Spy Girls

Rithmatics: Part 3, the potential for 8 point defenses

In the previous installments we have covered acute triangles with 3 distinct angles, equilateral triangles, and all right triangle.  In this post we look at acute isosceles triangles.  

The Potential for 8 Point Defenses and the Hypothetical Owl Defense

Let's look at what happens when we have an acute isosceles triangle.  The altitude from the different angle will bisect the opposite side, which means the midpoint of the base will count as two points.  However,  the 7 remaining points are all distinct this gives us 8 separate points.  

It is interesting to note that, as with the 4 point construction, we have one side of the circle that is tangent to the triangle.  The 4-point Sumsion Defense has a tangent Line of Forbiddance at one of the bind points.  As this is the only defense we know with such a tangent line, it seems reasonable that its existence could be related to the fact that the 4 point circle is the only one we have examples of that has one tangent side with its corresponding triangle. (All three sides of the triangle for the 6 point construction are tangent, but including all of them would trap you - it isn't clear whether it would be a problem to include just one or whether this actually matters at all.  This is something else I hope to ask about at the signing.) Following this logic, I used the Sumsion Defense as starting point for constructing a potential 8 point defense.  It ended up looking rather like an owl :-)

Rithmatics: Part 6, 9 Point Conics and Triangle Centers

Note: From this point on we are drifting farther and farther from what we know from the book. The math is all solid, but its application to Rithmatics is much more speculative.

In rithmatics, the 9-point circle plays an important role in constructing lines of warding and identifying bind points.  We also know that there exist elliptical lines of warding and that they "only have two bind points."  Now, in math we are frequently told things like "You can't take a square root of a negative number", which are true in the given system (real numbers) but not true in general.  The construction for the 9-point circle, as described in the book, doesn't work for ellipses.  However, there is a generalized 9-point conic construction.  To understand it, we need to start with a little bit of terminology.

A complete quadrangle is a collection of 4 points and the 6 lines that can be formed from them.  For our purposes, we will be concerned with complete quadrangles formed from the vertices of the triangle and a point inside the triangle.  The 6 lines are then the sides of the triangles and the three lines connecting the center point to the vertices.

The diagonal points of a complete quadrangle are the three intersection points formed by extending opposite sides of the quadrangle.  If we have a triangle ABC with center P, then the intersection of AB with PC is a  diagonal point.

If you take the midpoints of the 6 sides of a complete quadrangle and the 3 diagonal points of that quadrangle, these 9 points will always lie on a conic. This conic is the 9-point conic associated with the complete quadrangle.

Note that if we choose our point in the center of the triangle to be the point where the altitudes meet (known as the orthocenter), then this construction is exactly what we have been doing to create 9-point circles.

There are four classical and easily constructable triangle centers - the orthocenter, circumcenter, centroid, and the incenter.  There are over 5000 other possible notions of the center of a triangle, but most of them cannot be easily geometrically constructed and they get increasingly complicated. 

Let's look at each of these 4 triangle centers and the conic they produce for a particular triangle. We will use a 40-60-80 triangle in each case for illustration purposes, but the results will be very similar for any acute triangle with 3 distinct angles.

Orthocenter: We already know about the orthocenter (that is what most of this series has been focused on so far).  For reference, here is what the 9-point circle for this triangle looks like:

Circumcenter: The circumcenter of a triangle is found by finding the midpoint of each side of the triangle and drawing in the perpendicular bisectors.  The points where the perpendicular bisectors meet is the circumcenter.  Note: This point is also the center of the circle that can be circumscribed around the triangle.

Unlike with the orthocenter, the lines we use to construct the circumcenter (the dashed lines in the diagram) are not part of the complete quadrangle, so we have to finish the quadrangle after we have identified the circumcenter.  The resulting conic is an ellipse.

Centroid: The centroid of a triangle is formed by finding the midpoint of each side of the triangle and connecting it to the opposite vertex.  The intersection of these median lines is the centroid.

The lines used to construct the centroid are part of the complete quadrangle, but we have the interesting situation where the centers of each side are also the diagonal points of the complete quadrangle.  This means that, regardless of the triangle used, we will only ever have 6 distinct points.  The resulting conic is an ellipse that is tangent to all three sides of the triangle.

Incenter: The incenter of a triangle is the intersection of the  angle bisectors of the triangle.  

Note that the lines used to construct the incenter of the triangle are also the additional lines of the complete quadrangle.  In addition, as long as the angles of the original triangle are distinct, the 9 points in the construction will all be distinct.  The resulting conic is an ellipse.

In Summary:  There are lots of ways that we could potentially construct a 9-point ellipse from a triangle.  Of these options, I would guess that the construction using the  incenter of the triangle is the most likely to produce valid rithmatic structures.  I lean this way because, as with the orthocenter, constructing the incenter also constructs the complete quadrangle and its diagonal points.  Furthermore, the 9 points of the construction will all be distinct (except in special cases). As such, we will explore 9-point ellipses constructed with the incenter more thoroughly in the next post. 

