by Decoding the Heavens- Solving the Mystery of the World's First Computer (retail) (epub)
On the front dial, Bitsakis and Tselikas read ‘Parthenos’ (Virgo) and ‘Chelai’ (Libra), as Price did before them. But diving under the surface with the CT they see the next sign ‘Scorpio’, further proof of the zodiac scale running clockwise around the dial. They are also able to add a few letters here and there to the parapegma text on the front of the device, and see more reference letters on the dial, enough to show that the calendar probably ran through the alphabet twice.
One of the most extensive, newly revealed texts comes from the front door plate. They only have the middle part of each line, but from the surviving words they can tell that it is clearly discussing the planets: ‘Venus’ is mentioned, and ‘Mercury’, plus the ‘stationary points’ that Price saw, and there are also some numbers that might relate to the distances between the planets and the Sun.
And on the back of the mechanism they find a long list of operating instructions. Mechanical terms such as ‘trunnions’, ‘gnomon’ and ‘perforations’ are mixed with astronomical references. As well as the spiral inscription, the numbers 19 and 76 appear – the number of years in a Metonic and Callippic cycle, respectively. And there are references to ‘golden little sphere’ and ‘little sphere’, probably referring to the Sun and Moon pointers on the front zodiac display.
The text near the lower back dial includes the number 223, possibly the word ‘Hispania’ – the earliest known mention of Spain as a country – and a number of other geographical references (some new, some read earlier by Price), such as ‘from the South’, ‘towards the East’ and ‘West-North-West’. The CT also shows that the little dial next to the lower back spiral is divided into three. One of the three divisions seems blank, while the other two are mysteriously inscribed with letters that stand for the numbers 8 and 16.
Finally, Tselikas spends a long time staring at the wheel of Fragment D, with its letters ‘ME’. They are tantalisingly clear, but he can’t say for sure what they mean. The inscription might be short for the Greek word ‘messon’, which means median or ‘the one in the middle’. If the letters were meant to be read as digits they might stand for the number 45. Or perhaps they are the initials of the maker himself.
In all, Bitsakis and Tselikas have more than doubled the number of legible characters on the mechanism to well over 2,000, out of what may originally have been around 20,000. Dating the text precisely is difficult, because the tiny carved letters are quite different to any other writing that survives from the period. But the style is in line with around 100 BC or perhaps a few decades either way. What Tselikas became sure of during his lonely nights, however, is that the Antikythera mechanism was not meant to be used by the person who built it. Everything about its workings was explained step by step. Rather than being an astronomers’ instrument or workshop tool he feels it had to be a luxury item made for a wealthy, non-specialist owner.
While the inscriptions were being translated, Tony Freeth turned his mathematician’s mind to the arrangement of the gearwheels. He had been following every detail of Michael Wright’s publications and knew Wright believed that the gearing on the front of the device, now lost, had modelled the varying motions of the planets, as well as wobbles in the speed of the Sun and the Moon. The inscriptions found by Bitsakis and Tselikas supported the idea that the planets had been shown, but without the lost pieces Freeth felt it was impossible to prove the case either way. He decided to restrict himself to the parts of the mechanism that had survived.
The first task was counting the gear teeth. Instead of counting by eye, Freeth used a computer programme to crunch the maths for him, making the tooth counts more certain than ever before. He soon confirmed Wright’s reading of the gear train that drove the Sun and Moon pointers, the Moon-phase indicator on the front dial, and the train leading to the upper back dial to show the 19-year cycle. But he also discovered a striking new feature that explained how the spiral reading was displayed. Wright had suggested that marker beads might have been moved around the spirals to mark specific dates. But with the CT images Freeth could see the details of the end of the surviving pointer: it had an extendable arm with a pin at the end, which had travelled around the spiral groove like the stylus on a record player. It would have taken 19 years to travel all five turns of the spiral, then the arm could have been lifted and set back at the beginning.
Then he came to the lower back dial. Wright’s interpretation – that the spiral showed draconitic months divided into 218 half days – didn’t feel right. But here Freeth had a distinct advantage, because Fragment F – found by Mairi Zafeiropoulou in the museum stores – was a key section of this dial. It came from the bottom right corner of the mechanism, and it showed parts of all the rings of the spiral, with their scale divisions. This allowed him to make a much more confident count of the divisions than had been possible before. It came to 223.
Etched into the segments on this scale, Bitsakis and Tselikas identified 16 blocks of characters or ‘glyphs’ at intervals of one, five, and six months. Some of the glyphs contained the character ‘Σ’, some contained an ‘Η’, and some had both. Then there was what looked like an anchor sign followed by a number, and one more letter at the bottom. Two of them were visible and had been seen by Price as well, but all the others were hidden under the surface and could only be read with the CT.
All the evidence pointed in one direction – that this dial was used for eclipse prediction. The geographical references and directions inscribed around the dial fitted that idea; solar eclipses occur only at certain locations, and ancient eclipse observations often mentioned the direction from which the shadow approached. Lunar and solar eclipses tend to occur at intervals of one, five and six months from a particular start date. And the pattern repeats almost exactly after what’s called a Saros cycle: 223 months. This is what the 223 divisions of the spiral had to be showing.
