3 ms·

From rocks to icebergs, the natural world tends to break into cubes

28 points by pabo 6y ago

pabo 6y ago
The original PNAS publication can be found at [0]. I copy here (most of) the abstract, I think it's very nicely written: "Plato envisioned Earth’s building blocks as cubes, a shape rarely found in nature. The solar system is littered, however, with distorted polyhedra—shards of rock and ice produced by ubiquitous fragmentation. We apply the theory of convex mosaics to show that the average geometry of natural two-dimensional (2D) fragments, from mud cracks to Earth’s tectonic plates, has two attractors: “Platonic” quadrangles and “Voronoi” hexagons. In three dimensions (3D), the Platonic attractor is dominant: Remarkably, the average shape of natural rock fragments is cuboid. When viewed through the lens of convex mosaics, natural fragments are indeed geometric shadows of Plato’s forms. Simulations show that generic binary breakup drives all mosaics toward the Platonic attractor, explaining the ubiquity of cuboid averages." [0] https://www.pnas.org/content/early/2020/07/16/2001037117 https://www.pnas.org/content/early/2020/07/16/2001037117
twic 6y ago
The PDF of the paper is on the arxiv: https://arxiv.org/abs/1912.04628 https://arxiv.org/abs/1912.04628 And ResearchGate: https://www.researchgate.net/publication/343041685_Plato%27s_cube_and_the_natural_geometry_of_fragmentation https://www.researchgate.net/publication/343041685_Plato%27s... Previous postings which didn't get much attention: https://news.ycombinator.com/item?id=23922393 https://news.ycombinator.com/item?id=23922393 https://news.ycombinator.com/item?id=23975716 https://news.ycombinator.com/item?id=23975716
lawwantsin17 6y ago
Great, so we live in a voxel game engine.
- amiga 6y ago
  Like Minecraft, but with much higher resolution.
frodo_77 6y ago
Sounds like Minecraft.
- arkanciscan 6y ago
  Proof that we're living in a simulation
cheschire 6y ago
This seems intuitive with a little prior knowledge. When I learned how to load cargo airplanes, I was taught that you have to use dunnage to spread the weight of heavy objects across the floor of the plane to overcome specific weight limits in the floor. So if you have a 5 ton truck, you would need to use dunnage under each axle to distribute the load a bit so the whole 5 tons isn't focused on effectively 6 points the size of a sheet of paper. When adding the dunnage, we were taught to envision the weight spreading at 90 degrees from the axle centered downward in order to add the dunnage height to the total vehicle height during our load planning. More simply, I remember when I was a kid the local barbershop was vandalized with bb guns. The holes in the windows were tiny on the point of impact, but spread at nearly 90 degrees on exit. I am not claiming to know more than some anecdotal experiences here, and I may have drawn the wrong conclusions altogether. When I look at how force is typically distributed though, it seems to be regularly distributed in right angles. Poetically, I like to think how this is in direct opposition to the spirals one can find everywhere in nature. Yin and yang.
- LargoLasskhyfv 6y ago
  A barber-shop? Vandalized? Someone had a bad-hair day?
- kian 6y ago
  That poetic thought at the end is beautiful. Forces and actions (dual tothings) have shapes that are dual to living things - most likely because those spiraling shapes are more protective against forces than right angles.
  - mojomark 6y ago
    Actually, spirals found in nature are indications of the presence of 2 perpendicular force vectors: one in the direction of the spiral path, and one pointing towards the center of the spiral. See centripedal force (1). 1. https://en.wikipedia.org/wiki/Centripetal_force https://en.wikipedia.org/wiki/Centripetal_force
annoyingnoob 6y ago
Its interesting, we think of the building blocks as atoms and we almost always represent atoms as being spherical. Everything breaks down to cubes made of spheres?
mojomark 6y ago
This seems to have some overlap with the proposed "Constructal Law" of thermodynamics that is supposed to explain the natural evolution of 'design' in nature (1, 2). Granted, this concept is not without controvercy, and I'm not 100% sold just yet, but I was curious enough that I bought the 'Design with Constructal Law' text book to see if I can get to the truth of the matter by reviewing the math and perhaps running a few experiments. I'm working on it. 1. https://youtu.be/lLAYHnJVmjE https://youtu.be/lLAYHnJVmjE 2. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2871904/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2871904/ 3. text book purchase link: https://www.wiley.com/en-us/Design+with+Constructal+Theory-p-9780471998167 https://www.wiley.com/en-us/Design+with+Constructal+Theory-p...

