Is there any reason to think that this shouldn't be possible? Why hasn't this been done in the book?

Sections 1.1-1.3: Making general information about 9-point conics accessible

9-point conics are central to Rithmatics, but it's pretty hard to find good documentation about them. I've literally only been able to find 4 sources yielding any information (besides the 17th shard) about 9-point conics. All of them... kind of suck

Most of the doc covers facts hardcore Rithmatic theorists already know from @KalynaAnne (namely what the 9-point conic is and the criterion for determining type of conic (circle, ellipse, or hyperbola) -- but actually has proofs for them.

I'm quite happy with how these turned out overall -- I haven't seen other sources do everything in terms of the centered conic matrix (they just use the raw conic formula), and I think using the matrix helps a lot in making things understandable.

I also have a section on what I'm calling the Conjugate Diameter Property, which I haven't seen anyone mention before. I think any aspiring Rithmatists will find the associated corollary (the Tangent-Direction Property) very useful for drawing defenses

Section 1.4-1.6: Classifications of sub-9 point configurations

Enumeration of the different n-point configurations and their properties, taken from the hardcore rithmatic theory thread. I also have what I think is a satisfying mathematical explanation that explains why the only valid 4-point and 2-point circles are the ones described in the book, despite being able to draw circles through any rectangle and in many ways through 2 points, that generalizes well to ellipses and hyperbolas.

Section 2: Inverse Algorithms

If I and the other suckers at the game thread ever get our act together and really create a game, we need to be able to take a collection of attachments to a Line of Warding and detect whether a corresponding quadrangle that admits the given conic exists. The algorithms here should cover all circle, ellipse, and hyperbola cases

Link to overleaf: https://www.overleaf.com/read/khgdzgrmnjzd#e3571f

9_Point_Conics.pdf

If anybody is interested in contributing, please let me know.

• The whole thing is pretty wordy and can probably be trimmed down; it's pretty long
• I'm the only person who has looked at the math. Though I think it looks good, a check for readability and correctness is very welcome
• I got tired of writing and don't have much covering parabolic and degenerate conic configurations -- which probably should be covered, if believers in Line of Forbiddance (and, as @IlstrawberrySeed has suggested on our mostly-dead discord server, the Mark's Cross) as an instance of a segment of a degenerate conic are correct -- is totally lacking in both the classification and inverse algorithm sections of the doc

Quote

“Well, it is June,” she said. “Still, it’s not that bad. I doubt you’ll be able
to find a scoop for less than seven cents anywhere on the island, and five is
the cheapest I’ve seen in winter.”
Joel blinked. Were things really that expensive? 

“How much do you have?” she asked.
Joel reached in his pocket and pulled out a single silver penny. It was as
wide as his thumb, and thin, stamped with the seal of New Britannia. His
mother made him carry it with him, should he need to pay cab fare or buy a
ticket on the springrail.
“One penny,” Melody said flatly.
Joel nodded.
“That’s all the allowance you get a week?”
“A week?” he asked. “Melody, my mother gave me this for my birthday
last year.”

Currently, the national American average for one scoop is about $5.35, and a quick google search didn't give much, but I found some mentions of a nickel per scoop back in the 1900's. I don't know how much time Brandon put into the monetary value part of the system, but I'm guessing he just used whatever it was for the 20th century. Joel also says that a penny is enough cab fare or a springrail ticket(which I'm also assuming to be about the same as a railroad ticket), which is entirely identical to its real-world counterpart, but train tickets ranged from 2-3 cents per mile up to tens of dollars, which matches. According to https://www.nist.gov/nist-museum/fare-fair-taximeter-testing-1920s-and-today#:~:text=Although horse-drawn for-hire,new U.S. industry was born., A cab fare would be about a 50 cents per mile, compared to the penny in world, but maybe they charge less for the short rides Joel is most likely to take

Anyway, I didn't see any existing discussions on this, and I was wondering if there was a deeper meaning, or if I'm looking to deep into this.

It's far from finished, but I have a basic framework set up and it's moving smoothly. The code is currently on a private repo on github (I wanted to keep it private for now because I feel like I could run afoul of copyright law somehow), but if anyone wants to help me, email me and I can let you in!

Since the new attack line was basically a line of vigor and forbiddance, is the sound-muffling line is a line of making paired with a line of warding? The muffling one has curves and the line of making is really flexible depending on how you use it. 

What objects were planted by Harding in extons desk?

When Harding was attacking Nalizar and Joel in the dorm, the chalkings came from Harding's mouth. This makes sense because the chalkings are a 2D being so they can exist inside his throat, stomach, lungs etc, etc. But wouldn't the stomach acid and wetness of his insides smudge and destroy the chalkings but they could reform, so how did Harding not feel chalkings smudging and reforming inside his chest throughout the day?

How did Joel's father die? Joel is told that he died in a spring rail accident, but on page 202 his mom hints that he didn't die in an accident and that it had something to do with his research. ¨your father... he sacrificed so much. He might have made it, too, if his blasted research hadn't ended up costing his life¨ 

Anyways, moving onto my actual thoughts, I really really like rithmatism as a magic system. I'm pretty good at math and geometry is one of my stronger math areas, so a geometry math system just makes me happy, ignoring the fact I have abhorrent handwriting and would make a terrible rithmatist. I also really like the springworks technology. Clockwork machinery and mechanical systems are some of my favorite aesthetics ever, so the fact that there are clockwork creations everywhere in this world of math magic is just the icing on top. The imagery is as impeccable as always. The scene where the wild chalklings crawl out of Harding's mouth is probably one of my favorite descriptions in the book, as eerie as it is. There isn't much that I can say about this book that I didn't like, but if I were to pick something, it would be the characters. Not that I think the characters were badly written or anything like that, but they didn't resonate with me as much as in other novels. All in all, I really like this book and it saddens me to think that a sequel is still a ways off. I know the sequel has been a topic of debate for some time now, and now I see what the outrage is about. I think between books like Elantris and Warbreaker, this is definitely the most cliffhangery of the endings. However, I did look around a bit and saw that Brandon said that he might work on Rithmatist 2 after Stormlight 5, which if that can be trusted is moderately soon, plus I can't really complain about him working on Stormlight 5 since I kind of want that more anyways...

Uh, I hope you enjoyed my rant. I only wrote this because I saw other people writing their thoughts about other books in other forums. Anyways, I hope anyone reading this has a great day and whatnot.

For context, I'm contemplating reading the book to 3 of my kids, the youngest of which is 9. The piece I'm worried is about is any sort of romantic subplot. If there is any romantic subplot more than something like Alcatraz the 9 year old is going to groan and run away. I already shelved the Skyward series for that reason.

My idea: Line of gravitation

This would be a Fibonacci spiral, it has to have at least 2 loops to work. This line would pull lines of vigor and chalklings off target, and toward themselves. They can take 2-3 lines of vigor before breaking. the gravity can't go through lines of forbiddance or line of warding, so a boxed in line of gravitation wouldn't really attract anything. it's range is approximately 15 yards for lines of vigor, 2 yards for chalklings, a really good one being able to take more hits, pull stronger, and from a farther distance. Here's a picture of a Fibonacci spiral and a little animation of how everything interacts 

On 2/2/2024 at 3:32 PM, Pineap-spider said:

After a line of vigor is drawn, does the wave extend until it can't reflect, and then the tail follows, or does the section you drew just go?

There is little definitive discussion in the text. However, based on the Lines of Vigor interior art (see link or below), the tail stays where it was drawn, the front proceeds until it stops at something it can damage (rather than reflect) - then the whole line goes away since it is done (that's based on multiple times they point out that lines of vigor pass through or sweep away chalk left behind by destroyed Lines of Making - but never mention chalk left behind by Lines of Vigor).

@Pineap-spider Also, note this section from Ch 1 during the duel:

Thank You!

Does anybody know how to get in contact with the creators to get access to it again?

