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The Impossible Physics of Allomancy


Pagerunner

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I'm sure you guys are already aware, but the WoA ch. 8 annotation says this that says anchor quality is a pretty big consideration. 

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The second reason for metal vials is more simple. Allomancers with the right powers can Push or Pull on sources of metal–the larger the metal source, the harder the Allomancer can Push on it. So, little flakes of metal make a terrible Anchor, and so if you’re caught wearing your vials, you aren’t giving much of an advantage to your enemies.

 

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On 6/9/2017 at 3:06 PM, Argent said:

You are, actually, when you are very very young. It's something you learn to anticipate and control as you grow up. Allomancers, even experienced ones, don't have anywhere near as much practice slinging items (or themselves) around as they do moving their limbs. 

Pagerunner's point is that the force changes instantaneously in some cases, but *not* in others. He's basically just looking for a crazy mathematical way to bridge the gap between those observations.

It's not a matter of different skill levels. You can pick the same character and find instances of both. He was just saying that the difference between Wax and Vin is more stark.

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  • 2 weeks later...
On ‎6‎/‎9‎/‎2017 at 3:06 PM, Argent said:

You are, actually, when you are very very young. It's something you learn to anticipate and control as you grow up. Allomancers, even experienced ones, don't have anywhere near as much practice slinging items (or themselves) around as they do moving their limbs. 

Zane, specifically, is really good with steel, and Vin's ability to (nearly) match him is an indication that so is she. Wax... he doesn't often use his pushes in such precise controlled fashion, he usually just either throws himself about or adds acceleration to his bullets. He doesn't do fancy work.

As for the rest of your comments... It looks like you interpreted my reply as dismissive, and maybe insulting? It wasn't meant to be that way, and so I apologize. All I wanted to say that, similarly to atium's mind enhancement, there is a very clean and easy-to-understand explanation of steel/iron works (i.e. they work like telekinetic limbs) that fits all the evidence, and (at least to me) sounds like it was Brandon's intent with the system. In the face of that, I found that doing extensive math that can only approximate magical components to be... bemusing. 

No offense taken whatsoever. But the whole problem is that the simple explanation falls apart when you think too hard about it. Because a hypothetical steel-arm is massless and infinitely extendable, it will behave differently than an arm in ways that are significant, which we discussed earlier in the thread in the context of pushing against a wall vs pushing a basketball. While on the surface, it may match everything, it requires the underlying behavior to be inconsistent.

If you're using your arms, you need to push off an anchor to propel yourself because your arms can only reach so far, not because you can't push hard enough. When you throw your arms forward unimpeded, you are actually pushing the rest of your body backwards. Try standing against a wall, hands on your chest, back not quite touching the wall. Throw your arms out to full extension in front of you - you'll feel your back contact the wall as your body moves backwards with the force of your push. You don't build up a lot of speed, because your arms get there so quickly and then your body pulls itself together so you don't fly apart. But you are still pushing with enough force to propel you backwards; it just operates for a small amount of time. But that's not what happened for Vin; she wasn't pushed backwards until the coin reached the wall, because she couldn't push with enough force until the coin reached the wall. If you go and stand against the wall again, and move your arms forward slowly enough you don't hit your back against the wall, you wouldn't be pushing hard enough to push yourself off of anything. You'll need to increase your exertion once your hands are on the wall.

When babies surprise themselves with their strength (I've been watching my 6-month-old niece hit herself in the face with her toys, and it never stops being funny!), they're not adjusting their strength, they're going full-bore the whole time like little maniacs. They're surprised, but they've been pushing too hard to begin with. That runs counter to the examples we've seen in Steelpushing, where the force changes even though the Allomancer does not actively change it.

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  • 1 year later...
On 5/29/2017 at 2:24 PM, Pagerunner said:

You know how the physics regarding Steelpushes have always been kind of screwy? (And I don't mean in a rotational dynamics kind of way.) I've dove deep into the math, looked at five different models I've seen proposed, and debunked them all. I've also developed my own model, which will all the perceived inconsistencies with Allomancy. I don't like my model, but it works.

