Theory on the Physics of Allomancy (and some Feruchemy)

[Scriptorian]

I read the mistborn series while taking a class on calculus-based Newtonian physics, so I couldn't help but formalize a theory on how steel/iron allomancy would actually work. There has already been a topic on how weight is related to the strength of push/pulls, and you can read it here http://www.17thshard.com/forum/topic/3307-weight-has-nothing-to-do-with-allomantic-pushpull-strength/?hl=%20allomancy%20%20mass%20%20weight.

But I want to introduce a new theory (with a bit of math) that I think clears up a lot of the confusion. I'm not incredibly physics-savvy, so I explain something terribly wrong, I apologize.

 

(For the sake of efficiency, when I say allomancy, I am referring specifically to Iron and Steel)

 

The Force of Pushes and Pulls

 

First, I am operating under the assumption that weight is only tangentially related to the force an allomancer can exert. Instead, it is actually the mass involved that is important. Weight is the force exerted on an object by the planet equal to the mass of the object multiplied by the acceleration due to gravity. Most people (including the mistborn characters) probably mean mass when referring to allomancy.

 

So I came up with an inverse-squared formula to determine the force an allomantic push/pull can exert.

 

F= (A x (m₁ x m₂))/(r²), where F is the resultant force, A is the coefficient of Allomantic strength (I'll get into this later), m₁ is the mass of the allomancer, m₂ is the mass of the object, and r is the distance between the two masses. (The force is positive for Lurchers, and negative for Coinshots).

 

I based this off of the Newton's Law of Gravitation since the principles involved appear very similar to me. When the earth pulls on an object, the object is actually pulling on the earth with the same force. However, the earth has so much more mass than the object so it effectively doesn't move. If a much larger object, like another planet, were to come near the earth, then both it an the other planet would move towards it at noticeable speeds. And again, if a much more massive object, like the sun, where to come near the earth, you wouldn't see the sun move,, just the earth. This is very similar to how a Coinshot can send a coin flying, but be pushed into the air by a much heavier object. 

 

The coefficient of allomantic strength accounts for the varying levels of power between different allomancers. This variable changes depending on how hard the allomancer is pushing/pulling (i.e. by flaring). In this way, both the mass and strength of the allomancer are important to the amount of force he/she can exert. Both the allomancer and the object are affected by the same force, but the less massive object accelerates much faster. The force also decreases quadraticaly as the distance between the object and allomacer increases. 

 

So I did some math the figure out about what this coefficient of allomanctic strength would be...and kept doing things wrong. At first I made the mistake of assuming a coinshot was pushing on a coin in free space, which resulted in a Coinshot strong enough to move planets. Then I tried having him push against the mass of the planet, which came out to him being ridiculously weak. I finally realized that when you are pushing off of a coin, your effectively pushing off a certain amount of ground, not the entire planet. I have no idea how you would calculate the mass of the ground however, so my formula is now un-provable without some more concrete measurements of allomancy  .

 

Feruchemical Iron

 

This theory requires some pretty weird physics concepts. There's been a lot of discussion about what is actually stored with Feruchemical iron, but I think this theory coveres it pretty well. 

 

Basically, there are two different measures of mass: gravitational mass and inertial mass. Gravitational mass affects the gravitational field exerted by an object, and also how it is affected by other fields of gravity. Inertial mass is how much an object resists changes in motion. So far as we know, the two values are the exact same for any object and are functionally the exact same concept, in the real world. However, in the Cosmere, it appears you can change one without changing the other. I propose that Feruchemical iron merely stores the feruchemist's inertial mass.

 

This means that nearly every force will affect the feruchemist as though they had gained more mass when the feruchemist is tapping, and vice-versa for storring. Gravity, however, affects the feruchemist the same as normal. The difference is, say when the feruchemist jumps while storring, the force of the jump affects him much more, with gravity affecting him the same, resulting in a much higher jump. Similarly, while falling, drag affects the feruchemist much more, resulting in a slower fall. This also solves the issure of the feruchemist suffering not crushing themselves while tapping, because their atoms become more resistant to motion in direct correlation with the increase of inertial mass.

