Welcome To The 2015 Cross Cosmere Rithmatics Olympiad!

I just finished Brandon Sanderson's The Rithmatist. Now, any time I read a fantasy novel with an interesting magic system, I imagine what it would be like to have said magic (don't we all?).  This magic system seems particularly well suited to me - it calls out to both my math and artistic sides.  I think I could make a rather good rithmatist.  The freaking 9 point circle is an important part of the magic system.  I can't even.  

I bet that the 6 point defenses don't actually require that the 6 points be equally spaced.  I bet they could actually be anywhere as long as you build the rest of the defense properly.  The Mystic Hexagon theorem has got to be relevant to this magic system.  I bet you can even use the Mystic Hexagon theorem to build 8 point defenses where the extra two points come from the line dictated by the Mystic Hexagon.  And when that line doesn't intersect the circle, it would be a natural (possibly required) place to put a Line of Forbiddance. There will probably be rithmatic drawings showing up here...

Also, my math notes often have non-math doodles in them.  <3 chalklings

Melody and Joel are fantastic. I like them a lot. There are things I need to process before you get more about them though.

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

Kickstarter

Spacefunk!

Space is the place! A collection of science fiction stories and poems by authors of African/African Diaspora Descent.

Hey tumblr, I stumbled across this kickstarter for a sci-fi anthology featuring stories and poems by authors of African and African Diaspora Descent. It sounds cool and when I tried to dig up a tumblr post to reblog about it I couldn't find one, so I'm making it myself.

The kickstarter is running through noon eastern on July 19th, 2024. The pledge level for the ebook with over 40 stories and poems is just $10. For $30 there's an ebook bundle with this new anthology and their previous anthologies (Steamfunk!, Dieselfunk!, Cyberfunk! ,and Spyfunk!). There are also options to get a physical copy of the anthology, cool posters, and more.

If you are interested in sci-fi from voices that are currently underrepresented in the community, go check it out!

https://www.kickstarter.com/projects/1268017280/potions-a-curious-tale/widget/video.html

Potions: A Curious Tale - Adventure through an enchanted world where your wits are your greatest weapon and combat is not always the answer. - http://kck.st/1oIP0qQ

The leading creative director of this project is Renee Gittins. She was a frosh at Harvey Mudd my senior year so while I didn’t know her well, she and I have several mutual friends who are excited about this. From what I’ve seen on the kickstarter, this game looks like it has a lot of potential so I wanted to spread the word.  

Hey guys, let's think about bendalloy ferrings, aka Subsumers, for a minute.

We know they can store nutrition and calories in a metalmind which means they can eat as much as they want when there is lots of food and then tap it later.  

Think about a Subsumer at a Scadrial eating competition.  "Sure, I can scarf away as many hot-dogs as you want. No problem."

Think about a Subsumer at an all-you-can-eat buffet.  They get to try everything and then go back for as much more as they want of everything they like. Such restaurants would have to have special rules for subsumers...maybe a pay by the hour thing?

Imagine if Lift gets a hemalurgic spike that lets her become a bendalloy ferring. She would have the best stormlight storage system.   She could eat loads, store most of it in her metalmind(s), and then tap into it whenever she needs stormlight.  Unlike spheres, it wouldn't leak away and if she is tapping it from the metalmind she isn't sucking the energy out of her body.

On the darker side of things, you probably also get the occasional Subsumer who is desperately afraid of gaining weight and always stores everything they eat in their metal minds and never taps them.  Most people don't know that they are a ferring and everyone sees them eating, so people don't realize there is a problem until it has gotten really bad.

Shallan's Journey: Chapter 4, In Which Pattern Gets to Play

This morning started as the last few had, with Shallan meeting the others for breakfast and then returning to the library to study English with the girls while Molly tried to wrangle the boys into helping her clean the house. Today, however, there was something going on that called Molly out of the house and left the kids to their own devices. Sirius was still home, of course, but he spent most of his time upstairs moping with Buckbeak and when he did come out was rather more likely to cause mischief than to be a responsible adult. As the oldest Weasleys left in the house, Fred and George had decided this meant they had free rein to do as their hearts desired. Naturally, this meant that Ginny had bright green hair and Hermione's pens were dancing away from her every time she reached for one. A few minutes ago, Hermione had finally snapped and begun laying into the twins about how irresponsible they were being and trying to insist that they set everything to rights and then leave them alone. Ginny had joined in and now there was a full scale argument making it difficult for Shallan to think. She narrowed her eyes as she contemplated the best way to handle this.

