RIP Terry Pratchett... I can't see anything like this without thinking of him, and missing his regular biting criticism yet still somehow optimistic novels.
I'm not sure if the Quanta article adds any technical content, but it's certainly a nice read.
> “I found someone who was willing to read that part of the book for me and translate it back into human language,” Domokos said. He found the theorem for any number of dimensions. That confirmed that cubes were indeed the 3D answer.
I'd like to know who this someone is, that's an unsung hero of science right there! So much existing knowledge is locked away in "daunting tomes"
In Minetest, Terrain is generated using Perlin noise (or Simplex noise?). Voronoy noise is used to put a landscape on top of it. The result is quite convincing. even if you use a bit crazy values for noise parameters, you can get arches and "floating islands" that remind of fantasy landscapes.
Any sufficiently complex process looks like randomness (that's what we colloquially call "luck"). Therefore randomness (PRNG, coherent noises) can look like a complex process with enough trickery.
In addition to being a really cool result, this is a really approachable article with a lot of interesting ideas in the background information. I expect pop math education youtube is gonna have a field day.
Would this give any insight into what type of cement/stone laying tile pattern should be use to mitigate future cracks?
Quoting the paper to give an idea of the formation being modeled:
These patterns have been reproduced in experiments of mud and corn-starch cracks, model 2D fragmentation systems, where the following have been observed: Fast drying produces strong tension that drives the formation of primary (global) cracks that criss-cross the sample and make “X” junctions; slow drying allows the formation of secondary cracks that terminate at “T” junctions; and “T” junctions rearrange into “Y” junctions to either maximize energy release as cracks penetrate the bulk or during reopening–healing cycles from wetting/drying
“How in the hell does nature let this happen?”
MFW we all live in Minecraft
Read the article
> given most scientists hold the naive empiricist worldview in which only particulars exist
What do you base your beliefs on? Intuition?
Math; not geology.
But sure, the fact that this is a model that starts with making the least amount of assumptions completely invalidates it as geology and makes it pure maths. Because as we all know, no useful model in physics was ever built up from the ground like that, only introducing complex caveats as required to make sense of empirical data as necessary.
 the simplest way that one can cut a shape is with a straight line (2D) or flat plane (3D). In this case no new concave shapes can be created unless a concave angle was a part of the initial shape. Ergo, if the starting shape is convex and we cut away parts randomly, then all shapes produced this way will be convex. If the initial shape has concave parts, then on average most shapes derived from it will be convex. This is even more true if we apply this "cutting away" recursively to the shapes that were cut away. This makes the assumption of shapes being (mostly) convex quite reasonable, unless there is a specific reason to expect concavity, like specific crystalline structures perhaps. Also, for the record, I just reasoned this out on the spot, it's not exactly difficult.
I don't know if that was your intent, but if not it might be worth reflecting on what you meant to say instead, and why you did not notice that what you wrote instead comes across so negative. Because then there would be no need for heavy sarcasm.