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Math Science

Mathematician Theorizes a Crystal As Beautiful As A Diamond 302

Posted by Zonk
from the i-prefer-my-stones-blood-free-thanks dept.
Roland Piquepaille writes "Why are diamonds so shiny and beautiful? A Japanese mathematician says it's because of their unique crystal structure and two key properties, called 'maximal symmetry' and 'strong isotropic property.' According to the American Mathematical Society (AMS), he found that out of all the crystals that are possible to construct mathematically, just one shares these two properties with the diamond. So far, his K4 crystal exists only as a mathematical object. And nobody knows if it exists — or if it can be synthesized."
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Mathematician Theorizes a Crystal As Beautiful As A Diamond

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  • I'm sure... (Score:2, Insightful)

    by Deltaspectre (796409)
    that the women won't think it as beautiful as a (natural) diamond!
    • Re:I'm sure... (Score:5, Insightful)

      by ludomancer (921940) on Monday January 07, 2008 @03:52AM (#21939602)
      ... and only because it doesn't cost as much? I hope not, but I could imagine that. It makes me sick how brainwashed some people are in this regard (let alone others).

      Because of all the dirt surrounding the diamond industry, I will never buy one, and when/if I propose to my girlfriend she's getting a ring with any gem other than a diamond. (And not because I'm some cheap-ass.)

      Of course, any woman that doesn't accept you as life-partner because you didn't spend enough money on her engagement item is superficial, materialistic trash anyway.

      • Re:I'm sure... (Score:5, Insightful)

        by dasunt (249686) on Monday January 07, 2008 @04:08AM (#21939694)

        If you did want a diamond, there are non-African diamonds out there.

        For example, there are Canadian diamonds.

        Of course, there are also artificial diamonds, which, if I was getting hitched to a geek girl, I'd consider to be the perfect gift. :D

        • Re:I'm sure... (Score:5, Insightful)

          by The One and Only (691315) * <[ten.hclewlihp] [ta] [lihp]> on Monday January 07, 2008 @09:07AM (#21941092) Homepage
          It doesn't matter where your diamond in particular comes from. If you buy a diamond at all, you're contributing to the high demand for diamonds. It's the same reason that US oil consumption props up the Saudis, even if we buy more oil from Canada than we do from Saudi Arabia.
          • Except that I don't need to buy a diamond every week in order to drive to work.
            • Which makes the purchase of diamonds far less excusable than the purchase of petroleum products. I'm not giving anything near a complete moral accounting of purchasing either product, I'm simply explaining how the economics works.
        • by rssrss (686344)
          "The Breakdown: Synthetic Diamonds [bostonmagazine.com]
          One of these rings gets its sparkle from a foreign diamond mine, the other from a lab in a Boston suburb. Can you spot the engineered ice?" By M. Elizabeth Roman in Boston Magazine for January 2008:

          "Its technology allows Apollo to control the impurities that give a diamond its hue. As a result, the company's ice boasts the same broad color range--clear, pink, blue, yellow, and even black--as the naturally occurring stuff, says Alexandria Matossian of Bostonian Jewelers (cur
      • by RuBLed (995686) on Monday January 07, 2008 @04:13AM (#21939722)
      • Re:I'm sure... (Score:4, Insightful)

        by syousef (465911) on Monday January 07, 2008 @04:18AM (#21939762) Journal
        ... and only because it doesn't cost as much? I hope not, but I could imagine that. It makes me sick how brainwashed some people are in this regard

        Companies have invested a large amount of time and money to do that brainwashing. So much so that it's become part of our culture (as in everyone knows a wedding ring is a diamond ring...even though in reality the "tradition" is quite new). What's worse is that it understanding these things doesn't change the traditions, and will still want the traditional item.
        • by Trogre (513942)
          I assume you meant engagement ring. Wedding rings are usually simple 9ct gold bands, with the occasional variation.

        • by Stooshie (993666)

          ... as in everyone knows a wedding ring is a diamond ring ...

