Pagerunner

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Pagerunner last won the day on August 19 2018

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About Pagerunner

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    Searching for the Mask of Investiture
  • Birthday 04/29/1990

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    Male
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    Texas
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    I've read a fair amount of Fantasy: Wheel of Time, Sword of Truth, 1/2 of A Song of Ice and Fire. These days, I don't have time for much more than Cosmere.

    I'm also big into Sci-Fi. I used to be crazy for the Star Wars EU, but recent events have hit me hard.

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  1. There's an event coming up in about two weeks in Kansas City. Here's the link to Brandon's site, with details about his signings and panels: https://brandonsanderson.com/upcoming-events/#17493. And here's the Arcanum page for the event, for when it will eventually be needed: https://wob.coppermind.net/events/386-planet-comicon/. Friday's got a panel on creating fresh stories in fantasy, followed by a signing line. Saturday's got a "spotlight" panel (which I assume will involve readings or Q&A), a panel on writing, and another signing line. Is anybody going to this event? Anybody able to record, especially the signing lines and the spotlight panel?
  2. The audio is all up and ready to be transcribed in Arcanum. I'll drop the link again, why not: https://wob.coppermind.net/events/385-orem-signing/
  3. Here's the link to the Arcanum event for this signing: https://wob.coppermind.net/events/385-orem-signing/
  4. That's not a lot of advance warning. Brandon's site says it's for those with a Costco membership only. So if anyone was thinking about signing up, this is your chance to get your WoBs in bulk.
  5. Crafty Games, the makers of various Mistborn gaming paraphernalia, had an update in their latest newsletter about an upcoming Kickstarter. There is no published Kickstarter yet (I'll add a link when it happens), but for now, I've copied the relevant portion of the update below: I had just managed to get my hands on the Kickstarter exclusives I missed from the first round of dice; I don't know if that's good timing or bad on my part, since it looks like those (and more) will be a part of the standard offerings. I'm curious what the stretch goals will look like. (There must be a reason they're doing a Kickstarter campaign, after all.) How large will the new dice packs start, how much could they expand to, and will any be Kickstarter exclusives? However they do it, it will be nice to see if they can get all the acrylics to match this time; with the existing print runs, the five "exclusive" dice are noticeably lighter than the ten "standard" dice. For sure, the symbols aren't in the same orientation (some have a 2 on the face below the bottom of the symbol, some have a 4), and I'm not sure if they even have the same handedness. None of which affect functionality, but little details like that bother people like me. (Or maybe just me.) Metal dice will be interesting. They said they're pouring, not machining, which surprises me a little bit. I expect they'll be more pricey, and the mockups look like there will be two kinds. The collector in me would like to get every possible combination of metals and symbols, but that might get too pricey. There are a lot of symbols: 24 Allomancy (16 + atium + malatium + lerasium + harmonium + 4 that are only used for the alphabet [that I'm sure are some deeply buried secret]), 18 Feruchemy (16 + atium + lerasium), and then 23 Allomancy from Era 2 (everything but harmonium). If each of those are in acrylic and two metals, that makes a whopping 195 dice. And we can always hold out hope we'll get additional symbols, like the Era 2 harmonium or even (dare I say) trellium, if Dragonsteel is generous with Crafty to get some good stretch goals. If they do make this many, and I hunker down and get them all, I may start thinking of a way to display them. So it's not a bunch of dice sitting on my shelf collecting dust. Maybe I make a frame and put them on my wall to collect dust, and then can pull them down if I ever need an obscene amount of dice.
  6. Our earliest looks come from readings at signings and conventions. Since there's another upcoming book we haven't gotten any looks at yet (Skyward 2), I expect that's what we'll be seeing the most of. There's a convention at the end of this month in Kansas City, some Europe visits in May, I think, and then DragonCon later in the year. Depending on how far Brandon gets and how comfortable he feels with his drafts, it's possible that we'll get excerpts at one or more of those events. But, on the other hand, I wouldn't be surprised if it isn't 'til the Skyward 2 tour in November.
