Pagerunner

The Conundrum of Conjoiners: an Analysis of Navani's Airship

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So, we've got some fancy new fabrial applications from RoW chapter 3.

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Behind her, over a dozen ardent engineers tended the open-air command station. Ka—a scribe from one of the Windrunner squads—sent the order to Urithiru via spanreed. When in motion, they couldn’t write full instructions—spanreeds had trouble with that. But they could send flashes of light that could be interpreted.

In Urithiru, another group of engineers worked the complex mechanisms that kept this ship in the air. In fact, it used the very same technology that powered spanreeds. When one of them moved, the other moved in concert with it. Well, halves of a gemstone could also be paired so that when one was lowered, the other half—no matter where it was—would rise into the air.

Force was transferred: if the distant half was underneath something heavy, you’d have trouble lowering yours. Unfortunately, there was some additional decay; the farther apart the two halves were, the more resistance you felt in moving them. But if you could move a pen, why not a guard tower? Why not a carriage? Why not an entire ship?

So it was that hundreds of men and chulls worked a system of pulleys connected to a wide lattice of gemstones at Urithiru. When they let their lattice down along the side of the plateau outside the tower, Navani’s ship rose up into the sky.

Another lattice, secured on the Shattered Plains and connected to chulls, could then be used to make the ship move forward or backward. The real advancement had come as they’d learned to use aluminum to isolate motion along a plane, and even change the vectors of force. The end result was chulls that could pull for a while, then be turned around—the gemstones temporarily disjoined—to march back the other direction, as all the while the airship continued in a straight line.

Alternating between those two lattices—one to control altitude and a second to control horizontal movement—let Navani’s ship soar.

...

Work on this vessel had helped sustain her during the months following his death. Of course, it hadn’t been her math that had finally made this ship a reality. They’d learned about the interactions between conjoined fabrials and aluminum from the Azish scientists. This wasn’t the direct result of her engineering schematics either; the ship was a fair bit more mundane in appearance than her original fanciful designs.

This doesn't make sense. But, of course, I can't just come out and tell you why it doesn't make sense. We'll have to build up our theory of conjoiner mechanics so that we can properly evaluate this and show you where I'm getting confused.

 

Conjoiner Basics

The way I understand conjoiner fabrials, when you draw a free-body diagram, you treat both halves of the conjoiner as the same object. There's no "force" between the two objects; any forces that act on one act on the entire set. There's an additional "magical friction" term that will act against the direction of movement, whose magnitude is determined by the distance between these fabrials. (This force does not have an equal and opposite, which means we're going to break energy conservation, but we're doing it the opposite way often enough that I think we'll be fine.) I'm going to ignore that for the time being in all of my drawings below, because I can and I feel like it and it won't matter for the sake of this analysis.

The opposite of a conjoiner fabrial, a reverser fabrial (which I'm probably going to call a disjoiner on accident, although reverser fabrial is the term used in the Ars Arcana), is going to still apply everything to the same force balance; but when you draw the balance, you're going to have to invert everything across the origin for one of the two halves.

For the sake of visualization, let me share a quick example that you can recreate at home yourself using simple six-sided dice. I'm going to use the original Allomancy Dice from Crafty Games, since some of the dice are actually laid out backwards. (Which still perturbs me, but at least I can put it to use here.) For those who aren't familiar with this product, it's a set of regular 6-sided dice, but the 6 face on each dice has been replaced with a different piece of iconography from the Mistborn series. I'm going to use three dice to represent two kinds of fabrials; left and center are a conjoiner pair, center and right are a reverser pair.

