Summer of Math Exposition

First 20 minutes are unnecessary - Anyone not familiar with this material will not understand the latter half.

I love the book recommendation! The graphics are absolutely fantastic. It’s clear this production was a labor of love. Very well done, fun to watch, easily motivated.

Motivation: 2.5 / 3 Clarity: 2.5 / 3 Novelty: 3 / 3

I liked the visuals and editing. Maybe the video was bit too long.

I’m not sure what is the goal of the video. From the introduction and description I have expected that the video would be more focused on some kind of insight and simplification, and making conclusions from first principles. Instead, there was a long chapter about Snell’s law, which started from assumption that the light “likes” to travel in shortest path. I don’t really understand why, it sounds more like kind of emergent behavior than fundamental principle. So I didn’t get any special insight, and then it was followed by calculation dump that I, to be honest, didn’t care to follow. I don’t think this is better than the usual wave-propagation intuition and deriving the formula from that. I would just prefer to save some time and skip all the discussion about Snell’s law and just take it as a fact.

As for the rest of the video, I think I’ve already seen other videos that show how the light bends inside raindrop and how it hits your eye, so it’s nor particularly original. You maybe got bit more into the geometry and actual calculation, but to be honest, I don’t care that much about that.

introduction is to long, and the history of the mathematician doesn’t help. The motivation is good, but could be shorter. The mathematical basics should probably have been explained in a separate previous one, which was against the rule, and they are necessary. … mhh

It’s really cool to see how rainbows are formed!

The section from 7:35 from 19:08 felt a bit slow to me. You introduce it as getting the viewer up to speed on Snell’s law, and only get to stating Snell’s law over 11 minutes later, at the end of this section, and then only then do you finally get to proving Snell’s law.

Maybe I’m not your target audience, but I feel like introducing the sine function from scratch wasn’t really necessary, or you could’ve done it much more quickly. The section on linear approximation is important, but I think it might’ve been better to reorder it so it wasn’t between the sections about introducing Snell’s law, because you don’t really need it to state Snell’s law. It could go either before you start introducing Snell’s law or after you’ve stated it but before you start proving it.

The other thing that stuck out to me is when you said “When we think about it, all we really care about is the angle at which the light hits the water […] and the angle it bends to after hitting the surface of the water […]”. Perhaps when we think about light reflecting, it’s obvious these two angles are all we care about. But since we’ve thus far mostly been working with the problem of running to help someone in the water, it’s not obvious to me that all we would care about in that case is just these two angles.

Anyway, lovely video, and once we get to seeing the rainbow, it’s really rewarding!

This video is very visually appealing - both the general animation and the animated math held my interest for a while. The part with the different parts of the rainbow hitting the cats eyes stuck with me. I did lose interest in the math at around the 30 minute mark, I just wasn’t seeing that this was headed towards a payoff. I think you need to motivate the final result and tell us what it is that all the equations are pointing towards - a destination that we’re trying to get to. Also I think you need to decide on an audience and stick with that. Someone who is hasn’t learned radians before is not gong to be interested in or be able to follow the harder stuff, and anyone who does follow the harder stuff will not need the review of basics. I hope you keep creating!

This is an excellent video, especially for your very first full-length video on your channel. I can really tell that you spent a TON of time and effort on it. Your graphics really stand out as being exceptionally good. You also tell a very good “story”, with your emphasis on Arnold at the beginning.

Some constructive criticism (i.e. ways to improve future videos):

*The “audience” needs to be defined a little more clearly. At some points you felt the need to explain “angle” and “sine”, but other places the video seems to assume a much higher level. I did appreciate, however, that you gave a different kind of explanation of angle and sine than what we’re used to seeing. However, if someone didn’t know those concepts a priori, they would have a very difficult time following it.

*It would be helpful to have a clearer overall “big picture” summary of the topic. Make sure that the most central ideas to understanding the topic are the ones that are explained most clearly.