Shallan had been reluctant to use any of the moderate supply of stormlight she had brought with her in case she ended up really needing it later, but she decided that it probably wouldn't hurt anything to use a small bit of it. She flipped to a clean page of her notebook and drew out a fierce image of Molly shaking her finger along with a few other quick sketches that would allow the image to move. “Pattern,” she whispered, “would you like to startle them?” Pattern buzzed excitedly in response, but Shallan quickly shushed him. “We are going to sneak out into the hall where I'm going to attach an image of their mother to you and then...” she continued to whisper instructions as they sneaked around the argument and out into the hall. She infused Pattern with stormlight and triggered the illusion before quickly slipping back into the room to watch the results.

She had just gotten back to the table when Molly's voice boomed from the door, “Fred! George! What is the meaning of this?! I told you to leave the girls alone!”

Everyone immediately froze and looked toward the door while Fred and George jumped away from the others, “Mum!” “We didn't know” “you were” “already back!” “Of course” “we were” “being nice” “to the girls” “anyway, but...” they trailed off in confusion as the image of their mother flickered out and died and they noticed Shallan trying and failing to hide her snickering.

Ginny was the first to figure out what must have happened, “Whoa! You can do wandless magic? That was a really impressive illusion! How did you do it? What else can you do?!”

Shallan shrugged. She was getting much better at understanding English, but was still shaky when it came that fast and still not particularly confident speaking it herself. “It is... not your magic... Ummm...” she pulled out the sphere she had already pulled some of the stormlight from. “I am a...” she searched briefly for an appropriate English word and gave up “lightweaver, so I use these,” she held up the sphere, “to... to make things.”

Hermione began bouncing on her toes, “Oh! But that's fascinating! May I see it?” She held out her hand in question. Shallan handed the sphere to her and Hermione examined it carefully. “Oh wow. That looks like an emerald! And it glows... Can you show us how you do it?”

Shallan nodded, “Sure,” as she took the sphere back, “um, what should I make?”

Ginny grinned at her, “Can you show us your boyfriend?”

Shallan gave her a slightly sad smile and turned to her notebook to draw out the sketch of Adolin that she would need for the illusion. She breathed more of the stormlight in from the sphere so that she was just slightly glowing and breathed it out as she created an illusion of Adolin standing there grinning at them in his impeccable Kholin blue uniform. Storms. She had been so caught up in dealing with everything that, even when telling the girls about people from Roshar, she hadn't realized how much she missed him. Seeing her illusion standing there now though... It looked just like him, of course, except that the storming man never stood that still...

She sighed and buried her head in her arms on the table as she wondered what Adolin and Jasnah and the all of the others were doing. She knew Jasnah wouldn't give up on her, but, storms, she didn't know where she was, how did Jasnah have any chance? A gentle touch on her shoulder pulled her back and she looked up to see that Ginny had slid into the seat next to her and was now giving her a concerned look. Shallan didn't have the English to fully explain, so she just shrugged as she whispered, “I miss them.” She let Ginny pull her into a hug as she put herself back together. It wasn't easy, but then nothing in her life ever seemed to be.

The others looked on somewhat helplessly as Ginny comforted Shallan. Hermione desperately cast about for a distraction. She wasn't good at these things like Ginny was, but she did know that her own usual response to being upset was to throw herself into a project. From her interactions with Shallan over the last few days, she figured there was a good chance that Shallan was the same way. Her eyes flew around the room for inspiration and finally lit on the wand that Fred was holding loosely at his side. “Oh! Of course!” She blushed as everyone immediately turned to look at her, “Well, it just occurred to me that we know Shallan has something like magical abilities, but we haven't done anything to test whether she can use our magic.” She looked beseechingly up at Fred, “Could Shallan borrow your wand for a minute, just so we can see if she can use it?”

Ginny rolled her eyes at Hermione,“Really? You think this is what we should be doing right now?” In the mean time, Pattern had buzzed over to Shallan and explained what Hermione was suggesting. Shallan gave Ginny a small smile, “It's ok, I want to know too,” and then looked eagerly over to Hermione. This was good. As long as she didn't think about home she would be fine. Pattern would probably fuss at her later for having too many lies, but it wasn't like there was anything productive she could do.

Fred shrugged curiously and handed Shallan his wand, “Just be careful with with.” Shallan nodded seriously as she reached to accept it, “I will.” When her hand closed around the handle, her eyes widened and she stared down at the wand. She swore she could almost feel it vibrating. “Pattern, what is this thing? It looks like a fancy stick, but...”

“Mmmm, it says it is a wand.”

“Well, yes, that is what they told us, but what is it?”

Pattern seemed to shrug. Shallan could never quite figure out how his twisting mass of lines mimicked human gestures, but he managed it some how. “It says it is a wand.”

Shallan rolled her eyes. Sticks, even fancy, magical sticks, were hopeless. She looked back up at her new friends. “Sorry. I was...distracted.”

