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Found 18 results

  1. Edit 2: Following Jofwu's footsteps, I had a conversation with /u/Phantine on reddit and am reconsidering how distance affects the Allomantic Force. I was originally confident in an inverse square relationship between Allomantic Force and the distance between the Allomancer and target, but through testing, a *linear* relationship has better handling and feels more reminiscent of Allomancers' movements in the books. I've added both as options in the game: The Allomantic Force is proportional to the inverse of the square of the distance between the Allomancer and the target When the target is right next to the Allomancer, the Allomantic Force approaches infinity. When the target approaches an infinite distance away from the Allomancy, the Allomantic Force approaches 0. The Allomantic Force decreases linearly with the distance between the Allomancer and the target. When the target is right next to the Allomancer, the Allomantic Force is at its maximum. When the target is at the max range (arbitrarily at 50 meters), the Allomantic Force is 0. I've also added the option to control the strength of your push through two control schemes: The player sets the *percentage* of the maximum possible force they can push with, or The player sets a *constant force* to try to push at, if possible. Edit 1: If you want to play the current build of the game, you can find it here on my GitHub. Aside from that, I've looked back at [8], @digitalbusker's post and see I misunderstood it a bit. I've re-read it and realized that I agree with it much more than I thought I did originally. In one paragraph, they said, This sounds just like the Allomantic Normal Force idea I used in the game. If you push on a target and the target can't move, the target pushes back on you as if there were a long, tangible line between you and the target. In this way, the ANF does work somewhat like an elastic collision. I did some more testing in the game and anything that involved directly manipulating velocities of the target or Allomancer worked poorly. I feel like sticking to forces rather than energy is the right way to go. Table of Contents I: Introduction I-a: My intent I-b: Current game progress & Videos I-c: Referenced forum posts I-d: Definitions II: Force, mass, and acceleration of a push III: Anchors and the pole analogy IV: Math V: Summary & Final points Part I: Introduction Over the summer I’ve been rereading Mistborn and have been thinking about the mechanics of Allomancy. I decided to have a go at recreating the physics of Ironpulling and Steelpushing in the Unity physics/game engine. I don’t intend on actually creating a game to sell (that’d be a bit illegal), so this is mostly an endeavor for personal fun. What follows is my current progress on the game as well as my current thoughts on the math and physics of Pushing and Pulling. Part I-a: My intent My goal is to take what Brandon describes in his books and do my best to create a working model of them in the Unity engine. My purpose in posting this here is to record my thoughts so I can be internally consistent, encourage discussion, and improve the game’s mechanics with your suggestions and criticisms. I don’t expect to perfectly recreate Allomancy as Brandon describes it in the books because there are some things with little connection to real-world physics (such as Feruchemical weight). I’ll try to give the pros and cons for all my decisions. If you disagree, tell me! I’ve been in my own personal bubble while making this, so I’d love some external input. Part I-b: Current game progress & Videos So far, I’ve implemented most of the physics and fundamentals of Ironpulling and Steelpushing. Here are some short videos: The setting: The sandbox I use for testing is based on Luthadel. There are metal poles stuck in haphazardly-placed buildings, and a few windows with metal frames/latches. At the intersection are metal objects of various masses, including coins, ingots, and 16-ton steel blocks. Blue metal lines: When the player (the grey sphere) begins passively burning metal, they see blue metal lines pointing towards nearby metal sources. The wider the line, the heavier the metal, and the brighter the line, the closer the target. Basic pushing/pulling: The player can “target” a metal. They can then push or pull on that metal. They can increase or decrease the strength of the push, as indicated by the wheel near the bottom. They can target multiple metals simultaneously (as indicated by the bright blue number beneath the wheel). Pull targets vs. Push targets: The player has separate targets for pulling (indicated by blue) and pushing (indicated by red). When the player pushes or pulls with specified push targets and pull targets, the player only pushes on the push targets and only pulls on the pull targets. If the player only has pull targets or only has push targets, they can push and pull on any target. Pushing/pulling with coins: The player can throw, drop, and pick up coins. The number in the lower right corner indicates the number of coins in the player’s pouch. Flying around Luthadel: It’s a bit tricky, but the player can fly between buildings by pulling on metal latches and pushing on coins. Some things are still a bit buggy, namely the camera, coin physics, and width of the white part of the blue/red line pointing at a target while pushing. Part I-c: Referenced forum posts Many of the ideas used in the calculations come from the work previous Sharders have done on making sense of Brandon’s magics. Here are some that I used, which I recommend to anyone interested in the physics of Allomancy: When I use specific ideas from these threads, I’ll mark it with a [#]. Other threads I found interesting: Part I-d: Definitions Key statements are italicized. Key terms are written in bold for their first appearance. Push – unless I specify otherwise, I’ll simply say “push” instead of “push/pull” to refer to the math of both steel and iron. It’s a lot easier to read while still means the same thing. All physics and rules of a pull are the same as a push, just in the opposite direction. Target – the metal that an Allomancer is currently pushing on. Coins are often a target. Distance – the distance between an Allomancer and their target. Anchor/anchored – a target is an anchor if it does not move. A lamppost, a coin stuck on the ground, and a metal roof would all be anchors. Note that the metal is the anchor, not the nearby wall/ground/stone. A target is unanchored if it is moving freely with no resistance. A target is partially anchored if it meets some resistance but is not fully anchored (i.e. a coin skidding on the ground). Allomantic Force – the force that an Allomancer directly exerts on a target while pushing. Equal in magnitude to the force that the target directly exerts on the Allomancer while pushing. The Allomantic force does not change if the target is anchored or unanchored. Now, let's jump into the physics of Allomancy. Part II: Force, mass, and acceleration of a push When Allomancers in the books refer to “weight,” they almost always mean mass. [1] Let’s ignore Feruchemical weight for now. When an Allomancer pushes on a target, the Allomancer exerts a force on the target that is equal and opposite to the force that the target exerts on the Allomancer. It’s F = ma, it’s Newton’s third law, and if anything else were the case, the physics of Mistborn would be far too distant from our world for a good simulation. This explains one of the core features of pushing and pulling: If you push on an object heavier than you, you will accelerate more than it (and vice-versa). You push on a coin out in front of you. The force is the same between you and the coin, but the coin has less mass, so it accelerates more than you. The coin goes flying, but you hardly move. Likewise, heavier objects (like cars) have more mass than you, so you accelerate more than them. The previous statements are most apparent with an Allomancer and target in free-fall or space, where the Allomancer and target (such as a coin) won’t be anchored by anything (such as the ground). When the Allomancer or target are anchored by a wall or the ground, things get complicated. Part III: Anchors and the pole analogy In the books, if an Allomancer is falling through the air, throws a coin downwards, and starts pushing on it, the Allomancer doesn’t feel much while the coin is falling through the air and unanchored. The Allomancer pushes on the coin, but their acceleration from the push is not enough to stop their fall. Once the coin hits the ground and stops moving, the Allomancer suddenly “can get a stronger push” and decelerate more strongly. Here is my interpretation: Pushing against an anchored coin on the ground has a similar effect as holding a long pole and physically pushing against the ground. The Normal Force due to the Allomantic Force (Allomantic Normal Force, or ANF) that the ground/wall/etc. exerts on the target is transferred to the Allomancer. If you held a long vertical pole and pushed down on the ground, the ground would push back on you and the pole. If you tried to push the pole into the ground, the ground would resist, and you could climb upwards relative to the ground. Allomancy mimics this effect. When pushing on the coin, it is like you are physically connected to the coin. If something resists your push, you experience that resistance. I drew some free-body diagrams that hopefully help explain what I’m saying. In these, an Allomancer and coin are falling down. The Allomancer is pushing on the coin. Let me discuss two of the other theories as to how Allomancers get stronger pushes from anchored targets: When the coin is airborne, the allomancer is only pushing on the mass of the coin. But when the coin is anchored to the planet, they are also pushing on the mass of Scadrial/the ground around the coin, which causes the Allomancer to accelerate more. [not a quote, but the concept taken from 1] I’ll get into how mass affects the force later in the math section, but I want to now make something clear. With my interpretation, Allomancers push on the mass of metal, not the combined mass of metal and nearby non-metal (the planet). When pushing against an anchored coin, the Allomancer is only indirectly pushing on the ground – they are pushing on the coin, which pushes on the ground, which resists back on the coin, which resists back on the Allomancer – similar to holding a long pole and pushing on the ground. An Allomancer’s strength is the amount of kinetic energy they can add to the system of the coin and allomancer. When the Allomancer pushes on an unanchored target, that kinetic energy is distributed between the two, proportionally to their masses. But, when the target is stationary, their velocity is zero, so all of the kinetic energy is given to the allomancer (and vice-versa). [paraphrased from 8] I like this explanation. Honestly, I may agree with it more than with my own ANF theory. I tried it out, but it was a lot more difficult programming-wise than the ANF idea. Unity has easier force manipulation than energy manipulation, so I framed