 

This increase in inertial mass would also factor directly into my above equation for allomancy. Since the force is directly proportional to the mass of the allomancer, tapping iron results in a greater force, both on the allomancer and the object. However, the increased force accelerates the allomancer the same as normal force the allomancer is now proportionately more resistant to motion.

 

Now a potential hole in my theory is that the reverse should also be true. Decreasing your inertial mass would make forces affect you more, but would also reduce the strength of your Push/Pull. In the AoL, Wax is more affected by Pushing while storing Iron, and I can't figure out how to account for this mathematically...

 

I wanted to have a bunch of physics and math extrapolated from this...but most of my calculations were really flawed....

 

 

Anyway, thoughts? Criticism? Any real physicists who wants to tell me I explained this all wrong?

Edited October 13, 2013 by Serendipity

[name_here]

One thing I've noticed is that it seems like the equation for the system is force on Allomancer *A = force on object. Vin and Elend both occasionally throw objects harder than they get thrown; during Vin's training exercise with Kelsier, they both go flying back at high speed even though Kelsier is at least twice her mass, and during Elend's escape from Yomen's manor he explicitly notes that his greater strength is letting him shove back Coinshots much harder than he's being shoved back. Also, while this isn't exactly part of the physics, it seems like when Allomancers are pushing/pulling, they set a desired acceleration and automatically increase the force until they reach it; this would explain why they can get thrown back unexpectedly when they shove on an object that turns out to be braced, or when a coin hits an obstacle.

 

Furthermore, I don't think the Allomancer's mass is in the force equation. Granted, we can't confirm or deny this, but it seems the main limiting factor on pushes is resisting the counter-force; braced Allomancers can push pretty hard. Again, it seems like one of the limits is net acceleration; an Allomancer can only push as hard as it takes to produce a certain relative acceleration of the two objects in the system. This means more massive Allomancers are more powerful by virtue of needing more force to move them.

[DocHoliday]

Just a note to add to name_ here, Allowmancers are definitely able to set the amount of acceleration of there Pushes.

I.E. Zane "balancing" a few feet above a fountain.

[Gagylpus]

Oh, the physics of magic. I love these kinds of discussions.

 

One caveat to start off with is that Brandon, of course, is not a physicist. (And thank goodness, otherwise he would probably spend too much time doing math and not enough time writing books.) So his magic systems won't always act consistently with physical principles.

 

Zane's balancing act with steelpushing is a good example of this. The book describes him as being able to carefully manipulate his orientation, twisting around in the air. But the books also explicitly state that Allomantic force always acts on your center of mass. A force that acts on your center of mass can never cause that kind of turning or twisting motion. So something is wrong here.

 

Another problem is Vin and Kelsier's coin-pushing match, which flattened the coin between them. (Disregarding the fact that such a configuration is highly unstable, and the coin would never have remained between them long enough to get flattened - it would have been flung away just like the rest.) The only kinds of forces capable of always acting through an object's center of mass are body forces, forces distributed throughout the volume of the object. Whereas the kind of force required to flatten the coin would have to be stronger on the faces of the coin, compared to the middle, something that looks more like a surface force.

 

The confusion is understandable, since the only body force we are familiar with is gravity or other inertial forces from accelerating reference frames (for example, an elevator that is starting or stopping, or a roller coaster) and we mostly only feel those by comparison with surface forces (I 'feel' gravity because my feet are supporting my weight - but that is actually the reaction force from the ground, a surface force).

