Of Popular Mechanics
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A new analysis suggests that the rocks are likely to break in their Plato-assigned form: cubes.
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Platonic solids are 3D shapes that Plato also gave a “classical element” value.
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Participating scholar Gábor Domokos discovered the first true “straightened” gömböc.
New research shows that a Platonic ideal may be true after all: The world can be divided mainly into cubes, and not just Minecraft. In a new article, researchers from the US and Hungary simulate the world’s “natural 3D fragments” and find that, in fact, most fit a cube-like form factor.
What does Plato have to do with all this? Well in the TimaeusPlato wrote about “classical elements”, which is the general term for the group that generally includes earth, water, fire and air. Before the discovery of individual elements and the idea of atomic structure, “natural philosophers”, the ancestors of modern scientists, came up with the classical elements, sometimes including the fifth element “ether”, to explain what the world was made of.
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Plato turned that into Platonic solids, which are a series of regular 3D shapes, that is, with sides that are all square, for example, or equilateral triangles, the 3D versions of different regular 2D polygons. And the cube was linked to Earth in Plato’s system, but his decision to refer to all regular solids in this way carried over to the work of real geometers like Euclid.
Neither of these forms occurs literally, and no one is finding 20-sided water segments or real earth cubes. But many minerals naturally form into cubic crystals, and many rocks naturally break into roughly cubic forms. And there is an intuitive sense here: things break according to the force that is breaking them, and it is easier to divide it into a more or less right angle than a small piece of cake to fracture.
“We apply the theory of convex mosaics to show that the average geometry of natural two-dimensional (2D) fragments, from mud cracks to tectonic plates on Earth, has two attractors: ‘Platonic’ quadrangles and ‘Voronoi’ hexagons.” , explain the scientists. in his role
The Voronoi polygon is part of a different algorithmic way of dividing material. What the scientists mean is that, say, a mud drying area or a ceramic sheet that falls on concrete is likely to break in Voronoi’s polygons, or in Plato’s “Earth” squares.
But when scientists simulated the same ideas in three dimensions, Plato’s cubes dominated over the Voronoi polygons. They explain:
“Surprisingly, the average shape of natural rock fragments is cuboid. When viewed through the lens of convex mosaics, the natural fragments are in fact geometric shadows of Plato’s forms.
All of this was sampled and calculated using a simulator and rock breaking software to process the results using Voronoi and Platonic forms as “attractor” parameters.
This research follows a 2019 article on Plato’s margin of error, which involves one of the same researchers, Gábor Domokos, a maths luminary who helped give the first real example of a self-straightening object called gömböc.
In fact, platonic solids are the subject of this new article, but Plato would have loved the gömböc. Perhaps the neoclassical element “oobleck” has finally found its Platonic solid.
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