Antikythera Mechanism

[Michael GilliganParticipant @michaelgilligan61133]

As promised; here is my updated spreadsheet :

.

.

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.

.

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.

[David TocherParticipant @davidtocher94033]

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.

[Michael GilliganParticipant @michaelgilligan61133]

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.

[Martin ConnellyParticipant @martinconnelly55370]

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

[Michael GilliganParticipant @michaelgilligan61133]

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.

.

.

MichaelG.

[Michael GilliganParticipant @michaelgilligan61133]

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

.

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

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

[SillyOldDufferModerator @sillyoldduffer]

Posted by Michael Gilligan on 08/10/2021 21:51:37:

As promised; here is my updated spreadsheet :

…

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

…

MichaelG.

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

[egaParticipant @ega]

Posted by SillyOldDuffer on 09/10/2021 10:18:41:

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

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.

[Michael GilliganParticipant @michaelgilligan61133]

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.

.

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

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

[Michael GilliganParticipant @michaelgilligan61133]

Posted by SillyOldDuffer on 09/10/2021 10:18:41:

[…]

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

.

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.

.

[duncan webster 1Participant @duncanwebster1]

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

[Michael GilliganParticipant @michaelgilligan61133]

Posted by duncan webster on 09/10/2021 17:40:06:

[…]

but you don't get a cumulative error.

[…]

.

Just 351 that are all [ very probably ] in the wrong places

First hole = Last hole … So that one should be right.

MichaelG.

[duncan webster 1Participant @duncanwebster1]

I was going for 352 as in your recent post. 351 is 9*39,which gets us nowhere, except you could do 39 by trial and error, followed by 11 ditto

Edited By duncan webster on 09/10/2021 19:39:17

[Michael GilliganParticipant @michaelgilligan61133]

Posted by duncan webster on 09/10/2021 19:34:17:

I was going for 352 as in your recent post. …

.

So was, I Duncan !

… All I was saying was that 351 of them will [very probably] be in the wrong place.

Although Dave has moved this to a problem of placing 352 holes … The real [Antikythera] issue is estimating the number of holes in a circle, based on a relatively small sample thereof.

The level of accuracy required to do that prediction successfully, to the nearest integer value, is astonishing.

From my table … if 352 is the right answer: we can only get it if we know the angle per step is greater than 1.020° and less than 1.026°

As I am sure you will realise … this is a VERY small tolerance.

MichaelG.

[BazyleParticipant @bazyle]

Added to the problem the original might have been distorted in the sinking of the ship, whatever point it got broken, the stresses of corroding etc.
However I would also expect to go to more depth than just a single x-ray of the object as nowadays there is more sophisticated 3D x-ray imaging, multiple wavelength, and possibly going into neutron scans.
That data would need to be examined for each hole effectively treating the light to dark transitions at the edge as if it were a sloping crater, then decide on possible values for how far down the crater you take as the edge. Process that round the hole and decide where the centre is depending on what you have taken as an edge value.
Once you have the multiple possible centres for each hole you can then process the array of holes.

Having recently had a presentation on machine learning (aka neural network) I feel this is just the sort of problem it can work on, almost instantly testing hundreds of variables from the data I outlined above and giving you a probability of the fit to each of your hole counts. Surely someone has done this as a 3rd year university project.

[John HaineParticipant @johnhaine32865]

Even back when Michael Wright was working on it he was using X-ray tomography for imaging the object in 3D, and I'm sure they are using more sophisticated studd now.

I haven't really been following this, but are people saying that the project written up in HJ which I linked to, one of the authors being Clickspring, which concluded that the device incorporated a lunar calendar, is wrong?

Edited By John Haine on 09/10/2021 20:46:19

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Bazyle on 09/10/2021 20:31:14:

[…]
However I would also expect to go to more depth than just a single x-ray of the object […]

.

Have you looked at the paper that Neil linked ?

The image is a composite from multiple ‘Computed Tomography’ scans

My worry is that the authors seem to have built the composite in Photoshop, and then picked-off values from the screen. As I have said repeatedly … I am not convinced that the accuracy of their data points is sufficient to make the ‘count’ estimate that they have provided.

Look at the “point” that they are using to define location #1 … That’s why I chose to start at #2

MichaelG.

