Antikythera Mechanism

[John HaineParticipant @johnhaine32865]

Neil, I'm registered with Academia.edu, I just emailed you a copy to your mytimemedia address.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Neil Wyatt on 05/10/2021 15:51:10:

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Unfortunately that site will only let me in if I allow it to download my contacts!

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Sorry … forgot about that little scam, and the iPad didn’t mention it

… and I did not need to log-in to just read the paper

I’ve been warning people not to use it for a while now.

MichaelG.

Edited By Michael Gilligan on 05/10/2021 17:30:43

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Michael Gilligan on 05/10/2021 15:08:59:

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Thanks, Neil … it also answers the question posed in my P.S.

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But, unfortunately, I am not entirely convinced by their Least Squares Fit

… see the substantial deviation from the circle within my green Region of Interest :

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MichaelG.

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If we are trying to decide how many holes there must be in the full circle, then we need a good estimate of its radius.

[Dave HalfordParticipant @davehalford22513]

Posted by Michael Gilligan on 05/10/2021 18:03:53:

Posted by Michael Gilligan on 05/10/2021 15:08:59:

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Thanks, Neil … it also answers the question posed in my P.S.

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But, unfortunately, I am not entirely convinced by their Least Squares Fit

… see the substantial deviation from the circle within my green Region of Interest :

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MichaelG.

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If we are trying to decide how many holes there must be in the full circle, then we need a good estimate of its radius.

That also looks like an area of damage, I suspect that without all the corrosion it would no longer be attached to the rest.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Dave Halford on 05/10/2021 20:28:43:

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That also looks like an area of damage, I suspect that without all the corrosion it would no longer be attached to the rest.

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Good point, Dave

… so we’re down on valid hole locations

MichaelG.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Michael Gilligan on 05/10/2021 20:35:23:

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Good point, Dave

… so we’re down on valid hole locations

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Taking Neil’s best available image : **LINK**

https://www.researchgate.net/figure/Fragment-C-showing-degrees-of-longitude-on-the-zodiac-scale-as-well-as-the-holes_fig5_252678779

They have obscured the hole numbered 1, so I suggest we need to start at 2

The presumably-displaced group starts at 73 … so realistically we have 2 to 72 available for investigation.

I plan to measure the angle subtended by various groups of holes and do some simple statistics

… The big problem is the low resolution of the image, and therefore the difficulty in locating centres of holes !

360/355 is difficult to distinguish from 360/354 when you are measuring fog. …

MichaelG.

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Edited By Michael Gilligan on 05/10/2021 23:13:40

[Neil WyattModerator @neilwyatt]

Posted by Dave Halford on 05/10/2021 20:28:43:

Posted by Michael Gilligan on 05/10/2021 18:03:53:

Posted by Michael Gilligan on 05/10/2021 15:08:59:

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Thanks, Neil … it also answers the question posed in my P.S.

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But, unfortunately, I am not entirely convinced by their Least Squares Fit

… see the substantial deviation from the circle within my green Region of Interest :

.

.

MichaelG.

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If we are trying to decide how many holes there must be in the full circle, then we need a good estimate of its radius.

That also looks like an area of damage, I suspect that without all the corrosion it would no longer be attached to the rest.

The paper mentions the fracture.

On the plus side, i measured the distances from hole 1 to 41 and 41 to 81 as being the same.

(They shouldl have numbered the holes 0-80 IMHO).

Neil

[Neil WyattModerator @neilwyatt]

Posted by John Haine on 05/10/2021 16:20:13:

Neil, I'm registered with Academia.edu, I just emailed you a copy to your mytimemedia address.

Thankj John,

Neil

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Neil Wyatt on 06/10/2021 09:43:35:

[…]

The paper mentions the fracture.

On the plus side, i measured the distances from hole 1 to 41 and 41 to 81 as being the same.

(They shouldl have numbered the holes 0-80 IMHO).

Neil

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(a) True, but [rather worryingly] they appear to be using those displaced holes

(b) What were you measuring ? … chords and/or subtended angles ?

(c) Agreed

MichaelG.

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Note: The white dots at [or near] holes1, 9, and 81 are theirs, not mine.