This feels like a crazy long shot, but do I know anyone who plays Pokemon Go in the Uxie region?

Gunnerkrigg Stormlight Mashup

Because I saw the first panel of today's Gunnerkrigg Court update and my reaction was "Dude!  When did Paz become a Windrunner?" I don't think Paz is actually a windrunner though.  She would hang out with Shallan and they would go meet all of the creatures.  Paz would absolutely be up for tracking down a chasmfiend for a chat. (Oh man, Shallan in Gillitie Wood.  She would be so excited.) 

More below the cut, but it kinda got long.

Eglamore, on the other hand, would totally be a Windrunner. Parley might be as well, but she also might be a Willshaper.  I'm not sure. 

Kat would hang out with Navani and they would be awesome engineers turning magic things into technology together.

Annie is half Horneater and inherited the ability to see and interact with all of the spren.  She discovers she is a Lightweaver (I guess, unless she finds a way to get transportation and illumination, but that doesn't appear to be a thing) and quickly learns to navigate Shadesmar.  (Blinker stones are totally infused spheres).

Zimmy is a Lightweaver who didn't have a mentor to teach her to navigate Shadesmar and sometimes she gets sucked in unintentionally and sometimes she accidentally pulls other people in with her and sometimes she managages to only get partway pulled in and accidentally projects an image of Shadesmar into the physical realm.  The whole situation is a mess. She finds it relaxing to stand out in the riddens after each highstorm. It helps to ground her.

Ysegrin would be one of the Parshendi leaders.

Coyote is Wit. Or...no... maybe Jones is Wit and Coyote is the Stormfather.  Yes, I think that works better.

I can't decide where Reynard would fit in and it's bugging me.

EDIT: I figured Reynard out.  He is totally a Kandra.  

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... 

In the chasms in Way of Kings, Dunny creates an insult poem by making the rhythm fit the song Mari’s Two Lovers. Rock then goads Dunny into singing it before joining in.  Ashiok and I have been working on lyrics for the song.  This is what we have so far, but this is a Rosharan drinking song and we are pretty sure it has many, many more verses, so we are releasing it into the wilds of the cosmere fandom to see if anyone else happens to have any verses to add. Current lyrics under the cut.

Dunny’s poem:

Hey you big buffoon, 

you smell like a wet hog,

so go out by the moon, 

And jump yourself in the bog.

Mari’s Two Lover’s (lyrics by Kalyna and Ashiok)

Gather round and hear

this tale I have to tell

of our young Mari dear

and the men she loved so well

Mari was a lass

Though Not the brightest sphere

She often cut her class

to a wander far and near

There she met a lad

who took her out for wine

But she arrived with Khad

and left with his brother Stine

Khad and Stein were twins

who looked  so much the same

it was beyond her ken

that the two had different names

The twins had a tell:

two eyes of different hues

they were distinguished well

cause their eyes were switched, it’s true

Their town had a dance

And Mari begged to go

While there she whirled and pranced

Always watching for her beau

As she spun around

She fell/came into Khad’s arms

She was extremely proud

Khad had fallen for her charms

Then she came to Stine

And danced with him a turn

She stared into his eyes

Oh but still she didn’t learn

Khad had brown and blue

While Stine had blue and brown

But our dear Mari knew

Her beau was the best in town

Over in a lait

An axehound pup bit Stein

To keep up the charade

Stein cut khad with some fork tines

Now this song must end

I sadly have to go

But Mari and her men

Oh their tale goes on you know

Happy Pi Day! Have some chocolate π   

F is for Frillbloom.  For more on frillbloom, visit the coppermind!

Yahoo Groups Will Be Shutting Down - What Each of You Can Do

This post will be frequently updated - check the Google Doc linked here for the latest version. Follow this Tumblr for more information in the days ahead.

Yahoo Groups will be shutting down key features and restricting access to Groups, with user-uploaded content being deleted on December 14, 2019. With this shutdown, decades of fandom history will vanish. But there is something that every member of the fandom community can do now - whether they’ve ever used Yahoo Groups before or not.

I am a member of a Yahoo group - what can I do?

Immediately contact the admins to find out what their plans are.

Download PGOffline, a Windows tool to save the files and messages. Any member of the Yahoo Group can use this tool - you do not have to be an admin to save the mailing list. 

Since many admins are busy or inactive, install the free Windows software program yourself and start downloading - focus on Files, Photos, Links, and Messages. A step-by-step walk through is available here and a video tutorial here.

Submit your plan to download here.

 Export the messages and backup up the files and photos by copying them to another folder on your computer. Then contact Open Doors, the OTW preservation program. The OTW is open to providing storage of Yahoo Groups backups that are assembled by moderators and non-moderators alike. Details are here.

If you are a member of a Yahoo Group and have downloaded the files and messages, and the admins do not respond, please contact your fellow mailing list members. Remember, anyone can save a mailing list messages, files and photos and submit them to Open Doors.

