Jump to content

The Impossible Physics of Allomancy


Pagerunner

Recommended Posts

It might not work like you think it does.

In the first book, the first time Vin uses steelpushing to elevate herself above the street, she pushes either all her strength and comes to rest at a particular height, at some kind of equilibrium height, where Kelsier is also waiting. It doesn't make sense as a force or an acceleration, because in either case she would rocket above the resting position.

This alone suggests that there is more than the obvious going on here. Not forgetting that the use of powers is so heavily tied to intent, which you can't quantify. 

Edited by windrunningmistborn
Link to comment
Share on other sites

On 5/29/2017 at 8:43 AM, windrunningmistborn said:

It might not work like you think it does.

In the first book, the first time Vin uses steelpushing to elevate herself above the street, she pushes either all her strength and comes to rest at a particular height, at some kind of equilibrium height, where Kelsier is also waiting. It doesn't make sense as a force or an acceleration, because in either case she would rocket above the resting position.

This alone suggests that there is more than the obvious going on here. Not forgetting that the use of powers is so heavily tied to intent, which you can't quantify. 

That is accounted for. The parametric push graph will change when depending on the distance between the Allomancer and the target object. 100% of your strength when you close to the object corresponds to a greater maximum force/speed when than 100% of your l strength when you are far away. When Vin reached her "equilibrium distance," the maximum force she could exert at 100% of her strength is equal to her weight.

EDIT: I added some more math to the OP. It's a better analysis all around, but the equations operate on a much higher level.

Edited by Pagerunner
Link to comment
Share on other sites

2 hours ago, 8bitBob said:

That being said, there's another thing I noticed in my searching: coins are way worse anchors than we give them credit. In most situations, they were used to do things like jump roof to roof, or jump from the street to the top of small dwellings and go from there. In situations where anything was described as large or far, like a keep wall or something, they looked for larger metal sources to use. In addition, they never used coins to carry someone while Steelpushing, which I think is telling.

On her first training night, Kelsier hands Vin a "large ingot" of metal to clear a thirty meter wall. Unfortunately, we have no idea how this compares to a clip. Just in circulation today, a coin can weigh anything from 2.5 grams (American penny) to 34 grams (Mexico's 100 peso coin), while an ingot can weigh anything from a couple of pounds to over forty, depending on the use. Personally, I'm guessing it's 5-10lbs, but that's just it, a guess.

Even if it was just five pounds though, that would make it weigh nine hundred times more than the American penny, which I'm guessing makes it a substantially better anchor. What I'm saying is that the mass of the target metal probably has significantly more effect on its effective pushing power than we give it credit, and that the requirement of more mass for more force over a distance naturally limits the velocity that an Allomancer can impart on a coin, and doesn't need any special rule governing force vs speed to make sense. Once the coin gets a substantial distance or goes supersonic, the drag force is quickly going to equal the force that the Coinshot is capable of pushing with.

I still think they could break the sound barrier, which isn't that hard, but I don't think they're going to be hitting Mach 8 any time soon. Well, without Duralumin, that is. But that's cheating. Stop cheating, cheater.

You make a good point about how smaller anchors cannot support as much of a Push; I had forgotten about that aspect. The parametric push graph must also change with the mass of either anchor, not just the Allomancer.

2 hours ago, 8bitBob said:

My disagreement is most related to Model 4, which posits the idea that Newton's Third Law is not obeyed, and that the the Allomancer only moves if the "effective mass" of the target is greater than the Allomancer. For starters, we can mostly discount this idea due to this line from Kelsier:

This shows us that Newton's Third Law is indeed being obeyed, even for objects not fixed in place. It's also explaining a very important concept that I don't believe any of your models take into account, which is why they don't make sense: inertial mass. In essence, your models fail to account for the fact that smaller masses are less resistant to a change in motion.

To explain this concept for the layman, I will describe four similar situations, where you push your arms forward with equal force, but encounter different objects.

Spoiler

 

1. You push your arms out against nothing but empty air

You're still generating a force, but the tiny mass of air means that you're experiencing effectively zero normal force on your hands, the only force being the feeling of wind on your hands if you push fast enough.

2. You push your arms out while holding a basketball

While generating the exact same force, your hands are going to experience far more normal force than the previous situation. This is because the greater mass of the basketball more effectively resists a change in motion. This is what generates the normal force. It won't be enough to overcome friction and push you back, but your sensitive hands will feel it.

