Jump to content

Allomantic Friction


killersquirrel59

Recommended Posts

NOTE: THIS QUESTION HAS NOW BEEN ANSWERED DIRECTLY BY BRANDON. ANSWER CONFIRMED THAT ALLOMANTIC PUSHES AND PULLS DO GENERATE FRICTION. SKIP TO PAGE 2 TO SEE THE QUOTE.

 

This debate came up in another thread and is somewhat out of place there, so I thought I'd bring it up in a new post since it's an interesting question in its own right.

 

Simply put, do allomantic pushes and pulls create friction? Several in the other thread have contended that they do not. I contend that they do. I'd like to put it to the community and here the reasoning of all concerned.

 

Here is my argument for why they do:

 

  • Vin and Kelsier are able to keep a coin suspended between them by both pushing on it. If there was no friction, this could not happen, the coin simply falling as normal due to gravity. 
  • Multiple anchor points: If there was no friction from an Allomantic push, multiple anchor points would be largely meaningless, as any push not directly beneath you would slide right off. 
  • Dropping coins to jump: Same argument as multiple anchor points. The coin would only provide a firm enough anchor to jump from if there was sufficient friction to keep it in place. This would require friction both from the top and the bottom. Without friction, Allomancers could only use coins to jump straight up, not at angles.

 

Those are my main points. I'd be interested to see what is made of them.

Edited by killersquirrel59
Link to comment
Share on other sites

  • Vin and Kelsier are able to keep a coin suspended between them by both pushing on it. If there was no friction, this could not happen, the coin simply falling as normal due to gravity. 

Yes they could, if they were both pushing towards each other and slightly upwards the combined upwards force from their pushes could counter gravity.

 

 

 

  • Multiple anchor points: If there was no friction from an Allomantic push, multiple anchor points would be largely meaningless, as any push not directly beneath you would slide right off. 

Not sure what you mean here, slide off of what? The object would still have friction with the ground.

 

 

 

  • Dropping coins to jump: Same argument as multiple anchor points. The coin would only provide a firm enough anchor to jump from if there was sufficient friction to keep it in place. This would require friction both from the top and the bottom. Without friction, Allomancers could only use coins to jump straight up, not at angles.

It would still have friction with the ground, which is what is needed, my response would be that it's impossible to jump off of a coin that isn't on the ground, therefore the grounds friction must be what is preventing the coin from moving and so providing a stable anchor.

Link to comment
Share on other sites

Yes they could, if they were both pushing towards each other and slightly upwards the combined upwards force from their pushes could counter gravity.

This only works if it is possible to vary the force of a push far more minutely than we've seen proven, not to mention essentially pushing on it twice each (once straight out to generate enough force to crush the coin between them and again very slightly at an upward angle to prevent it falling to gravity). This degree of precision seems extremely unlikely given that this happened accidentally in the middle of a battle.

Link to comment
Share on other sites

This only works if it is possible to vary the force of a push far more minutely than we've seen proven, not to mention essentially pushing on it twice each (once straight out to generate enough force to crush the coin between them and again very slightly at an upward angle to prevent it falling to gravity). This degree of precision seems extremely unlikely given that this happened accidentally in the middle of a battle.

It requires no precision, it could happen by accident, the coin just needs to be the right height above them when they both push on it, the allomantic push force travels in a straight line, so two pushes like you suggest would be completely impossible.

But if the coin were slightly above both allomancers the line between them and the coin would have a vertical component, add those two vertical components together and you get the total upwards force they generate, if that upwards force is equal to gravity then the coin will be suspended.

Link to comment
Share on other sites

No one's arguing that it isn't highly improbable for the coin to be suspended in that way, I don't think. Simply that it is possible, just about as possible as it being perfectly between the two.

 

And I believe you're misunderstanding the scenario Voidus proposes, squirrel. It's not that both are Pushing the coin twice, but instead that the coin is simply slightly higher than their centers of gravity. If you imagine a straight line connecting Vin and Kelsier, the coin would just be a smidgen above it, enough that both of their Pushes are impelling the coin upward at a slight angle, rather than parallel to the ground.

