# arc-length

I think the reason why Infinity Train flows so well is because it’s structured like a full length movie, only 10x faster.

It’s got the 3 acts structure and full character arc of a full length movie, but every sequence takes 1 minutes instead of 10 minutes.

• ban ryu: alright then han sung. since you say you're that smart, solve this without using any calculator. find the arc length of three x times the square root of seven minus two from x equals zero to one half.
• han sung: *stares at equation while deeply thinking* well, there are two 'twos' in the equation- minus two and the denominator from the one half. the number two sounds like the letter 'u', and u is between the letters 't' and 'v' in the alphabet.
• han sung: but tvs aren't really relevant anymore because everybody has computers now, so it's kind like... if you have two tvs, what is it even-
• han sung: *out loud* four.
• ban ryu:
• han sung:
• ban ryu: ... that's right...
Formulas to Remember for the Math Section of SAT

## Algebra

Percents:

Percent Change= Change/Original × 100

Part = Percent /100 × Whole

Examples:

75% of 300 is what?

Solve x = (75/100) × 300 to get 225

45 is what percent of 60?

Solve 45 = (x/100) × 60 to get 75%

Example: 30 is 20% of what?

Solve 30 = (20/100) × x to get 150

Average Speed = total distance/total time

Distance =rate × time

FOIL: (x + a)(x + b) = x ^2 + (b + a)x + ab

Difference of Squares:

a)     a ^2 − b ^2 = (a + b)(a − b)

b)    a ^2 + 2ab + b^ 2 = (a + b)(a + b)

c)     a ^2 − 2ab + b^ 2 = (a − b)(a − b)

Distance Formula:  SQRT (x2 − x1) ^2 + (y2 − y1) ^2

Mid-point of the segment AB: x1 + x2 /2, y1 + y2/2

Slope of the line: y2 − y1 / x2 − x1 = rise run

## Geometry

Opposite Angles are equal, so a+b and 180 degrees.

All the “a’s” are equal and all the “b’s” are equal. Any “a” plus any “b” equals 180 degrees.

Right Triangle Formulas***

Triangle area= ½*b*h ***

Angles in a triangle add up to 180 degrees.***

Circles

Area of a Circle = πr2 ***

Circumference = 2πr ***

Full circle = 360◦ ***

Length Of Arc = (n ◦ /360◦ ) × 2πr

Area Of Sector = (n ◦ /360◦ ) × πr2

Total number of degrees in the interior of an n-sided polygon= (n-2) × 180 where n is the number of sides.

For example, an eight-sided polygon (or octagon) has:

(8 – 2) · 180 = 6 · 180 =  1080 degrees

## Arithmetic

Arithmetic sequence formula: an=a1+d(n-1)

a1=first term, d =distance between the numbers, and n= term to find

Example: Find tenth term in 3,7,11….

a10=3+4(10-1)= 63

Geometric sequence formula: an=a1×r(n-1)

a1=first term, r =rate  between the numbers, and n= term to find

Example: Find 6th term in 3,6,12…

a6=3×2(6-1) = 3×2 5=3×32= 96

## Functions

I was putting together a cheat sheet for studying for the math section of the SAT. Hope this helps some of you! :)

*** on the SAT given formulas, but still good to know by heart.

Beneath The Waves

Submitted by: Arc (http://arcanity.tumblr.com/)

Length: Short

Nothing calms me more than the sight and sound of the rolling waves. The smell of the crisp, salty air. I love everything above the waves, from the gulls to the clouds. I love everything below the waves, from the smallest mollusk to the largest whale. The ocean is home to me.

Or, it used to be.

Now, the ocean holds no welcome for me. The waters send chills through me when I merely think of them. I have violent nightmares, and anxiety that haunts me persistently.

I was out on my small boat in the deep sea, quite a ways from land. I had just passed the point in the area where the ocean floor dramatically drops, and the water visibly darkens due to the change in depth. I come to this spot often and relish the silence, the calmness of the waves gently splashing against the boat. Today, however, I felt uneasy. I felt… exposed. Nervous.

Suddenly, the silence broke. A thundering, guttural resonance was all around me, shaking the boat, disturbing the waves. My first thought was the foghorn of another boat, but quickly I dispelled it because there was none in sight. And, this sound was much, much deeper. Organic.

And it was coming from far below me. Something utterly massive was in the depths beneath me, calling. I could feel its presence, waiting for something.

The noise continued, and I could do nothing but lay in the boat quivering, clasping my hands over my ears to no avail.

I am a rational man, and not afraid of the unknown. But the titanically large creature below me made me lose my wits, and left me feeling like a helpless, terrified child. It can’t be a whale, the call is too… monstrous. Too primordial.

And then the noise stops.

I sit in my boat, paralyzed, listening intently for nearly an hour, in complete silence once again. I know it’s still there, I can feel its presence. Finally, I steel myself to start the engine and turn back to land, and resolve to never go out in that part of the water again.

However, just as I was beginning the journey back, the noise starts again. No, a different noise. Coming from a different place. The same creature, but farther out, deeper down. And then the noise erupts below me again as well.

My God.

It was not alone.

I have never gone back to the ocean, and I never will. I sleep fitfully, and am always haunted by the noises echoing in my head.

The ocean is not my home, for I fear what lies beneath the waves.

Credits to: Arc (http://arcanity.tumblr.com/)

Am so pleased you loved Mad Max: Fury Road! I would love to hear your thoughts on how the female characters are portrayed compared with in Avengers: Age of Ultron. Also wonder if you have seen Anita Sarkeesian's tweets proclaiming that Mad Max isn't feminist, which I couldn't disagree with more.

