΡΙΟΣ [...] Ι{Ο} || ... evening
| Ν || ΛΥΡΑ ΕΠΙΤΕΛΛΕΙ<br />ΕΣΠΕΡΙΛ [...] Δ || [[Lyra]] rises in the evening
|-
| Ζ || [...] ΡΙΑΙ [...] Κ || ... {evening}
| Ξ || ΠΛΕΙΑΣ ΕΠΙΤΕΛΛΕΙ<br />ΕΩΙΑ [...] Ι || The [[Pleiades]] rise in the morning
|-
| Η || ΙΧΘΥΕΣ ΑΡΧΟΝΤΑΙ<br />ΕΠΙΤΕΛΛΕΙΝ [...] Α || [[Pisces (constellation)|Pisces]] begins to rise
| Ο || ΥΑΣ ΕΠΙΤΕΛΛΕΙ ΕΩΙΑ [...] Δ || The [[Hyades (star cluster)|Hyades]] rise in the morning
|-
| Θ || [...] {Ι}Α ||
| Π || ΔΙΔΥΜΟΙ ΑΡΧΟΝΤΑ<br />ΕΠΙΤΕΛΛΕΙΝ [...] Α || [[Gemini (constellation)|Gemini]] begins to rise
|-
<!-- | || || -->
|rowspan="2;" colspan="3;" style="background:white;"| 
| Ρ || ΑΕΤΟΣ ΕΠΙΤΕΛΛΕΙ ΕΣΠΕΡΙΟΣ || [[Altair]] rises in the evening
|-
<!-- | || || -->
| Σ || ΑΡΚΤΟΥΡΟΣ ΔΥΝΕΙ Ε{Ω}{Ι}ΟΣ || [[Arcturus]] sets in the morning
|}

The ''parapegma'' beneath the dials reads:

{| class="wikitable"
|-
| Α || ΧΗΛΑΙ ΑΡΧΟΝΤΑ<br />ΕΠΙΤΕΛΛΕΙΝ [...] Α || [[Libra (constellation)|Libra]] begins to rise
|rowspan=12 style="background:white;"| <!-- blank column to separate separate sides -->
| Μ || ΚΑΡΚΙΝΟΣ ΑΡΧΕΤΑΙ<br />[...] Α || [[Cancer (constellation)|Cancer]] begins {to rise}
|-
| || {Ι}ΣΗΜΕΡΙΑ ΦΘΙΝΟΠΩΡΙΝΗ<br />[...] Α || [[September equinox|Autumnal equinox]]
| || ΤΡΟΠΑΙ ΘΕΡΙΝΑΙ [...] Α || [[Summer solstice]]
|-
| Β || [...] ΑΝΑΤΕΛΛΟΥΣΙΝ<br />ΕΣΠΕΡΙΟΙΙΑ || ... rise in the evening
| Ν || ΩΡΙΩΝ ΑΝΤΕΛΛΕΙ ΕΩΙΟΣ || [[Orion (constellation)|Orion]] precedes the morning
|-
| Γ || [...] ΑΝΑΤΕΛΛΕΙ ΕΣΠΕΡΙΑΙΔ || ... rise in the evening
| Ξ || {Κ}ΥΩΝ ΑΝΤΕΛΛΕΙ ΕΩΙΟΣ || [[Canis Major]] precedes the morning
|-
| Δ || [...] ΤΕΛΛΕΙΙ{Ο} || ... rise
| Ο || ΑΕΤΟΣ ΔΥΝΕΙ ΕΩΙΟΣ || [[Altair]] sets in the morning
|-
| Ε || ΣΚΟΡΠΙΟΣ ΑΡΧΕΤΑΙ<br />ΑΝΑΤΕΛΛΕΙΝΑ || [[Scorpio (constellation)|Scorpio]] begins to rise
| Π || ΛΕΩΝ ΑΡΧΕΤΑΙ<br />ΕΠΙΤΕΛΛΕΙΝ [...] Α || [[Leo (constellation)|Leo]] begins to rise
|-
| Ζ || [...] ||
| Ρ || [...] ||
|-
| Η || [...] ||
| Σ || [...] ||
|-
| Θ || [...] ||
| Τ || [...] ||
|-
| Ι || ΤΟΞΟΤΗΣ ΑΡΧΕΤΑΙ<br />ΕΠΙΤΕΛΛΕΙΝ [...] Α || [[Sagittarius (constellation)|Sagittarius]] begins to rise
| Υ || [...] ||
|-
| Κ || [...] ||
| Φ || [...] ||
|-
| Λ || [...] ||
| Χ || [...] ||
|}

At least two pointers indicated positions of bodies upon the ecliptic. A lunar pointer indicated the position of the Moon, and a mean Sun pointer was shown, perhaps doubling as the current date pointer. The Moon position was not a simple mean Moon indicator which would indicate movement uniformly around a circular orbit; rather, it approximated the acceleration and deceleration of the Moon's elliptical orbit, through the earliest extant use of [[epicyclic gearing]].