3. You push your arms out against another person about your size. Not only are your hands going to experience more normal force, if you fail to brace yourself when pushing, you will also be thrown back. The force you generate by pushing and the normal force your hands experience will be about the same, and you'll both both be moved.

4. You push your arms out against a wall, which you cannot move at all. All of the force you generate is directed back at you and you are thrown back. You feel foolish.

 

 

If you keep the concept of inertial mass in mind, then all three of your described situations make perfect sense.
 

Spoiler

 

1. Vin pushes a coin

As the coin flies through the air, its small inertial mass means Vin experiences very little push back, which her body barely registers and compensates for like it does with all small forces. Once it hits the wall, the coin's inertial mass is combined with the house, which Vin has no chance of moving, so she is thrown back by same force that she was always generating.

To use the wall pushing metaphor, this would be the equivalent of pushing a basketball, but halfway through your push you hit a wall and are thrown back violently (assuming you pushed hard enough.)

2. Wax pins a book

Bit different here, but still makes sense. Wax is generating force, but it's a small force, so the friction of the table against the floor and Wax's chair prevent anything from moving. Pretty easy to replicate just by pushing on something you place on the wall.

3. Coinshot slows their descent

There's two things at work here, but I'll finish my previous explanation first.

As the Coinshot is pushing on the coin in flight, his body is experience a very small normal force which is technically slowing his fall, but it's negligible. It's only when the coin hits the ground and gains far greater effective inertial mass that the Coinshot actually begins to slow his descent.

So, why doesn't his descent immediately stop once he generates enough force? Because it's important to remember that there's no rigid bodies involved, just pure force. Consider a rocket. When attempting a retrograde burn to descend from orbit, it has to generate a force long enough to undo the Work it did to get up there. Similarly, the Coinshot has to undue the Work that gravity has done before he flies in the opposite direction.

The easiest way to see this phenomenon is by dropping magnets on each other in a tube. If the poles are matched, and thus generate a repulsive force, then the falling magnet will briefly overcome the force generated before bobbing back up and eventually settling at a constant height where the force of gravity is equal to the force of repulsion.

 

And with that, all of the situations are reconciled under a model dictated by force.

Spoiler'd for length. Just to clarify, the first five models are ones I have seen proposed, and I am just explaining why I think they all are wrong. Having shown the necessity for a new model, I present the one I developed, Model 6.

Inertial mass is just regular mass, not a separate concept - it is accounted for in the free body diagram that applies to all situations, and is why the slopes of the orange and blue lines are different. I think the concept you're getting at is how I have ignored how all these values are functions of time. I recently uploaded an addendum to my original post, which approaches the math from a different angle, which basically says the same things repackaged using math that fewer people will be able to follow. I don't know if you noticed it before posting your reply, but it may address your concern.

Because that's really where the issue with your examples comes in: with time-dependence. In each of the four situations, exerting force forward will also exert an equal force backwards; that's what Newton's third law says. That's not talking about the normal force equaling the force you're applying; that's saying that the force of drag on your hand is the same as the force of your hand on the air, and the force pushing your hand forward is the same force pushing your arm backward. You've suggested that the force on the coin is not the same as the force on the Allomancer, which actually is a violation of Newton's third law.

In the first example you present, look at the sum of the forces on your hand: strong forward, nothing backward. With the very small mass of your hand, that's going to give it a very high acceleration forward. Look at the sum of forces on your body: strong backward, nothing forward. But, because the mass of your body is so much larger, you have a much smaller acceleration than your hand does. You can calculate the time it will take to reach full extension, and the velocities that each piece will be travelling at that time. It will be a very small time, a negligible velocity of the body, and a high velocity of the hands. (We'll conveniently stop looking at our model right before you need to stop your arms from moving, since we don't particularly care what happens then.) You've interpreted the lack of movement as meaning there is negligible force, but it actually means that a moderate acceleration has operated for a negligible time.

This is where time becomes important: if you exert the same force in every situation, then higher mass objects will take longer and longer to reach the 'end state' of your push, with your arms fully extended. That gives that same force on your body more time to act; it takes longer to push the basketball forward (we'll just model that as a piece of your hand, and then any 'normal forces' are all internal strain), so your body is moving faster at the end. A longer time, not a larger force, is why you are moved backwards.

