Antikythera Mechanism

To which you can add it was found in a ship wreck and may not have been as round the day after it went down as it was when new.

Apart from the absolute number of holes mattering when deciding on the calender version used does the accuracy matter that much? At least as far as that the mechanism must have had a re-set option and that spacing errors likely cancel out when any ring completes a full circle?

pgk

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Quite so … but the measurements of the available fragment [or rather it’s X-Ray image] have been used in the attempt to determine that number.

My own feeble effort has demonstrated [to my own satisfaction] that such determination is basically futile.

Personally … I think we have a ‘duty’ to discuss such matters.

MichaelG.

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With the greatest respect to all concerned … My own measurements “suggested” anywhere between 335 and 366 [but probably 352] … Indicating that the methodology is flawed.

MichaelG.

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It’s worth looking at the paper that Neil referenced, Martin

… Here’s a short snippet:

“Our investigation was based on a set of x-ray computed tomography (CT) images provided by the Antikythera Mechanism Research Project. The image set consisted of 51 x-ray “slices” spaced at 0.1 mm depth intervals. Using Photoshop software, we built up mosaic, composite views, each created from many dozens of layers.”

MichaelG.

Well, I find the study of this sort of thing fascinating, even if we may never know the full details of this device. It does give us a glimpse of the sort of things that the ancients were actually capable of. The existence of this one device obviously implies the existence of a workshop capable of making it, and although one does not expect them to have been mass produced, there were quite likely more than one made, as well as possibly simpler variants when the ideas were being developed. The problem of course is that metals does not always survive well, both due to corrosion and also due to the fact that it is very recycleable.

As well as this, we know about Hero's simple steam turbine. I wonder what else they might have been playing with?

John

Perhaps I should explain why the number of holes matters.

The whole device had many gears, some of which can be reconstructed accurately, others estimated, as based on text fragments we can know the sorts of cycles it was displaying. The Greeks knew the lengths of these cycles (from days to decades) with surprising accuracy (the longest cycle is about a lifetime) and were able to calculate their ratios accurately.

It's likely the holes would have been used for some sort of indexing - there are fragments of dials which would have read out various cycles - and the obvious contenders for this are:

365 days = 1 year

354 days = 12 lunar months

355 days = 13 sidereal months (the time for the moon to return to the same place in the sky)

360 degrees

But who knows!

I have extended my little spreadsheet, and will post a ‘grab’ later this evening

[currently in a microscopy Zoom meeting]

MichaelG.

The Baghdad Battery or scroll storage..

As promised; here is my updated spreadsheet :

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It uses the same raw measurements, but I have manipulated the data a little more …

Angle per step is now presented to five decimal places … not because it is realistic to do so, but because it highlights the tiny differences.

Notional Count is now presented to the nearest integer value, because that makes more sense in the context.

I have added a row for AVG of the values in the 13 data rows … the fact that these match the values computed for the 70 hole span is hardly a surprise; but it’s a useful check on the formulæ.

I have then added a further 8 data rows, each for a span of 35 holes

… and another AVG row for those 8 rows.

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The results are, I think, pretty clear :

1. Based on my measurements ; the most likely count for the complete ring would be 352
2. The counts predicted from small groups of holes vary enormously !
3. [because] The predicted count changes dramatically with a tiny change in Angle per step
4. Obviously, more holes in the span averages-out placement errors and gives more reliable estimates.

Please … Would someone else repeat my exercise [or some reasonable variation upon the theme], so that we can compare results.

MichaelG.

An alternative method would be to use a least squares to fit the 50+ data points to a circle or ellipse. This will give the centre coordinates and radius/radii for a circle or ellipse. If an ellipse gives the better fit then it's likely the x-ray image was oblique view. Once the best fit circle/ellipse is known then finding the number/position of holes that best fits the observations should be relatively straightforward again by using a least squares fit.

It should be possible to combine the two stages into one but I'd need to think about it.

There are numerous articles on least squares fit of data to a circle/ellipse which can easily found via Google.

Thanks for the comments, David

… If you can do it, I will be very interested and most impressed.

I am no expert in statistics, but it seems to me that the available data have too much variance for such a ‘fit’ to be credible … but I am happy to be proved wrong.

MichaelG.

Neil, is there any reason you didn't include 366 sidereal days in a year? Wouldn't that track the stars through a year?

Martin C

There is nothing clever about this tabulation, but it might illustrate the scale of the problem:

It assumes equispaced holes on a pitch circle, and it makes clear that accurately estimating the number of holes in the circle [from a fragment thereof] demands implausibly accurate measurement of the image.

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MichaelG.

[ sorry, we had a Broadband drop-out  … this should have been an edit ]

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 __ I am reminded of the Infinite Improbability Drive : **LINK**

https://youtu.be/nCf53ses22w

Edited By Michael Gilligan on 09/10/2021 08:53:14

Many sources of error in this ancient mechanism make it difficult to be certain about anything, but I think Michael has shown conclusively that there aren't 365 holes. Therefore the dial can't be indexing earth days. It is however a good match to the moon. And although we today are used to a solar calendar, the ancients went lunar. The Islamic Calendar is still lunar.

So although Michael's results don't prove the ring is lunar, they are consistent with the suggestion. The lunar hypothesis is strengthened rather than weakened by Michael's analysis, but nothing is solid yet.

I enjoy watching 'The Curse of Oak Island' on TV (Blaze channel on Freeview). In it a large team use high-tech methods to search for treasure mysteriously buried and elaborately booby trapped by the Vikings, Knights Templar, Spanish, Pirates, or the British army. See Money Pit. The fun is in deciding which 'evidence' is meaningful and what's utter rubbish. So far I've seen no evidence whatever of treasure on the island. Instead absurd coincidences are taken as gospel. I feel it's unlikely that the garden layout of the Palace of Versailles is a minora deliberately aligned with a marker in Nova Scotia by someone hiding treasure! Archaeology on acid. The whole programme is based on proving a negative - there is no treasure - when science knows it's impossible to prove a negative.

The Antikythera Mechanism is far more predictable than Oak Island, but still tempts false conclusions. Proceed with care!

Never mind drilling the holes, I don't know how they were laid out. Assuming the number is correct, how would you draw 352 equally spaced dots on a 6" diameter with a pen?

Dave

Edited By SillyOldDuffer on 09/10/2021 10:20:52

I think GHT proposed a way of working in his Workshop Techniques: as I recall, he suggested first calculating the distance between points, setting dividers to this and adjusting as necessary. A refinement where possible would be to divide the circumference into a convenient number of divisions so as to minimise cumulative errors.

I went for a ‘bus ride [outward] and walk [home] this morning … and had a little ponder about 352

The prime factors are 2 and 11

11 is the duration of the Sunspot cycle, in years

Mmmm …

MichaelG.

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Ref. __ https://scied.ucar.edu/learning-zone/sun-space-weather/sunspot-cycle

Edited By Michael Gilligan on 09/10/2021 13:55:34

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Here’s another little ‘sanity check’ …

It was easier for me to generate a ‘gear’ … but this is about the scale of that task:

MichaelG.

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Using dividers and straight edge it's easy to construct a right angle. Then by bisecting you can get 32 points. Then it's trial and error to split them into 11s, but you don't get a cumulative error. Do it all oversize and use a radial arm to reduce to the actual size. That arm doesn't need to be straight, a pivot, an indicator point for the big circle and. A sharp point for the inner, give it a biff to mark