There’s this guy, you see, who knitted his way to a solution to an infamous problem in Roman history. This might be a bit premature (since academic journals haven’t weighed in yet), but I am persuaded that the mystery of the ancient Roman dodecahedrons has been solved. And why I’m persuaded affords a handy example for teaching how Bayesian reasoning works in making good historical inferences. [Update: This case likewise shows how Bayesian reasoning can incorporate new facts so as to change what’s likely: experts in the comments to this article subsequently persuaded me that a full accounting of the facts in my Bayesian model does not get as positive a result for this thesis as I had initially thought.]
I suppose I should begin by explaining what a “mysterious ancient Roman dodecahedron” is. It’s not just any dodecahedron from ancient Rome (I’ll show you an unrelated example shortly), but a very peculiarly consistent oddity that no one has been able to explain (mainly because no writing survives mentioning it). It’s a common object. Some hundred or so have been found, originating in the 2nd century A.D. and spanning a couple of centuries afterward. But only in France and northern and eastern Europe. It’s weird looking. And has peculiar features. Some are of stone manufacture, but most are cast bronze.
Some typical examples (one from Wikipedia, another from the Birmingham Musem) are shown to the right. Each is a twelve-sided hollow object, the sides generally symmetrical (an isohedron, so it looks a little like a twelve-sided die, something old-school role-playing-gamers will recognize), but every side has a circular hole in it, and the holes are different sizes, but the pattern of sizes (the sequence and arrangement) is the same on every object, even though the size of the object (and thus size of the holes) varies considerably, from kind of tiny (one and a half inches total diameter) to about the size of what would have then been a large adult fist (a little over four inches). The holes also sometimes have a sequence of parallel carved rings around them (sort of like gutters or guidelines in the face of the object), but many do not, so these appear to be a decorative flourish (a typical accent found in Roman tech of the time, where common utilitarian objects can be prettied up with some artsy flourishes like that).
But importantly, every corner of these objects has a solid knob sticking out of it, a bollard narrower at its base than at its tip (many of these just look like attached spheres), for twenty knobs in all. This most of all prevents the twelve-sided die analogy from quite being right, that plus the fact that the holes being of different size means each face has a different weight. They also aren’t inscribed with anything…a fact that is far more crucial to determining their purpose than you might at first think.
Just search “Roman dedocahedron” in Google Images and you’ll find dozens of examples. And yet…