Real-world values of spheres?

[Ironeyes he/him]

Soulcasters mess that up too. Bread will cost less when you can make it out of air when necessary. 

[Argent he/him]

I would like to remind you that the title of this topic and the actual idea behind it are a little different - while the title says "real-world values," the topic itself is more about the real size and quality of the gems inside the spheres, not the Roshar-to-Earth conversion ratios. Which, let's be fair, cannot be estimated with any level of accuracy because the two planets have so very little in common.

[Shardlet he/him]

Agree. But bread are the kind of thing that are bound to have less flutuation given the fact that this is one of the most basic human needs.

 

One must earn enough his buy is food at leas.t so of all things that we could compare (Bread, medical supply(Kaladin) and books(Shallan) that is the best one. But even so that is no more than an educate guess, because for sure Roshar bread and our own must cost different =)

 

That is true, but Rosharan bread is not made from wheat which is grown in vast fields, planted and harvested using time and man-power saving machinery, is benefited by advanced fertilizers and has been hybridized to produce high yields, low disease and blighting, pest resistant, and drought resistant.  Further, Rosharan grains are grown within gourd-like plants which protect the grain from storm and harm, and are benefited by crem which may have supernatural growth properties.  It is also noted that the gourds must be cared for manually to prevent infestation by worms.

 

So, even something as seemingly simple as bread does not yield itself to ready comparison.

[Ironeyes he/him]

I would like to remind you that the title of this topic and the actual idea behind it are a little different - while the title says "real-world values," the topic itself is more about the real size and quality of the gems inside the spheres, not the Roshar-to-Earth conversion ratios. Which, let's be fair, cannot be estimated with any level of accuracy because the two planets have so very little in common.

What, you expected us to stay on topic?  

[Shumei he/him]

So, to sum up the discussion thus far:

 

Physical properties of the gems in spheres:

 

We can reliably come up with numbers about the luminance of spheres, but have no real idea of any other property of the gems within the sphere other than relative mass, which can be estimated via comparing luminosity.  The color of the gems is, according to WoB, fixed, but the other properties (mass, clarity, cut) are unknown.  Therefore, we cannot yet compare (or create an authentic-looking movie-prop glass replica) of a Rosharan sphere.

 

I'd like to throw in the "fact" that my thumbnail is 15mm across, so that a sphere based on the size of my thumbnail would be ~16-18mm wide and contain a gem that is (especially when we consider chips) quite tiny, probably 1mm or less in size.

 

Scarcity:

 

Gems on Roshar appear to be rather more common than here on Earth.  They are probably a renewable resource, grown by some kind of organ within many of the crustaciform life on Roshar.

 

Monetary value:

 

A clearchip is worth about one loaf of bread, which due to economic differences, is hard to equate to Earthly money, though it could be estimated to lie within the range of $1.00-$10.00.

 

Any other points to be made besides these?

 

Thanks to everyone for your thoughts on the matter so far.

[ccstat he/him]

Here is a description of an emerald broam from Ch 55 of WoK.

Kaladin rolled the sphere between his fingers. The otherwise pure glass had cooled with a thin line of bubbles permanently frozen along one side. The bubbles were tiny spheres of their own, catching light.
[…] Hanging in the very center of it was a large emerald cut in a round shape, with dozens of tiny facets along the sides. A small rim of suspended bubbles clung to the side of the gemstone, as if longing to be near its brilliance.
Bright, crystalline green Stormlight shone from inside the glass[…]like part of the storm, captured by the emerald. The light wasn’t perfectly steady; it just seemed that way compared with the flickering of candles, torches, or lamps. Holding it close, Kaladin could see the light swirling, raging.

 

There are a few extra details there, but the main point for me is that the gems (at least in broams) are definitely cut and faceted. (When I was finding the quote to post it I thought that there was also something about the size of the gem relative to the sphere, but it doesn't say anything about that.)

 

Edit: Found another quote to add to my earlier luminance post, but the upshot is that a broam is between 3 and 5 times the size of a mark, depending on your use of "several."