5f20adc41b40c_Fabrialdice.jpg.72c7bfb66df40002cf5d18209c05ef71.jpg

Lets look at our conjoiner. The two dice will be basically stuck together through invisible wires and always move the same direction. If the left dice moves in the direction of 3, the center dice will move towards its 3. If you rotate left 5-to-3, the center dice will also rotate 5-to-3. Any forces being applied to create those movements and any forces that act in opposition to those movements will be mathematically evaluated together on the same free body diagram. (The sum of all forces equals mass times acceleration; that's how we mathematically relate forces to movement.) Like, for instance, if these dice represent an active spanreed, let's draw the diagram using blue forces being the one writing, and green forces being the one receiving. We'll look at the force balance the moment the pen starts to move towards the right (or towards the 1, for this example).

5f20b27e8374f_conjoinerforcebalance.JPG.94ddc8b32a9b41fd9ce601e1a2ebdee5.JPG

Seems fairly straightforward, right? It's just like holding two pens at the same time. (Cue the Bart Simpson super chalk holder.)

For a reverser fabrial, look above at the center dice and the right dice. You'll see that each of the six faces is oriented oppositely. (For those who are not familiar, the opposite faces on a six-sided dice should always add to 7. 1&6, 2&5, and 3&4 are all on opposite sides of each other.) If you try to do this with two identical dice, it will never work. (Go ahead, try it. I dare you.) You need to have dice that are mirror images of one another (opposite handedness or chirality, if you prefer those terms). Line up the 1, 2, and 3 as shown below to check if your dice are mirror images of each other or not.

5f20b43448c97_dicechirality.jpg.2e4ee81463d0c9eec79d575976483a8c.jpg

And here's where the mathematical trick comes in; your force balance is drawn using the face numbers as reference. Depending on which dice you start with for drawing your force balance, half of your lines will look super weird; gravity going up and stuff like that. But that's okay, just focus on the face numbers and trust the math. If I take my two dice above (from the first dice image) and say that they're one of Navani's early fabrial towers caught in a highstorm, with blue being the counterweight and orange being the archery platform:5f20b64ed0399_reverserforcebalance.JPG.6d54fbb61445b628077dba2e3937fafb.JPG

When we calculate the sum of the forces and determine our final direction of acceleration, it will be in terms of a face. And, looking up at the two dice (way far above; you can scroll up, it's okay, I'll be here when you get back), you'll see how the direction specified by the force balance makes it so the dice move in opposite directions in real life, in the absolute terms. I drew up the free body diagram in terms of stable operation, where the counterweight is sitting on the ground. But imagine they're in an intermediate position, where both the counterweight and the platform are in midair, so the normal force of the ground and the static friction aren't there. You've got a lot of net force in direction 2; referencing our dice drawing, that sends the center dice down and the right dice up. You've got a little bit more wind on the platform driving it towards its face 6, so the counterweight will actually move against the wind. But everything is going to happen relatively slowly, since forces that act in the same direction in real life (wind pushing, gravity pulling) are being opposed on the free body diagram.

In terms of rotation, things get really easy. If I take my center dice above and rotate it 3-to-5, envision which way it will move. Now, look at how the rightmost dice will move. You need to remember that 5 is opposite 2, and 3 is opposite 4. Do you see it? The dice rotate exactly the same direction from an absolute perspective! So reverser fabrials still rotate together; only linear movements will be opposite.

 

Navani's Airships

I've got three dice in my example, and that's been intentional the whole time. It will represent the Fourth Bridge; the left-most dice is the chulls, the center dice is the airship itself, and the right-most dice is the cliffside arrangement. The center dice will technically represent two halves from two different fabrial arrays; it's got a lattice of conjoiner fabrials with the chulls, and a lattice of reverser fabrials with the cliffside. But I'll just represent it with a single dice, since it will be two dice who occupy the same space and have their orientations locked together by being built into the same ship.

