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Mathematician Theorizes a Crystal As Beautiful As A Diamond
Posted by
Zonk
on Mon Jan 07, 2008 02:41 AM
from the i-prefer-my-stones-blood-free-thanks dept.
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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I'm sure... (Score:2, Insightful)
Re:I'm sure... (Score:5, Insightful)
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.
Parent
Re:I'm sure... (Score:5, Insightful)
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
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Re:I'm sure... (Score:5, Insightful)
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Re:I'm sure... (Score:4, Informative)
That said, I've seen some very, very high quality diamonds (I forget the correct way to refer to it, but it was around 2 carats, no inclusions, and a D - completely colorless. Essentially, diamonds don't come any higher quality). Side by side with a nice piece of moissanite [wikipedia.org], I'd take the moissanite. A quick search on it will find better sources and images that show why, exactly, but I don't want to link to a commercial site and seem biased.
Parent
Re:I'm sure... (Score:4, Insightful)
Thats 3 of the 4 C's, Carat, Clarity, and Color. A bad cut could definately impact the appearance of even a high quality core stone like that, and if the diamond wasn't certified, there's a lot of leeway in what the merchants call color D and no inclusions. (was it truely flawless under a 10x scope (IF or FL) or mearly to the unaided eye? Even w/ a bad cut and "no visible inclusions to the unaided eye, VS2), that would be a $20K stone, $30k if well cut, and was truely "ideal cut" and IF thats an $80k stone discounted.
Man made stones are still having trouble getting past .5 carats when I last checked. Moissanite looks good, but check w/ the one you love before substituting. Its not about the money but about trust, truthfullness, and respecting what she wants. When I spoke to my fiancee about it, and the various trade-offs (she loved that I already knew the trade-offs), we wound up going a non-traditional route that I would never have chosen by myself. I still spent what I budgeted, but the result is both stunning and practical (huge solitaires have lots of impracticalities it turns out); and it now represents not only the promise to marry her but how well we communicate.
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Re: (Score:3, Insightful)
There's a particular kind of sea bird that nests in the SF Bay Area. To find a mate, the male goes into the bay, and brings back the biggest fish it can catch. Females wait on shore for a particularly good offer from a male who can provide a big fish.
That's what diamonds are... just big fish.
Just make them.. (Score:4, Funny)
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Re:I'm sure... (Score:4, Insightful)
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.
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Re:I'm sure... (Score:5, Insightful)
Ha. Actually, you may be interested to know that advertising for diamond rings is actually targeted (albeit surreptitiously) at men. The message is: Women want a diamond ring. You don't need to ask them if they want it. It's such a deep part of our culture and their psyche that they want one. Just buy one.
The reason for this is, the companies who make money out of diamonds did a survey of couples considering marriage, and asked the women if they wanted a diamond ring. A lot of women knew how expensive it was, and replied that they didn't want a diamond ring, and they'd much rather put the money towards a house, furnishings, a car, etc.
This is obviously bad news for the diamond companies, so a few decades ago, the whole 'Diamonds are a girl's best friend' type advertising campaigns started, the whole purpose of which is to stop the man asking the woman if she'd like a diamond. Because quite often, she'd say no.
Parent
Re:I'm sure... (Score:5, Funny)
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 !
Parent
Standard Disclaimer: (Score:5, Funny)
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
Parent
Re: (Score:3, Funny)
Re: (Score:3, Insightful)
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:
Its simply the manifestation an evolutionary mechanism: the handicap principle [wikipedia.org].
Re: (Score:3, Interesting)
Re: (Score:2)
There's a lot of silly property rights nonsense tied to the institution of marriage ingrained in our law structure
These were in place to protect mostly females in a male-dominated and run society and relied on their "provider". Now they appear silly as women are more "free fought", yet they still enjoy the same protection and rights as decades ago put in place to secure their lives. It's called "tradition". It's why there are alot of silly laws. They once made alot of sense, but didn't evolve with the fast evolving society.
In other news... (Score:5, Funny)
Actually, the diamond cartel PR will love it (Score:5, Insightful)
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.
Parent
Re: (Score:3, Funny)
Lisa Simpson: Superliminal?
De Beers Executive opens a window and yells: Hey, you! Buy diamonds!
Re: (Score:3)
As beautiful as a diamond... (Score:2)
Re: (Score:2, Funny)
that's great (Score:5, Funny)
curse you, mathematics!
Re:that's great (Score:4, Funny)
Parent
That's not right (Score:5, Funny)
Re: (Score:3, Insightful)
Re:That's not right (Score:5, Insightful)
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.
Parent
Re: (Score:3, Interesting)
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
Re: (Score:3, Interesting)
Against (Score:3, Insightful)
Yes, you should.
But let's compare:
Demand was inflated through marketing (Score:5, Informative)
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.
Parent
Re: (Score:3, Insightful)
Re: (Score:3, Funny)
Kind of interesting, but.... (Score:4, Insightful)
4 points, in which any two vertices are connected (Score:5, Informative)
"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.
Re:4 points, in which any two vertices are connect (Score:2, Informative)
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*...
Re: (Score:3, Funny)
Re: (Score:3, Informative)
Or something.
What makes you think that glass isn't stable? (link [ucr.edu], link [unl.edu])
I have an archeologist friend who works with Roman glass found along the Silk Road. Looks perfectly stable to me (well, at least those pieces that aren't smashed to bits).
Dimonds arn't wanted for their beuity (Score:5, Insightful)
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.
Re:Dimonds arn't wanted for their beuity (Score:4, Insightful)
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.
Parent
Re: (Score:2)
Re:Dimonds arn't wanted for their beuity (Score:5, Insightful)
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.
Parent
How about a down payment on a house? (Score:3, Insightful)
Article is complete hogwash (Score:5, Informative)
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.
Re:Article is complete hogwash (Score:4, Informative)
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,
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.
Parent
Re:Article is complete hogwash (Score:4, Informative)
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.
Parent
High index of refraction? (Score:2)
What about other single element crystals in A4 ? (Score:5, Informative)
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 thought... (Score:3, Insightful)
Diamond is just a very ordered lattice, and it sounds to me like this mathematician is just out to get his name published.
index of refraction (Score:3, Informative)