Units of Investiture?

[Shumei]

So I got to thinking:  I've read some about certain characters converting their need for magic from Breath to Stormlight.  While we don't yet have a way to measure how the various magic systems interact, or their relative proportions of Investiture, I propose that we standardize the units that Investiture is measured in.

 

Obviously, Breath is the easiest to quantify, as it comes in units of 1 Breath.

 

Stormlight-- while it clearly can be subdivided further, the amount that can be held by one (diamond?) chip seems to be a good unit.

 

Metallic arts-- the amount of Investiture that can be held by a metalmind weighing 1 oz/g/something else? The amount of investiture held in enough Atium to burn for 1 second?  Some thought here would be appreciated.

 

Dor-- I don't have any idea how to measure these magic systems.

 

Any thoughts?

[Anomandaris]

Brandon has stated that there is some sort of set conversion between Breath and Stormlight when asked about a certain character, but he either hadn't actually set the amounts yet or couldn't recall the ratio off the top of his head.

[Kobold King]

I imagine that Allomancy could be measured through ratios--"metal burned:energy produced". While "energy produced" might be problematic to measure (how do you measure Soothing or Rioting?) I think you could get a good idea of energy production by observing a Pewterarm lifting various objects and calculating his limits.

 

Once you've calculated the force produced by burning a metal, you can then experiment with Hemalurgy to find out how much potential force is lost in the spiking process. Feruchemy, by definition, does not produce or reduce Investiture, but figures could be computed concerning "how much" of an attribute could be stored and at what rate.

[Chromium Compounder]

Stormlight-- while it clearly can be subdivided further, the amount that can be held by one (diamond?) chip seems to be a good unit.

 

Actually, that's not a good way to measure Stormlight.  In the beginning of WoR Kaladin and Sigzil talk about it, and I think Lopen suggests the same thing, but Sigzil says it won't work because every sphere has different amounts of stormlight they can hold, depending on the exact size and the quality of the cut of the gem.  

 

And even assuming that all diamond chips got the same amount of stormlight as every other in every storm, and assuming that they all lose stormlight at the same rate (which is also likely not true), you would have to take into account how long its been since the chips were infused.  The day after the storm they're going to have significantly more stormlight than a week later.

 

Quantifying the amount of stormlight in something is pretty much impossible from our point of view.  Perhaps Navani could make a fabrial that could measure that kind of thing, but until that happens, there's no good unit of measurement for stormlight.

 

As you said above, the only good unit of investiture is breath, but even that the book talks about the differences in strength for individual breaths, so they're not all the same.

[PorridgeBrick]

I imagine that Allomancy could be measured through ratios--"metal burned:energy produced". While "energy produced" might be problematic to measure (how do you measure Soothing or Rioting?) I think you could get a good idea of energy production by observing a Pewterarm lifting various objects and calculating his limits.

 

Once you've calculated the force produced by burning a metal, you can then experiment with Hemalurgy to find out how much potential force is lost in the spiking process. Feruchemy, by definition, does not produce or reduce Investiture, but figures could be computed concerning "how much" of an attribute could be stored and at what rate.

 

I think the best way to measure allomancy is through Feruchemical nicrosil. Have each possible Feruchemical nicrosil twinborn measure how much of their metal it takes to fill one metalmind of x mass. From that, you can compare the relative Investiture provided by each metal. Same with the other Feruchemical metals– just convert to a Nicrosilmind. Really, Nicrosilminds are the perfect unit of measure for Investiture Cosmere-wide, since you can store all the powers in it, and it will always be the same. Breaths vary, stormlight fades, the Mists are hard to quantify... but Nicrosil is permanent and exact.

[Argent]

Actually, that's not a good way to measure Stormlight.  In the beginning of WoR Kaladin and Sigzil talk about it, and I think Lopen suggests the same thing, but Sigzil says it won't work because every sphere has different amounts of stormlight they can hold, depending on the exact size and the quality of the cut of the gem.  

 

And even assuming that all diamond chips got the same amount of stormlight as every other in every storm, and assuming that they all lose stormlight at the same rate (which is also likely not true), you would have to take into account how long its been since the chips were infused.  The day after the storm they're going to have significantly more stormlight than a week later.

