I'm Having Trouble Getting The Next Chapter Of My Shallan In HP Land Crossover Right, So I've Been Rereading

I sat down to work on the “Sh is for Shalebark” page and got the basic layout and text done. Then I started contemplating which kind of shalebark I wanted to draw.  I’m bad at decisions, so you get this instead... If you want to know more about Shalebark, the Coppermind page is good :-) 

Rithmatics: Part 1

Hello!  I'm rather fascinated with Rithmatics (the magic system in Brandon Sanderson's The Rithmatist) at the moment, which means you are going to be getting a series of mathy posts.  They will all be tagged with #rithmatics .  I've been encouraged to add the cfsbf tag.  If this bothers anyone, please let me know.

In this first post we explore how all of the binding patterns for circular defenses can be derived from 9 point circles. You might be able to get everything from the pictures, but I give explanations as well.

9 Point Defenses

Let's start by talking about 9 point circles.  Start with a triangle.  Absolutely any triangle will do, but for 9 point defenses we want acute triangles (all angles less than 90 degrees) where all of the angles are distinct.  Mark the midpoints of each side and draw in the three altitudes (start at each vertex and draw the line perpendicular to the opposite side) of the triangles.  Mark the points where the altitudes intersect the sides of the triangles (there are 3 such points, one for each altitude).  Note that all of the altitudes meet a single point. Mark the midpoint of each segment connecting P to one of the vertices of the triangle.  This gives you three more points for a total of 9.  These 9 points will be distinct and lay on a circle.

This explains how to get the bind points for any 9-point defense.  However, not all defenses have 9 points.  These turn out to be very special cases of 9 point triangles where some of the points coincide.  

6 Point Defenses

To get 6 points, start with an equilateral triangle.  Any time two angles of a triangle have the same measure, the altitude from the third angle will bisect its opposite side.  Since all of the angles are the same here, all of the altitudes bisect their opposing sides.  This gives us a "9-point" circle with 6 evenly spaced points.

4 Point Defenses

This time we want an isosceles right triangle (you might know it better as a 45-45-90 triangle).  In right triangles, the legs are also altitudes, which means that the vertex at the right angle is also the point where the altitudes intersect each other. It is also the point where each leg "intersects" the other and the "half way point" between the intersection of the altitudes and itself, so it counts as 3 of the 9 points.  The resulting 4 points form a square and so are evenly spaced around the circle.

2 Point Defenses

This is the strangest case.  Here our triangle is degenerate - one of the sides has length 0, which means that the "triangle" is just a line.  To see how to follow the 9 point construction in this case, we can look at a limit.  Start with a really skinny isosceles triangle.  If you follow the construction, you get three points grouped near each approximately half way up the triangle.  The other 6 points are clustered down near the narrow base.  Now pretend the narrow point is a hinge and slowly close it. As you do, the three points in the middle get closer and closer together, the base gets narrower and narrower and the 6 points near it get closer and closer together.  In the limit this gives us a line segment and a circle which uses half of the line segment as a diameter

I finally got around to reading Sanderson's Shadows for Silence in the Forests of Hell (I've had the anthology checked out from the library for a couple of weeks). It has a lullaby. My brain provided a tune for the lullaby (I do not know where the tune came from, I don't recognize it and if it sounds like anything it was unintentional).  Getting this file into a form tumblr would take was a stupidly convoluted process and I'm not entirely happy with the recording quality (I really don't know what I'm doing with recording), but, here, have a cosmere lullaby.

Shallan's Journey: Chapter 3, In Which Pattern Declares English Full of Lies

Shallan heard her name and glanced up warily. The group was clearly asking Albus about her, but she had no idea what they were saying and was already trying to process too many things to want to add anything else. The stove woman noticed her looking up and came over with a plate of...something, a fork and a glass filled with a drink that appeared to be some sort of orange juice or wine. Shallan realized that she was hungry and took a deep breath to calm herself before offering the woman a small smile and accepting the plate with a “Thank you” even though she knew it wouldn't be understood. She inspected the food and realized quickly that she had no idea what it was, though at least the utensil was mostly familiar. She took a bite and contemplated it. It was very different, but at least it was edible. The woman gave her an encouraging smile and said something Shallan couldn't understand before bustling back over to the discussion at the table.

