Steel and Iron: We've been thinking about it wrong

[Mushroom Catalog]

The Problem:

I've been reading a whole bunch of threads about how steelpushing and ironpulling shouldn't work. The main complaint that I saw was how the strength and amount of push needed for one thing doesn't line up with the way it should.

In the books: Vin push coin, coin hit wall, Vin go back

Should be: Vin push coin, coin hit wall, Vin barely move as she realizes the amount of force needed to move a coin that far is super small and not enough to move a person OR Vin push coin, coin go so fast it breaks the universe, Vin go back. Except the universe is broken...

A better description and exact details with math and stuff can be found here and here with much thanks to Jofwu and Pagerunner.

The Solution:

So, I think I have an idea on how it works.

The general perception of steelpushing and ironpulling are that they apply a force to an object. If an allomancer pushes on a coin, their weight is applied to the coin, along with some other math stuff, which basically means the coin gets pushed. Pulling does the opposite. 

What I think actually happens: Instead of directly applying a force on an object, the investiture from preservation/harmony and the metal instead works to increase/decrease the distance between the allomancer and target. Imagine an unbreakable pole, leading from the allomancer to the target. When the allomancer burns steel and pushes, the investiture changes this distance, causing a force to be applied.

Say you are pushing against a wall with a given amount of strength. You can keep increasing the amount, and (hopefully) the wall will just stay there, but you will be expending more energy without actually doing anything. Now switch the wall with a coin. You can push against the coin as much as you want, and it will move that much, but you can only push so fast. For a given strength, there is a maximum speed an object will go. The speed an object moves is not always directly related to the amount of force against it.

This is what I call the max speed rule: an object will move at a certain speed, unless it cannot be moved at that speed, in which case it will be moved as fast as it can. This will NOT surpass the certain speed that was previously stated.

Using this idea, the maximum speed rule, pushing a coin is really just moving a coin away from you. This causes a force on the coin. The idea here is that the force moving the coin is a result, not a cause. An allomancer pushes on a coin, the distance is increased. The coin is much lighter than the person, and as such it will be moved instead, because it has the least resistance to increasing the distance. Once the coin hits the wall, it no longer can move. Thus, to increase the distance, the person must go, but they will move slower than the coin because of the max speed rule.

One more thing: Every allomancer has an innate strength. This strength determines how much investiture is put to work increasing the distance.

The rules:

Max speed rule: an object will move at a certain speed, unless it cannot be moved at that speed, in which case it will be moved as fast as it can. This will NOT surpass the certain speed that was previously stated.

Innate strength rule: Allomancers do not determine how much investiture goes to work when they push or pull (Edit) but can influence it by flaring metals or pushing harder.

How a push works with these:

An allomancer pushes a coin. They set the max speed, intentionally or not, and the investiture put to work is determined by the innate strength. The investiture pushes the coin to its maximum speed until it hits a wall. The coin can no longer move, the investiture applied not being strong enough to push through the law. However, since the investiture has to go somewhere, it pushes the allomancer, since they can be moved. They do not reach the maximum speed, but are instead pushed as fast as they can by the investiture, which is determined by their innate strength. 

Edit: The investiture works to increase the distance between target and allomancer. This means it applies a force to move it up to a certain speed. Think of car that can only go up to 60 mph. You could go slower in it, but you have a hard limit of 0 to 60. The kind of car and the limit imposed is chosen by the allomancer. The investiture is like the gas- it will move the object, but only up the max speed, and once it reaches that it will just be wasted. 

The Tests:

Example 1: Vin's training

Vin is being trained by Kelsier on steel and iron. She pushes on a coin, and it goes flying. Once it hits the wall, she falls over and stops pushing.

Vin pushes, meaning she wills the distance between her and coin to increase, even though she thinks she is just pushing on the coin- the distance between her and coin is increased, but the investiture can only move it away at the speed she tries to push it- It will not be the max speed of Vin's pushing capability because the investiture has to move it, and can only do it so fast. The coin hits the wall, but the distance still needs to be increased. So instead, Vin gets moved by the investiture, not as fast as the coin because it takes more speed to move her- this is her max speed for the given push and circumstances. So this checks out.