 

Another reason that Allomantic forces must be distributed across your body (and across the volume of the object you are pushing or pulling - it would be strange if they worked differently at the other end) is that, if the force actually acted on your center of mass, it would be like a hook in your gut yanking you around. Not particularly pleasant. And there is no simple (or even unique) way for the forces to be distributed across the surface of your body so that the net force acts through your center of mass, so it wouldn't make sense at assume we are dealing with surface forces.

 

(Now I'm rambling a little bit. The more I think about it, the less it makes sense that Allomantic forces always act through your center of mass. There isn't any natural way to make this happen. Also, I'm contradicting myself because I just thought of a way to create a simple distribution of surface forces, though it still doesn't satisfy the center of mass requirement... though it will act through your center of volume whenever a related body force field would act through your center of mass. But I don't want to start postulating Allomantic ether theories.)

 

...

 

Okay, so that was a long way of saying that, while we can try our best, no theory is going to catch all of the phenomena that we see in the book. But I think your main premise about Allomantic force is right. Here's how I would nuance it a bit.

 

Allomantic force follows an inverse-square law. It has to decrease with distance. Otherwise, you could pull yourself to Luthadel all the way from Fadrex city by yanking on the spires of the Kredik Shaw. And inverse-square laws just make sense, given our three dimensions of space. (There's a nice image showing why here: http://en.wikipedia.org/wiki/Inverse-square_law)

 

Allomantic force is a body force, distributed proportional to mass. In other words, just like gravity. This is where the advantage of the inverse-square law comes into play. Inverse-square body forces act between objects' centers of mass when the distance between the objects' centers is much greater than their sizes. So when Vin is up on the wall of Luthadel, pushing on a steel bar at the bottom to slow her decent, the force is basically through her center.

 

Basically, I'm postulating that each little bit of mass of the Allomancer pushes or pulls on each little bit of mass of the metal, with a force that is proportional to the masses (actually, their Allomantic charges, see below) of both the little bits and inversely proportional to the square of the distance between the little bits. The force on each bit of mass is pointed directly towards or directly away from the other bit of mass. (Then you integrate over all of the bits of mass on each body to get your total force.)

 

This reduces to your theory, for the case where the Allomancer and the metal are far apart, and (I think) is the most natural way that the forces would be distributed. The snag is that when the Allomancer and the metal are close together, the total force no longer acts through the center of mass (and is also no longer exactly inverse-square, though it still diminishes with distance). However, I have an idea that might help solve this problem.

 

Metals that can be pushed and pulled have an Allomantic charge, distributed proportional to mass. The charge has a special identity unique to each individual piece of metal, kind of like an electric charge, but only interacting with other charges that have that unique identity.

 

Pushing or pulling on a piece of metal floods your body with the Allomantic charge unique to that piece of metal. Ironpulling obviously uses an attractive charge, and steelpushing uses a repulsive charge. The reason I put these unique identities on the charges is obviously because you only push or pull on certain objects at a time. Wax's steel bubble could involve a more general charge.

 

The total amount of Allomantic charge that you can put on your body is proportional to your metal burn rate. So if you weigh less, you will be able to accelerate faster using the same push as someone who weighs more, because you have a higher charge per unit weight. (I think a similar thing happens with pewter and tin - as Ham explains it, part of the reason Vin packs such a punch is that she's enhancing a smaller body with the same amount of Allomantic power.) It is also quite possible that you get more Allomantic charge per unit metal burned if you have a higher innate Allomantic strength.

 

Here's my idea that helps solve the center of mass problem.

 

An Allomancer's Allomantic charge is somewhat mobile within their body (but the equilibrium state is distributed proportional to mass). So when you push on a coin directly beneath you to launch off the ground, here is what happens. Your feet are much closer to the coin than your head is, so initially the force on your feet is much greater, and the total force is acting way below your center of mass. But the Allomantic charge responds to the force to some degree as well, so it ends up being pushed away from your feet, concentrating higher up in your body. This moves the center of action of the force closer to your center of mass.