 

EDIT: NINJAAAAA!  :ph34r:

Edited by Kurkistan
Link to comment
Share on other sites

That logic only makes sense if both can push on only a part of the object, which we know they can't. Even so it still wouldn't work. The reason that force can keep an object suspended is friction between the forces pushing on it. It's a basic physics function to measure the coefficient of friction between two opposing forces on a given object. If the static coefficient of friction between the coin and what it is contacted is effectively 0 as you put forward, the coin would fall. The only possible way this could work without friction is if the two opposing forces were not actually pushing on the coin but rather pushing on each other, thus creating a sort of cloud the coin could rest on, but we know that isn't how Allomantic pushes work. 

Link to comment
Share on other sites

Okay then, thought experiment:

 

What happens if you get a ping-pong ball and place it directly above a nice big air jet? It's suspended.

 

What if you make it so that, rather than the air jet pointing directly upwards, it's pointing off at a bit of an angle? The ball rather quickly gets shot off and falls.

 

What, though, if you get a second air jet at a similar (if reversed) angle , such that the two jets intersect in the air? If you do it right, the ball should be suspended between them.

 

This keeps on working as you make the angles more and more sharp until the point where the jets are shooting parallel to the ground, at which point gravity generally wins—though there's a tad of air friction in this case, so probably a bit less than parallel, I think; still, the point stands.

 

P.S. And of course distances and amounts of force and all all create delightful complexities for this (a pair of actual jet engines would need quite a bit of distance between them for a "shallow" suspension, for instance). But an object being suspended against gravity by two forces that don't provoke much friction is quite thoroughly "a thing" that can and does happen.

 

---

 

This isn't a two-force (Push v. Push) problem. It's a three-force problem, so we're allowed to direct some Push energy upwards to counteract gravity.

Edited by Kurkistan
Link to comment
Share on other sites

That logic only makes sense if both can push on only a part of the object, which we know they can't.

 

Kelsier Pushes only one end of a metal bar, while Pulling on the other end, and Zane can hover using a single coin (implying he's pushing on at least three sections of it, else he'd fall over). Inquisitors also see tons of little lines to things made of metal. I definitely think pushing on a specific part is possible.

Link to comment
Share on other sites

It is specifically stated several times in TFE that it is not normally possible when Kelsier is teaching Vin. Kelsier's ability to do so is supposed to be a pseudo impossible Savant ability and is noted as such. Hovering is never stated as requiring 3 anchor points, only that it makes it way easier. Zane is just stupid good at Steel pushing (he was spiked for Allomantic steel on top of being Mistborn remember).

Link to comment
Share on other sites

It's all to do with vector forces, you need to split the forces on the coin into their component parts, each allomancer is pushing towards the coin, the line of force between the allomancer and the coin makes some angle relative to the ground, now as long as this angle is not 0 (eg. as long as the coin does not lie directly even with the allomancers but instead is slightly above or below their center of gravity) then these forces will have a vertical component in addition to the horizontal component, now assuming the allomancers are of similar strength, then their forces will be equal in magnitude and the horizontal components will be opposite in direction, the horizontal components will then cancel out, leaving only the vertical components to be considered.
If the vertical component is downwards (The coin is below their centre of mass) then the coin will be pushed downwards by both the force of gravity and the allomancers, falling faster than normal.
If the vertical component is upwards (The coin is above their centre of mass) then the coin will be pushed downwards by gravity but upwards by the allomancers, if this upwards component is equal and opposite to the force of gravity then the coin will be suspended.

Link to comment
Share on other sites

It is specifically stated several times in TFE that it is not normally possible when Kelsier is teaching Vin. Kelsier's ability to do so is supposed to be a pseudo impossible Savant ability and is noted as such. Hovering is never stated as requiring 3 anchor points, only that it makes it way easier. Zane is just stupid good at Steel pushing (he was spiked for Allomantic steel on top of being Mistborn remember).

 

Hovering mathematically requires three anchor points. You can do it with one, but only if you never encounter a horizontal force. The slightest breeze would push you over. Zane definitely had to be pushing on three different parts of the coin.

 

There's this WoB that stronger Allomancers get more precision with their Pushes and Pulls (Zane's spike having given him more precision),

sporkify (18 October 2008)

How much control do Allomancers have over pushing and pulling metals?

Brandon Sanderson (20 October 2008)

Depends on the Allomancer. Zane and Kelsier were both unusually skilled in this area, and represent the higher end of what is possible.

, which is definitely not the same thing as it being a pseudo-impossible savant ability. I imagine anyone could have done what Kelsier did and Push on one end of a huge metal bar, but only a few could do what Zane did and Push on three relatively close points on a coin and keep perfectly in balance and hover.