There were a few different parts to your ask, anon, so this ended up turning into a loooooong reply.

The main appeal of Mad Max for me personally is that it’s an amazingly well made action movie without any of the—pardon my French—unselfconscious dickwaving that makes the majority of action movies alienating for me as a female viewer. In fact, the film very clearly addresses how destructive toxic masculinity is. I wish I could say ‘big whoop’, but unfortunately this level of self-conscious criticism in mainstream films is incredibly rare, especially in the action genre. So just off the top of my head, here’s some of the things I feel Mad Max does differently from Age of Ultron (and the majority of other action movies out there) with respect to women and gender. (Mild spoilers under the cut.)

Algebra 2/Trig Exam Tips

A (slightly) more comprehensive guide than my previous one!

First things first, as soon as you sit down, make sure your calculator is in degree mode, Seriously, this is incredibly important. And if you’re solving for radians, remember to switch modes. In these last few days of review this is something to hammer into your brain.

• “Alpha”, “Y=“ in that consecutive order. The 4th choice down will help you go from fractions to decimals and vice versa. A simple task, but remember those buttons!
• The “window” key. Accurate windows adjusted to the problem are very helpful.
• “2nd”, “Graph” in that order. Looking at a table may be more helpful than looking at the graph. Remember this.
• The “Math” key, has Probability buttons for nCr and nPr. Also has the degree, minute, and facotorial symbols. Also where you’ll find the cube root button.
• “Stats” button. Very important. Type in list, go to calculate. Linear regression, exp regression, 1-Var stats, 2-Var stats etc.
• Inverse of Sin (sin^-1) + Inverse of Cos(cos^-1) to find missing angles.
• Log button, e button, natural log button (ln).

Also this:

1. Use the provided reference sheet as much as humanly possible. It is your friend and does a lot for you.
2. Draw diagrams for show work problems if possible. In a recent practice exam all I could remember was how to draw the diagram for the 6 pointer. That still got me 1 point. 1 point can be a huge difference, and it can determine passing or failing. That point got me a 71 instead of a 70.
3. Memorize the identities (sec, cot, csc, etc)
4. Unit Circle. Memorize it!!
5. Know the arc length formula and all variations of it. (theta=s/r)
7. Look for rounding directions. Round correctly.
8. Know the quadratic formula (-b +/- the square root of b^2-4ac all over 2a) Listen to this on repeat and you’ll never forget it.
9. Remember that for roots, Product = -b/a and Sum = c/a
10. Remember factoring methods: Grouping, GCF (Greatest Common Factor), Box Method, etc.

Good luck on June 19th all my buddies in NY!

I’m ready as fuck y'all… rationalizing substitutions???? u-subs?? Trig subs?? Techniques of integration? Parametric and polar coordinate systems?? Sequences and series?? Radius and intervals of convergence??????? Taylor and Maclauren series???? Surface area and arc length formulas??? Trig identities?? The mf unit circle??? Learn’t, memorized, gay

funny story

so last year during math class we were talking about circles and how to find the arc length (it’s a section of the distance around) and my 50 year old male teacher asks what we use to find this. no one was really in the mood to answer any questions that day, so I took it upon myself to answer it. now note, I’m usually pretty quiet in all my classes, but I’ll answer a question here or there. this is because I tend to stumble over my words and mess them up sometimes. so the answer was circumference, and I raised my hand to be called on. He calls my name and what do I say?

“You use the circumcision.”

my class just stared at me and a couple chuckles were heard from around the room. my teacher was mortified, and just replied “you mean the circumference?”

I said “yeah, what did I say?” and he just laughed and continued with the lesson. I had to turn to my seat partner and asked what had happened. she explained what all went down. now I avoid speaking in classes all together.

In The Wash

Zack Ryder/OC. For Anon: He’s visiting the reader while she’s sorting laundry. Among her ring gear he sees a lacy bra and starts joking around with her before things get steamy.

4

13th December 2016
This morning I spent around 1.5 hours revising over radians and arc length as it was the first topic for the SL ib students this year at my school and I am assuming it would be the same for me next year! It is so hot today :-( but that cannot distract me from studying!

ugh let’s just get this over with so it doesn’t become a thing

👏 CROSS 👏 BOWS 👏 ARE 👏 FOR 👏 THE 👏 FUCKING 👏 WEAK 👏

👏 YOUR 👏 GRANDMOTHER 👏  USES 👏 A 👏 CROSSBOW 👏
SO 👏  IT 👏  WON’T 👏  IRRITATE 👏  HER 👏 FUCKING 👏 SCIATICA 👏

you’re talking about sacrificing like 20 POTENTIAL units of kinetic energy for draw weights, lengths, arcs, speeds, and pulls that you can’t customize/adjust using your own body on the spot with a moment’s notice? that’s fine if you’re hunting a three-legged pig as long as it’s already fucking DEAD.

if you’re needing to actively manipulate the shot to accomodate wind resistance, gravity differences, timing, size and protective layers of target, and the bend of any potential obstacles, crossbows/bolts can’t do it.

but summer will be happy to demonstrate the differences between the two on your kneecaps so you can see for yourself

