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Pushing, Pulling, and Torque


Phantom Monstrosity

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It looks like there are a few in-universe misconceptions about pushing and pulling.

There are claims that they act in lines directly to/from your center of mass.

That's rather impossible, given what we see happen in the books. Why? Because if you've got a vector directed at your center of mass, it's by definition going to exert no torque (and hence, cause no rotation).

However, when Zane is hanging out playing 'the ground is lava' with Vin, he shows off his MAD SKILLZ by... hovering and rotating in place. That's something that should be completely impossible. We also see stuff like Kelsier's bar-spinning arrow-blocking, which would be EXTREMELY difficult to pull off using vectors from the center of mass. Not impossible, but really hard.

In addition, coinshots, and mistborn don't start gradually spinning midair from wind effects when they're suspended over a coin. They also don't spin when they really should - Wax's guns should start him rotating whenever he uses them for propellant.

Even balancing off a coin would be insanely difficult if you're using a point source for your pushes and pulls; there's a cylinder above the coin equal to its width where you can direct yourself inward, and in order to balance with a push and hover you have to keep within that cylinder at all times.

Zane's hemalurgic spike granted him 'extra precision' to allow him to pull this stuff off - but that doesn't really help with spinning if it's center of mass based.

We basically have two options to resolve this

A ) Iron and Steel can exert torques on objects as well as pushing/pulling. Like, steel might make objects spin clockwise and the user spin counterclockwise, or vice versa.

B ) Iron and Steel aren't necessarily restricted to your center of mass. It's just far easier to do it that way, and nobody has really trained otherwise.

Now, this part might just be a research issue, but it looks like it already isn't restricted to center of mass in canon. People consistently get the vector lines out of their chests.

Mistborn Chapter 5:"Translucent blue lines sprang into existence around him, visible only to his eyes. Each one

led from the center of his chest out to a nearby source of metal"

Mistborn Chapter 9: "Blue lines suddenly appeared before her—one end of each pointing at her chest, the other disappearing into the mists."

The center of mass of a person isn't their chest. It's actually slightly below the bellybutton.

Personally, I'm leaning towards the 'shift center of allomass' theory since it's a little more elegant, and actually helps with the coin hovering problem. If you can push from portions of your body, all you'd need to do is get an arm or a leg or a shoulder over the coin and then adjust - changing the target area from 'a single point' to the entire cross-section of your body. Much more reasonable.

It doesn't seem like anyone's actually trained to do this - it's more of a subconscious secondary power. Still, it seems like something that would be interesting to explore.

Edited by Phantom Monstrosity
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However, when Zane is hanging out playing 'the ground is lava' with Vin, he shows off his MAD SKILLZ by... rotating in place. That's something that should be completely impossible. We also see stuff like Kelsier's bar-spinning arrow-blocking, which would be EXTREMELY difficult to pull off using vectors from the center of mass.

They used quaternions to avoid gimbal-lock. Obviously.

Physics doesn't play nice with magic, sir B)

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On Zane he could have just obtained the angular momentum from something else and given that he's levitating he has the reduced friction to keep spinning. Kelsiers trick altered where he pulled on the metal, not which part of his body acted as the anchor. And both are at the far side of what's possible with control, with Zane needing Hemalurgy to accomplish it and Kelsier just being a freak of nature :P Not something 99% of mistings or mistborn are ever going to be able to accomplish.

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Also, kidding aside, Mistborn like Vin and Kelsier seem to have brains that just automatically compensate for the physical consequences of their actions.

There's no calculation involved.

It's a bit like saying there's no way you could walk in a straight line over very uneven ground because a bipedal robot can't. There's a giant gap in ability to intuitively understand the environment.

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They used quaternions to avoid gimbal-lock. Obviously.

Physics doesn't play nice with magic, sir

Brandon said that "For MISTBORN, for instance, telekinesis mixed with vector science was interesting to me". I figure that he considered that angle already, since this is pretty low level stuff.

On Zane he could have just obtained the angular momentum from something else and given that he's levitating he has the reduced friction to keep spinning.

It's a controlled rotation - he starts, spins, and stops.

Unless he's got some controllable nonallomantic source of angular acceleration (directional burping?) he isn't going to be able to change the rate he's rotating.

Also, kidding aside, Mistborn like Vin and Kelsier seem to have brains that just automatically compensate for the physical consequences of their actions.

There's no calculation involved.

It's a bit like saying there's no way you could walk in a straight line over very uneven ground because a bipedal robot can't. There's a giant gap in ability to intuitively understand the environment.