The key is that you can't move when both of these fabrial arrays are active. (I mean, you can, but it would connect the chulls with the cliffs. At best, everything would grind to a halt; at worst, you'll be playing a very sad game of 52-gemstone-pickup.) Here's the sequence of activating and flying:

  • Airship starts on the ground. Cliffside reversal lattice starts at the top of the cliff.
  • Activate the reversal lattic. Pull the cliffside down; the airship will rise  up.
  • Activate the chull conjoiner lattice.
  • Release the reversal lattice. The conjoiner lattice is now supporting the weight of the airship.
  • Move the reversal lattice side-to-side. The airship will move with it.
  • When you need to reorient the conjoiner lattice, stop the airship.
  • Activate the reversal lattice to take the weight of the ship.
  • Deactivate the conjoiner lattice. Reorient your conjoiner lattice.
  • Back to step 3.

 

Deactivated Interactions and the Aluminum Puzzle

At first, I couldn't figure out how aluminum fit in to all of this. Let's take a look at the behavior of the these fabrials when they are inactive. It's a little tricky, because the actual function of spanreeds isn't described in detail all that much.

What I thought was that, when spanreeds are deactivated, the dice are essentially unlocked from one another. You can move/rotate one dice, and the other doesn't move at all. Before you activate them, it's very important to have the dice aligned properly with their surroundings; the spanreed boards are described as having levels on the sides, and it's got a dot you need to start the spanreed at. But let's engage in a thought experiment to understand the ramifications of this model. Let's say Jasnah and Navani are in the middle of a spanreed conversation. Jasnah gets kicked out of her desk (don't ask me how, it's just a thought experiment), so she deactivates her spanreed, goes across the aisle, and sits down at another desk that faces the opposite cardinal direction. She sets up her spanreed board again from scratch and turns it on. Is Navani going to be writing upside down? Or will Jasnah, as a part of setting up her spanreed, orient it properly, regardless of the cardinal direction the board is facing?

In my first model (of the dice being unlocked from each other whenever both fabrials aren't on), there would be no problem. The reference frame is based on the spanreed itself, not an absolute sense of the cardinal directions. Essentially, you both turn your dice to an agreed-upon position and set your board and inkwell accordingly. This means you don't have to take the curvature of Roshar into account, and you don't need to align your board in a certain cardinal direction every time. (While levels are mentioned on the sides of the boards, there is no mention of a compass.) If Jasnah's at a desk facing south, and Navani's at a desk facing north, the dice wouldn't be facing quite the same direction in an absolute sense; but when Jasnah pushes her pen in the direction of 3, Navani's moves in the direction of her 3.

But that, in and of itself, should be enough to enable the chull trick, which Navani says requires a new advancement in aluminum. What gives?

The only solution I could come up with is that cardinal direction must matter in spanreeds, and you need to use aluminum to mess with that orientation. The problem has never been mentioned with spanreeds, but if it didn't exist, there wouldn't be anything for aluminum to solve. So let's make our model more complicated and account for it.

We've assumed conjoiner fabrials are dice. But now, let's assume conjoiner fabrials contain dice; they've got a little incorporeal dice in the center of their gemstone. So now you've got interactions between each object and their incorporeal dice, and between the incorporeal dice themselves.

  • When both halves are off:
    • There is limited interaction between the object and the dice. The dice will move side-to-side with the object, but it will not rotate.
    • The two dice can move independently side-to-side, but there is nothing to cause them to rotate.
  • When only one half is on:
    • There is a stronger interaction between the object and the dice. The dice will move side-to-side and rotate with the object.
    • The invisible dice are not locked in side-to-side movement, but they are locked in rotation. (So, if you turn the half of the fabrial that's on or that's off, the dice in the receiving fabrial  won't change orientation, so you won't be able to pull the chull trick.)
  • When both halves are on, then you lock in side-to-side movement and rotation. You are fully conjoined.

This is needlessly complicated... but it gives us a place for aluminum to show up. Placing one half in an aluminum box will be the only way to allow independent rotation of the dice, so you activate your fabrial, put it in an aluminum box, and rotate it without affecting the fabrial on the other side.

