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Science

M&M's Pack Tighter Than Gumballs 60

Posted by michael from the hexagonal-closest-packing dept.
icantblvitsnotbutter writes "In a rather humorous article, the New York Times reports that M&M's pack more tightly than gumballs (registration, blah blah... alternate source here). The upshot of this is what it means for manufacturing denser glass (here, the generic term for solids made of random arrangements of molecules). Some basic solid geometry and tongue-in-cheek quotes fill out the story, but the immediate applications are mind-boggling for the next time you grab munchies on a road trip."
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M&M's Pack Tighter Than Gumballs More

M&M's Pack Tighter Than Gumballs

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  • Well.. (Score:5, Funny)

    by hookedup ( 630460 ) on Friday February 13, 2004 @11:42AM (#8270368)
    They all have the same density when they come out of me :)
  • That's why Peanut M&Ms exist, so they can make the bag look just as full as regular M&Ms, but with less chocolate!
  • But what about Peanut M&M's?

    • Re:Ah, Nuts! (Score:2, Interesting)

      by Drakin ( 415182 )
      Well, they do mention the almond M&M's...

      If the spheroids are deformed in a second direction, into ellipsoids (in other words, stretched or squashed so the M&M shape is no longer circular when viewed from above -- like, say, an almond M&M), then the maximum packing density increases to 77 percent, more tightly than the simple neat stacks.

  • Duh! (Score:2, Funny)

    by RealityMogul ( 663835 )
    And mini-M&Ms can be packed even tighter! And ya know what - if you crush them into smaller fragments, you can pack those even tighter!

    Does anybody else feel insulted that this "story" was even posted here?
    • Well mini M&M's would pack only as well as regular (assuming they're the same shape), but I agree... must be a slow news day.

    • Re:Duh! (Score:3, Funny)

      by Valdrax ( 32670 )
      Compared to another article that I tried to get posted yesterday about biological evidence that aggressive people's brains react much more strongly to nicotine than non-aggressive people -- a little.

      I'm guessing Slashdot editors smoke and eat M&Ms all day.
  • and then I'll be impressed.

    perhaps this means we'll soon see more glass stuff, I like the feel of glass over plastic and such. beyond that, it would be cool to see glass replacing other materials. How about a glass computer case, or glass engines.

    • Re:show me transparent M&Ms (Score:5, Funny)

      by Tenfish ( 748408 ) on Friday February 13, 2004 @01:43PM (#8271913)
      I won't be impressed unless I see transparent aluminum M&M's.

    • perhaps this means we'll soon see more glass stuff, I like the feel of glass over plastic and such.

      Glass refers to a noncrystalline, random arrangement at the molecular level. Silicon dioxide glass is generally transparent, but most glasses aren't. I've even seen aluminum glass, but it was in a sealed package. We weren't allowed to open it, apparently access to ambient oxygen would have caused it's surface to start reverting to a crystal state. It wasn't transparent, though. Looked like aluminum.

  • Why this research is in any way interesting (Score:5, Informative)

    by IMSoP ( 659204 ) on Friday February 13, 2004 @12:08PM (#8270659)
    For those too lazy/rushed to RTFA, the key point of this research is this:

    Given a load of spheres, shaking them about won't get them packed as tight as if you stacked them all up neatly by hand. But take a load of squashed spheres (e.g. M&Ms) and shake them about randomly, and they take up much less room, because they naturally find a good formation. Even better if they're asymetrical in another dimension too (e.g. nutty M&Ms).

    Yeah, great. But I suppose it's important to someone to know what shape will find its way into tight formations best.

  • Yes, but.... (Score:3, Funny)

    by FroMan ( 111520 ) on Friday February 13, 2004 @12:15PM (#8270774) Homepage Journal
    Have they figured out if the melt in your hand at all?

    Or where the mutant blue M&M's came from?

    Or why M&M's are now missing their colors?

    Personally, I bet the new blue M&M's stole the colors from the rest of them. They are probably holding the color's hostage. They even put out a out a ransom for them! Luckly atleast the orange color has been found according [mms.com] to authorities.