As she ate, Shallan worked on talking herself down. You had already figured out you weren't on Roshar. The plant and animal life here is very different – the plants don't retreat into the ground and there are chickens that travel in fire. Of course the food is going to be different. The whole world is different. That also means they are going to have different sensibilities and different ideas about who should do what jobs. Shallan groaned quietly. On an intellectual level that seemed straightforward enough, though it wasn't going to make it any easier to navigate this world. Maybe it would be easier to handle if she viewed the situation as a scholar. She reached this conclusion as she finished her meal, so she carefully set the plate on the ground next to her, opened her sketchbook and began to document what she had seen so far. In addition to helping Shallan organize her thoughts, the acts of writing and drawing always helped to calm her.

Hermione rolled her eyes at the argument raging around her. She supposed it could be possible for the Death Eaters to try something similar to whatever was going on as a way to get a spy into the order, but she really didn't think they were that clever. Dumbledore's story also had too many details that made it clear that this new girl was not from anywhere they had ever heard of for the spy theory to be plausible. She watched the new girl as she pulled out a notebook and appeared to begin writing in it. Hermione smiled. That was something she would do. If you don't know what is going on, read, and if there is nothing to read, write down anything and everything.

Hermione noticed that Dumbledore was now standing quietly off to the side and shaking his head as he watched the argument unfold. She knew he would get his way eventually, he always did, but she supposed that if they didn't get the argument out of their system now it would just start again later. It probably would anyway - from what she could tell the Order seemed to spend an awful lot of time arguing. She pushed her chair back from the table and quietly approached Dumbledore. “May I take the new girl, Shallan, I think you said, up to the library?” He nodded his agreement to her, but kept his attention on the argument.

She smiled as she walked over to Shallan and collected her plate to take it to the sink. Shallan was sufficiently absorbed in her writing that she barely seemed to notice. When Hermione returned she greeted the girl, “Hi Shallan,” and when Shallan looked up pointed to herself “Hermione... Her-my-oh-nee.”

Shallan smiled tentatively back and repeated carefully “Her-my-oh-nee...Her-my-oh-nee...Hermione.” Storms! she thought, at least their language seems to use the same sounds, but they go together in such strange ways.” She watched curiously as the other girl, Hermione, mimed sitting at a table and writing and then gestured towards the stairs. Shallan nodded, tucked her sketchbook, which she was now treating as a notebook, and pen into her bag and stood. She didn't mind sitting on the floor, but she also wouldn't say no to having a proper table or desk to work at.

Shallan followed Hermione up two flights of stairs and a little ways down a hall to a room she decided must be Hermione's bedroom. Here Hermione dug a new notebook (it was always a good idea to have notebooks on hand, and they were so much more practical than doing everything on scrolls) and a few pens and pencils from her trunk before gesturing further down the hall. At the end of the hall Hermione opened a door and gestured for Shallan to enter. Her jaw dropped open as she looked in the room. “Pattern! Look at all of the books!” She stepped into the room and looked around in amazement as Pattern detached himself from her dress to explore the library as well.

Hermione's eyebrows shot up as she heard Shallan exclaim excitedly and saw something seem to float away from her. As Shallan looked around the library, Hermione walked cautiously but curiously toward the... thing? creature? that was now floating around the room. As she approached it she asked, mostly rhetorically, “Hello, and what might you be?”. She was somewhat surprised when the... whatever it was... buzzed back at her with something that almost sounded like it could be words. “I don't know why you are talking to me. Surely you know I won't know your language, you storming girl.”

Shallan turned at Hermione's voice and Pattern's buzzing and saw her examining Pattern with a bewildered look on her face. She laughed slightlyand walked over to join them. “Pattern,”she said pointing at her spren. Then she looked at Pattern pointedly, “This is Hermione. She seems to appreciate writing and books. We should be nice to her. She might be able to help us learn their patterns.”

Pattern swirled around more quickly and responded, “She can't understand what we say anyway.” Shallan raised her eyebrows at him and Pattern began to swirl more slowly again before drifting slightly closer to Hermione and buzzing, “Hermione.”

By this point Hermione was staring wide eyed at the two of them. Her mind was racing as she tried to make sense of what she was seeing and hearing. Dumbledore had said something about Shallan's companion, but seeing it was something else entirely. Apparently Shallan had a constantly changing sentient, talking fractal as a friend, or at least companion. Hermione knew that figuring out how to communicate well with Shallan was going to be a challenge when she decided to rescue her from the chaos downstairs, but now she began to think that she was in even farther over her head than she had realized. She wasn't sure if this Pattern was going to make things easier or harder and bit her lip in concentration wondering where to start before finally nodding and gesturing to the room around her, “library.”

