Reference / Paper · 2008
Supplementary notes to Nature 454, 614–617: Corinthian month names, the games dial, the Saros eclipse glyphs and the games/Callippic gear trains.
doi: 10.1038/nature07130 SUPPLEMENTARY INFORMATION Correction notice Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism Tony Freeth, Alexander Jones, John M. Steele & Yanis Bitsakis Nature 454, 614–617 (2008) In the version of the Supplementary Information originally posted online, there were minor errors in Supplementary Figs 20 and 25. In Supplementary Fig. 20, some glyphs were accidently omitted between months 26 and 67; in Supplementary Fig. 25, seven glyphs in the left-hand semicircle were inscribed one month too early. These have been corrected in the new version of the Supplementary Information; see Supplementary Information Table of Contents for details. doi: 10.1038/nature07130 SUPPLEMENTARY INFORMATION Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism SUPPLEMENTARY NOTES Tony Freeth1,2, Alexander Jones3, John M. Steele4 & Yanis Bitsakis1,5 Antikythera Mechanism Research Project, 3 Tyrwhitt Crescent, Roath Park, Cardiff CF23 5QP, UK. 2 Images First Ltd, 10 Hereford Road, South Ealing, London W5 4SE, UK. 3 Institute for the Study of the Ancient World, 15 East 84th Street, New York, NY 10028, USA. 4 Department of Physics, University of Durham, Rochester Building, South Road, Durham DH1 3LE, UK. 5 Centre for History and Palaeography, 3, P. Skouze str., GR-10560 Athens, Greece 1 www.nature.com/nature doi: 10.1038/nature07130 SUPPLEMENTARY INFORMATION Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism Supplementary Notes Table of Contents TABLE OF CONTENTS 1. OVERVIEW OF THE ANTIKYTHERA MECHANISM 1 1.1 The Fragments 1 1.2 The Architecture of the Mechanism 1 2. DATA ACQUISITION & ANALYSIS 4 2.1 Data Acquisition 4 2.2 Data Analysis 5 3. METONIC, OLYMPIAD & CALLIPPIC DIALS 6 3.1 Fragments that witness the Back Dials 6 3.2 The Calendar of the Metonic spiral 7 3.3 Structure of the Calendar 12 3.4 The Calendar’s Provenance 14 3.5 The Olympiad Dial 19 3.6 Gearing for the Olympiad Dial 22 3.7 The Callippic Dial 23 3.8 Reconstruction of the Upper Back Dials 23 4. SAROS & EXELIGMOS DIALS 24 4.1 The Saros Dial & the Glyphs 24 4.2 Matching the Glyphs with Observations 29 4.3 Babylonian Schemes for Eclipse Prediction 31 4.4 Alphabetical Index Letters 32 4.5 Models for generating the Antikythera Glyph Sequence 33 4.6 The Problem of the Glyph Times 37 4.7 The Four-Turn Saros Dial 39 4.8 The Exeligmos Dial 40 4.9 Reconstruction of the Lower Back Dials 41 5. SUPPLEMENTARY REFERENCES 42 Authorship & Copyright www.nature.com/nature 42 SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism Supplementary Notes 1. 1.1 1. Overview of the Antikythera Mechanism Overview of the Antikythera Mechanism The Fragments The Antikythera Mechanism was recovered in 1901 by Greek sponge divers from a Roman wreck of the first century BC1. Initially unrecognized, it was taken to the National Archaeological Museum in Athens amongst a large amount of archaeology from the wreck. It was almost certainly recovered in one piece and was not initially regarded as being anything remarkable. After some months it split apart, revealing some precision gearwheels. This caused considerable excitement, though its true nature was not understood1. Current evidence suggests that it dates between the second half of the second century BC and early first century BC6. Supplementary Figure 1 | The Fragments of the Antikythera Mechanism. Fragments A-G are in the top half and 1-75 in the bottom half. It is likely, but not definite, that all the fragments belong to the Mechanism. By 1974, it was known to constitute four main fragments (A-D) and about 15 smaller fragments1. Fragment E was found at the Museum in 1976. Fragment F together with a large number of minor fragments was found in 2005 in the stores of the Bronze Collection. These were then organized and numbered by the Museum staff so that the current known fragments now consist of seven larger fragments (A-G) and seventyfive smaller fragments (1-75)6,7. 