          Erm, isn't a wedding ring a plain band? I think you mean engagement ring. Not that I'm perpetuating the brain washing or anything.

      • by ultranova (717540) on Monday January 07, 2008 @05:35AM (#21940134)

        Because of all the dirt surrounding the diamond industry, I will never buy one, and when/if I propose to my girlfriend she's getting a ring with any gem other than a diamond. (And not because I'm some cheap-ass.)

        Why give a gem ring at all ? Give a simple ring, made of gold, with inscription inside, which comes visible and glows red when heated in fire.

        Yes, buy a wedding ring from Mordor Jewelers, Inc., and you'll never have to worry about your significant other abandonging you ! Guaranteed to be less evil than DeBeers.

        Mordor Jewelers Wedding Ring - because she's your precioussss !

        • by DarthVain (724186) on Monday January 07, 2008 @03:39PM (#21945404)
          Mordor Jewelers is not responsible for ring getting current owner killed, nor will there be any responsibility for alteration of the owner to a gollum like appearance.

          Ring may also bind to other rings in darkness. Also may find other rings and rule over them. Not responsible for types of other rings, nor of the of ruling of the afore mentioned rings.

          Ring is used, and did have prior owner, the "Dark Lord" who of course sits on a "Dark Throne". Mordor Jewelers is in no way associated withe the Dark Lord or his Dark Throne.

          When caring for your ring, it is suggested that you avoid places like Mordor, and melting may occur if dropped into magma in Mt. Doom. Loss of ring in this manner is not the fault of Mordor Jewelers, nor will any reimbursement be merited.

          Mordor is also not at fault if husband starts ignoring you, and you feel like he doesn't even see you anymore. Last but not least, one size fits all.

          Sauron, Saruman, and Smeagol Solicitors

           
      • Re: (Score:3, Insightful)

        by Peaker (72084)

        Of course, any woman that doesn't accept you as life-partner because you didn't spend enough money on her engagement item is superficial, materialistic trash anyway.

        By requiring that the male spend a lot of resources on the gift, the female:

        1. Makes it less likely that this male is wasting his efforts on competing females.
        2. Gets proof that the male has enough resources that its worthwhile for him to spend many of them on her.

        Its simply the manifestation an evolutionary mechanism: the handicap principle [wikipedia.org].

        • Re: (Score:3, Interesting)

          by Kelbear (870538)
          I was enjoying the theory your wiki-link offered up. About half-way through I realized I was engaged in the male geek equivalent of a "How to Trap a Man" article in a women's magazine. Except ours comes complete with graphed functions with optimal utility points.
      • Re: (Score:2, Informative)

        by kryliss (72493)
        If I remember correctly, the opal was the traditional wedding stone before all the "marketing" of the diamond.
  • by ScaryMonkey (886119) on Monday January 07, 2008 @03:45AM (#21939554)
    A Japanese mathematician has been found dead in his laboratory. Police say they suspect the killers to be jewelry-wearing silhouettes.
    • by Moraelin (679338) on Monday January 07, 2008 @06:24AM (#21940378) Journal
      Actually, if this wasn't already part of a PR coup, it will become one very soon. "Scientist proves that diamonds are the prettiest existing crystals" is a great way to remind people to buy diamonds, and give them a good excuse for conspicuous consumption too.

      The part about another crystal which could theoretically be as pretty, only it doesn't exist (and, as another poster noted, can't possibly exist because electrons aren't shared that way, plus it would be opaque) is just that extra bit of "science" to make it easier to swallow. It lets people feel that they've connected the dots themselves to reach your conclusion.

      I mean, "scientist proves that diamonds are the prettiest possible thing in the universe" is a superlative, plus you're feeding people your message a bit heavy handed. Some will resist it. "Scientist proves that only one thing could be prettier, except it doesn't exist in nature" lets people go, "haha, silly scientist, but in the meantime, out of the things one can actually buy, diamonds are the prettiest, right?" Only now it's their own conclusion, and they won't fight it. In fact, they'll feel all smug and smart about it.