Here's my model in a nutshell:

  • An Allomancer does not directly define either the speed of their Push or the force of their Push.
  • They define the "strength" of their Push, which in turn is used to find both the maximum speed and the maximum force they can Push.
  • Whichever of the two limits comes into play first limits behavior, and the most peculiar effects of Allomancy happen when the changing components of the force balance result in switching from one limiting factor to the other.
  • The relationship between maximum speed and maximum force at a given strength is not based in physics whatsoever; it is an entirely arbitrary connection, made so the math matches how we've seen Allomancy function.

The full explanation is attached as a PDF. I try to explain most of the math as I go along, so I don't think you need a thorough understanding of physics to follow along. Please, if anything about the physics is unclear, please let me know.

The Impossible Physics of Allomancy.pdf

 

Your model 1 seems correct. The allomancer determines a force. AFAICT your reason dismissing model #1 is flawed.

Quoting your pdf:

"This is the plainest explanation, but as poor Vin discovers, it is not a good fit, because that model
decouples the Allomancer and the coin."

Exactly. This is due to the normal force. It makes the second term go away. Which is exactly what is observed. As soon as the object an allomancer pushes against is securely anchored, it no longer matters. You are absolutely correct in complaining about the discontinuity. It arises from a model that assumes a full normal force as soon as the coin hits the ground. In reality there will be some deformation. But fundamentally if you introduce a new force (in form of the normal force) a discontinuity is not a problem. It is expected.

But I think you are conflating two things. That the allomancer determines a force does not give him an arbitrary range of forces available.

As far as we can tell, it certainly depends on

 

  1. choice of the allomancer (experienced allomancers can push weakly and all of them can flare their steel)
  2. inherent strength of the allomancer
  3. distance to the object pushed
  4. degree of investiture in the object pushed
  5. mass of the object pushed

And maybe time is also a factor. Hence an allomancer determines (if he is trained well) a force between 0 and the upper limit given by factors 2) - 5)

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  • 2 weeks later...
40 minutes ago, Croaker's Apprentice said:

It's magic; don't worry about it !

All of your equations missed out one very important variable, specifically the honorable literary device known as "hand waving" :)

We definitely understand that it's magic and that every problem could be solved with handwavium. However, the purpose of these conversations is to discuss and theorize how to represent magic with more rigorous math than just a wave of the hand. Leaving it to that wouldn't be very fun.

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1 hour ago, Croaker's Apprentice said:

It's magic; don't worry about it !

All of your equations missed out one very important variable, specifically the honorable literary device known as "hand waving" :)

Brandon tries really, really, really hard to ground his worlds in real-life science wherever possible, and only uses hand waving as a last resort.  The only hand waving example I can think of is that he had to get rid of the red shift from speed bubbles to prevent radiating everyone.  

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Wow, over a decade as a professional controls engineer and I've never had a real need to dust off my old Dynamics and Diff-EQ books, but Allomancy does it? I f-ing LOVE this place! 

 

Can you add the physics/behavioral assumptions to the write-up, for those of us that havent reread Era1 in a while?  I want to go through it with Wax's Crasher trick in mind. I vaguely recall some less than intuitive workings surrounding the Conservations before/during/after Impact events, and Ive never really tried to wrap my head around them in Higgs terms. 

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21 hours ago, Scion of the Mists said:

Brandon tries really, really, really hard to ground his worlds in real-life science wherever possible, and only uses hand waving as a last resort.  

Although, at the end of the day, his heroes (and villains) can do whatever the X-Men can do ;)

Please note I intended that much more as a joke than a criticism ! 

