Mathematicians have a concept, Omega, that is defined as something so huge that any attempt to define it actually defines something smaller. In a similar vein I reckon that any attempt to describe the ingenuity of the Antikythera Mechanism actually ends up describing something less ingenious instead. More research on the device has been published recently in the Journal for the History of Astronomy. I realise that people might be dropping on to this entry from a search engine, without having read any of the earlier posts, here’s a quick recap of what the mechanism is.
Around 1900 Greek divers found a shipwreck off the coast of the small island Antikythera. They found various statues and bronzes and some small lumps of corroded gunk that no one paid much attention to. Everyone ignored the gunk until parts of it broke. I’ll diplomatically not speculate on how it broke. What people found were that the lumps of corrosion were part of a mechanism that included lots of circles that looked like clockwork gears. This was a huge surprise, because no one suspected to find these kind of gears in the ancient world. Careful study suggested the machine was some sort of device for tracking the position of the Sun and Moon, and also a mechanical calendar. Various reconstructions were attempted and this video from New Scientist shows what people thought about the mechanism till a couple of years ago.
There has been a recent spate of articles on the mechanism. This is due in part to Antikythera Mechanism Research Project studying the remains through X-ray tomography. This has produced the most detailed view of the mechanism through all the corrosion. It’s also due to the same group being generous in providing other researchers with material. So while James Evans, Christián C. Carman and Alan S. Thorndike might not be members of the research group, they have had the material to write a new article on Solar Anomaly and Planetary Displays in the Antikythera Mechanism. Displaying the Solar Anomaly and the positions of the planets are two astronomical different problems, but how you solve one puzzle will affect how you solve the other.
The Solar Anomaly
The Greeks thought astronomical bodies moved through the heavens in circles. It’s an idea that hung around until the seventeenth century, because in any sensibly organised universe heavenly bodies would move in circular orbits. It wasn’t until 1605 when Johannes Kepler worked out that the universe wasn’t perfect and that planets move in elliptical orbits. Apart from not being circular, there are other problems with elliptical orbits. Planets do not travel with a constant speed. They’re faster when they’re closest to the Sun at perihelion and slower when they’re furthest away at aphelion. You should see this in the animation below.
The ellipse is exaggerated for effect, as is the speed. I doubt anyone would want to spend a year watching a real-time animation. In reality the difference between a circular orbit and the Earth’s elliptical orbit means that the Sun can be up to two degrees away from where you’d expect it. For scale, if you hold your hand out at arm’s length and look at your fingernail on your little finger, that’s about half a degree across. So the error is not a lot, but it’s noticeable. This is a problem if you’re creating a scale on your own Antikythera Mechanism to measure the position of the Sun. You can’t use a circle with a uniform scale, centred on the Sun gear, so what can you do? There are two obvious options.
One is that you don’t divide your circle evenly. You distort the scale slightly so that the longer half of the year covers sightly more than half the circular scale. The other way would be to have a circular scale, but make the centre of the scale slightly off-centre from the rotation of the Sun gear, so that the circular scale is divided into two unequal halves. This allows a for a uniform scale, because the Sun marker will have to travel slightly over half a circle to cover the longer half of the year. Evans, Carman and Thorndike looked to see if they could measure the divisions on the scale and see which solution the maker of the Antikythera Mechanism used.
The only reason this project was a remotely sane idea is due to the quality of the images the Antikythera Mechanism Research Project has produced. By sticking it in a X-ray machine like a medical scanner they’ve been able to peer beyond all the corrosion and patina on the gears and get a better look at the scale. They have also been able to creatively light the surface to texture map the exteriors. It gives unprecedented detail of the mechanism, and it’s allow Evans, Carman and Thorndike to say that the scale is not uniform. Each division is measured to match the elliptical orbit to the circular scale. The authors note that zodiac scale is not uniformly divided on some astrolabes. The scale does create some difficulties, it makes makes tracking the planets difficult. Just as the Earth has its own eccentricities when orbiting the Sun, the same is true for the other visible planets.
Tracking the Planets
Before working out how the planet displays fitted into the device, it’s first necessary to show that there were planet displays in the first place. It’s certainly more awesome if there is, but there’s not a lot of evidence for this. The gears needed to drive planetary displays are missing. Missing gears are not inherently a problem. In fact it would be stranger if there were exactly the right number of cogs for everything, because it’s highly likely that not all the parts of the mechanism have been found. What would you do with the extra bits if they were found? At the same time speculating on missing gears is an excellent opportunity to make the device you wish for. If you can just make up wheels and the number of teeth on the cogs you can have anything. The researchers have to walk a tightrope between what will work and what they have as evidence.
Evans et al. are obviously aware of this and make the point that you could make planets that whizz back and forth against the zodiac if you used enough gears. They also make the point that if you were going to do that, then making a non-uniform scale for the zodiac is odd. It’s not that you can’t work around it, it’s simply that you’d be making life unnecessarily difficult. So instead they’ve gone back to the inscriptions to see what they actually say about the planets. There is a reference to Aphrodite (Venus). It describes the ‘stations’ of the planet, the times when it appears to stop in the same place in the sky. Evans et al. argue that this is a bit weird. If you were turning the drive handle and the planet wasn’t moving much you’d see where the station was. There’s also a reference to a conjuction and they point out this would be visible too. They concede it could be something that the user could check with the device, but they suggest it could be something more interesting.