• Kuroko: I'm deeply sorry for calling everyone in here.
• Kise: That's fine, Kurokocchi!
• Aomine: It's not that I'm doing important things and it's been a while since you asked for my help.
• Murasakibara: Anything for Kuro-chin~
• Midorima: Takao said it's important to help my former teammates and since I don't have anything important, I decided to go.
• Akashi: Anything for my Tetsuya.
• Kuroko: Thank you, everyone.
• Akashi: So, Tetsuya, what can we do for you?
• Kuroko: Finals are coming up. Since Winter Cups are over, we are currently working to increase our grades... But knowing how stupid Kagami-kun, it's impossible for him to achieve learning things within a month. So I beg all of you to teach Kagami-kun.
• Everyone: Eh?
• Kuroko: It's a burden but... I'm only an average person.
• Kise: Wait, wait! So that's why Kurokocchi called us?
• Akashi: I even declined the offers some of the counselors offered for me...
• Midorima: I missed my usual training because of this.
• Murasakibara: I consider all of you are lucky since I ditched Muro-chin for our snack hunting weekend.
• Kagami: Tatsuya wouldn't mind though!
• Everyone: ...
• Aomine: And why are you here, Kagami?
• Kagami: This is my house, Aomine!
• Aomine: Ah, right.
• Kuroko: Everyone, please, pardon that tiger for a while and listen to me.
• Kise: Go on, Kurokocchi.
• Kuroko: Murasakibara-kun is good at Physics and Math, I suppose?
• Murasakibara: Hm? I do.
• Kuroko: Midorima-kun is good at Biology.
• Midorima: Certainly.
• Kuroko: Kise-kun and Aomine-kun... uh.
• Aomine: Hey, Tetsu! I'm good at something too, you know!
• Kise: I'm good at English-ssu!!
• Kagami: I don't need you to teach me that!
• Kise: You need to since you are in Japan now!
• Kuroko: I guess I can teach Kagami-kun Japanese since I'm pretty average on that.
• Akashi: That leaves to English and Social Studies to me, Tetsuya. Don't worry, I hate slacking off so I guarantee you will succeed, Kagami Taiga.
• Kuroko: Aomine-kun and Kise-kun can head home.
• Aomine: Wait!!
• Kise: We can do something else-ssu! We can!!
• Kuroko: How about keeping on guard in case Kagami-kun ran off?
• Kagami: I won't run since this is my house.
• Kuroko: Just in case. Shall we begin?
• ---
• Murasakibara: Kagami, it's easy if you memorize sine, cosine, and tangent. Also, that's not how you use Pythagorean Theorem~
• Midorima: Are you even listening to the teachers?! Atoms are the small ones!
• Akashi: Do you... even learn English in abroad?
• Kuroko: Kagami-kun... please, listen to me.
• Kagami: Ugh! I hate this! You guys are giving me hard times! Kuroko?!
• Kuroko: You're not listening.
• Kagami: Then don't look at me like that!
• Akashi: We don't have a choice, let's replace his brain with a newer and intelligent one.
• Kagami: Wait!
• Aomine: Ha! Sucks to be you, Kagami!
• Kise: Kagamicchi, I feel bad for you.
• Akashi: Oh, don't be envious, Daiki, Ryouta.
• Kise & Aomine: Eh?
• Akashi: I also got a brains for the both of you.
• Kise & Aomine: WAIT!!
• Akashi: How about we do a little quiz? Also, I want to test Shintaro and Atsushi for this.
• Murasakibara: Eh~
• Midorima: Akashi, I don't need such a thing.
• Akashi: Oh, don't worry. It's just a little review. I trust both of you to get a full mark.
• Kuroko: ...
• Akashi: Uh, Tetsuya...
• Kuroko: I get it, Akashi-kun.
• Akashi: Alright then. This is Math.
• Aomine: ...
• Kise: ...
• Akashi: Find the length arc with a 67 degrees and 3 radius. Round to the neare---
• Aomine: Just hold a fucking moment, Akashi! Why are you doing both?!
• Kagami: ... Even though that was English, it feel so foreign.
• Kuroko: Was that even Math?
• Midorima: ...
• Murasakibara: Can I go and buy some snacks?
• Akashi: Hold on a moment, you guys are not going anywhere until you answer my question.
• Everyone: ...
• Akashi: Now then, this study date shall begin.
• ---
• Imagine Kagami and Kuroko asking Kiseki to tutor them~
Creepypasta #618: The ARC

Story length: Super long

My buddy Dave was a game developer. A good one. He’s the only guy I know who could blend a game with reality on this level. But I’m scared to think what he actually accomplished.

He started in BASIC when we were in elementary school. Back then he’d just modify the demos that came included like the gorillas game where you throw the banana-bombs back and forth. By the end of middle school, he had a good grasp of C++.

After college we ended up living in different cities. He moved into New York City, I went out to San Diego. But he kept developing games, indie ones mostly. Back when indie was more synonymous with unsuccessful. And I was always the first to test them out.

So when I saw the package from Dave at my front door, I wasn’t too surprised.

Normally he’d just post the files for me but this had hardware. It was an attachment for my iPhone. A crude 3d-printed plastic device that connected to the bottom port and wrapped up around the lens.

“It’s a kind of augmented reality game,“ Dave said on a video chat with me that evening. "The hardware scans depth in the room, like the Kinect. It’ll do an on-the-fly scan of your apartment, creating a point cloud. It lets the ARC know what exists in his space.”

He would do this sometimes, talk like folks knew what he meant. “I don’t know what an ARC is, Dave. No one does.”

He sighed. "Augmented Reality Character. Imagine the The Sims, but it’s happening in your home, and you can watch it through your phone’s camera. The hardware and software scan the rooms you want and process it into 3D space. Then your character, your ARC, can walk around your apartment, or where ever you scan.” Whatever ever I scanned… I started to get it.