 

Quantifying the amount of stormlight in something is pretty much impossible from our point of view.  Perhaps Navani could make a fabrial that could measure that kind of thing, but until that happens, there's no good unit of measurement for stormlight.

 

Pretty sure all those things can be defined and quantified. Here's an example (I would be happy to revise if you find it incomplete): a single unit of Stormlight is defined as the amount of Stormlight a single diamond icosahedron* of edge length L holds immediately after being infused by the Stormfather during a highstorm**.

 

 * Icosahderons are 20-sided polygons with (20) sides that are all equilateral triangles - therefore all of their edges are the same length, which we can be used to define the precise shape of the polygon.

 ** This is the moment when Kaladin sees the face in the sky - the absolute calm in the middle of the storm whose passing infuses gemstones.

[PorridgeBrick]

But how do you compare that exactly once it's been a while since the last Highstorm? Besides, you'd have to be pretty industrialized to get enough perfect icosahedrons like that. Nicrosil's just so much more convenient, since the shape doesn't really matter if you can just get a precise enough mass. I guess a normal Rosharan wouldn't have access to that, but it's likely that Worldhopper organizations like the 17th Shard or the Ars Arcanum authors would use Nicrosilminds as a standard measure, unless some other magic system somehow provides an even more perfect universal unit.

[Argent]

I could easily make the same argument against necrosil - measuring one gram (for example) of it is going to depend on the planet you are on, so it would require multiple gravitational constants, not to mention that only Feruchemists can verify its composition. Plus, if you are going for simplicity, you might as well use one Nalthian Breath as the core unit.

 

No, I would much prefer an approach where we quantify each type of Investiture separately, using whatever means make the most sense in the different Shardworlds, and only then trying to figure out conversion formulae between them. 

 

To answer your first question - gems of the same type, shape, and size must decay at an equal rate. Otherwise you have a randomness factor that's literally impossible to account for. So, assuming mathematically predictable decay rate of Investiture trapped inside gemstones, it should be pretty easy to form a few hypotheses (linear decay, cubic decay, luminescence-based decay are three that come to mind right away) and test them. I agree it's not exact science, but I strongly suspect the results will be accurate.

Edited April 7, 2014 by Argent

[Tempus]

Necrosil is for measuring the investiture in Lifeless, right? =]

Anyway, there are a variety of in world ways of identifying investiture - life sense, allomantic bronze, etc. There is no reason to suspect that a sufficient amount of technology and finesse applied to these skills would not be able to quantify investiture at least in a relative sense. I suspect that such a method that exists on Sel would be particularly precise and easy to use, due to the nature of Selish magic.

Edited April 8, 2014 by Tempus

[akasketch]

 

I think the best way to measure allomancy is through Feruchemical nicrosil. Have each possible Feruchemical nicrosil twinborn measure how much of their metal it takes to fill one metalmind of x mass. From that, you can compare the relative Investiture provided by each metal. Same with the other Feruchemical metals– just convert to a Nicrosilmind. Really, Nicrosilminds are the perfect unit of measure for Investiture Cosmere-wide, since you can store all the powers in it, and it will always be the same. Breaths vary, stormlight fades, the Mists are hard to quantify... but Nicrosil is permanent and exact.

 

As most measurements are arbitrary, having a bunch of nicrosil Ferrings run around the Cosmere and compare investiture storage notes would be the best option, as it would provide a universal basis for all investiture conversions. Please note that this would not be a cure-all, completely universal measurement, but a means of relatively accurate conversion between the forms on each world. Each form of Investiture, however, would require it's own separate base unit (i.e., 1 Breath, 1 Diamond Chip at max capacity, etc.).

 

As for converting Nicrosilmind storage into Allomantic power, you would have to set the bar at one second of drainage whilst burning a metal at its lowest "setting," if you will.

 

Converting Nicrosil to Dor would probably require a similar approach, and would most likely require insane amounts of testing (not to mention Hemalurgy) to discover (Using AonDor as an example and base):

1. Which Aon requires the least amount of energy from the Dor?

2. How much extra Dor does each power-increasing modifier draw?

3. How do the other Aons compare to the base Aon?

4. How do the other forms of Dor control compare to the base Aon?

 

I realize that this would not be completely exact, as the qualities of metallic alloys, Breath, and jewel cuts vary, and I assume that one's connection to the Dor would as well, but I feel that this is about as comprehensive and universal that Investiture conversions could get.