Hermione smiled, “That's ok. Do you feel anything from the wand?” Shallan pursed her lips, “Yes, but I don't have the words...”

“Ok, well, let's try something. Your magic system seems to involve light, so let's start there.” Hermione grabbed a pencil, “You move the wand like this and say 'lumos' and the tip of the wand should light up.”

Shallan tried unsuccessfully. She gave a slight sigh. There was no promise this was going to work, and even if it did, she shouldn't have been expecting it to work on the first try. George pulled out his own wand and stepped over to her. “First off you should be holding the wand like this,” he held his wand out in front of him so that she could see and imitate. “Then you move it like this.” He demonstrated the motion and the encouraged her to do it with him, “You don't want to whip the wand around too fast, but you do want a nice smooth motion.” They practiced the motion a couple of times before George was satisfied. “Now, when you get to this point in the motion, you say 'lumos'”. George demonstrated and the tip of his wand lit up. Shallan concentrated as she tried again and, to her delight, the wand tip actually lit this time! Interestingly, casting the spell almost felt like pushing stormlight into something...

She grinned before narrowing her eyes briefly at the wand in contemplation and then laying it carefully on the table. She grabbed her sketchbook and drew out a quick sketch of an axehound. She picked the wand, still lit, back up and, imagining that the light on the end of the wand was stormlight, pushed it out into an illusion of an axehound.

Shallan's whoop of victory was drowned out by Ginny's shriek. Even though she knew on some level that it was just an illusion, she leapt backwards and her voice trembled slightly as she squeeked out, “What is that thing?! It looks like something Hagrid would love...” The twins examined the new image excitedly and Hermione looked it over cautiously. Shallan grinned at them, “It's just an axehound. My brother,” her voice caught slightly, but she pushed it away and kept going, “my brother used to raise them. We keep them as pets back home.”

Having recovered from sudden appearance of the strange creature, Hermione looked back up at Shallan with eyes shining in excitement, “Regardless of what it is, you made it with Fred's wand instead of one of your glowing marbles! We have to get you a wand!”

At this point Ron wandered into the room, “What is all the screaming about?” Ginny gave her brother an unreadable look and pointed at the axehound in the corner. “Oh bloody hell!” He scrambled back towards the door. “That thing has way too many legs! Did Hagrid stop by?”

Ginny smirked at him. Her brother's reaction helped her get past her own, “Nope. Shallan used Fred's wand to create it. It is apparently like a dog where she comes from.”

Ron shook his head. “No way anyone would keep something like that as a pet.”

Ginny rolled her eyes, “I know we wouldn't, but if you grew up with them they would seem normal.”

“If that thing is normal, her world must be completely creepy.”

“Ron! Shallan is right here! If you can't be nice you can just bugger off again.”

Ron threw his hands up in the air and grumbled as he stormed off, “The crazy alien girl shows up with creepy creatures and suddenly she is all anyone cares about....”

Ginny shook her head as she turned back to Shallan. “I'm sorry about my brother. He isn't good at accepting new things.” Shallan nodded with a sigh. “I understand. I also have several brothers and, umm.. they are not always exactly...” she trailed off. She did not want to try to explain her family.

Hermione cut in, “Let's go find Sirius. Maybe he will know how we can get Shallan her own wand.” She led them farther up the house than Shallan had yet been. “You've met Sirius at dinner a few times, but he tends to keep to himself. I don't think he's very happy here.”

As they entered the room, Shallan's eyes were immediately drawn to the large creature in the room. Hermione had immediately turned to talk to Sirius, but Ginny caught Shallan's arm before she could rush over to it. “Whoa, Shallan. Buckbeak is friendly, but you have to meet him properly. Like this.”

She walked slowly until she was in Buckbeak's direct line of sight and then bowed. Buckbeak blinked at her and returned the bow, so she stepped in to stroke his neck.

While Shallan was watching this, Pattern buzzed up beside her “Is that a horse chicken?”

“I don't know anymore than you do, but it certainly looks like it. Storms. And they thought my axehound was strange...” Ginny gestured for Shallan to come closer and bow. It took a little longer this time for Buckbeak to respond, but he eventually did and Shallan stepped closer to join Ginny in stroking his neck. “Ginny, what kind of creature is Buckbeak?” Ginny looked at her slightly surprised, but then shook her head, “I guess you wouldn't know, would you... Buckbeak is a hippogriff.”

Shallan frowned as she examined him. “He can't be happy in this room. Does he even have space to stretch his wings?” Ginny sighed. “I think so? The reason he is here is complicated.” Shallan was distracted from her thoughts by the sound of her name.

“Hey, Shallan!” Hermione called. Shallan promised Buckbeak she would be back later, he was a fascinating creature, and walked over to Hermione and Sirius. “Can you show Sirius your axehound?”