“The phone’s camera is like window into the ARC’s world. A mirror of ours.”

I scanned my apartment, but started off simple. Just the living room and the kitchen. After a bit of processing, a crude 3D character (like the first version of the Sims) appeared in the middle of the room. He looked around cautiously before bumping into my coffee table and navigated around it.

It was incredible. It really felt like he was there. I looked out into my empty room, then back into my phone. It was like I was watching an alternate dimension.

You guys run an amazing blog and I'm constantly impressed by your knowledge. Very often, people write asking "My MC is __ and he/she does ___. Is this realistic?" And often, the answer is no. However, the majority of readers have no understanding of fighting, and also, fiction implies a breaking of rules. Generally, where do you draw the line between "This could work" and "aw, c'mon" (and further between "this is all wrong, but it ROCKS!")? I figure the rules of the world play big into this...

The question is usually: well, which rules are you breaking?

In a fictional context, realism is entirely dependent on the fictional world you build for your characters. You have to define what those rules are before you can break them. When most readers go “oh, that’s not realistic!” what they are actually responding to isn’t the part where it goes against their “real world”, it’s a sign the author failed at communicating their world’s systems or broke their own rules. “That’s not realistic” is really just a higher brow way of saying “something’s not right here” or “that shouldn’t be possible” but the fictional work is defining what is possible.

With most MCs, it’s more about getting the writer to start thinking outside of their character. On one level: it doesn’t matter if it’s unrealistic. It really doesn’t. The question is, does the author realize that they can’t just make the rules one way for one character and not for anyone else?

If your MC can do it, more than likely your villain can. The average mook could. The kid wandering by on the street too. Anyone. Anywhere. Probably someone else.

It’s not about what will happen. It’s about what can happen because a story is more than a single character. For violence, there’s no safety net. To unironically take the best lesson from Avatar, when Aang attempts to learn to Earthbend “there’s no special trick-trickety trick that’s going to defeat that rock”. You can’t find a way around it with 100% certainty.

You’re always risking something when you put your character into combat and the sooner that gets internalized the better off you’ll be. Don’t believe your character will make it to the end of the story when you write combat. Believe they could die at any time. From any mistake. Completely by accident. Make your characters earn their right to survive. You’ll write better, I promise.

A writer who writes with the understanding that every fight they put their character into that character can die and has them act accordingly will always be in the “This is all wrong, but it ROCKS” category. Tamora Pierce’s fight scenes, for example, especially the ones in Protector of the Small when the kids are in genuine danger. They are dealing with the situation, there is a sense of a threat, a worry that they could die, and they are thinking it through or accepting the necessary sacrifices they need in order to win.

The author who uses the violence as a means for something else or primarily as a message, who has their character acting in a way that makes no sense because they already know they’re going to survive lands in the “No” category for me. There is no guarantee your character won’t fail. There should always be a chance they will and the scene should be written from the perspective that they might just. They can get themselves killed. More importantly, they can get someone else killed. Stupidity does that. Charging into a group of eight guys intent on killing someone else doesn’t mean they’re all automatically going to turn around to fight the protagonist.

The character needs to feel like they are dealing with the situation in front of them. The author should keep the overarching narrative view in mind, they should think about the consequences of their characters actions. Fight scenes are often treated as throwaways, a character can commit them with zero consequences. The average mook does not have family or friends or anyone who will come back to take the MCs head. The character beats up some poor idiots on the side of the road, sometimes in a place they visit often, and that’s it. It’s over. No more needs to be said. Except… violence has a ripple effect and often the effects are unintended. It spirals well beyond a single individual character, events may end up affecting everyone in their left regardless of their original intentions.

Think about the real world for a second, not in terms of “what is real” but your own life. What would happen if you took a baseball bat to school? What would happen if you started a fight? What would happen if you punched someone out? What would happen if you shoplifted? What would happen if you went to Walmart tomorrow and bought a gun? How would people react? People in general? The people in your life? Do you get detention or jail time? Do people approve? Do they condemn you? What do they say? If you were beat up by some idiot what would happen? If you saw them again with a group of your friends, what would you do? If you died tomorrow, what would people say?

We get so caught up in our main characters that sometimes it’s easy to forget that every character in your story is you. They all have friends, they all have family, and they all have lives that will continue on long after the Protagonist has moved on.

Allow me to use the titular “teach girls to defend themselves as a solution to stopping violence against women” which crops up often in literature, especially in lately in YA. I will list one example where it is well done and another where it fails utterly.

Page by Tamora Pierce.

In Page, Keladry acquires a new maid named Lalasa. Lalasa has a history of abuse and has been targeted by both servants and nobles in the palace for her shy nature. Kel takes Lalasa on as a favor to Lalasa’s uncle Gower, even though she’s reticent about it. When dealing with Lalasa’s abuse in the novel, Pierce hammers out all the different ways in which the abuse is allowed to continue as part of the world building. She makes a point of noting that the abuse is systemic, that victims are persecuted and they are blamed, were Lalasa to take her complaints those higher up both she and her uncle risk being turned out. She also notes that you can’t command people to change, the attitudes which allow the abuse are perpetuated even after someone powerful says “no, stop it” are important to understanding why it happens. They will no longer do it within the hearing of said powerful person, but you can’t just snap your fingers and expect immediate change to happen.
Page makes a point of saying in the actions of the surrounding characters and the events it relays in regards to Lalasa’s situation that sexism and abuse are systemic. Change takes time. And indeed it does, because Lalasa’s character arc runs the length of the novel.
While she think its silly not to, Kel respects that Lalasa does not initially wish to learn to defend herself. She waits for Lalasa to make the choice and it takes time. They both accept that self-defense is mitigation, not a solution. This is harder for Kel, who comes from a privileged perspective, than Lalasa, who is more practical. Lalasa’s learning self-defense is part of her regaining her confidence and taking her life back, she does not take just a few lessons, once she agrees to begin then she works at it and she works hard. She practices often and learns so well that when it finally all wraps up, she takes what she knows and passes her knowledge on other girls. Indicating that while systemic change takes time, people can change and work to aid others who suffer similar circumstances. Both women learn from each other, Kel in teaching and Lalasa in learning. Lalasa is a minor character in Page but her narrative is powerful. Both girls embody change in a system that fights tooth and nail to keep them in their place. Their struggles are difficult and they are real.

