Summer of Math Exposition

The top half of the video (before “exploring 4D” chapter), is really easy to understand, and I actually learn a lot way to treat 4D, but I started to not being able to understand after you starting exploring, the difficulty gap is too huge to me.

The abstract and motivation and explanations are all very good for the most part, but I feel like it jumps straight into the visualizations a bit too quickly. Seeing how the rotations actually work is still very confusing.

This animation shows very well how to start from a basic knowledge of 2d geometry and extend to 3d and logically to 4d.

The idea of the video is good and it starts off with a good energy. The video explains extending the point through to the hypercube well.

. However the jump into 4d motion is inevitably confusing and that part of the video is handled to quickly. Once the camera starts moving around in 4d it is very hard to maintain attention.

I do not know exactly how to fix this but the viewer needs to have some kind of reference point as to where they are in the overall 4d space during the larger visuals. Such as the small 2d map in the corner of a 3d game.

Overall the topic was interesting and certainly allowed me a better idea of how 4d works, but the ending was conceptually confusing although enjoyable to watch.

This looks like some cool software to play around with!

On such a long video I would have liked some some sort of outline near the beginning saying what the plan for the rest of the video was.

The topic could also have been aimed at high-school students, but it should have been presented differently (for example, starting from a lower dimension and mentioning Flatland). As presented here, it is beyond their reach; it might work for university students, but they would probably understand the subject much better by starting from the algebraic approach and then moving on to visualize it with appropriate projections. I believe the software used could be useful for a mathematician, but the presentation itself is decidedly long-winded, and attention risks dropping due to the monotony of the images and the lack of engaging and original elements.

Your video did genuinely give me a better appreciation for an intuitive spatial understanding of the fourth dimension. I would have liked for you to have spent just a bit more time showing/explaining the 4d rotations in their chapter.

I can’t claim to have watched all 45 minutes with full attention, but I found it not so easy to grasp the main idea. If something is presented as new, it might help to compare it with earlier work, since projections have been looked at before. Still, it’s clear that a huge amount of work went into this. I also really appreciate the time codes and subtitles. This video definitely deserves more views.

I found this very hard to follow and very slow. Sad to say, it didn’t keep my interest.

Your grasp of the English language is very good, and I’d like to make a suggestion to make it even more impactful! Try to vary the speed at which you speak depending on the importance of the information you are sharing. At around 5:30, you move through what I feel is a really important note regarding our assumptions of 3D projections. The point was loud and clear, but during such an important point, speak just a bit more slowly (relative to the rest of your script) to help the listener understand just how important it is. The vision section is similarly very consistent in its presentation speed. Small pauses here and there would help digestibility.

Honestly, a very interesting video and it gave me a great understanding of 4D geometry that I didn’t have before. I think the script could have been tightened up and shortened to increase the focus. By the end of the video, I felt it was dragging on a bit.

Initial Thoughts

Great video! I enjoyed it, and came away with a better understanding of how 3D projections of 4D objects work. Thanks for sharing!

What Went Well

My favorite part of the video was the first half, when you were explaining the dimensionality and going over the basics of how that works. I also enjoyed the parts toward the end when you talked about extruding into the 4th dimension and double rotation. I think you kept your explanations simple enough for the high-school audience you listed, so well done!

Ideas for Improvement

The main thing that’s coming to mind for me is the length of the video. The simulation part felt a little long to me, mostly walking through all the different ways to move in the simulation felt long. That would be very helpful to anyone who decides to try out your simulation though, so if that was part of the goal, I think it’s good you included it.

Overall, very well done!

The creator does a good job of setting up the analogies in 2D and 3D that will be used moving to 4D. Unfortunately, like many other attempts, the transition from 2D/3D to 4D is still jarring and difficult (for me). I suspect the creator did gain true insight into 4D using the methods they describe.

Once they move to 4D topics and images/projections, the lower dimensions are completely left behind. I wish this part of the video was expanded to more actively tie things together as the 4D world becomes more complex. I’m not sure exactly how one would to this but I think it would continue reinforcing and repeating the connections and analogies. I think they need repetition to help the viewer internalize them successfully.

I also wish the graphics in the 4D sections of the video had the same quality as the earlier parts of the video - thickened lines, anti-aliasing, etc.