The cycle works because for an eclipse to happen you need three things. First, the Moon has to be either at full Moon (for a lunar eclipse, where the Earth passes between the Sun and the Moon) or new Moon (for a solar eclipse, where the Moon passes between the Earth and the Sun). So if an eclipse happens, you can only get another identical one after a whole number of synodic months has passed. Second, the Moon’s path has to be crossing the plane of the Earth’s orbit around the Sun, so that all three bodies are in a line. If the Moon orbited in the same plane as the Sun, we’d get eclipses every new and full Moon. But it’s actually tilted with respect to the Sun’s orbit by about five degrees, so you only get an eclipse if the new or full Moon happens just as the Moon crosses the line of the Sun. The time period between these crossings is the draconitic month.
After a period of time in which both a whole number of synodic months and a whole number of draconitic months has passed, eclipses will start repeating themselves. The Saros cycle is such a period, equal to almost exactly 223 synodic months, and 242 draconitic months.
There’s one other reason why the Saros cycle is particularly good for predicting eclipses. Because the Moon travels around the Earth not in a perfectly circular orbit but in an ellipse, its size and speed with respect to us vary as it goes around. The Moon looks bigger and faster when it’s at the nearest point of its ellipse, and smaller and slower the further away it gets. The time taken for one complete ellipse is about 27.5 days and this is called an anomalistic month. It’s very slightly longer than a sidereal month in which the moon returns to its same place with respect to the background stars, because the direction of the furthest point of the ellipse is gradually moving around the Earth, at a rate of about once every nine years. Where the Moon is in its ellipse determines how long an eclipse lasts (if the Moon is going faster it’ll be over quicker) and whether we see a total eclipse or just an annular one (if the Moon is far away, it isn’t big enough to blot out the whole Sun). A Saros period contains almost exactly 239 anomalistic months. So every 223 synodic months – or just over 18 years – eclipses don’t just happen at the same time; the characteristics of eac
h eclipse will be similar as well.
The Babylonians first came up with the Saros period, although that isn’t what they called it. As with the 19-year Sun-Moon cycle, they didn’t understand the theory behind why the pattern worked, instead they learned it from centuries of observations, all carefully noted down on clay tablets like the ones Tom Malzbender uses his flashbulb dome to read. Lunar eclipses in particular were one of the most powerful omens that could occur. They generally meant that some terrible event was about to happen, such as the death of a ruler, which could only be averted with the appropriate ritual or sacrifice. Knowing in advance when an eclipse was going to happen helped preparations no end, and made sure that the priests didn’t miss one, even on a cloudy day.
Around the second century BC Greek astronomers found out about the Babylonians’ eclipse cycle. Eclipses didn’t have the same superstitious meaning for the Greeks as they did for the Babylonians, but Greek astronomers had other reasons to be interested in their timing. Lunar eclipses give a regular and precise record of when the Moon is exactly opposite the Sun in the sky, so they used the data to derive numbers for their geometric models of the Moon and the Sun.
There is one problem with the Saros period, however, which is that it doesn’t add up to a whole number of days – instead it lasts 6,585 and a third days. This means that during any particular Saros cycle, eclipses occur eight hours later than in the one before. And solar eclipses, which are only visible from certain locations, occur 120 degrees further west, because the globe has had time to go through an extra third of a revolution. So the Greeks came up with the idea of a longer cycle consisting of three Saros periods or 54 years. They called it the Exeligmos cycle (from the Greek for ‘revolution’). This does add up to a whole number of days, so after an Exeligmos period the eclipses repeat in almost exactly the same pattern.
This explained why the subsidiary dial was divided into thirds. After each 18-year cycle the stylus arm on the spiral would have been reset by hand and the pointer on the subsidiary dial would automatically reach the next segment to show which third of the Exeligmos cycle the device was displaying.
Translating the glyphs fitted this picture. The Σ stood for ΣΕΛΗΝΗ (Selene), meaning ‘Moon’, and the Η stood for ΗΛΙΟΣ (Helios), meaning ‘Sun’, and these letters indicated whether a solar or lunar eclipse was due in that month. If both types of eclipse were due in a particular month, the glyph contained both letters. The anchor sign was really a combination of two symbols, Ω and Ρ, meaning ‘hour’, and the number following it indicated the predicted time of the eclipse after sunrise or sunset. The numbers inscribed in two of the sections of the subsidiary dial – 8 and 16 – indicated that this number of hours had to be added to the predicted eclipse time during that particular Saros cycle.
That was when Freeth knew he had the breakthrough that would make the whole project worthwhile. It was the first evidence that the Greeks had used the Saros cycle in this way. And in Freeth’s mind, the discovery completely changed the identity of the device once again. Where Price had presented a calendar computer and Wright had described a planetarium, Freeth saw an eclipse predictor.