Edited January 25, 2014 by ccstat

[Arondell]

Just to throw another wrench into this issue I would point out that the diamond market (real world) is heavily manipulated to maintain the high prices.  Without such manipulation their market value would be far less then it is.

 

http://www.straightdope.com/columns/read/2524/is-a-diamonds-price-a-true-measure-of-its-value

 

Edit : I would think that the general value of gemstones on Roshare would probably be higher since they can be used to make things.  Making them more useful in general then real world gems.

Edited January 25, 2014 by Arondell

[Swimmingly he/him]

[blue]All the pretty shiny baubles[/blue]

[Ironeyes he/him]

<-------- [/blue]

[ccstat he/him]

The recent preview chapters have confirmed that even chips contain cut gems, and that "gemstones are precisely weighed before being encased in glass." The context implies that all chips weigh the same.

So each denomination is a specific karat of gem, and all gems are cut and faceted before being put into spheres. I think we're getting closer.

[FingerstyleFunk he/him]

Weird that this would be where I decide to throw in my first post, but as it happens I've been in the market for a diamond recently so I can throw in some insights on diamond size.

I'm going to use round brilliant cut diamonds as my reference point, just since they're the most common on Earth... though my guess is that Rosharan gems would be cut differently. We like to cut diamonds so they sparkle from reflected light (resulting in one large flat "window" facet on the top, and a bunch of smaller "mirror" ones around the sides/bottom), while their gems have an internal light source. My instinct is that a Rosharan gem would be cut as more of a regular polyhedron, then, and so for a given weight the diameter would be smaller. But anyway...

Based on the thumbnail reference, let's for the sake of round numbers say that a sphere is 15mm diameter. Since broams are the largest gems that we see encased in spheres, they might be close to that diameter... accounting for some space for glass around the sides, a 10mm broam seems a reasonable upper limit. That would put you in the range of 4-5 carats.

So a breakdown of denominations and carat weights might look something like:
Chip - 0.2 carats, ~4mm diameter
Mark - 1.0 carat, ~6.5mm diameter
Broam - 4.0 carat, ~10.5mm diameter

That'd be the upper end of possibility. But I just looked up the apothecary scene where he examines Kal's dun spheres and found this:

 

Kaladin brought out his four marks. He hesitated when he saw them, however. Only one was still glowing with its soft crystal light. The other three were dull, the bits of diamond barely visible at the center of the drops of glass.

[...]

He brought up a jeweler's loupe, removing his spectacles and holding the sphere up to the light.

 

Implies that clearmarks have much smaller gems than I thought above. The diamonds in chips would apparently be practically invisible if they don't have stormlight.

 

That makes it seem more likely that it could go something more like:

Chip - 0.05 carats, ~2.5mm diameter
Mark - 0.25 carat, ~4.1mm diameter
Broam - 1.0 carat, ~6.5mm diameter

 

Very possibly even smaller, though I'd be surprised if they could accurately cut gems much smaller than that, even with magnifying lenses being common enough that a non-jeweler would have a jeweler's loupe. Accurately weighing very small sub-carat diamonds would be a challenge as well.

 

The other factor I'm considering is that Jasnah's "very valuable" soulcasting focal stones are still a reasonable size for her to wear on the back of her hand at all times, sometimes under a glove. Say, something like 10 carats (~15mm),which is still enough, relative to "currency" gems, to be noteworthy (would that qualify as being worth "many spheres each"?), but still small enough for Shallan to afford copies of. But it might suggest that even my revised gem weights are too high.

[Shardlet he/him]

Implies that clearmarks have much smaller gems than I thought above. The diamonds in chips would apparently be practically invisible if they don't have stormlight.

 

Great post Fingerstyle.  Welcome.  I would suggest though that the reason the diamond in the diamond mark was nearly invisible was due to a clear gem being encapsulated in a clear medium.  If you put a loose diamond on a glass of water it is likewise nearly invisible.  However, were the gem to be infused with stormlight, then the diamond would be clearly visible.