[PorridgeBrick]

I could easily make the same argument against necrosil - measuring one gram (for example) of it is going to depend on the planet you are on, so it would require multiple gravitational constants, not to mention that only Feruchemists can verify its composition. Plus, if you are going for simplicity, you might as well use one Nalthian Breath as the core unit.

 

No, I would much prefer an approach where we quantify each type of Investiture separately, using whatever means make the most sense in the different Shardworlds, and only then trying to figure out conversion formulae between them. 

 

To answer your first question - gems of the same type, shape, and size must decay at an equal rate. Otherwise you have a randomness factor that's literally impossible to account for. So, assuming mathematically predictable decay rate of Investiture trapped inside gemstones, it should be pretty easy to form a few hypotheses (linear decay, cubic decay, luminescence-based decay are three that come to mind right away) and test them. I agree it's not exact science, but I strongly suspect the results will be accurate.

Er, that's kinda what balances are for. And while Nalthian Breaths are simple, they're hardly exact– even laymen can tell differences in power between Breaths, and all the Heightenings are approximate.

You certainly could measure each separately– but most of the Shardworlds have Investitures that are difficult to measure (the Dor), are rather inexact (Breaths), or require extensive infrastructure and time to calculate (Stormlight). Nicrosil, however, is pretty easy to use, and a universal measure removes conversion altogether.

@akasketch

You're attempting to measure Dor and Allomancy by powering them with Nicrosil, right? That certainly works, but it's for more time-consuming than necessary. Instead, I'd measure by storing their Investiture into the Nicrosilmind. No calculation necesarry: just store until full.

[WeiryWriter]

I could easily make the same argument against necrosil - measuring one gram (for example) of it is going to depend on the planet you are on, so it would require multiple gravitational constants, not to mention that only Feruchemists can verify its composition. Plus, if you are going for simplicity, you might as well use one Nalthian Breath as the core unit.

 

Actually no, grams would be a perfect measurement because they don't change based on gravitation.  It is a measure for mass not weight, and mass does not change based on gravitational forces.  A kilogram is a kilogram no matter where it is.

 

Anyway, using grams of nicrosil to measure Investiture would actually be a pretty standard measurement.

[Argent]

Eh, right, but the problem remains - you still need to figure out the different gravitational constants, because the likelihood of two Shardworlds coming up with the same gram is practically nil. A Selish gram will be different from a Rosharan one, so you would either need a worldhopper travel from one world to the other and enforce the first world's measuring system (which is not happening), or keep the two independent and convert between them. Which brings us back to the gravitational constants. 

[WeiryWriter]

Eh, right, but the problem remains - you still need to figure out the different gravitational constants, because the likelihood of two Shardworlds coming up with the same gram is practically nil. A Selish gram will be different from a Rosharan one, so you would either need a worldhopper travel from one world to the other and enforce the first world's measuring system (which is not happening), or keep the two independent and convert between them. Which brings us back to the gravitational constants. 

 

Or they come up with a third universal constant, which personally I think they should be doing anyway once any significant inter-world communication starts.

 

Edit: and in reality, mass is determined by comparison anyway so they would actually need to determine the exact constants.  They just need to pick an arbitrary amount of full Feruchemical nicrosil and say "This is one unit of whatever"  That is how the kilogram works on earth, there is a hunk of metal in a Parisian basement that is the definition of a kilogram.

Edited April 8, 2014 by WeiryWriter

[Argent]

But that's because we are a stupid species confined to a single planet. When we find ourselves in a situation where we need to deal with multiple planetary civilizations, we'll most likely redefine what a kilogram means instead of coming up with a conversion factor between Earth kilo and Earth 2.0 kilo. The same way we did with... meter, was it? Didn't the SI definition of a meter get recently updated to read "the distance light travels in X fraction of a second," with second already being defined in terms of the hydrogen atom or something? So a good unit of mass would be the mass of N iron atoms, for example - which would weigh differently on each planet, but that wouldn't matter, because the number of atoms would be the same.

