Semantics and Physics of Allomancy

[Shattered]

Okay, so this post will probably get edited when I come up with more theories and questions. Let's get down to business right now:

 

1. Force of a Steelpush or Ironpull

This has been bothering me for a while. Whenever I reread the Mistborn books, I notice just how much damage Pushed coins are doing. In WoA, one of Cett's soldiers actually has a chip of their tooth pop out of their mouth when they're hit with a coin. Coins frequently puncture through someone's entire body. Yet, it's mentioned frequently in the books that your weight governs the effects of your Pushes and Pulls. Yet, this may refer to the total force applied in a Push or Pull, or perhaps just the effect (whether you or your target or both moves). To add to the confusion, we can tell from Vin and Kelsier's Pushing match in FE that seems like weight might be more of a factor than just determining who moves, if we're thinking that way, yet at the same time, we can tell that since Vin's Spiritweb had already been affected by Preservation that she could Push with more force. So, what determines just how hard you can Push or Pull? It must be powerful enough to break bones with a coin, yet must be governed by weight in some way. But it can be affected by how powerful an Allomancer you are. Is it possible that it is governed by the weights of the involved objects? Thoughts?

 

2. Center of Mass of a Push or Pull

Frequently in the books, the characters flare pewter when performing extreme feats with iron or steel to 'stop from being crushed or pulled apart.' That begs the question: Just where on the body are these forces being exerted? Steel or iron lines point from the chest to different sources of metal. It is possible that this is where Allomancers Push or Pull from. Yet, if that were the case, how would forces being enacted on this nebulous 'single center of mass' threaten to crush or pull apart the entire body? That description makes it seem as if the forces are evenly applied and distributed around the exterior of the body. This doesn't seem likely to me, but I suppose it's possible. A theory I've been toying with is that Pushes and Pulls actually originate from the metals in an Allomancer's stomach, but it doesn't have much supporting evidence. What do you think?

 

3. Limits of Emotional Allomancy

I don't like the way that emotional Allomancy is depicted in the books. It leaves things far too open-ended for my liking. The 'emotions' that a Soother or Rioter can affect are shown to be anything between chattiness and desire for a debate. Even boredom is shown, which I definitely don't think of as an emotion. It certainly causes other ones, like aggravation or something similar, but boredom is just another term for 'having nothing to do or think about.' It sort of ruins the rigid logic of Allomancy for me. It seems like anything that might have a remote possibility of being described as an emotions can be affected by the use of zinc or brass. So, my question is: does anyone know more about this? Are there actually limits that govern what can be affected by emotional Allomancy and I'm just being ignorant? Please tell me.

[Vaidd]

Regarding the  "weight vs. weight" thing, I regard that as the character/narrator having an incomplete understanding of Newton's laws of motion, which may not be widely known on Scadrial.  The second law says "force = mass x acceleration", while the third law says that whenever one object exerts a force on another, the second object exerts the same amount of force back on the first object in the opposite direction.

 

To a physicist, or physics student, "acceleration" means any change in speed or direction. (Those who know what I'm talking about, please don't sidetrack the discussion by nitpicking "speed" versus "velocity.")  The force exerted will always accelerate the object in the direction of the force.  If a bullet is flying straight toward Wax, and he Pushes the bullet straight away from himself for a brief instant, he may only slow the bullet down.  This slowing is still "acceleration" because it's a change in speed. (Pushing to the side or at an angle is also acceleration because it changes the bullet's direction.)

 

Meanwhile, by the third law, the bullet is pushing back on Wax with the same amount of force, and where there's force, there's always acceleration.  Because Wax's mass is much greater than the bullet (feruchemical tricks notwithstanding), he won't be accelerated nearly as much.  He'll still feel a slight backward push, but he won't suddenly accelerate to the speed of the bullet.

 

If you don't have a friendly physics professor to show you all the math involved--and it does involve some elementary calculus--you could easily simplify these concepts in your head as just saying "it's the allomancer's weight against the object's weight."  That's close to the correct interpretation, but it's not quite right.  Since Brandon tells his story through third-person limited viewpoints, we never really know facts; we only know what the character thinks are the facts.  If a character has a flawed understanding of Newtonian physics, that will show up in their narration.

[Stormwalker]

I don't think allomancy works that simply with respect to Newton's laws. When you push on a coin that is blocked by a fixed object (like the ground) you go flying into the air, but if it isn't fixed in place, then the coin goes flying and you barely move. If the knock-back was governed entirely by Newton 3, than it should be the same in both cases. Empirically, it seems like when you push on something, one object (out of you or the pushed-on object) feels a lot of force, while the other feels a small amount of force. Which one (and I imagine the proportions as well) is determined by the relative masses of the two objects. Hence (if that is the case) weight would come into play with allomantic strength in that more of the pushing force is applied to the object instead of you.