[11thorderknight]

Weird that this would be where I decide to throw in my first post, but as it happens I've been in the market for a diamond recently so I can throw in some insights on diamond size.

I'm going to use round brilliant cut diamonds as my reference point, just since they're the most common on Earth... though my guess is that Rosharan gems would be cut differently. We like to cut diamonds so they sparkle from reflected light (resulting in one large flat "window" facet on the top, and a bunch of smaller "mirror" ones around the sides/bottom), while their gems have an internal light source. My instinct is that a Rosharan gem would be cut as more of a regular polyhedron, then, and so for a given weight the diameter would be smaller. But anyway...

Based on the thumbnail reference, let's for the sake of round numbers say that a sphere is 15mm diameter. Since broams are the largest gems that we see encased in spheres, they might be close to that diameter... accounting for some space for glass around the sides, a 10mm broam seems a reasonable upper limit. That would put you in the range of 4-5 carats.

So a breakdown of denominations and carat weights might look something like:

Chip - 0.2 carats, ~4mm diameter

Mark - 1.0 carat, ~6.5mm diameter

Broam - 4.0 carat, ~10.5mm diameter

That'd be the upper end of possibility. But I just looked up the apothecary scene where he examines Kal's dun spheres and found this:

 

Implies that clearmarks have much smaller gems than I thought above. The diamonds in chips would apparently be practically invisible if they don't have stormlight.

 

That makes it seem more likely that it could go something more like:

Chip - 0.05 carats, ~2.5mm diameter

Mark - 0.25 carat, ~4.1mm diameter

Broam - 1.0 carat, ~6.5mm diameter

 

Very possibly even smaller, though I'd be surprised if they could accurately cut gems much smaller than that, even with magnifying lenses being common enough that a non-jeweler would have a jeweler's loupe. Accurately weighing very small sub-carat diamonds would be a challenge as well.

 

The other factor I'm considering is that Jasnah's "very valuable" soulcasting focal stones are still a reasonable size for her to wear on the back of her hand at all times, sometimes under a glove. Say, something like 10 carats (~15mm),which is still enough, relative to "currency" gems, to be noteworthy (would that qualify as being worth "many spheres each"?), but still small enough for Shallan to afford copies of. But it might suggest that even my revised gem weights are too high.

 

Remember that the value of gems increases exponentially, so there's a point where doubling the size of a gem could make it 10 times as valuable

[FingerstyleFunk he/him]

And here I go with another wall of text. Hopefully the reasoning is (semi) worthwhile:

 

Re: Shardlet - I agree that the clear gem in clear medium isn't the best test for size if you're considering visibility, but a quick googling turned up the picture below of diamonds set in wineglass stems. My guess is that the scale is probably similar to what we're looking at with spheres (based on the look and price mentioned, I'd guess they're 1/4-1/2 ct diamonds, which is about where I placed a mark). I can't see naked eye visibility being a problem at that size, suggesting to me that that's probably the upper limit for what you'd expect a clearmark to be.
 
There's potentially the problem of counterfeit diamonds justifying using a loupe, but I doubt they have the technology to make carbon-based diamond analogs, and quartz couldn't survive being set in glass (the melting point is too low). The simple fact of being set in a glass sphere is probably a pretty safe guarantee of being a legitimate gem.
 

 

Remember that the value of gems increases exponentially, so there's a point where doubling the size of a gem could make it 10 times as valuable

 
As to this, overall I agree with your point, but I think that sort of value spike is hit at a much larger size than we'd expect, since we're likely to fall into the trap of comparing too much to Earth economy/ecology. Earth diamonds start hitting noticeable exponential effects around 1 carat because they really do start becoming infinitesimally rare at weights much above that.
 