Example 2: Vin and the wall

Vin is still being trained, and is told to leap over the wall around Luthadel. She stands directly on top of an metal ingot and pushes.

Vin works to increase her distance between the bar. The bar cannot move, so instead the distance is increased her direction. The force applied against Vin to move her up is the result. She gets up to the wall, freaks out and gets saved by Kelsier, blah blah blah. This works too.

Example 3: Vin, Kelsier, and the tree.

Vin and Kel are in a pushing match, with Kel against a wall and Vin against a tree. We know that Vin has a higher innate strength due to mist and stuff. Because of this, when the coin is trapped between the two and they both have sufficient anchors, neither of them move, and neither does the coin between them. The tree is being slowly weaked by the pushes, until it breaks. Once it breaks, the investiture can move Vin again and she will fly backwards because she still is easier to move than Kelsier up against the wall. This also works.

I kind of ran out of example ideas, but I think this demonstrates the point.

Summary:

Steelpushes and Ironpulls work by changing the distance between the allomancer and target. The strength an allomancer pushes or pulls is what determines the maximum speed the distance will be increased and amount of investiture used in this action. When the amount of investiture working to increase this distance is not enough, the object will either move slower or not move at all. This is why some objects can and can't be pushed. Allomancers have a degree of control over the maximum speed, but the investiture is determined by the allomancers innate strength. 

Any thoughts on this?

Edited May 11, 2019 by Mushroom Catalog
Clarification

[Karger]

16 minutes ago, Mushroom Catalog said:

Steelpushes and Ironpulls work by changing the distance between the allomancer and target. The strength an allomancer pushes or pulls is what determines the maximum speed the distance will be increased and amount of investiture used in this action. When the amount of investiture working to increase this distance is not enough, the object will either move slower or not move at all. This is why some objects can and can't be pushed. Allomancers have a degree of control over the maximum speed, but the investiture is determined by the allomancers innate strength. 

Are you saying that allomancers are producing space or do you meen that they are applying speed to an object?

[+Artemos]

Good theory, I like it a lot. The long pole analogy is a great visualizer. It reminds me of the theory that Pushes try to increase the speeds/energies of the target and Allomancer (I think that first popped up with Pagerunner's Model 3). You've probably already read it, but works like this in my interpretation:

1. Burning steel gives the Allomancer the literal power of Preservation, that is, the ability to add (kinetic) energy to a system over time.
2. Following conservation of energy and momentum, this kinetic energy results in an increase in velocities between the Allomancer and target, depending on their masses.
3. If the target can't move, the Allomancer speeds up as it gains the target's unused energy (vice-versa for an anchored Allomancer)
   • If both Allomancer and target are anchored, then, uh... apply...

so anyways the main difference is that you propose the increase in distance, whereas the other theory frames itself more in terms of velocities and acceleration. I think the most important thing you've said that force is a result, not the cause. Even if both the Allomancer and target are anchored, as long as the Allomancer is Pushing, the Push will still try to increase the distance - which still manifests as a force. That could be applied to the other theory: The power "added" to a system where neither the Allomancer or target can move will at least try to do the work that would otherwise be done.

The one thing that nags me is correlating distance with force. Forces are inherently separate from distance - they only deal with changing velocity. That's semantics though. Like many of the models for Allomancy, it works sufficiently well.

My only other thing to add: This maximum speed would have to be inversely proportional to the mass of the target. Coins move fast, iron bars move slow.

3 hours ago, Karger said:

Are you saying that allomancers are producing space or do you meen that they are applying speed to an object?

Do you mean "producing space" in an Alcubierre drive-sort of way? I guess this falls back to increasing distance ⇒ a force not well-represented by real-world physics. Applying a force for a distance (i.e. work) signifies an addition of energy, but a force itself is only ever caused by a change in velocity, not position.