 

And voila! An Allomantic force that seems to act through the center of mass. This could even explain Zane's balancing act, since he could be skillfully exploiting the fact that it isn't exactly through the mass center (it would be incredibly difficult, so Vin is rightfully impressed). I'm not sure yet if it explains the coin-flattening. I'll have to give it more thought.

 

 

I'm gonna tackle your theory about iron Feruchemy next.  (After the edit.)

 

Edit: Okay, adding in commentary on your Feruchemy theory. Basically all I have to say has probably been said already in other threads about iron Feruchemy. The gravitational mass vs. inertial mass distinction has some merit - if I recall, Sazed's description as he floats down to the Conventical of Seran makes it sound like iron Feruchemy does affect them differently. But the theory is sadly put to rest in Alloy of Law. Wax changes weight while he arcs across the dining hall and specifically notes that this doesn't change his motion in any way, which means that his inertial and gravitational masses are still identical. So iron Feruchemy just changes your density, straight up. (With the added side bonus of immunity to self crushing.)

 

 

Edit: About your attempts to calculate the proportionality constant. It sounds like you're looking for how much force you can exert on something before you start moving as well. In free space, of course, any amount of force will start you moving. There's nothing wrong with that, as that same force will also move whatever you are pushing or pulling on, whether its a coin or a planet. (The planet won't move by very much, of course.) On the ground, the force that will start you moving is just going to be equal to the maximum static frictional force between you and the ground. In general, this is proportional to your weight (with the coefficient of friction depending on the composition of the ground and of your shoes).

Edited October 15, 2013 by Gagylpus

[Satsuoni]

Ah, physical discussion. Fear me, for I channel the spirit of Auotpwail, and came here to victimize you, as I did poor Kurkistan! Verily, all I speak is true (except for inaccuracies introduced by imperfect human channel)

 

First, the OP:

First, I am operating under the assumption that weight is only tangentially related to the force an allomancer can exert. Instead, it is actually the mass involved that is important. Weight is the force exerted on an object by the planet equal to the mass of the object multiplied by the acceleration due to gravity. Most people (including the mistborn characters) probably mean mass when referring to allomancy.

True enough, most people in real world don't make that distinction.

 

F= (A x (m₁ x m₂))/(r²), where F is the resultant force, A is the coefficient of Allomantic strength (I'll get into this later), m₁ is the mass of the allomancer, m₂ is the mass of the object, and r is the distance between the two masses. (The force is positive for Lurchers, and negative for Coinshots).

That would mean that Allomancer push is stronger against heavier piece of metal. That is not quite so - at the very least there is an upper limit to Allomancer's force , and certainly not so if m2 refers to mass of metal, since a coin embedded in stone wall works (when close enough to be affected) just as well. See the thread you have referenced for details   The inverse square law may be in effect, true. There is also a visibility cutoff, after which an Allomancer can no longer "see" the metal to affect it - see Vin balancing near the wall on the very edge of her ability (still enough force to keep her in the air).

 

 This is very similar to how a Coinshot can send a coin flying, but be pushed into the air by a much heavier object. 

This is similar to the fact that you can't break your hands on the air by punching it, but can on the wall, while your muscle strength remains the same. Again, read through the whole thread

 

Basically, there are two different measures of mass: gravitational mass and inertial mass.

Three, not two. Inertial, passive and active gravitational. That is important They kind of have to be the same in our world, but Cosmere is another matter.

 

This means that nearly every force will affect the feruchemist as though they had gained more mass when the feruchemist is tapping, and vice-versa for storring. Gravity, however, affects the feruchemist the same as normal.

This is patently not true. A feruchemist stores to soften his/her fall, reducing the force acting on him. If the gravity still affected him with the same force (same passive gravitational mass), but his inertial mass decreased, he would fall faster, not slower (a=F_g/m_i). As it is, his acceleration is unchanged and force is lower, resulting in air drag being enough to counteract gravity at survivable velocities. So, globally speaking (there is a thread on why he can still be cut, involving locality), Feruchemist stores all of his masses, with the possible exception of active gravitational one (will a feruchemist collapse into black hole with enough tap?). Note here that the drag does not depend on mass in any way, just velocity and body shape - and you need to counteract gravity *force*, not acceleration, which in your assumption is the same.