 

Again: if you can't push off-center of a piece of metal's center of mass, Inquisitors should not have been able to read metal plates (since they'd only have online pointing to the center of mass, but instead they had tons of little lines). I was under the impression you Push/Pull by tugging/pushing on one of the metal lines, based on this WoB:

Pushing and pulling metals is basically telekinesis, right? But by making it center of mass, you can only pull directly towards yourself or push directly away from yourself... Number one: it’s vector science. It has one foot in sciences. Number two: it feels very natural to us because this is how we manipulate force ourselves. Number three: it limits things so much that it forces creativity upon the characters. There’s that sweet spot, where they can be creative and do cool things, where it doesn’t become too limited, but it also keeps you from having too much power in the hands of the characters, so they are still being challenged. I’m looking for all that, and on top of that I want to have good sensory ways to use magic. I don’t want to have two wizards staring at each other, and then be like “and they stared at each other very deeply! And then they stared harder!” I don’t want it all to be internal, which is where the lines for the metals came from. You see something, you push it forward. The pulses that some of the allomancers use, they’ll hear. I wanted sensory applications.

 

So Inquisitors could just Push/Pull on one of the various little lines they see and they'd Push something's non-center of gravity.

Edited by Moogle
Link to comment
Share on other sites

No, the coin scenario is not possible without friction for any meaningful amount of time, because if it was suspended only by a slightly upward push, the coin would be in a pposition of unstable equilibrium. I'm talking about the physical meaning of it. Its derivative is zero, but it is a local maximum. As soon as the coin moves a tenth of millimeter under its position, the upward push would diminish (as can be easily seen by trigonometry; it would change the angle of incidence of the push), and the coin would fall down. if it moves upward, the upward push would increase, pushing it more up until it flies away. if it moves laterally, it gets thrown laterally.

 

First and weakest argument, the likelyhood of something like this happening with such a precision is of the order of one in billions of billions. Let's do some math. kelsier can push enough to lift himself and another person, so let's assume he can push 200 kg.  a coin only wheight a few grams, let's make it 4 for the sake of simplicity. so kelsier's push would need to only convey 2 grams of upward push (the other 2 are given by vin's push, in the simple case this is simmetric). that's 1/10000  of the total push. that requires that the sinus of the angle between kelsier and the coin is approximately one thousandth of degree. if kelsier is 10 meters away from the coin, that would mean that the coin is lifted by exactly 0.1 millimeters compared to the perfectly horizontal line. if the coin was lifted by 0.2 mm, it would shot upwards with a starting acceleration of 1 g. even 0.01 mm would start giving it an acceleration of 0.1 g. But as it goes higher, the upward force increases, and the coins sped up. once it moves 0.09 mm, it already accelerates at 1 g. And to move 0.1 mm by accelerating at 1 g starting from standing still, you need roughly 1/20 of second. that's not taking into account that the acceleration would be growing progressively. So, if we want the coin to hover in the air for a few seconds, we need it to be placed within a few hundred nanometers from the point of equilibrium. that's a thousand atomic radii. and the slightest gust of wind - what I say, just the very brownian motion even if the air was perfectly still - would push it out of place.

 

But, even more convincing: the coin was moving, then it stopped in midair. so there must have been a force acting on it to place it there, a  force that put the coin back in place if it get moved by small amounts. that force do not exist: we demonstrated before that if the coin underwent the slightest movement, it would exit the equilibrium. so, while it would theoretically possible for the coin to remain there if it was placed with extreme accuracy, it is impossible that it got caught there. Well, unless it also was thrown against the force pushing the coin out of there, with exactly enough kinetic energy to reach the unstable equilibrium and stop there. that's the equivalent of launching a ball with exactly enough speed to climb a slope and stopping on top of it without falling on the other side. with the top of the slope being less than one micrometer wide.

 

So, no, that's not going to happen. I always arbitrarily assumed that allomantic pushes had no friction, but the coin episode indeed proves it does. That's it.

Link to comment
Share on other sites

Probability is not in favour of the coin being suspended between two allomancers no matter how it works, friction only provides a slightly greater leeway, not to mention the myriad of problems you'd get into trying to apply friction to a situation like this, the force is acting on the objects centre of gravity, a point, not on its whole surface, so where is the frictional force applied? What's the coefficient? If the friction is generated by the allomancers then why do they maintain ease of movement, they should be undergoing equal friction when Steelpushing.