She still had Fred's wand so she nodded as she carefully lit it with Lumos and then pushed the light from the wand into the image. Behind her she heard Buckbeak snort and Ginny calm him.

Sirius raised his eyebrows. “That's a mighty unusual way to use magic.”

Shallan shrugged. “It works.”

“Ah, that it does.”

Hermione cut in impatiently, “Do you see why we need to get her a wand? It's silly for her not to have one when she is capable of that!”

Shallan looked at them, “How would I get one?”

Sirius frowned at her, “That's the question, isn't it. I have more money than I know what to do with, so that's not a problem, but people usually get a wand by going to Ollivander's, and I'm not sure how we are going to get you to Diagon Alley. I'd take you, but Dumbledore won't let me leave the house.”

“Why not?”

“I was accused of a crime I didn't commit. You see...” he proceeded to explain the mess his life had been since the decision to make Peter the real secret keeper. At the end of his story he shook his head “I don't know why I'm telling you all of this. It can't be very interesting.”

Pattern buzzed appreciatively “Mmmm... so many layers of lies...I like this one...He would fit with your guards back on Roshar.” Shallan laughed helplessly at Pattern's comment. “He would, wouldn't he...Oh why do I keep finding myself in this kind of position...” She looked back over to Sirius. “I, ah, might be able to help with a disguise that would let you go out without being caught.”

Sirius's eyes lit up at the idea of being able to escape the house, but Hermione cautiously chimed in, “We'll have to make sure it holds long enough and isn't easily dispelled.”

Sirius wilted when Shallan nodded, but looked back up slightly hopeful when she added. “Yes, but we can test it. If we have enough light, I think it could work.”

I just finished part 4 of The Final Empire and I need to rage for a bit before I can keep reading.  Don't mind me. Ranting and wild theorizing under the cut.

"I represent the thing you've never been able to kill, no matter how hard you try. I am hope."

 speech and presented yourself as a STORMING IDIOT MARTYR and LET THE LORD RULER KILL YOU WITHOUT FIGHTING BACK. DAMMIT KELL.

This is why you spent all of that time building your reputation among the skaa and getting them to practically worship you. This is why you were asking Sazed about the Valla. You were reassuring yourself that the movement would continue even stronger after you sacrificed yourself. You hoped it wouldn't come to this, but you knew it would. You've trained Vin as your replacement.  She proved her competence in her fight against Shan and her power by seeing through your copper cloud. In the process she helped you understand what happened with Mare so that you could let it rest. SHE JUST ASKED YOU A COUPLE NIGHTS WHEN YOU WERE GOING TO LEAVE HER and you hedged. You didn't know exactly when, but you knew this was coming. You knew it would probably be soon. Dammit Kell.  

Elend, you lovable naive fool of a nobleman, you need to find Vin and help her hold herself together so she can take over. Or maybe so the pair of you can take the lead if you can rally your friends and make them actually care enough to act. She has just had her brother's training that everyone will abandon her reinforced though, so she's probably going to try to push you away in a form of emotional self defense. I hope you don't let her. She is unbelievably strong, but there is power in having people you truly care about that she doesn't fully understand yet (The very last thing Kelsier said to Vin was "You still have some things to learn about friendship, Vin. I hope someday you realize what they are."  Dammit Kell. That sounds like you knew you weren't going to be there. Maybe you had already decided that today was the day to get yourself martyred afterall.)

Other Thoughts:

* IF there really is an 11th metal (which I'm skeptical of), then there needs to be a 12th.  They come in pairs.  

* There is more to gold that Vin currently understands. Gold is disturbing and creepy and no one wants to burn it which also means no one has fully explored it.  

* Feruchemisty is going to become important.  Vin's experiment with Sazed's metal is going to come back.  It could have just happened to answer the question of whether the two can interact (because I was definitely questioning it before it happened) but I will be surprised if it never surfaces again. 

* In fact, some combination of Feruchemistry and Allomancy could very well be what lets the Lord Ruler survive things like having a spear run through his chest.  Oh Storms.  What if the reason he has been so intent on killing Keepers is because there is a way to store their life force in a metal (Gold? If I had to guess it would be gold) and then he can steal that life force by burning the metal.  It would be like Allomancy meets Feruchemistry meets Chromatic Breath and the immortality of the Returned in Warbreaker.  

So I just started reading Mistborn...

and I really, really want to introduce Vin, as we meet her right at the beginning of the story, to Lift. They wouldn't trust each other at all at first and for quite a while, but they would cautiously work together because it is better than the alternatives. It's possible they would see each other as rivals, but I want Vin to eventually take Lift under her wing like a little sister and they can be awesome magic scrawny teenage girl street thieves together. They could get up to so many ridiculous shenanigans and steal *everyone's* dinner...