The Epoch Dates of the Antikythera Mechanism
(With an Appendix on its Authenticity)

1. Introduction.

The Antikythera Mechanism, a gearwork chronological-astronomical simulator whose corroded metallic (chiefly bronze) fragments were recovered from a Hellenistic shipwreck site off the island of Antikythera in 1901, is an artifact of undisputed importance for the history of Greek mechanical technology, astronomy, and calendrics.¹ Since it first came to notice in 1902 in the National Archaeological Museum (Athens), there have been many attempts to date it. (For occasional allegations that it was not a product of antiquity at all, see Appendix 2.) An obvious terminus ante quem is the date of the shipwreck; and while that cannot be determined exactly, ceramics, such as transport amphorae that constituted part of the cargo and tableware that likely were the effects of the crew or passengers, point to the middle of the first century BCE, while a small hoard of 36 silver cistophoric tetradrachms minted at Pergamon and Ephesos, the portable wealth of someone on board, includes Pergamene issues ranging from approximately 104-98 BCE through approximately 76-67 BCE, but none from after the resumption of minting of these coins in 58 BCE. Taken collectively, the evidence of the coins and ceramics suggest a probable shipwreck date of 60 ± 10 BCE, with a date more than 20 years before or after 60 rather unlikely.²⬈#p1

The fragments of the Mechanism bear remains of inscribed Greek texts, ranging from single letters and words on the scales of the output dials to extended explanatory texts, using letter forms similar in general character to Hellenistic lapidary inscriptions but smaller in size, with letter height ranging from about 1.2 to about 3 mm. Starting within days of the 1902 "discovery" of the fragments, experienced epigraphers (as well as a few less qualified people) have repeatedly offered date estimates for the letter forms, but this approach has proved inconclusive; there is growing consensus among Greek epigraphers that without knowledge of the place where an inscription was made and an extensive body of dated comparanda from that place (ideally with identified individual cutters), paleographical dating has an imprecision on the order of plus or minus a century.³ Here are three recent epigraphers' verdicts on the Mechanism's inscriptions:⬈#p2

"… the style of writing could date the inscriptions to the second half of the 2nd century BC and the beginning of the 1st century BC, with an uncertainty of about one generation (50 years). Dates around 150 BC to 100 BC are a plausible range." (Haralambos Kritzas)⁴

"It seems better, accordingly, to widen the palaeographical dating range for the Antikythera inscriptions to the end of the third to the beginning of the first century BC, with a preference for the earlier half of this period." (Charles Crowther)⁵

"… unless further securely dated examples of such tiny writing on bronze can be found, the most that can be said is that the writing dates from the end of the 3rd to the middle of the 1st century b.c." (Paul Iversen)⁶

In other words, so far as the letter forms go, the Mechanism could have been made any time from say 225 BCE to immediately before the shipwreck, a range that does not rule out any plausible date likely to be offered for the Mechanism on other grounds. Within this range, the intervals favored by individual epigraphers are liable to be influenced by the inscriptions that they use as comparanda or of which they have the most experience.⬈#p3

Another approach is to seek datable evidence in the dials and inscribed texts—their contents now, not their paleography—or in the configuration of surviving mechanical parts in the fragments. Following earlier attempts of this kind that were received for a time as definitive but eventually proved misguided, two separate papers that appeared in 2014 deduced that one of the bodies of data inscribed on the Mechanism, a series of descriptions of possible eclipses, had been computed for dates in the interval 205 through 187 BCE.⁷ Each paper's argumentation follows a different methodical route, and both routes are complex and challenging to follow for a reader who is not well versed in ancient Greek and Babylonian astronomy and especially ancient eclipse theory. Moreover, the proposed date range is significantly earlier than the datings that had most commonly been suggested for the Mechanism (typically the second half of the second century or the first half of the first). Among the ways by which one might try to deal with this disparity are to consider whether the later datings could be mistaken, or to look for a rationale for inscribing on the Mechanism data pertaining to a period many decades, perhaps more than a century, in the past. But first one would like to be confident that the eclipses have indeed been correctly dated.⬈#p4

In the present article, I first offer a more direct approach to the problem of dating the eclipse descriptions, taking advantage of certain key points in the interpretation of the evidence that are now settled so that one may assume them with passing reference to the earlier literature. Following this, I bring into consideration evidence, some derived from recent publications and some new, pertaining to other parts of the Mechanism's dials, texts, and the remains of its pointers. My conclusion is that the date range of the eclipse sequence was determined by a set of chronological, astronomical, and esthetic choices that combined to constrain a somewhat artificial epoch or "zero" setting of the Mechanism's pointers and gearwork. The constraints could account for the selection of an epoch date quite far in the past, despite certain significant drawbacks to having a long interval between epoch setting and the present when the Mechanism was being operated.⬈#p5