What I love about B's stories (in reverse order of importance) are-

1. The kinetic, super-cool imagery of his action set- pieces/ stunt- filled frenetic- balletic fight scenes

2. The humor

3. The moral wisdom

4.The great characters and emotional heft and power of their sagas

I don't really care how the pseudo-science of Cosmere super-powers works; not being either a physicist or an RPG rules- lawyer, I don't feel the need to 'lift the hood' to see how they work, especially because I don't think they would stand the scrutiny (and nor should they).

The 'true magic' of the stories we love lies in the interface between character journey/development, plot foreshadowing, an element of mystery, and dramatic resolution. I agree that fantasy magic having some delineation and rules is a good thing, but probably the most important thing about magical rules is that they *exist to be broken* (although as I say, the breaking must be properly earned). 

BS himself is hardly above employing a "Deus ex Machina" resolution where warranted - or should we say "Deus ex Caligo" ? - at the end of "Final Empire".

"Magic Before System" as they say...

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52 minutes ago, Croaker's Apprentice said:

I don't really care how the pseudo-science of Cosmere super-powers works; not being either a physicist or an RPG rules- lawyer, I don't feel the need to 'lift the hood' to see how they work, especially because I don't think they would stand the scrutiny (and nor should they).

The 'true magic' of the stories we love lies in the interface between character journey/development, plot foreshadowing, an element of mystery, and dramatic resolution. I agree that fantasy magic having some delineation and rules is a good thing, but probably the most important thing about magical rules is that they *exist to be broken* (although as I say, the breaking must be properly earned). 

Different people have different reasons for liking Brandon's works (or any author) - there are not "true" reasons and "false" reasons for liking a particular story.  Liking (or disliking) a story for its plot is not any more or less valid than liking it for its intricate magic system.  

There are plenty of people on this forum who, like you, don't care about the specifics of the various Cosmere magics and how they work together.  However, there are tons of people who do and who have pried into almost every aspect of them (just look at any signing on Arcanum).  The mechanics behind the Cosmere are so grounded in reality (with a few modifications, or course) and consistent that people on this forum (who are much smarter than me) are able to extrapolate from observations make in some books to correctly predict things in future books, just like real-life science does.  

1 hour ago, Croaker's Apprentice said:

BS himself is hardly above employing a "Deus ex Machina" resolution where warranted - or should we say "Deus ex Caligo" ? - at the end of "Final Empire".

"Magic Before System" as they say...

Despite his heroic efforts to mesh his worlds with reality, there are going to be some situations where that's not possible.  He always puts story first or, as his Zeroeth Law puts it "pick the more awesome choice."  

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22 hours ago, Scion of the Mists said:

Different people have different reasons for liking Brandon's works (or any author) - there are not "true" reasons and "false" reasons for liking a particular story.  Liking (or disliking) a story for its plot is not any more or less valid than liking it for its intricate magic system.  

There are plenty of people on this forum who, like you, don't care about the specifics of the various Cosmere magics and how they work together.  However, there are tons of people who do and who have pried into almost every aspect of them (just look at any signing on Arcanum).  The mechanics behind the Cosmere are so grounded in reality (with a few modifications, or course) and consistent that people on this forum (who are much smarter than me) are able to extrapolate from observations make in some books to correctly predict things in future books, just like real-life science does.  

Despite his heroic efforts to mesh his worlds with reality, there are going to be some situations where that's not possible.  He always puts story first or, as his Zeroeth Law puts it "pick the more awesome choice."  

Hi Scion; I absolutely hear what you say, I just strongly wanted to get across my own feelings on the subject ! I definitely agree it's not a case of right and wrong, though. 

Would also add that, though scientific analysis may be able to predict things in future books, the best predictor of future events is always going to be knowledge of the wonderful cannon that is 'human literature', and specifically here Fantastic literature - which is very much an art, not a science ;)

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37 minutes ago, Croaker's Apprentice said:

Hi Scion; I absolutely hear what you say, I just strongly wanted to get across my own feelings on the subject ! I definitely agree it's not a case of right and wrong, though. 