      Sad to say, that's how PR works.

      PR isn't marketing. PR is marketing's evil stealthy brother. It loves to masquerade as news, science studies, etc. Marketing plants the seeds, but PR ploughs your mind first.

      Marketing just goes and tells you "Buy Mars chocolate bars, they're great." PR comes and tells you, "Scientists prove that chocolate is good for you! Valuable enzymes found in cocoa beans!" (Except, what they don't tell you, those enzymes are no longer present in chocolate.) That was an actual PR stunt sponsored by Mars.

      Marketing just tells you "The suit is back! Buy Men's Warehouse suits, they look all professional and stuff!" PR goes and tells you "The suit is back! Here's a ton of interviews with managers swearing that they'd never hire someone who doesn't wear a business suit 24/7." That was an actual PR stunt debunked that was linked to even on Slashdot.

      So, anyway, they write some piece of news and then carpet bomb sites and newspapers with it. A lot of newspapers, especially local ones, are even happy to just print whatever PR sends them, because it's written well and it's more interesting than local "raccoon found in Mr Smith's car" stuff. So pretty much any PR agency can get you in those. A really good one can get you on TV and on Reuters. Those tend to be a lot more expensive.

      And faked scientific studies aren't new stuff either. A _lot_ of PR stuff is published as stuff backed by science and (pseudo)maths. The way that goes is, some PR hack writes some pseudo-science babble. It doesn't have to make any sense. It can add different units, or claim that a theoretical crystal is pretty when the electron structure would make it a metal, and thus look like Tin. It doesn't matter. If you can spot that, you're not in their target demographic anyway. Then it starts fishing for people with a Dr or Prof title who'll sign it. A lot say "fuck off", but eventually one has nothing to lose, noone takes him seriously anyway, and he could use the money. He'll take the pie in the face for their money.

      Now I'm not saying that this particular paper is necessarily PR. It could be, but it also could be just someone who wanted to see his name in a journal. But even if it wasn't written as PR for the diamond cartel, that cartel could very easily use it as PR if they need some. Far from sending someone to kill him, they're probably happy right now.
      • Re: (Score:3, Funny)

        by ari_j (90255)
        De Beers Executive: We routinely use three kinds of marketing. Liminal, subliminal, and superliminal.
        Lisa Simpson: Superliminal?
        De Beers Executive opens a window and yells: Hey, you! Buy diamonds!
      • Your rant on PR is dead on. Another side effect of PR is the mistrust of science by the public. My parents refuse to believe in science and medicine and instead mostly opt for "natural" treatments. The reason, they say, is that they're always hearing on the news about how stuff like chocolate is good for you and then a few months later go back to saying it's bad for you. They never look into it further than the 10 'o clock news, so they don't trust scientists.
  • ...too bad it wants to erase all life.
  • by circletimessquare (444983) <circletimessquare@NoSpaM.gmail.com> on Monday January 07, 2008 @03:47AM (#21939570) Homepage Journal
    just as the price of diamonds are threatened by artificial sources, questions about funding evil regimes, and anger at diehard debeers monopolies, promising that men can give women what they want for only $10 someday, this mathematician a**hole comes along with a totally new need-to-have impossible-to-obtain subtance that guys must fork over big bucks for

    curse you, mathematics!
  • by Profane MuthaFucka (574406) <busheatskok@gmail.com> on Monday January 07, 2008 @03:48AM (#21939576) Homepage Journal
    The reason diamonds are so beautiful is that every one of them represents gallons and gallons of blood and broken bones laying in the bottom of a diamond mine. Nothing is quite as shiny as pure human misery.
    • Re: (Score:3, Insightful)

      by ConanG (699649)
      Oh, what a load of crap. Not all diamonds are blood diamonds. Not "every one" of them. And diamonds have always been in demand. Long before the blood diamonds of Africa. It's okay to be against blood diamonds, but don't go around thinking diamond==blood diamond.
      • by catbutt (469582) on Monday January 07, 2008 @04:30AM (#21939820)
        Well duh.