  7. We're about to wrap up the Social Media part of the review. Getting pretty close. TWG 100%: Brandon 100% (116/116), Peter 100% (116/116), Isaac 100% (75/75), Ben 100% (38/38) 17S 100%: Brandon 100% (97/97), Peter 100% (103/103), Isaac 100% (103/103), Ben 100% (92/92) Reddit 68%: Brandon 100% (126/126), Peter 100% (99/99), Isaac 0% (0/17), Ben 0% (0/80), Adam 0% (0/8) Twitter 39%: Brandon 100% (119/119), Peter 12% (14/119), Isaac 11% (14/126), Adam 28% (14/50) Blog 100%: Brandon 100% (206/206) Social Media Total: 79% (1332/1690) Theoryland Review: 3% (35/1183) Events and Signings Review: 0% (0/397) I don't expect Reddit will take much longer. Isaac and Adam don't use it a ton, and while I haven't looked at Ben's comment total yet, I don't expect there'll be too much worth adding. Next step will be finding a good Twitter archive. I'm pretty sure I found one a while back and saved a link. For Brandon's, I had been using the one his assistants maintain. But they don't include anyone else's Twitter accounts in there, so I'll have to find a third-party archive, or leave my computer open for months while I scroll through. I'm sure there's something out there, though. I'm thinking of pausing on social media for a month or two, though, and jumping over to the Theoryland review. I'm not sure if I'll be able to go to JordanCon this year, but if I do, I'd like to be up to speed on the Wheel of Time stuff. So I'd be multitasking; catching up on WoT tidbits, and making sure any of Brandon's non-WoT stuff has been carried over. As far as Peter's Reddit comments, when it was all said and done I added 22 items to Arcanum between this month and last month. You'll find them scattered around in General Reddit events. A good chunk of them are super niche stuff, or only added for historical purposes. But the one I found most interesting was the following: One of his names in the Dragonsteel series will be this mysterious reference. We know of two names from Dragonsteel Prime (Topaz, Cephandrius) and two names from Liar of Partinel (Midius, Hoid). Hoid being the name of his old master, and Topaz from a stone he used to wear. Midius, being the first chronological name we've seen him have, would seem to make sense as this reference, and it's a name that has appeared in canon (through Oathbringer). How exactly it works out... well, I've got no ideas, there. But I'll hazard a guess that we know which name he was alluding to. And what the heck, I'll add a second, sillier one, that I'm sure a lot of people have been wondering about:
  8. Sorry, guys. It's been another really busy month for me, and I've been hard-pressed to keep up with this project... SIKE! I have actually been busy, but I did manage make some progress this month. TWG 100%: Brandon 100% (116/116), Peter 100% (116/116), Isaac 100% (75/75), Ben 100% (38/38) 17S 100%: Brandon 100% (96/96), Peter 100% (102/102), Isaac 100% (102/102), Ben 100% (91/91) Reddit 58%: Brandon 100% (125/125), Peter 63% (62/98), Isaac 0% (0/16), Ben 0% (0/79), Adam 0% (0/7) Twitter 38%: Brandon 100% (118/118), Peter 11% (13/118), Isaac 10% (13/125), Adam 27% (13/49) Blog 100%: Brandon 100% (204/205) Social Media Total: 77% (1284/1676) Theoryland Review: 3% (35/1183) Events and Signings Review: 0% (0/397) 63% complete on Peter's Reddit comments is a little deceptive, since I count month-by-month for my progress, and Peter spent a lot of time doing very little on Reddit before ramping it up more recently. But a good chunk of that is personal use, as well, so there isn't too much coming from there. Don't expect too much new stuff; however, here's one that I just added: This has made rounds on the forum before, but it could use some more airtime. This was, like, nine months after WoR was released, so I can't imagine Peter's referring to Mraize's collection. There's gotta be another reason they're part of the canon. After Bands of Mourning, I found the Southerner masks very reminiscent of an Aether, and Iyatil's presence in WoR means that she could have been what Peter was referring to... not much to go on, but I'm stumped for other options. It must be something well and truly buried.