my theory using that. Energy is just force with extra steps. See Edit 1. I’ll talk more about the Allomantic Normal Force and partially-anchored targets after the math in Part V. Part IV: Math Now, I’ll introduce the formula that I used to calculate the Allomantic Force. After that, I’ll describe each of the terms in detail. Allomancy is a lot like magnetism, so let’s start by looking at the formula for the magnetic force between two poles. In Allomancy, the “two poles” would be the Allomancer and target. Magnetic Force = Constant * q1 * q2 / r2 Constant – some constant that depends on the medium between the poles. q1and q2 – the magnitudes of the magnetic charges of the poles. r – the distance between the poles. The greater the charges, the greater the force. The greater the distance between the two poles, the weaker the force – and through the inverse square relationship, greater and greater distances cause much weaker and weaker forces. Now, the Allomantic Force: Allomantic Force = A * S * b * c1 * c2 / r2 A – some constant. This depends on how all pushes and pulls are described in the book and can be increased/decreased for overall stronger/weaker pushes. b – Burn rate. See below. S – Allomantic Strength. See below. c1 and c2 – the Allomantic Charges of the Allomancer and target. r – the distance between the Allomancer and target. Burn rate – the rate at which an allomancer burns their metals. For my purposes, burn rate is a range between 0 and 1, where 0 is “not burning at all” and 1 is “pushing as hard as you can,” possibly without flaring. I bound this to the triggers on a gamepad and to the scroll wheel on a mouse, which allow me to variably control the strength of a push using the burn rate. Allomantic Strength – the most magic-y of the all the components of the force. Some Allomancers are naturally stronger than others, perhaps by sDNA. Allomancers get better with training and experience. These factors get bundled into the Allomancer’s Allomantic Strength. The Allomantic Force is not proportional to the Allomantic Strength (see [3]). Rather, the Allomancer’s maximum burn rate is proportional to the Allomantic Strength. In this way, Allomantic Strength acts as a sort of limiter. Stronger Allomancers must be able to burn more metal faster for a stronger effect. I won’t incorporate this in-game. Allomantic Charge – Analogous to magnetic charge. Contributes to the Allomantic Force. A property of both metals and Allomancers. I recommend now reading [1], which has a very interesting theory on this. I’m not adhering to it completely, though. An Allomancer or target’s Allomantic Charge is a function of its mass. To make the mass relationships of Mistborn work, we need to satisfy a few factors: The more massive a target is, the stronger a push an Allomancer can get off of it. The less massive a target is, the weaker a push an allomancer can get off of it. “[Wax] shot outwards in a grand arc above the city, flying for a good half a minute on the Push off those enormous girders” (AoL ch 1 pg 34) [3]. “…the lamp was a good anchor - lots of metal, firmly attached to the ground - capable of pushing [Wax] quite high” (AoL ch 1 pg 32) [3]. Both of the targets in these quotes are equally anchored, but the girders are much more massive and provide a stronger push. I don’t have any direct quotes, but we know that Allomancers get less of a push from coins than they do from, say, enormous girders. The “heavier” an Allomancer is, the stronger their push. This argument comes from Feruchemical weight, not mass, but it nonetheless impacts Allomancy in the books, so I should bring it up here. While tapping weight, Wax thought, “with this incredible conflux of weight, his ability to Push grew incredible” (AoL) [2]. I can’t quite remember the context or quote, but I recall that one of Kelsier’s surprises about Vin was her Allomantic Strength/Charge was large “for her size,” implying that smaller/less massive Allomancers usually have less charge. It’s symmetrical with the target’s mass impacting the Allomantic Charge. It’s intuitive and makes sense. There should be some soft maximum cap and minimum cap to the force. If an Allomancer pushes off of an absolutely massive multi-ton solid block of gold, they shouldn’t be pushed into the stratosphere. Likewise, coins are very light relative to lampposts and roofs, but they still provide a reasonably strong push. This leads me to the most disgusting part of the math. What exact relationship do the masses have with the force? The relationship can’t be zero. If this were the case, mass would have no effect on the force, which I argued against. Also, an Allomancer could push on a “metal” with a mass of 0 and still get a push, which doesn’t make sense. The relationship can’t be linear. If this were the case, a target 10 times as massive as another would provide 10 times a push as the other, which doesn’t appear to be the case. If an Allomancer pushes first on a 30g coin and then on a 30kg metal block, the Allomancer would receive 1000 times more the force from the block than the coin. In the books, Allomancers push off of girders and roofs which are much heavier than 30kg, but they certainly don’t describe such a massive difference in forces from coins. That’s duralumin-levels of strength. I’ve tried out a lot of relationships. Logs, sum of logs, product of logs, and roots. Eww. My solution was to take the root of the masses of the Allomancer and target. Specifically, the, ah, sixteenth root. It provided a good combination of strong-enough pushes from light coins and weak-enough pushes from very massive targets that felt most similar to the books. The number 16 was arbitrary. I figured I might as well use Scadrial’s base number for legitimacy. If I used a more elegant root (i.e. the square root), coins provided practically no force, and massive targets still pushed to the stratosphere. Higher roots “level the playing field” more than lower roots. c1 = sixteenth root of (m1) c2 = sixteenth root of (m2) m1 – mass of Allomancer m2– mass of target Because of how roots work, we can also say that c1 * c2 = sixteenth root of (m1 * m2). Regarding the maximum to the force that an Allomancer can get from an extremely massive target: The heavier and heavier the target, the less and less the increase in force. No pushes to the stratosphere. I’m not actually sure if this is the case with roots, but it felt like it was: the lighter and lighter the target, the less and less the decrease in force. Coins are very light, but still provide a significant push. In the end, I’m not actually trying to figure out how mass affects the force in the books. I am fairly confident Brandon didn’t consider the exact relationship while writing the books. I’m just finding ways to emulate it in a physics engine. Part V: Summary & Final points And here’s the final, composed formula for the force an Allomancer experiences while pushing: Force on Allomancer = Allomantic Force + Allomantic Normal Force = Allomantic Constant * Burn rate * sixteenth root of (target mass * Allomancer mass) / squared distance between Allomancer and target + Allomantic Normal Force Burn rate is between 0 and 1. A Burn rate of 1 gives the maximum Allomantic Force. When target mass is 0 or the Allomancer mass is 0, the Allomantic Force is 0. The closer and closer the target is to the Allomancer, the greater and greater the Allomantic Force. Like other normal forces, if the target isn’t fully anchored (e.g. a coin sliding across the ground, or a thin metal rod that bends as you push on it), the Allomantic Normal Force ranges from 0 to the Allomantic Force, depending on how anchored the target is. This means that an Allomancer pushing on a perfectly anchored target will be pushed back with twice the force as a perfectly unanchored target, assuming they have the same distance. This last bit about the distance is key. If an Allomancer is falling through the air and throws down a coin, the coin quickly falls further and further down. The Allomantic Force quickly becomes very small. Only once the Allomancer falls further and is near the coin – now anchored to the ground – does the distance stay small enough for the Allomantic Force to be large enough for a long enough time to scale a building. Friction (and air resistance) can also be a normal force, in this context; any (normal component of a) force that resists the Allomantic Force can be an ANF. Gravity, too, can be an ANF. An allomancer hovering in the air (whose push cancels out gravity) exerts an ANF equal to gravity back to their target. Theoretically, the Allomantic Normal Force could be greater than the Allomantic Force if the target accelerated in the opposite direction of the push. If you pushed (not pulled) on a target, and the target moved towards you (e.g. a very determined Steel Inquisitor, resisting your push and walking towards you), that normal force would push on you harder. This could result in “pushing matches” between Allomancers who try to move towards each other for even stronger pushes. Allomantic Normal Force works both ways. If the Allomancer is anchored (e.g. braced against a wall), the target will experience an Allomantic Normal Force. Other details: There are two main coins in Mistborn: Imperial boxings (gold) and clips (copper or bronze). In real life gold coins are usually around 30 grams, but I’ve experimented with increasing their mass by about 10-100 times for the game. Currently, I’ve kept them as 30g. When pushed with any reasonable force, 30g coins instantly fly off of the screen like bullets. There’s no user feedback that they pushed on that coin, other than, “that coin no longer appears to exist.” If you drop a coin from the air, it is on the ground by the next frame. Coins are sometimes described as behaving like bullets, but I don’t like how that works in the game. With heavier coins, you can see the coin after you push on it, but it still moves very quickly. Another option (which is the one I’m using in the game) is to simply cap their maximum velocity. I’ve left it at around 120m/s, which feels good. That’s about 1/3 the speed of sound. It causes some problems with calculating the Allomantic Normal Force from the target, but those have been resolved with coding (more or less). The image on the coins in the game is taken from Shire Mint. Fun fact: Unity doesn’t let you modify force vectors individually, which makes this a bit hard. You can only add forces/accelerations/velocity changes one at a time, then they are all applied to the object at the end of the frame. Calculating the Allomantic Normal Force is absolutely disgusting. See my code on GitHub, if you’re curious. I hope you all enjoyed the read! Please discuss this and give your opinions on the physics and maths of Allomancy. Specifically, Are there any more elegant relationships between Allomancer/target mass and Allomantic Force that you think I should try? Does anyone have any esoteric knowledge of Unity’s Rigidbody/Force systems that you think could be helpful? Any general ideas for the game? Any suggestions from what you can see in the videos? Any spelling/formatting issues with the post? Thank you.
