Antikythera Mechanism

I have just watched Jo Marchant's talk on the Antikythera mechanism given to CU in 2020 and found it a fascinating account, so much so that I would like follow it up with a book on the subject. The obvious one to buy perhaps is Jo Marchants own book “Decoding the Heavens” published around 2006 but before making the purchase I just wondered if there may be a more modern account taking in recent developments and discoveries surrounding the mechanism.

Have you had a look at the other (five) threads on this subject on this forum? They contain some links and thoughts which may be of interest.

This thread on the subject, for example, which elicited the greatest response references, amongst other sources, a BHI paper on the subject of the possible lunar calendar.

Regards,

Phil

Apologies for my post immediately above - wrong links added!

Oh well, at least has bumped the thread so may elicit more helpful responses. (\Every cloud, etc., etc.)

Phil

Edited By Weary on 22/11/2022 08:58:38

Greensands:

Thanks for the pointer to this talk.

This mechanism is fascinating.

I ask myself that if the makers had the means to produce many wheels and gears, then surely they could have made a reasonable precision tool to locate these holes? The radius of the hole circumference seems quite consistent, but the angular spacing is quite inconsistent in places.

These holes could not have been used to drive another gear because that gear would bind up between some of the holes owing to the random spacing. So it seems more likely to have held a single indicator pin, which could be moved around the circumference according to some factor. Or maybe a pencil put through one of the holes to draw an arc?

I don't know how you would calibrate a tool to locate 'n' number of holes around a circumference, but I am sure many clever people could.

Edited By John Doe 2 on 24/11/2022 09:33:37

GHT pointed out that you just need to know the number of degrees between the holes. Some time ago a programmer friend wrote routine to do this trick; this was in C but I expect it could be done in BASIC.

No C or BASIC or electronic computers in those days

Would there have been 360° protractors even?

Some years ago I went to an exhibition of items from Pompei; the most interesting item for me was a bronze colander.The skill of the drilling was exceptional and the amount of holes on a helix with incedible accuracy astounded me considering that they would have used a hand drill.These artisans were capable of working out complex problems and the same goes for the Antikythera.

Frank

I often wonder about this. We assume they didn't have machine tools, but for example; drill presses could have been constructed from wood - or even stone - and would have given reasonable accuracy and repeatability in this non-critical context. Over the centuries, the wood will have completely rotted away, the stone broken up and robbed-out or scattered around; its origin and purpose unidentifiable. Any small metal parts fixed to the structure e.g. plates to carry metal shafts etc., might have corroded away or not have been identified as to their purpose or origin.

Most of us could make a fixture out of wood to hold a particular job if we didn't have a machine tool, or bracket, so I am sure the ancients could too.

The gear wheel in this thread could obviously have been secured to a table by a pin at its centre and rotated under some sort of drill-head fixed at a set radius to drill the holes - the radius the holes are set at from the centre seems very consistent, so I don't think it was drilled freehand. But the angular displacement between the holes is much less accurate, so they presumably didn't have an accurate dividing head.

Agreed! but I think they could have made protractors.

I mentioned GHT's comment about angular indexing which is in his book Workshop Techniques. In the the same work he gives detailed instructions for setting out divisions of a circle with the use of rule, dividers, etc, techniques which could have been used by the ancient craftsmen.

I have just read every post on this thread. Thanks to all contrutors! A lot went over my head, but in all very enlightening.

One thing that struck me is the presumption that the maker "got it right" for the number of holes! Has anyone else considerd this?

If , as Neil stated - the device was a teaching aid, would it matter that the hole count was not perfect? Also, another contributor suggested that these ancient people had better ways of calculating the future view / changes in the cosmos than the AM. If I was the teacher, and gave the students a problem I would be keen to get a result before the students - without a lot of work, and be able to demonstrate the correct answer - quickly.

