Ferchemical Storage - Linear, Quadratic, other?

[Duxredux he/him]

Not quite sure why I've been more or less cool with F-Steel for the last decade only to wake up look at it and no longer have it make sense to me. Well, there you go. At the core, I'm wondering if we're skipping some crucial steps when we try to calculate Feruchemical storage and tap utilization. I suspect this realization subconsciously came from a YouTube video about how we're bad at teaching rates and averages, but let me talk it out.

Feruchemy is the power to convert an attribute such as heat, weight, calories, physical mass, or speed into Investiture, store it in a metal, and then at a later date withdraw the Investiture and convert it back into the original attribute - boosting the practictioner beyond the norm. Feruchemists can store discrete blocks of power in the form of memories, but they seem to measure it in a percentage of a whole - like Wax walking around at 30% weight.

Here's where I think we're starting to cut corners - we talk about percentage weight stored and then tapped, but I think it would be better practice to view it as total Investiture stored and then utilized to produce an effect. In the Cosmere, energy, matter, and Investiture follow the laws of thermodynamics - none of the three are created or permanently destroyed, they simple change from one form into the other. In other words, we can broadly assume that we can plug Investiture into the energy requirements needed for physics equations. Here's the thing, some attributes may follow what appears to follow a straight linear relationship. Memory is stored at a 1:1 ratio and weight seems to be fairly easy for Wax to recoup.  An Allomantic example of this is how gram for gram, different metals have varying burn rates with Copper and Tin being some of the slowest burners and Pewter, Iron, and Steel the fastest burning metals. This utilization rate is determined by the work being done by the Investiture. Sensory enhancement requires much lower energy costs than launching yourself through the sky via Steelpushes. I assume that this is how Feruchemy works as well, you spend time siphoning off mass, energy, or Investiture of one form or another, storing it for a time, and when tapping the effect you get is based on the work the Investiture is required to do.

This becomes a problem for an attribute like speed - the energy requirements are not linear, they are quadratic. If running at 5 kph, your kinetic energy isn't doubled when running at 10 kph, it quadruples. What complicates it more is that if you run at half speed, 2.5 kph, it follows that same quadratic relationship (I assume) so you are not exerting anywhere close to the full energy you would use at full speed. It also wouldn't surprise me if speed storage was actually related to the extent the muscles were in motion during storage - or in other words, perhaps you could get more attribute if storing while running a marathon and siphoning off the energy used to power those muscles in contrast to sitting on the couch and watching television with only unconscious muscles used for systems like digestion or respiration slowed down. In essence, in Feruchemy the power needs to come from somewhere, even if it's just storing heat while sitting next to a fire. That said... it doesn't look like storing strength requires you to have been doing anything with those muscles, nor do I see Sazed eating the same diet a body builder would need to use gigantic muscles without tiring out. Maybe Investiture is divided between huge muscles and the equivalent caloric needs. 

I'll ask the more physics minded Sharders like @DrPhysics or @therunner if this matches the energy requirements they would expect as well as if there are any other storages that shouldn't be calculated linearly. Thoughts?

[Treamayne]

30 minutes ago, Duxredux said:

It also wouldn't surprise me if speed storage was actually related to the extent the muscles were in motion during storage - or in other words, perhaps you could get more attribute if storing while running a marathon and siphoning off the energy used to power those muscles in contrast to sitting on the couch and watching television

This does not seem to match the scene shown with Sazed:
 

Spoiler

WoA Ch 50:

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That made him feel even more guilty to be sitting in the kitchen nook, beside a warm hearth, sipping broth as his metalminds sapped his strength, health, senses, and power of thought. He had rarely tried to fill so many at once.

“You don’t look so good,” Clubs noted, sitting.

Sazed blinked, thinking through the comment. “My…goldmind,” he said slowly. “It draws my health, storing it up.” He glanced at his bowl of broth. “I must eat to maintain my strength,” he said, mentally preparing himself to take a sip.