  2. I've been thinking about the physics and realmatics of soulcasting. We have seen quite a bit of it on screen, but there are, of course, still mysteries. Going down the soulcasting rabbit-hole, I came across the following WoB: https://wob.coppermind.net/events/105-17th-shard-forum-qa/#e1139 Unfortunately, this seems to disagree with the canonical description of soulcasting. I imagine Brandon said this because in general he likes to preserve the laws of physics. (In this case the conservation of mass.) But how does mass conserving soulcasting contradict canonical soulcasting: 1) Soulcasting is shape preserving. We have seen this in every case where it is possible to see the shape of both the original object and the soulcast object. However, not only is it shape preserving, soulcasting also seems to be volume preserving. We have never seen a soulcast object, when soulcast into a denser material, shrink. This would be a very visible effect. It looks like marble has a density of about 2.7 g/mL. A human body has a density(if we include the air filled lungs) a little less than water, so let's call it 1 g/mL. If soulcasting conserved mass, a body soulcast to marble would shrink in volume by about 63%. This would cause a 6 ft. man to become a 4' 4" statue. 2) If soulcasting conserved mass, soulcasting to a lighter density material would cause catatrophic explosions. The analysis would be easier if she had soulcast it to air, but let us consider the example of Jasnah soulcasting the boulder to smoke. The smoke floated upward so it is less dense than the surrounding air. It looks like air at Standard temperature and pressure is about 1.3e-3 g/mL. If the boulder was 1m diameter sphere (This is being generous, it was likely much larger), it would have a mass of about 1.4 million grams of 1400 kg (using the density of marble as above). If soulcasting conserved mass, this would result in smoke that really wants to occupy about 1 million liters. To put that in D&D terms, that is 307 5ftx5ftx5ft cubes. Upon being soulcast the smoke would initially be at a pressure of 770 atms. A rough estimate would put the resulting expansion of the smoke at the equivalent of 55 lbs of TNT. (This last figure is very detail dependent and it is possible that I made some mistakes in the calculation. To make the conversion to equivalent pounds of TNT, I referenced http://ftp.feq.ufu.br/Luis_Claudio/Segurança/Safety/GUIDELINES_Chemical_Process_Quantitative_Risk_Analysis/0720X_02e.pdf) My conclusion? Soulcasting doesn't preserve mass, it preserves volume. Breaking conservation of mass is always problematic if you want to have physics behave in any way like we are used to, but I have some realmatic thoughts about that that I will share soon. I think that you can avoid the troubles associated with non-conservation of mass in a realmatic way.
  3. Creating this topic for Oathbringer-related discussion concerning Roshar's moons, as a continuation of this topic: With that said, here's some things I've been meaning to record... (1) Private message with Peter via Reddit about a reference to Salas in Oathbringer: (2) Also an interesting observation concerning the Oathbringer endpages in the Tor edition (Herald artwork): Ishar - Notable that we apparently see the three moons depicted in the background. Not much interesting about this as far as I can tell, but I figure it's worth pointing out. Jezrien - Look very closely at the "buckle" on his belt. There's a circle of the ten polestones, with heliodor at the top. And inside of that circle are three other stones spaced at different angles, seeming to be purple, blue and green... Vedel - Those are also depicted in the stained glass window behind Vedel. We can also see their positions inside the circle with a bit more accuracy here. Also note that we can compare their sizes: the purple one is slightly smaller than the green, and the blue one is definitely largest. I think it's pretty clear that the three stones/circles we see in Jezrien's and Vedel's artwork are depictions of the moons. I believe their positions are actually indicative of their timing--presumably the time that they rise. Think of Vedel's stained glass window as a 10-hour clock (matching Roshar's 20-hour day). Rather than splitting the day by noon/midnight, they split the day by sunrise/sunset. So if you have exactly 10 hours of light/dark, the sun would rise and set at 0:00 (or 10:00, depending on convention) and noon/midnight would be at 5:00. Eyeballing the position of the moons around this circle in Vedel's image, it would suggest that Salas rises around 3/4 of an hour after sundown. Fits pretty well with the descriptions that it rises right around full dark. Nomon is only about 2 hours later, suggesting that Salas moves pretty darn fast. I think there's a WoR reference suggesting Salas reaches full height in half an hour, so that would actually work well. (if I remember right). Nomon sets as Mishim rises, which means it's up for a good 4 hours. Then Mishim would be up for another 2.5 hours or so until sunrise. It's hard to say how exact those positions are meant to be. And I could be interpreting something wrong here? But I think it seems to generally fit the right idea, if nothing else. It also reinforces the idea that they follow the same rise times everywhere. (somehow) It's curious to me that the artist (I think it's supposed to be the same one in both of these?) would inscribe the moons inside of the ten polestones. That's some interesting Vorin (?) imagery and I'm not sure what the meaning could be. The fact that they both have it suggests to me that it has some kind of significance.
  4. EDIT: There's been a lot of discussion and revision to my original ideas, and I would recommend basically skipping this first post for the most part. It is, however, important to read the first two sections ("Observations" & "Related Information") as they set up some of the information given in the books and by Peter which is used to support the rest of the findings. Here are links to my most recent analysis: The orbits of the moons precess as the planet orbits the sun: http://www.17thshard.com/forum/topic/6334-the-moons-of-roshar/?p=103069 (I've since dropped the notion that they share exactly the same orbit, better language would be to say the moons share the same period and have very similar orbits....more on this in the posts below.) The orbit of the moons is in the opposite direction compared to Roshar's rotation: http://www.17thshard.com/forum/topic/6334-the-moons-of-roshar/?p=103135 (more details in the next link...) More about the orbits being in the opposite direction & how the orbits must be inclined when compared to the plane of the Roshar's orbit around its sun: http://www.17thshard.com/forum/topic/6334-the-moons-of-roshar/?p=103175 Preliminary calculations for the orbits: http://www.17thshard.com/forum/topic/6334-the-moons-of-roshar/?p=103350 There is, of course, a lot of good discussion and contributions between all these posts that I would recommend! I'm in the processes of re-organizing all of the information that has been deduced into a single document, so it can be read without the need to jump between posts and it would skip past the incorrect hypotheses. ----Orignal Opening Post (read the first two sections, the rest is now discarded)---- All this talk about the moons of Roshar in the other two threads got me thinking… Based on the "observations" provided in the book and the comments from Peter, I’ve come up with some speculations about the moons of Roshar. First…the data! Observations: “The sun set in the west, but the wagons kept rolling. Violet Salas peeked over the horizon to the east, seeming hesitant at first, as if making sure the sun had vanished.” WoK Chpt 2 “Nomon—the middle moon—had begun to rise, bathing the city in pale blue light. Staying up this late had been a rare privilege for her in her father’s house…” WoK Chpt 8 “Szeth looked over his shoulder, wishing that the Second Sister—known as Nomon to these Easterners—had risen to give a little more light.” WoK I-3 “Salas’s violet light shone in the sky outside, but the small moon wasn’t bright enough to illuminate the barn’s interior, and the creature had moved into a shadowed recess.” WoK Chpt 19 “Nomon—the middle moon—shone with his pale, blue-white light.” WoK Chpt 23 “Nomon was setting in the west, and the small green disk of Mishim—the final moon—was rising in the east.” WoK Chpt 23 “Two hours later, at Salas’s first violet light, Rock and Kaladin walked back into the lumberyard. It was just past sunset, and many of the bridgemen would soon be going to sleep.” WoK Chpt 27 “Kaladin smiled, leaning back, looking upward toward the dark sky and the large sapphire moon.” WoK Chpt 73 Related Information: PeterAhlstrom, on 06 Feb 2014 - 2:06 PM, said: Each moon is in the sky only once per day and moves across the sky in a couple to a few hours. What does that tell us about their orbits? http://www.17thshard.com/forum/topic/5854-setting-limits-on-the-size-of-roshar-the-planet-and-roshar-the-continent/?p=94890 PeterAhlstrom, on 06 Feb 2014 - 5:15 PM, said: I expect the moons were put in their current orbits artificially, but by whom or what I do not know. On astronomical terms, these are not stable orbits, but astronomical terms means millions of years. A few thousand or even a few hundred thousand years are no problem. http://www.17thshard.com/forum/topic/5854-setting-limits-on-the-size-of-roshar-the-planet-and-roshar-the-continent/?p=94976 PeterAhlstrom, on 27 Feb 2014 - 11:37 PM, said: They are very small. Think Phobos and you'll be in the ballpark. http://www.17thshard.com/forum/topic/6249-will-we-see-interplanetarlunar-travel-in-future-books/?p=102426 ------ Here are the “facts” based on the observations: Salas and Mishim are both described as “small” moons. (WoK Chpt 19 & 23) Nomon is described as a “large” moon. (WoK Chpt 73) Salas always rises first, Nomon always rises second, and Mishim always rises third. [szeth refers to Nomon as the Second Sister (WoK 1-3), Nomon is refered to as the “middle moon” (WoK Chpt 8 & 23), and Mishim is called the “final moon” (WoK Chpt 23), by process of elimination Salas is first.] Orbital Locations of the Moons: Since the moons always rise in the same order (Salas, Nomon, Mishim), all three moons have to be the same distance away from Roshar. They all have to be in the same orbit. Otherwise they would appear in a different order on various nights over time. And this means… the moons are at Lagrangian points! The Lagrangian points are stable locations where objects can share the same orbit. Jupiter, for example, shares its orbit with asteroids at Lagrangian points 4 and 5. Using the above image to describe the Sun-Jupiter system, the Sun is at the center, Jupiter is the purple body to the right (between L1 and L2) and the Jupiter Trojan asteroids are found around L4 and L5. Lagrangian points 4 and 5 are always about 60 degrees from the body on the right (Jupiter, in this example). In the case of these moons, Roshar would be the central body, while the most massive moon (based on the size, this would presumably be Nomon) would take the purple point near L1L2 (where Jupiter was), and the other two would have to sit at the other Lagrangian points. There is one final piece of information that helps us lock down the locations of the moons: from WoK Chpt 23 it’s clearly states that Nomon is setting just as Mishim is rising, i.e. they are 180 degrees apart…on opposite sides of their orbit. For the Roshar-Nomon system I propose that Salas is at Lagrangian point 4 and Mishim is at Lagrangian point 3. In regards to the orbits of the moons not being perfect circles… Jupiter has an orbital