Carl Sagan covers the Platonic Solids in Cosmos
(basically speaking of Ionions)
There can be an infinite number of polygons, but only five regular solids.
Four of the solids were associated with Earth, Fire, Air and Water
The cube, for example, represented Earth
These four elements they thought - represented all of terrestrial matter
So the fifth solid, they mystically associated with the Cosmos
I remember that cubes are Earth, because they tile together to make a solid. Tetrahedra are Fire, because the sharp corners make them destructive. And icosahedra are Water, because the nearly-spherical shape lets them roll over each other and be fluid. I can’t remember if octahedra or dodecahedra were Air, though, and what the reason was.
Ether was the dodecahedron, and if you want a mnemonic, pentagon = fifth element.
Like I’ve said before, given the actual demonstrated Roman bronzeworking skill and its application to such mundane items as candlesticks and lamps, this is an ignorant argument.
The elegant reverse proof that there are only 5 regular solids leads to an equation where 1 ÷ p + 1 ÷ q . > 1 ÷ 2
p (number of edges per face) and q (number of faces meeting at a vertex)
p = 3 allows only 3 solutions for q, 3 - Tetrahedron, 4 - Octahedron, or 5 - Icosahedron and they’re all triangles so maybe less remarkable.
p = 4 is a cube, q=3
p = 5, pentagons, also leads to q=3 for a dodecahedron
p = 6 leads to q < 3 which is impossible
p > 6 will never be satisfied
They can’t rule out luxury good. They can rule out purely utilitarian use-cases, where there are much cheaper methods of producing the same ends.
What I liked about the quote is that it was a short very non-definitive list of concerns that any hypothesis must address. The article implied that it decisively indicated that the objects were religious, something I don’t accept. Mangetout’s hypothesis about it being an apprentice’s skill-demonstration project wasn’t falsified for example. We’ve discussed other plausible scenarios.
Of course there’s the maxim that “when it doubt say it had ritual significance” is the non-explanation for everything in archeology.
While that’s probably truer than my colleagues might want to admit, in the period concerned, which is literate, with a high survival of texts and images relating to normal life, we can be pretty comfortable that we can at least sort objects into sub-categories like - [formal] religious practice, local cultic religious observance, superstition and associated behaviours, and consumerist non-utilitarian crap [ie why would someone buy this?]. The bounds of those are pretty well understood and there is enough find context to think dodecahedra fall into the last.
There is nothing pushing us to a ritual / religious / sacral use or meaning. Its an equivalent to the stupid mugs at the back of the kitchen draw that say ‘Worlds Best Teacher’ - vaguely too useful to throw away but far too useless and pointless to ever being used for anything [cf Gizmodern - a mailing site with useless shit, but made special with a USB port]
The proof that there are only five regular solids was the last proof of Euclid’s Elements, but he screwed it up by not defining “regular solid” tightly enough. Under his definition, the triangular bipyramid and pentagonal bipyramid would also qualify, as well as a variety of non-convex shapes.
Yeah. It really looks to me like a lava lamp. That is, an object that a person with some disposable income might buy because it looks cool, and that is “used” by putting it on a shelf and looking at it. And that’s common enough that people know what it is, and say, “oh, i see you have a lava lamp”.
Not out of the question I guess. But why just that one specific object? If there was a culture of useless consumer objects wouldn’t there be other varieties? And why only in NW Europe, nowhere else in the empire?
To me the ritual object interpretation makes the most sense. Quite possibly a neo-Celtic cult of some sort, which maybe got suppressed when Christianity became the state religion.
For me, the interesting questions are:
Why only bronze? Other roman doodads and small household items exist in examples made from clay, bronze, bone, sometimes carved stone, sometimes glass. Dodecahedra appear to have only been made in bronze. Of course other materials are less durable, but we’ve found hundreds of these things, and only ever bronze - we should probably have at least found fragments of their clay counterparts, if they existed. There are various carved stone mace heads and possible fishing weights and other knickknacks that sort of look similar-ish, but are arguably just unrelated objects.
Why only in the north-western part of the Roman empire? - Why not in the Mediterranean or eastern parts?
Why do they have knobs on? - it’s pretty much the only common feature apart from the material of construction - not all examples have holes of different sizes; not all of them are made to the same scale; not all of them have large through-holes at all, but they all have knobs on the vertices - indeed it seems important that they have knobs on, because in some examples, the knobs are soldered on as repairs (either repair of damage, or of casting failure).
Also (and this might have an easy answer that is ‘metal detectors’): Why no context? - we’ve found hundreds of these things, but apparently never in any interesting or relevant archaeological context like a grave or a temple.
The bronze items I’m talking about weren’t just luxury goods. Even an undecorated, purely utilitarian bronze oil lamp takes just as much skill as one of these dodecahedrons. And the Romans used cast bronze for lots of other non-luxury things like fibulae and buckles.
So no, they can not rule out the purely utilitarian.
That’s the exact opposite of what I’ve heard - that they are commonly found in either a funerary or military context.
Well, if they are just a showy doodad, and you bought one that originally had knobs, and one breaks, well, you don’t want to show off a broken dodecahedron.
That detail escaped me somehow. I would have thought a funerary context would provide other clues, at least to the status and role of the person who owned them, unless they were the only item in the grave.
Military context might be a red herring unless it’s really specific, since ‘military context’ was just everywhere in the northwest of the empire at that time.
Certainly, but if they were a showy doodad, I might have expected some variation in the knobs - like little claw-and-ball things or maybe spikes or stars or whatever - the knobs are really consistent across a lot of the examples. That might suggest they had some function.
Bronze is the only one in that list that’s electrically conductive. Given the timeframe, though, I can’t think of a reason why that would be important.
Even if the Dodecahedrons have something to do with religion/mysticism or fortune telling, the knobs seem to have a utilitarian purpose.
Could they be part of a Wizard’s Staff? {PRATCHETT}
BTW–I still say Gambling or Fortunetelling.
Both of which obsessed Romans.
The problem with a lot of these guesses is that they don’t explain certain characteristics of the Dodecahedrons. As noted by Mangetout, they’re all made of bronze. I don’t know much about materials & fabrication, but I would guess making it out of other materials would be easier and cheaper. If it had something to do with religion/mysticism or fortune telling, why not make it out of wood? And why are they hollow? It just doesn’t add up.
I’m confident we will eventually discover a drawing or painting that shows one. And when we learn what they were used for, there will be a collective, “Of course! So obvious. Why didn’t we think of that?”