  9. Hmm... pulse-width modulation of a steelpush as the mechanism for adjusting the force of a push, while the steelpush has a constant target acceleration, gets around the two-parameter problem I had been bringing up before. This could be an interesting model; Vin was just learning how to pulse, but a skilled allomancer can concentrate and pulse so rapidly that it appears to be a continuous weaker force. A screen flickering so quickly between black and white that it appears to be gray. Let's run it through its paces and see what shakes out. The steelpush will put enough force into the system to create a target relative acceleration at any given time. That TRA is a constant; the steelpush always wants things to go apart that quickly. Based on the circumstances, the force of the steelpush will be set a certain magnitude, which would accomplish the desired effect. When circumstances change, the magnitude of that force changes. There are other factors (distance, size of anchor, flaring, etc) that limit the maximum magnitude of the force. So that's why you reach your maximum height; the math is saying "PUSH THIS HARD" and the steelpush is saying "I can't push that hard under these conditions, you dope." But at any time, a skilled allomancer, through pulsing, can weaken the force to any degree they like. They're not saying "accelerate less fast away from me"; they're saying "exert less force." So, when Wax is holding the book underneath the table, the force of the steelpush itself would enough to propel the the table up in the air at the TRA. But, because he is pulsing, the force the book experiences a small fraction of that; not enough to lift the table off the ground at all. There are cases where there is no way to create acceleration. Two allomancers, each firmly anchored, pushing on a coin between them. They'll push until one of them runs out of energy or metals. To solve that situation, You'll have to divide by zero, which would be an infinite force; but since we're limited to a maximum force, it makes intuitive sense that we settle out with that instead. (Also, PID control, which I'll get to later.) We're looking pretty good so far. But one thing will come back to bite us, and that's the steelpush physics simulation from a few posts back. When you push against another allomancer, your steelpush calculations will be dependent on one another (the force I push with depends on the force you're pushing with), and you'll get into an infinite force situation (also, PID control, which I'll get to later) that winds up with both allomancers exerting their maximum force. You're not pulsing here, because why would you? From that point, the forces will only vary with distance - and as we've seen, that will produce oscillation. It won't freeze the coin in midair, like is described in the books. First-order effects, a relationship between force and velocity, is what was able to provide the damping we needed. And this model doesn't have any first-order effects, either. So, let's talk about velocity. What if the force of the steelpush is dependent on velocity, not acceleration? When the coin is moving away from you at the TRV, it would require so much force. But when you're moving instead, it requires more force. It sounds nice. But the math is far less clean; there's no simple relationship between force and velocity. At steady-state, you could look at how much force is required to sustain terminal velocity. But that's not what you're pushing with, because you can drop a coin off the Empire State Building and it will reach terminal velocity without killing someone at the bottom. You need to look at the transient - and there, you have to integrate to relate force and velocity. Your final velocity is the TRV, and your initial velocity is set by circumstances; but how long does it take you to reach that velocity? What happens when you reach that velocity? And a change in velocity over time... the math would work out exactly like the acceleration-based model! So, let's look at a different relationship. One I've hinted at a few times already; PID control. This is a process controls way of putting the cart before the horse, so to speak. One of the simplest processes to control is the level of liquid in a tank. You want your liquid to stay at a certain level. You've got a drain line with a valve that you can partially open or close to adjust how much liquid is flowing out of your tank. And you've got a whole bunch of disturbances; other pipes flowing into your tank, which are putting in varying amounts of liquid, based on other things going on in other parts of your process. When you think cause-and-effect, you know that the drain valve controls level; the level doesn't control the valve. (And that's kind of what we have with all these kinematic approaches steelpushes; in physics, the force controls the velocity, not the other way around.) What PID control does, is it takes a feedback of our controlled variable (tank level) and uses it to calculate what should happen with our manipulated variable (the valve). Every moment, the controller evaluates where we are at (are we higher or lower than desired level), and determines what should be changed (open or close the valve). It doesn't care how much is flowing in from the other pipes; all the information it needs is obtained from the tank level. That's the relationship we want between velocity and force; velocity is our goal, force will be adjusted accordingly, and we don't need to directly measure what is happening with normal forces and forces from other steelpushes. We can determine how to control our own steelpush based entirely on the behavior of the target. There are three criteria we compare our velocity to, the three pieces of the acronym "PID." Proportional. How fast is my current velocity, compared to my target velocity? If I'm going slower, I will exert more force. If I'm going faster, I will exert less force. If I am going the right speed, I will keep exerting the same amount of force. Integral. The integral of velocity is distance. How far have I gone, compared to how far I would have gone if I had been traveling at my target velocity all along? If I haven't gone as far, I will exert more force. If I have gone farther, I will exert less force. If I am at the right position, I will keep exerting the same amount of force. Derivative. The derivative of velocity is acceleration. Derivative control is quite frankly not intuitive and stupid, used mostly to smooth out noise in high-variance situations. It's not always needed in application; in my plant, I don't think we have anything