Would also add that, though scientific analysis may be able to predict things in future books, the best predictor of future events is always going to be knowledge of the wonderful cannon that is 'human literature', and specifically here Fantastic literature - which is very much an art, not a science ;)

Sometimes it's fun to argue with Doyle, other times it's fun to argue with Watson.  Both are valid. 

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1 hour ago, Croaker's Apprentice said:

Hi Scion; I absolutely hear what you say, I just strongly wanted to get across my own feelings on the subject ! I definitely agree it's not a case of right and wrong, though. 

You're absolutely entitled to your own feelings.  But coming into a thread where people have been working for over a year, trying to tease out the intricacies of Brandon's magic system, just to tell them "It's magic; don't worry about it" seems super unnecessary.  

By all means, start a new thread about how people spend too much time digging into the mechanics of the Cosmere, but don't derail this one.  

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15 minutes ago, Scion of the Mists said:

You're absolutely entitled to your own feelings.  But coming into a thread where people have been working for over a year, trying to tease out the intricacies of Brandon's magic system, just to tell them "It's magic; don't worry about it" seems super unnecessary.  

By all means, start a new thread about how people spend too much time digging into the mechanics of the Cosmere, but don't derail this one.  

I'll leave you to it ! (He vanishes in a puff of smoke) 

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The really hard part is giving even a sensible formula for the maximum strength an allomancer can push with. In particular the relationship with distance is odd. For almost any physical influence we find that the strength drops off with the square off the distance. Allomancy clearly does not follow that rule. We have three observations hard to reconcile.

 

  1. pushing duells make sense
  2. pushing up at full power from a close anchor does not kill you
  3. pushing with full force against a close anchor pushes you up swiftly.
  4. there is a maximum height you can support yourself at from a given anchor and that is below the sensing range

That means in effect that the force cannot drop off much until you get relatively close to maximum range. If it depended strongly on range, the weaker allomancer could push back anything as soon as it got close enough.

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1 hour ago, Oltux72 said:

The really hard part is giving even a sensible formula for the maximum strength an allomancer can push with. In particular the relationship with distance is odd. For almost any physical influence we find that the strength drops off with the square off the distance. Allomancy clearly does not follow that rule. We have three observations hard to reconcile.

 

  1. pushing duells make sense
  2. pushing up at full power from a close anchor does not kill you
  3. pushing with full force against a close anchor pushes you up swiftly.
  4. there is a maximum height you can support yourself at from a given anchor and that is below the sensing range

That means in effect that the force cannot drop off much until you get relatively close to maximum range. If it depended strongly on range, the weaker allomancer could push back anything as soon as it got close enough.

In another good post about the physics of Allomancy Jofwu suggested a model that I don't think has been mentioned in this thread: With a force F and distance r, F is proportional to e^-r. It doesn't look like a very natural formula, but it works out very well. See a graph here (the green line represents e^-r, with a constant coefficient). At close range, the force isn't magnitudes stronger like with the r^2 relationship. The force decreases with range at a reasonable rate, approaching zero as the distance approaches infinity. We talk a bit more about this theory in another thread about making a mistborn video game (shameless plug).

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14 hours ago, Artemos said:

In another good post about the physics of Allomancy Jofwu suggested a model that I don't think has been mentioned in this thread: With a force F and distance r, F is proportional to e^-r. It doesn't look like a very natural formula, but it works out very well. See a graph here (the green line represents e^-r, with a constant coefficient). At close range, the force isn't magnitudes stronger like with the r^2 relationship. The force decreases with range at a reasonable rate, approaching zero as the distance approaches infinity. We talk a bit more about this theory in another thread about making a mistborn video game (shameless plug).

Pushing duells make these calculations dubious. If the maximum force an allomancer can push with changes a lot over the distance he can push, there is always an equilibrium point between two allomancers. Hence almost all of the decay in maximum force must be close to maximum range.