In comparison, we have no real idea of rarity at various weights in the Rosharan ecology. Gemhearts from greatshells can get up to head-sized, so after apparently hunting most of them worldwide into near-extinction, even very large stones would be significantly less rare. We know from the Parshendi beards that not all gems are nearly that large (though not where they come from...), but it seems like gems even larger than could be found on Earth are within reach for the upper-middle (merchant) class. For example, from the Rysn interlude:
 

The pale yellow gemstone, at least two inches in diameter, was fixed inside a metal framework. [...]
She'd been astonished at what Vstim had paid for the device [...]
"But if it warns us of bandits in the dark, it'll repay its cost a dozen times over"

Granted that "a dozen times over" is probably more figure of speech than accurate valuation, but it's still likely not costly enough to expect that even a gem that size has an exponentially higher cost than an equivalent weight of sphere-weight gems. At least not to the extent that we would expect of Earth gems. More googling shows diamonds of 50-odd carats selling for around $1million/carat (that's about 300x the per-carat price at 1ct), and that's about the size of a thumb joint. The Great Star of Africa is over 500 carats and "priceless", but that looks to be what it takes to get into the 2-4 inch range.

 

Not knowing the monetary relation that heliodor falls into (if it's used for currency at all), even assuming it's only on par with garnet (5x diamond), that sort of weight (if things are linear) would amount to 2-3 years wages for a "common darkeyed soldier." Now, I'll agree that it's probably not linear at this point, but even if your per-carat price goes up by a factor of 5, you're looking at Vstim trading off more than a year's wage for all his guards for this thing, and he's not likely to have that much liquid cash, even as a one of the best traders around

 

Judging from the Rysn WoR reading

His trip to the Reshi sea has him leveraged enough to ruin him if the trade doesn't go through, and that's just to cover his overhead... the actual trade goods are inexpensive.

Compare to Shallan's journey from Jah Keved to Kharbranth over several months, costing (with, admittedly, a steep family discount) significantly less ("several magnitudes!") than 10 emerald broams, whereas the conservative estimates above would put his fabrial gem at
300 carats garnet * 5 (size inflation factor) / 10 emeralds/garnet = 150 emerald broams.
And it's very possible that heliodor is intrinsically worth more than that, even at small sizes... so it seems unlikely that the size inflation factor is even that high, even at MUCH larger than a broam could possibly be.

[ccstat he/him]

Great reasoning, Fingerstyle, and thank you for the size estimates. I particularly like the wineglass photo, at it gave me a good visual of what we're looking for. I agree that those appear to be upper-limit mark sized.

 

I had interpreted the loupe being used to look for counterfeits, but I didn't know that quartz melted too low to be inset. Is that true for all types of molten glass or just the formulation we use today? I know that the process for making glass a few hundred years ago was probably very different than ours now. I'll have to go look up glass blowing etc. now.

 

I definitely follow your logic all the way through, and agree to the valuation ratio limits you arrived at. I would add that the newly developed technology of a proximity-detecting-fabrial is likely to be a huge portion of the cost, as compared to the gemstone "battery" that powers it. The fact that Rysn is surprised by the fabrial's cost suggest that it is much more than she (a trader) would have assumed for the metal and gem it's made from. Using the figures above, that reduces the size inflation factor by whatever the actual-to-expected cost ratio is. That puts it well below 3, in my mind, and probably closer to 2.

 

EDIT: Also, welcome to the forums! Glad to have you here.

Edited January 30, 2014 by ccstat

[FingerstyleFunk he/him]

Thanks for the welcomes, everyone. Been lurking for a while, but I felt the need to do something now that there's no new preview material to wait for.

 

Great reasoning, Fingerstyle, and thank you for the size estimates. I particularly like the wineglass photo, at it gave me a good visual of what we're looking for. I agree that those appear to be upper-limit mark sized.

 

I had interpreted the loupe being used to look for counterfeits, but I didn't know that quartz melted too low to be inset. Is that true for all types of molten glass or just the formulation we use today? I know that the process for making glass a few hundred years ago was probably very different than ours now. I'll have to go look up glass blowing etc. now.