Graceling by Kristen Cashore.

When Katsa travels to an Inn, she sees a serving girl being assaulted by one of the tavern’s patrons and moves to intervene. She proceeds to think that if girls were taught to fight then they wouldn’t have to suffer because more violence is what solves violence problems.
However, she gives no thought to whether or not the girls want to learn. No thought to what would happen to them after she leaves. No thought to how this would affect the tavern and the girl’s ability to work or continue working. No thought to whether or not they’d even be able to fight the way she (super powered character) fights.
The total train of thought is “if the girl knew how to fight then she wouldn’t be assaulted” which is ultimately just another form of victim blaming and lacks the awareness that whatever they do or don’t know affects other aspects of the character’s life. This includes their ability to keep working, the fact they may be rejected by other people in their life, what happens to them next, and an understanding that introducing violence into a situation is a great way to escalate it.
It never occurs to Katsa when she witness the scene that the reason the girls aren’t fighting back may be because they can’t or a response to other circumstances, not that they don’t know how. It doesn’t even matter that she’s right (they don’t know how), the problem is the thought never occurs. This is why one of these is “that’s amazing” and the other is “No”. One thought it through while working to ensure reminder to long term consequences and the other didn’t.

Good scenes are all about asking questions and then answering them. Drama is something happens and then there is fallout. Cause and effect. One action leads to another and then another and then another, each building every higher into what eventually becomes a story. If you can justify your character’s actions in story then it doesn’t matter, but if you’re giving them preferential treatment then be prepared to justify it through the other characters. This requires treating them like characters as opposed to nameless mooks or a cheerleading section.

More importantly, a good author needs to recognize that violence creates as many problems as it solves. It’s a short term solution only, one with long lasting consequences. Being good at fighting doesn’t mean the protagonist can brute force their way through their problems and doesn’t mean that they are safe from someone else hurting them.

Respect that there are characters in the setting who are better at fighting than the protagonist. Understand that not all combat training is created equal. Learn what good combat training looks like as opposed to sensationalized training like in Divergent. Respect characters who put the time in to be good at something, even if they are just a throwaway enemy.

Recognize all characters in the right circumstance (or any circumstance) can kill your MC.

Act accordingly.

You will get into the “That’s not right, but it’s AWESOME” category.

That’s my two cents, anyway.

-Michi

i was thinking the other day that the two anime-only arcs of truly significant length, noah’s virtual world and the legendary dragons thing, are like… totally wild for seto kaiba. like in the virtual world he gets all of his traumatic family history dragged out from under the bed for the viewing pleasure of yuugi and company, mokuba yells at him again and then falls under noah’s mind control, when seto finally breaks mokuba OUT from that mind control they get turned to stone, then fucking GOZABURO who’s supposed to be DEAD shows up again and they stake their lives on a duel. they straight-up try to kill each other

and THEN!!! JESUS!!! in legendary dragons he effectively LOSES KAIBACORP and then here comes amelda, who’s like, “you’re a product of the military industrial complex, there’s blood on your hands, everything you own is paid for with murder and death*; you’re just as bad as gozaburo!!! also, here are some visions of children dying in wartime. get fucked” like. are you having a nice time, seto? no?? how about a nice game of chess? btw it’s chess in the dirt with some bullet shells. your opponent looks like your baby brother. also he dies. oops. someone please let this kid take a vacation

*side bar: yugioh, a show about a children’s card game, has a minor plotline wherein a major character is forced to confront the fact that their position in the world and their massive amount of inherited wealth is a direct result of the military-industrial complex ? ! ? i mean, it doesn’t really alter seto’s perspective all that much, because he already knows that weapons-era KC was #Evil and gozaburo was also #Evil, and he’s already taken steps to redeem the Sins of his Stepfather, and i think he knows only all too well that he’s absorbed the responsibility for KCorp’s involvement in wars and institutionalized violence, but regardless, god bless the amelda duels. what a good, top-notch, A-grade conceit

Part 1- Fluxed Up

LAL raised his arm cannon, which began to charge with an ominous whirring noise, a blue glow emanating from its barrel.

So why did D&D think Ramsay needed more focus then Stannis? Do the words Creator's Pet perhaps apply here?

I suspect it’s partly an outgrowth of the fact the writers don’t care about plots north of Moat Cailin, and partly general misunderstanding of Ramsay’s original dramatic purpose.

The writers have never been interested in Northern politics, Ned’s legacy, or Jon Snow’s fraught relationship with Winterfell. They’ve never understood Stannis or invested effort into Sansa. They’ve all but ignored the fact that the Ironborn have occupied large chunks of the North since season two. And those are the central pillars of the plot in the North (except for Sansa, as of AFFC, but I expect that to change in TWoW). These things are all factors that take multiple seasons of thoughtful writing to get across properly.