Shallan nodded and made a similar gesture around the room and repeated “library.” They repeated this process with a table, chair, book, pen and pencil before Shallan realized there was no way she was going to remember everything and pulled out her sketchbook. She sat down at the table and began making a list. Hermione sat next to her and watched as Shallan drew small pictures representing each of the words they had covered and then drew out an elongated symbol next to each. After finishing with the library words, Shallan added a small portrait of Albus with his name and Hermione with hers. She then sketched the woman who brought her food and looked questioningly over at Hermione as she pointed to the picture. Hermione broke out into a grin as she realized the elongated symbols must be Shallan's form of writing.

“Oh that's brilliant!” She then pointed to the picture and said “Molly.” Shallan repeated, “Molly,” back and wrote it in next to the picture. Hermione grabbed her own notebook, flipped it open to the first page drew a quick sketch of a book and wrote “book” next to it. She then gestured between the two notebooks. Shallan grinned and nodded as she pushed her notebook over so that Hermione could write each of the words using her script. Pattern hovered over them buzzing with excitement. When she had finished, he commented, “Mmmmm...patterns..not perfect, but close...”

Shallan looked up at him curiously. “What patterns do you see?”

“Mm, her small symbols mostly pair with yours. But not all... chair has too many...”

Shallan thought about this for a second before nodding to herself and flipping to the next page of her notebook where she wrote out each letter of the Alethi alphabet while Hermione watched curiously. Shallan then pointed to the first symbol and spoke its sound while looking at Hermione expectantly. Hermione repeated the sound and drew the appropriate letter or blend of letters next to it. When they finished, Hermione pursed her lips. The chart they had just made was mostly accurate, but not completely. She pointed to the letter “g”, which she had written next to the symbol Shallan had indicated was for the hard g sound and gave both the hard and soft g sounds. Shallan raised her eyebrows. Hermione thought for a moment and then pulled over her notebook and said “gem” as she wrote the word, underlined the “g” and repeated the soft g sound. She then repeated the process with the word “gap.”

Shallan sighed. Of course. Hermione's script wasn't completely phonetic. That would have been too easy. Well, at least it did actually use letters and she wasn't going to have to learn a huge collection of glyphs. They made another pass through the chart with Hermione giving some of the most common alternate ways to form the sounds. Pattern watched this process somewhere between amused and annoyed. “Mmmm, this is a terrible pattern. Full of all kinds of lies.” Shallan glared at him.“That may be, but it is going to let us understand the people here.”

They spent the rest of the afternoon naming objects to slowly increase Shallan's vocabulary. Shallan found the process to be a strange combination of tedious and exhilarating. There were so many words to try to remember, but learning something new was always exciting.

Dinner that night thankfully involved many fewer people than lunch had. Hermione introduced Shallan and Pattern to Molly, Ginny, Ron, Fred and George and made the twins promise to at least give Shallan time to adjust before including her in any pranking. She told them about how they had spent the afternoon and asked Mrs. Weasley if they happened to have any pictures books that might be useful for helping Shallan learn English. It turned out that the Weasley's had a large selection of picture books that could read themselves to children, so there was an expedition to the burrow to collect them and bring them back to headquarters.

Ron had no patience for spending the day helping Shallan and Pattern with English, and Hermione angrily kicked out the twins after Pattern caught them teaching Shallan lies, but Hermione, Ginny, Shallan, and Pattern spent the next several days focused on getting to a point where they could communicate things that required more than gestures and pointing. Whenever Shallan felt like her capacity for new words and grammar was saturated, they took breaks during which she would teach the other girls a little Alethi.

Pattern naturally caught on more quickly and so occasionally wandered off to discover what kinds of lies the twins were creating. The fact that he was able to warn Ginny and Hermione of the pranks the twins were setting up helped the girls to accept him and quickly become fond of him despite the fact that Shallan was unable to satisfactorily explain the idea of spren. Ginny giggled that having Pattern as a friend was way better for spying than those extendable ears her brothers had created. Shallan laughed along and thanked the Almighty that there weren't other Cryptics here to bond with the boys. She could only imagine where that would lead.

Recess: That's right. They'd break recess and turn it into a session of advanced algebra instead. (Note: The same thing happens when you go to middle school or junior high. Sorry.)

Alcatraz Smedry (in The Shattered Lens)

From Alcatraz’s handy list of things Librarians would break if they could.

Rithmatics: Part 2, the potential for 5 point defenses

In the last post we looked at what happened with acute triangles with three distinct angles, equilateral triangles, and the isosceles right triangle.  In this post we consider non-isosceles right triangles.

