Planets and Anomalies in the Antikythera Mechanism

May 14, 2010 Alun Featured, Science, The Past 1 Comment Antikythera Mechanism, Archaeoastronomy, Archaeology, History of Astronomy, Research Blogging

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?

A recon­struc­tion of the Anti­kythera Mech­an­ism. Photo (cc) Tet_Sy

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), 1–39