We live in a world full of debris, from nanoparticles to rock avalanches, from glaciers to continents, to the solar system itself, all of which are made up of distorted polyhedrons Understanding and controlling fragmentation is essential to assess natural disasters, exploit natural resources, and even make a safe landing on other planets. < / P > < p > in a new study, four scientists have proved the validity of an old idea. Plato, an ancient Greek philosopher who lived in the 5th century B.C., believed that the five “substances” – water, gas, fire, earth and ether, which made up the world, corresponded to a specific geometric shape, namely, the so-called Platonic polyhedron (that is, polyhedrons with equal sides). The shape corresponding to the soil element is a cube. < / P > < p > now, researchers have used modern scientific methods to prove that this seemingly absurd idea is essentially correct. In a new paper published in the proceedings of the American Academy of Sciences, researchers have proved by means of mathematics, geology and physics that the average shape of the natural three-dimensional debris on earth is a cube; the average geometry of the natural two-dimensional debris is a “Plato” quadrilateral and a “voronoy” hexagon. < / P > < p > for researchers, this is a very interesting discovery, which links our understanding of nature with the concept of “soil” in Plato’s vision, proving Plato’s idea that soil elements are composed of cubes, just like the real statistical average model. < / P > < p > this exploration began with a study by mathematician Gabor domokos. In 2019, domokos published a paper describing a series of geometric models. Among the five polyhedrons proposed by Plato, only cube can fill space in a completely compact and seamless way. Therefore, domokos quantified the gaps produced by the other four geometries with the geometric model, and developed an approximate average geometric model. < p > < p > he spent three years thinking and testing the model. He found that if we randomly cut a three-dimensional polyhedron into two pieces, and repeat the cutting step again and again, the average approximate shape of a large number of polyhedrons with different shapes is cube. After < / P > < p > < p >, physicists Ferenc Kun and J á NOS t ü R ü K joined the research team on this problem. Kun is an expert on fragmentation, while t ü R ü K specializes in statistical and computer modeling. After discussing the discovery together, they decided to take the question to the geophysicist Douglas jerolmack to discuss the question: how does this happen in nature? < / P > < p > jerolmack was very surprised by the results of the model, which he thought was either a mistake or a major discovery. They’re trying to figure out what shapes rocks form when they shatter and understand the physical principles that produce them. < p > < p > fragmentation is a ubiquitous process, which means that the parts separated from the original solid must be able to be reassembled without any gaps. However, it turns out that the only Platonic polyhedron satisfying this condition is cube.
in order to test whether this mathematical model is correct in nature, they collected hundreds of different kinds of rock samples and measured them, and also retrieved thousands of rock information from the existing rock data sets. Whether the rocks were naturally weathered by outcrops or artificially blasted, the measurements were consistent with the average cubes they found. However, the existence of some special rocks seems to break the cubic rule. For example, the road of giants in Northern Ireland is an example. The giant’s road is a series of towering columns made of basalt cooled by some unusual process. Although these structures are rare, the mathematical concept of fragmentation in the new study can still include these fragments formed by unusual processes. < / P > < p > jerolmack explained that if a piece of rock is pulled, squeezed, or sheared, it is likely to form cube shaped fragments. Generally speaking, these forces act simultaneously; other shapes are formed only when the applied force is very special, but this is not the normal state of rocks on earth. < / P > < p > in addition, when researchers explored two-dimensional shaped fragments, the average polygon shape formed by the fracture was consistent with the model prediction, although these fragments had different fracture modes. They found that for two-dimensional materials, there is a similar probability of getting a rectangle and a hexagon. < / P > < p > there are a lot of sand and pebbles on the earth, which are evolved by cutting in a common form. When we pick up a stone in nature, we will probably find that it is not a perfect cube, but they are all statistical projections of the cube. It’s reminiscent of Plato’s fable about caves: he proposed an idealized form that is essential to understanding the universe, believing that what we see is a distorted projection of that perfect form. However, from the perspective of practical application, the analysis of fracture modes can be applied to the fracture of ice sheet, dry mud and even crust in nature; the identification of rock patterns can help to predict the risk of rock falling and the flow of fluids (such as oil or water) in rocks. It is a very strange experience for researchers to discover the possible basic laws of nature from thousands of years of thinking. This also makes modern scientists feel that Plato’s insights may be derived from his unusual sensitivity to geometry, his intuition, and his profound thinking about the difference between science and ordinary people.