    [/hat:tinfoil state="off"]

  • Packing density only one contributer to strength (Score:5, Interesting)

    by G4from128k ( 686170 ) on Friday February 13, 2004 @12:36PM (#8271047)
    Denser packing of powders in sintered materials should improve their strength. But I bet the ultimate properties of materials made with ellipsoidal powders will be more complex than predicted from the packing density.

    Granular materials tend to be weakest at the grain interfaces. Such materials tend to fail by breaking the grain-to-grain contacts, rather than shearing through the grains themselves. Thus, the geometry of the contact points will play a big role in the material's strength. I'd bet that ellipsoidal particle aggregates have more contact points because the elongated grains reach across the aggregate to touch more other grains. This should increase strength (materialsmade from ellipsoidal powers will be eve stronger than expected).

    But the story might be even more complicated if large collections of grains have correlated orientations. If all of the grains in a region are oriented in the same way, that region will have highly anisotropic properties (extra weak in some directions and extra strong in other). Parts made with ellisoidal powders may have nonuniform strength in two senses. First, the parts may be weak in some directions, stronger in others(very good or very bad depending on how the design handles strength vis a vis the particle orientations). Second, if the packing orientations vary from part to part (or within macroscopic domains in parts), then the parts may vary in strength across different parts or across batches of parts (bad because inconsistent quality is bad).

    Interesting story, but more research is needed.

  • You might remember me (Score:3, Funny)

    by Anonymous Coward on Friday February 13, 2004 @12:58PM (#8271358)
    Hi. I'm Troy McClure. You might remember me from such candy-packing films as "Don't Break the Pixie Sticks" and "990 Milk Duds per Cubic Metre". I hereby deny that I was ever in "Fudge Packin'"

  • It'f true!! (Score:4, Funny)

    by seanmeister ( 156224 ) on Friday February 13, 2004 @12:59PM (#8271363)
    I ab ferifying thif af I fpeak!
  • M&Ms are also denser because gumballs are hollow.

    I mean, duh.

  • Another piece of worthless info (Score:5, Interesting)

    by Quill_28 ( 553921 ) on Friday February 13, 2004 @01:21PM (#8271671) Journal
    If you have a box filled with big and little spheres the big pieces will rise to the top when shaken.

    Yet if you have a cone with the point down, the big pieces will sink to the bottom.

    For some reason this makes sense in my mind but I am not sure why.
    • This would make an interesting science experiment. Have a link or ref handy? I'm genuinely curious now.
      • Can't take credit for it, I think I read it in
        a Marie von Savant(sp?) newspaper article.

        But i will look around.

        • Thanks. I've been flipping through Google for a few minutes, without any luck. I know some science/math teachers who'd love this sort of thing.
        • I think I read it in a Marie von Savant(sp?) newspaper article.

          I hate to use the term "dumbass," but she comes close. Many (if not most) of her articles range from very misleading to flat-out wrong. Yet people believe the self-proclaimed "world's smartest person."

          Regarding the balls-in-a-box: are the "bigger" balls the same density? It's density that matters, not size--if you put a ping-pong ball and a similarly-sized ball bearing in a box of sand and shake it, the ping-pong ball will "float" and the bal

          • I don't know what article you are refering but large ones should rise to the top. Think of it this way: the small ones fit in the pores between the large ones and can go down while the large ones can't do the same so they stay at the top. The large ones act as a sieve for the small ones. Density probably also matters but I don't know how much. If they have the same density my reasoning works. If the large ones are much denser they might settle down. I think Slashdot mentioned this years ago but am too lazy
          • The large balls floating to the top of a shaken mixture has been the subject of quite a bit of research lately. Since it is one of the rare areas of inquiry where the problem is easily explained, it has been covered a lot in the popular science press.