[WeiryWriter]

But that's because we are a stupid species confined to a single planet. When we find ourselves in a situation where we need to deal with multiple planetary civilizations, we'll most likely redefine what a kilogram means instead of coming up with a conversion factor between Earth kilo and Earth 2.0 kilo. The same way we did with... meter, was it? Didn't the SI definition of a meter get recently updated to read "the distance light travels in X fraction of a second," with second already being defined in terms of the hydrogen atom or something? So a good unit of mass would be the mass of N iron atoms, for example - which would weigh differently on each planet, but that wouldn't matter, because the number of atoms would be the same.

 

To my knowledge there are number of people trying to define the kilogram using fundamental constants but that is beside the point.

 

On your point on Earth kilo vs. Earth 2.0 kilo, I'm confused on why there would be an Earth 2.0 kilo?  Why would they come up with a new unit when the original kilo would still work perfectly fine?  What would be the point in creating a new measurement just because they are on a different planet?

[Tempus]

The point he is making, Weiry, is that if Roshar has a gravitational constant of 0.7 or whatever, Sel a gravitational constant of 1.1, and Scadrial 0.9...

 

Then the same WEIGHT of nicrosil provides a different VOLUME of nicrosil. So measuring weight would not be a good method between planets. Measuring volume should be fine, though.

[Argent]

Earth 2.0 was a poorly chosen example on my part. I was thinking of a planet that's had no connection to Earth, so naturally the only thing that came to mind was the most Earth-like name ever...

[WeiryWriter]

The point he is making, Weiry, is that if Roshar has a gravitational constant of 0.7 or whatever, Sel a gravitational constant of 1.1, and Scadrial 0.9...

 

Then the same WEIGHT of nicrosil provides a different VOLUME of nicrosil. So measuring weight would not be a good method between planets. Measuring volume should be fine, though.

 

I understand his point.  The point I'm trying to make is that measuring mass, which is what the kilogram is used for, is what is really  important in this discussion (not weight), and it acts independently of gravity.  (And personally having it determined by mass rather than volume feels more scientific to me?  Since volume is measured by derived units while mass is not?)

 

@Argent, in the case of two planets controlled by two different peoples with two different units for measuring mass, they would just determine the conversion rate between the two.  That is what is easiest/most logical.  With three or more, they should come up with a universal unit, like a lingua franca but for mass.

[name_here]

Uh, mass is in fact universal. You can measure mass in any significant gravitational field with a balance where one side has a known mass. You could even measure it in freefall with a device that applies a known force and measures acceleration, but that would be somewhat more complicated. Weight is the force on a given mass due to gravity, which does vary depending on what planet you're on, but we use mass because it's exactly the same on any planet or in space.

 

The kilogram is presently defined as the mass of a specific hunk of metal, and I don't think there's any particularly convincing reason to change base units. We could define it as a multiple of the mass of a proton, I guess. "Investiture stored in a unit mass of Feruchemical nicrosil" is probably the best Cosmere-wide measure because it's convertable, but Roshar could create a standardized diamond chip for measurement purposes. Breaths aren't actually a very good measurement, because while they can't be broken into smaller portions not all of them are the same size. This is especially obvious with Divine Breaths, but even normal ones vary in strength based on the health of the source.

[RShara]

You can use a balance scale on any planet you want.  That will measure mass for you, independent of the gravitational constant.

 

Put a chunk of item A from planet Xog on one side of the scale.  Put a chunk of item B from planet Gox on the other side of the scale.  When they balance, you gots the same amounts of chunks.

[akasketch]

You can use a balance scale on any planet you want.  That will measure mass for you, independent of the gravitational constant.

 

Put a chunk of item A from planet Xog on one side of the scale.  Put a chunk of item B from planet Gox on the other side of the scale.  When they balance, you gots the same amounts of chunks.

 

Hence why Feruchemical nicrosil is the best option for making unit conversions.

 

Wait, has it been proven whether or not metalminds can be filled completely? If not, that changes the entire discussion.

[RShara]

Yep I was agreeing with ya

[MistLord]

Even breath would need a smaller unit, because despite coming pre-quantified in the amount of breaths, people can have a 'strong' breath or a 'weak' breath - with the grandest example being Divine Breaths.

 

I would definitely measure by volume, however, which may be slightly confusing dealing with different pressures... But what else? Metal's easy, but stormlight is a kind of energetic gas (for the sake of simplification). 

 

We need an Elsecaller on this... 

[RShara]

For Stormlight, use a gemstone of the same cut and carat, preferably from a greatshell, since it wouldn't have any impurities that way.