Roman Dodecahedrons Part III

I was pretty happy with my previous hypothesis on the dodecahedron, the string idea fits so well with the observed shape of the nodules, and the device is very satisfying to use and play with.

However one thing that it didn’t explain at all was the differing hole sizes on the faces. I’d initially written it off as either the blacksmith conserving metal (bronze is expensive), adding artistic flair, or maybe being used for a string game variant (e.g. threading through holes worth different values).

However, hundreds of dodecahedrons have been found, and differing hole size is a consistently observed feature. Surely if differing holes were an ‘optional’, rather than  functional, then at least some of the builders would have come up with different versions. But no, an array of different sized holes is a too strongly conserved a feature for them to be non-functional.

Let me cut to the chase, and I’ll explain how I got there. Basically, here’s the idea:

Roman Dodecahedron, and a contemporary device

So, I’d previously considered whether the differing holes implied mounting on a cone, and, since that would allow up to 12 different mounting heights, that it might possibly imply it was a calendar style device. I’d discounted it however, as the Romans used the Republican/Julian calendars which, although it does contain 12 months (usually), has month lengths which are very irregular, and I didn’t see a calendar-dodecahedron as an appealing labour saving device, or ‘desk toy’, given that.

However recently I was watching a Clickspring video, when I heard him mention the Egyptian Civil Calendar: https://en.wikipedia.org/wiki/Egyptian_calendar

Which neatly divided the year into 12 months of exactly 30 days, and then had an intercalary month of 5 days to make it fit neatly with the solar year. Simple and elegant, and I’d imagine it made planning business and trade very straightforward:

C:\Users\gsmith\AppData\Local\Microsoft\Windows\INetCache\Content.Word\Month_length_variation_horiz_Egyptian_v01.png

Compare that to the nightmare of the calendar of the Roman Republic (with months lasting either 22, 23, 27, 28, 29, or 31 days, but never 30):

C:\Users\gsmith\AppData\Local\Microsoft\Windows\INetCache\Content.Word\Month_length_variation_horiz_RomanRep_v01.png

Or even the slightly more logical Julian calendar:

Watching Clickspring’s explanation and hearing of the simplicity of the Egyptian calendar made me suddenly realise that while the Romans obviously used their own calendar, the outlying portions of their empire may not have. I did a brief bit of searching, and found this Gaulish calendar for example:

https://en.wikipedia.org/wiki/Coligny_calendar

Which has 12 months, all consisting of 29 or 30 days. (As well as a couple of further tweaks, to ensure solar accuracy on a longer cycle. For example, the month ‘Equos’, which normally lasts 30 days, drops to either 28 or 29 days on two out of every five years. As well there are two 30 day intercalary “bonus” months each of which only occurs once every 5 years). While that all might sound complicated on paper, in a diagram it actually looks much simpler:

C:\Users\gsmith\AppData\Local\Microsoft\Windows\INetCache\Content.Word\Month_length_variation_horiz_Coligny_v01.png

The point being, that while for an ancient Roman a calendar is a wildly varying thing (with months varying between 23 and 31 days), whereas for an ancient Gaul, it’s a far more regular object, almost always involving 12 months of 29 or 30 days. That makes it very amenable to representing with the dodecahedron.

I’ll lay out my hypothesis for how the device functioned, and in a separate post I’ll explain the strengths & weaknesses of the idea, as well as proposing some specific predictions & falsifiable tests that I’d wager will be supported under closer examination of the artefacts.

I took a spare  broom handle, and spent some minutes on a belt sander until it was approximately conical. I’m sure using a wood lathe (even one made from saplings) would get a far more regular outcome:

I then lasercut 12 washers, with differing inner diameters, and installed them on one of my previous dodecahedrons, taking care that opposite sides should not have very different diameters, as it would cause fouling:

There is then the consideration of how the hole sizes should be distributed to make a good calendar. To my mind there are only two simple choices. The first is a simple linear sequence, with the hole sizes either smoothly increasing or decreasing throughout the year, e.g.:

The second way would be to arrange the holes such that the position on the cone shows some aspect of the season. (e.g. length of the days, or height of the sun at zenith being the two most obvious properties). In such as case the arrangement would look something like this, which I dub the “Analemma sequence”.