1.2 The Architecture of the Mechanism The fragments contain the remnants of thirty bronze gearwheels with teeth about 1.5 mm long, as was confirmed in the first X-ray study1. These gearwheels enable the Mechanism to make calculations based on cycles of the Solar System. A recent study showed that all the tooth counts of the surviving gears (with a single exception) can be explained in terms of two cycles of the Solar System, known by both the ancient — 1 — www.nature.com/nature SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism Supplementary Notes 1. Overview of the Antikythera Mechanism Babylonians and the ancient Greeks: the Metonic & Saros cycles (Supplementary Boxes 1 and 2). The basic structure and functions of the gearing were previously described6. Here, we publish a revision of this gearing diagram that takes into account the newly discovered Olympiad Dial. The overall architecture of the Mechanism was published in 1974 in a pioneering study1, though the functions of nearly all of its dials have been radically reassessed since then6. Supplementary Figure 2 | Schematic showing the overall architecture of the Mechanism in a 2006 model6. The present model revises the Back Dials: the function of the upper subsidiary dial and the geometry of the main lower dial. The Mechanism consists of a case, which is about 33 cms x 18 cms x 10 cms (with the last measurement being the most uncertain). It has an input on one side, which was probably turned by hand and drives the rest of the gears via a crown gear. On its front and back faces are a number of output dials. The Front Dials consist of two large concentric displays: a Zodiac Dial with the Greek names of the signs of the Zodiac and a Calendar Dial, marked with the months of the Egyptian calendar in Greek1. This calendar consisted of 12 30-day months and 5 extra days (epagomenai)— making 365 days in the year. Because it lacked the extra quarter day of the solar year, the Egyptian calendar moved relative to the seasons. This was accommodated on the Mechanism with a moveable calendar scale. The scale can be moved by one day every four years, facilitated by a pin on the underside of the scale that engages with a sequence of 365 holes under the calendar scale. On the Calendar scale, a Date pointer would have shown the date in the Egyptian calendar. In a previous study, this Date pointer also indicated the mean position of the Sun in the Zodiac1. However, it is probable that there was a separate pointer that displayed the variable speed of the Sun, according to a solar theory related to that of — 2 — www.nature.com/nature SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism Supplementary Notes 1. Overview of the Antikythera Mechanism Hipparchos26. There was also a pointer that showed the position of the Moon in the Zodiac and this is now understood to have incorporated the variable speed of the Moon according to an epicyclic lunar theory related to that of Hipparchos6. At the centre of the front dials is an additional mechanism, which uses a semi-silvered ball to display the phase of the Moon5. This is calculated from the differential rotations of the Sun and Moon. It might also have shown the age of the Moon in days with an additional scale and this study reinforces this proposal. It seems likely that the Mechanism also displayed some or even all of the five planets known in ancient times26, but there is considerable debate about this. The Back Dials and their functions are the subject of this study and are described in detail in the Main Text. — 3 — www.nature.com/nature SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism Supplementary Notes 2. 2.1 2. Data Acquisition & Analysis Data Acquisition & Analysis Data Acquisition In the autumn of 2005, three types of data were gathered on the Antikythera Mechanism under the auspices of the Antikythera Mechanism Research Project6,7. 1. High-resolution still photography on 6 cm x 7 cm film. 2. Digital surface imaging using Polynomial Texture Mapping (PTM)12, gathered by a team from Hewlett-Packard (USA) with specialist equipment. 3. Microfocus X-ray tomography (CT) acquired by a team from X-Tek Systems (UK), now part of Metris (NL), using a prototype high-energy X-ray machine13. Supplementary Figure 3 | Fragment A being mounted in X-Tek Systems’ Bladerunner X-ray machine by Gerasimos Makris, Head Conservator at the National Archaeological Museum in Athens. The fragment was mounted at an angle to minimize the maximum path of the X-ray beam through the sample as it was rotated in front of the X-ray source. The fragments themselves are in a very delicate state and in danger of decay despite conservation measures. Microfocus X-ray computed tomography (CT) is a completely non-destructive technique, which has enabled the rich store of information hidden inside the fragments to be preserved for all time6. The primary data for this study were microfocus CT scans13. These were acquired using a specially modified Bladerunner X-ray machine, manufactured by X-Tek Systems (UK). Both 450kV and 225kV microfocus X-ray sources were used. These were directed at the sample, which was placed on a rotating turntable while the X-ray image was projected onto a detector. A two-dimensional Perkin Elmer flat panel detector provided all the data for this study. To avoid any mechanical shock to the samples, they were rotated continuously (through just over 360°) while X-ray — 4 — www.nature.com/nature SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad Display and Eclipse Prediction on the Antikythera Mechanism Supplementary Notes 2. Data Acquisition & Analysis projections were gathered at regular intervals as 2,048 x 2,048 16-bit TIFF images. The number of images acquired varied between 1,492 and 2,957 for different scans. The resolution of a scan depends on the geometric magnification of the sample onto the detector—with smaller sample yielding higher magnification and hence higher resolution. The resolution varied from 46 microns to 136 microns for different fragments. All the known 82 fragments of the Mechanism were scanned—the larger ones individually and the smaller fragments in batches of up to eight at a time. About 600GB of X-ray data were gathered. 