We’re in the thick of a new Monogatari season now, and this one’s shaping up to be a fine followup to Second Season. A whole bunch of that comes down to Ougi – Ougi both forces Araragi to consistently confront his own deepest fears and just possesses a great deal of charisma in her own right. This Araragi-Oikura story also has plenty of momentum so far, and seems to be pushing Araragi’s character forward far more consistently than Tsukimonogatari did. What do you know, when you replace Yotsugi lolicon shenanigans with Ougi’s mockery and psychological battles, you can actually make a damn good Araragi arc.

You can check out my full writeup over at ANN, or my episode three notes below!

“Five years ago – in other words, what kind of person was Koyomi Araragi in seventh grade?”

“Young Araragi was mediocre”

This Bond parody image

The influence of his parents as police officers, giving him a strong sense of justice

Panicking about his poor final exam results, particularly in math

The opening is all geometry puzzles, fitting in with the arc’s themes. It also feels a little bit like a Bond opening, too

More beautiful shots of the house surrounded by dead trees – **like the construction sites, everything in this world is either half-finished or already destroyed**

Sodachi Oikura’s waiting in the house

“Let’s study. Let’s become wiser together.”

All of Sodachi’s lines are framed as silent film interstitials

Sodachi taught Araragi to love math. **She guided his destiny in her own way**

The mathematical instruments keep blocking out Sodachi’s face. **Likely because she wasn’t personally a meaningful person to Araragi – she was just the facilitator of this interest**

“Don’t ask me what my name is” was one of the conditions for their study sessions

Doing it for the love of sharing mathematics

But then she disappeared. However, his grades improved. **And we see the red lights turn green – he’s able to grow beyond that stage**

The honest joy in mathematics was all that was left to him when his sense of false righteousness was destroyed by the class trial

**“That girl who taught him how amusing life is”**

Ougi keeps offhandedly “solving” the riddles, because they’re not really riddles at all. They’re issues that have become tangled in Araragi’s mind, but are in practice simple

“Apologizing won’t do anything, but I need to apologize, so I will”

She left him an empty envelope

This shoujo Oikura is great

Ougi rightly points out that Araragi’s trying to apologize as his usual bandaid solution without actually understanding the nature of the problem

“Araragi disappointed Oikura. What did she expect from him? Hint: it has something to do with the occupation of Araragi’s parents.” So did she expect him to seek justice for her, fitting in with her general “people are responsible for each other” ethos?

Oh dang, Oshino’s old ruins were a cram school. That’s nice

“Five years ago, this was not a ruined house. This was where she lived.” **Perception creates reality. Ougi pierces the veil**

“It seems Oikura had to grow up in quite the tragic family environment.” **While Araragi’s family taught him to respect justice, it seems Oikura’s taught her not to believe in it**

Oikura was expecting Araragi to report the damage at her house to his parents

**One more of Monogatari’s broken homes**

“That envelope represented me – empty and disappointing. I was a guy she couldn’t count on.” **Again, bringing it back to a challenging of Araragi’s lessons**

“As happy as I am, I’ve come to despise myself a little bit.” “Then that little bit is how much I will love you.”

Hanekawa points out that Oikura shouldn’t know his parents are police officers

The only thing that bothers me about this arc, and it seems to come up in anime from time to time, is people forgetting large and important chunks of their lives. Does this actually happen? Do I simply have an outstanding memory?

Maybe you don’t remember what you’re forgetting.

I think in this case, it’s both an exaggeration to emphasize how much Araragi takes his life for granted and possibly the influence of Ougi. She’s definitely manipulated people’s perceptions of their lives before.

I’m enjoying this season

somuch more than Tsuki, and absolutely thrilled about it. On top of executing *monogatari-fundamentals superbly, they’re even pandering to my educational background with the math – Euler’s Identity indeed!So as I understand it, the basic phenomenon of Euler’s Formula is:

Any positive real number (and maybe negatives too), to a negative power will get a result on the complex plane in the circumference of the circle of radius 1. Since it’s a circle, there is a number x at which any a^(bi) is equal to a^[(b+x)i]. I’d like to call this the wavelength.

This implies every number can be a wavelength for some sort of number.

When you represent complex numbers with the same absolute value as a circle, the circumference of that circle is the value * 2pi. In this case, since the value is 1, the circumference is 2pi. There must be some number with a wavelength of 2pi, which would allow its imaginary powers to be calculable in terms of the radian sine and cosine functions.

That number is the exponential constant.

#3 is the big “what.” moment. i and pi have a not-so-obvious relationship in mathematical conventions. But when you look for the number that links them together concretely, you get e, a third fundamental constant! For me, that’s the big “what”.