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On 12/8/2018 at 10:07 AM, Oltux72 said:

Pushing duells make these calculations dubious. If the maximum force an allomancer can push with changes a lot over the distance he can push, there is always an equilibrium point between two allomancers. Hence almost all of the decay in maximum force must be close to maximum range.

Can you elaborate on your pushing duels argument?  I'm not sure why they're incompatible with a more normal range-based drop off.  

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1 hour ago, Scion of the Mists said:

Can you elaborate on your pushing duels argument?  I'm not sure why they're incompatible with a more normal range-based drop off.  

Well, if you want to have a push duell to make sense, the pushed object must be able to reach one of the participants. For that to happen the point where the push of the weaker, defending party would be able to stop the pushed object would have to be inside his or her body or very close to it.

If we assume the pushing duell to begin with an object at rest right between the allomancers (easiest assumption - it doesn't change much), the stronger allomancer will accelerate the object towards the weaker allomancer. However, as the distance towards the weaker allomancer is shrinking and the distance to the stronger allomancer is growing. As far as strength depends on distance the weaker one's push is growing stronger and the stronger one's push is growing weaker.
If the influence of distance is large enough they will eventually grow equal.
Now looking at your graphs they still have a change of a factor of two to three over sensible distances. Allomancers would have to be intrinsically very variable in strength to overcome that effect.

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52 minutes ago, Oltux72 said:

Well, if you want to have a push duell to make sense, the pushed object must be able to reach one of the participants.

I don't remember this type of "pushing duel" happening (where one Allomancer overpowers another's Push to force an object into them).  

The ones I remember involve an equilibrium happening - or at least both Allomancers getting pushed away.  

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2 minutes ago, Scion of the Mists said:

I don't remember this type of "pushing duel" happening (where one Allomancer overpowers another's Push to force an object into them).  

The ones I remember involve an equilibrium happening - or at least both Allomancers getting pushed away.  

Why then doesn't tell Kelsier Vin that pushing duells don't make sense but tell her to get a firm grounding?

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@Oltux72 Here's what happens in Vin's "pushing duel" with Kelsier:

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    One of the coins lurched in the air, hanging directly between the two of them. The rest of the coins disappeared into the mists, pushed sideways by conflicting forces. 

    Vin flared her steel as she flew, and heard her opponent grunt as he was Pushed backward as well. Her opponent hit the wall. Vin slammed into a tree, but she flared pewter and ignored the pain. She used the wood to brace herself, continuing to Push. 

    The coin quivered in the air, trapped between the amplified strength of the two Allomancers. The pressure increased. Vin gritted her teeth, feeling the small aspen bend behind her. 

The stalemate is only broken when Vin breaks the tree that she's pinned against.  

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2 minutes ago, Scion of the Mists said:

@Oltux72 Here's what happens in Vin's "pushing duel" with Kelsier:

The stalemate is only broken when Vin breaks the tree that she's pinned against.  

Yes. That tells us two things.

  1. Some strange interaction of their push is happening. The coin should actually be rammed into the ground.
  2. It is right between them. They are equally strong. A position right in the middle is compatible with every kind of decay.
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28 minutes ago, Oltux72 said:

Yes. That tells us two things.

  1. Some strange interaction of their push is happening. The coin should actually be rammed into the ground.
  2. It is right between them. They are equally strong. A position right in the middle is compatible with every kind of decay.

Why would the coins be "rammed into the ground"?  It's in a static equilibrium - all the forces are perfectly balanced so it doesn't move.  

 

 

Your argument was that the force has to be roughly constant with a steep drop off near maximum range because otherwise "pushing duels" wouldn't make sense (with "pushing duels" being defined as two Allomancers pushing on the same object, but one overpowering the other, resulting in the object reaching one of the participants).  However, there's no indication that these "pushing duels" exist in the books (at least as you're defining them).  

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