It's not calculation - it's the physical capability. It's more like saying 'there's no way you can walk without any legs'. The issue is that pushing against the center of mass automatically means you can't have any torque.

...

The fact that nobody exploits the ability probably means it's like shielding other people's emotions with copper - theoretically possible, but really difficult, and nobody's figured it out to any great extent yet.

If, under normal circumstances, every part of your body was used equally as an anchor to push or pull on a target, it would (to a first order approximation) work out to roughly your center of mass. Using an off-center push or pull would involve 'precision' in selectively using some parts of your body for a particular push and not others - that would explain why Zane's extra precision spike would help.

He could use a very tiny push backwards with his left arm and a very tiny push forwards with his right arm, for instance, and get a torque that way.

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There is still some air resistance so slowing and stopping is to be expected, but I'd have to re read the chapter.

I have the ebook, so...

As Vin watched, Zane rotated slowly in the air, hand outstretched beneath him, twisting like a skilled acrobat on a pole. There was a look of intense concentration on his face, and his muscles—all of them, arms, face, chest—were taut. He turned in the air until he was facing her.

Vin watched with awe. It was possible to Push just slightly against a coin, regulating the amount of force with which one was thrown backward. It was incredibly difficult, however—so difficult that even Kelsier had struggled with it. Most of the time, Mistborn simply used short bursts. When Vin fell, for instance, she slowed herself by throwing a coin and Pushing against it briefly—but powerfully—to counteract her momentum.

She'd never seen an Allomancer with as much control as Zane. His ability to push slightly against that coin would be of little use in a fight; it obviously took too much concentration. Yet, there was a grace to it, a beauty to his movements that implied something Vin herself had felt.

Allomancy wasn't just about fighting and killing. It was about skill and grace. It was something beautiful.

Zane rotated until he was upright, standing in a gentleman's posture. Then he dropped to the wall walk, his feet slapping quietly against the stones. He regarded Vin—who still lay on the stones—with a look that lacked contempt.

So it looks like he slowly rotates to face vin, stops, then rotates to stand upright, and then stops and drops to the ground.

There's also this from chapter 11

She Pushed slightly against them all, then burned duralumin. The sudden crash of force was expected—the wrench in her chest, the massive flare in her stomach, the howling wind. What she didn't expect was the effect she'd have on her anchors. The blast of power scattered men and horses, throwing them into the air like leaves in the wind.

I'm going to have to be very careful with this, Vin thought, gritting her teeth and spinning herself in the air. Her steel and pewter were gone again, and she was forced to down her last metal vial. She'd have to start carrying more of those.

She hit the ground running, pewter keeping her from tripping despite her terrific speed.

Vin seems to intentionally spin herself in the air - but she is using duraluminum at that point, so who knows... then again, she's out of steel... not really sure what's up with that, probably using iron, or steel after she replenished.

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I have the ebook, so...

So it looks like he slowly rotates to face vin, stops, then rotates to stand upright, and then stops and drops to the ground.

There's also this from chapter 11

Vin seems to intentionally spin herself in the air - but she is using duraluminum at that point, so who knows... then again, she's out of steel... not really sure what's up with that, probably using iron, or steel after she replenished.

The second scene here, as well as issues with Wax firing in midair shouldn't be much of a problem. In both scenarios you have a significant amount of wind speed and it is only a matter of moving your limbs to adjust how the air flows over you, and can therefore spin you (this is no harder than turning at will while skydiving). The scene with Zane is harder to explain. The only thing I can think of is that by moving his limbs, he might have been able to generate enough wind resistance to control his movements (like turning yourself while floating underwater but much harder), but I find that hard to credit.

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C'mon folks. It really isn't that hard.

The original poster is correct. The pushes and pulls, to work as described in the books, can't be based strictly off of center of mass. There has to be an ability to tweak it slightly to get some torque.

I find this not at all disturbing. Any force, applied anywhere on a mostly rigid body, will largely get transferred to the center of mass in any case. This means that rough pushes and pulls will mostly affect the centers of mass, explaining the description given in the training. Small tweaks are then needed to fix the other little problems that might come up, and allomancers do that instinctively.

Remember how Inquisitors see? They see little lines to all the little pieces of metal. Clearly a bar of metal consists of many small pieces, and someone with detailed control could probably push/pull on one end more than the other---voila, torque, and forces not strictly on the center of mass anymore!

