Ougi Formula left us with Araragi’s sense of justice wounded, and a reunion with Oikura Sodachi imminent. Let’s see how things play out, I can tell you right away it’s not going to be a pleasant meeting…
00:00-00:50 — The Next Equation
As Koyomi lays out the story that we will be told, we get the above striking shot of the city, the sky lit blood-red. Desks flying through the air, the class assembly and its toll on Oikura has not been forgotten one bit. My favourite thing about the above shot is how the sun used to centre us on Araragi and Sodachi is partially covered by clouds on Sodachi’s side, whereas Koyomi’s side is searing bright. Perhaps to highlight that he does not reciprocate the hatred represented by the smoky clouds around him.
00:51-2:21 — OP – mathemagics – Marina Inoue
A spinning geometric shape with its perfect reflection on the other side, fading to Oikura’s face. No, it’s half of her face, reflected dead centre, as we see her move into the “centre”, her hair sweeping behind her to create a beautiful symmetrical effect.
The thing that strikes me most about the OP isn’t the lyrics, as in the case of Ougi Formula, but how the reflection in the centre warps both Koyomi and Sodachi’s faces, making them look frightening and inhuman. Mathematics may be clean and pristine, right angles and reflections, created by humans, but there’s an ugliness to their precision.
2:22-3:48 — Retracing steps
Araragi and Ougi visiting his old middle school, a tale from the past, where Ougi Formula was the tale from 2 years ago, Sodachi Riddle will focus on the tale from 5 years ago, how Araragi met Oikura, where it all began. Never one for chronology, was Isin, so here we also begin first with where Araragi and Ougi have gone, and will later come back to where the prior episode left us, the inevitable, “coincidental” reunion.
As soon as Ougi shows Araragi the letters in his shoe locker, the memories are triggered, beginning first with the harsh summer, the loud cicadas blaring. It was a formative summer break indeed.
3:49-10:59 — “There is no meaning!”
Back to where the previous episode ended, Hanekawa with Araragi outside the classroom. Naively, perhaps idiotically, Araragi thinks Sodachi’s grudge would have long passed, but his sweating face shows he isn’t fooling anyone, even himself.
Of course, the most vexing thing is that now Araragi has a girlfriend, and this looks like all sorts of an awful situation for our playboy of a protagonist. Araragi is still putting on a brave face as Hanekawa takes her leave, but his composure is immediately lost upon entering the classroom. The classroom which has taken on a sickly hue, Araragi makes a big show out of his “surprise” in seeing Oikura once again:
Oikura’s first words are absolutely terrifying. Spoken in the husky voice of one who hasn’t spoken in a long, long time (whose fault was that, eh), her broken voice causes Koyomi to gulp and tremble.
The next few minutes are a total verbal beatdown, get it all out Sodachi, it’ll be okay… maybe. The key point of this speech is that of exposing Araragi’s oblivious nature, Sodachi emphasises that he does not understand what his fortunes are founded upon, what has brought him thus far.
“What has driven her to this? Was it the class meeting? Was it two years of despair?” – Araragi’s onscreen thoughts. As we’ll find out, he doesn’t have a clue, the hatred was born five years ago, not two.
Sodachi catches herself after she goes a step too far in stabbing Araragi’s hand with her pen. Tension is temporarily dispelled, well that is, until Senjougahara makes her appearance, who has just been witness to Sodachi’s stationery-based mutilation of her boyfriend.
11:00-13:08 — The Cat does not approve of this catfight.
“The only one who’s allowed to stab Araragi with stationery is me. The character trait was discontinued, but I reserve rights to it” – Glad to see Araragi’s cold-blooded Senjougahara back, at direct contrast to the girl we saw back in Koimonogatari.
The next scene is quite comedic despite all concerned parties being deathly serious. From Hanekawa being dragged along the ground trying to hold back Senjougahara, to the chibi-faces and slapstick effects.
The main piece of loaded dialogue is the contrast between Sodachi and Hitagi’s world-view, particularly in regards to helping people, and what they want in return. Hitagi says Sodachi likes to help people beneath her, and in retort to Sodachi claiming that the thankless Araragi will not offer recompense for her help, she states that she is helping him voluntarily, in order to achieve the outcome (Araragi studying in the same University as her) for her own benefit. Sodachi demands compensation, she thinks the act of helping someone, saving someone, is something special, an act that puts the other party in debt to her.
13:09-16:18 — The Monty Hall Problem
Araragi explains how Sodachi had “lured” him with the envelope in his shoelocker and the Monty Hall problem. The Young Araragi who hated math had changed his answer to find the map in envelope c, but there was no logic behind him taking that decision, he didn’t know the mathematics behind it. Before Araragi and Ougi leave the middle school, we see Nadeko’s shoe locker, a “foreshadowing” of sorts for the Nadeko Medusa arc, which we’ve seen, though it takes place chronologically after this one.
16:19-22:40 — Cracked Mirrors
Once again, the solution to the riddle is lampshaded right away by the author, through Ougi (as I’ve commented on before, Ougi is the closest thing Monogatari has to an author self-insert) – She comments on the house having a nameplate, pondering about who might have lived here in the past. Araragi simply replies that he wouldn’t know, and that his middle school self did not pay attention to it. To that line, the crows squawk, can’t get more blatant than that, eh?
Ougi nonchalantly breaks down the locked door. Not allowing anything to get in the way of her poking and prodding of the mind of her prey. Another key point is brought up very early on, as Araragi comments that breaking into the house would be “going off the straight path”, Ougi immediately jumps on it, getting Araragi to “reveal” to her that his parents are both cops.
As we learn from Ougi’s deduction, Sodachi knew who the culprit of the class assembly two years ago was, coming back to school as soon as the teacher left. Therefore the source of her hatred must be different. As the audience, we already know that the story from five years ago is linked to Sodachi, but Araragi does not. Ougi already knows the answer too, so this is a forgone conclusion. What is happening here is digging up a grave, exposing the ugly secrets, it is Koyomi Araragi’s past, the one he must make peace with, and understand, to square his self-image against it in the path to adulthood.
The mirror imagery is used multiple times, each for different purposes:
The next loaded line of dialogue: “To fight, one must understand the enemy’s sense of justice” – A very Araragi line, the emotions must be justified, rationalised, exist under a coherent line of thinking. This is the kind of naive belief system he must learn to grow out of.