        Even so, if you buy a diamond that is not technically a "blood diamond", you are still supporting the market for diamonds and raising the price of those blood diamonds. And unless you are admiring your "good diamond" in private, you are supporting the culture of diamond-lovers.

        Which is a long winded and less clever way of saying what the parent poster said.
        • Not to mention the pricing of diamonds due to hoarding and artificially low supply. I bought my (now) wife a diamond engagement ring. She knows that's the last diamond she'll ever get from me. Now it's all gold, pearls, and other stones (which suits her fine :-) ).

          At some point someone is going to flood the market with artificial diamonds that cannot be distinguished from real ones and the market will collapse. Here's hoping.
        • Re: (Score:3, Interesting)

          by LWATCDR (28044)
          "Even so, if you buy a diamond that is not technically a "blood diamond", you are still supporting the market for diamonds and raising the price of those blood diamonds. And unless you are admiring your "good diamond" in private, you are supporting the culture of diamond-lovers."

          I just don't see it. Taking the time to make sure that you are not buying a blood diamond will increase the value of the diamonds that are legally produced. Making the effort to buy an Australian or Canadian diamond seems like a wor
      • by aepervius (535155) on Monday January 07, 2008 @05:52AM (#21940222)
        It is well known that before the ad-campaign of mid 20th diamonds were not that much in "demand". Heck, it is well known that before the oversupply of the 19th century diamond were relatively rare. Look at wiki for more detail.

        quote The De Beers diamond advertising campaign is acknowledged as one of the most successful and innovative campaigns in history. N. W. Ayer & Son, the advertising firm retained by De Beers in the mid-20th century, succeeded in reviving the American diamond market and opened up new markets, even in countries where no diamond tradition had existed before. N.W. Ayer's multifaceted marketing campaign included product placement, advertising the diamond itself rather than the De Beers brand, and building associations with celebrities and royalty. This coordinated campaign has lasted decades and continues today; it is perhaps best captured by the slogan "a diamond is forever". End Quote


        Source wiki [wikipedia.org]

        Despite being in over surplus from mid 19th to mid 20th, diamond were not that popular and high in demand.
        in such context "And diamonds have always been in demand." the always is too much. If you change that to mid 20th century onward, you will be right.
        • The only reason diamonds are expensive is because of the cartels which tightly control the supply.

          These people have millions of diamonds stockpiled and only release as many as needed to keep the price high. They could flood the market tomorrow if they wanted to.

        • by ConanG (699649)
          I guess I used the wrong word. I meant desire, not demand. Diamonds have always been "desired". What De Beers was able to do was translate that desire into actual demand and increased sales.

          Before the mid 19th century, diamonds were quite rare and expensive. Very few people could actually afford to have diamonds and there was very little demand for them. People still desired them, they just couldn't afford them. Just like Ferraris. They are very desirable, but there is little demand for them. De Beers cr
        • by user24 (854467)
          you do realise that wiki can by definition be edited by anyone and thus that any citation involving wikies is comparable to saying "some guy at the bar said this...". Right?
      • I agree that at least the crystal structure can't be the sole reason why diamonds are coveted. I should point out that silicon [webelements.com] has the exact same crystal structure as diamond, and no one's killing people over that.
      • They may not be Blood Diamonds(tm), but most of 'em sure are bloody. The vast majority of diamonds come from South Africa and Botswana where the labor record is less than glowing. Sure, it's not Congo, but only precious few diamonds come from places like Canada and Australia where labor standards are at least slightly above appalling.
      • Re: (Score:3, Insightful)

        by chrish (4714)
        Buy Canadian diamonds. Not only are the mines not owned by DeBoers, but we've got labour laws!
        • Re: (Score:3, Funny)