using derivative control, we do it all with PI control. But, hey, if I'm taking the time to explain it, I'm gonna do my due diligence. So, every instant, the "steelpush controller" compares the relative velocity of the system to the target in those ways, and determines a force. When you pulse, you're limiting that force to a fraction of what it should be, which has a corresponding effect on the system. This matches pretty well with all of our edge cases. When you push a coin like Vin, you get an initial burst of force to quickly bring the coin up to TRV, and then you back off to just enough required to sustain it. When it hits the wall and stops moving, your controller ramps up again. When you're pushing under a table like Wax, your controller is ramped all the way up to its max, but by pulsing you're not exerting that much force. When you get into an anchored steelpushing duel, that keeps your controllers all ramped up to their maximum output. (That's why I mentioned it above in the acceleration section; it takes care of your transient behavior in a situation where the math is unsolvable.) And it also provides first-order effects to dampen out duel oscillation. But, unfortunately, we need to throw out integral control. If you actually wanted to control the velocity, it would be essential, because proportional control does not respond well to disturbances. When a new disturbance is introduced to the system, you'll never be able to get back to your stable control point using just proportional control. It would take a full 75-minute controls lecture to explain why, so for now, just take my word for it. But when we introduce pulsing, that is a disturbance that proportional control will never be able to completely overcome. Integral control, however, will ramp you up to your maximum controller output. It just depends on how quickly it's tuned. It will either have: 1) A quick response, and whenever you pulse you will go straight to your maximum controller output. This simplifies to Model 1. 2) A slow response, and will have no discernible effect. 3) A moderate response, where whenever an allomancer pulses, the steelpush will slowly but noticeably gain strength, something we don't see described. So, we've thrown out integral control, because it counteracts pulsing. We've thrown out derivative control, because I hate it. And now we have an effect that just reduces the force based on how fast you are moving away from each other. In other words... the relative velocity correction factor. It's a slightly different mathematical relationship, since it's based on a constant target speed. But, meaningfully, it's no different; we could just swap out an exponential equation with something like F = Fmax*(1-V/Vmax). On one hand, I like how the pulsing is an extrapolation on what Kelsier teaches Vin in the books. But on the other hand, an allomantic steelpush PID controller seems less elegant to me. For the sake of thoroughness, let's go back to an acceleration model with PID control. I think it was easier to introduce the concept with a velocity-based controller. But I needed to introduce the missing first-order in an acceleration-based system before I could suggest a velocity-based one. Which is why this may seem a little out of order. But when you look at it, it doesn't solve any of the issues we had (other than giving us a good explanation for how we get to maximum force in mathematically unsolvable situations). This is a slightly different control scheme; instead of a valve controlling level, it's a valve controlling flow rate. You directly measure the flow rate through a valve, and adjust the valve accordingly. The dynamics are much more responsive to pulsing; "pulse" by closing and quickly reopening other valves on the line, and I promise you your valve's gonna fly full open and stay there petulantly while you screw around with all the other valves on your line. So an acceleration-based PID model is going to approach Model 1 behavior quicker, and it still doesn't gain any of the first-order effects that we need. So. All that to say, I don't think pulsing is an improvement over the relative velocity correction factor with regards to the "impossible" physics. I do like it as a mechanism for "strength"; the force is determined by all those other factors, and an allomancer weakens it by learning to rapidly pulse it on and off. It's getting to be a couple years since I've been through the books, so I'm not sure if that contradicts how Kelsier presents that tactic to Vin. (Is pulsing the first step to weakening? Or is it explicitly a separate way that is easier but less effective?)
  10. That is what I describe as Model 2. The major issue with it is that there are situations where the "linkage" is not expanding, or it switches from expanding to contracting when the target contacts a surface.
  11. What do you mean when you say "conservation of impulse"? What are the variables involved, and what is the equation relating them? Impulse is a term used for an instantaneous change in momentum (and, correspondingly, velocity). When the coin hits the planet, its velocity drops to basically zero. The planet accelerates from zero to basically zero. Impulse is the integral of an infinite large normal force of the collision over an infinitely small time of the collision, which will work out to be a step change in momentum at that time of contact. But we've already fudged past all that by switching over to the mass of the planet in our equations; it's part of our assumptions, and doesn't provide any additional information to constrain the system. So I'm not sure how it is relevant in this situation. If you're suggesting that the rate of change of momentum is conserved, then you have an equation where m1a1 - m2a2 = m1a3 - m3a4. But this model breaks down in the same situations as Model 2; there are times, like when Wax pushes the notebook up against the bottom of the table, where there is no addition of momentum to the system. a3=0, and a4=0. But in that situation, since the force balances are more complicated (with normal forces between the allomancer, the ground, the table, and the notebook), there are a range of forces that all result in no momentum added to the system. You can push all the way from "just above the weight of the coin," all the way to "just below the weight of the table," and from a point of view of the system's momentum, they're all indistinguishable. In this situation, we can't come up with a single solution for the allomantic force based on a desired rate of change of momentum; therefore, it's not a strong enough model.