Life is made out of cells. Each of the cells in our body are relatively basic, having only a few simple functions. When combined with trillions of other cells, they make living organisms which are able to act and think independently. It would be easy enough to draw a 'cell' chalkling, and then give it the commands it needs to contribute to the system. If you practiced enough, and used small enough chalk, you might be able to get the shape down to (random estimate) the size of a dime. Then if you repeated this process trillions of times, keeping them close together and connected all the cells to each other, you could make a brain. An insanely massive brain, but a brain all the same. If you could accomplish this, would it make a sentient chalkling? 

EDIT: Google puts the size of a dime at 18mm. Therefore, the area of one cell would be 2.54 x 10^-4 km². Multiplied by 37 trillion cells in the average human body, the surface area the chalkling would cover is 9398 km². That's about the size of Jamacia. Which is smaller than I thought it would be. But that's for the whole body. There's only about 100 billion cells is the human brain. So just to make the brain, you'd need an area of 25.4 km². I'm not sure if you'd need other organs like the heart as well to make it work, or if it could survive on its own. 

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Finished Rithmatist, and now I can join everyone else in a painful wait for the sequel. Loved the book. Bad at giving explanations, so I'll leave it there and just give thoughts below.

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I tried so hard not to fall for tricks, but still fell for Nalizar's red herring redemption... Welp, that's why I love Brandon.

---

I actually wonder if Joel will somehow win Nalizar over eventually, because of the latter's curiosity. Of course, a redemption arc may be too cliche.

---

I did expect the ceremony thing to fail, but I also sort of expected he'd still get power somehow. Though there's always the sequel.... But honestly I like him not having magic, and having to work together with Melody to counteract each of their flaws. That does however leave them vulnerable if they're separated. I expect Melody to develop her skill and be capable of holding her own without Joel, but I'm curious what'll happen to him.

---

Current theory on Rithmatists, they're bonded to Shadowblazes, in a more symbiotic form of a Forgotten's possession. This gives an easy explanation for why one Rithmatist needs to die before another can gain power. This does however leave me curious why what I assume was the Shadowblaze left without bonding Joel. I hope Joel and Melody talk about Melody's inception or whatever it was called, so they can wonder about this themselves. Also, I hate characters refusing to communicate. So please *talk*.

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I can definitely see the Cosmere influence. Rithmatics would be right at home on Sel (if you lived in a circular country, which you could probably blame Adonalsium for). I think "the Tower" may have something like a Perpendicularity. I believe Brandon has said that avoiding Cosmere stuff in it would require changing where he intended the story to go a lot, and I could see a Perpendicularity being one of those things left over.

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But yeah, the magic just screams Sel. Very specific instructions, shapes made in a specific way and pattern, Intent.... However, Brandon had a different Shard planned that would have been in Rithmatist, so it can't even have originally taken place on Sel. So probably just a similar thing to there.

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I remember Brandon saying certain creatures (I don't remember which) were originally beings from the Spiritual Realm. I assume these are the Forgotten and possibly Shadowblazes. I remember him giving a fascination with time as one effect of that, and Forgotten and chalklings both seem to exhibit this. Shadowblazes are similar to both and so probably are as well. Assuming they're even different.... I could see them being the same as Forgotten and just choosing not to fully possess or something. Though I'll need to wait for the sequel to learn that...

---

So glad that Joel and Melody didn't kiss at the end, no offence to those who like it but I hate the "celebratory first kiss" sort of thing. Now that I think about it, I don't know that Joel and Melody have moved on beyond "good friend" yet. I really hope they don't go romantic, because we need more platonic opposite-gender besties. This is probably the thing I feel the most relief at from the ending, honestly. I would bet money that they'll become romantically involved in the sequel, but for now I can pretend.

---

I'll leave that as my last thought on the book.

• We know the Forgotten in Harding was "killed" with the acid after it was driven to reveal itself by the clockworks. We also know that Harding was not a rithmatist before being taken by a Forgotten (or after it was banished/destroyed).
• We "know" a Forgotten (or something similar) has Nalizar and was unaffected by the acid thrown on him because it was entirely inside Nalizar when Joel tossed the acid at him on the stairs. 
• We know that the Forgotten in Harding seemed "unintelligent," not capable of speech beyond grunts and screams. The Forgotten in Nalizar seems much more intelligent and cunning. 

Conclusion: The Forgotten in Nalizar is smarter/stronger because Nalizar already had a Shadowblaze bond (iow: Harding himself was corrupted by the Forgotten; but in Nalizar, it was his bonded Shadowblaze that was corrupted). 

Also, a bit of Fridge Horror:

They mentioned a number of times that the Northern Isles (what would become the United Isles) were depopulated before the Europeans arrived. 

I believe we can characterize our 3 OG Rithmatic lines by what they do in terms of E&M analogues.

• Lines of Vigor, as we have heard over and over again, are the equivalent of waves. They carry energy along the line that they travel, and the chalk is just a visualization of the magnitude of the electric field at a given point in a transverse plane wave.
• Lines of Forbiddance are just conductors. A flat sheet of conductor is able to reflect an electromagnetic wave, just as a line of Forbiddance reflects a line of vigor. It is, however, not a superconductor, and therefore some energy is lost when a line of vigor bounces, which goes into breaking the line of Forbiddance
• A line of Warding, at the moment of drawing, is a conductor in which free-flowing charged particles are dumped in. The charged particles distributes across the conductor, which then "cools down" and becomes insulating, locking the charge in place. The charged particles are what actually give the Line of Warding strength, which is why the Line of Warding is stronger along curved areas.

I think that seeing as Rithmatics functions in 2 dimensions, the laws that Rithmatic charge would follow would also be in 2 dimensions. From a quick Google there seems to be a mathematical analogue for electrodynamics in 2 dimensions: https://www.reed.edu/physics/faculty/wheeler/documents/Electrodynamics/Miscellaneous Essays/E&M in 2 Dimensions.pdf. My E&M/calc skills are too scrubby for me to understand basically anything of what's going on here, but I hopefully the theory doesn't break down.

Before I continue, if you haven't seen it already, you guys really need to read KalynaAnne's awesome series on Rithmatics first. She has a guide on how to construct different Lines of Warding, including a couple that were not mentioned in the book: the five-point and the eight-point circles, both of which have been confirmed by Brandon. She even has theories about Lines of Vigor that have also been confirmed, which is pretty cool.

KalynaAnne also speculated about elliptic Lines of Warding, including the mysterious Blad Defense (I think her version of that looks very promising). But while most of her work had been quite brilliant, ellipses is where she had one tiny problem.

Since elliptical Lines of Warding are stronger where the curvature is greater and weaker where the curvature is less, she initially theorized that smaller circles (which have greater curvature) must be stronger than larger circles. But this theory had one obvious flaw: If larger circles are weaker, then the Great Circle of Nebrask would be pathetically weak, and that's not very likely.

Confronted with this, she gave a list of possible alternatives. The only one in her list that actually solves the problem of the Great Circle is this: She proposed that each Line of Warding has a total amount of "charge" directly proportional to its circumference (i.e. the bigger the Line of Warding, the more charge it has). This "charge", which determines the strength of the Line at a given point, is distributed along the points of the line based on curvature, so points on the line with more curvature attract more of the "charge" and become stronger. Since circles have constant curvature, the charge is evenly distributed all throughout.

This solution works perfectly well, but I'd like to analyze this problem using a different approach, create a solution that is essentially compatible with KalynaAnne's proposal, and then discuss its implications.
 

Here is what the book says about the strength of an elliptic Line of Warding:
 

Quote

[An elliptic Line of Warding] will be stronger where it curves more than a circle, and be weaker where it curves less than one.

The question an observant reader might ask is "Which circle?" This is because, as KalynaAnne correctly pointed out in her discussion on curvature, the curvature of a circle depends on its radius. This means it varies depending on the circle's size, so there isn't a single curvature for all circles that can be compared to that of a point on an ellipse. So, which circle?