2. The dial plates and their inscriptions.

The basic layout of the Antikythera Mechanism, comprising two bronze dial faces (conventionally designated "front" and "back") and, between them, a wooden casing that enclosed the complex system of gearwork driving the dial pointers, was discovered by Derek de Solla Price.⁸ In this preliminary section I review the evidence for the dial faces and what can be deduced from them and from the other inscriptions of the Mechanism concerning the various outputs, making minimal reference to the remains of the internal gearwork. As well as providing background to the following sections for readers who are not conversant with the consensus reconstruction of the Mechanism achieved since the early 2000s, this will reveal the robustness of this consensus: even if all the gears had vanished and we had just the exterior fragments, in principle we could have obtained an extensive knowledge of the Mechanism's functions and assumptions underlying them.⁹⬈#p6

Fig. 1 shows a reconstruction of the back dial plate of the Mechanism, which was approximately 31.5 cm tall and 17.0 cm wide, to the nearest half centimeter.¹⁰ About a quarter of the plate, almost entirely from its right half, survives in four fragments. Fragment B alone preserves part of the upper half, including about a third of the spiral scale of the large Metonic Dial, and the small Games Dial in its entirety. Of the lower half of the plate, about a third of the spiral scale of the Saros Dial in addition to some of the plate outside the scale (inscribed with the Back Plate Inscription, or BPI) are extant in Fragments A, E, and F, and the greater part of the small Exeligmos Dial is also in A. Fragments A, B, and E have physical joins, so that the relative placement of the upper and lower dial systems is known within a tolerance of less than a centimeter.¹¹⬈#p7

Before discussing details of the dial plate, it will be helpful to quote for reference the fragmentary lines of "Part II" of the Back Cover Inscription (BCI) that described the upper and lower dials:¹²⬈#p8

3         [  ̣  ̣ ἐ]ν ὅλη⟨ι⟩ τῆι ἕλικι τμήματα σλ̅ε [⬈#p9

4         ται δὲ καὶ αἱ ἐξαιρεσιμοὶ ἡμέραι κα̣[⬈#p10

17        [γ]νω̣μόνια δύο ὧν τὰ ἄκρα φέ[ρεται⬈#p11

18        ε̣ἰ̣ς τέσσαρα, δηλοῖ δ᾿ ὁ μὲν τὰ [⬈#p12

19        [  ̣  ̣]ς τ̣ὴ̣ν τῆς    οϛL    ιθL    του[⬈#p13

20        μ̣ος ε̣ἰς̣ ἴσα σκγ σὺν τέσ[σαρσι⬈#p14

21        τ̣ε  ̣α̣  ̣  ̣ος διαιρέθη⟨ι⟩ ἡ ὅλη [⬈#p15

22        μ̣ο̣ν̣[  ̣  ̣  ̣  ̣]οι ἐγλειπτικοὶ χρ̣[⬈#p16

23        ὁμο[ίω]ς̣ τοῖς ἐπὶ τῆς ε[⬈#p17

24        ἄκρον̣ φέρεται κ[  ̣]  ̣  ̣[⬈#p18

3          … in the entire spiral, 235 segments…⬈#p19

4          … also the skipped days…⬈#p20

17         two pointers whose tips travel…⬈#p21

18         four…, one of which indicates the…⬈#p22

19         … the 19-year period of the 76-year period…⬈#p23

20         … into 223 equal (segments) with four…⬈#p24

21         … the whole… is divided…⬈#p25

22         … ecliptic (i.e. pertaining to eclipses)…⬈#p26

23         in the same way as those of the…⬈#p27

24         tip travels…⬈#p28

The Metonic Dial's spiral slot and scale make five complete turns winding clockwise from inside to outside, starting and ending at points directly below the pointer axis, and the surviving scale divisions, along radial lines through the pointer axis, confirm BCI II.3's statement that the entire scale was divided into 235 cells, corresponding to the 235 lunar months of a 19-year "Metonic" period.¹³ Each turn thus comprised exactly 47 cells. Every cell was inscribed with the name of a calendar month (of a calendar to be discussed below in section 5), and the cell corresponding to the first month of the calendar year also contained a year number, from 1 through 19, so that the scale described a complete 19-year calendrical cycle.¹⁴ The lines forming the cell divisions were continued slightly inside the interior of the spiral, and 22 of these partial cells (identified in Fig. 1 by numerals prefixed with "e") were inscribed with numbers that are "skipped" (ἐξαιρεσιμοί, cf. BCI II.4) day numbers within all months along the same radius—that is, while all months of the cycle were nominally 30 days long, by omitting the specified day, the 110 months along these radii became in actuality 29-day months, in conformity with the Metonic period relation as it applies to lunisolar calendars:⬈#p29