If you wanted to get super fancy, you could even incorporate this as part of a sundial, with, for example, an external gnomon casting a shadow at noon to the dodecahedron at the appropriate height. This is a strictly unnecessary embellishment though, and as far as I know nothing in the dodecahedrons implies that it was done.

I’ll go with a simple linear sequence of hole sizes for my model, but if we find dodecahedrons with definite non-linear arrangement of hole diameters, then analemma spacing (either symbolic of day length, or a literal measurement as with a gnomon arrangement) is the obvious hypothesis to consider.

Then after assembling the model, I spent a while considering what the natural way to mark the days would be. In other words, how might you wind the string so that the number of days represented is most visible with the minimal of effort. (Absolutely no pointing or counting on fingers should be needed to interpret the result).

If the dodecahedron is mounted vertically through a pair of holes, as seems most likely, then a series of layers in the edges immediately become obvious. The top and bottom faces have 5 edges each, then there are 5 verticals leading down the equator, which is exactly 10 edges around.

And if we start from the bottom, this way of winding is most obvious, as it allows quickly counting in groups of 5:

I think starting from the bottom is most likely, as unused string will hang down out of the way. (Whereas if wound from the top it will hang down and be potentially confused with a legitimate edge to count). Also, by attaching the string to the base of the cone, after being looped around to show the appropriate number of days, the remaining string can then be tied back around the base of the cone, firmly securing the dodecahedron in place. That would make the whole arrangement suitable for travel, without any danger of losing your place in the calendar.

Here’s the result. You can see at a glance that it’s showing the 5th month, and the 11th day:

C:\Users\gsmith\AppData\Local\Microsoft\Windows\INetCache\Content.Word\Roman dodecahedron calenda v01.jpg

When one considers the dodecahedron, with its 12 faces, and 30 edges, it seems perfectly natural to associate that with calendars & timekeeping. Even without any mystical element, it’s a good fit, and I’d be happy to use it as a desk ornament.

But then if you throw in a bit of a religious or mystical connection, (e.g. a strong cultural attachment to the 12 signs of the zodiac, the apparent shape of the celestial sphere, a somewhat overenthusiastic devotion to the platonic solids, etc.), then I can easily imagine the dodecahedron being not only a functional village calendar, but also an object of reverence, both functional and cultural. Would the winding of the new day have a ritualistic aspect to it? I can imagine that getting to day 15 (and celebration entering the new fortnight) being accompanied with some joy. I can certainly imagine that recording getting to the end of winter being a time of celebration.

This might easily have been carried as a sceptre or staff by someone of importance (chief, village elder, druid?). Imagine a farmer scurrying up and asking them how long till they can plant their crops. They inspect this mysterious and arcane object at the end of their staff carefully, before nodding sagely and answering “Exactly 17 days”. Wow, clearly they’re a wise and erudite chap!

There’s one more bonus to this hypothesis. Although Roman Dodecahedrons are by far the most common shape, there’s at least one example of a Roman Icosahedron which has been found as well:

https://en.wikipedia.org/wiki/Roman_dodecahedron#/media/File:2018_Rheinisches_Landesmuseum_Bonn,_Dodekaeder_&_Ikosaeder.jpg

An icosahedron also has 30 edges. Is there also a similar natural way to wind it? Yes, here’s one approach:

Note that this is essentially the same as the dodecahedron winding (with layers of 5,5,10,5,5). This is not surprising, as the icosahedron and dodecahedrons are ‘duals’ of each other, and from memory the midpoint of each edge is the same between both?

But here’s the nifty thing. Since the 20 faces of the icosahedron are not a useful number for counting months, we can predict that any Roman Icosahedrons found will not have the same series of varying diameter holes on their faces. (Instead, to count months, the obvious way would be to use the 12 nodules instead, e.g. by tying a ring, ribbon or other marker to the nodule, or just to start the string winding there).

This is indeed what we see on the example of the Roman Icosahedron above. The 20 faces do not have varying diameter holes, but instead have what appears to be the same pattern repeated on faces (presumably just decorative).

In the next blog post I’ll examine the strengths and weaknesses of this hypothesis, as well as proposing some ways of falsifying it.

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1 Response to Roman Dodecahedrons Part III

  1. Pingback: Roman Dodecahedrons – Part IV | Tinkerings

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