.

Edited By Michael Gilligan on 09/10/2021 21:31:58

[Michael GilliganParticipant @michaelgilligan61133]

Posted by John Haine on 09/10/2021 20:45:48:

[…]

… are people saying that the project written up in HJ which I linked to, one of the authors being Clickspring, which concluded that the device incorporated a lunar calendar, is wrong?

.

Not in so many words, John

What I am saying, however, is that [based on the evidence I have seen] … I do not find the estimate of the number holes on one particular ring to be convincing.

… It could conceivably still be the right answer … but , I would suggest ; only if the holes in the missing portion are positioned closer together than those in the image.

… it’s a matter of acknowledging uncertainty !!

MichaelG.

[Ian PParticipant @ianp]

I think that determining the number of holes in this mechanism is unlikely ever to be solved from the currently available (physical) fragment. If in the future more of the mechanism was ever retrieved then it might be possible to count more accurately.

It seems to me than no amount of measuring, statistics, probability or other methods will give us the exact answer because we know there is a variation in hole spacing in the ones we can see and there may be similar variations in the missing ones.

Ian P

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Ian P on 09/10/2021 21:31:47:

I think that determining the number of holes in this mechanism is unlikely ever to be solved from the currently available (physical) fragment. […]

.

Thank You, Ian

That’s what I have been trying to demonstrate !

MichaelG.

[Michael GilliganParticipant @michaelgilligan61133]

John,

I have just had another look at the BHI articles and, although the statistical analysis seems exemplary, I remain concerned about the quality of the input data.

[ remember the aphorism Garbage IN — Garbage OUT ]

On p3 they state:

“ Our procedure first set the scale in Fiji to match the provided reference of 50 μm per pixel (20 pixels per mm). ”

and then, on p4

“ Note that while the image's resolution limits direct measurement to only two decimals, we present all data to three decimals to reduce information loss when rounding mean measures of hole locations. ”

.

I took a different [and perhaps better?] approach : I first enlarged the published image by 500% and saved it as .png to avoid additional .jpeg artefacts … and then measured angles, instead of XY coordinates.

Honestly : I am not convinced that measuring inter-hole distances to only two decimal places of mm is good enough for this exercise.

MichaelG.

.

Edit: __ just re-posting this image, for ease of reference: 

 

Edited By Michael Gilligan on 09/10/2021 23:30:09

[Michael GilliganParticipant @michaelgilligan61133]

A quick calculation :

Radius 77.493
resolution of inter-hole measurement 0.01mm

0.01 ÷ 77.493 = 0.00012904391364
atan (0.00012904391364) = 0.0073936716

So each 0.01mm of their inter-hole measurement represents more than 0.007° of angle.

Now look back at my tabulation of hole counts.

MichaelG.

[Neil WyattModerator @neilwyatt]

Posted by Martin Connelly on 09/10/2021 08:32:22:

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

True.

One of the things it does is derive the sidereal movement from the solar day, so it might be redundant.

Neil

[Neil WyattModerator @neilwyatt]

Posted by John Haine on 09/10/2021 20:45:48:

Even back when Michael Wright was working on it he was using X-ray tomography for imaging the object in 3D, and I'm sure they are using more sophisticated studd now.

I haven't really been following this, but are people saying that the project written up in HJ which I linked to, one of the authors being Clickspring, which concluded that the device incorporated a lunar calendar, is wrong?

Edited By John Haine on 09/10/2021 20:46:19

It contains a lunar calendar, but if these holes are for the master motion stepping the device around, it makes logical sense for it to fit the calendar year, with each step a solar day, rather than one of the derived motions.

[Neil WyattModerator @neilwyatt]

Posted by Michael Gilligan on 09/10/2021 21:34:16:

Posted by Ian P on 09/10/2021 21:31:47:

I think that determining the number of holes in this mechanism is unlikely ever to be solved from the currently available (physical) fragment. […]

.

Thank You, Ian

That’s what I have been trying to demonstrate !

MichaelG.

I think that's what Mike Edmunds feels, more or less, he's writing a paper suggesting that errors in the manufacture mean we can't be certain of the actual hole count.

That's why he was interested in the possible accuracy with which the holes could have been drilled.

Neil

[Author]

Posts