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Whilst those Euclidean techniques are ‘philosophically’ entirely valid … the practical difficulty of physically doing it for a large number of holes would be immense [i.e. nearing impossible]

A couple of pages back [16-Nov-2021] I mentioned that I had been doing an exercise in QCAD

… I will, later today, post what I think is a convincing ‘reality check’ on the practicality of that approach to the dividing.

MichaelG.

Edited By Michael Gilligan on 26/11/2022 08:32:25

As a bit of light reading, I offer this link to a PDF of Euclid's Elements. It gives a good insight into what was possible with rule and dividers and the advanced achievements of Ancient Greek Geometry. Euclid lived a century or two before the estimated manufacture of the Antikythera mechanism (possibly as early as 178BC), and his book was based on the efforts of earlier Greeks; Pythagoras predated Euclid by a few centuries.

Roughly 200 years after the mechanism was made, Ptolemy popularised the 'Earth is the centre' model of the universe, and provided the rather convoluted mathematics needed to predict planetary movements. However Ptolemy's thinking wasn't original - he credits Hipparchus, who lived around the time the Antikythera mechanism was made, and seems to have been the first mathematician to make a start on trigonometry.

To me the Antikythera mechanism presents two problems:

• Who was clever enough to understand the astronomical maths and design a gear system that computed results, and,
• Who was skilled enough to understand what the mathematicians were on about and build a complex gear box, not just a rough and ready prototype, but a well finished object of desire.

There's no doubt that the Ancient Greeks had the mathematical and astronomical skills needed to design such a mechanism. It's the building of it that's surprising. What we don't know is how common such devices were. They may not have been unimaginably high-tech at the time. Too expensive for ordinary folk, but perhaps the sort of thing the leisured super-rich of the day might indulge.

Later, Greek civilisation fell apart, and it's not surprising development stalled because Roman society didn't value mathematics or astronomy much. Later still, Rome fell to cultures even less interested, and Europe entered the Dark Ages. The ideas weren't entirely lost, and were revitalised first by monks wanting to worship at fixed hours, and then by the flood of rational thought that characterised the Renaissance and led via the Industrial Revolution to the problems of the modern world.

Dave

Perhaps they could have made a really basic rotary table by mounting say a 150mm diameter disc to be drilled in the middle of a say 10 meter diameter turntable, or even just had a 10 metre long beam of wood pivoted in the middle and the far end free to describe a large circle. So the number of holes to be drilled could be stepped out with dividers etc on the large 10 metre radius circle within say 1mm easily enough. So a 1mm error at the end of the 10m radius beam or turntable would be a tiny fraction of that.

An idea utilised by SF writer E.E. 'Doc' Smith in one of his Skylark series trilogy if I recall. Could be 'Skylark three'?

The beam would not even need to describe a full circle merely swing through several divisions or perhaps even just a single division..

Thanks for these interesting comments.

I look forward to MichaelG's reality check.

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As promised …

I prepared this little sketch when we were attempting to ‘reverse engineer’ the number of holes in the full circle, from the segment remaining.

It was sufficient to convince me that it is impossible to do that with confidence.

With a starting point of Hole_0 … at which the first hole for every circle would be co-located

… this is a screenshot of the Hole_7 cluster, showing the position of the seventh hole on each circle.

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It also illustrates the difficulty that would be faced when setting-out the holes ‘by chords’ or even by the use of Hopper’s long arm … the positional tolerance at the hole is tiny.

Simple in CAD … Difficult to execute by marking-out and drilling.

MichaelG.

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Edit: __ Nice to see that S.O.D. linked the conveniently readable version of the Elements 

The first two of Euclid’s Definitions say it all, really :

1. A point is that of which there is no part.
2. And a line is a length without breadth.

Edited By Michael Gilligan on 26/11/2022 15:46:59

Why not simply use a " geared pointer " to indicate the holes positions?

dave8

Is this a commercially available device? it sounds really useful

Ian P

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Sorry, Dave … I’m confused

Was that a response to my post or a general comment ?

MichaelG.