2.2 Data Analysis The data was processed into viewable X-ray volumes using Filtered Back Projection by X-Tek Systems’ proprietary software CT Pro13. These volumes were then viewed with Volume Graphics’ VGStudio Max software. This software has the ability to isolate single X-ray ‘slices’ through the fragments and these can be angled to coincide as far as possible with the planes of the Mechanism’s plates and gearwheels. The high resolution of microfocus X-ray tomography, together with its ability to isolate a single plane through a sample, are at the heart of the new readings of the inscriptions reported here. As far as we know, the use of this technique on the Antikythera Mechanism6 is the first time that significant inscriptions have been read inside an archaeological artifact. Analysis of the structure of the Mechanism was carried out both within VGStudio Max and by exporting CT slices into computer-aided design software (Nemetschek’s Vectorworks), where measurements could be made and ‘geometry’ superimposed. This was the basis of the analysis of the gearing reported previously6. Despite two thousand years under water, fine details in the fragments of the Mechanism have been preserved at sub-millimetre scales. Inscriptions in Greek cover the external plates of the Mechanism, with text varying between 1.2 mm and 5 mm in height. As a text, the Antikythera Mechanism is an extremely rare original document that give us critical information about the astronomy and technology of its era. Analysis of the text was carried out by viewing slices through the fragments both within VGStudio Max and in image-processing software (Adobe’s Photoshop). The planes of the bronze plates on which the text is inscribed may not have been completely flat at manufacture and have certainly distorted over time. This means that the whole of an inscription cannot be seen in a single CT slice. Sometimes only a single character can be read in a slice and this character cannot be seen in a parallel slice just 20 microns apart. In order to read as much of the text as possible, multiple slices were exported from VGStudio Max as image stacks into the layers of a Photoshop file, where the text in the different layers could be traced and deciphered. — 5 — www.nature.com/nature SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism Supplementary Notes 3. 3.1 a 3. Metonic, Olympiad & Callippic Dials Metonic, Olympiad & Callippic Dials Fragments that witness the Back Dials b Supplementary Figure 4 | Orientation of the main fragments involved in the Back Dials. A, From top to bottom, Fragments B, E and F with Fragment A in the background. B, CT slices of B, E and F with a radiograph of A in the background. The Upper Back Dial system is witnessed by Fragment B, whose orientation relative to the main Fragment A was previously determined by observation of a common axis shared by the two fragments and the horizontal alignment of text imprinted onto the back of the fragment1. The Lower Back Dial system is witnessed by Fragments A, E and F and their relative orientation was determined previously6 by CT analysis of the hidden text and scale divisions in these fragments and the understanding that it is a Saros eclipse prediction dial. — 6 — www.nature.com/nature SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism Supplementary Notes 3. Metonic, Olympiad & Callippic Dials a b Supplementary Figure 5 | Fragment B. a, The external face is covered in a layer of inscriptions in mirror writing that are a cast of text originally on the inner face of the back door. b, The internal face shows the back of the scale rings, held together with a bridging piece. The remains of gear o1 (Supplementary Figure 13) can also be seen on the axis that drives the newly-identified Olympiad Dial. Fragment B, one of the major surviving fragments, is an amalgam of several separate features from the original device. These include the partial scale rings of the upper back dial system; inscriptions from the Back Door impressed in mirror writing into fine material covering much of the scales; a small part of the Back Door itself (new identification); and a hidden subsidiary dial on the back plate with a single gear underneath. 