 

The Future of Conjoiners

I think this is foreshadowing a science fiction application, the same way Mistborn's getting its seeds laid with ettmetal, time bubbles, and mechanical Feruchemy. I envision the Rosharan space fleet operating from conjoiner/reverser fabrial centers on the planet itself. There is a distance limit to conjoiners, of course; however, according to the Ars Arcanum, that's due to the method of creation, so I fully expect that will be overcome by the time late eras of the Cosmere roll around.

Quote

There appears to be some sort of process used during the creation of the fabrial that influences how far part the two halves can go and still produce an effect.

 

In Conclusion

I've couched everything in terms of dice that are locked so they move together. The actual math would probably be more elegant, but I (and I suspect all the readers) will not be able to internalize it and understand it as quickly quickly. We'll probably need some true math if we wanted to understand how to incorporate the curvature of Roshar into the situation. But let's at least see how the book plays out, first. We're only in chapter three.

In trying to understand this application of fabrial science, my confusion arose from the airship mechanisms being concerned with absolute cardinal directions, while the spanreeds apparently did not. I can only conclude that spanreeds do indeed care about cardinal direction, but that has never been stated, for otherwise I don't see what problem they need aluminum to overcome.

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"The real advancement had come as they’d learned to use aluminum to isolate motion along a plane, and even change the vectors of force. The end result was chulls that could pull for a while, then be turned around—the gemstones temporarily disjoined—to march back the other direction, as all the while the airship continued in a straight line."

I think the use of the aluminum is specifically with the horizontal movement. My assumption is that in this lattice there are two sets of fabrials. Conjoiners and Reversers are in the lattice and one is sheathed in aluminum. When you are moving the chull in the same direction as you want to move the ship you have the Reversers sheathed in aluminum. When you turn the chull around to pull the lattice back, you switch which set of fabrials is sheathed. This should allow you to do half as much Work.

 

The thing I don't get is how they changed the vector or force. Am i wrong in assuming that they didn't inverse/rotate the force vector and instead increased it?

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58 minutes ago, Pagerunner said:

In trying to understand this application of fabrial science, my confusion arose from the airship mechanisms being concerned with absolute cardinal directions, while the spanreeds apparently did not. I can only conclude that spanreeds do indeed care about cardinal direction, but that has never been stated, for otherwise I don't see what problem they need aluminum to overcome.

This is more or less the conclusion I've arrived at as well; it's the only explanation that I find is consistent with all the data (as well as some data we pretend exists but is not actually in the text, but adding it doesn't actually contradict anything; it's just an omission, probably due to Brandon not having thought the entire thing through at the beginning).

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35 minutes ago, GudThymes said:

"The real advancement had come as they’d learned to use aluminum to isolate motion along a plane, and even change the vectors of force. The end result was chulls that could pull for a while, then be turned around—the gemstones temporarily disjoined—to march back the other direction, as all the while the airship continued in a straight line."

I think the use of the aluminum is specifically with the horizontal movement. My assumption is that in this lattice there are two sets of fabrials. Conjoiners and Reversers are in the lattice and one is sheathed in aluminum. When you are moving the chull in the same direction as you want to move the ship you have the Reversers sheathed in aluminum. When you turn the chull around to pull the lattice back, you switch which set of fabrials is sheathed. This should allow you to do half as much Work.

 

The thing I don't get is how they changed the vector or force. Am i wrong in assuming that they didn't inverse/rotate the force vector and instead increased it?

Then there would be even less of a need for aluminum, because if there were two sets of fabrials, you could definitely just turn one off and move the fabrials independent of one another. But the text does specify that there are only two lattices, which are alternated between: one for vertical, one for horizontal. What you suggested would be three lattices: two for horizontal (which are switched between), and one for vertical.

 

8 minutes ago, Argent said:

This is more or less the conclusion I've arrived at as well; it's the only explanation that I find is consistent with all the data (as well as some data we pretend exists but is not actually in the text, but adding it doesn't actually contradict anything; it's just an omission, probably due to Brandon not having thought the entire thing through at the beginning).

