Stormlight retention as a function of gem size

[Kurkistan]

Just a quick theory that occurred to me as I was considering the economics (or lack thereof) of re-infusing gems.
 
So we know (WoK, Ch 17) that the light from spheres last for about a week: "all you had to do was leave [a dun sphere] out in a highstorm, and it would recharge and give off light for a week or so."

 

We also know that nobles light their homes with spheres and Kharbranth lights literally one of the largest structures on Roshar with the emerald broams from its treasury.

 

This has always struck me the wrong way. A week (a five day week at that!) is not a long time. In fact, it is a short time. The broams in the Palanaeum, then, have to be taken out into a high storm every five days or so. We have gotten a few hints, I think, that there exist fabrials to transfer stormlight between gems, but even then!

 

Because of this, and also because it tickles my fancy, I hereby suggest that gems actually radiate stormlight the same way that black bodies radiate heat: namely, the larger the gem, the longer it radiates stormlight for.

 

This is due to the square-cube law: as the size of an object goes up, its volume increases much faster than its surface area. Because of this, the amount of <thing> it contains will be grow much faster than the rate at which <thing> is lost from the surface.

 

So in the case of gems, larger gemstones, such as broams, contain much more stormlight and radiate it very slowly--at least in proportion to the amount they contain. So you might keep your broams down in the pit for a month or two before needing to recharge them. If this is the case, then the exposition I quoted above is just how long chips can retain stormlight (though it might differ for different types of gems).

 

Assuming uniform radiation for all types of gems, it might actually be fairly easy to do some mathematical hi-jinks using rough estimates of size from the books, and figure out exactly how long each denomination's stormlight will last/how much each denomination holds just after a highstorm.

 

Thoughts/math from people with stronger math-fu than me?

 

Tl;dr: Bigger gems both hold more stormlight than smaller gems and lose it--in proportion to their total capacity--much more slowly than smaller gems do.

Edited June 28, 2013 by Kurkistan

[WeiryWriter]

I dig it.

 

It makes perfect sense to me, so enjoy an upvote.

[Phantom Monstrosity]

I'm going to just say 'hey it's just like hemalurgic spikes where you lose charge stormlight more quickly on smaller spikes gemstones, and nothing can hold charge stormlight perfectly except for atium voidbringers.'

[Kurkistan]

@Writer

 

Thanks, I do like my upvotes.

 

@Phantom

 

Except mine is grounded in PHYSICS, rather than magical hapenstance

Edited June 28, 2013 by Kurkistan

[Shardlet]

It makes me wonder how Lirin was able to keep 'his' diamond broams infused in Hearthstone.  A mob came once to take them directly.  It seems an enterprising person could have slipped out once it was reasonably safe to do so and pilfer one or two while they were out for re-infusion. 

[Kurkistan]

I wouldn't be surprised if he had a money-lender-quality cage for the broams. He was given them in semi-permanent trust to facilitate his work--which work always happened at his home--so it would make sense for Wistiow to pay to install such a cage for Lirin to be able to re-infuse the broams securely and with ease.

Edited June 28, 2013 by Kurkistan

[happyman]

I wouldn't be surprised if he had a money-lender-quality cage for the broams. He was given them in semi-permanent trust to facilitate his work--which work always happened at his home--so it would make sense for Wistiow to pay to install such a cage for Lirin to be able to re-infuse the broams securely and with ease.

 

Except he wasn't actually given them, was he?

[Binnut]

He was given them as a loan to use as illumination, so Wistow needed Lirin to be able to reinfuse them.

[happyman]

He was given them as a loan to use as illumination, so Wistow needed Lirin to be able to reinfuse them.

 

OK.  I'll have to reread WoK.  The flashbacks are the ones that got the least attention, so I'm very rusty there.

[11thorderknight]

I've noticed this contradiction as well. Clearly, spheres do lose stormlight eventually, since Kaladin says so, and since there's socially developed mechanisms for recharging them. However, broams seem to be much bigger than chips, and therefore, would probably hold a charge for months. Larger gems like what Jasnah uses for Soulcasting would hold a charge almost indefinitely.

[Windrunner]

The book mentions them being dun at least once

[DocHoliday]

The book mentions them being dun at least once

Can you be specific as to which gems? The surgeons spheres are never mentioned as being dun (I believe).

Jasnah has gems run out but only during Soul-casting. Which makes sense since Surge Binding uses the Stormlight

[Windrunner]

During the Weeping, so broams probably don't last for months.

“Father spent another of the spheres, Tien,” Kaladin found himself saying. Each time their father was forced to do that, he seemed to grow a little more wan, stand a little less tall. Those spheres were dun these days, no light in them. You couldn’t infuse spheres during the Weeping. They all ran out, eventually.