The simplest interpretation is that each Line of Warding has its own reference circle. This reference circle would of course have a constant curvature (hence a constant strength at each point), and by comparing the curvature of a point on an ellipse to the curvature of that circle, we can determine the Warding strength at that point through this ratio:

σ_P = (κ_P / κ_C) * w

Where σ_P is the strength at point P of a particular Line of Warding, κ_P is the curvature at point P, and κ_C is the curvature of the reference circle. As you can see, points of greater curvature with respect to the reference circle would be stronger than the reference circle, and points of less curvature are weaker. Finally, w is the coefficient of Warding, which has a constant value for the unit of "Warding strength" being used. We don't know any Warding strength units, so we'll just set w to 1 and ignore it.

Note that this equation should also apply to perfectly circular Lines of Warding because circles are also ellipses. In this case, it would make sense to assume that a circular Line of Warding is its own reference circle, meaning κ_P=κ_C, so σ_P=1 for all circles. This solves the Great Circle problem.

(Edit: I've been reminded by ccstat of this recent WoB showing that there is in fact some sort of weakening involved when creating large circles, but not as fast as the curvature would indicate. So in fact σ_P is not 1 for all circles. I formulated a possible explanation, but please read the rest of this post first.)

Either way, we still need to define what this reference circle is for non-circular ellipses. I could think of three natural candidates:

• The inscribed circle of the ellipse ("incircle"), a circle whose radius is equal to the ellipse's semi-minor axis
• The circumscribed circle of the ellipse ("circumcircle"), a circle whose radius is equal to the ellipse's semi-major axis
• The circle whose circumference is equal to that of the ellipse (let's call this the perimeter circle or the "pericircle" of the ellipse)

(Conveniently, when the ellipse in question is actually a circle, then all four circles are equal to each other. This jives with our assumption that the reference circle of a circular Line of Warding is itself.)

Here's a badly drawn diagram of an ellipse and its incircle, circumcircle, and pericircle:

In one of her diagrams, KalynaAnne called the incircle of an ellipse the reference circle of that ellipse. Later I'll explain why I don't think the incircle's curvature is the best candidate for the basis of Warding strength.

The "pericircle" is an appealing choice because it shares something quite fundamental with the ellipse: the circumference. It also jives with KalynaAnne's "charge" theory which uses the circumference as a basis of total strength charge. However, the equation for getting the circumference of a non-circular ellipse (which involves a factorial, a double factorial, and the sum of an infinite series) is so complex that I doubt Brandon would bother with it. (Although there is a nifty rough approximation of the elliptic circumference involving tau: τ * sqrt((a² + b²) / 2))

I'm going with the circumcircle as the reference circle, mainly because it is the largest of the three (for non-circular ellipses), and therefore has the lowest curvature. If the front and back of an elliptical Line of Warding really are "much stronger" than a circular Warding, then the κ_C ought to be pretty low compared to the ellipse's greatest κ_P. Using the circumcircle of the ellipse as the reference circle creates stronger elliptic Lines of Warding than using the incircle or the pericircle.

I am open to counterarguments, though. Feel free to defend either the incircle or the pericircle. Even as I type this, I am growing more fond of the pericircle. Perhaps it's because I invented the term; there is no widely used name for the circle whose circumference is equal to that of an ellipse, so I had to make a name up as I developed this theory. Alas, I need a stronger argument in favor of the pericircle before I actually switch.

(Edit: I now believe that the reference circle is the one whose area is equal to that of the ellipse, as I explain later on in the thread.)

(More talk about curvature and its relation to circles.)

Now for the fun part.

Let us play with extreme values for the numerator κ_P (or the denominator r_O, if you prefer the equation I gave in the spoilered note on osculating circles) and see the results σP.

If κ_P is negative, then you're looking at a non-convex part in your Line of Warding (either that, or you managed to draw a hyperbola, which stretches to infinity, so... no). Well-drawn circles or ellipses are convex all throughout.

If κ_P is zero, you've got a line segment (another solution is two parallel lines stretching infinitely in both directions, but that's impossible). P is somewhere on the line segment other than the endpoints, and σ_P is also zero. A line segment is a degenerate ellipse whose foci are on its endpoints, meaning it's so squashed that the foci have moved as far apart as they possibly can.

If κ_P is ∞, then you are on an endpoint of a line segment. If you used the incircle as the reference circle, you get a weird strength value: σ_P=∞/∞. Otherwise, you only get the slightly less weird σ_P=∞.

What does it mean that a Line of Warding that looks like a line segment has infinite strength at its bind points while having no strength at all anywhere else along the line? In real life, things get really weird when they start involving infinities; for example, a portion of spacetime with infinite curvature becomes a black hole. I believe something similar happens in the 2D universe of Rithmatic lines when Rithmatic Lines involve infinities in their construction: the very fabric of the "chalk space" is affected, and the effects leak towards "people space".

You already know where I'm going with this. I think a Line of Forbiddance is actually a Line of Warding whose infinite curvature at its endpoints has transformed it into something that warps "chalk space", and this is what causes the electromagnetic-like force field that affects both the world of chalk and the world of people. A Line of Forbiddance is a degenerate Line of Warding.

Can this theory of degenerate Rithmatics be generalized to other Rithmatic lines? I believe it can. Let us look at two more pairs of Lines: the Line of Vigor and the Line of Revocation.

Vigors are basically sinusoidal waves of varying frequency and amplitude. They are used to either move or destroy other Lines. Sine waves are generated through the following function of time:

f(t) = A * sin(τft + p)

Where A is the amplitude, f is the frequency, and p is the phase of oscillation. The "sin" is, of course, the circular function sine.

In Rithmatics, the amplitude is defined by how large your Vigors are. Frequency is probably defined by how many individual waves are drawn. The phase is probably just zero.

You could add different sine waves together to form different-looking periodic waveforms, some of which can look quite weird. Such waves are difficult to draw (remember, you need at least two repetitions of a waveform for the Line of Vigor to work) and would be impractical when used as Lines of Vigor.

But what if we add an infinite number of different sine waves? Well, that could be interesting.

Consider the following summation of an infinite series:

f(t) = 2A * (Σ(-1ⁿ * sin(nτtf) / n) from n=1 to n=∞) / τ

When graphed, that function looks like a sawtooth wave, which looks exactly like Lines of Revocation. The Line of Revocation is just a degenerate Line of Vigor, which is how it can affect things beyond the chalk universe.

(More talk on Lines of Revocation in the second part of this post.)
 

Alas, the remaining Lines aren't circle-related. Let's just discuss them briefly.

Lines of Making are able to actually harm people once given the Glyph of Rending as an instruction. This Glyph must be a degenerate form of other Glyphs, which seem to all involve straight lines. This makes me think the Glyph of Rending is just a dot.

The Line of Silencing, which is four spiral loops combined, is already degenerate because it can affect the outside world. I just don't know what it is a degenerate form of.

It kinda looks like this, though.

I think I need to read up on fractals.

EDIT: It has been brought to my attention that I may be in error, and this could be a valid sentence construction.

During the duel between Fitch and Nalizar (pg 18-19 in the eBook), there are 4 separate instances of the word "board" being used for the floor. I know Brandon originally had this fight take place on a chalkboard on the wall, then changed it to the floor, so I imagine this is just an artifact.

This is the paragraph I will be milking for all it's worth. I was reading the rithmatist, saw this, and thought to myself, 'Fourth entity removed'? At first I saw this more as like how people are related (Ex: Fourth cousin, twice removed), but that didn't quite make sense. 

So if a Shadowblaze is the fourth entity removed, where or what is it removed from? My basic idea is the Tower, but that's not heavily supported. If the Shadowblaze is the fourth (Rithmatic?) entity removed from the tower, their must be at least 3 more. 

Categorizations of creatures: I began to categorize forgotten, Shadowblazes, and actually, wild chalklings. Here's what I got:

Shadowblaze (Fourth entity removed): Bonded to people (Vessels) to create rithmatists? [This bonding is important] When bound to vessel, vessel- is made a rithmatist/body preserved/vessel remains in control

Forgotten: Bonded to people (Possesion) When bound to vessel, vessel-is made a rithmatist/body preserved/vessel loses control

Wild chalkling?