But Theon and Jeyne Poole getting tortured, those plots they could get their heads around. They saw nice, discrete, season-length character arcs in that. And so they built nice, discrete, season-length character arcs around Theon and Jeyne Poole Sansa being tortured. Since Ramsay is the chief torturer in those arcs, he’s on screen a lot. In terms of plot, with all the book plots I listed pared back to almost nothing, Ramsay has become a blunt dramatic instrument, there to be a roadblock preventing Yara from rescuing Theon and Brienne from rescuing Sansa and the vague, amorphous Northern society from participating in any sort of plot-relevant anti-Bolton activity. Need something accomplished between Moat Cailin and the Wall? Too bad, Ramsay time!

It’s a boring role, though, Ramsay. One-note and intentionally so on GRRM’s part. It would be easy to think you were wasting an actor. So they gave him more to do, dramatically speaking, a bit more nuance, forgetting why it was GRRM chose to make Ramsay Snow so utterly one-dimensional (and also a minor character). They have the time to expand Ramsay’s role, now, since they edited out Jon’s concern for his sisters, Stannis’ campaign in the North, and the fantastic stuff with the Northern lords convening in Winterfell. (With regards to Stannis, I suspect we’ll see Jon Snow take over his role, as we saw Tyrion take over Barristan’s and Dany’s narrative roles in Meereen. Ramsay, I think, is simply the instrument of removing Stannis as a military power in this case.) That’s how we get from the gleeful torturer in season three, through an increased focus on Ramsay’s daddy issues in seasons four and five, to poor sad Ramsay mourning his dead abuse victim girlfriend (she was never scared of him, honest!) in season six.

I suspect this is the case because this is pretty similar to what happened with Tywin Lannister in seasons one to four. Book!Tywin is nowhere near as one-note as Ramsay, but he is an ice-cold emotional abuser (and a lot of other bad things) without a shred of humour to him. Personally, I find scenes where Tywin interacts with his children painful to read precisely because Tywin does not give them anything, emotionally speaking, not the slightest indication that he’s affected by them and therefore that they matter to him. The emotional range he displays in public is very limited. That has to be hard to write for screen.

With Tywin, the writers took a shortcut to showing depth. Hence stern grandpa Tywin talks about Jaime’s dyslexia with Arya, going so far as to laugh at her “most girls are idiots” comment, displays actual passion when talking to Tyrion (even if it’s seething rage over his failed murder attempt), and reframes the Red Wedding as something he did to protect his family.

This “depth” and “nuance” means that the nature of how book!Tywin abused his family on a day-to-day basis is necessarily dulled.

Likewise, misunderstanding why Ramsay’s a one-dimensional villain means the writers have missed the broader thematic point (I know, I’m as shocked as you are). Ramsay’s one-note evil is not an asset. As far as problem-solving goes, all Ramsay has is a hammer, and to him, every problem looks like a kneecap. Unsurprisingly, this is not a good way to win friends and influence people. It’s not a good way to keep allies. Ramsay’s gone past the Machiavelli point of “avoid being hated.” The point of a lot of the Winterfell stuff in ADWD is to see how people nominally in Roose’s own camp are plotting against him - not just to see Theon tortured more.

But yeah, between not caring and not understanding, that’s how we got Ramsay the Villain Sue. Thanks for the question, @cynicalclassicist!

What are your thoughts on the pi v. tau debate?

(For those unaware of the Pi. vs. Tau debate, read the Tau Manifesto and then the Pi Manifesto).

I’m actually extremely pro-tau, but only under certain conditions. I’ll explain.

Warning: The following is my personal take on these subjects. I’m no authority. This is pretty much late night armchair philosophy and ramblings of a madman. It’s just how I make sense of some of these ideas, and it’s the first time I’m trying to put these into words. Hopefully, they’ll make some sense and I won’t look like a complete nut.

## On the merits of the debate

Mathematics thrives on conventions. Being able to symbolically convey a very precise idea is one of its greatest triumphs and strengths. For that, we have developed a set of (ideally unambiguous) conventional notations. Notation is pretty damn important. Learning this mathematical language takes a lot of effort, and it is a skill we should respect. A lot of important knowledge is being carried by these crazy symbols, knowledge built upon centuries of intense thought and research by some of the smartest people who have ever lived.

The use of the Greek lower-case letter pi (π) to denote a particular irrational number is one of such conventions developed in mathematics. As a convention, it is extremely valuable as it is. There’s little reason to change it. The fact we agreed with π as the ratio of a circle’s circumference to its diameter is of little consequence to any underlying mathematics, it changes nothing, so this isn’t really a point to be argued. The important thing is merely consistency.

In this respect, the tau vs. pi debate is a waste of time in my view. Saying equations are prettier because of a factor of two somewhere is missing is a bit ridiculous and non-mathematical, and entirely misses the point of having a constant defined in the first place. Are we arguing over mathematics or typography/aesthetics?

However, conceptual differences are important. This is where the debate can be fruitful, I think, so dismissing it completely can be (and I believe it is) a bad thing. Oddly nobody else seems to be making this particular point, at least not how I’m going to expose it here.

## Pi

You see, π shows up everywhere in math by itself, no factors of 2 attached at all. It’s a pretty remarkable number on its own. It shows up even when things don’t seem to be related to circles. For instance, the integral of the Gaussian is √π, which is a surprising result (and it’s one of my current math animation projects). The sum of the reciprocal of squares, also known as the Basel problem, is π2/6. No circles in sight here.