The ancient Greeks were keenly interested in heliacal risings. As the Earth travels round the Sun, the background stars appear to move. The light of the Sun blots out different stars depending on the time of year it is. The first appearance of a star in the morning sky is its heliacal rising, and it happens once a year. So if you known what rises when, you can check the time of year each morning — if there’s no clouds blocking the view.
If that’s the case, then the inscriptions be a method for mentioning this kind of event, that wouldn’t be obvious from just looking at the device? Evans et al. say that the Venus display wasn’t a little planet trundling round the zodiac. Instead they say it was a pointer that rotated once ‘in approximately 584 days’. Around the zodiac scale were Greek letters and when the pointer faced a letter the user could read what that meant, like Venus is in conjunction with the Sun. The word approximately is the key to this. Venus completes eight revolutions of the Sun for every five Earth years. So if you see Venus in the sky at 8pm on day then, if you come back to the same spot eight years later at 8pm, you’ll see Venus in the same place in the sky. That’s not quite accurate, it’s four days too long, but it’s close enough for most people. Whoever designed the Antikythera device wasn’t ‘most people’.
Evans et al. say that better approximations were known. One better approximation known to ancient astronomers is that Venus completes 1151 revolutions around the Sun every 720 years. Viewed from the Earth that means that Venus will complete 720 revolutions against the background stars (a synodic period) every 1151 years. That is better, but gives us problems. How do you cut a gear with 1151 teeth, and where would it fit into the mechanism? Most of the gears tend to have 20–70 teeth, though there is a freak one with 224 that has no obvious astronomical purpose. There’s nothing like a 1151 tooth gear, so that’s quite an invention. What the authors propose is that if you can’t have a simple ratio, you need to get close, and then use another ratio refine it. They go through a few possibilities around the ratio 64/40. This is the 8/5 ratio that most people use to track Venus, scaled up so that there’s a realistic number of teeth in the cogs. That allows them to see if something can be done with a variety of ratios between 62/40 and 66/40. After a lot of division they get a gear train 7/40 x 63/25 x 29/8. The problem is that like the 8/5 ratios, you couldn’t cut reliable gears with so few teeth as 7 and 8, so they had to scale up the numbers. What pops out is 90/20 x 63/25 x 29/224.
This could explain why there’s a 224 tooth wheel in the mechanism (it also explains another 63 tooth gear that no one had a use for), but by itself I’m not convinced. There’s plenty of planets and plenty of multiples for the ratios. It could be cherry-picking to select the one that conveniently has 224 in the answer. Fortunately, they provide evidence that it wasn’t just Venus that was displayed but Mercury and Mars too. They point out that Babylonians recognised that 133 synodic cycles for Mars is 284 years and that neatly factorises into 128/19 x 71/224. That 224 wheel appears again. They find similar simple gear trains based on the 224 wheel for Mercury, Jupiter and Saturn. What makes me more convinced is they recognise this all has to fit into a box 18cm (about 7 inches) wide. A diagram in the paper shows the gears could all fit inside the box comfortably.
What Does the Antikythera Mechanism Tell Us About Ancient Astronomy?
What I like about this paper is that it’s not just about the numbers. Evans, Carman and Thorndike relate it back to what we know about ancient astronomy. They use evidence of Babylonian observations to explain the mechanism, but that is reasonable. After the conquests of Alexander the Great Babylon became part of a Greek Hellenistic Kingdom, and there’s evidence that the Greeks were aware of Babylonian astronomy before then. They point out there’s been some attempt to relate this to the astronomy of Hipparchus, but they also note some problems with that.
One obvious problem is that we don’t have much of Hipparchus’s work. We have the works of Claudius Ptolemy, and they survived because the Christian church found them useful, but if Ptolemy had the right answers the why keep any others? For this reason what we have is a keyhole view of ancient astronomy. The ratios in the Antikythera mechanism are consistent with some of this, but other bits aren’t. It doesn’t look like there was just one canon of astronomical knowledge. It’s possible there were a number of different methods used for different jobs. If that’s the case then the historical evidence is simply the tradition most useful to Arabic and Christian scholars.
It also means that the reconstruction opposite is sadly too simplistic. It looks like there would have been displays for each of the planets as well as the Sun and Moon. Evans et al. even suggest that there could be an display for the winds. That’s not as bizarre as it might sound. The winds are generally seasonal, so they loosely correlate with the Sun. We also know from other Greek inscriptions that astronomical observations like Arcturus is rising are also intermingled with meteorlogical and ecological signs, like the return of swallows from migration. A solar gear could drive a winds display and there seems to be enough space for one.
How do I know there’s enough space? It would have been nice to finish with a diagram of the completed model, but copyright laws being what they are it’s difficult to be sure if I can reproduce one. As it happens that’s not a problem because there’s something better than that. You can download the paper yourself from James Evans’s website. Scroll down to Selected Articles: History of Science and the pdf of the article is linked in the list of other papers.
Evans, J., Carman, C.C., & Thorndike, A.S. (2010). Solar Anomaly and Planetary Displays in the Antikythera Mechanism Journal for the History of Astronomy, 41 (1), 1–39Google+