(I was wondering what the other entities of the four we know exist may be, and remembered warbreaker, and the categorization of awakened objects. So what if the body of the vessel wasn't preserved?)

Wild chalkling: Bonded to people to create wild chalklings? When 'bound' to vessel, vessel- body removed/ vessel loses control

If this proves true, than the other entity would likely be:

Entity: when bonded to vessel, vessel- Body removed/ vessel remains in control

Just some thoughts and ideas I had, but there's a chance they could prove to be somewhat true.

What happens when a line of vigor hits a line of forbiddance with an axis parallel to its own? Does it just repeatedly skip across the line of forbiddance (GIF attached), or does something else happen? It's a weird edge case that won't occur in most Rithmatic duels, but it's something to think about.

Could this potentially be a powerful method of destroying enemy lines of forbiddance? Or would the normally negligible energy loss from bouncing off lines of forbiddance make this not an effective strategy?

https://github.com/CrypticSpren/Rithmatics

It's very much incomplete: there aren't any lines of making or bind points at all right now. But in the interest of making it easier for @smartycope and/or other programmers to access the code I'm just pushing the whole thing out.

This project is made using Godot Mono. If anyone wants to look at the code, copy the main folder and put into res:// in a godot mono project. If anyone wants to contribute to the code, contact me for an GitHub API key.

If anyone just wants to test it out for kicks, open the executable folder and run the .exe. Draw with the mouse to draw rithmatic lines. Space to pause. D to activate debug mode (line errors show in the top left corner).

Things are quite messy behind the scenes, so y'all probably won't see any observable developments in the near future while I clean stuff up (sorry to whomever I promised bind points at the end of the month to). But progress is being made.

Also mods I wasn't sure if this should go in the Rithmatist thread or in the fan works thread. I figured most people in Fan Works probably don't care about non-cosmere happenings so I posted here. Sorry in advance if that was the wrong choice.

https://www.youtube.com/watch?v=Umu19quwinI&t=173s

This explains why Melody's entire huge family is Rithmatists, as her parents married as Rithmatists, so her siblings, as a part of an all-Rithmatist family, thought that they would undoubtably become one as well. For each child, the amount of faith needed got smaller.

Joel is a Rithmatist if this theory is to be believed. When he draws the chalk line during the Inception, it is stated that "he knew what would happen. His hand passed over the line." His hand passed over because he didn't believe.

The Shadowblazes serve as a test of faith. They probably flee from every person who becomes Incepted, just to test whether the person will believe even after the Shadowblaze departs them.

The Forgotten do not possess Rithmatic powers; they simply allow their possessees to know that they are, indeed, Rithmatists. This is why Harding could make chalk lines.

_______________________________________________________________________________________

If you think this theory is plausible, give it a comment and perhaps an upvote, and I will send you a cookie via forum.

Seems more effective than a chalk circle that can be broken with effort. If nothing else, you can still put the chalk circle outside of the moat.

   So I'm bored and totally in love with The Rithmatist, and I've currently lent the book to a friend so I can't re-read it. So... thoughts on the rithmatist? Questions? Hopes/concerns for book 2? Someone please help me get thinking about it again.

Now. Any chance of a sequel to Rithmatist happening any time soon? I just got done reading it again and have had many students of mine read it. We're all looking for more! No pressure though! You keep on with whatever process you use to bring us these awesome books! Thanks again!

I know that it’s a fairly major part in the ending, but it’s also?? So aesthetic?? 

The crabs that clip the lawn, the idea of sleek metal and gears turning smoothly, the fact that even the trains are clockwork. 

This book is excellent for its magic, its characters, its illustrations, but also for the aesthetic.

To me, the world seems like sunshine and grass and chalk dust and cogs, the elegance of neatly drawn diagrams and the fluidity and motion in the messy ones. You can hear the scratching of chalk on concrete and wood, as well as an ever present ticking and clacking. You smell the chalk and fresh air, and feel the formal cut of a school uniform. 

There’s a feel that this book captures that I love, and here’s my best representation of it. 

One thing that's not clear, though, is how the circle determines them first. I mean, once you draw a circle, does the circle know if it's supposed to have 2,4,6 or 9 points?

Say you decide to draw a 2 point circle. those points could be north and south, or east and west, or any other way. how are they determined? the first point can be drawn at any place, and it determines the new point opposite to it?

But then, those two points are councident with 2 of the 6 points in a 6-point circle. Can you turn a 2 point circle into a 6 point one by adding more points?

Intent always matters in sanderson magic, so maybe you have to think of the triangle when you draw the circle, and it determines the bind points?

i couldn't find anything on the coppermind

1. How do Lines of Vigor(LOV) interact with Lines of Forbiddance(LOF)? In the book, Joel states that LOV can be used to break through LOF, but in one of the diagrams(I think it was before Chapter 22) it states that they bounce instead of damaging them, so which is it?
2. When are bind points determined? If I draw a circle, then attach chalklings on opposite ends(as if it was a 2-point circle), can I add a circle on the side(as if it was 4-pointed) later?
3. Can LOV bounce forever? If I draw a LOV and trap it with a bunch of LOF will it bounce endlessly, or will it run out of energy after a while?
4. Can a LOV damage my own circles/lines/chalklings? If someone reflects a LOV back at me, will it damage my other creations? Could a very skilled rithmatist win by only reflecting LOV?
5. How do Rithmatic lines deal with corners? For example, if I draw a LOV at a wall, will it bounce off of the wall or will it travel up the wall and down the other side?
6. Can LOV trick-shots please be something Rithmatist's do for fun? How cool would it be to have a Dude Perfect type group in the sequel.
7. How would a large scale Mark's cross work? Would it be weaker at the intersection? Could you cross 4 LOF to make a stronger square as it wouldn't have any corners?
8. If you knew your circle was about to be moved(because you didn't anchor it properly, it got damaged, etc.) could you jump/move with it to prevent being disqualified?
9. How much could a Rithmatist do with intent? Could you make a LOF that switched from being active to inactive? A Line of Warding that spins in place?
10. How long do lines other than LOF take to dismiss? Is it instant, or does it just take less time than a LOF?
11. Is Melody's ability with chalklings a learn-able skill, or is it something unique to Melody?
12. At Nebrask, do the Rithmatist's defend from inside or outside the circle? Why can't they just redirect a river/make a moat?
13. Are Rithmatists something that is limited to the American Isles, or are there Rithmatists all over? If they are all over, do they all go to defend Nebrask? Are there other Nebrask-like locations in the world?
14. When fighting Harding, Fitch uses 2 chalk pieces to draw. Is this allowed in dueling, or is it just too hard to be regulated?
15. How is a Line of Revocation(LOR) drawn? Is it drawn straight piece first, or squiggly piece first? Joel initially mistakes it for a LOV, but those are drawn out to in, which doesn't fit with the LOR.
16. Does the amount of chalk/thickness of the lines have anything to do with the power of the lines? If I draw a LOW with chalk that is 2 times as thick, is it 2 times as strong?
17. How do LOV move? Do they leave a trail of chalk as they move from where they start, or do they erase themselves, leaving only 2 periods at all times?
18. When a LOV hits a LOW, does the LOV just dissipate/get erased, or does it break apart/fall apart?
19. How much strength would you lose on a LOW if you missed bind points? Could you bind more than 9 circles/chalkings and have them cover the weak-spot they create?

OK, wow that was more questions than I anticipated. If anyone has answers to any of these questions, please leave them down below. If not, I guess I'll just have to wait for a sequel.

Part 1  Here I outline how to get all of the binding patterns in the book from special cases of 9-point triangles

Part 2 How you could get a 5 point defense as a result of looking at right triangles.  Brandon confirmed the existence of 5 point defenses at the signing today, but said they haven't been well explored in-world.

Part 3 How you could get an 8 point defense as a result of looking at right triangles.  Brandon confirmed the existence of 8 point defenses at the signing today, but said they also haven't been well explored in-world.