But that's explicitly different than what we see in the text. There is a discontinuity in force on an Allomancer's body. If Vin launching the coin is like your example of pushing your arms out, the coin would need to move almost instantaneously to the wall, not giving the Push enough time to noticeably accelerate her. She can clearly identify two regimes: when the coin is in the air, there is no force on her. When the coin hits the wall, there is force.

 

Edited by Pagerunner
Link to comment
Share on other sites

On 05/31/2017 at 0:14 PM, 8bitBob said:

1. You push your arms out against nothing but empty air

2. You push your arms out while holding a basketball

3. You push your arms out against another person about your size.

4. You push your arms out against a wall, which you cannot move at all.

I wanted to back up what @Pagerunner is saying here. This seems to be a common misunderstanding of the physics involved.

I can push a wall with 1 pound of force just as I can push a wall with 100 pounds of force. One I will hardly notice. The other will require me to brace myself. The exact same thing is true of a ball rather than a wall. Or a person or the air.

You are imagining a soft, steady push on a basketball and a full strength push on a wall. It's not an even comparison. When Vin pushes a coin into a wall, why would she suddenly increase the magnitude of her pushing? If pushing the free coin with X Newtons didn't knock her over, pushing it against a wall with X Newtons won't knock her over.

Link to comment
Share on other sites

On 5/31/2017 at 1:27 PM, Pagerunner said:

She can clearly identify two regimes: when the coin is in the air, there is no force on her. When the coin hits the wall, there is force.

 

The way I see it, this probably has to do with anchor quality (as does, IMO, much of the weirdness of Iron/Steel Allomancy).

IMO, your Model 6 is close to right, but I think anchor quality is the 'reconciling' factor.

I'd propose Model 7: the Allomancer chooses a "push strength"; the "push strength" combined with the "anchor quality" determines the force. Mathematically, the "anchor quality" would act like an 'efficiency' term.

Force = push strength x anchor quality

Regime 1 (coin in flight): The coin in the air is a bad anchor, so the force is small. There *is* an equal-and-opposite force on Vin when the coin is in the air, but it is small enough (since Vin's mass is vastly greater than the coin's) that in practice the friction of her feet on the ground (or the force of gravity & air resistance, if she's in the air while pushing on it) means it's not really noticeable.
Regime 2 (coin against wall): When the coin hits the wall, it's held in place and becomes a far better anchor. Thus, while Vin keeps her push strength constant, the force increases dramatically, and Vin is thrown back. (Now the coin-plus-wall-plus-ground-it's-anchored-to system has a vastly higher mass than Vin, so the force doesn't do anything noticeable to it.)

Link to comment
Share on other sites

17 hours ago, jofwu said:

If pushing the free coin with X Newtons didn't knock her over, pushing it against a wall with X Newtons won't knock her over.

I see it this way:

Coin:
Captura.PNG.65fbd4d21acc8789590c1be0cbf7bbed.PNG


The coin’s mass is really small so the acceleration is big and the force of the push will make the coin fly away


Vin:
Captura2.PNG.63f435b13a3b9ab7e4051c7cf3e04b86.PNG


Vin’s mass is much larger so her acceleration is insignificant, she doesn't move.

If we divide the two equation(taking modulus because I am lazy)


Captura3.PNG.3cdd6a1611ed2d43e180b6f9ee54d19d.PNG


So while in the air, the coin’s mass is small and its acceleration big, Vin’s mass is big, when you compare it to the coin’s mass, and hence her acceleration is insignificant.


But when the coin hits the wall Vin is pushing something incredible heavy so:


Coin’s mass is huge and Vin’s mass is insignificant, coin's acceleration is insignificant, in order to fullfill the equation Vin’s acceleration has to be pretty big, so she moves backwards.

Probably there is something wrong with my model, but I can't see it right now.

PD:this model don't take into account the friction forces so when I say insignificant in the practise it's going to be 0.

 

 

Edited by Idealistic Mistborn
misspelling
Link to comment
Share on other sites

20 hours ago, cometaryorbit said:

The way I see it, this probably has to do with anchor quality (as does, IMO, much of the weirdness of Iron/Steel Allomancy).