[Mushroom Catalog]

4 hours ago, Karger said:

Are you saying that allomancers are producing space or do you meen that they are applying speed to an object?

 

47 minutes ago, Artemos said:

Do you mean "producing space" in an Alcubierre drive-sort of way? I guess this falls back to increasing distance ⇒ a force not well-represented by real-world physics. Applying a force for a distance (i.e. work) signifies an addition of energy, but a force itself is only ever caused by a change in velocity, not position.

I can see why this would be confusing. I meant that the investiture gets put to the task of increasing distance between the 2. The allomancer wills the object to move, and the investiture they are able to summon moves it. The investiture applies the force, but not for the reason generally thought of as to move it away. I am saying the investiture moves it to increase the distance between allomancer and target at a certain speed dictated by the allomancer. The amount of investiture depends on the allomancer's strength, flaring or not, so on.

[Karger]

21 hours ago, Mushroom Catalog said:

I can see why this would be confusing. I meant that the investiture gets put to the task of increasing distance between the 2. The allomancer wills the object to move, and the investiture they are able to summon moves it. The investiture applies the force, but not for the reason generally thought of as to move it away. I am saying the investiture moves it to increase the distance between allomancer and target at a certain speed dictated by the allomancer. The amount of investiture depends on the allomancer's strength, flaring or not, so on.

That makes more sense.  The allomancy is not trying to apply a force it is trying to increase the distance.

[Calderis]

It kind of has to be applying a force though... We see the feel of that force when Vin needs to use pewter with her duralumin pushes to withstand the impact of her push. And there's also friction applied or there would be no way for two Allomancers to pin a coin in the air. 

Quote

Questioner

Do Allomantic Pushes and Pulls generate friction?

Brandon Sanderson

Do they generate friction. So... *sighs* I've had to ask myself this because if they didn't generate friction certain things that I do in the books wouldn't happen. I assume if you've seen the physics of it you've noticed. I have to go with yes. But the physics of it I'm a little wishy-washy on. I mean it's pretty obvious from the way I do things that they do.

Questioner

Yes! I have won the argument on the 17th Shard.

Brandon Sanderson

I mean, you've seen the science of it, right? You Push things up and they stay there. And so if they didn't generate friction, two people couldn't both Push on a coin to hold it in place, but it does get held in place.

Questioner

I just won a 17 page argument.

Brandon Sanderson

But I have to tell you... Peter is going to have to break his brain making the physics of that work. But I mean, it's canon. I put it in the books so it’s not like we can just ignore the fact.

Firefight Seattle Public Library signing (Jan. 7, 2015)

How exactly do you increase the distance between two objects without an application of force? 

[SwordNimiForPresident]

I think that math is a poor way to define steel and iron Allomancy. All of the math threads that I have seen seem to dwell on the physical aspects of steel and iron (based on real world physics) while ignoring that they are magic systems in the Cosmere, and almost certainly have interactions on a cognitive or spiritual level. Maybe the speed at which something is pushed is determined by how fast it thinks it should be going, or if it thinks it should be moving at all. Small coin gets pushed and says "I wanna go fast" (thank you Ricky Bobby). Big wall gets pushed and says "shove off mate".

This would also explain why Feruchemical iron changes the strength of your pushes, rather than just how resistant you are to being pushed. Those same objects now see you as something much more massive and change their reactions accordingly.

[+Artemos]

18 minutes ago, SwordNimiForPresident said:

I think that math is a poor way to define steel and iron Allomancy. All of the math threads that I have seen seem to dwell on the physical aspects of steel and iron (based on real world physics) while ignoring that they are magic systems in the Cosmere

You're absolutely right. Brandon didn't write his books with any exact mathematical model in mind. The Rule of Cool was by far the most important law for him.

Still, as fans, we like to discuss what he's created. Compared to magic (hard and soft alike) in the rest of fantasy, Pushing and Pulling are a rare case where we even have a chance to describe magic with real-world physics. So, we do it. Because it's fun.