It also tracked the precession of the Moon's elliptical orbit around the ecliptic in an 8.88&nbsp;year cycle. The mean Sun position is, by definition, the current date. It is speculated that since significant effort was taken to ensure the position of the Moon was correct,<ref name=freeth-06-1/>{{rp|20, 24}} there was likely to have also been a "true sun" pointer in addition to the mean Sun pointer, to track the elliptical anomaly of the Sun (the orbit of Earth around the Sun), but there is no evidence of it among the fragments found.<ref name=freeth-12/> Similarly, neither is there the evidence of planetary orbit pointers for the five planets known to the Greeks among the fragments. But see [[#Proposed gear schemes|Proposed gear schemes]] below.

Mechanical engineer Michael Wright demonstrated there was a mechanism to supply the lunar phase in addition to the position.<ref name=wright-05/> The indicator was a small ball embedded in the lunar pointer, half-white and half-black, which rotated to show the phase (new, first quarter, half, third quarter, full, and back). The data to support this function is available given the Sun and Moon positions as angular rotations; essentially, it is the angle between the two, translated into the rotation of the ball. It requires a [[differential (mechanical device)|differential gear]], a gearing arrangement that sums or differences two angular inputs.

====Rear face====
[[File:Computer graphic for back of Antikythera mechanism.jpg|thumb|right|Computer-generated back panel]]
In 2008, scientists reported new findings in ''[[Nature (journal)|Nature]]'' showing the mechanism not only tracked the [[Metonic calendar]] and predicted [[solar eclipses]], but also calculated the timing of panhellenic athletic games, such as the [[ancient Olympic Games]].<ref name=freeth-08/> Inscriptions on the instrument closely match the names of the months that are used on calendars from [[Epirus]] in northwestern Greece and with the island of [[Corfu]], which in antiquity was known as Corcyra.<ref name=wilford-08/><ref name=connor-08/><ref name="Auto82-35"/>

On the back of the mechanism, there are five dials: the two large displays, the Metonic and the [[Saros (astronomy)|Saros]], and three smaller indicators, the so-called Olympiad Dial,<ref name=freeth-08/> which has been renamed the Games dial as it did not track Olympiad years (the four-year cycle it tracks most closely is the Halieiad),<ref name="Auto82-36"/> the [[Callippic cycle|Callippic]], and the [[exeligmos]].<ref name=freeth-06 />{{rp|11}}

The Metonic dial is the main upper dial on the rear of the mechanism. The Metonic cycle, defined in several physical units, is 235 [[Lunar month#Synodic month|synodic months]], which is very close (to within less than 13 one-millionths) to 19 tropical years. It is therefore a convenient interval over which to convert between lunar and solar calendars. The Metonic dial covers 235 months in five rotations of the dial, following a spiral track with a follower on the pointer that keeps track of the layer of the spiral. The pointer points to the synodic month, counted from new moon to new moon, and the cell contains the [[Hellenic calendars#Corinthian|Corinthian month names]].<ref name=freeth-08 /><ref name="Auto82-37"/><ref name="auto1"/>

# {{lang|grc-x-doric|ΦΟΙΝΙΚΑΙΟΣ}} ({{transliteration|grc|Phoinikaios}})
# ΚΡΑΝΕΙΟΣ (Kraneios)
# ΛΑΝΟΤΡΟΠΙΟΣ (Lanotropios)
# ΜΑΧΑΝΕΥΣ (Machaneus, ''"mechanic"'', referring to [[Zeus]] the inventor)
# ΔΩΔΕΚΑΤΕΥΣ (Dodekateus)
# ΕΥΚΛΕΙΟΣ (Eukleios)
# ΑΡΤΕΜΙΣΙΟΣ (Artemisios)
# ΨΥΔΡΕΥΣ (Psydreus)
# ΓΑΜΕΙΛΙΟΣ (Gameilios)
# ΑΓΡΙΑΝΙΟΣ (Agrianios)
# ΠΑΝΑΜΟΣ (Panamos)
# ΑΠΕΛΛΑΙΟΣ (Apellaios)

Thus, setting the correct solar time (in days) on the front panel indicates the current lunar month on the back panel, with resolution to within a week or so.

