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).
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.
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).
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).
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.
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.
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.
> 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.
When I'm measuring my food, I like to shake it, so I can fit more in the measuring cup without increasing the calorie count. ;) Oatmeal will pack down quite a bit with some shaking.
The title is funny. I realize it's sometimes hard to translate and summarize scientific results for the layperson, but the paper wasn't comparing stirring or shaking. They compared rotating the container to tapping the container. Rotating is, ironically, a type of shaking, and closer to shaking than tapping. I would expect a good deal of dice packing in this experiment using vertical shaking, as opposed to lateral tapping.
Vertical shaking would unpack just as many things as it would pack. Horizontal shaking works because gravity is biasing the reorganization toward more packed arrangements.
Maybe you're thinking of (the equivalent in a crystalline solid) of "boiling"? E.g., giving a bump on the bottom of the cylinder, that would have enough force to scatter individual cubes, but not enough force to unlock cubes from the crystal.
It sounds like you're imagining a difference in magnitude, as opposed to a difference in type of motion, you seem to be assuming that I'm suggesting a very large magnitude. I would call bumping the bottom a type of vertical shaking, if the container is allowed to move vertically, regardless of how far (or short). A vertical shake that moves less than the height of one die doesn't move far enough to allow unpacking, and empirically it works for me. Fast and small vertical shaking, or boiling, if you prefer, will "liquefy" the particles and allow them to settle. Fast and small horizontal shakes would probably do the same, I just speculated above that vertical boiling packs faster than horizontal "tapping", but who knows, I could be wrong, I'd have to do the experiment.
Hmm, good point; I wasn't considering <1.0h shakes. (I was mentally considering anything worth being called a "shake" as raising and lowering the entire packed column between the top and bottom of the cylinder, such that it would repeatedly bump both the top and bottom.) A 0.5h shake is indeed effectively equivalent to a Newton's-cradle-like bump.
I think their definition of "ordered" is different from most people's when it comes to something like dice. Cool effect, but it makes for a pretty misleading headline.
You have to apply the context before you call the (correct) headline misleading. This is a physical sciences context so this is the correct use of "ordered" -- as in "order and disorder", i.e. symmetry and correlation. You're talking about "ordered" as in "ordinal", meaning "related to position in a series", which makes more sense in a computer science context (and we are on HN), but still -- it is your job to apply the context to the situation, not anyone else's.
If it's all about bloodless scientific rigor, why'd they choose to highlight "Dice" in the headline when it is probably a property of "cubes" in general?
I'm imagining some biologists studying how human cells have some unique negative reactions to C3H8O, and then they title the a report "Humans just can't resist alcohol."
Ordering alignment of rectangular prisms under simple shear is well established by now.
As is the variable effects of shaking - can increase or decrease packing fraction and order depending on magnitude.
In addition ordering in packings of rectangular prisms extend up to 8 particle lengths from the side walls - and are variable with time and history. This experiment's results could be partly due to edge effects.
That's what I was thinking. Vibratory sorting/feeding machines are common and a lot of engineering effort has gone into optimizing them. I'd be very surprised if rotary oscillation had not been tried, and probably used, on many occasions.
I have a friend who's got a doctorate in CS. He always adamantly insists his work was utterly pointless as any company interested in solving the problems he solved would simply throw people at it and solve it independently in a couple of months, they'd never find his work.
To be fair there aren’t many questions on stack overflow about, “How can I design my hyperblock selection algorithm for improved performance on a block-structured data flow processor?”
There might be if you first go out of your way to answer questions about dataflow throughput by pointing people toward block-structuring and mention keywords like "hyperblocks" there. People already do this; I've noticed a good few times now that I've done a number of increasingly-specific searches as I understand a problem better, and each time the answer that actually guides me to the next step comes from the same person/place.
Isn't there also a probabilistic angle? On the second video, on the outer circle I see that same sides repeat at most 3 times. Can this be a true random number generator?