This also solves the issure of the feruchemist suffering not crushing themselves while tapping, because their atoms become more resistant to motion in direct correlation with the increase of inertial mass.

But not in respect to bullets? Since those ignore the fact that they'd need a lot more energy to move atoms around, and cut through Feruchemist normally. If the atoms were more resistant, bullets would never penetrate past skin at 100x tap, at least. Maybe even 10x.

 

And now, to Gagylpus:

 

 

One caveat to start off with is that Brandon, of course, is not a physicist. (And thank goodness, otherwise he would probably spend too much time doing math and not enough time writing books.) So his magic systems won't always act consistently with physical principles.

This is very true, though he does check with physicists sometimes.

 

 

Zane's balancing act with steelpushing is a good example of this. The book describes him as being able to carefully manipulate his orientation, twisting around in the air. But the books also explicitly state that Allomantic force always acts on your center of mass. A force that acts on your center of mass can never cause that kind of turning or twisting motion. So something is wrong here.

Well, you could turn your body around by twisting and moving the body, while balancing on the coin. The force from the coin won't spin you, the force from your twisted body, however, can (without changing the position of your center of mass).

 

Another problem is Vin and Kelsier's coin-pushing match, which flattened the coin between them. (Disregarding the fact that such a configuration is highly unstable, and the coin would never have remained between them long enough to get flattened - it would have been flung away just like the rest.)

Here is the  thing - the instability is caused by the fact that the forces affecting the coin differ in direction in different positions of the coin, roughly corresponding (in generic push, see below) to direction from Allomancer's CoM to that point in the coin. With the two Allomancers pushing from the opposite sides, the total horizontal force is 0, but the vertical component is not negated, resulting in the coin being pulled outwards from center, flattening it. Add to this the thickness of the coin resulting in different distances to the coin parts from either allomancer, and you get the coin that goes squish.

Note that gravity on the planet also does not affect every part of the body equally - see spaghettification, and remeber that a body is not homogenous to begin with...

 

Also remember, that a trained allomancer can push/pull at different parts of the metal object at will, as evidenced by Kelsier rotating a metal bar in the air. So the generic force spread over the metal (not allomancer, allomancer is affected as a single body, equally, as you said) may vary.

Also remember, there are no "surface" forces - all forces are derived from "body" field forces carried by little bosonspren

 

[Kurkistan]

I am so sorry that you drew Auotpwail's attention. So very sorry... ( )

[happyman]

I've become more and more certain that the allomantic force doesn't actually work on center of mass.  Like others here, I believe that it generally pulls on metals, and pulls most cleanly on metals that are one object, but that with practice, you can successfully learn how to push or pull one side of an object.  This would allow the torque to be exerted.  The center of mass comes from a mechanism like Gagylpus references:  pulling on the entire object with the same force tends to produce something very close to center-of-mass behavior.

[Dysphoric Kitten]

I've become more and more certain that the allomantic force doesn't actually work on center of mass.  Like others here, I believe that it generally pulls on metals, and pulls most cleanly on metals that are one object, but that with practice, you can successfully learn how to push or pull one side of an object.  This would allow the torque to be exerted.  The center of mass comes from a mechanism like Gagylpus references:  pulling on the entire object with the same force tends to produce something very close to center-of-mass behavior.

 

 

I, personally, thought it was clear that it is possible to do that. How else would Kel spin the rods while fighting the Inquisitor? If I am remembering correctly, the narrator actually says that "Kelsier Pulled on one side, Pushing the other, making the rods spin", or something like that. This means the lines are actually not thick, but so many, so close together, they appear to be one bold line.