50 minutes ago, Calderis said:

It kind of has to be applying a force though... We see the feel of that force when Vin needs to use pewter with her duralumin pushes to withstand the impact of her push. And there's also friction applied or there would be no way for two Allomancers to pin a coin in the air.

How exactly do you increase the distance between two objects without an application of force? 

I didn't read this as, "there is no force." Rather, "you don't decide the force; you increase the distance between yourself and the target, which manifests as a force." It's just that you can't directly correlate a force with a change in distance (rather than an acceleration). That's why the force is the "result, not the cause."

Really, the idea of a force being a "cause" versus a "result" is kind of arbitrary in real-world physics, but dealing with magically increasing distance between two objects makes it a necessary distinction, I think.

There might be some crazy space-time-bending analogue in the same vein as the Alcubierre drive. I don't know. That's beyond my level, and probably Brandon's, too.

[SwordNimiForPresident]

43 minutes ago, Artemos said:

You're absolutely right. Brandon didn't write his books with any exact mathematical model in mind. The Rule of Cool was by far the most important law for him.

Still, as fans, we like to discuss what he's created. Compared to magic (hard and soft alike) in the rest of fantasy, Pushing and Pulling are a rare case where we even have a chance to describe magic with real-world physics. So, we do it. Because it's fun.

I didn't mean that you were wrong to do it, just that you were unlikely to ever come to a solution that fits with real physics.

My point was that trying to describe Allomancy with just math means dropping two thirds of Realmatics. Its like trying to solve "1+  =  ".

[+Artemos]

8 hours ago, SwordNimiForPresident said:

My point was that trying to describe Allomancy with just math means dropping two thirds of Realmatics. Its like trying to solve "1+  =  ".

That's a very good point. I'll try to think about that more.

[StanLemon]

I have my own pet hypothesis as to what happens when Steel/Iron is used. When either of those metals is being burned it creates a connection to all the metal around them (a connection that is at least partially based on perception as shown by Wax's flashback with the bullet). When an Allomancer then Pushes or Pulls they are using their Investiture to create a force through that connection that affects both the Allomancer and the object evenly. This would give the illusion that weight versus weight is what happens during Pushes/Pulls as the weaker of the counter-forces would be the one moved. This would explain situations like in Hero of Ages where Elend goes up against the Inquisitor as the amount of force going between him and the metal both him and the Inquisitor were pushing on was greater than the force that the Inquisitor's connection to the metal was supplying and as such all that force got transferred to the Inquisitor.

Hopefully that made sense, I find it hard to explain without a visual to help.

[+Artemos]

1 hour ago, StanLemon said:

a force ... that affects both the Allomancer and the object evenly

1 hour ago, StanLemon said:

the weaker of the counter-forces

I think I'm misunderstanding, what do you mean by counter-forces? If the force between the Allomancer and object are even, then why would one be weaker? Or is the counter-force something else?

I agree that iron/steelsight is a matter of Connection and perception.

[StanLemon]

3 minutes ago, Artemos said:

I think I'm misunderstanding, what do you mean by counter-forces? If the force between the Allomancer and object are even, then why would one be weaker? Or is the counter-force something else?

I agree that iron/steelsight is a matter of Connection and perception.

Sorry, I know it wasn't a good explanation. So basically, when the Allomancer Pushes the force is sent through the blue line evenly to both the metal and the Allomancer and that is when Newtonian physics take over and that is why weight is important in standard Steelpushes/Ironpulls.

This dynamic is a little different though when two Allomancers are pushing against the same object. When that happens, if the two are roughly equal in strength as most Allomancers are then it get's back to weight and leverage to decide who wins. However if there is a large enough disparity between the two Allomancers then each of them are applying their own force onto the object and one of the two is applying more force. When this happens the greater force subsumes the weaker force. That's when weight isn't the deciding factor as much as the amount of force being applied.  