(1)    19 calendar years⬈#p30

                 = 235 calendar months⬈#p31

                 = 125 30-day months + 110 29-day months⬈#p32

                 = 5 × (25 30-day months + 22 29-day months)⬈#p33

                 = 6940 days⬈#p34

The decision to make the Metonic Dial a five-turn spiral was thus not arbitrary, but intended to take advantage of the fact that not only the total number of months in a 19-year period but also the numbers of 30-day and 29-day months are all divisible by 5.⬈#p35

The subsidiary Games Dial is a simple circular dial divided into four equal quadrants by engraved radii that are approximately 7–8° counterclockwise from the 12-o'clock, 3-o'clock, 6-o'clock, and 9-o'clock orientations. It is situated close to the inside of the Metonic spiral, at the Metonic Dial's 3-o'clock position, that is, its center is horizontally aligned with the pointer axis of the Metonic Dial. The interiors of the quadrants are inscribed with year numbers from 1 through 4, running counterclockwise starting with the lower right quadrant—this is the Mechanism's only dial for which the prevailing sense of the pointer's motion in forward-moving time is counterclockwise. Outside each quadrant are inscribed the names of two panhellenic athletic festivals, indicating that, for example, during year 1 of the four-year cycle the Isthmian and Olympic festivals were held.⬈#p36

Following a longish passage (omitted above) concerning the mechanically complicated pointer of the Metonic Dial, BCI II.17-19 speaks of two pointers, and despite the gaps in the text, it is clear that these pointers belonged to a pair of dials similarly divided into four quadrants. One of this pair, described in the lost part of line 18,¹⁵ must have been the Games Dial, while the other's quadrants, we are told, counted 19-year periods within a 76-year "Callippic" period. This Callippic Dial was probably situated on the left side of the Metonic Dial's axis, and perhaps symmetrically situated with the Games Dial as shown in Fig. 1. Wright's straightforward reconstruction of the missing part of the gear train to this dial's pointer results in a clockwise sense of motion. We lack physical evidence not only for the precise location of this dial relative to the Metonic spiral, but also for the orientation of the scale divisions and just what was inscribed in the four quadrants.⬈#p37

The slot and scale of the Saros Dial, the Metonic Dial's counterpart in the lower half of the dial face, make four complete turns clockwise from inside to outside. For this dial the starting and ending points are directly above the pointer's axis, and it is probable (allowing for some uncertainty in measurements on the extant fragments) that the endpoints of both the Metonic and Saros Dials' slots were one and the same, as shown in Fig. 1. The surviving radial scale divisions, similar to those of the Metonic scale, imply that the entire scale was divided into 223 cells, evidently the "223 equal" things mentioned in BCI II.20, and corresponding to the 223 lunar months making up a Saros eclipse cycle.⬈#p38

Not every cell contained inscribed text. Running clockwise along the scale, four or five consecutive empty cells repeatedly alternate with one or two consecutive inscribed cells, with a distribution approximating the average number of lunar months separating the successive alignments (at intervals of about 5.87 lunar months) of the Sun's longitude with the Moon's nodal line, as shown in Fig. 2. A syzygy sufficiently near such an alignment, potentially bringing the Moon's latitude close enough to zero for an eclipse to be possible, may be called an "eclipse possibility" or EP for short. The inscriptions are highly abbreviated statements that an eclipse of the Moon, or of the Sun, or both may take place during the relevant month, accompanied by a time expressed as a whole number of hours, explicitly or implicitly of daytime or nighttime. All inscribed cells include index letters, forming two complete 24-letter alphabetic sequences plus one additional letter at the end, which keyed the cells to additional information pertaining to the eclipses in the Back Plate Inscription. On the basis of the 20 extant cell inscriptions (commonly referred to as "glyphs"), it can be inferred that 49 cells were inscribed on the entire scale, as indicated by the numbered cells in Fig. 1.¹⁶ These comprise 17 glyphs having both lunar and solar statements (meaning that a lunar EP at the middle of the month is followed by a solar EP at the end), 11 pairs of consecutive glyphs having respectively a solar and a lunar statement (meaning that a solar EP at the end of the first month is followed by a lunar EP at the middle of the second), and 10 glyphs having a lunar statement (a lunar EP at the middle of the month) unpaired with a solar statement. The total of lunar-solar pairs, solar-lunar pairs, and lunar-only, 38, is the number of times that the Sun crosses the nodal line during one Saros. Every such crossing is associated with precisely one lunar EP, whereas fewer than three-quarters of them are associated with a single solar EP, the remainder with none. The fact that solar EPs either fall in the cells preceding those containing lunar EPs or follow lunar EPs in the same cells implies that the lunar month was considered to begin slightly later than conjunction.⬈#p39