It was an odd process. His thoughts moved so slowly that it took him a moment to decide to eat. Then his body reacted slowly, the arm taking a few seconds to move. Even then, the muscles quivered, their strength sapped away and stored in his pewtermind. Finally, he was able to get a spoonful to his lips and take a quiet sip. It tasted bland; he was filling scent as well, and without it, his sense of taste was severely hampered.

HoA Ch 78:

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He eyed the metal grate. The lock was of fine steel, the grate itself of iron. He reached up tentatively, touching the bars, draining a bit of his weight and putting it into the iron. Immediately, his body grew lighter. In Feruchemy, iron stored physical weight, and the grate was pure enough to hold a Feruchemical charge. It went against his instincts to use the grate as a metalmind—it wasn’t portable, and if he had to flee, he’d leave behind all of the power he’d saved. Yet, what good would it be to simply sit in the pit and wait?

He reached up with the other hand, touching the steel lock with one finger. Then, he began to fill it as well, draining his body of speed. He instantly began to feel lethargic, as if his every motion—even his breathing—was more difficult. It was like he had to push through some thick substance each time he moved.

He stayed that way. He had learned to enter a kind of meditative trance when he filled metalminds.

It would seem that storing Pewter affects how much force a muscle can apply (straining to lift a spoon), and storing speed affects how quickly a muscle can contract/extend (lethargy in movement). I feel like storing speed would make you incapable of running anything, much less a marathon. 

Hope that helps

[therunner he/him]

44 minutes ago, Duxredux said:

Not quite sure why I've been more or less cool with F-Steel for the last decade only to wake up look at it and no longer have it make sense to me. Well, there you go. At the core, I'm wondering if we're skipping some crucial steps when we try to calculate Feruchemical storage and tap utilization. I suspect this realization subconsciously came from a YouTube video about how we're bad at teaching rates and averages, but let me talk it out.

Feruchemy is the power to convert an attribute such as heat, weight, calories, physical mass, or speed into Investiture, store it in a metal, and then at a later date withdraw the Investiture and convert it back into the original attribute - boosting the practictioner beyond the norm. Feruchemists can store discrete blocks of power in the form of memories, but they seem to measure it in a percentage of a whole - like Wax walking around at 30% weight.

 

You can think of it (for non-memories) as siphoning of certain amount of Investiture that realizes a given attribute. I.e. your spiritweb says you are supposed to be XX heavy, but you siphon off part of that Investiture in PR into your metalmind. Similar for speed, you should move at X m/s, but you siphon part of that into your metal mind.

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Here's where I think we're starting to cut corners - we talk about percentage weight stored and then tapped, but I think it would be better practice to view it as total Investiture stored and then utilized to produce an effect. In the Cosmere, energy, matter, and Investiture follow the laws of thermodynamics - none of the three are created or permanently destroyed, they simple change from one form into the other. In other words, we can broadly assume that we can plug Investiture into the energy requirements needed for physics equations. Here's the thing, some attributes may follow what appears to follow a straight linear relationship. Memory is stored at a 1:1 ratio and weight seems to be fairly easy for Wax to recoup.

I agree that considering total amount of Investiture stored could make sense, however per one old WoB, you get loss relative to what you stored.
So if you stored e.g. 10kg for 1 hour, you can tap 10 kg for 1 hour, but 20 kg only for 25 minutes. This implies that not just quantite of stored attribute, but also quality (in the sense of which percentage what stored) matters when tapping.

It is possible this will no longer hold, and the losses for tapping will be simply for going above e.g. 2x of your attribute.

Even Wax follows this, he wastes year of weight stored in seconds, which would be tapping millions of tons (1 kg/s stored for a year amounts to ~31,5 million kg/s to be tapped. Clearly, this is not supported by those scenes, hence there must be a loss involved.

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This becomes a problem for an attribute like speed - the energy requirements are not linear, they are quadratic. If running at 5 kph, your kinetic energy isn't doubled when running at 10 kph, it quadruples. What complicates it more is that if you run at half speed, 2.5 kph, it follows that same quadratic relationship (I assume) so you are not exerting anywhere close to the full energy you would use at full speed.