It's the classic steelpush physics problem. Brandon is coming up with end results based on what is intuitive to him, but that doesn't mean it's self-consistent when analyzed. At least, not without some work on the analyst's part. Which, in this case, seems to be a minor restriction retroactively applied to spanreeds.

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1 hour ago, Pagerunner said:

We've assumed conjoiner fabrials are dice. But now, let's assume conjoiner fabrials contain dice; they've got a little incorporeal dice in the center of their gemstone. So now you've got interactions between each object and their incorporeal dice, and between the incorporeal dice themselves.

  • When both halves are off:
    • There is limited interaction between the object and the dice. The dice will move side-to-side with the object, but it will not rotate.
    • The two dice can move independently side-to-side, but there is nothing to cause them to rotate.
  • When only one half is on:
    • There is a stronger interaction between the object and the dice. The dice will move side-to-side and rotate with the object.
    • The invisible dice are not locked in side-to-side movement, but they are locked in rotation. (So, if you turn the half of the fabrial that's on or that's off, the dice in the receiving fabrial  won't change orientation, so you won't be able to pull the chull trick.)
  • When both halves are on, then you lock in side-to-side movement and rotation. You are fully conjoined.

You lost me here...

 

3 minutes ago, Pagerunner said:

It's the classic steelpush physics problem. Brandon is coming up with end results based on what is intuitive to him, but that doesn't mean it's self-consistent when analyzed. At least, not without some work on the analyst's part. Which, in this case, seems to be a minor restriction retroactively applied to spanreeds.

My thoughts precisely. :)

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17 minutes ago, Jofwu said:

You lost me here...

Basically two of these bad boy baby bowls: https://babyfeedme.com/products/unspillable-bowl

The outer ring is the fabrial itself, and the interior bowls are the alignment references. The two interior bowls are conjoined rotationally at all times. When you activate either of the fabrials, you'll permanently align the ring to its bowl; basically drive a nail through all the layers, so when you spin the ring, you also spin the bowl. And when both are activated, you align the interior bowls positionally as well.

The only way to get the interior bowls aligned in opposite directions would be to use aluminum to temporarily disjoin them rotationally.

The conjoining reference field must always be active, even when both fabrials are off, or else you'd be able to just spin the chulls around while it's off and call it a day. But we know that nothing is positionally locked in place until everything is on, since you need to turn both spanreeds on to start typing. So that's why we need this inelegant invisible entwined gyroscope stuff, to basically tie a conjoined pair to a cardinal direction even when one or both halves is off.

Edited by Pagerunner
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I don't think it's exactly the cardinal directions. It shouldn't operate differently if you activate it near the poles. The directions that the fabrial is tied to should change based on where it is activated. If you take the locations where the two halves of the fabrial are activated, then find the largest circle passing through those points on the planet's surface (ignoring altitude), that is the line that should be treated as the equator.

Edited by Chiberty
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46 minutes ago, Pagerunner said:

The two interior bowls are conjoined rotationally at all times.

Ahhh, I think I've got the picture now. I like that conceptualization.

So... if I understand this right, doesn't this have issues if we want to use one spanreed at the equator and another at the north pole? The dice have their rotation fixed relative to one another. So I carry my spanreed to the north pole and you stay at the equator. We both point our reeds down toward the center of the planet. We both active our spanreeds. Doesn't this mean you sliding your reed north would cause my reed to go up?

Edit:

lol, I see @Chiberty and I had the exact same thought. :)

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I don't get why there is a problem. Your dice analogy in my opinion was exactly correct. They need to use aluminium because otherwise when they would rotate the chull latice, the airship would also rotate.

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My crackpot theory I am not sure makes sense as is was that spanreeds that are active but trapped behind aluminum still work you just can't move them.  Basically if I Jasnah starts writing to Navani and then puts her spanreed in an aluminum box Navani's spanreed will stay upright as long as it is infused even though "nothing" is supporting it.  From this is Jasnah's aluminum box is much bigger and includes Jasnah Jasnah could close the door move the pen and Navani's reed would stay where it was put before.  However Jasnah's pen would be in a different space.