eccentricity of about 0.049. The Earth’s eccentricity is only 0.016. Even Mars, with an eccentricity of 0.093(!!), still has trojan asteroids at its Lagrangian points. I think it’s safe to say the Roshar-Nomon system has Lagrangian points. It is, however, notable that L3 is typically a very specific point and it can be unstable…I’m hoping the “artificial placement” of these moons helps to explain how Mishim ended up in such a perfect placement. Size Approximations: Since Peter suggested Phobos was a ballpark, I’m going to go ahead and copy it as a template for the moons of Roshar. First, Phobos orbits at approximately 9000 km from Mars, so I’m going to put the Three Sisters at that distance from Roshar. Because Nomon seems to reflect enough light to see by at night (WoK Chpt 8), which our Moon does as well, and I don’t have anything better to go on, I’m going to assume that Nomon looks to be visibly the same size as our Moon. Our Moon is about .5 degrees in diameter on the night sky. An object at 9000 km away would have to be 80 km in diameter to appear as .5 degrees in diameter on the night sky. As for the small moons, I’ll look to Phobos as an example again. Phobos is 22 km in diameter. From the surface of Mars, Phobos would appear to be about .14 degrees big on the night sky. In other words, a moon the size and distance of Phobos would appear to be a little under the diameter of the Moon as seen it from Earth. Assuming that the small moons, Salas and Mishim, have relatively the same diameter and mass, and that Nomon is significantly larger, these numbers seem decently reasonable to me. It would make the two “small” moons appear to be about 1/3 the size of the “large” moon, and the “large” moon would appear similar in size to our Moon. Closing Thoughts & Questions: It’s after midnight, so I don’t want to try and figure this out now, but I think we can get some more solid information on the orbital period of the moons based on what is presented in the Observations and Information sections. Peter said the moons were in the sky “only once per day,” which is interesting.... Especially considering that all observations of the moons only seem to take place at night (anyone have any daytime references?) There are two comparisons between sunset and Salas moonrise that I can recall; WoK Chpts 2 and 27. In both chapters, Kaladin observes Salas rising just after the sun had set. I don’t recall any mention of Salas and Nomon being in the sky together, but if my Lagrangian point theory holds I would keep an eye out for it in the upcoming books. It is, however, clear that Noman is setting when Mishim is rising (WoK Chpt 23). If the moons are only in the sky at night (as visible from Alethkar at least), does Salas always rise just after sunset? I’d love some lunar observations from Shinovar to see if the moons are visible during the day over on that side of the world! It is also possible that the two small moons are simply too small to reflect enough light, and the large moon, being blue, might just blend in with the sky. Still it seems really really weird to me that we only have nighttime lunar observations. Something to consider! I can’t wait to read of additional lunar observations in Words of Radiance!!!!!! ((edited for ugly formatting error I didn't notice in the previews))
  5. So I've mentioned this a couple of times in different threads, about how I view the relationship between the realms, as well as investiture, matter, and energy. I've explained it a couple times as 3 sheets of paper close together, and investiture is a weight that draws them together. But this isn't really entirely right. Paper isn't the right analogue. The three sheets are more like how space time is pictured in 2D: stretchy, not stiff like paper. Then three of these "sheets" are how I view realmatics. I also associate Matter with the physical realm, and Investiture in the Spiritual, which suggests that energy is related to the cognitive realm, which I'm still working on an explanation for that. Also, in a 2D view of spacetime, matter creates a dip, (as does energy, but to a lesser extent, given that matter is more... concentrated according to E=Mc^2. ) Investiture also does the same thing to the Realms, and that is key to how I picture realmatics. I will now use this model to explain how some various events work. First off, Highstorms. Highstorms are HUGE sources of investiture. The constant "weight" of that investiture has drawn the realms really close together on Roshar, so Spren appear. Furthermore, I have theorized that according to the fact that Shinovar never sees the brunt of the highstorms due to the mountains, that the realms are farther apart there. This (I think) is why spren don't appear there. It is ALSO (i think) why the plants have no life to them. They basically have no cognitive self compared to normal Rosharan grass and such. This also lends weight to the idea that perhaps the plants of Roshar are able to detect highstorms due to the investiture. When the realms start coming closer together, the trees and grass snap into their holes. Now of course it might be also a response to vibrations or something like that. Second, Kaladins dramatic oaths. Someone asked at some point why (in world, for writing purposes it's for a Climax) Kaladin always bursts alight when he does his oaths, unlike the other radiants. The fact is, most of the other Radiants have constantly progressed towards their oaths. Kaladin, on the other hand, recedes during WoR and WoK. Then, suddenly, he makes the decision to follow his oaths, and snap! He bursts alight dramatically. Now in my picture of realmatics, I describe it like this. The oaths that bring the realms together are fading, therefore Syl isn't able to manifest or think as well, and his abilities recede. Then, he changes and suddenly his oaths are much stronger, snapping the realms much closer together. Ergo, investiture suddenly flows to him, and he becomes significantly more invested. Now I'm going to make some speculation. Normal people aren't invested enough (aren't making enough of a dent in the realms) to use investiture. But people who are invested make enough of a dent to suck in investiture. By this method, Vasher should be able to suck in stormlight, because he's invested with breaths. I also think that a misting actively burning their metal might be able to make enough of a dent to ingest Stormlight. Finally, perpendicularities. Brandon described a shardpool as "spiking" the realms together. This perfectly fits with how I picture it. Investiture, the "weight", formed into a spike and driven through the realms to bring them entirely together. Else calling would be more like a needle. Also, a little more theorization. I think that aluminum pushes the Realms apart, countering the "weight" of investiture. Because of that, that would mean that maybe a large block of aluminum could prevent spren from appearing. However it may be that the property of aluminum is totally within the aluminum itself, which would mean that it would be a moot point, because why would a spren materialize within a block of aluminum or any metal anyway. However, based on the fact that you only need a hat made of aluminum, and not an aluminum head to prevent emotional allomancy from affecting you, I think that the aluminum has a somewhat local effect, forcing the realms apart around the aluminum. Therefore, according to this model, a radiant wearing enough aluminum shouldn't be able to suck in stormlight.
  6. Need any help with it? Come over here! Want to talk about it? This thread's for you! Want to hate on it? Go somewhere else because that's not what this thread is for. These people make excellent resources for help. Math/Calc: Chaos Classical Physics: Glamdring804 Micro/Nuclear Physics: Idealistic Mistborn Chemistry: Pagerunner Biology: Pestis the Spider Circuits: Silverblade5
  7. Hi, While trying to uncover the secret location or Urithiru, I found myself totally at a loss about the size of Roshar and the relative distances between places. This is most probably because most characters so far have been confined in specific areas, and the book doesn't really deal with travel in the way some other books do (LotR, NotW, aSoIaF to name a few). So I decided to try and look for clues in the book which may help me set at least a few limits on the size of the planet and the continent. The first and most solid clue that we have is the gravity on Roshar. gRoshar = 0.7 * gEarth.. (I'm not sure where we know this from, since I've only been a fan for about a year, and it has been on the stormlight wiki for at least that long) Now in a simplified model g is related to the size of the planet by the formula g = G*M/R2 = G*d*V/R2 = G*d*4*pi*R/3 where G is Newton's constant, d is the density of the planet and R its radius. So constant multiplicative terms aside, the acceleration due to gravity should be proportional to d*R. If you look at the densities of the terrestrial planets in our solar system, most of them seem to have a pretty typical value, that of around 5.5 g/cm3 , If we assume Roshar to have the same density, then that would mean that its radius is 0.7 times that of Earth. However, I think Roshar is likely to be a tiny bit denser if anything, given that it seems to have a sandy or soily crust only on about a sixth of its area (Shinovar) and seems to be made of solid rock everywhere else (which is presumably denser). If it is denser, then that would mean that its radius is smaller than 0.7 times that of Earth. In any case, the point I'm trying to make is that we can safely say that Roshar has at max 0.7 times the radius of Earth. This would put its circumference at 28000 km. Our next, and to the best of my knowledge, only other clue about distances in Roshar is the following epigram from WoK Ch 39. So we know that there are two places on the Roshar continent that are far enough apart that it takes four months to travel by foot. Now one Rosharan year is 1.1 Earth years, and has 10 months. So 4 months would be about 0.4*1.1*365 earth days ~ 120 days. I assume if you're traveling on foot, you'll walk for at least 9-10 hours at a leisurely pace of 5 km/h. So that would make a total distance covered in 4 months of 120*5*10 =6000 km. Now this might seem like a small number compared to the circumference of 28000 km quoted above, but to put things in perspective, that is the approximate distance between Geneva and Mumbai. So that's at least how wide Roshar (the continent) is in one dimension, assuming Alezarv whoever he was had to travel across the continent to get wherever he got to. The original motivation of this study was to check if Roshar the continent covers most of the planet, because that would put more weight into the idea that Urithiru was somewhere in Shinovar, and westward in the place nearest to honor is actually pretty near the Origin of Storms which is in the East. After all these calculations, I don't think I can say anything either way. Alezarv may have travelled within Alethela, in which case the continent could ver well span Roshar, or he could have crossed the entire breadth of Roshar in which case over half the planet is as yet unexplored in the novels. As they say in academia, no result is still a result, and while I may have been unsuccessful in pinpointing the location of Urithiru, at least we have a better idea of how big Roshar really is. In case there is some more information available about this (WoB etc.) please let me know. I think both these questions (how big is the Rosharan continent in comparison to the planet, and how big is it in absolute terms) are really fascinating, so if any of you get a chance to ask Brandon, I'd be really grateful if you did!