3.2 The Calendar of the Metonic spiral Supplementary Box1 | Metonic & Callippic Calendars From ancient times, astronomers have distinguished a number of different orbital periods of the Moon. The sidereal month is the period of the Moon in its passage from a particular star back to the same star (27.32 days); the synodic (or lunar) month is the period from one phase of the Moon back to the same phase (29.53 days). Ancient calendars were based either on the synodic lunar cycle, the solar cycle or both. Twelve lunar months is about 11 days short of a year, so calendars on this basis do not remain synchronized with the seasons. Attempts to rectify this meant finding integer periods of years, which are also integer numbers of lunar months. One of the most accurate of these is the 19-year cycle of 235 lunar months, attributed to Meton of Athens in the 5th Century BC. The Metonic Cycle is one of the two basic cycles that underlie nearly all the known gearing of the Antikythera Mechanism. The length of the mean lunar month (29.53 days) can be well approximated in a 235-month calendar by making 125 of these full 30-day months and 110 hollow 29-day months. 19 12-month years would make 228 months, so 7 years need to contain a thirteenth intercalary month in order to make up the 235 months of the 19-year period. Based on these ideas, artificial lunisolar calendars can be devised that as far as possible evenly distribute both the hollow months and the 13-month years over the 19year period. 125 30-day months and 110 29-day months add up to 6,940 days, which is the period of the Metonic calendar. In the fourth Century BC, Callippos pointed out that the 6,940 days of the Metonic Calendar implies a year length that is 1/76 days longer than the length of a year, taken as 365 1/4 days. So he proposed an improvement on the Metonic Calendar, which is based on a 76-year period, consisting of four 19-year Metonic sub-periods minus a day. So the Callippic Calendar has (4 x 6,940) – 1 = 27,759 days. — 7 — www.nature.com/nature SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism Supplementary Notes 3. Metonic, Olympiad & Callippic Dials Supplementary Figure 6 | A CT slice through Fragment B, showing some of the text of the month names. A proposal that the main upper back dial is a Metonic calendar1,8 is now well established6. The scales of the five-turn Metonic Dial are covered in inscriptions over two or three lines bounded by scale divisions that define each month of the 235month scale. These inscriptions are identified here for the first time as the months and year starts of the Metonic Calendar and its organization is now understood. It is noteworthy that nearly all the text has been lost where surface material has been removed in the past to reveal the scales. In order to read as much of the text as possible, sixty CT slices of Fragment B at 70micron intervals were imported into the layers of a Photoshop file. Where text was hard to decipher, additional ‘region-of-interest’ image stacks were created at higher resolution and more closely spaced (down to 15 microns). Several hundred CT slices were used for the analysis overall. To help decipher obscure text characters, the CT volumes were also viewed directly in VGStudio Max, where the exact orientation of the slice and its brightness and contrast could be altered to enhance the text. — 8 — www.nature.com/nature SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism Supplementary Notes 3. Metonic, Olympiad & Callippic Dials Supplementary Figure 7 | Fragment B X-ray CT with observed text traced in red. The label below each cell indicates its month position in the 235-month scale, followed by its year number and month number within that year. 13-month years have yellow labels. Very few of the months could be identified from the text deciphered in a single month cell. Knowing the structure of the Metonic calendar enabled the identification of other cells with additional text evidence for the same month. Software improvement by XTek Systems in the reconstruction of the X-ray volumes enabled higher resolution and dynamic range. Just enough details of the text characters were finally pieced together to be sure of the identification of all twelve month names. When complete, the Metonic Spiral had 235 cells, one for each lunar month of a Metonic period, running clockwise and outward from a starting point at the inside bottom of the spiral. We number the cells from 001 through 235. Every cell contained an inscription giving the name of a calendar month, divided over two or three lines. In the cell corresponding to the first month (Phoinikaios) of each of the 19 calendar years, the