But whenever tau (τ = 2π) shows up, people like to talk about circles. They’re missing the point, I think. 2π isn’t the circle constant. It’s the ANGLE constant. The circle just happens to be related to the concept of angles, and not the other way around.

The most mathematically natural way of measuring angles is in units of radians. Everything works out so simply when we use radians that it’s tempting to call it the one true way of doing so.

## “Dimensions” vs. “units”

Now, before I go a little bit more into this argument, I need to clear something up. A lot of people say “radians don’t have units”, but that’s an incorrect use of terms. What these people are trying to say is that radians don’t have a dimension, that is, they are a dimensionless unit. See how we can use both terms together and still make sense? That’s because they have distinct and precise meanings.

A unit is a standard we use to measure other similar things. For instance, you can measure length in several units: meters, feet, the nearest spoon’s length, light-years, (toenail growth rate)·century, (your own name here)’s nipple-to-nipple distance, etc.

What all these units have in common is that they have the same dimension: length, or simply [L]. The other base dimensions in nature are time, [T], and mass, [M]. There are other dimensions that are used, but these are the more basic ones.

One way to understand this is to think of [L], [T] and [M] as the “real” physical quantities, or kinda like how Nature “understands” these quantities. When you read “2 meters”, you should be seeing 2 × (“1 of something we use to define a meter” × [L]).

The “meter” has a certain amount of [L] hidden in it, you see, because we defined it in terms of something else that has a length dimension. The 2 in “2 meters” is just there telling us just how much of that something we are talking about. The 2 is a pure, dimensionless number.

Using these three dimensions, we can build all sorts of quantities. Here’s a few, and some example units:

• Force = [M][L][T]-2 → newton, pound-force
• Energy = [M][L]2[T]-2 → joules, calories, kilotons of TNT
• Frequency = [T]-1 → hertz, radians/seconds

Dimensions can be treated just like variables: you can multiply, divide, take powers and square roots of them, but they don’t “mix” together. You can even add different dimensions, though just like variables, you get nowhere with that: a+b is just a+b. While it makes little physical sense something with dimensions [L]+[M] (think, 1 metre + 1 kg), there’s no reason why you shouldn’t be allowed to have it, if you’re really into that kind of thing. Weirdo.

By the way, this topic is called dimensional analysis, and it’s a very interesting subject.

Radians are an unit defined as the angle enclosed by an arc around a circle that is as long as that circle’s radius. Here’s an animation I created that explains it:

External image

It doesn’t matter what radius you pick (that’s why in the animation the radius is just a generic “r”), the angle is always the same because the arc’s length is also proportional to the radius, so the length of the radius always cancels itself out when you actually end up calculating radians.

But also, notice that the arc-length is a unit with dimension [L], and so is the radius. If you divide one by the other, the [L] dimensions cancel out, just like variables would. We end up with a quantity that’s just a number, a dimensionless quantity. A full turn has about 6.28 radians in it, that is, 1 turn ≈ 6.28 × (“1 of something we call radians” × [no dimension whatsoever]).

So, radians have no dimensions. We can treat them just like any other pure number. This is usually how everyone does it: they say it is a pure number, no meanings attached to it, and call it a day.

This is where my take on the subject takes a weird turn…

## “Dimensions” vs. “Concepts”

But conceptually, these numbers are still measuring something. Two instances of the same number associated with the same dimension can represent two entirely different things, so there’s more to these quantities than dimensions.

For example: “1 hertz” and “1 radian per second”, while dimensionally and numerically identical (both are “1 second-1”), are totally different conceptually. Something happening once every second is completely different than something rotating one radian every second.

In the same way, a torque of 1 newton-meter is numerically and dimensionally equivalent to 1 joule of energy, but the two ideas are very different. That’s why we explicitly write torque with units of “newton-meter” instead of joules. (In fact, it can be argued that the torque would be better expressed in SI units as joules per radian.)

So, here’s where my take on all these things gets weird: I think that beyond dimensions, we also attach “concepts” to numerical quantities and units, and these are also subject to a “conceptual analysis” similar to the dimensional analysis I mentioned up there.

While dimensions have a physical meaning, “concepts” are, well, abstract. (For consistency, I’ll denote concepts in single quotes from now on. E.g.: ‘angle’)

An 'angle’ is such a concept, attached to the unit of a radian: 1 “radian” = 1 × (“something we call radian” × 'angle’), where “something we call radian” is the same as “ratio between length of an arc of a circle and that circle’s radius”, that is, the definition of the radian. So, hidden inside a radian, is the concept of 'angle’ being multiplied by the number, just like a dimension such as [L] would be.

In fact, in terms of concepts, we could say: 'angle’ = 'circular arc’ / 'line segment’, so that we have: 1 radian = (1 × [L] × 'circular arc’) / (1 × [L] × 'line segment’).

In other words, what I’m trying to say here is that even if the dimensions cancel out in the definition of a radian, the concept of 'angle’ shouldn’t really go away with the number we’ve got. The concept 'angle’ is intrinsically in the “radian” unit, and it is not a dimensional quantity.

I love to play with this idea of “conceptual analysis”, and it has given me some weird and accurate insights before.

## Dude, just get to the point

All right, all right, here’s my point. I think we should have two definitions:

• π = 3.14159265…

Notice the difference?

π is just a pure number, like 1, 2.5 or √2. It has no concepts attached to it.