IMO, your Model 6 is close to right, but I think anchor quality is the 'reconciling' factor.

I'd propose Model 7: the Allomancer chooses a "push strength"; the "push strength" combined with the "anchor quality" determines the force. Mathematically, the "anchor quality" would act like an 'efficiency' term.

Force = push strength x anchor quality

Regime 1 (coin in flight): The coin in the air is a bad anchor, so the force is small. There *is* an equal-and-opposite force on Vin when the coin is in the air, but it is small enough (since Vin's mass is vastly greater than the coin's) that in practice the friction of her feet on the ground (or the force of gravity & air resistance, if she's in the air while pushing on it) means it's not really noticeable.
Regime 2 (coin against wall): When the coin hits the wall, it's held in place and becomes a far better anchor. Thus, while Vin keeps her push strength constant, the force increases dramatically, and Vin is thrown back. (Now the coin-plus-wall-plus-ground-it's-anchored-to system has a vastly higher mass than Vin, so the force doesn't do anything noticeable to it.)

Mathematically speaking, 'anchor quality' isn't a meaningful parameter. This sort of gets back to my issue with Model 4, which talks about 'effective mass,' which isn't meaningful either. What does it mean to be a good anchor? You'll look at the force balance to determine if the anchor is immobilized.

Qualitatively speaking, whether or not something lets you push off of it (like kicking off the side of the pool versus an inner tube floating in it) depends on whether or not the thing will move on the other side. That's obvious and intuitive. But what's the math behind how that works?

  • You apply a force to both objects.
  • You calculate the acceleration each object experiences (F=ma).
  • You calculate the velocity and position of each object, as a function of time (a=dv/dt, v=dx/dt).
  • You find what time the objects get so far apart you cannot exert force anymore (or just when you stop exerting force).
  • You look at the velocity of each object when you stop pushing.

Bad anchors move away from you, so you can't push on them for as long. Good anchors don't move, so you can push on them for longer. Work equals Force times Distance; you will apply a force (equal and opposite) for a set distance (until you've gotten so far away you can't push anymore). You'll do a constant amount of work in total; whichever object moves farther will have more work done on it, and will thus have more kinetic energy at the end. So, if whatever you're pushing on doesn't move, all the work you do goes to making you move faster. If whatever you're pushing on moves a lot easier than you, then all of the work will go to making the object move faster.

So, the best way you could define as 'anchor quality' is acceleration of the Allomancer over the acceleration of the anchor. But, since you need the force balance to determine those accelerations, you can't use anchor quality as an input to that same force balance. You need a solved force balance to even discuss the concept of anchor quality.

3 hours ago, Idealistic Mistborn said:

I see it this way:

Coin:
Captura.PNG.65fbd4d21acc8789590c1be0cbf7bbed.PNG


The coin’s mass is really small so the acceleration is big and the force of the push will make the coin fly away


Vin:
Captura2.PNG.63f435b13a3b9ab7e4051c7cf3e04b86.PNG


Vin’s mass is much larger so her acceleration is insignificant, she doesn't move.

If we divide the two equation(taking modulus because I am lazy)


Captura3.PNG.3cdd6a1611ed2d43e180b6f9ee54d19d.PNG


So while in the air, the coin’s mass is small and its acceleration big, Vin’s mass is big, when you compare it to the coin’s mass, and hence her acceleration is insignificant.


But when the coin hits the wall Vin is pushing something incredible heavy so:


Coin’s mass is huge and Vin’s mass is insignificant, coin's acceleration is insignificant, in order to fullfill the equation Vin’s acceleration has to be pretty big, so she moves backwards.

Probably there is something wrong with my model, but I can't see it right now.

PD:this model don't take into account the friction forces so when I say insignificant in the practise it's going to be 0.

 

 

The last equation you've described is true, regardless of force applied. You cancelled it out. Even if the force doesn't increase when the coin encounters the wall, and Vin is still only accelerating imperceptibly, the acceleration of the coin will be even more imperceptible. The ratio will change because the circumstances change, but why do the force and Vin's acceleration increase, instead of the force remaining constant and the coin's acceleration decreasing?

What you've done appears to be a modification of Model 2. But instead of relative velocity, you've defined relative acceleration. When the coin hits the wall, there is no reason for the relative acceleration (a_coin - a_vin) to be preserved; unless, of course, that is the variable that the Allomancer defines. But I laid out the issues inherent to that that approach in my original document; the relative acceleration is not always preserved when a coin encounters an obstacle.