month name was preceded by the standard L-shaped symbol for etos (‘year’) and an alphabetic (‘Ionic’) numeral for the ordinal number of the year, from 1 through 19. Parts of these inscriptions, sometimes complete, sometimes as little as a single letter, have been detected in 49 cells in the surviving portion of the spiral (which is roughly one-third of the whole, centred on the bottom right). Occasionally one of the longer month names appears to have been curtailed by simple omission of the final letters. In our transcription below, which merges the evidence from the various cells, we indicate letters that are visible but not entirely legible in any cell by underdots, and letters that cannot be seen in any of the cells are enclosed in brackets. Question marks designate cells containing traces that are insufficient to guarantee the identity of the month name in that cell. — 9 — www.nature.com/nature SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism Supplementary Notes 3. Metonic, Olympiad & Callippic Dials Supplementary Figure 8 | The numbers (23) and (27) can be seen at the bottom, inscribed inside the spiral scale of the Metonic Calendar. These represent excluded days—see 3.3. Additionally, alphabetic numerals are inscribed below (i.e. inside) some cells of the innermost turn of the spiral: 1 (probably) below cell 1, 2 below cell 33, 6 below cell 35, 11 below cell 37, 15 below cell 39, 19 below cell 41, 23 below cell 43, and 27 below cell 45. — 10 — www.nature.com/nature SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism Supplementary Notes 3. Metonic, Olympiad & Callippic Dials Evidence for the names has been traced from the CT and (in one case) a PTM. The month cells are arranged in five columns for the five turns of the spiral dial. The cell label ‘088-08.01’ means ‘Month 088-Year 8.Month 01’. Cell labels in purple are for 13-month years. Supplementary Figure 9 | The evidence for the names of the months on the Metonic calendar. — 11 — www.nature.com/nature SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism 3. Metonic, Olympiad & Callippic Dials Supplementary Notes 3.3 Structure of the Calendar The study of ancient chronological systems27,28 and of Greek calendrics in particular29,16 depends on dispersed literary and archaeological evidence, supplemented by much conjectural reconstruction. The Metonic Spiral is an important new document that illuminates many imperfectly understood aspects of these subjects. A Metonic cycle specifies which seven of the 19 years have a thirteenth month. In Greek calendars the intercalation was made by repeating one of the twelve regular ones, and the cycle should therefore also determine which of the twelve is repeated in each intercalary year; the intercalated month need not be the last, and could be different in different intercalary years of the cycle. An example of a Metonic cycle of intercalations—in fact the only one from antiquity that is completely known—is the Babylonian calendrical cycle of the last five centuries BC, which had intercalary twelfth months in years 1, 4, 7, 9, 12, and 15, and an intercalary sixth month in year 1830. For the calendar of the Mechanism, we can deduce from the inscriptions that two intercalary months fell between cells 2 and 37, one between cells 49 and 87, two between cells 96 and 133, one between cells 142 and 175, and one after cell 189. A good intercalation scheme will spread the intercalary years as evenly as possible, so that the number of years between intercalations will be some rotation of the sequence 2-3-3-2-3-3-3 (as in the Babylonian calendar). Geminos (Isagoge 8)9 expressly states that this kind of distribution was used for Metonic cycles. Since we have found that two intercalations have occurred by the end of year 3, the pattern would have to be either 2-3-3-2-3-3-3 or 2-3-3-3-2-3-3. The latter can be ruled out because it would put the first month of year 12 in cell 137. Hence the intercalations are very likely to have been in years 1, 3, 6, 9, 11, 14, and 17. Unfortunately, no clear instance of two consecutive cells containing the same month name survives. The intercalary month of year 3 must have been before month 12, and that of year 11 must have been before month 9. A simple hypothesis, among many possible ones, is that the intercalated month was always month 6, in which case cells 31 and 32 would both have contained Eukleios. In the Babylonian calendar, the length of each month (29 or 30 days) was not determined by its position in the cycle but by direct observation or by an astronomical calculation independent of the cycle31. Geminos tells us that the month lengths in Greek Metonic cycles were determined by first assigning each of the 235 months month a nominal thirty days (7,050 days) and then deleting 110 days at intervals