          by Detritus (11846)
          Aye, but have you noticed a decline in the local moose population? It isn't caused by excessive hunting or climate change. The noble Canadian moose is now fodder for the diamond mines of the North. The mine owners discovered that a moose can do the work of a human miner, and isn't subject to labour and safety laws. Thousands of moose are now living a short and miserable existence in Canada's diamond mines. Don't buy moose diamonds!
    • by Greyfox (87712)
      Actually pure human greed comes pretty close. Yes yes yes, we all know the issues associated with diamonds on this site, and I think that most people would shrug it off if they found out the diamond they just purchased had, lets just say, resulted in the deaths of an entire village of Africans. In my view such avarice makes any such gift an ironic one at best, even if both parties involved are unaware that this is the case.
  • by Jugalator (259273) on Monday January 07, 2008 @03:53AM (#21939612) Journal
    The difference with diamonds here is that not only do they have a documented mathematical structure, but they can also already be constructed artificially. But hey, he might just be the guy who takes the second place for... erm... a kind-of-diamond-looking artificial crystal. It would be interesting to know if any other properties than a fancy look could in theory be attributed to this one thanks to its structure.
  • by Animats (122034) on Monday January 07, 2008 @03:56AM (#21939632) Homepage

    "4 points, in which any two vertices are connected by an edge." Isn't that a tetrahedron?

    There are tetrahedral crystals. [mindat.org] The last picture on that page is an unusually nice one.

    The possible crystal forms for an element depend on the bond angles, and I don't think carbon will hold a stable tetrahedral lattice. Not sure, though.

    • by Anonymous Coward
      > I don't think carbon will hold a stable tetrahedral lattice.

      Tetrahedral, good call. What do you get when you put carbon atoms into a tetrahedral lattice? Surprise: diamonds!

      http://www.iit.edu/~felfkri/report_files/image005.jpg [iit.edu]

      This article doesn't even say what this new-fangled structure *is*...
    • If one looks at the K-4 crystal picture, it is composed of objects that have 3 connections. Carbon can't be used, as it likes to form 4 bonds, and the resulting two single and one double bond would deform the symmetry. The Nitrogen family on the periodic table like to form 3 bonds with symmetry. Phosphorus is also in the same column, but it can form up to 5 bonds, and I think would be troublesome to use to form the crystal.
      • The Nitrogen family on the periodic table like to form 3 bonds with symmetry. Phosphorus is also in the same column, but it can form up to 5 bonds, and I think would be troublesome to use to form the crystal.

        But from a symmetry perspective, they also have a lone electron pair which acts somewhat like a bonded atom when forming molecules. Thus, N and P tend to have bond angles that are close to tetrahedral if one imagined that the lone pair were part of the tetrahedron. A perfect tetrahedron has bond ang

  • by Bo'Bob'O (95398) on Monday January 07, 2008 @04:02AM (#21939666)
    The value of diamonds has nothing to do with actual aesthetics. Of course, a dimond with a good cut and clarity is worth more, but it's not what makes people want them for jewelry, it's conspicuous consumption, little more.

    After all, look at the value of often superior synthetics. Or look how people's taste for pearls rapidly decreased as the price decreased.

    Of course, diamonds have plenty of other uses, but there is no shortage of them for that, seeing as DeBeers grinds up diamonds for industrial possess in order to keep the supply artificially low.
    • by Opportunist (166417) on Monday January 07, 2008 @04:13AM (#21939724)
      That's exactly what makes diamonds valuable. A monopoly. And that people think they're rare, and thus precious. I doubt the monopoly holder is going to change that any time soon, else... well, why slaughter the goose that lays the golden eggs?

      You can rest assured that, if some process can be found to actually manufacture that superspecialawesome new crystal, it will be monopolized as well. If nothing else, a patent will do that. Then this crystal will be the new diamond, especially if the manufacturing process involves machinery that you can't simply hide in some clandestine lab (where you could try to circumvent and ignore the patent). The creation process will be described as incredibly expensive and high-tech, we'll get to see shiny jewelry using it, and people will buy into the hype. Just like they do with diamonds.