I actually think I have something.  Think of it this way.  Let us say that Navani wants the ship to move forward.  She has the chulls move their end of the conjoiners a certain amount.  So far so good.  However if unless she wants to just levitate the thing and let the chulls walk behind her for the entire trip across Alethekar she needs to find some way of "turning off" the fabrails.  It has been suggested that you just disjointing it but that has problems and I noticed one odd thing.  She never says she has more then one set of chulls.  I would think she would one for forward/backward movement and one for left and right movement but evidently not.  She only has one set.  She also says she can isolate a plane of movement not "turn it off."  Somehow putting aluminum in the way continues to allow and already activated conjoiners to work but at the same time alters something about how they work.  I think that if you leave a spanreed on and then throw into an aluminum box the other end will continue to move forward even after the first one has come to rest.

Edited by Karger
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1 minute ago, The_Truthwatcher said:

They need to use aluminium because otherwise when they would rotate the chull latice, the airship would also rotate.

The aluminum wouldn't be necessary. Here's what you do when the chulls reach the edge of the plateau and need to turn around:

  1. Chulls and airship come to a stop
  2. Activate the Urithiru lattice so it is conjoined with airship
  3. Deactivate chull lattice so it is no longer conjoined with the airship--the airship is held up by the Urithiru lattice
  4. Turn the chulls around.
  5. Activate chull lattice. Deactivate the Urithiru lattice.
  6. Cardinal directions are irrelevant, forward for chulls is forward for the airship. Chulls go forward, airship goes forward.
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1 minute ago, The_Truthwatcher said:

I might be wrong, but aren't they using aluminium to do what you call deactivating?

No, you can "disjoin" spanreeds. They're not always on.

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1 hour ago, Pagerunner said:

Then there would be even less of a need for aluminum, because if there were two sets of fabrials, you could definitely just turn one off and move the fabrials independent of one another. But the text does specify that there are only two lattices, which are alternated between: one for vertical, one for horizontal. What you suggested would be three lattices: two for horizontal (which are switched between), and one for vertical.

In my model the "two horizontal lattices" are rather one lattice with both sets of fabrials in the frame. You're just switching the "forwards/backwards" setting when you switch the chulls.

2 hours ago, Pagerunner said:

The reference frame is based on the spanreed itself, not an absolute sense of the cardinal directions.

This is the piece I missed with my thinking. I'm fully on board with everything you said now. 

 

4 minutes ago, Jofwu said:
9 minutes ago, The_Truthwatcher said:

They need to use aluminium because otherwise when they would rotate the chull latice, the airship would also rotate.

The aluminum wouldn't be necessary. Here's what you do when the chulls reach the edge of the plateau and need to turn around:

This cinches everything together for me.

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3 minutes ago, Jofwu said:

The aluminum wouldn't be necessary. Here's what you do when the chulls reach the edge of the plateau and need to turn around:

So there is clearly a difference between using aluminum and disjoining the fabrial.

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7 minutes ago, The_Truthwatcher said:

I don't get why there is a problem. Your dice analogy in my opinion was exactly correct. They need to use aluminium because otherwise when they would rotate the chull latice, the airship would also rotate.

The aluminum is also needed to allow for horizontal movement while the ship being held in the air. Otherwise, the chulls would be linked to the cliffs, trying to push the pulleys sideways.

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1 minute ago, Jofwu said:

No, you can "disjoin" spanreeds. They're not always on.

But spanreeds are very, very different from these. You can send signals through them(flashing), I think that we cannot instantly apply what we know about spanreeds here.

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5 minutes ago, The_Truthwatcher said:

But spanreeds are very, very different from these. You can send signals through them(flashing), I think that we cannot instantly apply what we know about spanreeds here.

