Rithmatics Digression

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Friends. Readers. Fellow nerds with impeccable taste. We are officially in the home stretch. The final 24 hours. The last lap. The dramatic climax of the movie where everything explodes in slow motion and the music swells and someone says something heroic right before punching a fascist in the face. (Okay, that last bit’s just wishful thinking, but after the week we’ve all had, I think we…

Last Chance to Pledge for Full Negative Book

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Truth

White people need to tell each other the hard truths. This includes the fact that No, you aren’t colorblind. Nor should you strive to be. The point isn’t whether or not you see that a person is black. They are. The question is what you see when you see that they are black. Do you see competency? Do you see worth? You should.

(paraphrased (because I didn’t write it down during the service) from the sermon at the First Presbyterian Church of Atlanta on 25 September 2016)

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.

Rithmatics: Part 5 - Curvature, Ellipses and a Guess at the Blad Defense

Let's start by considering a snippit from one of the diagrams in The Rithmatist:

(Note: full diagram can be found at http://brandonsanderson.com/books/the-rithmatist/the-rithmatist/rithmatist-maps-and-illustrations/ )

Now we have a problem, namely, circles don't all have the same curvature. In fact (a slight simplification of) the idea of calculating curvature is to determine what radius circle would best approximate the curvature of the line at that point. A circle of radius r has constant curvature 1/r.

The basic idea here is reasonable though – apparently, lines of warding are stronger when they have a higher curvature. You can think of an ellipse as a circle that has been stretched along one axis. This means that if you start with a circle and then stretch it, we can talk about the resulting ellipse being stronger than the original circle where it curves more and weaker where it curves less. Here is what that diagram might look like if we add in the relevant reference circle:

Assuming this interpretation is correct, there are some important implications. The biggest is probably that the size of the circle used to form a defense matters. If you have two otherwise completely equivalent defenses and one of them is a scaled up version of the other, every point in the wall of the smaller defense will be stronger than the equivalent point in the wall of the larger.

Note: There are at least two potential underlying explanations for what is going on here. One option is that there is a certain strength inherent in a portion of a curve of a given curvature. This is the assumption that I am going to work from here. There is also the possibility that there is a fixed total strength for any closed curve of warding and that this strength distributes itself based on curvature. If we stick to circles and assume that strength and curvature are proportional, the two notions are equivalent. The second option is intriguing, but leads to rather messy calculations when we start looking at more interesting constructions. If I stick with this long enough we may eventually get there. I have no idea which option is correct or whether there is a third one I haven't considered.

One way to think about this (and this is almost certainly an oversimplification of things) is that it might take approximately the same amount of chalkling effort to destroy the entire dark blue segment as to destroy the entire dark green segment in the figure below:

 The important take away is that it should be easier to break a small hole in a large circle than it is to break an equally sized hole in a smaller circle. This means that when you are drawing your initial circle for your defense, you should be actively thinking about how large you really need it to be. It also means that even the weakest point on an ellipse could still be stronger than the wall of a much larger circle.

From an offensive standpoint, this means that the small circles and Mark's crosses added to your opponent's main circle are going to be much harder to affect than their main line of warding. They aren't just in the way – they are actually stronger.

We will talk about ellipses in more depth in future installments, but for now let's close with a guess at what the Blad Defense might look like. All we know about it is that it combines four ellipsoid segments in a non-traditional manner and that it is strong enough that some people think it should be banned from competitions.   

I live near Atlanta and Labor day weekend is approaching, aka that time of year that Atlanta turns into nerd central - we get both Dragon Con and the Decatur Book Festival on the same weekend.

I love the idea of Dragon Con. I love seeing all of the amazing costumes people make for it. But as a person who is easily overwhelmed by large crowds and who has a distinct preference for books over tv and movies, the Decatur Book Festival is much, much more my speed.  Sadly, there is a distinct lack of anything fantasty/scifi on the book festival talk schedule this year. And Sanderson is going to be at Dragon Con... It makes it tempting to consider...

Realistically though, I’m going to be happier at the book festival. 

If anyone else is going to be hanging out in Decatur that weekend looking at books and wants to meet up for ice cream (there are a couple of great ice cream shops in Decatur) or tea or something and chat about the Cosmere, or Imperial Radch, or Wayfarers or... let me know :-)

Ok.  Completely new post because the other one keeps reverting to the cut off version.  This is my interpretation of Shallan's Lullaby from Words of Radiance. So far as I am aware the tune doesn't belong to anything else.

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.

I hear it’s face day, so here’s my face XD. But also, look at the shiny new hat that I test-knit for @thechronicferuchemist ! It probably should be blocked, but even without blocking I’m super happy with how it came out :D (Her post about the hat is here)