of 64 days, resulting in a total of 6,940 days9 (Supplementary Box 1). (Geminos actually says at intervals of 63 days, because he is not counting the omitted day itself.) Most of these ‘excluded’ (exairesimoi) days would fall in the middle of a month, so that for example in one month the day called the ‘9th’ might follow immediately after the ‘7th’, while two months later it would be the ‘13th’ immediately following the ‘11th’. Geminos does not say whether, in a calendar regulated by the Callippic cycle, the deletion of days at 64-day intervals is to run continuously through all 76 years of the cycle or whether it starts afresh with each of the four Metonic cycles making up the Callippic cycle, nor does he explain where an additional day is deleted so that the Callippic cycle will have the requisite 27,759 days instead of the 27,760 that would result from concatenating four Metonic cycles of 6940 days. It has been conjectured 32 that in a Callippic cycle days would have been deleted at uniform 64-day intervals — 12 — www.nature.com/nature SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism Supplementary Notes 3. Metonic, Olympiad & Callippic Dials continuously through the 76 years, with one further deletion at the end of the final month of the cycle. Many historians, however, regard Geminos’ account of the ‘excluded’ days as an implausible fiction15. Supplementary Figure 10 | Proposed structure of the Metonic Calendar. All months have 30 days, except those with excluded days, which have 29 days. On the far left are the excluded days, with those in red being observed in Fragment B. The excluded day is taken out of each month across all five turns of the spiral—in other words all months on the same horizontal line in the diagram. All the gaps between excluded days are 64 days, except those indicated by the blue boxes, which are 65 days. 13-month years are in purple. In the Antikythera Mechanism, chaining successive Metonic periods together maintains the regularity of the excluded days scheme, whereas Geminos’ scheme is left with an irregular 74-day gap at the boundaries between Metonic periods. This is one possible scheme amongst several with different distributions of the 13-month years and different repetitions of months in these years. The scheme of the Antikythera Mechanism is designed fundamentally with the Metonic rather than the Callippic cycle in mind, and agrees with Geminos in achieving a distribution of 30-day and 29-day months by skipping over days at different stages in the middle of nominally 30-day months, but not invariably at 64day intervals. If 110 days are ‘excluded’ at 64-day intervals, the last omitted day of the cycle will be 74, not 64, days before the first omitted day of the following cycle. On the Mechanism, this discontinuity is smoothed out by lengthening ten of the intervals to 65 days. The Metonic cycle thus naturally divides into five sub-cycles of 47 months, in each of which the 65-day intervals come approximately ¼ and ¾ of the way through the sub-cycle. This accounts for the fact that the Metonic spiral has five turns, each turn representing one 47-month sub-cycle and having the identical — 13 — www.nature.com/nature SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism 3. Metonic, Olympiad & Callippic Dials Supplementary Notes distribution of omitted days, which are indicated by numerals written on the inside of the first turn (Figure 1, Supplementary Figure 8). The first omitted day, surprisingly, is the first day of the first month of the sub-cycle. This means that there would be no New Year’s Day in this year! If, as we believe, the calendar displayed on the Mechanism was meant to be regulated in the longer term according to the Callippic cycle, one more day would have to be skipped in every fourth Metonic cycle. This might have been the last day of the last month of the fourth cycle, in which event the day count would have proceeded directly from the 29th of the final month (Apellaios) of the Callippic cycle to the 2nd day of the first month (Phoinikaios) of the next cycle. It clearly would have been difficult to exclude days in a lunar month if there was no easy means on the Mechanism of counting them—so a display of the days of the lunar month seems essential. It is evident that this cannot be done on the back dials since the pointers rotate too slowly for the inclusion of days on the scales. However a previous suggestion was made that this could be done in conjunction with the Moon Phase mechanism on the Front Dials5. In this proposal the differential movement of the Sun and Moon pointers shows the days of the lunar month, which are indicated on a scale of days attached to the Sun pointer—the angle between the Sun and Moon pointers being the elongation of the Moon from the Sun. A modification of this idea is to attach the scale of days to the Moon pointer with the day indicated on the scale by the Sun pointer. This could neatly explain the cylindrical feature of the Moon Phase mechanism, which could easily have been inscribed with a scale, since it appears to be redundant otherwise. However, we have not as yet found any evidence for this in the CT, possibly because the cylinder is covered in corrosion. 