Immediately inside the innermost turn of the Saros Dial slot, at the 3-o'clock orientation with respect to the pointer axis, is a short engraved radial line, presumed to be one of a set of four such marks at the 12-o'clock, 3-o'clock, 6-o'clock, and 9-o'clock orientations.¹⁷ These would have indicated the 16 dates during a complete Saros at which the Sun's longitude aligned with either the lunar apogee or the lunar perigee, at intervals of approximately 13.94 lunar months. (A syzygy near such an alignment brings the Moon's anomaly close to zero.) The divisibility of 16 by 4 motivates the choice of a four-turn spiral for the Saros Dial; BCI II.20 probably contains the word for "four," which could refer either to the number of turns or the number of marks inside the spiral.⬈#p40

The subsidiary Exeligmos Dial, like the Games Dial, is a simple circular dial, but this one is divided into three equal sectors by radial lines at the 1-o'clock, 5-o'clock, and 9-o'clock orientations. The dial is just inside the right side of the Saros spiral, practically tangent to the slot, but slightly above the Saros Dial's 3-o'clock position, probably to make room for the graduation mark discussed in the preceding paragraph. The surviving gear train would have caused the Exeligmos Dial's pointer to revolve once clockwise in three complete Saros periods as displayed on the Saros Dial, a period designated Exeligmos (ἐξελιγμός, literally "revolution of a wheel") in ancient Greek astronomical texts (Geminus, Introduction to the Phenomena chapter 18, and Ptolemy, Almagest Book 4, chapter 2). The sector clockwise of the 5-o'clock graduation is inscribed with the numeral 8 (Greek Η), and the one clockwise of the 9-o'clock graduation has the numeral 16 (ΙC). The remaining sector seems to be vacant.¹⁸ The meaning of these numbers arises from the motivation for tripling the Saros period to make the Exeligmos: an average Saros is approximately 6585 ⅓ days, i.e. 6585 days 8 equinoctial hours, so that syzygies (and thus eclipses) in the corresponding months of successive Saros periods lag by an average of 8 equinoctial hours per cycle. If one assumes that the Saros period is an exactly constant time interval, the Exeligmos Dial indicates the number of equinoctial hours to be added to the times indicated in the Saros Dial glyphs for Saros periods succeeding the "base" cycle inscribed on the dial. Hence each Exeligmos cycle begins when the pointer is towards the 1-o'clock position, and the (presumably) vacant sector represents the base cycle and cycles separated from it by multiples of three Saros periods, requiring zero adjustment of the times.⬈#p41

Similar wording in BCI II.17 and 24 suggests that the latter belongs to a description of the Exeligmos Dial. The use of the singular "tip" (ἄκρον instead of ἄκρα) probably means that there was only this one subsidiary dial inside the Saros spiral, and for that matter a second dial circle of the same size as the Games and Exeligmos Dials, if it had existed, ought to have been partly preserved on the extant region of the plate around the Saros Dial's pointer axis.¹⁹⬈#p42

Putting together the various kinds of information represented in the Saros and Exeligmos Dial inscriptions, we can state the Saros period relation in a form directly relating to the dials, as follows:⬈#p43

(2)    223 lunar (calendar) months⬈#p44

                 = 38 coincidences of the Sun's longitude and a lunar node⬈#p45

                 = 16 coincidences of the Sun's longitude and the lunar perigee (or apogee)⬈#p46

                 = 1/3 day (8 equinoctial hours) over integer days⬈#p47

This form of the relation follows directly from the more conventional version:⬈#p48