[Kurkistan]

Okay, Weepings.

They last for four weeks (20 days), apparently, with one highstorm thrown in the middle for fun. That's a tad irritating.

Given the highstorm in the middle, the Kaladin quote might not be 100% reliable, though. You can reinfuse gemstones in the middle of a Weeping, so you should only have two weeks total of non-glowy gems, at worst--one in the week before the highstorm and one in the last week of the Weeping.

 

EDIT 2: Though it could be a weird no-stormlight storm, which would allow for even broams to go dun, under my model.

I'm very strongly inclined to find a way to do away with this evidence, in fact. I hope not to have to resort to discontinuity, but I will if I have to. Five days is such a very short time .

So the options I currently see are as follows:

a) The broams last for weeks at a time, but Kaladin's family last reinfused them at some awkward time such that they ran out after the weeping stopped. The text heavily implies that this is not the case--implying instead that the Weeping is a necessary cause of the gems being dun (if only through denying them necessary reinfusement), rather than simply an incidental reason dependent upon other factors.

b.) This is a woopsie on Brandon's part: he didn't account for broams being broams and applied his "about a week" measure for chips accidentally. Annoying, continuity wise, but forgiveable if we get back on track for the rest of the series.

I'm rather dispairing at 'b' being true, if only because I can definitely see plot points where surgebinders can't get any stormlight during a Weeping or some such. You could still have those if stormlight was simply rare and fleeting--only available in large denominations of gemstones--but it wouldn't be quite the same.

---

I still really hope that my theory holds because a ~5 day limit is just so very fidly. If we want gemstones to be "magical batteries" with magitech and gem light-bulbs and stuff, we incur a massive cost if they have to be taken out of their delicate and/or hard to reach and/or necessary locations every week to be exposed to a super-hurricane. And also because I like being right.

----

As an aside, I've done some napkin-math on SA:V, though I'm unsure as to how it applies to black-body radiation. Here's some numbers, if we'll accept some assumptions:

Okay, so 1 diamond broam is worth 20 diamond chips. If we assume that they're proportional, then 1 diamond broam has 20 times the mass/volume of a chip. Similar proportions hold for the other gem types. We'll also assume equal "stormlight density" for different gemstones and that the different denominations are all the same size for all gem types.

So 1 broam has 20 times the volume of a chip. Using some handy dandy wikipedia, we can find proportions of volue to surface area for various shapes.

I just did some unnecessarily complicated mathematical thingamabobs to compare the retention rates of different shapes of gemstones when they're volume is multiplied by 20, only to "discover" that the shape doesn't matter if you're only messing with pure volumes, instead of lengths. So long as the shape stays the same when you scale up/down, you're all good. Things do get more complicated if broams are cut with more/less sides than chips, though, and I have not gotten into that as of yet.

Therefore, we find that multiplying the volume of a gem by 20 gives us ~2.7144 times more stormlight in proportion to surface area. If we take a chip as lasting for 6 days--just for the sake of roundness--that gives us ~16.3 days for a broam. 5 gives us ~13.6 and 7 gives us ~19.0.

I suppose that isn't too bad, actually, and might give us some small amount of leeway on the Weeping passage. Particularly if, for some reason, the highstorm in the middle doesn't provide stormlight. At the very least, it is by far more reasonable to reinfuse a gemstone once every 15 days than once every 5.

 

EDIT: Also, I am by no means knowledgeable as to the actual math behind black body radiation, so it likely isn't a straight comparison of volume and surface area. I do believe these are the right numbers if everything is in simple terms, though.

Edited July 10, 2013 by Kurkistan

[Crysanja]

maybe you should search for the composition of the different gem typs which store stormlight.

 

because crystals are actualy compressed salt. -> the question would be then, why are some salt grids holding stormlight and some not.

 

i dont remember if diamonds hold stormlight too, thouse are actualy very different to other gems.

 

 

is the stormlight stored in the grids of the crystals? or in the ionic bounds? or even the atoms itselfe.

if you would grind a gem to powder would it loose its ability to store stormlight?

 

stormlight seems not to be effected by the salt grid of glass -> so is the salt grid of a crystal(gem) blocking stormlight?

[Kurkistan]

I'm unsure where you're getting this talk of salt from. Diamonds aren't salt, amethysts aren't salt, rubies aren't salt. . .

 

The composition of the different gems apparently just serve as a "key" to the magic system, so I'd imagine that the "how" of it is less mechanistic and more similar to how metals are the "focus" on Scadrial: it is just in the nature of Roshar that gemstones of certain types are attuned to and hold stormlight.