Link to comment
Share on other sites

Very well, if we're to insist that varied and subtle Pushing on multiple points of the coin as necessary in order to achieve this effect, then I guess I'll have to be so crass as to cite actual evidence.

If you would care to open a copy of TFE, you will find Vin--on her very first night as a practicing Mistborn and her first time using Allomantic steel--hovering above a single coin. Kelsier is in no way surprised by this and explains this as making multiple minute adjustments, iirc. Pushing can be and is subconsciously quite sophisticated and subtle even as a matter of course, then, rather than needing super-awesome training/abilities.

The surprising thing about Zane is not and never was his ability to hover above a single coin. Rather, it was his ability to do so at low-altitude. During Vin's initial training we learned that its very hard to be so precise while also using less than the full force of a Push: while allomancers can vary the strength of their Pushes/Pulls, it is hard to do so. So Vin ended up hovering at her maximum possible height above the aforementioned coin. Zane, on the other hand, managed to say steady just a few feet above it, and precisely control how his body shifted, to boot.

@Voidus

Also, I for one doubt the idea that Pushes/Pulls are applied all and only to centers of gravity as points. Any point force is approaching infinite, so there has to be at least some distribution of the force over the object.

Link to comment
Share on other sites

No, the coin scenario is not possible without friction for any meaningful amount of time, because if it was suspended only by a slightly upward push, the coin would be in a pposition of unstable equilibrium. I'm talking about the physical meaning of it. Its derivative is zero, but it is a local maximum. As soon as the coin moves a tenth of millimeter under its position, the upward push would diminish (as can be easily seen by trigonometry; it would change the angle of incidence of the push), and the coin would fall down. if it moves upward, the upward push would increase, pushing it more up until it flies away. if it moves laterally, it gets thrown laterally.

 

First and weakest argument, the likelyhood of something like this happening with such a precision is of the order of one in billions of billions. Let's do some math. kelsier can push enough to lift himself and another person, so let's assume he can push 200 kg.  a coin only wheight a few grams, let's make it 4 for the sake of simplicity. so kelsier's push would need to only convey 2 grams of upward push (the other 2 are given by vin's push, in the simple case this is simmetric). that's 1/10000  of the total push. that requires that the sinus of the angle between kelsier and the coin is approximately one thousandth of degree. if kelsier is 10 meters away from the coin, that would mean that the coin is lifted by exactly 0.1 millimeters compared to the perfectly horizontal line. if the coin was lifted by 0.2 mm, it would shot upwards with a starting acceleration of 1 g. even 0.01 mm would start giving it an acceleration of 0.1 g. But as it goes higher, the upward force increases, and the coins sped up. once it moves 0.09 mm, it already accelerates at 1 g. And to move 0.1 mm by accelerating at 1 g starting from standing still, you need roughly 1/20 of second. that's not taking into account that the acceleration would be growing progressively. So, if we want the coin to hover in the air for a few seconds, we need it to be placed within a few hundred nanometers from the point of equilibrium. that's a thousand atomic radii. and the slightest gust of wind - what I say, just the very brownian motion even if the air was perfectly still - would push it out of place.

.

 

Not necessarily. In a different thread I postulated that pushing/pulling worked with an inverse square law (like electrostatics). If you assume that is the case then you will find the upward force produced by the two coinshots (at a distance of d to each of them) is proportional to r/(r^2 + d^2)^(3/2), where r is the distance above the centre of mass plane. As you can see in the following graph (in which d=1, mg =0.3), the equillibrium point will be stable as long as the equillibrium distance is large enough (over the maximum value of F, which is at 1/sqrt2 for the case of the graph).

 

Verticle Force (F) vs height ( r): (sorry, I don't know how to make it bigger)

F = r/(r^2 + 1)^(3/2) - 0.3

post-11878-0-66519400-1410996751_thumb.p

 

This would also explain why it stopped halfway between the two—as the horizontal midpoint is also a stable equillibrium point.

 

Funnily enough, this exact problem (without the gravity part), was a question for a homework assignment in my Electrodynamics class today (phrased as an electrostatic force problem of course). :lol:

 

I think that this explanation makes a lot more sense then that there is somehow friction caused by the pushes. Friction between physical objects makes sense. But as far as I know, there is never friction between forces and objects (like EM forces). Plus inverse square laws are a somewhat natural assumption and explain several other pushing phenomenon (like how it gets weaker as you get further away).