(3)    223 synodic months⬈#p49

                 = 239 anomalistic months⬈#p50

                 = 242 dracontic months⬈#p51

                 = 6585 ⅓ days⬈#p52

                 ≈ 18 solar years + 11 days⬈#p53

The front dial face (Fig. 3) was a single large circular dial inset in an approximately square plate having the same width, 17 cm, as the back face, but only about half its height (16.5 cm). Above and below it were two smaller, rectangular plates that were probably fixed to the Mechanism's wooden exterior frame, while the dial plate was held in place between them by means of sliding catches whose bolts could be slid in and out of bearings on the inside of the fixed plates.²⁰ The knobs of these catches are represented by solid gray circles in Fig. 3. About a quarter of each of two concentric dial scales and the part of the plate outside them survives in Fragment C. The inner scale, fixed to the dial plate, was graduated into twelve divisions corresponding to the twelve zodiacal signs, with each sign subdivided into 30 degrees. The outer scale, lodged in a ring-shaped sink of the dial plate and held in place in any of 365 possible orientations relative to the Zodiac Scale through a system of drilled peg-holes behind the scale and (probably) four clips gripping the scale's rim (shown as gray arcs in Fig. 3), was graduated into twelve larger divisions and one smaller one corresponding to the twelve 30-day months and five additional "epagomenal" days of the Egyptian calendar year.⬈#p54

The existence of the Egyptian Calendar scale, and the fact that its orientation could be adjusted manually, implies that there ought to have been a pointer revolving around the dial with a period representing one solar year. The scale ring would have been reset when needed to take account of the cumulative difference between solar years and Egyptian calendar years (which had a constant length of 365 days). The Zodiac Scale also implies such a pointer, because a double alphabetic series of index letters inscribed along the dial keyed specific degrees to the Parapegma Inscription, a list of annually repeating astronomical events such as solstices, equinoxes, and appearances and disappearances of constellations that was inscribed on the plates above and below the dial. The average spacing between degree graduations on the extant part of the Zodiac Scale (extending from the middle of Virgo through the middle of Sagittarius) is significantly less than 1° (as is apparent from the fact that the sector for Libra exposed on Fragment C spans just slightly over 29 day intervals on the Egyptian Calendar Scale instead of the expected 30 ⁵/₁₂ day intervals), and this is probably deliberate: a nonuniform division of the zodiac into larger degree intervals around the solar apogee and smaller intervals around the perigee would allow a single pointer to indicate simultaneously the Egyptian calendar date and the Sun's approximate true longitude, while also making it easy to see the inequality of the astronomical seasons without operating the Mechanism, by simply counting the day graduations corresponding to the quadrants of the zodiac.²¹⬈#p55

The extant fragment, however, has the surviving portion of the Egyptian Calendar Scale in an orientation relative to the Zodiac Scale that would not have been valid for any historical date within centuries of the first century BCE, so it had apparently last been installed more or less at random.²² What looks like an engraved radial line just outside the Egyptian Calendar Scale and approximately aligned with Libra 18° on the Zodiac Scale (treating the longer graduation separating the Virgo and Libra sectors as Libra 0°), has been interpreted as a mark indicating the correct orientation of the Egyptian Calendar Scale for an epoch date; since the apparent mark coincides with a repaired break through the fragment, however, not all researchers have accepted it as an intentional feature. We will return to this alleged "fiducial mark" in the following section.⬈#p56

At the center of the dial, a jar-lid-shaped casing, extant though in a displaced position in Fragment C, housed a differential gearing that caused a small particolored ball showing through a circular window to revolve to display the current lunar phase.²³ For this to work, the casing had to revolve at the rate of the Moon's longitudinal motion, and it may thus be presumed that a pointer was attached to indicate the Moon's longitude on the Zodiac Scale. Additionally, BCI I.18-25 preserves partial lines from a description of a set of pointers pertaining to the five planets and probably indicating their longitudes; we have no physical remains in Fragment C of these planetary pointers.⬈#p57

3. Rehm and Price on dating the Egyptian Calendar Scale.

In Fragment C's state as first identified in 1902, the front dial scales were entirely concealed behind layers of material that were removed in 1905 and now constitute Fragment G and many small fragments. Fig. 4, a detail of a photograph of the fragment taken by Georg Karo late in 1905 for Albert Rehm, shows how a bit of the Egyptian Calendar Scale, but none of the Zodiac Scale, was now exposed behind one of the displaced plates bearing the Parapegma Inscription. (Subsequent breakage of this plate resulted in the fragment's present state, with more of the Egyptian Calendar Scale and part of the Zodiac Scale exposed.) Shortly before, Rehm had inspected Fragment C in person, observing the graduated scale and reading and identifying the inscribed Egyptian month name Pachon (ΠΑΧΩΝ).²⁴⬈#p58