Click here for instructions on how to use the Chrome plugin

If you need help from fellow fans, try asking on the “Save Yahoo Groups” Discord Channel

Mac Users: try this Chrome based plugin

Instructions on how to use the Chrome plugin

Alternatively, if you are familiar with Python, please experiment with the tools found at https://www.archiveteam.org/index.php?title=Yahoo!_Groups

I am Admin - what can I do?

Communicate with your Group members - let them know your plans

Download your Group messages, files, photos, and links using the tools above. Don’t forget to download your members list.

Decide if you want to simply archive the old posts and disband the mailing list or start up somewhere else.

Please take a look at setting up a Dreamwidth community - it allows explicit material, threaded conversations, privacy locks and is free. Image uploading is limited to 500MB for free accounts and 1.5GB paid accounts. Also, if you are considering Groups.io as an option, please note that it does not allow any material that depicts sexual activity, even implied sexual activity or anything that could be considered a fetish.

I am not certain I have time to help download? Is there something else I can do?

If you are a member of a mailing list, submit the mailing list for consideration. It will help volunteers focus their efforts. Don’t forget check here to see if your group is already being downloaded.

Even if you are not a mailing list member, consider creating a page for the mailing list on Fanlore, so that there will be a place for people to talk about the mailing list, its history. Details here.

Login Problems?

Has your “inactive” email been purged? Is your email email address not linked to a Yahoo Group ID?

An “inactive” account is one where you haven’t sent an email or logged in for the past year. Receiving emails does not count as activity. The email address is then released, and can be used by someone else.

If you used your Yahoo email to subscribe to a mailing list, your access to the Yahoo Group is gone (along with all your emails). If your account was deactivated within the past 90 days, you may be able to reactivate it. (more here). Alternatively, you can try contacting Yahoo Mail support.

Outside the 90 day window: you can try creating a new Yahoo email account using the same screen name as long as no one else has snapped it up. Simply sign up as you would for a ‘new’ email account. Reclaim an inactive mailbox. Then log into your Yahoo Group.

Oathbringer Speculation: Soulcasters

We know that people who consistently use soulcasters over a long period of time are...changed. My theory is that they are being slowly turned into spren and sucked into Shadesmar and further that this is the source of Syl’s comment about how the power coalesces slowly  and parts become sentient and a spren is born.

First off, let’s visit our friend Kaza in Interlude 4. We learn that she is slowly turning to smoke, but it seems to hold together well enough that she can wear a glove over her smoke fingers and still use her hand. She is forgetting the “ordinary passions of human life” and increasingly not needing to eat or drink. The she says that “I have begun to see the dark sky and the second sun, the creatures that lurk, hidden, around the cities of men.” It is clear that she is starting to see into Shadesmar and it isn’t too much of a stretch that in Shadesmar there might start also being evidence of her. The Aimian cook notes that she is “barely human anymore.” At the end of the interlude she chooses to “go with the smoke,” but the other times that she almost goes it sounds like she almost goes all the way into shadesmar and doesn’t come back, not that she almost turns into smoke in the physical realm and drifts off. Later in Celebrant (chapter 102) Kaladin finds himself in a tent with a “single bewildered spren made of smoke,” confirming that smoke spren are a thing.

In chapter 81 Kaladin meets a grain soulcaster and notes that “The woman had an inhuman look to her; she seemed to be growing vines under her skin, and they peeked out around her eyes, growing from the corners and spreading down her face like runners of ivy.” Then in Celebrant we meet spren that “were made entirely of vines, though they had crystal hands and wore human clothing.”

In chapter 105, we meet a soulcaster that makes stone and learn that his “skin beneath [his cloak] was colored like granite, cracked and chipped, and seemed to glow from within.”   In Celebrant there “were other spren with skin like cracked stone, molten light shining from within.”

We don’t have a description of the Azish soulcaster that makes bronze, but it seems like a good bet that their description would match that of the Reachers, who “looked like humans with strange bronze skin—metallic, as if they were living statues.”

In Chapter 35 of Words of Radiance we meet a soulcaster that doesn’t quite fit any of the descriptions of spren that we meet in Celebrant, though she could potentially be in an earlier stage of the granite type: “Prolonged use of the Soulcaster had transformed the eyes so that they sparkled like gemstones themselves. The woman’s skin had hardened to something like stone, smooth, with fine cracks. It was as if the person were a living statue.”

We also hear about Honor and then the Stormfather making Honorspren, so soulcasters wouldn’t be the only way that sentient spren are formed, but I’m fairly convinced that it is at least one way that spren are born. 

For reference and as a side note, in Celebrant they meet Cryptics, Honorspren, Reachers (bronze), Cultivationspren (vines), Inkspren, the ones whose skin turns to ash, the glowing granite ones, the ones made of smoke and possibly also ones made of fog/mist, though I’m not completely convinced those aren’t the same as smoke. If the fog/mist ones are different from the smoke ones, then this gives us 9 different types of sentient spren to correspond to the 9 non-bondsmith orders of the Knights Radiant.