Energy is quadratic in velocity only in newtonian regime, more precise (i.e. special relativistic) accounting will show you that energy is linearly related to momentum.

In that way, it would make more sense for F-steel to store momentum, and not speed (that way it would also have more interesting relationship with F-Iron).

However, if you keep in mind that there is a certain loss when tapping a lot of attribute (exponential in fact), then this quadratic loss due to energy requirements could be hidden in that.

[DrPhysics he/him]

There have been some great answers already. Here's my small contribution:

1 hour ago, Duxredux said:

we can broadly assume that we can plug Investiture into the energy requirements needed for physics equations.

Yes, we can plug Investiture into the energy requirements, but that doesn't mean that all of the investiture needed to accomplish feruchemy is stored in the metal mind. If it were, the weight that Wax loses would increase the weight of the metalmind by the same amount, then add in extra weight to account for whatever investiture is needed to maintain an increased weight for a while. 

 

Instead, I like to think of it as a relay, a device which uses a little bit of current to open a switch that allows a lot of current to flow through a circuit. A feruchemist stores enough investiture to essentially open the gate to the spiritual realm and allow out the investiture needed to accomplish the feat. 

So when you say:

2 hours ago, Duxredux said:

we talk about percentage weight stored and then tapped, but I think it would be better practice to view it as total Investiture stored and then utilized to produce an effect.

that idea doesn't work. They aren't storing all the investiture needed, they are storing enough to access what they need.

[Treamayne]

2 hours ago, therunner said:

In that way, it would make more sense for F-steel to store momentum, and not speed (that way it would also have more interesting relationship with F-Iron).

However, if you keep in mind that there is a certain loss when tapping a lot of attribute (exponential in fact), then this quadratic loss due to energy requirements could be hidden in that.

Please keep in mind that Feruchemy is a result of the interactions between both Ruin and Preservation with the planet and the way they created the population. 

We still do not have a definitive answer, but the implication is that Preservation's Intent is expressed by preserving one of your attributes for later use. Ruin's Intent is expressed by the loss of Investiture when Compressing an attribute being tapped. 

Spoiler

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Questioner

Allomancy is of Preservation, correct?

Brandon Sanderson

Yes...

Questioner

What are Feruchemy and Hemalurgy of?

Brandon Sanderson

Hemalurgy is definitely of Ruin.

Questioner

Is it of pure Ruin?

Brandon Sanderson

Yes. That's a very Ruin thing. And Feruchemy is more of a blend. Though… there is more philosophy to that and human construct—like the Allomantic table—than I think I’ve made clear before.

Shadows of Self Chicago signing (Oct. 12, 2015)

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Questioner

With Allomancy is of Preservation, and you have Hemalurgy, which is of Ruin. Is Feruchemy a joint effort between the two? Or is it a third party?

Brandon Sanderson

Joint effort.

FanX 2018 (Sept. 8, 2018)

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Sporkify

This is more towards the whole physics stuff, but is Feruchemy really balanced? If it gives diminishing returns, wouldn't this end up as a net loss of power?

Brandon Sanderson

It doesn't diminish. Or, well, it does—but only if you compound it. You get 1 for 1 back, but compounding the power requires an expenditure of the power itself. For instance, if you are weak for one hour, you can gain the lost strength for one hour. But that's not really that much strength. After all, you probably weren't as weak as zero people during that time. So if you want to be as strong as two men, you couldn't do it for a full hour. You'd have to spend some energy to compound, then spend the compounded energy itself.

In more mathematical terms, let's say you spend one hour at 50% strength. You could then spend one hour at 150% strength, or perhaps 25 min at 200% strength, or maybe 10min at 250% strength. Each increment is harder, and therefore 'strains' you more and burns your energy more quickly. And since most Feruchemists don't store at 50% strength, but instead at something like 80% strength (it feels like much more when they do it, but you can't really push the body to that much forced weakness without risking death) you can burn through a few day's strength in a very short time if you aren't careful.