Based on the fact that the calendar month names are consistent with all the evidence of the Epirote calendar and that the Games dial mentions the very minor Naa games of Dodona (in Epirus), it has been argued that the calendar on the mechanism is likely to be the Epirote calendar, and that this calendar was probably adopted from a Corinthian colony in Epirus, possibly Ambracia.<ref name="auto1"/> It has been argued that the first month of the calendar, Phoinikaios, was ideally the month in which the autumn equinox fell, and that the start-up date of the calendar began shortly after the astronomical new moon of 23 August 205 BC.<ref name="Auto82-38"/>

The Games dial is the right secondary upper dial; it is the only pointer on the instrument that travels in an anticlockwise direction as time advances. The dial is divided into four sectors, each of which is inscribed with a year indicator and the name of two [[Panhellenic Games]]: the "crown" games of [[Isthmian Games|Isthmia]], [[Ancient Olympic Games|Olympia]], [[Nemean Games|Nemea]], and [[Pythian Games|Pythia]]; and two lesser games: Naa (held at [[Dodona]])<ref name=bbc-08/> and the [[Halieia]] of Rhodes.<ref name="Auto82-39"/> The inscriptions on each one of the four divisions are:<ref name=freeth-06 /><ref name=freeth-08/>

{| class="wikitable"
 |+ Olympic dial
 |-
 ! Year of the cycle
 ! Inside the dial inscription
 ! Outside the dial inscription
 |-
 ! 1
 | LΑ
 | ΙΣΘΜΙΑ (Isthmia)<br />ΟΛΥΜΠΙΑ (Olympia)
 |-
 ! 2
 | LΒ
 | ΝΕΜΕΑ (Nemea)<br />NAA (Naa)
 |-
 ! 3
 | LΓ
 | ΙΣΘΜΙΑ (Isthmia) <br />ΠΥΘΙΑ (Pythia)
 |-
 ! 4
 | LΔ
 | ΝΕΜΕΑ (Nemea)<br />ΑΛΙΕΙΑ (Halieia)
 |}

The Saros dial is the main lower spiral dial on the rear of the mechanism.<ref name=freeth-06 />{{rp|4–5, 10}} The Saros cycle is 18 years and {{frac|11|1|3}} days long (6585.333... days), which is very close to 223 synodic months (6585.3211 days). It is defined as the cycle of repetition of the positions required to cause solar and lunar eclipses, and therefore, it could be used to predict them—not only the month, but the day and time of day. The cycle is approximately 8 hours longer than an integer number of days. Translated into global spin, that means an eclipse occurs not only eight hours later, but one-third of a rotation farther to the west. Glyphs in 51 of the 223 synodic month cells of the dial specify the occurrence of 38 lunar and 27 solar eclipses. Some of the abbreviations in the glyphs read:{{citation needed|date=October 2019}}
* Σ = ΣΕΛΗΝΗ ("Selene", Moon)
* Η = ΗΛΙΟΣ ("Helios", Sun)
* H\M = ΗΜΕΡΑΣ ("Hemeras", of the day)
* ω\ρ = ωρα ("hora", hour)
* N\Y = ΝΥΚΤΟΣ ("Nuktos", of the night)

The glyphs show whether the designated eclipse is solar or lunar, and give the day of the month and hour. Solar eclipses may not be visible at any given point, and lunar eclipses are visible only if the Moon is above the horizon at the appointed hour.<ref name=freeth-06-1 />{{rp|6}} In addition, the inner lines at the cardinal points of the Saros dial indicate the start of a new [[full moon cycle]]. Based on the distribution of the times of the eclipses, it has been argued the start-up date of the Saros dial was shortly after the astronomical new moon of 28 April 205 BC.<ref name="Carman Evans" />

The Exeligmos dial is the secondary lower dial on the rear of the mechanism. The exeligmos cycle is a 54-year triple Saros cycle that is 19,756 days long. Since the length of the Saros cycle is to a third of a day (namely, 6,585 days plus 8 hours), a full exeligmos cycle returns the counting to an integral number of days, as reflected in the inscriptions. The labels on its three divisions are:<ref name=freeth-06 />{{rp|10}}
* Blank or o ? (representing the number zero, assumed, not yet observed)
* H (number 8) means add 8 hours to the time mentioned in the display
* Iϛ (number 16) means add 16 hours to the time mentioned in the display

Thus the dial pointer indicates how many hours must be added to the glyph times of the Saros dial in order to calculate the exact eclipse times.{{citation needed|date=October 2019}}