[+Artemos]

Is there anything special happening with the magic when two allomancers are pushing on the same object against each other?Or are we talking about simply the natural effect of two people applying a force to the same object, with one person being stronger than the other? Here's what I think you're trying to say: when two Allomancers (one stronger than the other) Push on an object, the force that the stronger one exerts on the object is transferred to the weaker one. Is that right?

Also, by weight do you mean mass or how well anchored you are to the ground?

Just to see if it helps with the discussion, what do you think of this simulation of two allomancers pushing on an object between them?

Does it describe what you think should happen when two allomancers with different strengths/masses push on the same object?

[Calderis]

I think, in using the Elend-Inquisitor example, he's saying that Elend strength overcomes and somehow negates the other push. 

I'm really not sure how hat works, but even the purely standard physics of that push are weird. Elend just pushed a full grown dude and send him flying. It's far more than the typical "weight" idea. And if Elend weren't anchored (which honestly I don't remember if that's determined or not, or who's PoV it's from) than there's plenty of other things to consider because the push never even rocked him backwards. 

[Karger]

12 minutes ago, Calderis said:

I'm really not sure how hat works, but even the purely standard physics of that push are weird. Elend just pushed a full grown dude and send him flying. It's far more than the typical "weight" idea. And if Elend weren't anchored (which honestly I don't remember if that's determined or not, or who's PoV it's from) than there's plenty of other things to consider because the push never even rocked him backwards. 

Their was a bunch of metal on the battlefield.  It would not have been hard for Elend to find a bunch of suitable anchores

[StanLemon]

48 minutes ago, Artemos said:

Is there anything special happening with the magic when two allomancers are pushing on the same object against each other?Or are we talking about simply the natural effect of two people applying a force to the same object, with one person being stronger than the other? Here's what I think you're trying to say: when two Allomancers (one stronger than the other) Push on an object, the force that the stronger one exerts on the object is transferred to the weaker one. Is that right?

Yes, that is more or less what I'm saying. An not quite accurate example but still would get the point across I think is think of the blue line as a bar. How strong the bar is represents represents the relative force. So in the Elend-Inquisitor example, Elend's bar is metal while the Inquisitor's is rubber, if those two push against each other they which would give out first? Now the blue lines cant bend or break so that force is blown back on the Inquisitor.

55 minutes ago, Artemos said:

Also, by weight do you mean mass or how well anchored you are to the ground?

 

Both kind of? Basically how much of a counter force is applied during a Push/Pull per Newton's Third Law. 

59 minutes ago, Artemos said:

Just to see if it helps with the discussion, what do you think of this simulation of two allomancers pushing on an object between them?

 

This does a good job of representing my thoughts but not quite exactly. I'm not particularly good at putting my thoughts into words. Kind of harkening back to the original poster, the force can be thought of as in the form of the blue lines getting longer in a Push and shorter in a Pull. So with Elend and the Inquisitor, the path of least resistance for each of their respective blue lines is to Push the Inquisitor away as both would be burning Pewter and be able to plant themselves pretty firmly (though Elend's was probably stronger still) and chull the Inquisitor would be providing less force to the confrontation he is the one who got moved.

53 minutes ago, Karger said:

Their was a bunch of metal on the battlefield.  It would not have been hard for Elend to find a bunch of suitable anchores

My one issue with this is Vin was pretty certain it was because of Elend's strength. Also back in the first book, strength of force is referenced as a factor back when Kelsier and Vin did their spar with the coin.

[StanLemon]

This is kind of how I imagine it with this crappy ms paint image

While factors such as mass and anchorage are factors I did this solely thinking about the force of the Push itself.

A represents standard strength push as it's kind of hard to properly represent it

M is the metal

I is for Inquisitor

E for Elend

The dots are the force being projected

The result is that the Inquisitor is being pushed at 1A by his own push and 4A by the superior strength of Elend's Push

While Elend is still also experiencing a 5A push on himself as well the piece of metal is experiencing a 4A Push towards the inquisitor. This is when the personal Masses of the objects start taking hold. Elend has much more mass than the metal and Newtonion physics dictates that it gets moved. Because now the Inquisitor and Elend both have the same amount of force from A projected on them yet the piece of metal is heading towards the Inquisitor it is the inquisitor that gets Pushed.