The Potential for 5 Point Defenses

Let's consider what happens when we look at non-isosceles right triangles.  As with the 4 point case, the right angle vertex counts as 3 of the 9 points.  The difference here is that the altitude from the right angle vertex no longer bisects the hypotenuse, which gives us a 5th point.  The three side midpoints and the right angle vertex still form a rectangle.  It is interesting to note that the resulting circle has 3 arcs of the same length - the arcs corresponding to the short sides of the rectangle and the one connecting the short leg of the triangle to the hypotenuse.  This seems like it would be important to keep in mind when constructing defenses based on such circles.  Also note that, as with 9 point circles, there are infinitely many variations on the 5 point circle since different right triangles can lead to different bind point spacing.

In the image below I include a speculative idea I've had.  Since there are vertices which count as multiple points in the 9 point construction, it seems from a mathematical perspective like you ought to be able to bind multiple things to this point.  Whether or not this actually works rithmatically is currently unconfirmed. I will hopefully be able to find out at the upcoming Atlanta signing.

1/24 Newnan signing report

*dances around* Not only did I get to meet Brandon Sanderson and have him sign my books, I ALSO got to meet Ben McSweeney (see previous post)!

While hanging out in the bookstore waiting for the signing to start, I met a couple of other fans.  One of them had gotten there early enough to get one of the special "get a seat at the front of the Q+A" wristbands but didn't have a question.  I got him to ask what Horneater stew would be like on earth.  It is apparently based on a spicy Korean seafood soup that traditionally is made by just throwing anything acquired from the sea (shrimp, clams, mussels, etc) into the pot whole, shells and all. He gave the name of the soup. It's Korean. I would probably butcher the spelling completely, so I'm not going to try.

When I got through the line, I asked if he could draw the Blad defense in The Rithmatist.  His response was a look that very clearly said "You expect me to remember which one that is by name?" I clarified and he just kind of laughed and drew me one of the 4 point circles and suggested that maybe I could get one of the more complex ones from Ben.

I asked for something about Kaladin when he was signing WoR.  Before I tell you what he wrote, I should mention that he was halfway through writing it when I opened my rithimatics notebook and kind of distracted him. "Kaladin has known multiple lightweilders." 

So. Rithmatics.  I pretty much just started flipping through my notebook asking questions about each page.  Most of the questions got a simple affirmative. For the other things, I'm paraphrasing: 

Yes, 5 and 8 point defenses could exist.  They haven't really been explored in world though.

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.

When I showed him the 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.

At this point he started to say that we shouldn't hold up the line too long as I flipped to a page titled Lines of Vigor.  I was going to let it go, but he glanced at the page and told me to go ahead and ask :D

Yes, Lines of Vigor behave like light waves. (I'm so glad I was right on this)

To clarify I double checked that 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.

GUYS.  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.  Ben then commented that he hadn't known that. *flails*

I got "Oh, wow"'s from both of them while I was flipping through the notebook :-).  At that point, Brandon passed me off to Ben and we chatted about inconsequential things while he took one of my spare sheets of paper from my notebook and drew me a picture *flails more*

I'm still on such a high guys, it's crazy. *dances around*

(very minor edit to fix a typo that was bugging me)

Welcome to the 2015 Cross Cosmere Rithmatics Olympiad!

The other night in FNCC I brought up the question of what would happen if someone drew a chasmfiend chalkling.  Things snowballed from there and dm-mo, ElderDragonMystic and I got carried away.  As a result, our friends from across the Cosmere are gathering to compete in games derived from one of Sanderson’s non-Cosmere magic systems.

Welcome to the 2015 Cross Cosmere Rithmatics Olympiad!  Teams are gathering from across the Cosmere to compete in an exciting assortment of rithmatic events! The games will be kicking off soon and we here at the Cosmere Chronicle will follow the action when they do, but in the mean time let’s introduce the teams.  

Roshar is fielding three teams this year.  

The first is their traditional team from the Alethkar Academy of Rithmatics.  This team’s roster is formed of brothers Adolin and Renarin Kholin, their cousin Elhokar Kholin, and Shallan Davar, a young woman who hails from Jah Keved.  As expected, these four all have solid groundings in classical rithmatics and should be a force to reckon with.  Rumor has it that there is some dissension in the group though and that they don’t always work particularly well as a team. It will be interesting to watch them and see how this plays out

The other two teams are a ragtag bunch known only as Bridge 4 that are not associated with the Alethkar Academy.  This motley crew appears to bring together students from nearly all regions of Roshar and has divided itself into a Division 1 and a Division 2 team. The senior team consists of Kaladin “Stormblessed”, Moash, Teft and Sigzil.  The junior team is comprised of Lopen, Rysn, Tien, Lift and Syl and coached by Numuhukumakiaki'aialunamor “Rock” of the Unkalaki.  We know very little about the rithmatic background of any of these competitors, but if what we have seen in the practice fields is any indication, they could shake things up - they appear to be bringing a style unlike anything we have seen before.