28 points by pabo 6y ago

pabo 6y ago

The original PNAS publication can be found at [0]. I copy here (most of) the abstract, I think it's very nicely written: "Plato envisioned Earth’s building blocks as cubes, a shape rarely found in nature. The solar system is littered, however, with distorted polyhedra—shards of rock and ice produced by ubiquitous fragmentation. We apply the theory of convex mosaics to show that the average geometry of natural two-dimensional (2D) fragments, from mud cracks to Earth’s tectonic plates, has two attractors: “Platonic” quadrangles and “Voronoi” hexagons. In three dimensions (3D), the Platonic attractor is dominant: Remarkably, the average shape of natural rock fragments is cuboid. When viewed through the lens of convex mosaics, natural fragments are indeed geometric shadows of Plato’s forms. Simulations show that generic binary breakup drives all mosaics toward the Platonic attractor, explaining the ubiquity of cuboid averages." [0] https://www.pnas.org/content/early/2020/07/16/2001037117 https://www.pnas.org/content/early/2020/07/16/2001037117

twic 6y ago

The PDF of the paper is on the arxiv: https://arxiv.org/abs/1912.04628 https://arxiv.org/abs/1912.04628 And ResearchGate: https://www.researchgate.net/publication/343041685_Plato%27s_cube_and_the_natural_geometry_of_fragmentation https://www.researchgate.net/publication/343041685_Plato%27s... Previous postings which didn't get much attention: https://news.ycombinator.com/item?id=23922393 https://news.ycombinator.com/item?id=23922393 https://news.ycombinator.com/item?id=23975716 https://news.ycombinator.com/item?id=23975716

lawwantsin17 6y ago

Great, so we live in a voxel game engine.

amiga 6y ago
Like Minecraft, but with much higher resolution.

frodo_77 6y ago

Sounds like Minecraft.

arkanciscan 6y ago
Proof that we're living in a simulation

cheschire 6y ago

This seems intuitive with a little prior knowledge. When I learned how to load cargo airplanes, I was taught that you have to use dunnage to spread the weight of heavy objects across the floor of the plane to overcome specific weight limits in the floor. So if you have a 5 ton truck, you would need to use dunnage under each axle to distribute the load a bit so the whole 5 tons isn't focused on effectively 6 points the size of a sheet of paper. When adding the dunnage, we were taught to envision the weight spreading at 90 degrees from the axle centered downward in order to add the dunnage height to the total vehicle height during our load planning. More simply, I remember when I was a kid the local barbershop was vandalized with bb guns. The holes in the windows were tiny on the point of impact, but spread at nearly 90 degrees on exit. I am not claiming to know more than some anecdotal experiences here, and I may have drawn the wrong conclusions altogether. When I look at how force is typically distributed though, it seems to be regularly distributed in right angles. Poetically, I like to think how this is in direct opposition to the spirals one can find everywhere in nature. Yin and yang.

LargoLasskhyfv 6y ago
A barber-shop? Vandalized? Someone had a bad-hair day?
kian 6y ago
That poetic thought at the end is beautiful. Forces and actions (dual tothings) have shapes that are dual to living things - most likely because those spiraling shapes are more protective against forces than right angles.
- mojomark 6y ago
  Actually, spirals found in nature are indications of the presence of 2 perpendicular force vectors: one in the direction of the spiral path, and one pointing towards the center of the spiral. See centripedal force (1). 1. https://en.wikipedia.org/wiki/Centripetal_force https://en.wikipedia.org/wiki/Centripetal_force

annoyingnoob 6y ago

Its interesting, we think of the building blocks as atoms and we almost always represent atoms as being spherical. Everything breaks down to cubes made of spheres?

mojomark 6y ago

This seems to have some overlap with the proposed "Constructal Law" of thermodynamics that is supposed to explain the natural evolution of 'design' in nature (1, 2). Granted, this concept is not without controvercy, and I'm not 100% sold just yet, but I was curious enough that I bought the 'Design with Constructal Law' text book to see if I can get to the truth of the matter by reviewing the math and perhaps running a few experiments. I'm working on it. 1. https://youtu.be/lLAYHnJVmjE https://youtu.be/lLAYHnJVmjE 2. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2871904/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2871904/ 3. text book purchase link: https://www.wiley.com/en-us/Design+with+Constructal+Theory-p-9780471998167 https://www.wiley.com/en-us/Design+with+Constructal+Theory-p...