 

EDIT: I do realise I forgot to account for the unstable equilibrium in the horizontal axis in the plane perpendicular to the axis connecting the two allomancers (i.e., the x axis, if up/down was the z axis and the allomancers were along the y axis), which my theory would not be able to account for. This would still make the occurance unlikely, but it would still be a lot more likely than without the inverse square law. IIRC, the book did say most of the coins were deflected when they did this, so it could have just been a chance event.

 

EDIT2/disclaimer: Because of said assignment, I only got an hour of sleep last night (it was due today), so I apologize if it turns out that any/all of my math is wrong. :unsure:

Edited by Stormwalker
Link to comment
Share on other sites

Good point stormwalker. I like people responding to accurate mathematical models with even more accurate mathematical models. My nerd scientist side revels in this.

Now, the first objection I was going to make was the unstable equilibrium on the horizontal axis, but you already edited this yourself.

I will also point out that, while I do believe that allomantic pushes are inversely proportional to the distance or to its square (allomancers can affect with less strenght objects that are farther away) the pushes of kelsier and vin were capable of deforming the coin. I don't know what kind of stress it would take for that, and I cannot calculate it without knowing the angles and torque moments involved and lots of other stuff, and I'm not familiar with that branch of physics anyway, But I can say for sure that it has to be thousands of times greater than the wheight of the coin. That means that, for the coin not to be pushed upwards, the sinus of the angle of incidence of the push compared to the horizontal must have been lower than 1/1000. That fixes that angle at less than 1/20th of degree. At ten meters away, that translates in a vertical shift of around one centimeter. I didn't take into account the different force of the push with vvarying distance in my original calculation because I assumed the variation in distance was negligible. Well, turns out by taking it into account there is a small island of stability, but it is extremely small, and only on the y axis. Furthermore, my calculation is probably conservative here. A coin cannot wheight more than a few grams, but the push transferred from kelsier to the coin to vin was enough to shove vin backwards, up against a small tree, and then crack the tree trunk. So, the force of the push was more likely at least several tens of kilograms, which would reduce the stability area to a fraction of a millimeter.

 

While I also always assumed that allomancy carried no attrition because forces normally don't, I think there are lots of instances proving that allomantic attrition does exist. not only that single coin episode. there are many times a character can balance with an allomantic push over a single coin. Not a tripod, a single one. think about it: you're up in the air supported by something with an area less than a square centimeter; it's like walking on stilts twenty meters long and  with narrow end, pretty difficult by itself. but if there is no attrition, then there is nothing to prevent you from sliding across the surface of the coin. it's still like having stilts, but no the bottom of the stilt is also extremely well greased. difficult to believe if the coin do not also offer some support against lateral forces, which can only be justified by attrition.

And I can't remember the specifics, but I'm pretty sure that there are other scenes with characters pushing and a single coin trapped between them. even the proponents of the "it is possible" theory admit it's extremley unlikely; can it happen several times? Doubtful.

So, I think allomantic pushes are better explained by assuing pushing against an object also causes some friction on it. Not much, or there would be many more coins trapped between pushes. I'd say somewhere around a friction coefficient of 1/100, although this is just a guess.

Link to comment
Share on other sites

Good point stormwalker. I like people responding to accurate mathematical models with even more accurate mathematical models. My nerd scientist side revels in this.

Now, the first objection I was going to make was the unstable equilibrium on the horizontal axis, but you already edited this yourself.

I will also point out that, while I do believe that allomantic pushes are inversely proportional to the distance or to its square (allomancers can affect with less strenght objects that are farther away) the pushes of kelsier and vin were capable of deforming the coin. I don't know what kind of stress it would take for that, and I cannot calculate it without knowing the angles and torque moments involved and lots of other stuff, and I'm not familiar with that branch of physics anyway, But I can say for sure that it has to be thousands of times greater than the wheight of the coin.

 

I don't think allomantic pushes would put any stress on the coin (other than minute tidal forces). In this, I would imagine the force acts analagous to gravity (which is itself analagous to electrostatics, classically): gravity acts on every single molecule of an object identically (i.e., the same acceleration). Thus it will never cause stress to the object (again, excluding tidal forces). Even if you were in a spcae with two identical, massive gravitational fields in opposite directions, there would be no stress on your body—the forces would cancel out at the atomic level. It should be noted that your body can't even sense gravity: when you feel your 'weight' pulling you downwards, what your inner ear is really feeling is the reaction force of the ground upward (the normal force). This reaction force acts directly on the bottom of said object, and is transmitted throughout the body via a compressive stress. (I should note here, I am not that sure on the physics of stresses either, so the terminology might be wrong, but I'm fairly sure the general principal is correct).