3.4 The Calendar’s Provenance The calendars of the Greek cities were always lunisolar, having twelve named months and a calendar year that was kept at a more or less fixed stage of the natural year by means of intercalary months. The actual month names and the alignment of the calendar year with the seasons varied from city to city, though often exhibiting family resemblances that usually reflect a shared ethnic background or a closer historical relationship; for example, cities founded by colonists from another city would normally retain or adapt the calendar of their ancestors. Our knowledge of the calendars of most cities is heavily dependent on dates in inscriptions. It is rare that we know all twelve month names, sometimes just one or two, and direct evidence for the sequence of months and their seasonal alignment is still rarer. Thus we know more details of the calendar of the Mechanism than we do for almost any Greek calendar except that of Athens. Two month names of the Mechanism’s calendar, Artemisios and Panamos, are found, in various orthographical forms, in numerous regional calendars belonging to more than one of the broadest ethnically-based groupings of calendars, especially the Ionian group and the Western Greek (Dorian and northwestern Greek) group. Their chief value for us is that they appear to have had strong seasonal associations, with Artemisios and its variants falling in spring and Panamos and its variants in late spring or summer. This would imply that the beginning of the Mechanism’s calendar, six months before Artemisios and ten months before Panamos, was late summer or early autumn. Others of the Mechanism’s months are characteristic of calendars of the Western Greek group and of its Dorian subgroup, though most Dorian calendars shared only a — 14 — www.nature.com/nature SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism Supplementary Notes 3. Metonic, Olympiad & Callippic Dials minority of months with the Mechanism. For example, all twelve months of the calendar of Rhodes are known, and the only ones shared with the Mechanism— allowing for orthographical variation—are Karneios (Kraneios), Agrianios, Artamitios (Artemisios), and Panamos. Similar considerations rule out identifying the Mechanism’s calendar with other Dorian calendars of the Dodecanese and southwestern Asia Minor, Crete, and the Peloponnese. Map prepared by M. Anastasiou, Aristotle University of Thessaloniki Supplementary Figure 11 | Map of distribution of the Antikythera month names. ■ (a) Blue markers for places with a version of at least one of Artemisios/Artemitios, Apellaios, Panamos but none of (b) and (c). ■ (b) Green markers for places with at least one of Karneios/Kraneios, Machaneus, Eukleios, Gamilios, Agrianos but none of (c). ■ (c) Red markers for places with at least one of Phoinikaios, Lanotropios/Lanotros, Dodekateus/Dyodekateus, Psydreus. A larger typeface has been used for place names with particular relevance to the text. The division of the months in the three categories is based on the following: 1. Arte/amit/sios, Apellaios and Panamos are very common months among the calendars of the ancient Greek cities, widely spread out also at Ionic regions where they were known as Artemision, Apellaion, Panemos. 2. Karneios/Kraneios, Machaneus/Machaneios, Eukleios, Gamilios, Agrianios/Agrionios are months known only from Dorian and northwestern calendars. Some of them are quite common. 3. Phoinikaios, Lanotropios/Lanotros, Dodekateus/Dyodekateus, Psydreus are four months known only from the calendars of Tauromenion, Corinth, Corinthian colonies and other cities that adopted part or all of the Corinthian calendar. A Dorian calendar recently reconstructed from inscriptional evidence33,16 was evidently shared by several cities of southern Illyria, Epirus, and Corcyra (these cities now being within southern Albania, northwestern mainland Greece and Corfu); for brevity we shall refer to this as the Epirote calendar. The months of this calendar include ten that are also found on the Mechanism: (in alphabetic order) Agrianios, Apellaios, Artemisios, Gamilios, Eukleios, Kraneios, Machaneus, Panamos, Phoinikaios, and Psydreus. In fact an eleventh match can be found with a month Deudekatos or Dyodekatos attested in two inscriptions (I.Apollonia 385 and IG IX.1 694) but not previously recognized as a month name. A single