Hungarian and American researchers have together proved Plato's millennia-old theory that the world is constructed from cubes.
As a result of nearly four years of research work, applied mathematician Gábor Domokos, head of the MTA-BME Morphodynamics Research Group, which belongs to the Eötvös Loránd Research Network's university research groups, theoretical physicists Ferenc Kun (of the University of Debrecen), János Török (of the Budapest University of Technology and Economics), together and geophysicist Douglas Jerolmack, a research professor at the University of Pennsylvania, have proved Plato's assertion from more than 2,500 years ago that the world is essentially constructed from cubes.
In his later work, Plato, one of the greatest philosophers of ancient Greece, opined that each of the four elements – earth, water, fire and air – that make up the universe are constructed from regular three-dimensional shapes. In the case of earth, these are hexahedrons, or cubes.
The research team composed of three Hungarian scholars and one American has proved that if a three-dimensional body is sliced apart many times across random planes, the resulting bodies (polyhedrons) will, in terms of their average number of faces, vertices and edges, tend towards six, eight and twelve, respectively, meaning that the average form is a cube. Through extensive computational experiments, the team examined the stress fields that cause natural fragmentation in rocks and demonstrated that the most common naturally occurring stress fields split masses in two, thus, on average, creating cubes. Therefore, the geometric average of the fragmented rocks and stones found on Earth (and other heavenly bodies) is the cube itself.
In nature, the cube-shaped cracked dolomite of Hungary's Kű Valley forms Platonic cubes.
Assembling the proof was the result of four years of outstanding research in the fields of mathematics, physics and geophysics. Reflecting the significance of the discovery is the fact that it was published in one of the most outstanding scientific journals in the world on 17 July 2020: https://www.pnas.org/content/early/2020/07/16/2001037117.
"The universe is full of stones and rocks of various sizes that are constantly being fragmented," said Domokos. "This article presents this universal process from an angle we have never seen before. The model of fragmentation connecting geometry and mechanics opens a new perspective as it connects not only patterns of fracturing appearing at the surface of the planet, but the form of stones resulting from fragmentation with the geological and planetological processes that create them. This means that we can deduce the history of the origin of the natural forms seen on Earth and other heavenly bodies. The new theory promises to be useful in helping with the design and monitoring of industrial processes built around fragmentation (such as ore processing).
As a result of the research that is now being wrapped up, the Gömböc, another research finding of Domokos and his partner, Péter Várkonyi, has also found its place in the context of the natural sciences. From the time it was introduced, the Gömböc was a scientific sensation, since this discovery is the first known homogeneous body to have a stable and an unstable (that is, a total of two) equilibrium points, and no matter which way it is placed on a flat surface, it always returns to its stable equilibrium point. It can be proven that it is not possible for a body with fewer equilibrium points to exist.
Previously, the Hungarian researchers also succeeded in proving that, due to abrasion, bodies found in nature are continuously losing their equilibrium conditions, and in this sense are becoming more like the Gömböc – although they never reach this final state. The Gömböc, therefore, is the invisible final stop in the processes of shape development, while the research currently being concluded shows that the cube is the – also invisible – starting point of these same processes. "In his allegory of the cave, Plato posited that all we see are imperfect shadows of perfect and idealised forms in the physical world," said Domokos. "The current result illustrates this Platonic idea by showing that the collection of physical fragments is nothing but a statistically distorted shadow of a regular Platonic body, a cube."
Thanks to the form's scientific significance, unique and numbered examples of the Gömböc can be seen in numerous spots around the world, in natural history museums and the permanent exhibitions of renowned universities.
The scientific publication has received extensive media coverage around the world, including an article in Science.