  12. @Oltux72, here's another way of looking at it. We need to solve a system of equations. There are a number of Givens (pieces of information that constrain the system in a specific case), Equations (relationships that constrain the system) and Variables (pieces of information we are solving for). And Constants. It is an algebraic principle that the number of Variables we have needs to equal the sum of number of Givens and the number of Equations. If you don't have enough Givens/Equations, then you can't solve the system. You need more information. On the other hand, if you have too many Givens/Equations, you still can't solve the system. You have too much information, and they can't all be true. From the force balances you've laid out thus far, we have six variables in play: The force of the push, before contact. (F1) The force of the push, after contact. (F2) The acceleration of the allomancer, before contact. (a1) The acceleration of the coin, before contact. (a2) The acceleration of the allomancer, after contact. (a3) The acceleration of the coin, after contact. (a4) We have four equations, the free body diagrams on the allomancer and the coin, both before and after contact. (Three constants among these equations, the masses of the objects in play. Let's say m1 is the allomancer, m2 is the coin, and m3 is the planet+coin.) In the simplified situation you've outlined above, with no other forces acting on any of the three objects (except the normal force between the planet and coin), these will work out to: Allomancer, before: F1 = m1 * a1 Coin, before: F1 = m2 * a2 Allomancer, after: F2 = m1 * a3 Coin, after: F2 = m3 * a4 We can have, at most, one given. That will specify the specific situation we're in; i.e. how hard the Allomancer is pushing. We cannot specify a second given for this system; that's inconsistent with the text. That would be like an allomancer specifying both the initial force and the final force, or their initial acceleration and their final acceleration. That's not how we see it work; if they set the initial force, the final force is determined by the math, and it catches them by surprise. Our current system is unconstrained; that means, algebraically, we need another equation to completely describe the situation. What possibilities do we have? Working with our existing six variables, we're pretty limited: We can say F1 = F2, a.k.a. my Model 1, which is how something like a magnet or pushing off of a wall would work. (Remember, I said before that when pushing off a wall, you're limited by how long you can push for, not how hard you can push.) This is an explicit contradiction of the text, though, since we know F1 does not equal F2. We can relate the initial accelerations to the final accelerations. This isn't quite my Model 2, but it runs into the same hangups. The acceleration of the allomancer changes upon contact, so a1 can't equal a3. The acceleration of the coin changes, so a2 can't equal a4. And while you could try saying that the relative acceleration remains constant (a1-a2 = a3-a4), that doesn't hold up in more complex situations. (As I lay out in my writeup.) We can say an allomancer is subconsciously changing the force based on what they expect the behavior to be, and we actually do have two givens. This is probably the most instinctual of understandings, but it relies on the allomancer operating on feedback they receive. They see or feel a coin hit a wall and respond accordingly. But this also breaks down in complicated situations, where the force changes even when an allomancer does not observe the object they are pushing on hit a wall. They have no feedback, so no reason to change how hard they are pushing, but we still see a change in all forces and accelerations. We can manufacture a new relationship between the force and the acceleration at any given instant, in addition to the Newton's Law equations. This could be based on the allomancer's acceleration, relating F1 to a1 and F2 to a3. Or it could be relating the relative accelerations, F1 to a1-a2 and F2 to a3-a4. But either way, we will be adding two new equations instead, resulting in an overly constrained system. So we make sure we add a new variable, the 'strength' of the push (from a scale of, say, 0 to 100%), which we incorporate into our new relationship. This strength will remain the same both before and after contact; it's our single constraint, our one given. You need to derive a relationship for any given instant between: force, strength, and at least one acceleration. The last option is the one I'm going with, and it actually has a lot of flexibility. You can make the relationship more complex, with additional variables, as long as you add a new equation to the system for each new variable you add. I took out the acceleration, and made my force dependent on strength and the relative velocities. added four variables to the system: the velocities of the allomancer and the coin, both before and after contact. And my corresponding four equations are the kinematic relationships between acceleration and velocity in all four instances, v1 = ∫a1. We'll need some more constants to describe the system, boundary conditions to say how fast we're moving when we start. But by incorporating this new relationship, I'm able to solve the system: eleven variables, ten equations, and one given. And the solution it gives makes sense and matches the text. (As evidenced by the simulations.) I am definitely open to hearing other proposed equations. (And I am sincere in this.) Artemos had one, a little more roundabout, with his allomantic normal force. It lets you come up with a solution for the system of equations. But, like I stated earlier, that one doesn't match the text as well, with regards to the magnitude of the change from F1 to F2. Can you think of a new specific relationship or phenomenon that we can evaluate? One that would match all the complex situations presented throughout the books as well or better than the relative velocity correction factor? The other variables you mentioned earlier, like mass of the allomancer and distance to the target, will also have an relationship to the force. But for the sake of the scenarios being discussed, they'll just be constants, so they won't help us algebraically constrain the problem.