Link to comment
Share on other sites

8 hours ago, Pagerunner said:

Mathematically speaking, 'anchor quality' isn't a meaningful parameter.

Well, not in our physics... but I think the observed behavior of Iron/Steel Allomancy in the books makes the most sense if you treat anchor quality as being fundamental and force as being derived from that.

Quote

This sort of gets back to my issue with Model 4, which talks about 'effective mass,' which isn't meaningful either. What does it mean to be a good anchor? You'll look at the force balance to determine if the anchor is immobilized.

Anchor quality isn't just whether it will move or not, though. From what we've seen in the books, it seems to depend on quantity/mass of metal, surroundings (both 'bracing' and whether there is material in between the actual metal and the Allomancer), and distance between the anchor and the Allomancer.

Link to comment
Share on other sites

4 hours ago, cometaryorbit said:

Anchor quality isn't just whether it will move or not, though. From what we've seen in the books, it seems to depend on quantity/mass of metal, surroundings (both 'bracing' and whether there is material in between the actual metal and the Allomancer), and distance between the anchor and the Allomancer.

And they should be able to apply greater force to a "better" A.K.A. more massive anchor as these can be detected by steel and pushed at a greater distance. If the force applied is a constant, then the mass of the metal shouldn't vary the distance at which they're able to apply it. 

Link to comment
Share on other sites

5 hours ago, cometaryorbit said:

Well, not in our physics... but I think the observed behavior of Iron/Steel Allomancy in the books makes the most sense if you treat anchor quality as being fundamental and force as being derived from that.

The whole exercise is to explain, using physics, exactly what happens during Steelpushing. Saying that physics works fundamentally differently is in direct contradiction with that stated goal. It is saying that Brandon can write discrepancies, and does not need to explain them. It means we cannot have a model that reliably predicts how Allomancy will behave.

Don't what I'm saying that the wrong way; it is an entirely reasonable approach, and it's what I thought for years. That there was no cohesive explanation, that Brandon wrote what he felt fit the situation best, without focusing on the details of whether the math actually make sense. Only as I was recently telling everyone else why all their models were wrong, did I realize there was an opening for some level of consistency by tying together maximum speed and maximum force. I still think that Brandon didn't start from a mathematical definition of any kind; he wrote Vin's steelpushing one way, and Wax's another way, and I'm just trying to make math that will fit both of them.

5 hours ago, cometaryorbit said:

Anchor quality isn't just whether it will move or not, though. From what we've seen in the books, it seems to depend on quantity/mass of metal, surroundings (both 'bracing' and whether there is material in between the actual metal and the Allomancer), and distance between the anchor and the Allomancer.

I think we're bouncing back and forth between definitions. Your equation has rolled a lot of these things together to determine the final force (which is fine, I rolled a lot into my parametric push graph, too), but none of those aside from the bracing has any relevance on the particular example we've been looking at. There are a lot of things that go into the force of a Push; but for the particular instance when there's a change in force when the coin is braced, everything else is constant. The application of the normal force changes the force of the Push.

Now, you might say that other parameters, like mass and distance, appear both in the force balance and in the equation for force, so why can't the normal force also be a parameter? But the normal force, by definition, is a response to the Allomantic push. The force exerted by the ground will be exactly enough to cancel the other forces on the object (Allomantic, and gravity). Trying to use that to calculate your force is putting the cart before the horse.

Link to comment
Share on other sites

Just now, Pagerunner said:

The whole exercise is to explain, using physics, exactly what happens during Steelpushing. Saying that physics works fundamentally differently is in direct contradiction with that stated goal. It is saying that Brandon can write discrepancies, and does not need to explain them. It means we cannot have a model that reliably predicts how Allomancy will behave.

Oh, no, that's not what I'm trying to say here. What I mean is that I think "anchor quality", while it's not  a concept/quantity that exists in our-universe physics, is a fundamental of the physics of Allomancy in the way mass is to gravity or charge is to electromagnetism.

2 minutes ago, Pagerunner said:

The application of the normal force changes the force of the Push

Hmm - but does it? Is it actually the normal force that makes the difference, or the change in the coin's environment (now placed against a massive solid object)?