  8. SEE POST BELOW < click here! I've rejected this original theory, but I'm leaving it here for reference! The original post is below the line. As an engineer, I've daydreamed about the physics of Iron Pulls and Steel Pushes a fair bit. There's some old threads, but they're pretty dead. And I don't think they provide very satisfying reads. There's a few problems I have and I'm curious what other people think. Yes, I realize that at some point we have to step back and say "it's magic, because obviously the world doesn't work this way". But humor me. Surely there's some other nerds out there like myself who think about these things. I guess I should note that this topic may contain spoilers for all Mistborn books so far. (I made a Stormlight comment at one point, but it's not a spoiler in my book.) The Basics So let's talk about Allomantic force. It's usually assumed to be a body force (like gravity), because there's never any indication (that I can remember) of a point force inside your body (which would be weird) or a surface pressure and because the accelerations involved would seemingly give severe whiplash otherwise. Most people assume that it follows the inverse square law (also like gravity) because effectiveness obviously decreases with distance and that's a logical assumption. Lastly, there's some level of Allomantic Strength involved to account for [1] your inherent abilities, [2] your current burn rate or something like that (to account for flaring, Duralumin, etc.?), [3] the desired strength of the force (though this may be subtlety accounted for in 2?), and [4] the difficulty of Pushing/Pulling some object (as it's hard to push on something Invested, like a metalmind, a spike, or metal inside a person). This gives you an equation something like: F = A / r² where A accounts for the Allomantic Strength and r is your distance from the metal. Alternatively it could be something exponential, along the lines of F = A e^-r, so that the max force is finite at r=0. Both of these allow for non-zero force at infinite r, though I think we can get around this by arguing that the force would be incredibly weak (enough to be very negligible) at great distances. And there is an argument that, while the equation is always true, there's some mental element to the magic- so that even if you are physically capable of Pushing something from many miles away, you can't do so if you don't have a mental and/or spiritual awareness of (or connection to) the metal you want to Push. The exponential equation actually makes a bit more sense to me, because I feel like the 1/r² version puts way too much weight in the distances involved. Doesn't feel right to me that Wax's strength increases by 4x if he moves from 4 meters away to 2 meters away (from some metal object). So I'm going to go with F = C1 A (e^-r)^C2, where the Cs captures whatever constants are needed to scale our equation appropriately. There also seems to be some debate on whether the Allomancer's own mass should be part of the equation as well, because there are a few instances where Keslier and Wax seem to suggest that heavier Allomancers are generally stronger. Those who disagree argue that they are only referring to how the extra mass makes you more resistant to the reaction forces and the pushes of others. I think it's debatable either way, due to unclear explanations. Problem: It can't be a simple applied force. I think there's a serious problem with assuming that Pushes and Pulls work like a simple force in the way I've described, and it's rooted in a simple example in The Final Empire (and pretty much every other book). When first learning her metals with Kelsier, Vin pushes a coin out of his hand and into a wall before she is suddenly thrown backwards. Newton's 3rd Law says that forces have to balance out, and people generally assume that this holds true for Allomancy. The text suggests it on many occasions. But if Vin is pushing this coin with a constant force it shouldn't matter that the coin stopped before she was thrown down. It's easy to assume this sounds right, but it's not. If Vin is pushing with a constant force then nothing changes when the coin hits the wall. She should be feeling a reaction force at all times, and it should be equivalent to the force she Pushes with. But what we see is a sudden increase in force after the coin is restricted. It's like standing with a garden hose, water flowing. You don't get pushed back less when you spray water into open air and more when you spray it against a wall. I assume this problem is rooted in a simple misunderstanding Brandon had when developing the magic, or maybe he just didn't care. But I've been trying to explain what we see in some other way. Solution? Violation of Newton's 3rd Law. The best solution I can see seems to require violation of conservation of momentum and energy. (Edit: Someone on Reddit has claimed that WoB says momentum is conserved, but I think the text suggests otherwise) But then, this really shouldn't come as a surprise considering Allomancy is "End-Positive" per the Ars Arcanum. So we're not really creating energy and momentum here, but taking it from Investiture. And this allows for an imbalanced force to exist. And this is where my solution comes in. I'm struggling to find the proper language to describe this, but what you basically have is more force going to the thing with less mass. Let's look at equations... So the force we calculate above, F = C1 A (e^-r)^C2, is actually the sum of two forces being applied when a Push or Pull happens. There are two elements involved: the Allomancer and the "Object". By Object I'm referring to the metal being pushed, plus any other mass it is attached to. Can't think of an example, but I'm pretty sure a coin tied to a bag of sand is harder to push than a free coin. The extreme case is where the piece of metal is pressed against some massive object (like Scadrial itself). So let the Allomancer be noted with subscript 1 and let the Object be noted with subscript 2. What we have is F = F1 + F2. F1 is the force on the Allomancer and F2 is the force on the Object. So how much force (F) gets directed to F1 and how much to F2? Let me introduce a new factor, X = m1 / (m1 + m2), which tells us how much force is directed into the Object. Then the amount of force directed into the Allomancer is 1-X. So F1 = (1-X) F = F - X F and F2 = X F. I'll illustrate the meaning with some examples below, so don't hurt your brain trying to interpret what I mean here. Examples: Let's consider the case where Vin pushes a coin in the open air. The coin's mass (m2) is much much less than Vin's mass (m1), so we essentially have X=m1/m1=1. The coin receives (almost) the full Allomantic force with F2 = XF = F while Vin receives almost no reaction force. Suddenly the coin hits the wall and Vin is no longer just pushing against a small coin, but also against the building the coin is pressed against and the ground the building is attached to. So now we have m2 >> m1, which means we essentially have X = 0. Now Vin receives (almost) the full Allomantic force while the coin receives almost none. This explains why suddenly she is knocked back with a higher force. The reaction force she feels dropped from almost F1=0 to F1=F in an instant. This also explains the "middle of the road" case where the Allomancer and the Object have a similar mass. If m1=m2 then X=0.5. Half of the Allomantic force goes into the Object while half goes into the Allomancer. As you can see, this does a reasonably good job explaining how pushing a small, free object produces little to no reaction force while pushing against a great mass throws the Allomancer with their own full strength. But it also accounts for the cases, in between, where Newton's 3rd law seems to apply normally. It also might provide a bit of an answer for why an Allomancer's own weight/mass plays into his strength. It doesn't actually boost the forces they are capable of, but it doesn't just provide resistance to a reaction force either. It actually tips the scales of how the force is distributed, in non-extreme cases. Other Problems... This isn't quite perfect however... It's pretty obvious in the case above, where the coin is pressed against the building. If the coin no longer experiences any force then it would drop to the ground. But we don't (apparently) observe this. You can imagine that the coin slipping a little means it isn't quite in full contact with the building, perhaps... And so then it's rapidly getting pushed back again every time slips. But this feels a little weird, and doesn't work great. My best solution is that maybe my X factor above isn't quite perfect. Perhaps there's some minimum amount of force that the Object will receive no matter what, for example. This also makes me consider the case where Vin and Kelsier have their little Push battle, with the coin between them. There's a few weird things there as well... First, we have the "center of mass problem" that I'll get to in a moment. Second is what does this mean for the mass in my equation above? For Vin pushing a coin that Kelsier is also pushing... what is the m2 in that equation? The mass of coin plus the mass of Kelsier? Plus the mass of Scadrial if Kelsier is anchored? What if he's standing free and relying on friction with the ground? Perhaps the calculation of m1 and m2 is a bit more complicated and involves some Cosmere concepts? Maybe there's some kind of "effective mass" that we have to determine? Third is explaining why the coin doesn't just fall down. If two equal and opposite forces are at work, why doesn't gravity take over? My best guess is that this plays into the "center of mass problem"... Kelsier and Vin are obviously keeping the coin balanced between them rather than letting it slip to one side. This configuration is unstable, so there has to be some means for them to balance the coin. And it's not a big leap from there to say that they're giving the coin some upward force as well, to balance gravity. The explanation deserves an eye roll maybe, but the scene is so awesome that letting it slide is easy. Then again, maybe gravity just does weird things when magic is at work. There's precedent... In Stormlight we see a bit of an oddity that's similar (perhaps) with the Surge of Gravitation... But I won't get into that. And maybe this also plays into why the coin against the wall doesn't fall, in my framework above. Fourth, we have to explain why the coin flattened. It's tempting to just give up on this one and say it's a mistake. If Allomantic force is a body force, then this is hard to explain. Gravity can squish an object, but only because it presses you against the ground. Two body forces just cancel out and don't causes any stresses inside the body. Technically the outsides of the coin experience a bit more force because they are closer to the Allomancers than the center... But that's definitely not enough of an explanation. Perhaps Allomantic force is more of a pressure applied along a body's surface? Not sure if there's much support for this elsewhere in the text, but I'll have to keep an eye out on my next read. The Center of Mass Problem I have a strong opinion on this one... The characters are convinced that you can't really control the vector of an Allomantic force. It's just a two way force pointing directly through the centers of mass. I am of the opinion that they are wrong about this. Wax proves that this isn't the case for the object itself, unless I'm mistaken. I seem to recall that he is able to break down a metal object into "smaller pieces" mentally and push on a single element out of a large piece of metal. (Edit: Someone on Reddit corrected my memory of this example and I no longer think it applies) Seems like Kelsier might also have done something like this by spinning spears (Edit: metal bars) midair? And of course there's evidence to suggest that Allomancy can be performed on trace metals. Logically, we know that any metal thing is ultimately made up of a bunch of smaller metal things. So it makes sense why it would work this way. It's likely that understanding how to manipulate metal this way is just not well understood. Might involve someone's power level. Definitely involves skill and understanding. Maybe a few more years down the road we'll see Allomancers who have a better understanding of this. The same seems to be true for the point in your own body that you Push and Pull from. I don't have as much hard evidence that this is possible, though the ability to balance on a single small piece of metal is a great start. Again, I'm betting that an Allomancer has some level of control over where they Push and Pull from. I would expect that this "point" must be located within your own body somewhere, but that you can shift it with the right understanding/skill/practice/etc. In fact, it seems likely to me that my simple "point force" equation above is a simplification. More than likely what we're dealing with is a field, which emanates from the Allomancer. He has some kind of mental control over which bits of metal he is effecting (down to the molecular scale?) with his field, which is dependent on skill (etc.) and which is largely performed subconsciously/intuitively. (atium gives you understanding of how to process the data you receive, so it makes sense that other elements do something similar) And he also has some kind of control over that field, by shifting around Investiture (or whatever) within his body. Thoughts? What do you guys think? Got any passages that support this theory? Or any that disprove some part of it? Maybe some idea on how to refine this? I'm curious what other people think!
