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Comment by ajarmst | Hacker News Reader

More accurately, cubes pack more closely when agitated one way than another. The fact that they are dice is irrelevant (they don't become ordered with respect to the facing side). To be honest, this isn't particularly odd, as the experiment removed the component of the agitation that would tend to displace the cubes vertically, which is the only dimension with an asymmetric force that would tend to increase the packing factor if undisturbed (gravity).

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The published paper: "Experimental Study of Ordering of Hard Cubes by Shearing", https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.11...

Calling them "dice" (which is what was actually used in the experiment) is fine for a summary of the research for laypeople. If confused, any interested reader will quickly know what "ordered" means in this context. As to the work itself, if someone had asked me one hour ago if this would happen, I would have guessed not. I know that light shaking of small objects will tend to organize them, and that large objects in particulate matter (such as sand) will tend to rise in such circumstances. But I still am surprised enough by this result to think it's notable - and, I assume, so were the editors of Physical Review Letters.

"Ordered" is accurate, as they mean it in the thermodynamic sense. It's not that precise because of the other meaning, though.

Actually, a similar distinction is important in thermodynamics as well. Even at 0K (with no movement of atoms), you can still have a "residual entropy" related to the randomness in the crystal structure. For example, a solid CO crystal at 0K still has disorder in the direction the molecule is oriented (possible because the C-O dipole is small but nonzero).

http://images.slideplayer.com/24/7362502/slides/slide_18.jpg

Dice are not perfect cubes, since there edges and corners are rounded, so it would not make sense to generalize the results of dice as applying to perfect cubes.

Perhaps, but the salient characteristic of dice is that the sides are marked. When you talk about dice becoming ordered, there is a very strong implication that you mean the sequence of facing sides, not the packing factor. If we must be pedantic, then the phrase "rounded cubes"---or even "dice-shaped-cubes"---would be more accurate and relevant than "dice" (which aren't even invariably cubes, but are invariably marked).

Platonic cubes don't exist

That's a really deep statement about the nature of existence. A mathematical theorem exists, even if the underlying structure is not represented in reality. We know that spacetime is warped by mass distribution, and is therefore non-Euclidean. However, the Pythagorean theorem is still something that exists, despite applying only to Euclidean space.

In the same way, a Platonic solid could be said to exist, even if it isn't represented in reality.

Casino dice are actually cubes, at least as close as manufacturing tolerances of 0.0001 inch can make them. For example:

https://www.casinosupply.com/collections/casino-dice/product...

This is to help make it easier to spot alterations or flaws which could affect their randomness; shaved corners become very easy to spot, when packing them together it's easy to spot ones with height differences, etc.

Tolerance you’re referencing relates to the distance of one side to another, not the shape of the corners; the dice you linked to have their corners rounded (aka shaved) if you look at the image.

Indeed. I think anyone who has done some work with a milling machine will know firsthand that a freshly cut 90 degree edge that has not yet been rounded over is sharp like a blade.

If casinos actually did use dice that were extremely cubic, the dice would be cutting patrons' fingers and wrecking the felted surface of the craps table.

Funnily enough, the website the parent linked actually calls them " Transparent with razor sharp edges" so I guess they are pretty sharp.

I may have been wrong in my previous post. Apparently "razor" is one of several styles of dice edge and is intended to prevent excess tumbling, so a craps throw doesn't take too long to come to rest. I'm tempted to buy some new razor dice to see for myself.

I can't find measurements for the radius of curvature on razor dice edges, but I'd be surprised if they're truly as sharp as claimed. Without even considering the liability aspect, it seems inconvenient for a casino to pause the game because someone is bleeding on the table or dice.

I also wasn't able to learn how often the felt of a craps table is changed, though I came across something that said the felt's useful lifetime is prolonged by a foam rubber underlayer.

But a cow is still basically spherical.

Most people would consider that an "edge case" which can be neglected in the model since it doesn't create any forces in the y direction.

An 8 edge case.

Dice have 12 edges.

So I went up to my friend and I was like "How many edges does a dice have?" and they said "eight."

"If it makes you feel any better, I thought the same thing. But we're both just idiots."

Not really, easy to make an error; for example, a cube has 12 edges, but a dice with rounded edges would have an infinite set of edges.

So it's a corner case?

Only if you are cornered.

As Lebowski would say, “Clearly, you’re not a golfer.”

In casinos, dice have sharp edges and corners.

Did you even look at the dice used in the experiment? The edges & corners are clearly rounded.

Casino craps dice are, I have a set for rolling my dnd characters stats for true randomness

> To be honest, this isn't particularly odd, as the experiment removed the component of the agitation that would tend to displace the cubes vertically, which is the only dimension with an asymmetric force that would tend to increase the packing factor if undisturbed (gravity).

The consequences here are still interesting with respect to object shape. Why do certain shapes easily reach optimal packings under perturbations like this? Will mono-disperse spheres reach their tightest theoretical packing under such a perturbation? Probably not. Ellipsoids? Probably. Tetrahedra? No idea. Anecdotally, I've heard this is why most candies are ellipsoidal and not spherical. Ellipsoids naturally gravitate to tighter packings and are thus more efficient to ship. Maybe we can now get cube-shaped chocolate candies.

And I was expecting a gamedev studio story...

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