[Dunkum]

The model I tend to use to vizualize iron/steel allomancy is something like this (it isn't perfect, but it helps me):

 

Imagine you have 2 electromagnets, with no power running through them at the moment.  you align them, while they are weak/off (this may not be how electromagnets actually work, but ignore that) so that they will push or pull on each other depending on whether you want to simulate iron or steel.  now turn the power on to both of them at once.  they will immediately start pushing against/pulling on each other, with each one exerting exactly the same force on the other as is exerted on it.  also note that since magnetism follows an inverse square law, once the two are separated by a certain distance, the other forces (gravity, friction, etc) will balance out the magnetic force and it will cease to be meaningful, which compares nicely to the point, say at the top of a steelpush jump, where the allomancer cannot get any higher (we see this in the books a few times).

 

here is where weight/mass comes in.  if one of them is substantially more massive than the other, than it will accelerate a lot less.  F=ma, so if F is the same, and m increases, then a has to decrease by the same factor.  to put that into more concrete terms, if one is 2x as massive as the other, then it experiences 1/2 the acceleration.  All of this is also ignoring friction, which increases with mass.  at some point, the friction experienced by the more massive magnet is sufficient to overcome the force exerted on it.  since it is unable to move, the other magnet will do all of the moving, until it moves far enough away to reduce the force past its own friction.  This is more or less the example of the coins.  they are substantially less massive than a person, so the same force acting on them will have a much greater effect than on the allomancer (to the tune of 50,000x greater for Vin, a bit more for someone larger).  this means that the allomancer feels some force, but it is extremely brief, since the coin is speeding away very quickly, and the force diminishes very rapidly (id guess it follows an inverse square law too, but have no real evidence of that).

 

now if instead of just being bigger, you have one of them attached to a wall, then what you see is that you have increased its effective mass to equal that of the wall.  In addition, the wall itself probably resists motion due to other forces acting on it.  In this case, the attached magnet cannot move, so all of the motion must carry to the unattached.  This is like the allomancer pushing on a steel bar in order to gain height.  the bar cannot move down, so the allomancer has to move up.

 

I admit this isn't perfect.  Using the above, pushing on any object, no matter how small, should produce some kind of recoil effect at the least, which doesn't seem to happen.  I haven't actually found a good way to reconcile this.  If the force (rather than just the acceleration) is actually proportional to the allomancer/target's mass, then pushing on something like TLR's castle should have basically launched Vin into the startosphere, but instead just seems to work like pushing on anything else, but if it isn't dependent on that, then that recoil should be there.  that said, I think it more or less works for a basic understanding, and at least some of it should be applicable regardless.

[Shattered]

To those who are explaining Newtonian physics and the effects of force applied to objects of different mass: I think you misunderstood my question.

 

Yes, a coin Pushed by an Allomancer accelerates much more with the same applied force, but what I was really asking was this: What determines the amount of force applied? Is there a difference depending on the mass of the object Pushed or Pulled? Is the force simply the required amount to accelerate the mass of the Allomancer X meters per second? I haven't been able to figure it out.

[Moogle]

The force applied to an object from a Steelpush or Ironpull is something along the lines of "essential Allomantic strength times your weight times the surface area of the object being affected". There may also be a division based on distance (squared?), since the way levitation works is you Push until you reach a equilibrium point.

 

It has to be based on your weight, due to how it works in Alloy of Law, but we also know Elend was superpowerful at Pushing, and we can say with some assurance that Vin accelerating some very small metal specks doesn't break the sound barrier (else she would have used that tactic to murder everything), which implies a pressure rather than a force (or something which scales with weight). There may be a constant in there, or it may be addition, but that's what it has to be as a minimum.

[Vaidd]

To those who are explaining Newtonian physics and the effects of force applied to objects of different mass: I think you misunderstood my question.

 

Yes, a coin Pushed by an Allomancer accelerates much more with the same applied force, but what I was really asking was this: What determines the amount of force applied? Is there a difference depending on the mass of the object Pushed or Pulled? Is the force simply the required amount to accelerate the mass of the Allomancer X meters per second? I haven't been able to figure it out.

 

The answer to this--and your question #2 in the original post--are really vague from the text.  Partly that's because none of the POV characters is a proper scientist (even Sazed doesn't deal in empirical measurements), and part of it is probably because Brandon doesn't want to bog down in details or paint himself into a corner.

 

For question #2 about where Pushes and Pulls originate, there must be some sort of Cognitive or Spiritual gobbletyblarthy to explain it.  If the force originated at a particular point, or even a particular bone, Coinshots and Mistborn would all have holes in their torsos.  Maybe the force pushes or pulls on the "whole entity" as seen in the Cognitive Realm.  I suppose the same idea might also go along with Moogle's point about Pushing on very small metal objects.

[BeskarKomrk]

Honestly, I never really think about it in terms of momentum and force as physics concepts. I think of Steelpushing and Ironpulling sort of like learning to throw a baseball or run on a rocky path. There are definitely physics concepts involved as to the mechanisms behind the actions, but that isn't how the brain thinks of them. Baseball players don't think "how much force do I need to throw the ball with in Newtons", they just practice until their brain makes the connection between the visual distance and the muscular force involved. That's how I imagine the strength of the Allomantic abilities. Some people have more raw strength to draw from (stronger Allomancer like Elend or The Lord Ruler), but everyone practices their Allomantic muscles to learn to judge the strength needed instinctively. So you can push a coin with just enough strength to sting, or you can push it hard and have it rip through someones bones (if you have a lot of control like Kelsier). Just a like a baseball player could toss a ball at your arm and have it lightly hit or throw as hard as they can and possibly break your bones.