Note: In these tumblr posts (which were written before the signing) I postulate that some bind points might be stronger than others.  Brandon told me that this is not the case. You can always bind more than one thing to a bind point, but binding multiple things weakens the point. It is a much better idea to add a small circle that gets 3 additional bind points. It doesn’t change anything if the point comes from multiple points in the 9-point construction.

Part 4 Where I analyze the 9-point circle construction on obtuse triangles and come to the conclusion that they don't give us anything new.

Part 5 Lots of thoughts on the changing curvature of ellipses and my guess at the Blad defense. I didn't get a chance to confirm any of this.

Part 6 So, there is a generalization of the 9-point circle construction in Geometry that allows for the construction of ellipses.  Here I talk about different triangle centers and how they could be used to produce 9-point ellipses. When I showed Brandon my page of 9-point ellipses constructed from different triangle centers   he stared at them for a moment before answering.  He hesitantly said that, yes, those constructions should be valid in theory, but that they shouldn’t be used in practice.  The sides of ellipses are weak enough that if you expect to need to defend your sides you really should be using a circle.

Part 7 More on 9 point ellipses

Part 8 Various thoughts on lines of vigor many of which were confirmed today! Things that Brandon confirmed for me at the signing today:

• Yes, Lines of Vigor behave like light waves.
• Yes, this means that higher frequency waves are better for doing damage, lower frequency waves are better for transferring energy (and thus moving things)
• Yes, Lines of Vigor follow the rule that the angle of incidence = angle of reflection when bouncing off Lines of Forbiddance.
• LINES OF VIGOR ALSO REFRACT.  I asked it in terms of whether they slightly change speed and direction when they move between materials like, say, concrete and asphalt.  He said yes and that you also get the wavelength adjusting.

There, ah, may still be more theorizing coming as I get it written up

Also, why do most people think that the larger the curvature, the stronger the line, when the strongest line has curvature 0?

Let me know in the comments what you think and how I can improve.  Thanks, and good Worldhopping!

I do not know about any of you but I think that a Rithmatist videogame if done correctly could be amazing and a popular game franchise. I would imagine the Rithmatist as more of a non canon spinoff story. Rather than being about the battle against the wild chalklings you play as a character who is starting out as a Rithmatist and wishing to become the best rithmatist in the entire world. I imagine this more like gen 6 of pokemon with you running around the city and other areas of the world exploring and challenging other people in Rithmatic competitions. The story mode has plenty of freedom but ultimately centers on becoming the best rithmatist by entering tournaments and defeating other rithmatists. In battles it is just like the game with the same rules, defensive circles, chalklings, etc. Cool animations to represent chalklings and circles with a very detailed appearance. I think difficulty modes would be important for this. On the hardest mode you have to be as good as the rithmatists whereas easier modes will be more forgiving of the awkward circles drawn.

Then have an online mode where you can compete on teams or one on one. Have a for fun mode and a for glory mode with the for glory mode being exactly like the hardest mode in single player where you have to be extremely precise with circles drawn. That is where the really skilled and competitive strategical players would compete with each other whereas for fun is more relaxed and less harsh on those who have trouble with circular precision.

I think this game would be perfect on a system like the Wii U or 3Ds because of the stylus you should be using to draw circles and chalklings. Any good handheld or console that can use a stylus to draw the circles would suffice. So really anything that could use touch screen for rithmatics would work perfectly. I feel that this game would fit well with a single player somewhat like pokemon where you can explore many places and do different things along with battling different rithmatists. Also as you level up you learn new circles and you can choose which skills to strengthen with stats gained on levelling. Finally as I also said before a good online mode with competitive and casual play.

I was not even a huge fan of the book but I would love this kind of competitive strategy game with a nice single player and great online. I am not necessarily sure how the gameplay in battles should work but I feel that the pokemon style rpg setting fits best. would anyone else love a videogame for rithmatics? Imagine if it got super popular and became a really popular strategy game with gaming tournaments for it. What would you all think of this kind of competitive strategy game with some smaller rpg features and a stylus as the main controller?

     I've heard descriptions of stuff like airsoft arenas, and have been in laser tag arenas, large, walled off areas where people who don't like conventional sports (and even those who do) can play a fun physical game. My idea is make something like that, only on 1 level. Essentially remake the melee arena in the real world, with something similar to smart boards as the floor. I've seen stuff like that done, a virtual tide pool that you can stand on top of and make ripples in. Just, ya know, melee sized. then have an uber-powered computer programmed to run a rithmatist-style game. the players would be given special shoes to detect where they are on the field to tell when they are taken out, along with some chalk, perhaps 3 sticks that they can customize before hand, color, hardness (essentially size), etc.

     So... what do you guys think? You would still be left with the problem of chalklings, you would be limited to the chalklings in the machine, then also the runes to control them... it would be rather annoying. The best thing I can think of is allow submissions from players of various level versions of creatures, skeletal, shaded, etc. you would then be able to select your chalkling based on various options. Offensive/defensive, attack/health/speed, skeletal/shaded, you would then set where it is bound to (if bound), then set where it is going to be as maximum distance (if bound), or start point. if bound it would bring the chalkling closer in and have a wavy chain/rope (players decision) going to that distance. you would then trace the creature and its chain, and it would receive stats based on its  base stats and how well you mimicked the chalkling.

Further improvements may include the ability to have an account that stores favorite chalklings, as well as a name to display on leaderboard, or perhaps the possibility of polychromatic chalklings with higher stats, perhaps capable of fire damage, bark skin, etc.

So... what do you guys think of this idea? as of now, I would be stuck on the theoretical team, my programming skills leave a lot to be desired, and as far as artistic capabilities... well, they aren't that great. Feel free to share ideas to improve this, or ideas on how to do the coding, perhaps ideas for sketches, stats, etc.

Anyway. What Chalklings would you have? What sort of creature, being, whatever do you want to have protect you and defeat your enemies? A type, maybe, where some are better at offense, some defense, some mobility?

Also, who is gonna be the first to say pokemon?

I think my grouping might be greek monsters... or possibly obscure creatures from various mythologies. A halcyon to fly around and attack a weak spot on the rear, a set-beast for aggression, maybe an oni for defense.

I wonder if the rock-paper-scissor mentality works at all... in that first duel, Finch fought off dragons with a knight. Does making a defensive chalkling with some mythical reasoning behind it to defeat the beast make it better against that specific chalkling? Can chalklings be ranged? If I make an archer, with a quiver of arrows, could he draw those arrows and fire them at other chalklings, or even at Lines of Warding?

Finally, I would like to see Melody at some point make an enormous chalking. I see it shaping up like an ouroborous; she draws a line of Warding, then around the outside starts at the tail and works forward, quickly filling in powerful scales for defense, many many legs along the length to give it speed, maybe spikes at the sides, powerful claws and crushing jaws for offense, built so big it circles entirely around her Warding Line... then, finally complete, it races to her opponent, crushing tiny chalklings like godzilla, destroying the enemy's defenses... I think that'd look cool. Granted she'd need a way to stay entirely protected for the many minutes it would take her to do all that, something like a large team in the melee, six teammates around her to play defensively and keep enemy Vigor lines and chalklings at bay while she completes her masterwork...

1) What are the effects of missing the exact bindpoint? For example, if I am trying to draw a line of forbiddance connecting two bindpoints and I draw wrong and miss one of them, does that simply mean that the line of forbiddance just doesn't anchor that bindpoint?

2) In a lot of the drawings of defenses at http://coppermind.net/wiki/Rithmatics, you can see that often the line of forbiddance is drawn through the bindpoint. Thinking of bindpoints and anchoring from a kinematics standpoint, it seems as if a single line of forbiddance that passes through a bindpoint constrains the line of warding in both translation and rotation (e.g. The Osborn Defense). However, in something like a Sumsion Defense without the rear line of forbiddance, would the large line of warding be able to rotation about the bindpoint connecting to the smaller, anchored circle line of warding? I am having a hard time understanding how much constraint a line of forbiddance adds to anchoring and whether tangent bindpoints have any kinematic constraints.

