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from the seems-like-a-square-view-to-me dept.
Plato, the Greek philosopher who lived in the 5th century B.C.E., believed that the universe was made of five types of matter: earth, air, fire, water, and cosmos. Each was described with a particular geometry, a platonic shape. For earth, that shape was the cube.
Science has steadily moved beyond Plato's conjectures, looking instead to the atom as the building block of the universe. Yet Plato seems to have been onto something, researchers have found.
In a new paper in the Proceedings of the National Academy of Sciences, a team from the University of Pennsylvania, Budapest University of Technology and Economics, and University of Debrecen uses math, geology, and physics to demonstrate that the average shape of rocks on Earth is a cube.
"Plato is widely recognized as the first person to develop the concept of an atom, the idea that matter is composed of some indivisible component at the smallest scale," says Douglas Jerolmack, a geophysicist in Penn's School of Arts & Sciences' Department of Earth and Environmental Science and the School of Engineering and Applied Science's Department of Mechanical Engineering and Applied Mechanics. "But that understanding was only conceptual; nothing about our modern understanding of atoms derives from what Plato told us.
"The interesting thing here is that what we find with rock, or earth, is that there is more than a conceptual lineage back to Plato. It turns out that Plato's conception about the element earth being made up of cubes is, literally, the statistical average model for real earth. And that is just mind-blowing."
Journal Reference:
Gábor Domokos, Douglas J. Jerolmack, Ferenc Kun, et al. Plato's cube and the natural geometry of fragmentation [$], Proceedings of the National Academy of Sciences (DOI: 10.1073/pnas.2001037117)
(Score: 1, Insightful) by Anonymous Coward on Wednesday July 22 2020, @06:50PM (2 children)
Buckminster Fuller repeatedly made a coherent argument in all of his writings that Nature preferred tetrahedrons.
A cube, as formed by 12 struts, joined at eight vertexes, is unstable. It requires reinforcement.
There is an elegant solution for creating a stable cube but it involves two tetrahedrons nested in the same space, in polar opposition to one another - see http://www.cgjungpage.org/images/stories/image006.gif [cgjungpage.org] for an illustration of the juxtapositioning I refer to.
The author refers interested readers to Buckminster Fuller's manual on his geometry, which he referred to as 'synergetics', and which is the title - Synergetics - specifically, he refers readers to pages 4-5, because this is introductory, elementary stuff.
More info:
- https://en.wikipedia.org/wiki/Synergetics_(Fuller) [wikipedia.org]
- http://www.rwgrayprojects.com/synergetics/s01/p0000.html#100.20 [rwgrayprojects.com] (an online copy of Synergetics)
Lacking evidence to the contrary I'm going to suggest that claims that the world is modeled on cubes is driven by a need for attention of some sort, probably the "publish or perish" variety.
~childo
(Score: 2) by hendrikboom on Wednesday July 22 2020, @08:16PM
It's much easier to do procedural generation of landscape on a lattice of square tiles than a lattice of triangular tiles.
And much, much easier to do it in 3D (maybe you're making a game of asteroid mining?) with cubes than with regular tetrahedrons. (hard to tessellate regular tetrahedrons in Euclidean space with out doing something like mixing them with octahedra).
(Score: 1, Interesting) by Anonymous Coward on Thursday July 23 2020, @04:15AM
in this paper the authors show that 12 sided objects are most common.
this is because of the way fault lines occur.