 

Similarly, as the coin is small, tidal forces should be negligible, and so the two pushes act on each molecule of metal individually and identically. In each of those molecules the two forces cancel out exactly, and so there is no net force on each molecule of the object. Thus there is also no stresses, and hence no deforming of the coin.

 

 

That means that, for the coin not to be pushed upwards, the sine [sic] of the angle of incidence of the push compared to the horizontal must have been lower than 1/1000. That fixes that angle at less than 1/20th of degree. At ten meters away, that translates in a vertical shift of around one centimeter. I didn't take into account the different force of the push with vvarying distance in my original calculation because I assumed the variation in distance was negligible. Well, turns out by taking it into account there is a small island of stability, but it is extremely small, and only on the y axis. Furthermore, my calculation is probably conservative here. A coin cannot wheight more than a few grams, but the push transferred from kelsier to the coin to vin was enough to shove vin backwards, up against a small tree, and then crack the tree trunk. So, the force of the push was more likely at least several tens of kilograms, which would reduce the stability area to a fraction of a millimeter.

 

I honestly didn't get how this followed from the previous statement about deforming the coin. It should be noted, in my model, the island of stability was for r > r_0 (where r_0 is point at which the verticle allomantic force is at a maximum), and thus is infinite. I do concede however, that, once one puts in the proper constants, the equillibrium position will probably be a lot more than a metre away from horizontal (but this just a guess, it is impossible to know without actually knowing the constants), as the maximum force is going to be a lot greater than mg.

 

As to your theory, if pushes/pulls caused friction, that would mean you could levitate an object by pulling and pushing on it at the same time (for a mistborn). Fine control over the position could then be achieved by increasing the strength of either the push or the pull, while keeping the other constant. I would think this would be a really useful application, as well as one that would be fairly easily discovered, yet it was never mentioned in the books.

 

Lastly, for interests sake, I wonder if you could derive an island of stability in the horizontal direction via special relativity. In my model, pushing is like the E field. Now, once you have electrostatics and you apply special relativity, you get the magnetic force as well (I should note I don't really know exactly how this works, but I should learn it in my aforementioned EM course by the end of the semester!). Thus applying special relativity to pushes/pulls (and assuming allomantic strength is invariant like charge is), one should get a corresponding magnetic effect. Thus, the analogy between EM and iron/steel would be complete. By applying this, we see that when the coin moves slightly to the side, the force on it (and thus the corresponding 'steel field') changes. A changing steel field then produces a magnetic steel field. The moving metal in the magnetic steel field then produces a force. I'm not exactly sure where this force would point, but it would make sense that it would oppose the movement (to offset the energy stored in the magnetic steel field). Hence there would be a tiny restorative force, which could create an even tinier island of stability. Even a very small island of stability is better than a single point (and would actually make it possible for it to happen by random chance). :P

 

EDIT: two lastly's :lol:

Edited by Stormwalker
Link to comment
Share on other sites

We do know that allomantic pushes put stress on the coin. Later that same scene Kelsier gives here the notably bent and crushed coin as a souvenir to keep. Allomantic forces most definitely put stress on the pushed object.

 

By the way, thank you so much to both Stormwalker and King of Nowhere for being the math nerds I'm not and being able to have this full physics debate. I haven't taken physics since high school and was trying really hard to remember lessons from 9 years ago and failing rather miserably.  

Link to comment
Share on other sites

We do know that allomantic pushes put stress on the coin. Later that same scene Kelsier gives here the notably bent and crushed coin as a souvenir to keep. Allomantic forces most definitely put stress on the pushed object.

 

 

Hmm... Maybe the tidal forces aren't as negligible as I thought then. A quick calculation shows that, for the mistborn at a distance of 10m from each other, with the coin (radius 1cm) directly in between, the tidal forces on the coin (which would be a compressive force) would account for about 1/100th of the force of each allomantic push on the coin itself. So the coin is compressed with only 1/100th of the force that Vin hits the tree (and cracks it) with. Perhaps this is enough to cause the coin to deform on its own? I don't know how much force it takes to deform gold, but I've heard it is a relatively soft metal.