3) It seems to me that at the start of any primary line of warding that the first construct added severely restricts the space of future constructs. For example, if a person tries to draw a line of forbiddance between two bindpoints of an assumed six-point circle and misses, then they have necessarily started one of the nine-points circle which have that chord as a possibility. This leads to the next question of "how close is close enough" to actually get a line of forbiddance to attach to a bindpoint? I will illustrate a scenario:

• I try to do a line of forbiddance between bindpoints on a six-point circle (imagine I am trying to start the Eskridge Defense). But let's say I mess up.
• Do I know I missed the exact bindpoint? Let say I don't know that I missed the bindpoint, so really I started the nine-point circle corresponding to my messup.
• I now try to draw the second line of forbiddance for the Eskridge Defense. The problem is that the bindpoints aren't where I thought they were.

So, the second line is still a valid line of forbiddance, it just doesn't anchor my circle, right? Or potentially only anchors it in translation but not rotation for the once anchor point I did hit? Well, since the first line of forbiddance anchored my circle line of warding, do I really care that the second line of forbiddance is slightly off? Is there some advantage in a lot of scenarios like this to actually be right on the bind points as long as the line of warding is already fully anchored/constrained?

The reason I ask this is because I have done a bunch of hobby iOS games in the past and started thinking about the actual mechanics of the game and it brought up a lot of questions about the importance of bindpoints. They seem really emphasized in the book, but they became less critical to me as I read through the wiki, various articles on here about all other circles being a specific case of the 9 point circle, and the concept of anchoring.

Thoughts?

Favorite? Sure. The Way of Kings is vast and sprawling, a remarkable achievement that I've no doubt is destined to be placed alongside Lord of the Rings and Wheel of Time as classics of fantasy. And it is a wonderful book- make no mistake. But it's just the start of the Stormlight Archive, just the beginning of bigger and better things. It's not like The Rithmatist. Mistborn brings us to world that turns fantasy tropes on their head, gives us the best magic system fantasy's seen in years, and brings ever-increasing stakes to resolution with three twist endings. But it's not like The Rithmatist. Alcatraz is pure humor and a delightful romp, a model I've studied for my own writing. But it's not like The Rithmatist.

Why do I like The Rithmatist?

There are lots of reasons, of course. I love the setting- steampunk, alternate history, and humankind holding out against an advancing evil. The magic, where chalk and drawings come to life in a fantastical RTS. The expectations turned on their heads- Hardin, you double subverted trope, you.

But most of all, I think I like The Rithmatist because of Joel. You see, Joel is a fairly normal kid. He's a smart kid, the kind I like to read about. But he's not magical. In this he differs from most of Sanderson's other protagonists: he has no superhuman powers of his own, and is forced to rely on his wits to save the day. Which he does. Multiple times. Do you know how refreshing it is to see that in fantasy? To see a hero survive by his wits and not his powers? I love that. It's fundamentally the story of an underdog, and of course we love underdogs.

But Joel also wants to be a Rithmatist. He wants it more than almost anything. I think most geeks can relate to this- don't we all want to run with Sazed on the walls, to fly with Vin on dropped coins? Isn't that why we read fantasy? But Joel's desire is especially personal to me. You see, I spent most of my early life almost obsessed with the idea of gain superpowers by some means. Magic, mutation, invention, it didn't matter- I just wanted SOMETHING. You might not have guessed it to look at me, but my nine, ten, eleven year old mind was always plotting some way to become something more than human. Puberty seemed like the best way, I thought. That was when the X-men always got there powers.

Puberty came and went as expected, and no powers were forthcoming from it. Would you believe that through my teenage years, in some part of me, that desire never died down? It's true. Even as it become less and less likely, that desire never quite vanished. It's really not dead today. All you have to do to is give me a book where someone has an interesting power, and I'll spend hours contemplating life with that power. Days. Thinking about how I'd use it, what I'd fix with it. Normal? I doubt it. But that's me.

I think Joel would understand that part of me. I think he'd understand what it means to have some part of you that wants to be something more, some part of you that won't rest until it has had its taste of power. Joel knows about that; he feels it every day. But Joel never lets his sense of desire hinder him. He doesn't let what he can't have wear him down. And more than that, he's not ashamed to let that part of him be. He studies Rithmatics. He loves Rithmatics, even though he knows he'll never have them. Why? Because that's who he wants to be. He's not defined by what others say he has to be, not limited by the strict dreams that everyone else wants to impose on him. No; Joel is his own man, at his core.

I sympathize with Joel's frustrations, too. All these people around him, all these people with the gift of Rithmatics, and they never seem to love it, only seem to waste it- that's a feeling I've felt many times. We're given so much, and at times we do so little with it. Sometimes I want to scream; I think Joel would scream with me. And then sometime we're given the chance to get what we've always dreamed of- as Joel was, when he went into the booth in church- and we don't get it. Sometimes we fail. Sometimes our dreams crash and burn and leave us without any pieces to pick up. Life is that way sometimes. Joel would understand.

But it's the ending that seals the deal for me. The moment in the tournament where Joel and Melody step into the ring, when their diverse skills come together into a single, sweet note of triumph, where everything that Joel loved becomes the key to his victory in a way he couldn't possibly have expected- that's the real kicker. It's the moment when Joel realizes that he's not a Rithmatist, that maybe he'll never be one- but yet, it's still all right. Because I think that's the real message of The Rithmatist. It's the idea that even if you never have everything you want, you can still have everything you need. It's the triumph of sheer normality in world that seems set against it. It's the victory of the underdog that we all long to see even if it's not the way we expected to see it. It is, in other words, a victory of the finest kind- a victory of the small man, a victory of the normal man. That's what I had to learn growing up. You're never going to be Vin. You're never going to be Sazed. You're a normal human being, and you're going to be a normal human being all your life. And that's okay. There are still triumphs, there are still victories, there are still wonders and gifts for you, too. You're a human being, and that's all it takes.

My name is Mike, and I am a normal person, the kind it seems like the world has it out for sometimes. My name is Mike, and I am facing the challenges of life without powers or magic to get me through them. My name is Mike, and as far I'm concerned, it's going to be enough.

We all know that drawing Rithmatic figures requires intent from the Rithmatist to actually take on any properties. You see this illustrated by the lack of  mysterious symbol that blocks out sound. This was explained by the lack of knowing what the symbol does. Fitch also explains why this causes it to fail

"...believe that a Rithmatic line functions based on the Rithmatist;s goals in drawing it...nothing comes to life unless we are explicitly trying to do a Rithmatic drawing.

OK so now we need to see if Joel was ever attempting to do a Rithmatic drawing after that encounter.

First he does the test with Melody. After he draws the line, he says that he knows it won't work. He didn't believe that he had become a Rithmatist and thus he never had intent and desire to draw a Rithmatic line

"Melody reached out with her anxious hand, but Joel knew what would happen"

Also, when he is drawing in the arena he isn't trying to draw Rithmatic structures. He is just trying to outline what Melody will draw.

Let me know your thoughts on this  one guys

-Trey

So what character do you think you're like?

What are your personal questions? And as the list grows, which do you think are the highest priority, especially in light of the promise in the State of the Sanderson that The Aztlanian is coming up soon?

I'll share the final list with the other sharders attending, and we'll try to make sure the best questions make it into the discussion.

The theory shows, that each known rithmatic circle, is, in fact, a special case of a nine-point circle. Also, this theory postulates a five-point and an eight-point circle.We start with the construction of a basic nine-point circle, as discribed on the graphic "the nine-point circle". For this, we need a sharp-angled triange cornered between the points A, B and C. We construct the middle-points of each side. Those we call M_a, M_b and M_c. We draw a circle through those three points.

We construct the heights on the sides a,b and c and call them h_a, h_b and h_c. Note, that the height meet our rithmatic circle d exactly at the intersections of d with a, b and c. We name the crossings of the h-lines with k with the names H_a, H_b and H_c as well as L_a, L_b and L_c. The M, H and L points now build the anchor points of the basic nine-point circle.