Scadrial is fielding two teams, one each for Division 1 and Division 2.

Scadrial’s senior team should look familiar to anyone who follows Intra-Cosmere Rithmatics.  It is, as expected, comprised of husband and wife team Elend and Vin Venture as well as The Survivors, Kelsier and Spook.  In case you don’t  usually follow ICR, Scadrial rithmatics is known for working in pairs and they should help make the pairs dueling exciting to watch.  The Ventures work seamlessly together while Kelsier and Spook always seem to be able to recover no matter what mess of a situation they find themselves in.

Oddly enough, Scadrial’s division 2 team has an odd number of competitors: the established duo Wax Ladrian and Wayne and newcomer Marasi Colms.  We caught Marasi to ask her how it is working in rithmatics on Scadrial without a partner. She informed us very matter of factly that she simply hasn’t found the right partner yet, but that there was no way she was going to let that cause her to miss the opportunity to come to the games this year.  Based on the rest of our conversation, we expect her to hold her own in the theory competition.

Sel is also fielding a team for each division.

To form its senior team, Sel held a local preliminary competition where it ended up choosing a pair each from two very different parts of the planet.  It is comprised of Sarene, Hrathen, Shai and Gaotona.  It will be interesting to see how the four members blend their styles for the team portions of the games, but they all seem quite focused and determined to win.  One thing is certain - we can always expect precision from Sel rithmatics.

Sel’s division 2 team is possibly the most unusual team - its captain, Raoden, isn’t actually a Rithmatist!  When we found Raoden to ask about this, he calmly reminded us that one doesn’t have to be a Rithmatist to be a scholar of rithmatic theory. His team is rounded out by a particularly laid back young man named Galladon and an enthusiastic but clearly intelligent girl named Kaise who is, we believe, this year’s youngest competitor.  

Political unrest on Nalthis has disrupted its rithmatics program, so it has only sent one team this year.  Veteran Vasher is back and should be a powerhouse in any event he competes in,  though rumors suggest that he may only be here for theory this year.  The team seems to be held together by the lovely princesses of Idris, Vivenna and Sisirinah.  It is rounded out by Siri’s quiet husband Susebron. Keep an eye on Nalthis if you are interested in chalklings.  No one is quite sure how they do it, but in the past we have seen chalklings from the Nalthiean competitors that seem almost sentient.

We here at the Cosmere Chronicle look forward to sharing the Cross Cosmere Rithmatics Olympiad with you in the coming days.  We will bring you the results from the events, analysis of different rithmatic styles, and stories from around Olympic Village.

Ohhh... this looks like fun...

Cinderella's fairy godmother is a lightweaver who sent her spren to the ball with Cinderella to maintain the illusion.  The midnight curfew is there because she could only infuse her spren with so much stormlight and the illusion will fail when it runs out.  Maybe the spren stays with the glass slipper and uses the little bit of stormlight it still has to continue maintaining just that part of the illusion...

Princess and the Pea is an easy one, relatively speaking. The princess in question is a tin-compounding Twinborn who got stuck in a touch loop at an early age. The easiest way I can think of for that to work is that she doesn’t know she’s doing it - perhaps she fundamentally doesn’t understand...

Your questions got me thinking and realizing that I have additional questions:

Szeth is likely going to summon his spren as a sword eventually. Is it going to make Nightblood jealous? Will they see it as a way to destroy twice as much evil? Szeth dual wielding blades? Or Nightblood getting frustrated because Szeth really needs a long spear for a sky battle right now and he is using the sprenspear instead of a sword?

Or, would Szeth summon his spren as a shield while using Nightblood as a sword?

What is the conversation going to be like when Nightblood and the spren talk?

Or, y’all, Szeth and Nightblood and the spren in a sort of threeway poly nahel bond. Maybe the bond could dampen the spiritual cracks in Nightblood so that they don’t automatically suck all of the investiture out of anyone holding them? 

I wonder what it’s like to be Szeth’s spren.  Like, the only thing they have to do is stick close enough that he can surgebind.  Nightblood takes care of everything else.  Did some Highspren just go: “This is gonna be the easiest assignment ever heck yeah” and then sleep through the rest of the book?  Are they annoyed at not having anything to do?  Were they tired of working with more conventional Skybreakers?  What do they think of Szeth siding with Dalinar over Nale?

I have questions guys