About
Come think differently with me
Hi, I'm Jake — a student of economics and cognitive science at Yonsei University in Seoul, South Korea. Another Angle is where I share animated breakdowns of ideas from my own notes.
I've always been drawn to looking at a single idea from more than one angle — tracing how a pattern that works in one field turns out to explain something in a completely different one. Between classes and studying on my own, I kept building little explanations for myself: wouldn't this make more sense if you saw it this way? Those explanations became the videos, and now they're becoming written pages too.
One long argument, then pictures
Every chapter starts as a written script, in Korean, argued until the logic holds without any visuals at all. If an explanation needs an animation to make sense, the explanation isn't finished yet. Only then does it get storyboarded into scenes.
The animation is manim, the open-source Python engine Grant Sanderson built for 3Blue1Brown. Every frame is code, which is slower to write than dragging shapes around but means a diagram can be rebuilt exactly when the argument changes — and it changes a lot.
The look is deliberately narrow: two palettes and nothing else. Chapters up to trigonometry were drawn in ink on cream parchment; from linear algebra onward the field is Deep Tide, a dark indigo-to-teal gradient with bright lines on top. This site uses both on purpose — paper where the reading happens, Deep Tide where the videos live.
Narration is English, subtitled into 36 languages, with titles and descriptions localised for 35 of them. If a translation reads badly in your language, I'd genuinely like to know.
What I'm working on
A running log, kept short: which chapter is in production, what changed and why, and the occasional thing that broke and taught me something.
A written home for the ideas
Started building this site. The videos have always been the main thing, but a video is a bad place to answer a specific question — you can't skim it, and search engines can't quote it. So each idea is getting a written version that finishes the thought on its own page. The first one is up: slope and angle aren't the same number.
Chapter 4 is out, and the whole channel changed colour
Linear algebra went live — vectors as blocks of movement, and transformations that move the entire space at once. The background also changed for good. Everything now sits on Deep Tide, the indigo-to-teal gradient you can see in the blocks on this site, replacing the cream parchment the earlier chapters used. Side-by-side renders settled it: bright lines on a dark field simply hold the eye better. The parchment isn't gone, though — you're reading on it right now.
Chapter 3: trigonometry, starting from a road sign
This one opens with a 10% road sign and a 30% treadmill, which are ratios rather than angles, and spends the rest of its time explaining what converts one into the other. The part I'm happiest with is tangent getting a real job — a ruler for slopes — instead of being the third item on a list.
Two-variable functions and the directional derivative
The nudge ratio, one dimension up. The decision that shaped this chapter: drop the scalar-multiple detour entirely. If the input nudge has size 1, the output nudge's size is the derivative — no stray constant to explain later. It costs a re-cut of a scene that was already finished, which is usually the sign it's the right call.
A chapter zero about schemas
The series keeps using the word "schema" and has never defined it on screen. Chapter zero is meant to fix that: what a way-of-seeing is, why installing one beats memorising a procedure, and a roadmap for where the rest is going.
Questions I get
What do you use to animate your videos?
Manim — the open-source Python animation engine originally built by Grant Sanderson for 3Blue1Brown. Some scenes use the community edition, others the original, depending on what the scene needs. Every frame is code rather than a dragged shape, which is slower to write but means a diagram can be rebuilt exactly when the argument changes.
What order should I watch the series in?
Chapter order: ratio, the derivative, trigonometry, then linear algebra. Each stands on its own, but the later ones lean on the comparison-index idea from chapter one, so starting there pays off.
Do I need to be good at math to follow along?
No. The series assumes you've met these topics before and came away feeling like you were following instructions rather than understanding anything. That's the audience. Nothing here requires you to remember a formula you were taught.
Why economics and business specifically?
Because that's where I kept hitting the gap myself. Economics uses derivatives constantly under the word "marginal", and elasticity is a ratio of ratios — the math isn't advanced, but the intuition is usually skipped on the way to the exam. Fixing the intuition fixes a surprising amount downstream.
What does the name "Another Angle" refer to?
The habit the whole channel is built on: looking at one idea from more than one angle, and tracing how a pattern that works in one field explains something in a completely different one. The logo is that literally — a serif letter A tipped over until it reads as an angle mark.
Are the videos available in other languages?
Subtitles are published in 36 languages, with localised titles and descriptions for 35 of them. The narration itself is English. If a translation reads badly in your language, I'd genuinely like to know — a comment on the video is enough.
Will you please make a video on some topic?
Suggestions are welcome, and several chapters exist because someone asked. The honest caveat: this series has a spine — it's walking from ratios up to multivariable calculus — so a request that fits that path has a much better chance than one that doesn't. The comments under a video are the best place to leave one.
Can I use your animations in my own work?
Ask me first and it's usually a yes for classrooms and non-commercial use. Please don't re-upload whole videos. If you want to build something similar yourself, manim is free and the barrier is lower than it looks.
Can I ask you a question about math, or about one of your videos?
About a video: yes, in its comments — I read them, and they've changed more than one chapter. General homework-style questions I usually can't get to, simply because there are more of them than there are hours. Corrections always get a reply.
What's the game about?
Open World Discover is a 3D world in the browser where the terrain
is a function: type z = f(x, y) and the island becomes that graph, and
then you can drive, fly, or walk across it. Same goal as the videos by a different route
— making coordinates and derivatives something you feel rather than solve.
I'd like to start making explanations online. Any advice?
Write the script until it works with no pictures at all. If the explanation only holds together once an animation is covering the gap, the explanation isn't finished — and you'll feel that gap again as soon as you try to animate it. The visuals should be the argument made visible, not the argument's replacement.