As far we have the usual nine-pointer. The only requirement for it was a triangle ABC with sharp angles.

Now let's make a step from general to special. Let us assume, that each of the angles of ABC would measure exactly 60°.

In this case, the points M and H on each side merge together, so we basically loose three points, leaving us with a six-pointer. Note, that a six-pointer absolutely must be regular under this constraints.

Anotther special case: let us assume, that one of the angles of ABC is exactly 90° and the other two 45°.

Here we have a lot of merging: the points L and M on the sides a and b merge togehter (note: L_a merges with M_b and vice versa), H_c and M_c merge with each other; all the other points merge with C.

The two-pointer is an even more special case: now we bring the points A and B together, making all points merging with either them or C. My graphical program is not capable of this construction, but theoretically it underlays the same laws as the nine-pointer construction.

Now: predictions.

The construction of a five-pointer requires ABC to have one 90° angle, but the other two to be different from each other. The Idea is the same as with the four-pointer, but M_c and H_c separate from each other. The pentagon in the five-pointer is irregular, but has a rectangle structure between four of it's points (all except H_c)

Also, you can construct an eight-point circle. It requires for ABC to have two similar angles, none of them 45° or 90°. In this situation only the points H_c and M_c merge. The octagon is irregular, but symmetrical around h_c.

Other forms might exist, but i didn't found a way to create three-pointers and seven-pointers. Properties, usefullness and rithmatic specialities of this circles are yet to discover.

So, the irregular nonagon, AKA the Line of Warding with 9 bind points. The important thing to remember is that while the 2, 4, and 6 bind point versions all look the same (apart from rotation), ones made with 9 bind points are much more flexible. Now, let's get down to business.

First, draw your circle. Then, pick 3 points on the circle and mark them. These are your first 3 bind points. The only restriction is: they can't all be in the same 180 degree section of the circle. You'll see why in a moment.

Now, you're going to need to mark down 3 lines to make a triangle where the midpoint of each of the lines is one of the bind points you marked in the last step. There's only one way to do this, so don't worry about messing it up! You'll probably notice that the lines of your triangle intersect the circle in more than one place. The extra spots where they intersect are your next 3 bind points! I forgot to mark them in the picture though. The only issue would be if you put all 3 of your original bind points on the same half of the circle - then your triangle would be obtuse, and you'd probably feel pretty obtuse too! Obtuse triangles aren't allowed here, so keep some healthy distance between those points, mister.

The final step now is to draw a line from each corner of your triangle to the extra bind points you marked in the last step. In order to do that you'll have to intersect your circle again, and you know what that means! That's your last 3 bind points, done! See, that wasn't so hard.

Now, it's pretty well known (thanks to the hard work of people like KalynaAnne) that you can make the 6-point, 4-point and 2-point circles with the irregular nonagon, and you can even create top-secret 5 and 8 point circles that aren't discussed in the books. How exactly you can do this I will show after I update my post tomorrow (or the day after), as I'm currently working on some swanky animations to get my point across better

Magic of Rithmatics

Story and World of the Rithmatist

Writing the books and Research for the Series

During the read, at the end of every Chapter(or start) there is a page explaining an aspect in Rithmatism like say a type of Defence or how you duel.

Who wrote them?

At first I thought it was Joel's father considering the scene where Joel enters his father's workshop after all this time to discover the new line. Surrounding the piece of paper with the new line there were sheets explaining defences and techniques used by Rithmatists around the world. 

But  then in the battle between Fitch and the Forgotten there was a page that was titled "Joel's sketch of the Rithmatic Dorms Second Floor that night"

So was it Joel who wrote the manuscripts or his father?

OK here's a mad theory that I got after I read Joels description of the Forgotten, he says that it looks like it was drawn from Charcoal. this got me thinking what if there's another power in the world other than Rithmatics. What if there are things in the tower of Nebraska that draw with Charcoal. They create the Forgotten and the Forgotten create the wild Chalklings? I don't really have any basis for this theory other than the Forgotten looking like it was made of Charcoal and my idea that something is in Nebraska creating these things. 

If you were to put the small circles of warding on the inside of the large one, would that be alright? It says in the Taylor defense that they have to be concentric, but it sounded like that was just so the bind points would line up. Also, would doing that with a mark’s cross in each have enough stability to forgo other lines of forbiddance?

The Line of Revocation was described as a mix between lines of vigor and forbiddance, so is it possible other lines can create mixes as well? My major thought is that if a Line of Vigor and a Line of Warding mix, they could create extra curves for the circle to add strength. It was implied that this type of thing could work when Fitch and Joel first inspected the Line of Silencing and thought it could be a strange Line of Warding. Does that work?

Lines of Vigor have always been shown as the same degree curve the whole way. Does it have to be like that, or could it change throughout? If so, would it continue out following the pattern, or the outermost curve?

Joel suspected the Line of Silencing at the crime scene had faded as time went on. Yet it still registered as a rithmatic line from the chalkling. Does that mean nothing, or had it perhaps faded only to the point where yelling is the only thing sucked in? I was thinking it might have not worked because the Scribbler was not directly present (Harding was in control at the time), similar to the way the chalklings changed back to people when the Scribbler was beaten. Or maybe, since the rithmatist’s intentions change the lines, the Scribbler made it stop working just by not wanting it to do so. If that is the case, could people do something like that? Perhaps by not waiting the full 4 seconds for a line to disappear? The way chalklings pause when touched with chalk implies that this could work, but then again, most of this probably means nothing.

Nalizar wondered why ‘they’ hadn’t picked Joel. Was he referring to the Shadowblaze? The Master is singular, so do rithmatics really have nothing to do with the church at all?

Will anyone ever make more specialized chalk? For instance, the rain was supposed to be a problem in Nebrask. Will they find a way to waterproof it? Or might they add bleach or some kind of base to make it kind of immunized to acid?

The historians have trouble finding whether the Isles were ever inhabited. Were there any natives that were turned into chalklings? Of course, a related question is whether only rithmatists can be turned into chalklings- the Calloway servants were killed, but that could be because the rithmatists were being kidnapped because they have a limited number. That would indicate that the natives were rithmatists, which could also explain the Shadowblaze seen by Estevez. Or are Shadowblazes themselves the natives?

Could one line have multiple purposes? For example, could a Line of Silencing be used as a chalkling if you intend it to be so? I ask this not really because it would be a good chalking, but for the purpose of determining whether Shadowblazes could really have life only because of lines of making, as speculated in the book.

Your intent obviously affects your lines. Could your opponents’ also? Perhaps for a line that could keep people from lying? Though now I think of it, I realize that rithmatics are more likely to do that for everyone rather than just the opponent.

Could they not just dig a moat around Nebrask and fill it with acid? Surely there aren't enough chalklings to dilute an entire moat.

Do all wild chalkling return to life when defeated, or just the human ones?

Well, those are my thoughts, though I'm sure there are some I've forgotten. I'll be sure to add them if I remember any. Some of them are pretty simple, but hey- you can't solve 5x = 15 if you don't know that 5*3 = 15.

Any thoughts?

In Rithmantist's alternate earth all native nordamerikans fled to southamerika because of the chalklings. But if the settlers from Britannia never met those tribes, why did they call one island "Dakote"??

And to everybody from north america: would your home be under water in the rhitmantist map?

There are many theories on whether Joel is secretly a Rithmatist. Time for another one I guess.

We know that Joel saw something--presumably a Shadowblaze--in the chamber, but Joel doesn't talk with anyone about it, so we don't really know what "It" is. Already we know that Joel doesn't manifest any Rithmatic power, before or after seeing the "It". We know that there are many new and unexplained things happening in the United Isles, as shown by the Forgotten, the Lines of Silencing, and Professor Nalizar. So my theory is this: could Joel have possible power that takes longer to show because he's a new kind of Rithmatist?

Let me hear your opinion on this.