 

One use for this (mistborn only, though) is using torque to spin a rod (by Pushing one side, this will also shift the mass to the side you Pushed on), then repeating (so it continues) with the other side. Every few times, you switch from Pushing to Pulling on the other side to avoid a diagonal line. It will be extremely hard to master, and might actually go in a circle, but still, oddly useful, especially for showing off.

[Gagylpus]

That would mean that Allomancer push is stronger against heavier piece of metal. That is not quite so - at the very least there is an upper limit to Allomancer's force , and certainly not so if m2 refers to mass of metal, since a coin embedded in stone wall works (when close enough to be affected) just as well. ... There is also a visibility cutoff, after which an Allomancer can no longer "see" the metal to affect it - see Vin balancing near the wall on the very edge of her ability (still enough force to keep her in the air).

 

From the books I got the impression that you did get stronger pushes off of large pieces of metal in the way described (with the weight of the anchor being another issue), or at least that it was easier to get stronger pushes that way. But if that is not the case, my 'Allomantic charge' theory would have to be modified to say that the effect of burning iron or steel is also to put charge on the metal, as well as the Allomancer him/herself. (This actually makes more sense, in the long run.) The total amount of charge being put out would still be proportional to the burn rate.

 

I would argue that the visibility limit is not a real effect, just a psychological one. You clearly don't need to have line of sight, just to be close enough and to know that the metal is there (courtesy of the blue lines). The 'close enough' restriction occurs because the force diminishes with distance (and I am guessing that the intensity of the blue lines is proportional to the force you can exert on that metal).

 

Well, you could turn your body around by twisting and moving the body, while balancing on the coin. The force from the coin won't spin you, the force from your twisted body, however, can (without changing the position of your center of mass).

 

But you couldn't change your angular momentum at all (at least not predictably). Anyways, I'll concede that.

 

...but the vertical component is not negated, resulting in the coin being pulled outwards from center, flattening it. Add to this the thickness of the coin resulting in different distances to the coin parts from either allomancer, and you get the coin that goes squish.

 

Ah yes! That makes sense. I'm still uncertain about whether the stability region is larger than a single point (if the coin were displaced a tiny amount, would the forces hold it there or would it go flying away), but you've explained how the coin gets flattened (stretched, really) quite nicely. 

 

Also remember, that a trained allomancer can push/pull at different parts of the metal object at will, as evidenced by Kelsier rotating a metal bar in the air. So the generic force spread over the metal (not allomancer, allomancer is affected as a single body, equally, as you said) may vary.

Also remember, there are no "surface" forces - all forces are derived from "body" field forces carried by little bosonspren

 

I don't remember Kelsier being able to push/pull on different parts of an object differently, but I definitely hope that's the case, 'cause it would be rather useful. It also lends support to the notion that the Allomancer puts the Allomantic charge on the metal, rather than the charge pre-existing.

 

Edit: Tal pointed out the reference, thanks.

 

If you want to get technical - 'surface forces' are no more real and no less real than 'surfaces' themselves. At the quantum scale, of course, everything is electromagnetic and weak and strong interactions, and Pauli exclusion, and there are no clear boundaries between one object and another because everything is particles/waves/fields. But we're working at the continuum scale.

Edited October 16, 2013 by Gagylpus

[Robot Aztec]

I Read not a long time ago that they Brandon and he was not sure about how it worked 100% himself so I am going to say that it probably is just a complicated thing that nobody int he book understands because they would have ot know more than tha author.

[Satsuoni]

From the books I got the impression that you did get stronger pushes off of large pieces of metal in the way described (with the weight of the anchor being another issue), or at least that it was easier to get stronger pushes that way. But if that is not the case, my 'Allomantic charge' theory would have to be modified to say that the effect of burning iron or steel is also to put charge on the metal, as well as the Allomancer him/herself. (This actually makes more sense, in the long run.) The total amount of charge being put out would still be proportional to the burn rate.