Meanwhile, τ is a number attached to the units of radians, which means τ carries the concept of 'angle’ with it everywhere it is used, always. Seeing τ immediately implies we’re talking about angles.

This is the important conceptual difference I talked about in the beginning. This is where τ really makes a lot of sense and where it would be useful.

## “The Conceptu-tau Manifesto” (groooan)

So, here’s my crazy proposal: let’s adopt tau as THE ANGLE CONSTANT.

Let’s face it, π isn’t going anywhere. It’s already well-established way beyond the scope of circles anyway. It makes no sense to fight it, and it has earned its place.

But whenever we talk about angles and rotations, there’s no question that τ is the proper constant to use, just as surely as the use of radians instead of degrees for angles. A full turn is the important idea, not a half turn.

Here’s the same animation as the one above, except this time using τ for the full turn instead of 2π.

External image

Notice that this time we can just keep using our unit of measure (the red arc of 1 radius in length) all the way around, counting each new whole radius (or radian) that fits, only adding a fractional bit at the end to complete the whole turn (the 0.28.. part). This makes much more sense, since that’s how we awalys used any unit of measurement: we count how many times our unit fits in the whole of the thing we’re measuring, not just in half of the thing.

With π, we are assigning a certain special name for a half-turn, even though it is the full turn the thing we are trying to measure. While this isn’t inherently a bad thing (a rotation of a half turn has a lot of importance in mathematics, hence why π exists), it is an odd special case that’s simply an arbitrary quirk of definitions.

The undeniable fact about all of this is that a full turn is more important than a half turn, so it deserves its own symbol.

However, notice that the foundation of that argument is not the numerical value of the full turn or half turn. That’s totally irrelevant, which is exactly why we’d like to use a symbol in place of these numbers! We don’t care about them! But for some reason, this is what most people seem to focus their attention on.

No. The foundation of that argument is in the word “turn”. It narrows down the single mathematical concept we are addressing in the discussion, and it’s in that context that τ really makes all the sense in the world, since it’s the one that represents a turn.

If you’re not convinced yet, just look at our language. We don’t even have a word (in common use, at least) to describe “half a turn”. We already talk about half a turn in terms of a full turn in our natural language. We all already use the definition π radians = τ/2 radians, but only when we talk about angles and rotation. It’s just how we naturally treat the concept, and it makes perfect sense that way.

If that doesn’t make it deserving of a mathematical notation, I don’t know what does.

## An example of the conceptual use of τ as the angle constant

Now, imagine we live in an alternate reality where τ = 6.28… radians, as I proposed. What could math feel like?

The following is obviously incredibly biased (this is an opinion text, so that’s kind of the point here), but it’s pretty close to the thought process I had when I was trying to make sense of the same ideas.

Euler’s Identity: eτi = 1

You see that mathematical expression for the first time in your life.

You see τ in there. Your brain attaches to it the idea of a “full turn”, as you have been trained to. Your brain is now thinking of things rotating and angles.

You see a representation of a “full turn” multiplied by the imaginary unit, i. You try to make sense of that, and you fail. As you should. But now you’re thinking about the complex plane and what could a “complex full turn” possibly mean.

But your brain doesn’t give up. I hasn’t finished reading the expression yet. So it reads the exponential function. You already know the e0 = 1, that’s one of the key properties of this function. But now, the exponential of a “complex full turn” (whatever that is) is doing something new. What it is? You look at the right of the equals sign.

You see the number 1, the multiplicative identity. This is the same value as e0 that you have already thought of. So, the exponential of a “full complex turn” is doing the same thing as doing nothing.

Your brain makes the connection: the exponential of “a full complex turn” (whatever that is) is bringing you back at the same place as you started. You know something is rotating, and you know this is happening on a complex plane.

Aha! Your brain finally gets it. It’s the only idea that makes sense now: the exponential function is performing a rotation in the complex plane itself.

And if you know trigonometry and think just a little harder, you should deduce that eθi = cos(θ) + i·sin(θ), Euler’s formula.

So, call me crazy or whatever you may, but this actually sounds like a nice convention to have around.

## Final words

To be honest, I feel pretty uncomfortable talking about these things. This notion of concepts attached to numbers may be a bit nutty, and I’m not familiar with this sort of approach to things anywhere. (Though a quick Google Search has brought up Bertrand Russell’s Theory of Descriptions), which sounds kinda alike)

But this is similar to the way my brain works, for better or for worse. This is how I learned to tackle math concepts, and this is the kind of approach I try to convey in all of my animations. I try to carry these 'concepts’ around using things like matching colors and visual styles.

Since so many people are fond of my animations, perhaps this idea has some merits, and I’m not a complete lunatic.

Either way, I don’t think there’s a magic trick to it or anything. It’s just about making sure you are keeping track of what everything represents at all times. This is the key approach to learning mathematics. The more stuff you can connect and correlate, the better and deeper your understanding will be.

And best of all, it’s supposed to make sense, even when it doesn’t. Usually, when it doesn’t make sense, it’s your intuition that’s wrong. It’s an odd lesson to learn, but these are the rules we play by in math.

“But I don’t want to go among mad people,” Alice remarked.

“How do you know I’m mad?” said Alice.

“You must be,” said the Cat, “otherwise you wouldn’t have come here.”

(from Lewis Carroll’s 1865 novel, Alice’s Adventures in Wonderland)

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23/2/2016 // 2/100

did some midnight studying on trigometry & arc length&sector area. went to sleep, woke up and made notes on speech features. made notes on ecology & started on literature notes. honestly the most productive i’ve been for the whole year but im rlly tired already lmao