Footnote: This question was asked when fueling Feruchemy with Allomancy had only been seen in Rashek. As such, the term compounding is used purely to reference tapping at a higher rate than can be stored.
Hero of Ages Q&A - Time Waster's Guide (Oct. 15, 2008)

Note: This WoB was before he chose Componding to be the term for Allomantically burning a Feruchemical Storage, and Compression to be the term for tapping attributes at a greater rate than they were stored. 

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Brandon Sanderson (paraphrased)

Feruchemy is about multipliers. The more the Lord Ruler aged, the less "multiplier" he could store in his metalmind. And the more he aged the more he would need to Compound to stay alive. There could exist an upper bound to the amount of time the Lord Ruler could survive off this trick.

Alloy of Law 17th Shard Q&A (Nov. 5, 2011)

Quote

Questioner (paraphrased)

How does compounding work in Mistborn?

Brandon Sanderson (paraphrased)

I can explain this better in person because I know things that the characters in the book don’t. So, they haven’t worked a lot of this out. All the magic systems in my work are linked because the books all take place in the same universe. In Elantris, magic works by drawing symbols in the air. What actually happens is that when they draw a symbol, energy passes through it from another place (which is my get-out for the laws of thermodynamics) and the effect of that energy is moderated by the symbol. In one case it may become light, in another it may become fire. In Mistborn, the metals have a similar effect. The magic is not coming from the metal (even if some characters think it is). It is being drawn from the same place and moderated by the metal.

In the case of Feruchemy, no energy is being drawn from this other place. So, you spend a week sick and store up the ability to heal. It’s a balanced system, basically obeying the laws of thermodynamics. So, while it’s not real, it’s still rational.

In compounding, when you have the power of both Allomancy and Feruchemy, you draw power from the other place through the metal and it recognizes the power that is already stored—"Oh, this is healing, I know how to do that”—and so you get the power of Feruchemy but boosted by energy from the other place. This is how the Lord Ruler achieved immortality.

Alloy of Law Milton Keynes signing (Nov. 21, 2011)

 

 

1 hour ago, DrPhysics said:

Instead, I like to think of it as a relay, a device which uses a little bit of current to open a switch that allows a lot of current to flow through a circuit. A feruchemist stores enough investiture to essentially open the gate to the spiritual realm and allow out the investiture needed to accomplish the feat. 

Since no external power is being used in Feruchemy (not including Compounding) I think it is more likely the Investiture storage is being attached to the object's Spiritweb when storing and being drawn from the object's spiritweb when tapping. It would fit with these WoBs:

Spoiler

Quote

Questioner

If a coppermind was to be split in half, would the contents of it be destroyed? Or would there be, in the two separate halves, <of different contents?>?

Brandon Sanderson

You should err on the side of being destroyed, though not permanently, is what I would say on that. There are ways to approach it that wouldn't, but generally if you're ruining a metalmind, the Investiture will stay in it, and if you know what you're doing you can make use of that, but in most cases, it's not gonna fare well.

DragonCon 2019 (Aug. 29, 2019)

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Questioner

So, about Feruchemy. If someone takes, for example, a copper metalmind, fills it with memories, and then a tin metalmind, fills it with senses, then melts them together into a bronze metalmind, would you be able to tap anything from it, and what?

Brandon Sanderson

If you made an alloy of them, you would not get anything out of them. You would know there's Investiture in there, but you wouldn't be able to pull it out. 

Questioner

Even if it's your own?

Brandon Sanderson

Even if it's your own, yup. They would interfere with each other to the point that you wouldn't be able to get anything out. Sorry.

Tel Aviv Signing (Oct. 18, 2019)

 

If you think about the explanations in Emperor's Soul, it makes sense that the "Coppermind's Spiritweb" is changed in those two examples (broken, Alloyed) so the investiture that was placed is still there, but no longer accessible as the "container" has changed. It may be that the storage is happening in the Cognitive, but we did not see indications of that in M:SH.