Summer of Math Exposition

Very nice video, the conclusion could have been more konstructive learning instead of instruction, so that the understanding can be more intuitive, but it was explained well enough to offset this.

Also the age range is more high school than middle school imo.

nice graphics

Superb. Great visualization, music fits content well, good hook. Accessible. Reasonable pacing, concepts are neither rushed nor labored on excessively. But what made me give you 9 instead of 8 is the usage of “Freddy” to present a model for how to analogize into higher dimensions. By seeing it through Freddy’s point of view, we can understand our own limitations in knowing 4D but also experience and come to know a method of thinking that lets us generalize up a dimension. Presenting this from Freddy’s point of view allows we humans to experience this new way of thinking, of analogizing up to higher dimensions, in a way that’s easy for us to grasp (because we CAN see in 3D). Hence, we have the conceptual framework handled before moving onto the case that’s more unintuitive for us. “Freddy” is a pedagogical and expository stroke of genius. Amazing work!

I found this most excellent in general, but there is one thing that really trips me up, even after rewatching that section multiple times. It’s the bit around 16 minutes where the street light and wall make their appearance. The narration still makes perfect sense to me there, but the visualisation switches to a different register, and that undoes a lot of the clarity that you’ve previously built up. Up until that point, everything is points, lines and planes in diagrams. Now certainly we’re in the ‘photoreal’ world. It’s easy enough to get that the streetlight represents a line and the wall represents a plane, but for this to work I need to think of myself as a point and that isn’t immediately obvious. But more importantly: all the other diagrams show the objects moving through time, while the diagram with the wall does NOT show a path where the wall persists through time while the point moves around it. You do this later on in the video with planes moving through time to form volumes, so you can already visualise it. I think it would make a major difference if you could show a point and a plane moving through time, with the point ‘sidestepping’ the plane for this section, that would really help in driving the explanation home.

Otherwise very impressive work, but you obviously know very well what you’re doing, so you probably don’t need me to tell you that :)

Nicely done! Difficult material, but really helpful use of animation. I feel like Freddie…struggling to see how planes and points intersect in unfathomable different dimensions. I really like the patterns that are found in the end. Thank you for making this video!

Absolutely stunning video. I can tell that you put a lot of passion into making this. The animations were novel and beautiful, and the topic was well-motivated, as I’m sure it is a common experience to wonder about the 4th dimension!

I found the method of teaching especially effective - analysing the pattern in 1D, 2D and 3D, then extending it to 4D. The tabular summary at the end of each visualisation also helped to tie it together.

One thing which could have improved it for me could be if you introduced the pattern a bit sooner and allowed us as viewers to imagine how to extend it ourselves into 4D (before revealing the visual), as that would help us to engage more with the direction the video was taking.

I also wouldn’t have minded an exploration into some of the maths which support the conclusions and graphics, although I appreciate that this was intended to be a more visual approach to teaching.

Perhaps what lost some clarity for me was the fact that this video was part of a series. I believe it worked well enough as a standalone video, but I did find myself sometimes wanting to go back to a previous video to fill in the gaps. This was most noticeable when Part 1 and the “hypervolume” was referenced.

Overall it was wonderful, thank you for putting it out there!

Major but not particularly helpful comment: I feel like I’ve seen a lot of videos/explainers in this realm but still got stuck around 15 mins when we hit 4D. This could also be a fact about me, more so than the video. Minor feedback: 18:12 the narration describes a ‘red line’ but it appears visually as a yellow line.

This was a good video, overall. It was well motivated and easy to understand. It was reasonably well animated to explain the concepts covered, though the first part with Freddy was a little different.

My major criticisms as a peer reviewer is that the topic is a fairly “straightforward” one, rather than some crazy memorable one. This is not necessarily a bad thing in general, but I feel I must lower the score within the framework of this competition.

Furthermore, while this point is justified by the title and concept, the video felt like it was mostly listing facts, rather than deriving higher concepts, as was done in a summary in the final five minutes, and the formulas in the final two. Again, this is not a huge deal normally, but it would have been nicer to see a more punchy video for this type of competition.

Please accept this subjective opinion regarding the SoME competition, while I believe that generally, the video was very good!

Good video interesting way to visualize 4D, I guess you explain how it works in another video.

Your explanation for really clear: you talked at the right speed, made pauses when needed and especially used clear animations. The concept you chose to talk about (visualizing the fourth dimension) is very mainstream, there are plenty of videos about it, but you chose to see it from a specific point of view using the intersections between geometric objects.

Neat! I’d never considered the concept of “degrees of parallelism” before! I think it could’ve been useful to take a little extra moment to explain what exactly it means and why Freddie feels the need to invent a new concept for this, but I understood it in the end.

I think this video stands pretty well on its own, but I’ll need to check out the other videos in the series!