I think Kelsier even says something about that when describing staying "afloat" above a coin--the body already knows how to keep it's balance. Allomancers know how to do the same thing with their pushes---which means they are subconsciously modifying their torque slightly while pushing.

So, long story short: The original poster is correct, and there are hints in the books that this is so. The center of mass thing is just a good first-order approximation.

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Remember how Inquisitors see? They see little lines to all the little pieces of metal. Clearly a bar of metal consists of many small pieces, and someone with detailed control could probably push/pull on one end more than the other---voila, torque, and forces not strictly on the center of mass anymore!

That has to do with not leading to the centre of something else, not the body.

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I think that we may be dealing with center of gravity here, not center of mass. In a uniform gravitational field like Earth's, the differences aren't really significant: in the real world you have to start dealing with non-uniform gravitational fields before the centers of gravity and mass diverge to any significant degree. But we already know that Cosmere-gravity is different from Earth-gravity. The end result is close enough to feel familiar in mundane situations, but the differences can be important when magic is involved. I forget exactly which of the Ars Arcanum sections mentions that Cosmere-gravity has something to do with spiritual bonds between objects, but I think it was the one in The Way of Kings.

The ironlines seem to point to the user's heart, as do Pushes and Pulls. That's not the center of mass by any stretch of the imagination, but it is the sort of thing that may have great importance to spiritual bonds. It's certainly common as a literary trope, but the role it has long been thought to play in emotions is not a coincidence: it turns out that they actually are governed by some of the same systems. As such, the heart might also function as a spiritual "center of gravity," which would explain the apparent discrepancy.

None of this, in and of itself, completely explains torque. Others here have already floated the possibility of Pushing and Pulling on different points of objects, and that may make sense for objects, but Zane applying torque to himself is another matter. Is it possible that Zane's control is so precise that he can Pull or Push based on specific locations in his heart, rather than simply the center point, and spin himself that way? This doesn't sound like a safe thing to do, but Zane's sanity is suspect enough that he might try it.

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I find this not at all disturbing. Any force, applied anywhere on a mostly rigid body, will largely get transferred to the center of mass in any case. This means that rough pushes and pulls will mostly affect the centers of mass, explaining the description given in the training. Small tweaks are then needed to fix the other little problems that might come up, and allomancers do that instinctively.

I don't think I can buy that. The ability to push or pull off of an extremity would have a large number of uses aside from providing torque in midair. If such a thing were possible, we would have seen mistborns using it. For instance, you could pull an object straight into your hand, rather than having to catch it before it hits you or move out of the way. You could also use push points off your hands to adjust the aim of an object after you have pushed it away a bit. Pushing off your legs hard would give the ability for some pretty crazy acrobatics.

If Brandon intended mistborns to be able to do this, he would have explained it thusly and explored the possibilities.

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I don't think I can buy that. The ability to push or pull off of an extremity would have a large number of uses aside from providing torque in midair. If such a thing were possible, we would have seen mistborns using it. For instance, you could pull an object straight into your hand, rather than having to catch it before it hits you or move out of the way. You could also use push points off your hands to adjust the aim of an object after you have pushed it away a bit. Pushing off your legs hard would give the ability for some pretty crazy acrobatics.

We know that Pushing and Pulling are mass-based; being heavier means that you're a lot stronger. The mass of your hand is, what? 0.56% of your body mass or so? If you were just trying to Pull something into your hand, it'd be about two hundred times as hard as it would be to just Pull it to your center of mass.

It's difficult enough to vary the strength of your Pushes and Pulls; off center isn't something that's easy, just something that's possible.

If Brandon intended mistborns to be able to do this, he would have explained it thusly and explored the possibilities.

There are already examples of things that are technically possible but not widespread (copper shielding other people, for instance). It could be that nobody's really done an in-depth investigation yet, and that we'll see it show up in Mistborn Ten as a super difficult training exercise.

Edited by Phantom Monstrosity
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We know that Pushing and Pulling are mass-based; being heavier means that you're a lot stronger. The mass of your hand is, what? 0.56% of your body mass or so? If you were just trying to Pull something into your hand, it'd be about two hundred times as hard as it would be to just Pull it to your center of mass.

It's difficult enough to vary the strength of your Pushes and Pulls; off center isn't something that's easy, just something that's possible.

Weight does not make one stronger, it allows one to push heavier objects more easily without being pushed yourself. The examples I provided would be easy enough. It true the hand has little mass, but by exerting the muscles of your arm, you can keep the hand from being pushed or pulled while manipulating something as small as a coin or ingot. Of course this wouldn't work well when said object hit another person or thing, but the precision of using other points on the body would not be useful in those situations. The one exception that I can think of is the acrobatics I was talking about, this would also be possible by exerting muscle force to keep the legs from bending as you push off with them.