 

I would argue that the visibility limit is not a real effect, just a psychological one. You clearly don't need to have line of sight, just to be close enough and to know that the metal is there (courtesy of the blue lines). The 'close enough' restriction occurs because the force diminishes with distance (and I am guessing that the intensity of the blue lines is proportional to the force you can exert on that metal).

 

Here is a quote from the book I refer to:

The stone wall was a blur of motion just a few feet away from her. The ground disappeared below, and the line of blue pointing toward the ingot grew fainter and fainter.

What happens if it disappears?

She began to slow. The fainter the line grew, the more her speed decreased. After just a few moments of flight, she crept to a halt—and was left hanging in the air above a nearly invisible blue line.

 

So for "visibility" I refer to the visibility of the blue line. As can be seen, at the "visibility" limit (barely visible line) the produced force is still enough to negate gravity. Presumably, the Allomancer cannot push on the metal he cannot see/feel, which produces a cutoff in power levels. Likewise, there is a limit of force produced by an allomancer while pushing that is independent of metal size - otherwise something the size of Kredric Shaw would have been enough to launch into orbit ( when compared to the size of the metal ingot), even if the distance remained the same (that is, one stopped pushing at the same distance). So, in summary - the size of the metal matters, and the distance matters, but it is a formula with several cutoffs, whether or not that formula is similar to the one proposed within cutoff limits.

 

If you want to get technical - 'surface forces' are no more real and no less real than 'surfaces' themselves. At the quantum scale, of course, everything is electromagnetic and weak and strong interactions, and Pauli exclusion, and there are no clear boundaries between one object and another because everything is particles/waves/fields. But we're working at the continuum scale.

That was a joke... Although... bosonspren, I say Tiny, metal bosonspren

 

I Read not a long time ago that they Brandon and he was not sure about how it worked 100% himself so I am going to say that it probably is just a complicated thing that nobody int he book understands because they would have ot know more than tha author.

So we need to make a working theory and explain it to Brandon

[Gagylpus]

As can be seen, at the "visibility" limit (barely visible line) the produced force is still enough to negate gravity. Presumably, the Allomancer cannot push on the metal he cannot see/feel, which produces a cutoff in power levels. Likewise, there is a limit of force produced by an allomancer while pushing that is independent of metal size - otherwise something the size of Kredric Shaw would have been enough to launch into orbit ( when compared to the size of the metal ingot), even if the distance remained the same (that is, one stopped pushing at the same distance). So, in summary - the size of the metal matters, and the distance matters, but it is a formula with several cutoffs, whether or not that formula is similar to the one proposed within cutoff limits.

 

There you have it... I bow to your superior knowledge of the Mistborn books.

 

 

That was a joke... Although... bosonspren, I say Tiny, metal bosonspren

 

Those poor W-bosonspren and Z-bosonspren, so symmetry broken and slow compared to their cousin the photonspren! I feel for them. And the gluonspren. You can always count on them to stick together.

[Wonko the Sane]

I'd like to add that many of the effects achieved in the book would be impossible if Allomancy was directed only from the Allomancer's center of mass. It seems likely that the Allomancer has a limited degree of control over the exact point from which she pushes and pulls, but that exerting this control consciously is relatively difficult. Instead, It would more often remain in the hands of the "instinctual" control of all the little variables in Allomancy that the books are so fond of referencing.

[Ete'ni]

Here we go: Whiskey and Magic!

 

Fortunately I didn't have classes in Phisics in ages, and I couldn't read all the staff... I think that Allomacers can adjust their pushes, so if Zane pushes right below him, he'd start up but there's also this falling thing, and if he can push only that hard as not not fall and constantly, he'd be able to pull the stunt. And we know Zane had extra-boost to his steelpushing resulting in the precision.

 

But yeah, I'm still sure that everything is about Whiskey and Magic.