Math, engineering and art are never very far apart. They're all creative processes.
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Stone balls in
the Terraba Plain, the Boruca region, Costa Rica. Smithsonian
Institution. Bureau of American Ethnology, 1948. (Courtesy Doris Stone) *
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A petrosphere
is 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 Rica, painted
pebbles from Scotland, plain sandstone balls from Traprain
Law in Scotland, and the Carved Stone Balls of Scotland.
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Roman dodecahedron.*
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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.
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Pre-Columbian stone
balls at Palmar Sur, Costa Rica.*
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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.
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 Neolithic
or 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.
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.