There are already examples of things that are technically possible but not widespread (copper shielding other people, for instance). It could be that nobody's really done an in-depth investigation yet, and that we'll see it show up in Mistborn Ten as a super difficult training exercise.

I guess it is possible, but I still have trouble crediting it. I think I'd need to hear Brandon answering this for me to be convinced.

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Weight does not make one stronger, it allows one to push heavier objects more easily without being pushed yourself. The examples I provided would be easy enough. It true the hand has little mass, but by exerting the muscles of your arm, you can keep the hand from being pushed or pulled while manipulating something as small as a coin or ingot. Of course this wouldn't work well when said object hit another person or thing, but the precision of using other points on the body would not be useful in those situations. The one exception that I can think of is the acrobatics I was talking about, this would also be possible by exerting muscle force to keep the legs from bending as you push off with them.

I guess it is possible, but I still have trouble crediting it. I think I'd need to hear Brandon answering this for me to be convinced.

While I think I've shifted over to your "change what parts of the metal you push on" camp, I think that you're wrong, irregardless, in saying that "weight does not make one stronger", at least functionally. Wax was able to de-building-ize an (admittedly rickety) building when he surged all his Weight together.

In the past (please read "momentum" whenever I say "energy" is concerved: my brain wasn't working well that week), I've theorized that the seeming increase in energy Wax gets is simply from the fact that he is staying close to his pushing target (as opposed to being pushed away). That may or may not be right, but we do know that he did a lot more damage when he weighed as much as a building than anyone in the original trilogy could have done without duralumin.

Edited by Kurkistan
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While I think I've shifted over to your "change what parts of the metal you push on" camp, I think that you're wrong, irregardless, in saying that "weight does not make one stronger", at least functionally. Wax was able to de-building-ize an (admittedly rickety) building when he surged all his Weight together.

In the past (please read "momentum" whenever I say "energy" is concerved: my brain wasn't working well that week), I've theorized that the seeming increase in energy Wax gets is simply from the fact that he is staying close to his pushing target (as opposed to being pushed away). That may or may not be right, but we do know that he did a lot more damage when he weighed as much as a building than anyone in the original trilogy could have done without duralumin.

We actually agree on this point, I just phrased it poorly :) . What I should have said was, "Weight does not make one stronger, it allows one to push heavier objects more easily without being pushed yourself. If you are heavier than the object you are pushing on, the extra weight is transmitted into that object." In the scenario we are examining, that just means if you were pulling an ingot into your hand, the muscles of your arm would have to make up the difference in weight between your hand and the ingot. But regardless, I don't believe that such a thing is possible under canon. :P

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I think there was a better confirmation on the weight=push strength elsewhere (currently looking for it), but I think Brandon would have corrected the question here if it were offbase.

Incidentally... not sure if it were a typo or a hint when Brandon said "Well, the Lord Ruler--don't forget--could compound any Allomancy he wanted." But that's for a different topic

EDIT: from Alloy of Law

Wax drew every bit of weight he had left, draining his metalminds completely. That was hundreds upon hundreds of hours of weight, enough to make him crush paving stones if he tried to walk on them. In the strange way of Feruchemy, he didn’t grow more dense—bullets would still cut through him easily if they hit. But with this incredible conflux of weight, his ability to Push grew incredible.

He used that weight to Push downward with everything he had. There were numerous lines of metal below. Nails. Doorknobs. Guns. Personal effects.

I think that's a pretty solid confirmation that more weight = stronger pushes.

If the issue were just 'avoiding being moved yourself', in any situation where Wax creates an expanding ring of force (like the ballroom bandit scene), it would be unnecessary for him to tap weight, since the forces in all directions would cancel out. But he *does* tap his weight there, and in the other circumstances where he's doing an omnidirectional push.

Edited by Phantom Monstrosity
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I think there was a better confirmation on the weight=push strength elsewhere (currently looking for it), but I think Brandon would have corrected the question here if it were offbase.

Incidentally... not sure if it were a typo or a hint when Brandon said "Well, the Lord Ruler--don't forget--could compound any Allomancy he wanted." But that's for a different topic

EDIT: from Alloy of Law

I think that's a pretty solid confirmation that more weight = stronger pushes.

