Science confirms Plato’s Theory: Earth is made of cubes

WHAT WOULD YOU get if you smashed the Earth into little bits? To answer that question, scientists from the US and Hungary ran a series of simulations illustrating the ways that rock fractures. The results help us understand the natural shapes on Earth and across our solar system. They also confirmed what philosopher Plato had theorised in ancient Greece: As you break down the Earth, it crumbles into cubes.

This explains the distinct fracture patterns observed in nature, says study co-author Douglas Jerolmack, PhD, a geophysics professor at the University of Pennsylvania. ‘Since fragmentation is a ubiquitous process that breaks rock and ice across the solar system, our findings help to explain the shape and size of planetary materials.’

In the first of the computer simulations performed by teams from the University of Pennsylvania, Budapest University of Technology, and the University of Debrecen in Hungary, researchers created a geometric model in which they carved an abstract cube into almost 600 000 pieces by randomly inserting a series of 50 2D planes. All of the resulting fragments were, on average, cubic. These pieces were then randomly split apart, many times, resulting in 13 million fragments. The numbers of sides, edges, and vertices were counted, and those outcomes were averaged. While the resulting fragments weren’t actually millions of tiny cubes, the averages are cuboid, down to multiple decimal places.

Next, the team conducted fieldwork at Hármashatárhegy, a mountain overlooking Budapest. Their analysis of a dolomite-rich outcrop revealed that fragments were, on average, cubic. These observations, paired with previously collected field data – both naturally weathered stone and rock that had been dynamited by humans – was compared to the 13 million computergenerated fragments by performing 4 billion computations. ‘It was a surprisingly good match,’ says co-author Gábor Domokos, PhD, a professor of mechanics at Budapest University of Technology.

To understand how rocks break down this way, the team then used supercomputers to create a series of mechanical simulations. Here they studied a molecular model, where a brittle rock-like material was modelled,

using what looks like virtual gumdrops and toothpicks. The gumdrops represent the rock-like substance while the toothpicks represent the bond holding it together, including a weighted failure criterion – which measures the force that can break each segment. In these simulations they studied the fault lines that shatter open when they break, like if you dropped a plate on to the floor. The simulations found that as you broke apart natural materials, on average, most pieces conformed, on average, to a cube-like shape.

The research could eventually help scientists identify regions on Earth’s surface that are susceptible to rock falls. As rocky outcrops are exposed to the elements, inherent flaws in the rock slowly grow into large cracks. When these fissures meet, they form unstable blocks of rock that can be loosened by an earthquake or by gravity over time. ‘The size and structure of the crack networks determine the size of the blocks that are produced, which ultimately determines, to a large extent, the hazard created when they fail,’ Jerolmack says. Their work, he adds, could eventually help to forecast how these rock blocks form on both 2D and 3D surfaces.

The discovery also supports an improbable theory that’s nearly 2 400 years old. Before the discovery of chemical elements and atomic structure, Plato and his fellow natural philosophers – the forebears of modern scientists – came up with the classical elements of earth, water, fire, air, and cosmos to explain what the world was made of. In Plato’s dialogue Timaeus, he theorised that the classical elements were each composed of a three-dimensional shape where all angles are equal, as are all sides. Of these five shapes, known as Platonic solids, he believed the cube was linked with Earth due to its ability to seamlessly fill space.

Jerolmack and Domokos both pointed out that their results are a twofold representation of Plato’s work, first as the Platonic solids, but second, and arguably more interesting, in combination with the philosopher’s allegory of the cave.

In Plato’s Republic, he tells a story about prisoners in a cave. They can only observe strange shadows on the wall, never what’s casting the shadows. Plato suggests that for people with no additional information, the shadows are reality, but that doesn’t imply that the shadows are the full reality. In an analogy straight out of calculus, he suggests that there are additional stages of reality with more dimensions of understanding. ‘Plato’s idea was that what we see with the naked eye are just distorted shadows of the true reality, so the reality which we perceive is a distorted version, and the ideas are the reality,’ Domokos explains.

By studying the rock fragments and the ‘shadow’ created by taking their probabilistic and arithmetic averages, Jerolmack says, the researchers inadvertently brought both of Plato’s ideas together. ‘What we’ve demonstrated is that, on average, rock or earth is made up of cubes, but you never see the cube,’ he says. ‘It exists only when you take all these distorted shards and bits and average them together.’ Domokos adds: ‘It is so much in the spirit of Plato – there are too many coincidences to say that it is just coincidence.’

Domokos and his team analysed the fracture pattern of a rock outcrop outside of Budapest. The fragments were roughly squarish.