… and I don’t think they are sufficiently accurately placed to decide between 354 and 355

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Michael Gilligan on 06/10/2021 10:02:50:

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… and I don’t think they are sufficiently accurately placed to decide between 354 and 355

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The angular difference between those two counts is less than 0.003° per step

MichaelG.

[Roger ClarkParticipant @rogerclark]

My random 2P's worth:

They knew about gears and ratios at that time so could they have made some kind of 'rotary table' out of the parts they had already made?

Tin hat now on

[David NobleParticipant @davidnoble71990]

A very tentative thought, would it be more accurate to mark out the holes on a much larger radius and then follow the radial lines towards the centre until the required diameter is met?

David

[Mick B1Participant @mickb1]

Posted by David Noble on 06/10/2021 15:41:10:

A very tentative thought, would it be more accurate to mark out the holes on a much larger radius and then follow the radial lines towards the centre until the required diameter is met?

David

Excellent idea in principle, but its implementation raises questions of its own, such as how to get a reliable straight radial line to mark from – a simple tight cord might not be easy to use.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Michael Gilligan on 05/10/2021 22:50:01:

[…]

They have obscured the hole numbered 1, so I suggest we need to start at 2

The presumably-displaced group starts at 73 … so realistically we have 2 to 72 available for investigation.

I plan to measure the angle subtended by various groups of holes and do some simple statistics

… The big problem is the low resolution of the image, and therefore the difficulty in locating centres of holes !

360/355 is difficult to distinguish from 360/354 when you are measuring fog. …

MichaelG.

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Well … I’ve had a go, and it’s even worse than I anticipated

First I scaled the photo up by 500% and then drew lines from the marked centre to [my best estimate of] the centre of various holes, and recorded the angle subtended by each five steps.

Tabulated and calculated:

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The result is, to say the least, unconvincing !

It is, however, reasonably predictable when we remember that tiny angular difference between 355 and 354 holes.

If anyone would like to repeat the exercise, as a check on my work … Please Do

MichaelG.

[Michael GilliganParticipant @michaelgilligan61133]

Here’s a ferinstance of the fog which we are attempting to measure:

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MichaelG.

[Martin KyteParticipant @martinkyte99762]

Regarding the deviation from circular. There are two reasons that the holes are non circular (assuming they were to start with). Firstly as has been mentioned that there is a physical distortion/fracture etc or that the XRAY image was not exactly normal to the plane of the hole circle. In the second case there will be some projection errors at right angles to the rotation axis. I assume that the images were obtained by 3D XRay scanning and reconstricted to show the relavent slice. It would be nice to know the origin of the data.

regards Martin

[Dave HalfordParticipant @davehalford22513]

Posted by Martin Kyte on 07/10/2021 11:09:20:

Regarding the deviation from circular. There are two reasons that the holes are non circular (assuming they were to start with). Firstly as has been mentioned that there is a physical distortion/fracture etc or that the XRAY image was not exactly normal to the plane of the hole circle. In the second case there will be some projection errors at right angles to the rotation axis. I assume that the images were obtained by 3D XRay scanning and reconstricted to show the relavent slice. It would be nice to know the origin of the data.

regards Martin

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.

[pgk pgkParticipant @pgkpgk17461]

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

[Michael GilliganParticipant @michaelgilligan61133]

Posted by pgk pgk on 07/10/2021 12:10:45:

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.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Neil Wyatt on 04/10/2021 21:48:01:

I've just come back from a talk at my new local Astronomy Society, by Mike Edmunds, President of the Royal Astronomical Society.

[…]

This matters because they are trying to calculate the diameter (and hence the number of holes) in an incomplete ring. On the face of it 360 or 365 seem right, but measurements of the hole spacings suggests 354 holes.

[…]

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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.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Martin Kyte on 07/10/2021 11:09:20:

[…]

I assume that the images were obtained by 3D XRay scanning and reconstricted to show the relavent slice. It would be nice to know the origin of the data.

regards Martin

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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.

[John OlsenParticipant @johnolsen79199]

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

[Neil WyattModerator @neilwyatt]

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!

[Michael GilliganParticipant @michaelgilligan61133]

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

[currently in a microscopy Zoom meeting]

MichaelG.

[pgk pgkParticipant @pgkpgk17461]

Posted by John Olsen on 08/10/2021 06:18:58:

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

John

The Baghdad Battery or scroll storage..

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