      Thinking that all those wonderful, incredibly useful, super-hard crystals are dangling pointlessly around some necks makes the geek in me sick.
      • by RuBLed (995686)
        and they would market it in a way that you would look so unthoughtful and unloving when you try to buy for your loved one from the second-hand market...
    • by phoebusQ (539940)
      You seem to misunderstand how these markets play out.

      "Superior" synthetics are not superior in the way that counts: rarity. A very large part of what makes a diamond "special" is its rarity, as well as the time taken and amazing natural processes that occurred to produce it.

      In addition, you have the cause and effect backwards for pearls. Prices dropped as demand decreased/supply increased, not the other way around.

      The diamonds "ground up" for industrial uses are not of the same aesthetic quality that
      • by Nursie (632944)
        "Superior" synthetics are not superior in the way that counts: rarity.

        And if that's the only reason people like them then I just lost a little more faith in humanity.

        The rarity is enforced by DeBeers. They're not all that rare (how can they be, they're at every corner jewellery shop in every town and village in the western world).
    • by Tlosk (761023) on Monday January 07, 2008 @07:56AM (#21940754)
      You seem to be assuming that diamonds are given to convey wealth from one person to another, in which case you would be correct, diamonds don't have a pragmatic worth anywhere close to what you pay for them.

      But it is precisely that quality which makes them useful. In forming trust relationships humans have developed a number of ways to indicate "I'm a person you can trust and spend effort/time/resources on me because I will reciprocate."

      One excellent way to do this is for a person to give something that was personally costly, but has little actual value to the receiver (other than the trust value it conveys).

      So why not just give something with actual value/utility to the person? It would cost the giver the same right? Well as counterintuitive as it seems, it's to protect the giver. If we gave items that had actual value then there would be a high temptation to seek out trust relationships then just keep it and move on to the next person. Now you may be thinking, you can resell diamonds, but as anyone who has tried to unload an engagement ring knows, the only chance you have to resell it for anywhere near the purchase price is to sell it directly to another suitor.

      It's the same thing with flowers I imagine, costly but little utilitarian value.

      And given the differences in the sexes it makes sense that men will have evolved to feel good about giving expensive gifts, and women in receiving them, as a means of establishing a cooperative relationship where you can have some confidence that the other person can be trusted not to take advantage of you.

      So whether it's diamonds, pearls, gold, extravagant chocolates, 8 dollar greeting cards, flowers or what have you, there will always be a use for gifts that are both costly to the giver and of little real worth to the receiver as a way to either establish or maintain trust (which is why women get so incensed if you forget to give a nice anniversary gift, to her it has profound implications for the state and future of your relationship). In other words, it's an artifact of the arms race that is sexual reproduction.
      • by Jugalator (259273)
        So it's a bit like just giving away a Stone of Jordan [gamespy.com] in Diablo II? No way!

        Only if I get at least ten perfect skulls in return!
      • No value to the receiver? How would that be selected for by evolution? You know what most women would actually prefer over a diamond? A down payment on a house. A nice little nest to raise some babies in says, "trust me, I'll provide for you." A sparkly gem that costs as much as a down payment on a house says, "I'm an idiot who will make poor choices about resource allocation without consulting you first." That is why marketing of diamonds is geared towards convincing men tosurprise a woman with a diamond.
  • by Anonymous Coward on Monday January 07, 2008 @04:43AM (#21939886)
    To get things out of the way: Yes, I am structural chemist, I did RTFA and I am not a native english speaker, so please bear with my broken english.

    I don't want to comment so much on the mathematical part of the paper, which might be interesting, but on the chemistry, which is non-sensical.

    First of all the style of the article is very un-scientific. Note how often he mentions how pretty this crystal structure is. This is completely subjective and I don't see how this structure is prettier than many others. There is many fascinating structures and I don't think this or the diamond lattice are the most fascinating ones.