[Voidus]

In terms of the center of mass question I believe that the push actually originates from your entire body simultaneously, so the average force would be on your center of gravity but it affects all of you.

On emotional allomancy I guess all I can do is shrug and say that what exactly constitutes an emotion is fairly nebulous and subjective. Breeze has manipulated a fairly large range of 'emotions' so it seems to be a pretty broad term in-world. However you could also argue that it's largely the skill of the Soother/Rioter. By carefully manipulating several emotions, you could produce one 'emotion' that's really more of a mindset like wanting to argue.

As for the force argument I think Moogle nailed it, I believe the equation would be something along the lines of massxAllomantic-constantxSurface area/distance^2

[Moogle]

The question of whether it should be based on surface area or mass is interesting, the more I think about it.

 

My intuitions ever since I learned there's Allomanic friction is that there's sort of a blast of some sort of material coming from you when you Push, so if something has a smaller surface area most of the blast is going to miss it. But in the case of electromagnetism (which there are clear links to, what with pushing around metal), it'd be based on charge (so based on mass in the average case where you're not ionizing things/magnetizing them weirdly).

 

Smaller objects also have smaller blue lines, I think, but I'm not sure if that supports either theory.

 

Pity we haven't had many scientific experiments on Pushing. We're getting some in Stormlight (I think?), so it'd be nice to have some for Mistborn.

[Voidus]

The question of whether it should be based on surface area or mass is interesting, the more I think about it.

 

My intuitions ever since I learned there's Allomanic friction is that there's sort of a blast of some sort of material coming from you when you Push, so if something has a smaller surface area most of the blast is going to miss it. But in the case of electromagnetism (which there are clear links to, what with pushing around metal), it'd be based on charge (so based on mass in the average case where you're not ionizing things/magnetizing them weirdly).

 

Smaller objects also have smaller blue lines, I think, but I'm not sure if that supports either theory.

 

Pity we haven't had many scientific experiments on Pushing. We're getting some in Stormlight (I think?), so it'd be nice to have some for Mistborn.

Was Allomantic friction ever confirmed?

[Moogle]

Was Allomantic friction ever confirmed?

 

It was.

[kinxer]

I apologize if this is the wrong place to say this or someone else has already put it forward, but it occurs to me that if we look at pushing (though it would work with pulling, too) as producing a total acceleration between the two bodies based on their combined weights with the individual acceleration being dependent on the weight fractions of the bodies (the allomancer and whatever they're pushing), that may explain something of the results.

 

Mathematically, I'd model this (guesstimationally) as

 

A(total) = K / (m1 + m2)

 

where K is some force dependent on the allomancer's strength.

 

Thus,

 

K1 (the force acting on object 1) = K * m2 / (m1 + m2)

K2 = K * m1 / (m1 + m2)

 

and

 

A1 = K1 / (m1 + m2) = K * m2 / (m1 + m2)^2

A2 = K2 / (m1 + m2) = K * m1 / (m1 + m2)^2

 

In any situation in which one of the objects can't accelerate, the other object's acceleration would become the total acceleration.

For example,

 

A2 = 0

A1 = A(total) = K / (m1 + m2)

 

I'm sure there are issues with this model. Anyone care to bring them to light (including issues with my mathematics)?

 

EDIT: Oh, um... Distance. Something about diminishing force based on distance, too.

 

EDIT 2: Assuming something like inverse-square, an equation could be A2 = K * m1 / (d^2 * (m1 + m2)^2)

Edited May 1, 2015 by kinxer

[Moogle]

...

 

You may be interested in this thread, which put forward a similar idea. I agree that something like this is necessary, based on how you only feel an extreme backwards force when you Push on a coin anchored to the ground.

 

I also think you got your ratios mixed up? I'd put A1 = acceleration of object 1 = K * m2 / whatever, rather than A1 = K * m1 / whatever. It's the lighter body that gets more of the acceleration, so the opposite weight should be used on top.

[kinxer]

You may be interested in this thread, which put forward a similar idea. I agree that something like this is necessary, based on how you only feel an extreme backwards force when you Push on a coin anchored to the ground.

 

I also think you got your ratios mixed up? I'd put A1 = acceleration of object 1 = K * m2 / whatever, rather than A1 = K * m1 / whatever. It's the lighter body that gets more of the acceleration, so the opposite weight should be used on top.

Thank you on both accounts. The ratio-based mathematics I've been doing lately have been with weight-percents of metals in alloys, so I'm used to that right now. Anyway, I think I've fixed it. As for the collision thing, I'd read it, but it hadn't occurred to me that it was so similar to my proposal.

Edited May 1, 2015 by kinxer