When I read Amelia Carolina Sparavigna's paper I was certain she was onto something. I figured calculating the eye distances based on the hole measurements she provided would show they were consistent with a normal arms length, and that would be a nice verification. But I did the calculations and one hole pair on each of the measured dodecahedrons didn't check out. It would need to be held 3-6 meters from the user's eye. We should expect something about 20" or less for a handheld portable device. Wouldn't a reasonable person just use smaller holes? Her theory also doesn't explain the knobs at the corners. She's definitely onto something, but it's not the whole story.
Another concern was that a much simpler device would have performed the same function better.
Consider that a single hole in an ordinary flat disk, and a cord equally divided into equal segments (by knots) would allow estimating ANY arbitrary distance as long as the approximate size of the viewed object is known. This would give a more accurate distance estimate and be much simpler to make.
But it would be possible to improve that simpler device. Fiddling with a measuring cord would be awkward if the user just needs a quick verification that his target is in range. So some means of quickly comparing actual range to a few standards (like the range of his ballista) without the cord would be desirable. The opposing holes of different sizes on the dodecahedron provide that. But it's an extra feature, not the primary function.
But if they want to keep the capability of the more accurate measuring using a cord they would want some means to wrap the cord when not in use.
Also consider that the cord could rot and be broken. If broken it would be difficult to replace in the field (a military campaign) with an accurately divided cord. A way to use an ordinary piece of cord that that somehow measures itself would also be nice.
The dodecahedron addresses these shortcomings of the simpler device. A few hole pairs are provided that can be used for quick range verification checks without a measuring cord. The large and small holes can be used to define the proper holding distance by the method of corresponding edges.
A measuring cord is provided to make arbitrary range estimates accurately. This would use those hole pairs that do not really work for the cordless method. A knotted cord would probably have been a provided initially.
The knobs or balls on the corners provide a convenient means to wind the measuring cord. This can be done without blocking the holes if adjacent knobs are used, the cord always following the dodecahedron edges.
When winding the cord this way it is naturally equally subdivided and self-measuring. Each segment of cord that is unwound is equal to one edge length of the dodecahedron. So a knotted cord is no longer essential. If the original knotted cord is lost or broken an unknotted cord can replace it. The cord would even be somewhat self-marking due to the tendency to discolor where it repeatedly rubbed on the copper alloy knobs. This makes the natural knot spacing for the cord equal to the edge length of the dodecahedron.
To measure range an object of known height (probably a man...an enemy fighter) is viewed through the hole in the dodecahedron. The user would hold the dodecahedron far enough from his eye that the height of the man appears to fill the field of view. The range is then proportional to the eye distance as measured with the cord. The actual distance in stadia or any other Roman units is irrelevant as long as the range of the ballista is known by the same method.
This is for rough range estimates with a portable device, not surveying. There are more accurate methods available when you have access to the down range position.
I think this is a reasonably complete explanation. All the features of the dodecahedron are explained and are consistent with this function.
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