  9. First, this forum is such a cool space to have conversation and speculation among people with similar interests yet such different backgrounds. The different experiences that we have definitely feeds into how each of us reads and interprets, which makes for such a fascinating opportunity to share insights and see things in ways that we might not have thought of or picked up on. Certainly, there are aspects of the fantasy genre that are meant for entertainment – I, for one, love to get lost in a different world every once in a while, disconnecting from ‘reality’ and plugging into dreams and imaginations. However, much of the world deems writing, poetry, imagination, fiction, especially fantasy, as a luxury that is separate from and irrelevant to what is commonly known as ‘real life.’ So I wanted to begin, since this is my very first post in the forum, with a word of encouragement to you fine folks. As the saying goes, fiction is the lie through which we tell the truth (I am sure the progression of Shallan Davar and Pattern would agree with this), and fantasy, as removed from ‘truth’ as it often seems, is a pertinent example of lies through which much truth is often spoken. To those of you who are mocked for choosing to spend your time in a corner, head buried in a book, take heart and confidence in what you learn from your imagination, and in that confidence share your insights with those who might be afraid of the truths they might find within the lies they tell themselves: that reality is what it seems, fantasy is only escape and distraction, and survival is for the ‘fittest.’ Imagination is not a luxury, it is life. I think Brandon Sanderson does well in showing this in the Stormlight Archive, making manifest what we cannot naturally see in our world through spren. As said in one of the books, spren is change, or, at least in Roshar, a visual manifestation of change. To relate this to our world, things are changing all the time. We do not notice, and we take it for granted, but it’s true. Cells are constantly dying and growing; when we stand still, we are moving with the earth’s rotation; we are thinking, always thinking; etc. etc. One thing I wanted to touch on specifically, however, is the nature of light, which I promise I will relate to Truthwatching and Illumination eventually, so bear with me. Questions of sight do not usually inspire responses of detailed reality, with the physics of how one actually sees, in terms of what might even allow for sight – that is, for example, one does not think to tell of the light that reflects off of opaque surfaces and into eyes, or the lack or distortion thereof that might affect vision, or the scattering of such that red might be distinguished from blue, black and white and the shades between. For most, light is rarely thought of as an independent actor, but just a medium through which we see. Even for the blind, however, light exists: at the very least they can feel its warmth, its energy – they would not see in the same way because light exists differently for them. The point is that light is everywhere but it is often not considered – perhaps we actually see more than we think. Perhaps spren really do exist. I first noticed the correlation between spren and quantum theory in the interlude chapter in Way of Kings where two ardents are measuring spren. As a disclaimer, I am not a theoretical physicist, nor will I include any math here on this forum, but it is fascinating to compare the similarities. In classical physics, what we all perhaps learned in high school in one form or another, measurement does not change the state of what is being measured. For example, the weight of one paperclip today will be the same tomorrow, more or less. In quantum physics, however, the rules are different – measurement changes everything. To tangent a little, this discovery in the early 20th century has made physicists rethink how even reality works – what if quantum theory applies not just at the quantum (very very miniscule) level, but to everything? Not just physically, but cognitively as well? This is the context I am placing the Stormlight Archive in. Through fantasy, Sanderson has made manifest and broken down certain theories that pervade contemporary thought. In the previously mentioned interlude chapter, spren stop moving when they are measured. This is similarly the case in quantum theory (if interested, look up wave function collapse). Okay, cool. But so what? Here is where my theory on Truthwatching comes in. When Renarin says he sees, what he means is that he actually sees. Not ‘see’ in the conventional sense, but literally sees. Wow, really clear man. I know, I know. The closest analogy I could think of is The Matrix, where at the end -SPOILER-, Neo literally sees reality as the code of the Matrix since it is a computer program. What I’m saying is the Truthwatching is a similar thing, except instead of code, what Renarin, and other Truthwatchers, see is the spren (quanta) of everything. Everything. This has nothing to do with his visions. I am in the camp that says his visions are not a result of Truthwatching since Dalinar, Kaladin (dream), and Shallan (drawings), have the same experience (I believe FeatherWriter has a really good and well-written post on this). This brings a new connotation to Illumination. What “illumination” means is to shed light on or clarify. If Lightweavers use Illumination to create illusions (perhaps because of its combination with Transformation), maybe Truthwatchers see through illusions. To relate, if we look at an apple sitting on a table, we see it as still. If we shine a strong light (must be coherent light) on it, however, the shadow that appears will show a hole in the middle; i.e. the solidity of the apple is an illusion. Or, if we shine a light on any object, the boundary of the shadow will appear fuzzy even though the boundary of the object is solid; i.e. static boundaries are illusions – this is due to the property of diffraction and the wave-particle duality that light has, another consequence that quantum theory attempts to explain. The perfect place to extend this theory from merely the physical to the cognitive, emotional, spiritual, etc., is the space of imagination and fiction, which are as real as physical reality. I think this is what Sanderson is experimenting with through the separation of Physical Realm, Cognitive Realm, etc. Truthwatchers might be the only ones able to see what is actually going on. In our world, our eyes often deceive us. Perhaps to see as Renarin does would be to see through the deception of reality. See spren. See what matters. See the stories behind people (Ym). See beauty. And to be able to see would certainly help knowing how to heal whatever is damaged – I am defining ‘heal’ here not as cure or fix, which implies some sort of wholeness, but ‘heal’ as in growth (i.e. Progression not towards, but Progression from). Sometimes a word of encouragement or a pair of comfortable shoes might go a longer way than stabbing someone with a Shardblade, deposing an incompetent king, or summoning highstorms, and this is what Renarin can see. Of course, this is all speculation, and I’m sure what I’ve written is full of holes. So, thoughts?
  10. After a brief conversation with Brandon on the matter, I think I might be onto something. This theory revolves our current understanding of Physics so it would be some time in the timeline before we could confirm these theories. However I cannot stop thinking about these ideas and Brandon confirmed a couple of my speculations. But if the skills that Shallan has displayed, along with the words of Pattern, we can extrapolate incredible future abilities. Now I could be wrong simply because we don't have an understanding of all the radiant groups as of yet, but here me out about this. So what do we know are Shallans abilities? Well the first and probably the most powerful (that we KNOW of) is the soulcasting. Shallan can separate her cognitive mind from her physical body and interact with shadesmar directly. Once she masters this skill she will be able to use storm light as a bargaining chip to convert matter and form. I'm excited to see what this entails and if there are any real limitations to this power. Like can they only soul cast into one essence at a time? Why do the soulcasters in the Alethkar army look like they have stone for skin? So many questions, but despite this ability, I want to focus on lightweaving itself. i just feel that transformation is "more powerful" than progression. No the ability to manipulate light is the real power here. Although "Lightweaver" is a deceptive name. Remember how Pattern said that Shallan could manipulate sound as well as light? When I read that the second time through I did a double take. I mean, on the surface these two are vastly different. Light is a collection of photons, where as sound is a vibration in moving particles. The only thing that these two truly share is that the nature of light and sound is determined by the waves and wavelengths that they maintain. So how could this be? If Shallan is creating false light barriers, then that should be the extent of her abilities. it would still be amazing and incredibly versatile, but that's it. Including the ability to affect sound waves tells me that there is something far greater going on. If Lightweavers actually shape the wavelength of physical particles and energy waves, then her powers become nearly unlimited. First I'll start with sound. If Shallan as a Lightweaver can control waves of vibration to create sounds, then what else could she do (Assuming stormlight were no object for the sake of speculation) Well she could most likely stun people with powerful sound waves. Especially in the water, large enough shock waves can actually stun of kill. Remember a noise is simply a managed vibration in particles including liquids and solids. If you can manipulate shock waves and add enough power, stunning people would not be too far fetched. Even Earthquakes are effectively massive shock waves that travel through the soil. They seem vastly different from a verbal shout, but on the large scale they really operate on the same physical premise. And we now know Shallan uses her powers to effect shock waves, so far just on the small scale. So we can presume that with enough stormlight, Shallan could cause an earthquake. Now to the real power. Light manipulation. Often times we get comfortable in our spectrum of light. We have the colors of the rainbow and every shade in between. Shallan had displayed the countless applications of light manipulation in stealth and espionage. However we are not so limited in Physics. Visible Light is a tiny part of the Electromagnetic Spectrum. The levels of light along the spectrum are only different in their wavelength and frequency. This is where things get exciting. First lets go to the large end of the spectrum. So if we have two lightweavers, perhaps standing on the peaks of two different mountains. If the lightweaver can manipulate radio waves, using stormlight to create a variable radio broadcaster and receiver, we would have the perfect way to communicate without anyone being able to listen in. This could be very useful, although span-reads honestly are better at this, so this is less exciting. More likely Lightweavers would become radio hosts in the future as they transmit music and voices into the homes of radio owning families in the future. I can imagine Lightweavers as traveling radio performers sharing their skills as actors of comedians across the radio waves. But it's the other end of the electromagnetic spectrum that gets really crazy. Imagine how soon x-rays for medical diagnoses could be used when your doctor can literally create x-rays out of thin air? Crime scene investigators will have a local Lightweaver create UV lights to help reconstruct the crime scene and look for trace evidence. But the ultimate form (That Brandon said would be too much to be practical both in needed stormlight and application) would be the control of Gamma Radiation. If this could be harnessed, Lightweavers could literally become mini nukes, or death guns. The biggest downside to making Gamma radiation would be the damage the lightweaver would most likely suffer. So gamma radiation is impractical but its a fun thought experiment. So that's the end of my thoughts, I just see people talking about how Lightweavers are cool, but not as powerful as Windrunners. Now you know the possible future of lightweavers! The best part of this whole speculation was how excited Brandon was about my train of thought. I don't know if anyone had brought up this train of thought before. But he was happy to remind me that things will get pretty interesting when Lightweavers discover lasers and start using them in combat. Seriously, he said that, I couldn't ever make this up. Hope you enjoyed!