 

I definitely follow your logic all the way through, and agree to the valuation ratio limits you arrived at. I would add that the newly developed technology of a proximity-detecting-fabrial is likely to be a huge portion of the cost, as compared to the gemstone "battery" that powers it. The fact that Rysn is surprised by the fabrial's cost suggest that it is much more than she (a trader) would have assumed for the metal and gem it's made from. Using the figures above, that reduces the size inflation factor by whatever the actual-to-expected cost ratio is. That puts it well below 3, in my mind, and probably closer to 2.

 

EDIT: Also, welcome to the forums! Glad to have you here.

 

Agreed that I totally didn't factor in the additional cost incurred by being part of a large, novel, and apparently complex fabrial. I figured that just helped make my numbers even more conservative.

 

And it looks like my hasty assumption about glassblowing was off a bit. Typical blown glass (soda-lime) apparently softens enough to be worked at about 1000C, and quartz is up around 1700C. I've even found some examples of quartz crystal (though not faceted) set in glass, now that I've looked for that specifically.

 

In fact, considering that Amethyst (a quartz variant, with the same melting point) is a polestone and so is likely used in spheres, it seems even more likely that it would be possible to counterfeit, and the loupe was indeed used for examining the gem more than for just spotting it. Quartz and glass have a very similar refractive index, while diamond's is much higher, so there would definitely be a difference in visibility and light behavior between the two, and use of the loupe suggests that a mark is small enough that this wouldn't be easily apparent to the naked eye. So I think my upper limit still seems pretty reasonable.

 

I guess the issue for realistically figuring a lower limit (beyond what's too small to cut/facet/weigh in the first place) is whether a dun chip could be determined as counterfeit or genuine, or if it really is a small enough gem that the only way to tell would be by trying to infuse it with stormlight and seeing if it takes. It seems economically unfeasible to have a form of currency that could take as much as a week to verify as genuine, but at the same time it probably also doesn't make much sense to counterfeit anything smaller than a mark... I wouldn't be suprised if chips cost nearly as much to produce (what with the glassworking and all) as their actual gem weight value. See, for example, that US pennies and nickels each cost the mint about twice their face value to produce.

 

Someone should maybe ask Brandon if we'll ever get some details about the Federal Reserve Bank of Alethkar?

[Cromptj he/him]

If people can and have counterfeited amethyst or any other gem, people probably already know about it and insist that any amethyst sphere they get is infused.

Gemstones seem to be more common on Roshar anyway so the gem sizes are probably a bit bigger than you might think. Also, judging from Roshar's current technological state, it is easier and probably cheaper to just soulcast the sphere around the gem.

[ccstat he/him]

it is easier and probably cheaper to just soulcast the sphere around the gem

Hmm... In the past I've been dismissive of suggestions that the glass of the spheres is soulcast, partly because of the apparent high cost of soulcasting, and partly because of descriptions of flawed spheres (i.e. with air bubbles in them, which you would expect from inserting a cut gem into molten glass.) I also doubt that in Vorin kingdoms people would be comfortable with the ardentia controlling the currency (since they are the ones with soulcasters). Memories of the Hierocracy are pretty strong.

 

On the other hand, molding clay around a gem and then soulcasting it would be incredibly easy, especially since gems themselves are immune to soulcasting so you wouldn't have to worry about accidentally destroying your wealth. And in a routine process like that, it would be unsurprising to have blemishes like air bubbles introduced occasionally (provided of course that the air doesn't also get transformed). This clay system is much more plausible than the air-to-glass versions I've heard before. It accounts for the flattened bottoms of spheres, and gets around the need to hold the gem somehow while the soulcasting happens.

 

For now I'm going to continue to assume that it is really glassblowers making the spheres. That technology does not seem at all out of place on Roshar, especially since we've seen stained-glass windows, glass bottles, etc.

...not that it matters much for this discussion of gem sizes. Sorry if this sidetracks us.