-KnightRadiant

The reason this might not have been done before is the high amount of trust and coordination needed to get it right, but surely after speaking it work so effectively it will soon become common practice? Please tell me what you think

Should chalkings be controllable by drawing symbols like in the books, or would it be simpler to just to have the chalkling stay still and defend its bind point or move forward and attack anything in its way depending on the chalking used.

Any thoughts on how they should work on a phone or computer game.

How did Trent discover it?

Thanks to KalynaAnne, we know a lot about the fundamentals of Lines of Warding, and other lines.

Lines of Warding are circles derived from significant points within a triangle.

Lines of Vigor appear to be simple sine curves.

Lines of Forbiddance appear to be simple line segments.

Lines of Making appear to be a fundamentally different kind of line, and I'm going forward on the assumption that as they are a different category, anything we know about them does not pertain to the Line of Silencing.

So. How did Trent discover it? It could have been by simply seeing it somewhere; on a cliff in Zona Arida, or at Nebrask, or in some obscure tome. I highly doubt it was by just drawing random things until he became convinced that one of them was rithmatic.

Or. He could have discovered it by looking at something geometric, and extending it somehow. I propose this is what he did. I think he noticed the arithmatic spiral, and decided to find a significant form which could be made from it.

That's the first turn or so of one arm of a basic arithmetic spiral. I can use it to construct a Line of Silencing... I just can't think of why doing it is obvious. Why someone would do it, and then insist, this must be rithmatic. A trait of the arithmetic spiral is, if you draw a ray from the origin outward, every line segment between times it crosses the spiral will be similar. I also note that the spiral is called arithmetic, which just sounds like the word rithmatic, but I'm unwilling to assume someone would assume this (and be right) based on happenstance of nomenclature; both names derive from the same root, but that means little. Also, technically this is only the positive values of the spiral; for all values you'd need to add the reflection in the y-axis, which would mean it would cross itself every time it crossed the y-axis.

Anyway. Take this (or, I believe, any) fragment of a spiral; double it, and rotate the double 180 degrees (or, if you prefer, reflect it through its origin) and you will get a doubled spiral.

Starting to look familiar? Take four of these segments (two rotated 90 degrees) and stick them together to get:

This might imply that more complicated LoS are possible, if you have more turns in the curve of the basic shape.

Maybe that one would dampen sound even further? Lower threshold for the decibel at which it triggers?

However, this is all pretty hollow. With a starting point, and the fact that I know where it goes, I can connect the dots... what's missing is, why is this OBVIOUS? How could Trent have started from the spiral and made his way to the LoS? What's so obvious about taking eight copies of a spiral, reflecting half of them, and looping them all together?

In addition, I would like to study more about the involution of a circle. Apparently, it's based on a circle, looks like a spiral, and has become fundamental in making gears work more efficiently. This has all the hallmarks of rithmatics; one unseen shape affecting the resulting shape, and it even ties in with gears, like the six, four and nine-toothed gears inside a dollar coin. This seems far more promising. I'm going to do more research and see what I can come up with.

Sounds a tad strange, but hear me out.

Say you had two pieces of wood arranged in a "T" shape. If a Rithmatist drew a line of forbiddance on the top of the T, wouldn't it create an invisible plane out from it? And, doing to the small nature of the item, it would be simple to move it around, therefore changing the location of the invisible plane. While it may not cut like a sword can, it would be an easy to use bludgeoning weapon.

So, what do you think? Are there any obvious errors in my logic? Would anyone actually do this in the United Isles? And would a person be able to push the plane, seeing as it isn't rooted in a sturdy floor or wall?

Why not draw a small Line of Warding then shoot it forward with a Line of Vigor? Sure, it might not have as much force, but it provides some much-needed AOE against a wave of chalklings.

or of course there could be no reason but this has been bugging me.

Found a Shadowblaze at this restaurant. It's not moving... I think it's dead.

*Makes Chalklings able to affect objects

**Turns people into Epics

Anyway, If you'd like to help, just message me on the site. It's brand new, so there are hardly any pages, but I'd appreciate anyone who'd like to join. Or even just tell others that it exists. Thanks

When I read this book, the reasoning for the nine-pointer (described via annotated depiction from what I assume is Joel's notebook on page 243) kinda blew over me, and I just wanted to experience the story for once, rather than get caught up in the world's physics. That said, I still promised myself that I would check it out after I was done. I finished the novel, then recommended it to my little brother's friend, who promptly inhaled the darn thing, then asked, "Any other suggestions?" with a huge smile on his face. After this, I finally looked it up on Wikipedia (mostly due to his own interest in Rithmatics), and the results I found then and afterwards were extremely intriguing.

First: The 9-point circle is an actual discovery made by Olry Terquem, and has some significance in the geometric world.

Second: (From here on out is a thought process) The 9-point circle doesn't quite work for equilateral and right triangles; what do the look like; what are their Rithmatic equivalents?

Third: Equilaterals would lend themselves to the six-point circle due to their nature of fusing together three different pairs of significant triangle points that would be fully represented in the 9-pointer (kind of shown in a picture on the top of pages 94-95; I just discovered this disproof of my originality in thought, as well as another in the history section of the aforementioned Wikipedia article).

Fourth (fittingly): If both the 9- and 6-point circles can be represented as a relationship between the circle and a single triangle, what about the 4-point circle? The four points form an inscribed square when connected, and a square is essentially two equilateral right triangles stuck together at the Hypotenuse. On a whim, I drew this on a piece of graph paper:

I noticed that all nine points were represented, and several at once in the peak (I had the hypotenuse on the bottom), and was then feeling nearly satisfied with my pursuit of Sanderson's use of Trig relations in his novel.

Fifth: What about ellipses? The first thing that came to mind was Isosceles triangles,  and thus I drew this on the same piece of graph paper:

I'm pretty sure that the points at which the ellipse passes through the sides are their midpoints. Obviously, all nine significant points are NOT represented by said ellipse, but it does pass through at least two, probably four, of them.

Sixth: This one is best described through simply showing a picture:

I was messing around with isosceles triangles, so naturally, I wanted to see what their complement circle would look like point-wise, so I essentially drew up this diagram on my graph paper.

That's it for the thought process, but I'm having trouble with a couple. For one, although Lines of Vigor are made from a sine or cosine graph, where did lines of revocation come from? And, I'm completely at a loss as to where the spiraling

line  comes from.

Comments, further proofs, or disproofs?

EDIT: sorry for the small pics.

I also noticed that the biggest weakness with the lines of forbiddance is the where they meet to form a corner

So if I was going to be trapped by Edit (Wild) chalklings but had a while before they got to me, this is the defense I would do. What do you guys think? It wouldn't allow for any offense.. but then again offense against chalkings isn't very effective unless you aren't the only person fighting. Do you guys have any interesting chalk defenses that you have kept pent up inside? I'd love to see some epic chalk ninja ideas!
...hmmm lets add cat to that. Epic Catchalkinja. cat-chalk-inja.

Cats seem to be like bacon. they go with everything.

(click on the images to make them bigger)

so now with the appropriate background out of the way here is the theroy. The more bind points over lap the stronger they become. 

now one might be wondering how i am rating the strength of every bind point

So in one of the illustrations It is noted that a chalking bound to a bind point is stronger than one that is not.

My rating for the strength of bind points is how much strength is added onto the chalkilings strength. and potentially with further evidence as to weather it is a multiplier or additional number. 

So three is stronger than two is stronger than one is stronger than none.

SO Comments thoughts questions, additional bits and pieces, proofs, disproofs, ectera, ectera. 

1. Why does the line of forbiddance affect the 3rd dimension even if the students are just juniors?

2. are you allowed to step out of the circle to draw distant objects and come back? Some of the line of forbiddance drawn to deflect / bounce Lines of Vigor seems to be quite far away from the circle, I don't think that's possible without stepping out of the circle?

Cheers!

The only person I currently have in my head is Molly Quinn as Melody.  She's a bit older, but when has that stopped Hollywood?

• Would you build a quick defense and go on the offensive or spend time on a stronger defense? 
• Would you use a variety of chalklings or lines of vigor?
• Would your chalklings be detailed or simplistic?