Summer of Math Exposition

At 2.40 you talk about F(4x4,k=6) but the graphics stil show a 3x3 grid etc.

The subject was not really motivated and was presented in a rather dry matter-of-fact way. I think it could have started in a more interesting way to bring the viewer in and make them interested in what the video will have to say about the problem at hand

The premise of counting videos with the coloring constraint is interesting, and I think the reductions you use to simplify the calculation are pretty clear.

I find the tone off-putting. It feels like you’re trying very hard to draw profound meaning from elementary algorithms. I’d much rather have the content presented plainly than have meaning imposed onto it.

There’s also a lot of repetition, which means the video drags a bit. And you never actually answer the driving question of how many videos there are.

The video solves a textbook combinatorial problem: how many proper k-colorings of Z_n×Z_m×Z_l are there. But the presentation of both the problem and the solution are extremely convoluted and confusing. And I find it misrepresentatives of how such problems are solved in practice.

The little mathematical formalism present in the video is glossed over very quickly.

I like seeing the thought process of people working through a problem, but I dont think the video has expository value.

Interesting video and topic. His explanation of how the tree worked was a little bit confusing. But I guess that’s what happens when a tree explodes exponentially to infinity. He later explains how his algorithm simplified the tree by removing the duplicate colors after each new branch. Which helped make the topic a little easier to understand toward the end.

Interesting, but a little hard to follow at times.

So I assume you know this, based on the other videos on your channel, but the narration in this video is stylistically stilted. Your sentences tend to run very short, with many “small” words omitted, sometimes to the point of creating fragments, without verbs or subjects. Done sparingly, this is a great technique for Xing. But with the regularity you do it here, lends a certain romantic vibe to your explanations that I think you should seriously reconsider when introducing people to a new topic. I will illustrate with an example, picked randomly based on when I decided to stop the video to write this part of the review. At 10:15 you start what feels like a new paragraph, beginning as follows:

“Let’s watch a single step in slow motion, because the whole engine is just this repeated. One, the cell above it can’t match that. Second, the cell to its left can’t match that. Three, the groupings of the rest of the frontier. Two kinds of move: reuse a color already on the frontier, and any of that is in above or left. Gray edge counts [comes?] one way. Or, invent a color never seen, orange edge. …”

• The first sentence is perfect. I can tell that you are about to show me something, and I have an idea about what it is, and why you want to show me.

• In the ‘one’ and ‘second’ list items, you present complete sentences that describe concepts with only moderate fuzziness. Namely, it takes a second to convert “can’t match that” into my dialect, but it’s clear that in each case you mean that you’re looking at a specific cell and comparing its color to the color of one of its neighbors. (Side note: you are saying “can’t”, not “can”, right? In context it feels like it has to be “can’t” but I can’t actually hear that “T” in the audio.)

• Both bolded sentences are incomplete; they need a verb. For “Two kinds of move”, I understand that you meant to say “There are two kinds of things we can do next”. For “Three, the… frontier”, I don’t know what you mean. It’s too different from the other two items in the list for me to draw a parallel, “the cell” present in the past two options is now absent, and while I understand why groupings are relevant to the counting problem, I thought their whole point was to be abstractions of the colors, so it’s strange to see them here presented in a choice ‘on the same level’ as choosing an actual color. (I want to stress that I am not pretending ignorance here to make a point; I still really have no idea what this third choice means.)

• The italicized sentences, are, I think, supposed to be informing us that you are defining a gray/orange edge-coloring on vertex-colored grid graph, and you’re describing what rules the edge colors have to satisfy based on the vertex colors. I’m only about 70% confident in this interpretation. I see orange and gray edges in the picture, although the orange edges seem rather more structured than this definition suggests, so that makes me doubt. Perhaps with some more specially tailored animations I might have had more clarity here. In any case, if I’m right about this interpretation, there’s a lot of heavy lifting you’re expecting of me here; these colors are very different, I think, from any of the ways we’ve talked about colors up to this point in the video.

• It’s also not totally clear how these two types of move related to the situation with “the cell” from before. Presumably “the cell” is one of the endpoints of the edge that we’re coloring, and the other endpoint is its neighbors… that have not yet been colored?

If this seems exhausting, you’re getting the point. For me to understand the content of your video, I’m constantly having to make “translations” of this sort for minutes on end. (The quoted passage, for reference, is about 25 seconds long.) This level of grammatical labor is reasonable to ask of a friend or colleague, if perhaps a touch impolite. But I hope it’s clear why this is a very hard sell for most YouTube viewers, who for a video like yours would be watching mostly for entertainment, and were probably expecting to spend most of their mental energy wrestling with the new math.

This issue is far too prevalent in the video to suggest specific changes. However, to avoid asking your viewers for this sort of labor in the future, my first suggestion is to very methodically making sure every sentence has a subject and a verb. This sounds a bit insulting (you are clearly fluent), but it’s harder than it sounds, because we often don’t talk that way in real life. It’s a lot more natural to do this in writing than when speaking, so definitely make careful scripts, giving you plenty of time to edit before recording. The second thing I’d suggest is to align your graphics more tightly to that script, but that’s significantly more work.

Despite this lengthy complaint, I do actually like the parts of the video that I was able to work with. Counting arguments like these are near to my heart, and the problem you’ve made here is a new twist on the classics, which I appreciate. The mathematics of the solution is quite sophisticated, and it’s an ambitious task to present it all in such simple terms. I love to see that ambition, and you handle it admirably! Not only that, but these graphics are beautiful; they are also stylized, but in a very pleasing way that I think works well for your goals here.