    Then the assumption that the prettyness of diamond is a direct result from the crystal structure is silly. Someone else noticed that Silicium (and also Germanium and Tin) have exactly the same crystal structure - and they are not "pretty".

    He doesn't mention space group nor atomic positions, which are absolutely fundamental when talking about a crystal structure.

    Now even if the crystal would form like he describes (with 1/3rd double bonds), there is just no way this would ever look anything like a diamond. The electronic structure is completely different - diamond is an insulator, a classic dielectric material, whereas this, due to its double bonds and it's extendef pi-electron system, would be a classical conductor. It would probably look like graphite.

    But, and this is the worst point, which even someone who only did very basic (highschool?) chemistry should immediately note, the compound can never form in this way. That's the first thing you learn about double bonds: they're flat or nearly flat. Admittedly, in fullerene and carbon nano-tubes, there is a certain curvation (making them not as stable as graphite), but if you look at this crystal structure, the double bonds have a dihedral angle of about 90 degrees. It's totally impossible to obtain this compound and everybody with scientific education should know this. The molecular orbitals can't form this way.

    All in all I have no idea how it comes that this non-scientific non-sensical article is published by the AMS. Maybe you could make something out of the math part, but all the babble about prettiness and chemistry has to go.
    • by HalfFlat (121672) on Monday January 07, 2008 @06:05AM (#21940306)

      Pretty is being used here not to describe the visual attraction of diamond, but instead to characterise simple but interesting properties of the structure. Quoting Sunada,

      The beauty would be more enhanced and its emotional appeal would be raised to a rational one if we would explore the microscopic structure, say the periodic arrangement of carbon atoms, which is actually responsible for the dazzling glaze caused by the effective refraction and reflection of light.
      Similarly, the crystal structure being discussed is a mathematical abstraction that captures key aspects of physical crystalline structures, while not purporting to be a complete or even entirely faithful representation of crystals in the real world: for example, real-world crystals are obviously not infinite in extent.

      The term pretty, when used in this sort of mathematical context, is not exclusive. Under a different set of criteria, other crystalline structures could well be regarded as being "the prettiest". The properties that Sunada has identified though, are elegant properties from a mathematical viewpoint: they relate the intrinsic symmetries of the structure as a graph with the extrinsic symmetries of the realisation of that graph in a three-dimensional configuration. That the standard realization of a crystal lattice corresponds to a minimal energy configuration (Theorem 1) also demonstrates links to analysis and is an introduction to methods of ab initio calculations of specific heat (see for example the paper of Shubin and Sunada cited in the article.) From considerations of abstract mathematical structure, the diamond crystal is indeed beautiful, and the K4 crystal similarly so.

      That the structure may be chemically impossible to realise with carbon atoms is certainly a valid and useful observation, but to criticise the whole article on the basis of 90 words of chemical speculation really is to misunderstand the article's topic and goals.

      • Well, the problem with the article is not with the mathematical abstraction or playing around with these ideas.

        The problem is not with whether such investigations and their elegant and pretty solutions ever need to have application to reality.

        The problem is that *this* particular article tries very hard to imply that the mathematical abstraction and that the elegant properties of the diamond abstract crystal might somehow explain the real observed properties of the diamond. To be fair, that may not be
        • by HalfFlat (121672) on Monday January 07, 2008 @06:59AM (#21940536)

          I have to disagree, it really doesn't try very hard to explain the observed properties of diamond in terms of its elegant abstract structure.

          There is a single throw away line in the introduction ascribing the refractive properties of diamond to its particular "periodic arrangement of carbon atoms" (which, essentially is true — other arrangements of carbon atoms certainly do not have the same optical properties.) And then the physical properties of diamond are never mentioned again! This is definitely not an article about the physical properties of crystals.

          Yes, the summary is crap — but this is slashdot, after all.