All of this is assuming I remember my physics properly. It's been a few years.

Edited May 13, 2019 by StanLemon

[Bigmikey357]

Ok, let's see if I got this. 

Allomancer 1 stronger connection to Preservation than Allomancer 2:

In this case mass of Allomancer does not factor as much. A-1 will win a push match with A-2 even if A-2 has more mass. A-2 only wins if they have an anchor and A-1 does not. 

A-1 and A-2 are equally connected:

Investiture cancels each other as force matches force. This allows other factors to weigh in. Mass and anchor strength determine who wins a push match. 

Vin was able to stand against Kelsier at least for a little while because she was stronger Allomantically. Just not strong enough to overcome the mass factor. Later when she is fueled by the mists her connection was stronger than even TLR despite having no anchor. She was thus able to push his bracers despite Investiture interference of bracers piercing skin. Elend was able to easily win a push match with an Inquisitor because his connection was much stronger than a being with Allomancy diluted by Hemalurgy.

[StanLemon]

Pretty much how I'm thinking.

[+Artemos]

8 hours ago, StanLemon said:

<snip>

I think I get it, thanks for the visual. The counter force is how much the Push is resisted - it would be higher for a heavy anchored Allomancer than a light unanchored one, yeah? 

Thought experiment time: consider the following two scenarios with your model:

1. The same scenario you described, where a weaker Inquisitor Pushes on a coin (with 1A) Pushed by a stronger Elend (with 5A)

2. A similar scenario, where a weaker Inquisitor Pushes on a coin (with 1A)...

but instead of using Allomancy, Elend runs up, grabs the coin, and physically pushed on it with the same 5A force as before using his hands and body instead of Allomancy. He's still just as anchored as before, but now, the force acting on the coin is coming directly from Elend's hand, not his Steelpush.

From the Inquisitor's perspective, is the force he feels any different? In both cases, the Inquisitor's Push is resisted equally; is it only because there is a blue line connecting Elend to the coin to the Inquisitor that Elend's counter force is transmitted to the Inquisitor?

I feel like the two scenarios should be identical from the Inquisitor's perspective, but I'm interested in hearing your thoughts.

[StanLemon]

That's a good question as the forces in that scenario are somewhat different but I think the answer would be yes as long as Elend could truly apply enough force in the opposite direction as the Inquisitor's Push. But I think there would be other factors that would affect it such as whether his hands can handle the direct Push from the Inquisitor on a smaller surface area whereas in a Push it is the whole body against the whole object.

[Karger]

23 minutes ago, StanLemon said:

That's a good question as the forces in that scenario are somewhat different but I think the answer would be yes as long as Elend could truly apply enough force in the opposite direction as the Inquisitor's Push. But I think there would be other factors that would affect it such as whether his hands can handle the direct Push from the Inquisitor on a smaller surface area whereas in a Push it is the whole body against the whole object.

If you accept this theory though Elend can now push so hard that his folds in space overwhelm the inquisitor's(if I understand this correctly).

[StanLemon]

40 minutes ago, Karger said:

If you accept this theory though Elend can now push so hard that his folds in space overwhelm the inquisitor's(if I understand this correctly).

I don't really consider it folds in space but my hypothesis is an attempt to describe what happens in the book versus the explanation given to us. It's already established that Elend can overwhelm the Inquisitor

[Calderis]

I think in that scenario, If Stan's idea is correct, the forces would actually be completely different. It would be purely the Inquisitors push strength against Elend's mass with know Investiture shenanigans whatsoever. 

If the force of Elend's allomantic strength somehow subsume the weaker push of the inquisitor, removing Elend's strength in steel from the equation reverts it to mass vs mass. 

Edited May 13, 2019 by Calderis