Great video!

This was really good. Your accent is a tad heavy, but workable, especially with subtitles, and there were numerous small issues throughout the video, patched in hindsight, so you’re aware of them.

I really don’t have that much in the way of constructive criticism here. Chug along.

I found the explanation incredibly straight froward and easy to follow, and still interesting for someone with experience with Snell’s Law etc. I might’ve of liked quickly seeing on screen a few more of the calculations and technical details that were skipped, but that is my only small comment. Otherwise, great job!

Motivation: The introduction to the video is way too long imo. Although the graphics are beautiful from an artistic point of view I just wanted to progress more quickly to the section where there is actually some maths/ physics. Although I believe you in that you are generally fond of Arnold’s book, the section feels a bit like a cheap advertisement.

Main video. Effects/ music overdone in my opinion. I find it strange that you keep referring to “Arnold’s Argument” when (as far as I’m aware) this is the standard explanation of the rainbow (at least it was the way it was taught to me). This is also not the first video on YouTube on Rainbows using this argument (see Veritasium video). As a graduate student (so part of your target audience) I feel that I took away very little from the video which I didn’t already know.

Overall a great video that taught me something new about rainbows! Very cool. I do think there’s some point to make known.

1. If you have AI images used, why not have changed them to NON-AI images if overall it doesn’t affect the video/delivery? That opens yourself up to some scrutiny and perturbs viewers about the rest of the video.

2. Small script errors/manim animation mistakes, but honestly not bad. If you had time to clean them up, then that would’ve been fine.

3. You built up the necessary mathematics used in the video, which took a while but serves it point to audiences that aren’t familiar with calculus and trigonometry. It wasn’t hard to watch through if you’re familiar with the math as the visuals provided even better reason to how it works.

4. The animations were fantastic and definitely were required to cover this subject in a broad audience. Very nice.

I had a good impression with the video, however an audience is going to be influenced by the use of AI for this video, which is still something that wasn’t necessary to use. You are clearly very well adept in video making, so avoiding them would’ve been better.

I think this really is an outstanding video that aims to make the explanation of the laws of optics intuitive and accessible not just to a technical audience, but really aims to a wider audience as well. I appreciate that it does not go too much into technical details, and primarily helps to create a picture for people to understand how it works, and understand the spirit of the argument. I especially liked the analogy of the start of the different mediums for people to take a grasp into what you are trying to communicate. I think with a bit more clarification, it can help to make this even more accessible to a layman. (e.g maybe having the maxima of theta function clearly explain what we do see in real life in terms of what is observed in actuality when we carry out the computation )

Thanks for telling me about your use of AI at the start of the video. Saved me 38 minutes of watching.

I don’t mind AI in principle but some images were too detailed or to obviously AI-generated

Too much time was spent proving snell’s law given that the video promised to explain rainbows

I’m fairly certain the rainbow explanation is incomplete as it’s not made clear in the video that it’s the reversal that causes the rainbow

To me the point of the video was not entirely clear at first. The title suggests that is is about the process of simplification and it only uses the rainbow as an example. But it really is only about rainbows, so I think the tutle is a bit misleading. When you showed the pictures of rainbows, some other effects such as double rainbows could be seen. It would be better to either explain these or use other pictures that only show what you explain. Also I don’t really like the style of the video, but this is just personal preference. In principle the way you explain things is good in my opinion.

Love the intro. I’m a big fan of Arnold too!

Positive comments:

• Absolutely loved the historical context which is always important
• Excellent animations
• Good musical background
• Breakdown of the complex concept into many smaller parts

Constructive comments:

• Too many corrections, a few corrections are typical for a video this long but there were a lot here. I would recommend spending a little more time with re-recording/reanimating. Particularly audio corrections are easy to do and take as much or less time than inserting visually the word you meant to say.

Although I love math, I dislike trigonometry, but your video got me invested in it. Definitely subscribed.