 

 

By the way, thank you so much to both Stormwalker and King of Nowhere for being the math nerds I'm not and being able to have this full physics debate. I haven't taken physics since high school and was trying really hard to remember lessons from 9 years ago and failing rather miserably.

Well, it's nice to finally have a useful application of all this physics knowledge. :P

Edited by Stormwalker
Link to comment
Share on other sites

do we know that those coins were made of gold? allomancers used the smaller denominations of coins, so it would seem unlikely that it was a gold one; while in a later scene kelsier files some gold from a coin to have vin experiment it, i doubt those smaller coins used for throwing are gold. copper and nickel are more likely. and tidal forces can only justify a few kilograms of force, which should not be able to bbend a coin, unless they were really thin. so it must mean that the force is not uniformely applied to all the metal. actually, that makes much more sense if we imagine the allomantic pushes as two thumbs pressing on the coin from opposite directions, flattening it. So, from those facts it appears that allomancy do not act like gravity or electromagnetism, but rather like an invisible hand pushing and pulling. being connected to the ccognitive and spiritual realms rather than the mere laws of physics, it makes kinda sense.

 

Now, back about equilibrium, and disregarding horizontal one: yesterday I didn't look at the formula in detail because it was 3 am and I wanted to go sleep, but now I did and I see your point. There is, indeed, a stable equilibriium point, where the upward push of both allomancers has become so weak with distance that it is just enough to support the coin. go upward, the coin falls down. go down, the coin is pushed up. That's the point at 1.25 in the x axis (i don't suppose the scale is significant). However, we have established that the horizontal push was of the order of hundreds of kg. so, in order to reach a point where the allomantic pushes were weakened by distance,  the coin must have been WAY up in the air. we're talking a few tens of meters, maybe even one hundred*. So the coin would not be "between" them in any way that could fit the description of the scene.

There is also a second point of equilibrium closer to the horizontal line, the one at x=0.4 in your graph,  but that's unstable. if the coin goes up, the upwaard forces increases and it gets pushed eventually to the stable equilibrium. if it goes down, the downward forces increase, until it falls to the ground. I was mislead by said factor of being 3 am into thinking that there was a small stable area  around that point, but no, it doesn't, as your graph itself proves.

So, basically, your graph is perfectlyy correct in expplaining the upward force, but it has a wrong scale. since the horizontal force acting on the coin is much greater thn the coin itself, the area with a net upward force would become much greater. an up-to-scale graph would have the first equilibrium point, the unstable one, at x=10-4 m (or so, depennding on accuracy of assumptions), while the stable equilibrium would be at x=100 m or something.

 

*actually, if an allomancer can push a coin with dozens of kilograms from a few meters, but cannot push a coin at 100 meters, it means that the decrease is not simply quadratic. it is much more chaotic than that. I think a quadratic drop could be a good base for the force of the push, but in addition one must also use another factor that takes into account the ease of sensing the metal. The farrther a metal is, the less  you can sense it, and that decrease your push, in addition to the effect of the distance. sensing is also affected by the medium between you adn the metal, and by the sie of the metal, and many other factors, so it would be pretty difficult to calculate.

In addition, I don't think the force is quadratic with distance either. there is no proof whatsoever that by pushing yourself against a heavy anchor that is one meter away you can get four times the force you can get at 2 meters, and everything would lead to believe otherwise. In fact, thinking about it, it seems as long as objects are reasonably close, allomancers can push on them at full strenght, with barely any reduction in going from 1 centimeter to 5 meters. But then it drops pretty quickly. So I think now an inverse quadratic dependence on distance is not a realistic model for allomancy. Probably an exponential decay of some sort would work better to describe how allomantic push diminishes with distance. (underlined it cause long post with technical stuff that many people may skip, so that way they would notice the conclusion anyway).

Link to comment
Share on other sites

As far as I know there is actually no evidence in book canon noting that the power of a push decreases with distance at all. I could be wrong but I don't remember anything specific.

it is mentioned a few times kelsier and vin balancing on top of a coin by pushing on it until their push is too weak to propel them further up. that strongly implies that pushes get weaker with distance. I'm pretty sure it is mentioned directly somewhere too, but can offer no proof of it

Link to comment
Share on other sites

it is mentioned a few times kelsier and vin balancing on top of a coin by pushing on it until their push is too weak to propel them further up. that strongly implies that pushes get weaker with distance. I'm pretty sure it is mentioned directly somewhere too, but can offer no proof of it

Huh. I do remember those. I don't know why that never clicked for me before. It makes sense I mean. Maybe I was thinking of it simply as a measure of absolute range (i.e. They can push on it at 200 meters but cannot at 201 meters so they keep starting to fall and pushing back up above the threshold) but this explanation makes far more sense. 