  13. If Lor has not gone beyond planning stages, then it cannot be part of the worldbuilding for Vax, which is already in canon. If Brandon doesn't get around to incorporating Lor, then what is Vax orbiting?
  14. I was speaking a little hesitantly earlier, but doubling the allomantic push is definitely not strong enough. In that case, a coin hitting a wall would be the same as the allomancer launching a second coin, and we see them launching coins by the fistful. So the increase in force when it hits a wall needs to be magnitudes greater than the force pushing on a solitary coin. Other than that, the principle starts off sound. You don't have to worry about the sum of forces on each object being identical; they don't have to be, that's why the allomancer has a nonzero acceleration while the coin is stationary. You don't have to worry about conservation of energy, since the steelpush is adding energy to the system. I'd say you don't even necessarily have to worry about conservation of momentum, since only certain kinds of interactions conserve momentum. The big one we're concerned with is: every action has an equal and opposite reaction. The Allomantic Normal Force would apply in one direction to the allomancer, and in the other direction to the object the coin is pushed up against. It would be like using your hand to push against a coin, and when the coin hits the wall you reach out with your other hand and push with that as well. There's the practical issue I said before, that doubling the force is not enough to cause the effects we see. Maybe you say that the 'other arm' is stronger, that the ANF could be three, four, ten, twenty times the Allomantic Force. That's when things get a little hairier. You are not only pushing on a piece of metal, but on something else that the metal is touching. (Which doesn't sit well with me philosophically, but hey, let's roll with it for the sake of the example.) This doesn't let you push the coin into the wall any harder than you were already pushing it before you hit the wall; your swole 'other arm' is direcly on the wall, throwing you back, while your wimpy original arm is unchanged. So now, when you push on Vin's earring, the bulk of the force is transferred to Vin herself, not to the earring. Which is counterintuitive, and it also doesn't match what's in the books. If puncturing with a steelpush is beyond the scope of your simulation engine, then you can still go for a souped-up Allomantic Normal Force. It's the first way I've seen to quantify something like an "effective mass" to modify the strength of the push in the first place. But the theory of it isn't quite up to the task of matching everything that's in the books.
  15. I haven't been following the other thread; what is this Allomantic Normal Force? Is it a separate force between the Allomancer and an object in contact with the pushed target? (Which would essentially double the force of the steelpush, which doesn't seem strong enough.) Or is an additive term to the existing steelpush? (Which I don't think would fit the scenario of an immobile Allomancer and immobile target, since the force would feed back on itself iteratively.) @Jofwu's got the wrong model, what you're describing here is Model 2. (Or a slight variation; I said velocity, you're saying acceleration.) Your basis is the acceleration between the allomancer and the coin, and that determines the force. But there are two issues with that: Newton's second law is not F=ma. It is ΣF=ma. You can fudge past the forces on the coin, which just has the Allomantic force and the normal force, by calling it an "effective mass," because the force balance on the coin only has those two terms. But the tricky situations happen when the Allomancer has an additional force, as well, either gravity or a normal force of their own. Like I say in my writeup, there are situations where there is no acceleration, but there is still an Allomantic force. Which changes; you can get in a pushing duel stalemate, nobody's moving; push harder, there's more force, but still nobody's moving. That means the force must be dependent on something other than the acceleration. As far as comparisons to a swimmer, that actually is Model 1. Pushing on the wall or the water, you are exhibiting the same force, and wind up with the same acceleration on the swimmer. The difference is that you are constrained by the extension of your arm. You're thinking in terms of total energy transferred, which is a good way of looking at things. You can calculate it as W=Fd (where distance is how far your center of mass moves before you are no longer able to extend your muscles), or you can do it by integrating your acceleration over the time you are extending your muscles (which will be longer when you are able to push against the wall, because it takes longer to reach full extension because only your body is moving and not your feet [from the reference frame of the wall]). In these scenarios, force is the independent variable, and acceleration is the dependent variable. But that doesn't match with Allomancy, because in the cases in question you are not limited by the extension of your "Allomantic arm."