Geometry Reveals How the World Is Made of Cubes

Plato was right: On average, the world is made out of cubes. [Click and drag the image to rotate; scroll to zoom in and out.]
On a mild autumn day in 2016, the Hungarian mathematician Gábor Domokos arrived on the geophysicist Douglas Jerolmack’s doorstep in Philadelphia. Domokos carried with him his suitcases, a bad cold, and a burning secret.Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research develop­ments and trends in mathe­matics and the physical and life sciences.The two men walked across a gravel lot behind the house, where Jerolmack’s wife ran a taco cart. Their feet crunched over crushed limestone. Domokos pointed down.

“How many facets do each of these gravel pieces have?” he said. Then he grinned. “What if I told you that the number was always somewhere around six?” Then he asked a bigger question, one that he hoped would worm its way into his colleague’s brain. What if the world is made of cubes?

At first, Jerolmack objected. Houses can be built out of bricks, but Earth is made of rocks. Obviously, rocks vary. Mica flakes into sheets; crystals crack on sharply defined axes. But from mathematics alone, Domokos argued, any rocks that broke randomly would crack into shapes that have, on average, six faces and eight vertices. Considered together, they would all be shadowy approximations converging on a sort of ideal cube. Domokos had proved it mathematically, he said. Now he needed Jerolmack’s help to show that this is what nature does.
“It was geometry with an exact prediction that was borne out in the natural world, with essentially no physics involved,” said Jerolmack, a professor at the University of Pennsylvania. “How in the hell does nature let this happen?”Over the next few years, the pair chased their geometric vision from microscopic fragments to rock outcrops to planetary surfaces and even to Plato’s Timaeus, suffusing the project with an additional air of mysticism. The foundational Greek philosopher, writing around 360 BCE, had matched his five Platonic solids with five supposed elements: earth, air, fire, water and star stuff. With either foresight or luck or a little of both, Plato paired cubes, the most stackable shape, with earth. “I was like, oh, OK, now we’re getting a little bit metaphysical,” Jerolmack said.
Gábor Domokos (left) and Douglas Jerolmack had previously collaborated on a project that spanned mathematics and geophysics.Courtesy of Gábor Domokos; Eric Sucar/University of Pennsylvania