  11. This is fairly straightforward. We all should know that one of the fundamental laws of the Universe as we understand it is that Matter cannot be created or destroyed. Technically you could argue that matter is organised energy levels but that's only speculation. However when a Allowmancer burns metals, they vanish completely. As it is said many times, these metals are poison to the body normally and they don't really just "pass" in a healthy way. So what actually happens when the metal is burned? Because we know that the Investiture doesn't come from the metal itself, but the metal acts as a conduit and determines the application of the power. So where does the metal go?
  12. Okay, so this post will probably get edited when I come up with more theories and questions. Let's get down to business right now: 1. Force of a Steelpush or Ironpull This has been bothering me for a while. Whenever I reread the Mistborn books, I notice just how much damage Pushed coins are doing. In WoA, one of Cett's soldiers actually has a chip of their tooth pop out of their mouth when they're hit with a coin. Coins frequently puncture through someone's entire body. Yet, it's mentioned frequently in the books that your weight governs the effects of your Pushes and Pulls. Yet, this may refer to the total force applied in a Push or Pull, or perhaps just the effect (whether you or your target or both moves). To add to the confusion, we can tell from Vin and Kelsier's Pushing match in FE that seems like weight might be more of a factor than just determining who moves, if we're thinking that way, yet at the same time, we can tell that since Vin's Spiritweb had already been affected by Preservation that she could Push with more force. So, what determines just how hard you can Push or Pull? It must be powerful enough to break bones with a coin, yet must be governed by weight in some way. But it can be affected by how powerful an Allomancer you are. Is it possible that it is governed by the weights of the involved objects? Thoughts? 2. Center of Mass of a Push or Pull Frequently in the books, the characters flare pewter when performing extreme feats with iron or steel to 'stop from being crushed or pulled apart.' That begs the question: Just where on the body are these forces being exerted? Steel or iron lines point from the chest to different sources of metal. It is possible that this is where Allomancers Push or Pull from. Yet, if that were the case, how would forces being enacted on this nebulous 'single center of mass' threaten to crush or pull apart the entire body? That description makes it seem as if the forces are evenly applied and distributed around the exterior of the body. This doesn't seem likely to me, but I suppose it's possible. A theory I've been toying with is that Pushes and Pulls actually originate from the metals in an Allomancer's stomach, but it doesn't have much supporting evidence. What do you think? 3. Limits of Emotional Allomancy I don't like the way that emotional Allomancy is depicted in the books. It leaves things far too open-ended for my liking. The 'emotions' that a Soother or Rioter can affect are shown to be anything between chattiness and desire for a debate. Even boredom is shown, which I definitely don't think of as an emotion. It certainly causes other ones, like aggravation or something similar, but boredom is just another term for 'having nothing to do or think about.' It sort of ruins the rigid logic of Allomancy for me. It seems like anything that might have a remote possibility of being described as an emotions can be affected by the use of zinc or brass. So, my question is: does anyone know more about this? Are there actually limits that govern what can be affected by emotional Allomancy and I'm just being ignorant? Please tell me.
  13. So in WoK, there are those two ardents in the the eighth interlude (Geranid). The one is studying Spren and discovers that if you measure a spren, and record your measurements, it locks it somehow. Size, shape, luminosity. I assume this had to do with the cognitive realm and I'm sure there's already somewhere on these forums about how recording it sets a law in Shadesmar or something. BUT! This isn't about that so much as it's about the similarity to the real-life scientific phenomenon called the Quantum Zeno Effect - or Turing's Paradox - where if you measure or observe an unstable particle enough times, it will stop decaying like it should. You can lock an unstable particle of Uranium by measuring it or watching it. Thought it was an interesting similarity and I didn't see it pointed out anywhere else here. Btw this is my first post here so yeah... Just thought it was worth mentioning. Don't know if it means anything...
  14. I've been following the "Weight has nothing to do with allomantic Push/pull strength" thread for a while, and I think we're using the wrong model for framing physics questions related to Pushing and Pulling. What is the behavior observed in the books? If Coinshot A Pushes with allomantic strength B on coin C, we observe that both A and C will experience acceleration proportional to B but inversely proportional to their mass. So as long as C is not anchored, it will accelerate rapidly while A is barely affected, but when C hits the ground or a sturdy wall suddenly its effective mass is increased to the mass of the combined system (coin plus wall, or coin plus planet), and its acceleration drops way off while A's acceleration spikes. When we use F=ma, the problem that arises is that the acceleration a Coinshot experiences when Pushing a coin should depend only on the magnitude of the force applied, not on whether the coin is anchored. If we view the magic as a simple action/reaction between the Coinshot and their target, the behavior we observe in the books is not preserved. There is a well defined physics model that deals with two objects interacting in a way that changes their velocities to a degree that's inversely proportional to their masses: elastic collisions. If we reframe this situation in terms of an elastic collision, then the allomantic strength term becomes not force but kinetic energy. A given allomancer's push strength is the amount of kinetic energy they can add to the system. What happens to the velocities of the components of the system is then subject to conservation of (the new, higher) momentum. This preserves the behavior we see in the books. (Actually a person's Steelpush strength would be delta-kinetic energy per unit time, but integrating over time is left as an exercise for the reader.) If you'd like a pseudo-concrete framework for thinking about this, imagine that the blue lines you see while burning Steel are tangible to the things at either end of them. Normally they are happy to simply change length to remain in contact with their endpoints, but when Pushed or Pulled, an Allomancer pours some Investiture into them and makes them grow or shrink with some amount of power. The line doesn't care where its center winds up, or how long or short it winds up being, it just knows how hard to push, and the end that resists less will be moved farther than the other. So to bring this back around to the question of whether your Push/Pull strength depends on your mass: Yes and No. There's some innate Allomantic Strength term that's independent of your mass, but in practice the things you can do with Allomantic iron or Allomantic steel are influenced by both your strength and your mass. (When you're trying to move yourself it's better to be lighter, when you're trying to move other things it's better to be heavier.)
  15. So, I am listening to the audiobook for WoK, and was listening to the part near the beginning when Kaladin is in the slave wagons and hopes that spring will come again, with the narrational aside that the seasons were unpredictable. This got me to thinking: how could seasons be unpredictable? On earth, the distance from the sun and the tilt of the Earth's rotational axis combine to give us seasons. What could be going on for Roshar to be having a random (to Kaladin) distribution of distances from the sun? My first thought is that perhaps Roshar orbits some sort of binary star system. (Perhaps locked in such a way as to only show one of the two suns at a time, but the differing distances causing irregular (but maybe predictable through math by stormwardens) seasons. This may also explain Braize, as it could be getting both suns, making it a place of fire and heat and eternal day. Thoughts?
  16. I've been unsatisfied with the definitions and explanations of investiture floating around here, and it's been causing me headaches, so I decided to gather up all the info I could, and make a theory. It's still under investigation, so I'd love it if people could contribute or poke holes in it. Hypothesis: Investiture is a form of Spiritual Radiation that follows the laws of Wave/Particle duality. Qualities of Investiture: • It has a pulse length • It has a frequency • It can infuse or suffuse an object • It can be removed from an object • Objects have a maximum capacity or tolerance for investiture • It can be transmitted • It forms systems • It is conserved within a given system • It leaves behind traces when an object has previously been infused with high concentrations • It is entropic • It is subdivisible • It can have a pressure, or more precisely, a directional force • It is constantly emitted from an invested object • One frequency of investiture interferes with another Given these qualities of investiture, we can notice a few things. Investiture is either a wave, or a wave/particle duality with very low mass. Investiture exists primarily in the spiritual realm (it affects emotions). Investiture behaves in many ways similar to a thermodynamic system, and obeys many laws similar to thermodynamic laws. Investiture behaves similar to radiant energy, such as light or electromagnetic radiation, and in other ways it is more similar to particle radiation. Conclusion: The conclusion I draw from listing these characteristics is as follows: Investiture is a form of radiation native to the Spiritual Realm of Realmatic theory. Shards emit a high quantity of this radiation, over a spectrum of frequencies determined by the intent of a shard. Any spiritual entity may become infused over time with this radiation, and invested spiritual entities also emit small quantities of radiation themselves (similar to being radioactive). Infusing a spiritual object with high amounts of radiant investiture will likewise mutate that spiritual object. A focus allows an individual with access to this radiation to convert raw radiant investiture to either a specific frequency of investiture, or to convert the energy of investiture to a physical force. An example of the former is feruchemy. An example of the latter would be Allomancy. The nature of the effect is determined by the frequency of the investiture, and the form of the effect is determined by the intent of the user. A selection of sources: (with all the organization of a dead duck) I say a selection because it is SO DARNED HARD to gather information for these things. Anyway, please discuss, refute, rephrase, or offer additions to the above definition of investiture. I have not spent the time yet to completely categorize and organize my thoughts on this into a formal theory, and would like to refine it before I do.