    • by vyrus128 (747164)
      I am not a native english speaker, so please bear with my broken english. Just FYI in case you read the replies to this, your English is flawless. :-)
  • I thought that diamonds were beautiful because they had a high index of refraction? Or was I mistaken?
  • We'll probably find out when this thing is eventually synthesized, at great cost, that it looks greyish brown, opaque, smells of sulphur, has no valuable electronic characteristics and is best used for plugging holes in trees with.
  • The next question is...will this K_4 crystal be as hard as a diamond is, or will it be just a lookalike? From what I could tell from TFA, it seems to be the latter.
  • by MrMr (219533) on Monday January 07, 2008 @05:11AM (#21940038)
    If the symmetry and isotropy give diamonds their shine, why are crystals of
    for instance Si, Ge, Sn not as beautiful? They have the same isotropy and crystal structure.
    And why is a low-symmetry sapphire prettier than high-symmetry table salt?
    I would guess high index of refraction, and the lack of absorption of optical wavelengths are the more relevant properties.

    (see any textbook on crystallography, or for instance http://cst-www.nrl.navy.mil/lattice/ [navy.mil] )
  • I don't know if this crystal will be possible to synthesize or not, but it doesn't matter. The schematic alone will be sufficient to cause a feedback loop that will destroy the entire Borg collective.

  • You know what's funny?  I look at a diamond, and I see a nice shiny thing, but nothing to get excited about.  It's just not that pretty.  I can't imagine spending much money on one.

  • out of all the crystals that are possible to construct mathematically, just one shares these two properties with the diamond. So far, his K4 crystal exists only as a mathematical object. And nobody knows if it exists -- or if it can be synthesized.

    Don't those conditions mean that "K4 == diamond"? Unless diamonds are impossible to "construct mathematically", then if there's only one that shares two of diamond's properties, then that one must be diamond.

    So I can say that it exists, it can be synthesized, but

  • The mathematics only explain why they are shiny; they are "so beautiful" because of a stupendous advertising campaign started in the 50s.
  • But I always believed that a diamond was so "shiny, sparkly, and beautiful" because of it's high refractive index. That's also why moissanite (which is often used a less expensive substitute for diamonds in jewelry) has such a similar "fire".
    • by Stonent1 (594886)
      Moissanite is distinguishable (other than the hardness) by the fact that it has more fire than a diamond. So technically we already have a prettier crystal, but of course don't let her find out that it isn't the real thing!
  • I thought... (Score:3, Insightful)

    by solitas (916005) on Monday January 07, 2008 @09:02AM (#21941072)
    ...that diamonds were "shiny and beautiful" because the cut pattern was optimized for the refractive index of the material and the final shape of the stone - so you'd get the most reflection & refraction - and that other cuts are optimized for the various materials used in fake stones to try to maximize the same effects.

    Diamond is just a very ordered lattice, and it sounds to me like this mathematician is just out to get his name published.
  • Am I the only one who does not understand why diamonds are considered beautiful and desirable? I admit, fancily cut diamonds can be interesting and neat to look at, and I can appreciate the skill required to produce them, but I have never seen one that I have considered beautiful. Perhaps I have simply never seen a decent, beautifully cut diamond.

    I think that gold is beautiful, onyx is beautiful, opals and sapphires are beautiful, but diamonds have no color, and seem industrial and cold to me.
  • by Wormholio (729552) on Monday January 07, 2008 @06:52PM (#21947774)
    While the beauty of gems is subjective, the one reason that diamonds are attractive is the high index of refraction of the material, which causes total internal reflection. Light from sources around the room can bounce around several times before it exits, giving the gem a "sparkle". The cut of the diamond can enhance this. The crystal structure determines which cuts are possible and which cuts give the best sparkle. But creating artificial gems with the same crystal structure will not give the same "sparkle" effect if the crystal does not have a high enough index of refraction to cause total internal reflection.

FORTUNE'S FUN FACTS TO KNOW AND TELL: #44 Zebras are colored with dark stripes on a light background.

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