            Firstly, all the balls are the same density. Also, the large balls are a small fraction of the volume, so it's not a matter of the small balls filling up the cracks. Finally, the large balls stick up a bit after the mix has been shaken for a while, so we ar
            • I'm wondering if it depends of the "average density"?

              Even if all balls are made from the same materials, you could say that on average large balls are less dense than the small one because when there is more free space between the balls..

              I'm curious what would happens if the density of the large balls was increased to compensate for the difference in "average density": what added density should be added so that the large balls sinks or don't move..
              • Larger balls have larger free spaces, fewer of them.

                If the balls are segregated the average density is the same.

                A mixture of large and small balls is denser than either alone, so if density is the controlling factor a few large balls in among small ones should sink to the bottom. Similarly, a few small balls should sink to the bottom of a bunch of large balls.

                So the questions is: Why do a few large balls in mass of small ones actually rise to the top?
          • It's density that matters, not size... ball bearing "shrink."

            No. You can put lead weights in a box of baby power and they will rise to the top if you vibrate it.

            The system is seeking a state of minimal energy, which occurs with the maximum amount of mass (i.e. the densest objects) furthest down in the gravity well.

            You're right that the minimum energy configuration is with the highest density objects at the bottom, but the rest is incorrect. You have to do work to vibrate the system and the system will
  • Stacked neatly, the spheroids still take up 74 percent of the space, just like spheres. But in random arrangements, computer simulations and experiments with M&M's showed that spheroids could be packed much more densely, filling up to 71 percent of the space.

    Umm, 71 percent is less dense than 74 percent. Yay for innumeracy!

    • Neatly stacked, as in a pyramid of oranges at a grocery store, the spheres occupy 74 percent of the available volume. Arranged randomly, however, the spheres fill only 64 percent of the space.

      Umm, 71 percent is more dense than 64 percent. Yay for illiteracy.

      • Re:error in post (Score:1, Informative)

        by Anonymous Coward
        No, in fact. Keep in mind that they are (presumably) using a set quantity of oranges, or m&m's, or whatever. So if the same amount of oranges takes up less space (ie, 64 vs. 74) in a random arrangement, the random arrangement is more densely packed. I thought that was pretty clear, personally.
        • I thought that was pretty clear, personally.

          Seriously. Apparently the jackasses pack pretty densely here on slash.
        • No, that's the percentage of the space of the container that the volume of the items actually occupy when the container is "full," i.e. you can't put any more items in. If you subtract it from 100%, you get the size of the air gaps between the items due to the fact that their shape prevents them from being perfectly packed.

  • configuration space (Score:5, Interesting)

    by epine ( 68316 ) on Friday February 13, 2004 @01:43PM (#8271922)

    Coding theory has many results based on sphere packing, computational chemistry deals with this kind of vast configuration space, and stochasitic algorithms often depend on properties of randomized configuration spaces. In other words, everyone return to their zsh and PHP scripts, nothing to see here but some real computer science.

    To those who remain this result ought to be unsurprising: the non-spherical M&Ms have a larger configuration space, because orientation (and not just position) of the M&M also matters.


  • While the research ended with M&M's, it started with peas. Dr. Paul M. Chaikin, a professor of physics at Princeton, assigned an undergraduate student, Evan A. Variano, to reproduce the work of an 18th-century English clergyman, Stephen Hales, who studied the packing of spheres with peas. Hales soaked the peas, which swelled and deformed, allowing him to see the precise arrangement of each pea with its neighbors.

    The fellow who [has appeared to have] solved the problem of three-dimensional sphere pack

  • Ok, but does the artcile mean random shapes would be more efficient yet? Allowing even more packing into empty space?
    • The most efficient use of the space would be one huge M&M shaped exactly like whatever container it is that you're trying to fill.

      Except it wouldn't really be an M&M then, would it? Just a big ol' lump of chocolate.

      However, the real question we should be asking is:

      If you fill a pint glass to the brim with skittles, how much beer can you fit in the remaining gaps? I guess that, if skittles have a similar random packing density to M&Ms (71%), then that leaves space for only 29% of a pint of

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