  17. With the recent releases from WoR has come much confusion on the nature of gravity on Roshar. This is not a new discussion, but I'm starting a new thread because my response was getting too long. As a brief introduction, there are several WoB that seem to imply that gravity has a Spiritual component. However, he has also claimed that the laws of physics work like they do in our universe. Reconciling these two ideas has lead to a great deal of confusion. In what follows, I'm going to use an important device from theoretical physics - the "toy model." These are simple models that attempt to explain the bulk of phenomenon by necessarily being incomplete. Their ultimate incorrectness (as they are too simple) is overshadowed by their usefulness, as grasping the fundamental ideas is often more important than explaining all of the nuances. As such, I am not claiming any of these models are correct, but rather I am using them to illustrate the ideas. We seek to answer two separate but distinct questions: "how" the universe behaves and "why" the universe behaves in a particular way. Despite popular opinion, physics does not claim to answer many of the "why"-type questions. Why is physics the same in all inertial reference frames? Why does the metric tensor obey Einstein's equation? Why do quantum mechanical observables correspond to Hermetian operators? However, postulating that these things are true in our universe answers many other "why" questions that are really "how" questions in disguise. Why does a superconductor expel all magnetic fields? Well, we observe them to do so, and so the question is how that arises from knowing the basic physics. Remember that this entire field is a observation-driven discipline and we only seek to model it using mathematics. I am going to make one concrete conjecture: The physical laws in the cosmere are the result of interactions between Realms. Without going too deep into general relativity, we will simply claim that "gravity" is the phenomenon of massive objects feeling an attractive force between them. Even in our universe, it it not known why this occurs (i.e why does mass bend spacetime). "Why" is not really relevant for predicting gravitational phenomenon - experiments show us that general relativity works. However, the in the cosmere, there is some underlying reason due to Spiritual interactions that this is the case. We can then rephrase the question of "why do masses attract?" as "how do Spiritual interactions generate attractive forces between masses?" The "why" question then becomes "why do Spiritual interactions happen in a particular way" which is easily answered as "Brandon set it up that way." Magic fits into this paradigm nicely. Let's look at two examples: The gravity Surge allows one to modify the direction and strength of the gravitational interaction on a massive object. Since we know that gravity is the result of some Spiritual interaction, we then understand the gravity Surge as modifying the Spiritual properties of an object which results in a change how the effective mass-mass interaction works. If we want to get slightly more technical, we could consider the following model. Imagine that gravity works as it does on earth - an effective force due to the curvature of the metric in spacetime. The metric becomes curved due to the presence of matter and energy. A quick and dirty model of the gravity Surge would involve using energy (in the form of Stormlight) to locally bend the metric tensor resulting in a change of the local gravitational field. And if the curvature of spacetime due to matter/energy is mediated through the Spiritual realm (say, energy causes the Spiritual realm to "bulge" locally and distort the Physical realm) then everything works precisely as expected. The atmospheric pressure Surge can be understood in a similar toy model. Ideal gases (and their interacting counterparts) shrink in volume when they are cooled down. The atmospheric pressure Surge then could work in the following way: the energy contained in the Stormlight is used to remove thermal energy from the air (i.e. make it colder) and thus drastically reduce the air pressure on a given surface. Then, the pressure from the atmosphere and friction would cause an object to be "stuck," much in the same way plungers can stick to a wall. To understand how this is implemented on Roshar, we might claim that the ideal gas law is a consequence of Spiritual energy investment. Heating up a gas stores energy in its Spiritual component, and this causes it to take up more room in the Physical realm. So now we understand "how" the ideal gas law works, as opposed to "why." What is the takeaway from all of this? Physics attempts to model the universe using mathematics. Whwne explaining phenomenon, we don't often consider "why" a given physical law is true. The statement that "physics is the same in the cosmere as it is on earth" means that the phenomenon obey the same sorts of mathematical relations. Why those relations are true is another question entirely. On earth, we don't know why physics is the same in all inertial reference frames. In the cosmere, there might be some Spiritual or Cognitive reason that this is the case. That doesn't, however, change the nature of the mathematical equations that describe phenomenon. What we want to understand is how the physical laws from our universe arise from the nature of the cosmere. Thanks for reading! Note: Understanding "why" laws work in our universe is actually a very interesting question when things go wrong. This is how we develop new and more complicated theories for the underlying physical laws. However, all this does is change current "why" for "how" and generate new "why." So I do not want to imply that the "why" questions are useless, only that in the cosmere this sequence terminates at "Brandon said so." Source: I'm a theoretical physicist.
  18. I read the mistborn series while taking a class on calculus-based Newtonian physics, so I couldn't help but formalize a theory on how steel/iron allomancy would actually work. There has already been a topic on how weight is related to the strength of push/pulls, and you can read it here http://www.17thshard.com/forum/topic/3307-weight-has-nothing-to-do-with-allomantic-pushpull-strength/?hl=%20allomancy%20%20mass%20%20weight. But I want to introduce a new theory (with a bit of math) that I think clears up a lot of the confusion. I'm not incredibly physics-savvy, so I explain something terribly wrong, I apologize. (For the sake of efficiency, when I say allomancy, I am referring specifically to Iron and Steel) The Force of Pushes and Pulls First, I am operating under the assumption that weight is only tangentially related to the force an allomancer can exert. Instead, it is actually the mass involved that is important. Weight is the force exerted on an object by the planet equal to the mass of the object multiplied by the acceleration due to gravity. Most people (including the mistborn characters) probably mean mass when referring to allomancy. So I came up with an inverse-squared formula to determine the force an allomantic push/pull can exert. F= (A x (m1 x m2))/(r2), where F is the resultant force, A is the coefficient of Allomantic strength (I'll get into this later), m1 is the mass of the allomancer, m2 is the mass of the object, and r is the distance between the two masses. (The force is positive for Lurchers, and negative for Coinshots). I based this off of the Newton's Law of Gravitation since the principles involved appear very similar to me. When the earth pulls on an object, the object is actually pulling on the earth with the same force. However, the earth has so much more mass than the object so it effectively doesn't move. If a much larger object, like another planet, were to come near the earth, then both it an the other planet would move towards it at noticeable speeds. And again, if a much more massive object, like the sun, where to come near the earth, you wouldn't see the sun move,, just the earth. This is very similar to how a Coinshot can send a coin flying, but be pushed into the air by a much heavier object. The coefficient of allomantic strength accounts for the varying levels of power between different allomancers. This variable changes depending on how hard the allomancer is pushing/pulling (i.e. by flaring). In this way, both the mass and strength of the allomancer are important to the amount of force he/she can exert. Both the allomancer and the object are affected by the same force, but the less massive object accelerates much faster. The force also decreases quadraticaly as the distance between the object and allomacer increases. So I did some math the figure out about what this coefficient of allomanctic strength would be...and kept doing things wrong. At first I made the mistake of assuming a coinshot was pushing on a coin in free space, which resulted in a Coinshot strong enough to move planets. Then I tried having him push against the mass of the planet, which came out to him being ridiculously weak. I finally realized that when you are pushing off of a coin, your effectively pushing off a certain amount of ground, not the entire planet. I have no idea how you would calculate the mass of the ground however, so my formula is now un-provable without some more concrete measurements of allomancy . Feruchemical Iron This theory requires some pretty weird physics concepts. There's been a lot of discussion about what is actually stored with Feruchemical iron, but I think this theory coveres it pretty well. Basically, there are two different measures of mass: gravitational mass and inertial mass. Gravitational mass affects the gravitational field exerted by an object, and also how it is affected by other fields of gravity. Inertial mass is how much an object resists changes in motion. So far as we know, the two values are the exact same for any object and are functionally the exact same concept, in the real world. However, in the Cosmere, it appears you can change one without changing the other. I propose that Feruchemical iron merely stores the feruchemist's inertial mass. This means that nearly every force will affect the feruchemist as though they had gained more mass when the feruchemist is tapping, and vice-versa for storring. Gravity, however, affects the feruchemist the same as normal. The difference is, say when the feruchemist jumps while storring, the force of the jump affects him much more, with gravity affecting him the same, resulting in a much higher jump. Similarly, while falling, drag affects the feruchemist much more, resulting in a slower fall. This also solves the issure of the feruchemist suffering not crushing themselves while tapping, because their atoms become more resistant to motion in direct correlation with the increase of inertial mass. This increase in inertial mass would also factor directly into my above equation for allomancy. Since the force is directly proportional to the mass of the allomancer, tapping iron results in a greater force, both on the allomancer and the object. However, the increased force accelerates the allomancer the same as normal force the allomancer is now proportionately more resistant to motion. Now a potential hole in my theory is that the reverse should also be true. Decreasing your inertial mass would make forces affect you more, but would also reduce the strength of your Push/Pull. In the AoL, Wax is more affected by Pushing while storing Iron, and I can't figure out how to account for this mathematically... I wanted to have a bunch of physics and math extrapolated from this...but most of my calculations were really flawed.... Anyway, thoughts? Criticism? Any real physicists who wants to tell me I explained this all wrong?