Edited July 10, 2013 by Kurkistan

[Crysanja]

i might be wrong in translation, but the grids the atoms form, os thouse gems are called salt grids. =)

[Morsk]

i might be wrong in translation, but the grids the atoms form, os thouse gems are called salt grids. =)

It has to be translation. I think you mean "crystal lattice" instead of "salt grid", but I'm guessing. I don't know much chemistry. Edited July 11, 2013 by Morsk

[happyman]

It has to be translation. I think you mean "crystal lattice" instead of "salt grid", but I'm guessing. I don't know much chemistry.

 

My chemistry is rusty, but this seems right.  A crystal lattice is the grid the atoms of a crystal are in.  Salts (the generic term, not specifically referring to Sodium Chloride) often form a crystal in solid shape, but technically, salt is a chemical which doesn't have to be in a lattice (they can be melted or dissolved, for instance).

In other words, it is logically possible to have crystals which are not salts and salts which do not form crystals.

[Isomere]

Salt grid does accurately describe many crystal lattices. "Salt" is just another word for ion: an atom that has lost or gained an electron and now has a positive or negative charge. If these ions are arranged in an alternating lattice they create a crystal held together by the magnetic charges.

Emerald and heliodor are both made of beryllium and aluminum salts. Be²⁺, Al³⁺, and Si0₃^2- which means the Beryllium atom has lost two electrons, the Aluminum atom has lost three electrons and the silicate molecule stole 2 electrons. They naturally form crystals with zero net charge, in this case grouping Be₃Al₂(SiO₃)₆. Diamonds in contrast are held together by covalent carbon bonds and are much stronger.

EDIT: So i was wrong about the definition of salt. The ions must be producible in an acid base reaction and must form a solid compound to be salt.

Edited July 11, 2013 by Isomere

[WeiryWriter]

Umm... "Salt" isn't another term for ion, salts are ionic compounds (which is what I think you were going for).  Specifically salts are ionic compounds of an Alkali metal and a Halogen (groups 1 and 7 on the periodic table).  That said "salt grid" isn't a term that is used in chemistry so i would refrain from using it here.  It is also important to note that even though Emerald and Heliodor contain ions (which is something I don't remember but I don't really have time right now to check that so I'm taking your word for it)  they themselves are not salts (I know Isomere didn't say this, but I just want to make sure no one misinterprets her post).

 

I hadn't really given any thought to the mechanics of how gems actually store stormlight.  I could see the crystal lattice being a part of it but I do think there's some funky realmatic stuff going on so I don't think we could come to a satisfactory decision at the moment.  This is probably worth a question to Brandon though.

[Shardlet]

I'm afraid that that is not accurate isomere.  A salt is an ionic compound which results from a neutralization reaction between an acid and a base.  So, while an oxide is an ionic compound, it is not a salt.  Thus several stormlight gemstones, such as amethyst (SiO₂), are not salts.  And, as an irrelevant side note, your beryllium aluminosilicate example is stable at room temperature whereas diamond is not.  Diamond appears stable because the kinetics of the allotropic transformation are so slow.  (Diamond is however very stable against chemical attack).

 

Edit:  While you are closer Weiry, salt is much broader than groups 1 and 7 ionic compounds.  For example Fe₂(SO₄)₃ (ferric sulfate) is a salt.

 

Edit2: corrected my terrible error (in the context of my post) of saying that it was a salt/base rex'n rather than acid/base rex'n <forehead slap>.

Edited July 11, 2013 by Shardlet

[Isomere]

I stand corrected. I'll edit the post. 

[WeiryWriter]

Edit:  While you are closer Weiry, salt is much broader than groups 1 and 7 ionic compounds.  For example Fe₂(SO₄)₃ (ferric sulfate) is a salt.

 

Yah, I misremembered.  The technical definition is "compounds which result from the neutralization of an acid/base reaction."

[Isomere]

So, while an oxide is an ionic compound, it is not a salt.

 

An oxide reaction is by definition an acid-base reaction. Acids steal electrons, and bases lose electrons, so any time a metal forms an oxide it is acting as a base. If it then forms a precipitate that would be a salt. If it forms a solution it would be an electrolyte. 

 

I previously said that salt is another word for ion. That is like saying a rectangle is another word for square, only true if the rectangle has equal sides. An Ion is only salt if it has precipitated.

 

Salt doesn't have to precipitate with the original acid/base pair, any electrically neutral precipitate of ionic compounds is called a salt. For example, if you have lithium bromide and silver nitrate salts and mix them together in water, the ions can switch partners. Silver bromide (AgBr) is still a salt even though it didn't have an acid base reaction together. 

Li⁺ (aq) +  Br^- (aq)  + Ag⁺ (aq) +  NO₃^- (aq) Li⁺ (aq)  +  NO₃^- (aq)  +  AgBr (s)

 

I was extrapolating that principle to call Beryl a salt of beryllium, aluminum and silicate. I still believe this is true, but I am not certain.