If the issue were just 'avoiding being moved yourself', in any situation where Wax creates an expanding ring of force (like the ballroom bandit scene), it would be unnecessary for him to tap weight, since the forces in all directions would cancel out. But he *does* tap his weight there, and in the other circumstances where he's doing an omnidirectional push.

*sigh*

This is getting off topic and is beside the point entirely, but I can't resist replying. I think it is all a matter of semantics. We have an equation of weight and the force of a push (or speed or whatever you want to call it; how much you are flaring steel; I'll call it the force of the push for the purpose of the discussion). We have seen what happens when the force of the push is increased with Vin using duralumin. In the first instance she is pushed off the wall of Luthadel with amazing force, speed, and distance. This is like a 120lb girl pushing 50 times stronger than she normally could. She exerts a significant amount of power into what she is pushing on, but most of it is transfered into her flying. In other instances such as when she opens the door to the WoA, when she anchors herself against something, she is able to exhert an incredible amount of strength against something with a duralumin steelpush. This second instance shows us an increase of push force and weight, as by anchoring herself she is increasing the weight that is coming into play. This is more like a girl who makes herself weigh 6,000lbs and push 50 times stronger. That power is distributed more evenly.

If you extend this out logically, when Wax increases his weight and steelpushes against the building, it is like a 6,000lb (or more) man pushing with the strength of a normal man against the building, but all of his weight is put behind it. It's like dropping those 6,000 lbs on every bit of metal in the building at once. It isn't a more powerful push, the weight behind it is simply making the push more powerful. And yes that does increase his ability to push by proxy. We also have to keep in mind when quoting from books that this is 3rd person limited. This description is through the filter of Wax's perception. He may perceive incorrectly.

As far as omnidirectional pushes go, there are several possibly explanations. He could be doing it to steady himself, as there were likely more objects on one side of him than the other, so that he wouldn't fall over. Also consider that if his center of mass were just a little above or below the mean altitude of the of the objects he was pushing on, he would have pushed off the ground or been forced to the floor. Or he could have just been doing it unnecessarily as a precaution and had never realized he didn't have to :).

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I see that my last post wasn't as clear as I would have liked, so I will refine the idea:

There are two things to discuss: giving torque to something else (e.g. spinning a metal bar) and the torque applied to the Allomancer themself.

Spinning metal things is just a matter of pulling one end more than the other. I believe that this can be done as long as you can tell the difference between the iron lines leading to one end and the lines leading to the other. With practice, this may be possible.

Applying torque to the Allomancer is a different thing altogether. I would have to say, from what is described in the books, that there is some ability to move the "pushing" location around slightly and that it's not perfectly at the center of mass; otherwise Zane's stunt would be impossible. It would also help with things like keeping your balance on a coin, and the like. Allomancers probably move it instinctively. There are doubtless limits, though; hence the hand trick not working.

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Spinning metal things is just a matter of pulling one end more than the other. I believe that this can be done as long as you can tell the difference between the iron lines leading to one end and the lines leading to the other. With practice, this may be possible.

I assume it's a matter of practice and raw power to be able to see the lines. We've got Kar's PoV using his Inquisitorsense...

He turned and smiled toward the group of Ministry priests, knowing full well the discomfort the gaze of an Inquisitor could cause. He couldn’t see anymore, not as he once had, but he had been given something better. A command of Allomancy so subtle, so detailed, that he could make out the world around him with startling accuracy.

Almost everything had metal in it — water, stone, glass... even human bodies. These metals were too diffuse to be affected by Allomancy—indeed, most Allomancers couldn’t even sense them.

'Most allomancers' couldn't sense them kind of implies that there are some who can.

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I assume it's a matter of practice and raw power to be able to see the lines. We've got Kar's PoV using his Inquisitorsense...

'Most allomancers' couldn't sense them kind of implies that there are some who can.

I'd guess only Lerasium Mistborn, and possibly Vin, can match Inquisitors in that area.

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I assume it's a matter of practice and raw power to be able to see the lines. We've got Kar's PoV using his Inquisitorsense...

'Most allomancers' couldn't sense them kind of implies that there are some who can.

Those quotes are what I needed. I'm thinking that for something like spinning a metal bar, though, it would be somewhat easier to see two blue lines (for each end) than it would be to see the lines for trace metals. Thus Kelsier, for instance, may have learned how to do that.

It would be a useful trick, and the way torque works, it would still always have the whole bar move towards you or away from you, while it also begins spinning, thus not contradicting the observed pushes/pulls in the books.

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