Link to comment
Share on other sites

do we know that those coins were made of gold? allomancers used the smaller denominations of coins, so it would seem unlikely that it was a gold one; while in a later scene kelsier files some gold from a coin to have vin experiment it, i doubt those smaller coins used for throwing are gold. copper and nickel are more likely. and tidal forces can only justify a few kilograms of force, which should not be able to bbend a coin, unless they were really thin. so it must mean that the force is not uniformely applied to all the metal. actually, that makes much more sense if we imagine the allomantic pushes as two thumbs pressing on the coin from opposite directions, flattening it. So, from those facts it appears that allomancy do not act like gravity or electromagnetism, but rather like an invisible hand pushing and pulling. being connected to the ccognitive and spiritual realms rather than the mere laws of physics, it makes kinda sense.

 

Yeah, I agree my tidal forces argument probably isn't enough to really deform the coins that much. But I don't like the thought of it acting like an external pressure, because then it doesn't really make sense when you consider that you can push on different parts of the metal seperately (we know Kelsier could, even if it was very difficult).

 

 

Now, back about equilibrium, and disregarding horizontal one: yesterday I didn't look at the formula in detail because it was 3 am and I wanted to go sleep, but now I did and I see your point. There is, indeed, a stable equilibriium point, where the upward push of both allomancers has become so weak with distance that it is just enough to support the coin. go upward, the coin falls down. go down, the coin is pushed up. That's the point at 1.25 in the x axis (i don't suppose the scale is significant). However, we have established that the horizontal push was of the order of hundreds of kg. so, in order to reach a point where the allomantic pushes were weakened by distance,  the coin must have been WAY up in the air. we're talking a few tens of meters, maybe even one hundred*. So the coin would not be "between" them in any way that could fit the description of the scene.

There is also a second point of equilibrium closer to the horizontal line, the one at x=0.4 in your graph,  but that's unstable. if the coin goes up, the upwaard forces increases and it gets pushed eventually to the stable equilibrium. if it goes down, the downward forces increase, until it falls to the ground. I was mislead by said factor of being 3 am into thinking that there was a small stable area  around that point, but no, it doesn't, as your graph itself proves.

So, basically, your graph is perfectlyy correct in expplaining the upward force, but it has a wrong scale. since the horizontal force acting on the coin is much greater thn the coin itself, the area with a net upward force would become much greater. an up-to-scale graph would have the first equilibrium point, the unstable one, at x=10-4 m (or so, depennding on accuracy of assumptions), while the stable equilibrium would be at x=100 m or something.

 

Yeah, I sort of realized this one myself a few posts back. Of course, in theory, it really does depend on the constants in the equation (which we don't know), and more importantly, whether it is a inverse-square law exactly, or some modified version of one. I mean, you could always come up with a force equation that has the properties necessary to cause this behaviour. My point was more along the lines that the existence of such a stable equillibrium point would depend on exactly what the force is as a function of distance (or at least, if anyone asks, that was my idea from the begining :P ). Of course, I would think it is unlikely it actually works with such a contrived law. Using some meta-analysis, I feel that B.S., if he has actually made a force law for pushes, would have probably made it either an inverse-square or exponential, as you suggested (as those are what arise in nature).

 

However, that is not to say that I agree with the idea of allomantic friction. I don't think you have any other evidence besides this one event for the presence of friction, and frankly, it just seems too weird for me to accept on that alone. In particular, if allomantic pushes had friction, wouldn't that resist sideways movement when there is only one push on a coin as well? IIRC we've seen many a time (or at least one time) where somebody was pushing off of a coin, which was then pushed away to the side by another allomancer. The coin in this scenario would then have regular friction plus allomantic friction—you'd think it would be hard if not impossible to move with a similar strength force (think of moving a coin trapped between two slabs of concrete). Also with Zane balancing on a coin, I agree with the others that it is more likely him pushing on 3 parts of the coin at once in order to balance himself.

 

In any case, I agree it's been awesome to have a real physics debate on this. :D

Link to comment
Share on other sites

Guest
This topic is now closed to further replies.
  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...