month of the Epirote calendar (Alotropios, editorially adjusted to Haliotropios) appears to differ from the Lanotropios of the Mechanism, though the names have obvious graphical resemblance. (Two further months hitherto proposed for the Epirote calendar, Datyios and Heraios, rest on doubtful evidence and probably do not belong.) Matches for eleven of the twelve months, and a near match for the remaining one, with the — 15 — www.nature.com/nature SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism Supplementary Notes 3. Metonic, Olympiad & Callippic Dials Mechanism's calendar confirm the validity of the hypothesis of a common calendar for the cities of this district, as well as establishing the order of the months and probably the beginning of the year, with Phoinikaios in early autumn. It might also appear that we have identified a provenance of the Mechanism in this district; but such a conclusion would be premature. The cities that shared the Epirote calendar either traced their origins, directly or indirectly, to colonizations from Corinth in the seventh and sixth centuries BC, or were in close cultural contact with the Corinthian colonies. Hence we should consider whether their calendar was the calendar of Corinth. Unfortunately the evidence for the months of the Corinthian calendar is extremely sparse, though so far as it goes it is consistent with the Epirote calendar: an attestation of a month Phoinik[aios] in a Corinthian inscription, and a reference to a Corinthian month Panemos (probably an Ionic representation of Panamos) in a speech of Demosthenes (Speech 18, 157). The Corinthian Phoinikaios is in fact the only attestation of this month name other than in the Epirote calendar and, now, the Mechanism. One further item of information comes from Demosthenes, that Corinthian Panemos was equivalent (in 339 BC) to the Athenian month Boedromion, which normally began with the third new Moon after summer solstice, thus late August or September. If the Panamos of the Mechanism's calendar normally had this position, its year would have begun in mid autumn, somewhat later than our other evidence suggests. Strong confirmation that the Mechanism's calendar is identical, or nearly so, to the Corinthian calendar comes from the calendar of Tauromenion (modern Taormina) in Sicily16. Inscriptions supply us not only with eleven of the twelve month names, but also their sequence, though not which one marked the beginning of the year. In the following comparison, we choose a starting point that brings out the relation to the Mechanism's calendar most clearly: Tauromenion Mechanism 1. Itonios Phoinikaios 2. Karneios Kraneios 3. Lanotr[opios] Lanotropios 4. Apollonios Machaneus 5. Dyodekateus Dodekateus 6. Eukleios Eukleios 7. Artem[isios] Artemisios 8. Dionysios Psydreus 9. (unknown) Gameilios 10. Damatrios Agrianios 11. Panamos Panamos 12. Apellaios Apellaios The two calendars have a remarkable relationship. Seven of their months match not only in name but also in their relative positions in the sequence, and these include the uncommon Eukleios and the exceedingly rare Lanotropios and Dodekateus. The remaining four known months of the Tauromenian calendar are completely different from their counterparts in the Mechanism's calendar. They can be found in other localities; for example Dionysios and Damatrios are both attested for Locri Epizephyrii (modern Locri, south Italy) and Itonios and Apollonios for Thessaly. — 16 — www.nature.com/nature SUPPLEMENTARY INFORMATION doi: 10.1038/nature07130 Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism Supplementary Notes 3. Metonic, Olympiad & Callippic Dials The explanation of this relationship must be situated in the history of Tauromenion, which was originally a settlement of indigenous Sicels but in 392 BC was settled by the tyrant Dionysius of Syracuse with his Greek mercenaries. The Tauromenian calendar is likely to have been adopted at the time of this refoundation. Where Dionysius' mercenaries were from is unknown, but the composition of the calendar suggests a fusion of elements from several distinct regional calendars, with the Corinthian calendar providing the structural framework as well as the majority of the month names. While the possibility cannot be ruled out that this framework is to be ascribed to the presence of soldiers from Corinth or the Corinthian colonies of northwestern Greece (or, less plausibly, to Corinthian influence at the time of the Sicilian campaigns of Timoleon of Corinth in 344-338), the most likely source for it would seem to be Syracuse itself, since Syracuse had been founded as a Corinthian colony in the eighth century and hence is likely to have retained the Corinthian calendar. The testimony for the Syracusan calendar is regrettably slight; such as it is,