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Mysterious stone balls

Math, engineering and art are never very far apart. They’re all creative processes.

Stone balls in the Terraba Plain, the Boruca region, Costa Rica. Smithsonian Institution. Bureau of American Ethnology, 1948. (Courtesy Doris Stone) *
A petrosphereis a round stone artifact shaped by human hands. Since no practical purpose has ever been assigned to them, they should properly be considered art.
Among known examples are the stone spheres of Costa Ricapainted pebbles from Scotland, plain sandstone balls from Traprain Law in Scotland, and the Carved Stone Balls of Scotland.

There’s definitely a Scottish bias in the distribution. Clearly, our Caledonian ancestors had a thing for stone balls.

Roman dodecahedron.*
Petrospheres shouldn’t be confused with Roman dodecahedra. These have no known purpose or meaning either. They are small, hollow bronze devices with twelve flat faces and knobs at the corners.  They are beautiful artifacts, but compared to carving a stone sphere from igneous rock, casting a brass shape was easy.
There are roughly 300 known stone spheres in Costa Rica. They range from pebble-size up to two meters in diameter. They were carved from granodiorite, which is a common, coarse-grained, hard, igneous rock. Since most of them have been removed from their original locations, scientists are guessing about their age. (It’s impossible to radiocarbon-date a rock.) But they’re generally thought to be “pre-Columbian,” which means they were there when Europeans arrived.
Pre-Columbian stone balls at Palmar Sur, Costa Rica.*
There’s no easy way to measure the rotundity of a large object, especially when it’s partly sunk into the ground. Photographs tell us that the Costa Rican stones are very spherical. The mystery to me isn’t why, but how. There was metallurgy in pre-Columbian Mesoamerica, but it would have been useless for carving rocks. All they had for tools were other, harder rocks. Even with that limited technology, they carved shapes that rival those we can make today. And, of course, they are pure abstractions.
Six-knob Scottish stone ball, Kelvingrove Art Gallery and Museum, Glasgow.*
The Scottish Carved Stone Balls are less abstract. They are usually knobby and sized to be comfortably carried in the hand. Many of them have six concentric circles incised on them. They are mostly made of igneous greenstone, but there are sandstone versions as well. There are almost 400 known examples. Their distribution suggests that they originated in Aberdeenshire, in the northeast corner of Scotland.
They are much older than the Costa Rican spheres, being generally ascribed to Neolithicor Bronze Age people. Their decorative, incised surfaces hint at meaning and purpose, but these hints vanish under hard scrutiny. Were they fishing weights? Ball bearings to move stones for Neolithic stone circles? The Scots are, after all, famous engineers. Weapons? Or, that last refuge of an unimaginative archaeologist, religious symbols? There isn’t enough context for us to know.
Six-knob Scottish stone ball, Kelvingrove Art Gallery and Museum, Glasgow.*
But what there is in both the Costa Rican and Scottish examples is a kind of mathematical perfection. We make modern stone spheres with machines; they did them with eye and hand, and they’ve lasted for thousands of years. They are a reminder that math, engineering and art are very closely intertwined.