I think this is one of those things like how a time bubble cares if you are on a large fast-moving object (train) or not. The fact that the coin's in physical contact with a massive object makes a difference in itself to its quality as an anchor, before normal force and such are considered.

Link to comment
Share on other sites

50 minutes ago, cometaryorbit said:

I think this is one of those things like how a time bubble cares if you are on a large fast-moving object (train) or not. The fact that the coin's in physical contact with a massive object makes a difference in itself to its quality as an anchor, before normal force and such are considered.

Okay, that's a little bit better, but it still will have problems matching the model of Allomancy we've seen. Lets look at when Kelsier was raiding Keep Venture; an enemy Coinshot fired a coin at him, Kelsier Pushed back, and the enemy Coinshot was launched out the window. That time, it wasn't any screwing with the mass of the coin; it was just the application of another force on the coin that made the first Coinshot's Push increase in force.

Link to comment
Share on other sites

5 hours ago, Pagerunner said:

Okay, that's a little bit better, but it still will have problems matching the model of Allomancy we've seen. Lets look at when Kelsier was raiding Keep Venture; an enemy Coinshot fired a coin at him, Kelsier Pushed back, and the enemy Coinshot was launched out the window. That time, it wasn't any screwing with the mass of the coin; it was just the application of another force on the coin that made the first Coinshot's Push increase in force.

I will have to re-read that scene (and Kelsier and Vin's pushing contest) and see exactly how it would or wouldn't fit.

I'm not talking about the mass of the coin changing, though. If it actually is analogous to the "time-bubbles mess up the movement of a carriage but a train is OK" thing we see in BOM, it might be enough that the coin is 'held in place'.

Link to comment
Share on other sites

@Idealistic Mistborn, your equations aren't wrong, but I think you are making a common mistake in interpreting what they actually mean. When the coin is pushed against a wall, Vin is suddenly thrown back. This implies the magnitude of the force of her push has suddenly increased. Pagerunner is trying to explain why that happens.

@cometaryorbit, I think the distaste for "anchor quality" (for me at least) is that it's so amorphous. Take that last example where two people pushing opposite on a coin feel an increase in force. Why do they suddenly get pushed back more firmly just because someone else is pushing on it? You can wave your hand and say "the anchor quality has changed", perhaps because of some cognitive matter. But that's not very satisfying when you're trying to explain the physics. I think the explanation would need to go further: defining what affects "anchor quality" and how.

@Pagerunner, I still like that notion that force is proportional to e^-v. I think it introduces an important concept that the books are awkwardly silent on, but it's definitely the most elegant explanation I've heard for the discontinuity in force.

Link to comment
Share on other sites

32 minutes ago, jofwu said:

I still like that notion that force is proportional to e^-v. I think it introduces an important concept that the books are awkwardly silent on, but it's definitely the most elegant explanation I've heard for the discontinuity in force.

Hey, I didn't mention that one over here yet, since I haven't had a chance to check up on it! But now that the cat's out of the bag, I am exploring a different model to restrict force based on relative velocity. Instead of it being a piecewise function where force drops to zero at the moment you exceed the maximum velocity, the force is gradually decreased as you increase in velocity. The faster something moves away from you, the less force you can exert on it. At the speeds a coin moves at, an Allomancer can only exert enough force to match the drag from the air. But when the coin suddenly becomes stationary, the force can be very large again and move the Allomancer.

It's another situation where the math works, but I need to convince myself that it truly fits every situation in the books. It would severely limit the Coinshot's maximum speed, which I think can be comparable to the speed of a coin. (That's what I need to research, if in any of the Vin/Zane or Kelsier/OtherGuysInAoL an Allomancer manages to outrun a coin or anything like that. I know they throw themselves to the side to dodge sometimes, but I'd like to find some scenes where the velocities are aligned, so we can actually get an idea as to how much faster coins are than Allomancers, if at all.)

But big picture, it's the same conclusion I make in Model 6; that if something is moving too fast, that will arbitrarily restrict the force you can apply to it. Model 6 does have some odd behavior as written when it comes to a steady-state Push, where the velocity of the coin will reach the max velocity, the force will stop, the coin will slow down, the full force will start again, the coin will reach max velocity... cycling on and off so quickly it seems to be a continuous force, which will average out to whatever force is required to overcome drag. But the new model will truly give a reduced force, which I would like slightly better.