Freeth didn’t break open the champagne just yet. First, he needed to back up his ideas by deciphering the gears that led to the eclipse dial. The best clue had to be the big turntable with 223 teeth. The machine’s maker was unlikely to have bothered with such a large prime number unless he needed it to calculate a particular astronomical ratio. Wright – without the benefit of Fragment F – realised that the number 223 was linked to an eclipse cycle, but had been forced to conclude that the wheel was originally meant for another device. Now Freeth knew that the appearance of the number 223 couldn’t be a coincidence. This wheel must have driven the main pointer on the 223-month Saros dial. He worked out that by adding an extra gearwheel next to it (the CT scans showed that there was already a broken shaft in the right place, where such a wheel might have broken off) he could get the turntable to drive the train that led to the lower back dial at just the right speed.
But there were some features that didn’t make sense. A 53-tooth gear (another prime number) altered the rotation rate of the 223-tooth gear, only to be exactly cancelled out by another 53-tooth gear on the other side. And there was still the mysterious pin-and-slot mechanism that the 223-tooth gear carried round like a turntable.
It took Freeth six months to come up with an explanation. Like Wright before him, he put together a huge spreadsheet of every possible rotation rate that could be achieved by the gears in this part of the mechanism – allowing for uncertainties in some of the tooth counts and in how some of the wheels were arranged. Then he sifted through the numbers, looking for astronomically significant ratios ranging from various types of month right up to 26,000 years – the period of the Earth’s wobble on its axis.
Eventually he realised that the speed at which the turntable was going around – about once every nine years – was the same speed at which the Moon’s elliptical orbit shifts around the Earth. Wright had already wondered whether the pin-and-slot mechanism might have had something to do with modelling the variation in the apparent speed of the Moon as it makes its way round its ellipse, but he couldn’t fit the idea with the rest of the gearing.
Now Freeth saw how it was done. The wheels in the pin-and-slot mechanism were going round at the speed of the Moon as it circles the Earth, with a wobble in speed corresponding to the near and far points of its elliptical orbit. Meanwhile, this entire cluster was carried round on a slow turntable, once every nine years, modelling the change in orientation of that ellipse around the Earth. But he still couldn’t work out how this would have been displayed on the back dials.
Freeth phoned Mike Edmunds to tell him the latest. Edmunds thought for a moment. Couldn’t the wobble be sent through to the front of the mechanism, to the lunar pointer, he suggested, so that as it moved around through the zodiac it varied in speed just as the real Moon does? ‘No, I don’t think so,’ said Freeth, since the gear train concerned clearly led to the back of the mechanism. But even as he put down the phone he realised that his friend was right.
The answer lay in the seemingly redundant 53-tooth gears. They enabled the 223-tooth turntable to be used for two different purposes, producing one motion that fed through to the front of the mechanism and one that fed through to the back. The first 53-tooth gear converted the turntable’s speed of rotation to match the Moon’s shifting ellipse, so that the pin-and-slot mechanism it carried could accurately model the lunar wobble. Once this had been transmitted to the front of the mechanism, however, the second 53-tooth gear reinstated the speed that was needed to drive the Saros eclipse dial on the back.
Michael Wright had been correct that the lunar pointer on the zodiac dial modelled the varying motion of the Moon. But he hadn’t needed to imagine an extra epicyclic turntable for this on the front of the device. This part of the mechanism had been there all along.
The revelation was stunning in several ways. Wright had partly predicted it, but Freeth now had direct proof that the device’s gears were used to model not just circular motion, but elliptical motion, and a slowly precessing ellipse at that. The ability it must have taken to think up such a scheme and then execute it was breathtaking – more impressive than a differential gear and beyond any but the most skilled clockmakers today. And the way in which the maker had doubled up the use of the 223-tooth turntable was effortlessly elegant – instead of simply adding gearwheels for extra functions, he had thought through how to strip down the mechanism to the most economic design possible. To mathematicians, the simplest solutions are the most beautiful and this answer – once Freeth grasped it – was everything he had hoped for. Where Price and even Wright had commented on the ancient designer’s apparent failings, Freeth now saw that his work made perfect sense.
Beyond the technical ability implied by Freeth’s scheme, everything changed too concerning the astronomical knowledge encoded in the mechanism. Whereas the so
lar and lunar models suggested by Price were pretty basic, and the planetary models suggested by Wright impossible to confirm, the eclipse data and the Moon’s wobble would have been state-of-the-art astronomy at the time the device was made. The mechanism was now not just of interest for the history of technology. It became a key piece of evidence in the history of astronomy, encoding the very latest in astronomical knowledge. Looking at the numbers used – the precise eclipse dates recorded, and the exact size of the Moon’s wobble – were new clues that could be compared with ancient texts, to tell us more about what Greek astronomers were capable of at the time and to help reveal where the Antikythera mechanism came from.
His quest completed, Freeth hurriedly wrote up the team’s results. Wright had published his work in obscure journals read by mechanics and clockmakers – the only audience that mattered to him. But Freeth had much bigger plans. He sent it to Nature.
The paper was accepted and scheduled for publication on 29 November 2006. Freeth set about organising a conference in Athens so that on the day that his paper was published he could announce the results to the world. It was to be held in the plush auditorium of the National Bank of Greece, just around the corner from Agamemnon Tselikas’s palaeography centre. Freeth invited the whole team, as well as a series of experts in ancient technology and astronomy. He even invited his rival, Michael Wright.