The text says it's the same thing though. From chapter 3:

Quote

 

In fact, it used the very same technology that powered spanreeds. When one of them moved, the other moved in concert with it. Well, halves of a gemstone could also be paired so that when one was lowered, the other half—no matter where it was—would rise into the air.

Force was transferred: if the distant half was underneath something heavy, you’d have trouble lowering yours. Unfortunately, there was some additional decay; the farther apart the two halves were, the more resistance you felt in moving them. But if you could move a pen, why not a guard tower? Why not a carriage? Why not an entire ship?

 

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1 minute ago, Jofwu said:

From chapter 3:

My argument is that spanreeds are much more complicated. It is possible that the mechanism that allows them to be switched on-off cannot be replicated on a larger scale.

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Just now, The_Truthwatcher said:

My argument is that spanreeds are much more complicated. It is possible that the mechanism that allows them to be switched on-off cannot be replicated on a larger scale.

Quote

The setting of the ruby is able to be rotated to switch between different "modes." One is to alert the possessor of the spanreed's twin that a conversation is desired. Another to alert the first that the message was received. The third and fourth notches sync the movements of the two pens, each notch makes one pen the transmitter and the other the receiver -- From Spanreed on the Coppermind

I second this opinion. I think the general principle of them is the same. However, there may be some nuance that Spanreeds are capable of that these more basic Conjoiners are not

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Do we know what happens if you turn on a set of spanreeds and then put an aluminum box over one?

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We didn't know you could use aluminum to mess with conjoined rubies until today, so I am gonna go with a no on this one :P

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5 minutes ago, Argent said:

We didn't know you could use aluminum to mess with conjoined rubies until today, so I am gonna go with a no on this one :P

Well we knew that you could not turn on a spanreed while inside an aluminum box and have the other side respond.

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My assumption was that the purpose of the Aluminium was to stop the counterweights from affecting each other. So you don't have to worry about accidentally launching the Chull team at the Shattered Plains into the sky. I don't know exactly how that would work, mind you, but it seems like an important possibility to cover for. 

Edited by Gilphon
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6 hours ago, Pagerunner said:

In my first model (of the dice being unlocked from each other whenever both fabrials aren't on), there would be no problem. The reference frame is based on the spanreed itself, not an absolute sense of the cardinal directions. Essentially, you both turn your dice to an agreed-upon position and set your board and inkwell accordingly. This means you don't have to take the curvature of Roshar into account, and you don't need to align your board in a certain cardinal direction every time. (While levels are mentioned on the sides of the boards, there is no mention of a compass.) If Jasnah's at a desk facing south, and Navani's at a desk facing north, the dice wouldn't be facing quite the same direction in an absolute sense; but when Jasnah pushes her pen in the direction of 3, Navani's moves in the direction of her 3.

But that, in and of itself, should be enough to enable the chull trick, which Navani says requires a new advancement in aluminum. What gives?

It would enable the movement, but the airship would suck. It would essentially be the platform already used for archery. Something needs to hold up the airship while you switch chulls. And you cannot just switch on the reverser and switch off the joiner, as an airship moving along without power actually does experience forces from wind resistance. The reverser at Urithiru would undergo lateral movements. You'd have to actually mostly stop the airship to switch chulls and each movement would be a very awkward switching exercise. An error would lead to an undesirable interaction with solid ground.

It seems to me that the key is the change of vectors with aluminium she mentioned. I suppose the reverser in Urithiru is inside a long, openended cylinder of aluminium with its long axis oriented vertically. And that shroud shields it laterally. Thus you leave it on permanently and just switch off the joiner while reversing and all is well, letting the airship coast but still held up by the reverser. You could even have the top and the bottom of the framework holding the joiner made of aluminium, so that you can go up and down with your airship without your chulls becoming airborne.

And unless you have a death wish you have a third set actually mortared into the solid ground which you can switch to for station keeping in bad weather or an emergemcy.

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