Link to comment
Share on other sites

I can't think of any examples where an Allomancer is racing a coin, but I'm highly skeptical they can achieve the same acceleration that they Push objects with. Coins seem to achieve the speed of early bullets within a meter or two. Let's say 300 m/s in one meter, which is probably a very low estimation. That's an average acceleration of 4500g. Allomancers can't match that. They'd die, even if it were brief.

That's only a 900N average force (200 lb), by the way, if we assume a 20 gram coin. The force has to drop off with distance. So if the force of a Push against a stationary coin at some distance (say 10 m) can knock you over, then the force at point-blank range should be pretty high. I expect that they can actually push with a force quite a bit stronger than what I've calculated above. Coins could probably reach much higher speeds without drag. Humans can reach speeds high enough for our purposes since they don't get into significant drag.

To hop 30 meters up (10 stories) an 80kg person uses 24 kJ of energy. That requires a constant force of 2400N of Pushing over 10 meters. Assuming a linear drop down to zero (because of distance/velocity increasing) that's an initial force of 4800N (1080 lb). About five times higher than what I calculated before. Seems like the right ballpark to me. An average force of 3000N on a 20g coin over 0.5m will accelerate it to 387m/s. You can push a coin at such high forces without falling over simply because their duration is so brief. The coin accelerates to a high velocity very fast (and gets further away) so that high force isn't sustained long enough to knock you over. Like a gun recoil.

Remember that a person doesn't necessarily have to be Pushing the whole time. Kelsier kills people with coins in relatively close range fighting without being thrown backwards himself. The implication is that the coins reach deadly speed early on and then he "lets go". Drag slows things down, but counteracting it isn't always necessary if you give them a high top speed to begin with. Vin wouldn't have fallen over if she had known to let go of the coin after accelerating it fast enough early on. But she was new to the powers and tried accelerating it as fast as she could the whole way.

Link to comment
Share on other sites

On 6/5/2017 at 8:49 AM, jofwu said:

I think the explanation would need to go further: defining what affects "anchor quality" and how

Well, I think the primary factors are quantity of metal (more metal makes a better anchor), Investiture (Invested objects are harder to Push/Pull), and (for lack of a better word) 'independence' or separation from other objects.

I do think the 'independence' factor is somewhat Cognitive, which maybe is unsatisfying on a physics level, but I think it's necessary for a complete model of Iron/Steel Allomancy - Kelsier points out when he's training Vin that an object can't be Pushed or Pulled if even part of it is inside someone's body. So somehow the metal atoms in the part outside the body 'inherit' the Investiture-interference of the part inside the body. To me, that very strongly implies that Iron/Steel Allomancy works on a whole-object basis not as a particle-to-particle force like electromagnetism. But that requires some definition of what a 'whole object' is.

IMO the coin-against-wall vs coin-in-air situation is the same principle. When the coin touches the wall it stops being an 'independent' object and 'inherits' the mass of the wall and maybe the entire tectonic plate/planet it's anchored to. Similarly, when another Allomancer gets involved, the coin 'inherits' the mass of the other Allomancer.

Link to comment
Share on other sites

I've always imagined the telekinetic Allomantic "link" between an Allomancer and the anchor they are Pushing (or Pulling) on to work similarly to an extension of the Allomancer. I've never been good at physics, and it's been some time since I've done any, but the Allomancer-coin scenario has always sounded very similar to me to a scenario where I am pushing on a coin with my hands. I can grab a coin, and just by extending my arm fast enough, I can push it away from my body (and even give it some acceleration once it loses contact with my palm) without really feeling any (normal?) force pushing me back. But if I tried doing exactly the same thing with a wall in front of me, the coin (and my arm) would hit the wall and propel me backwards.

I've always thought Steelpushes work exactly the same way, except the thing that propels the coin forward isn't my arm, it's the Allomancer's Push.

Everything else... I applaud the work that has gone into both the analysis and the following conversation. I am just not convinced there is much value in overanalyzing something like this...

Link to comment
Share on other sites

1 hour ago, Argent said:

I've always imagined the telekinetic Allomantic "link" between an Allomancer and the anchor they are Pushing (or Pulling) on to work similarly to an extension of the Allomancer.

Me too.