Back on topic:

I guess the issue for realistically figuring a lower limit (beyond what's too small to cut/facet/weigh in the first place) is whether a dun chip could be determined as counterfeit or genuine

Does anyone know anything about pre-modern gem cutting? I would be curious to learn about the necessary tech/tools and the size limitations. Edited January 30, 2014 by ccstat

[Cheese Ninja he/him]

Clay sounds pretty good.  What about mostly a slushy water/ice blend, that would would let them stick the gem in the middle, then they could Soulcast the water/ice?  That might also account for the air bubbles.

 

The problem with with encasing the gems in molten glass isn't just them shattering or breaking. (Which a brief web search shows to be an overwhelming issue for most people, regardless of the type of gem or glass used.)  Heat treatment can change the color of gemstones in the real world, and I'm not sure how that applies to Roshar.  I'm also not entirely familiar with how heat treatment works in the real world.

[Cromptj he/him]

In the real world, industrial, precision glass production, on the scale that the spheres would need, did not start until the mid 19th century. So I think the soulcasting clay idea would work.

Also, if I lived on Roshar, the Ardentia would be my first pick to be in charge of monetary regulation. They control all the soulcasters so they are ideally placed to manufacture the spheres. They are also not allowed any possessions so there would be very little danger of theft or embezzlement. The apparent cost of soulcasting is mostly, I believe, in the form of a duty set by the monarch so he could remove the duty on soulcasting entirely for making spheres. Also, it would make sense foe the Ardentia to waive their customary fee, if they ask for one, so they could control the money.

Btw, are spheres only used for currency in Vorin countries? Off the top of my head, I can't think of a scene outside a Vorin nation which features spheres as currency. This could be another pointer towards an Ardent controlled currency.

[FingerstyleFunk he/him]

I couldn't find any reference to spheres used outside of Vorin kingdoms in WoK, for example Rysn specifically mentions that the chickens would be "worth good spheres in the East," but (Steelhunt spoiler)

there are a few mentions in the Lift interlude of stealing spheres from the Bronze Palace, in Emul. Lift also mentions that you can get them from slitting pockets at the market, so probably not just a government thing. And no mention of safehands, or indication that any of the women mentioned are covering them.

It seems like spheres are pretty universal across Roshar, aside from possibly Shinovar.

 

I still don't quite buy the soulcast spheres... it seems possible, but the bubbles/imperfections seem more likely to come from actually working hot glass to embed the gems. Also, a lot of soulcast items are specifically called out as having unexpected textures for their materials (stone with wood grain, etc). Heat damage to the stones is definitely possible, though, which is an issue I can't get around, though it's possible (considering the "magical" way the mostly seem to form) that all known gems are of ideal composition and wouldn't degrade or change color.

 

I don't think it's likely that spheres require large-scale, industrial glass production, though. The supply of gems seems like it might not grow particularly fast, unless we start hearing specifically about gem mines anywhere (there are mines, but the products are never specifically mentioned)... but if they only come from greatshells, as seems somewhat likely, there aren't a whole lot of sources producing worldwide. So it would possible for gemcutters/moneychangers to produce spheres themselves.

[Dahak he/him]

Side question, Who they fix the gem in the middle(precisely) of the glass, I always had trouble to imagine how would look like a sphere in real life (if someone have a picture or ilustration plx drop here)

 

Watch

 

http://youtu.be/RU_lCrjfMaw

 

Then think about what happens if instead of adding strips of glass round the edge you press the end down on the gemstone and then add more glass on top.

 

Or it might be the same whay Sulphide marbles were made:

 

 

You might not get a perfectly centred stone and we know you sometimes get bubbles. And it comes with a way of getting a convienient flat side.

 

That's assuming the spheres aren't manufactured by soulcasting.

Edited December 17, 2014 by Dahak

[Oudeis he/him]

That's assuming the spheres aren't manufactured by soulcasting.

 

I had initially assumed they were, but on my last re-read of the Way of Kings Kaladin comments on air bubbles trapped in the glass of a chip. That doesn't sound like something Soulcasting would do.