I just imagine it as sort of springs.

Link to comment
Share on other sites

12 hours ago, Argent said:

I can grab a coin, and just by extending my arm fast enough, I can push it away from my body (and even give it some acceleration once it loses contact with my palm) without really feeling any (normal?) force pushing me back. But if I tried doing exactly the same thing with a wall in front of me, the coin (and my arm) would hit the wall and propel me backwards.

I suspect this is what Brandon was thinking when he created the magic system.

The fault in the logic is the magnitude of the forces involved. If you push a coin away from your body so fast that it accelerates to lethal speeds, you would absolutely feel something. This is what the recoil of firing a gun is. Though it's potentially even worse, because a gun only "pushes" as the bullet leaves the barrel. An Allomancer could potentially continue pushing (and feeling that recoil force) for the duration of the coin's flight.

It's confusing perhaps because it takes very little force to push something as small as a coin. You're not limited by how hard you can push, but merely by how fast your muscles can extend. By how much work it takes to move the arm itself. Even if you extend your arm as fast as possible, you're applying very little force to the coin. That same force applied to a wall would not knock you over.

It makes more sense if you replace the coin with something that takes a measurable amount of work to push. Imagine lifting a 5-lb object into the air slowly. Now imagine you try to throw that object into the air as high as you can. The second takes a lot more force. If I push you sideways with 5 pounds of force, it probably won't knock you over. If I shove you as hard as I can it probably will. Pushing a coin lightly across a table is the first case. Hurling it at the speed of sound is the second.

Link to comment
Share on other sites

Eh... is this why we are doing this? Because the idea that seems to be Brandon's intent doesn't stand up to math (math which doesn't account for any magical shenanigans, I should add)? Are we going back to irradiating time bubbles again?

Link to comment
Share on other sites

24 minutes ago, Argent said:

Eh... is this why we are doing this? Because the idea that seems to be Brandon's intent doesn't stand up to math (math which doesn't account for any magical shenanigans, I should add)? Are we going back to irradiating time bubbles again?

The specifics of Steelpushes have never been intuitive for a number of us, the most glaring concerns for me arising when I recently reread Era 1. If you're pushing with your arm, you are never surprised by the amount of force you exert; you feel the resistance and adjust accordingly, otherwise you just slap the coin against the wall and hold it there. But that doesn't mesh with the first lesson of Allomancy that Vin learned. This gets back to Sanderson's first law, and how I found myself skimming past all of Zane's and Vin's contests because their Steelpushing seemed fundamentally different to me than Wax's. (Why doesn't everyone just cap their maximum force so they're only slinging coins and aren't thrown back on accident?) Because my intuition didn't match what the author had wrote using his intuition, I found the passages to be entirely too detailed.

Because Brandon devoted so many words to the specifics of Steelpushing and how it interacts with the surroundings, it's not surprising that some of us can't help but look 'too closely' at the topic. When we see inconsistencies, it is not a satisfying resolution to step back and say 'don't think about it that much.' Rather, fitting a Frankenstein's mathematical monster to the situation lets us more accurately grasp the behavior that Brandon writes Allomancy to manifest, letting us engage more in the line-by-line of the battles. If you can read through all of Mistborn and never wonder "but wait, shouldn't that have done this instead?" then more power to you. I could not. For a while, it meant I just read "bla-bla-fly-through-the-air" instead of the actual text of the Allomantic battles. But now I think I see a better way to understand how Brandon designed Allomancy to behave.

Which is the goal at the end of the day for those of us who make these models. Like I said before, I don't think that Brandon has the mathematical formulas to describe this behavior, and pulls them out to check whenever he's writing Mistborn. He has an internal understanding of what Steelpushing is, which never quite matches up with simple explanations that we consider the first time around. My model hopefully captures the key idea that I think has been missing - that the maximum speed is inherently tied to the maximum force in a way unrelated to the actual physics - and does so in a quantitative way that assuages our quantitative-based questions.

Link to comment
Share on other sites

1 hour ago, Pagerunner said:

 If you're pushing with your arm, you are never surprised by the amount of force you exert;

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. 

2 hours ago, Pagerunner said:

This gets back to Sanderson's first law, and how I found myself skimming past all of Zane's and Vin's contests because their Steelpushing seemed fundamentally different to me than Wax's

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. 

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...