Summer of Math Exposition

That was a great explanation!

This is a phenomenal video! The question is both simple and deep, and conveyed in a strongly personable manner. The answers are simple but earned, giving that “of course!” feeling after you’ve seen it once. The animations are stylish but clean and clear. Really, I have no notes!

One suggestion for a follow-up project would be why quantum wave-functions obey different principles because of the different form of the Schrodinger equation compared to the standard wave equation - I’ve always wondered about that!

Anyway, great work.

This is an interesting presentation on waves but it does not answer its own introductory question. What is the medium of propagation which the light waves of the galaxy came through space?

I do not think it makes sense to bring the imaginary definition in to what is supposed to be a fundamental definition of waves. This is not an intuitive way to describe it at all.

The presentation of the different simple things that can be represented by waves at the beginning was good, but the ending did not seem to connect this to the introduction.

I wish you had covered some spherical radiation https://i.pinimg.com/564x/f5/5f/51/f55f5112d3c37ed041bb6c867797ccb5.jpg diagram by john stewart reid - cymatics and sonology

the intro of the universe spirals, felt a little disconnected from the rest of the presentation, cool but maybe not the best intro. Would have loved to see some examples of cymatics in nature forming turtle shell patterns or leopard print, connecting waves to physical traits.

5:13 it looks like these 2 animations are out of sync… minor point, doesn’t affect the score of the presentation.

12:20 I would have liked to see something more… https://youtu.be/RmHcX5oVzvs?t=63 minus clarity

15:00 really great visuals and explanation plus memorability plus clarity

15:40 great clarification on the shape and composition of waves. “starts to scramble them” would of liked more explanation on “scramble” plus clarity

16:32 “more complicated are packets of more complicated” unnecessary redundancy

17:24 “magnetosphere shorter waves travel faster then longer ones” wish there was more of an explanation as to why they get stretched out. minus clarity whistler waves & magnetosphere could have used more explanation. example: “Solar wind (composed of electrons and protons) compresses the dayside of this field and stretches the nightside into an asymmetric tail.

The aurora borealis occurs when charged particles travel in helical spirals along geomagnetic field lines and collide with atmospheric gases. This collision excites the atoms, causing them to release photons.”

Light travels though glass at different speeds, but why? (brachistochrone curve) more on light in this video https://www.youtube.com/watch?v=24GfgNtnjXc

21:16 slide then wait or wait then slide, diagram is overcomplicated with 4 images on screen. this could be presented simpler. also the mug example was a little hard to track with.

1-9 Motivation: 4 (gained a better understanding of waves) Clarity: 7 (missed some points I would have been keen to see, and intro/outro lacking) Novelty: 1 nothing in this is new Memorability: 3 (I might consider sharing or saving this for reference…) 15/4 = 3.75

Gonna bump up to 4.75 because audio was clear and animations were great.

Overall really good. My only minor critique is that the lede was still a little bit buried. The connection between a few simple things to why waves and wave behavior are so fundamental was really cool, but didn’t hit hard until late - I would have liked less of a hint at the beginning and more of a punch in the face.

Ok, this is crazy. The other videos are great, but this one takes so many positive attributes and adds a whole lot of fundamental questions which makes for a fascinating concept and video. Not much to critique, but I would have liked more about why the saw-tooth wave around 15:00 is not a stable minimum (can’t a trough have one steep and one shallow side and still oscillate?). Great intro, linking art and science (big questions about space) and outro linking back to intro. Looking forward to another video…

I believe this video to be a very helpful introduction to the topic of waves and I think it can be helpful as a resource for education. On the other hand, I feel like the video is not on a very novel topic and imo does not really represent a novel approach to waves, since its similar to textbook introduction to the topic. Still, it is a valuable entry to this competition.

Let’s start with: I love the format, layout, pace, length, visuals. As a physicist, nothing is really new to me, this is basically the “everything is a spring” explanation of the world around us. Though everything was interesting and the 27 minutes went pretty much instantly, I experienced no extra astonishing moment. I would like to see more relationship to propagation equation(s) such as Maxwell’s, Schrödinger’s or sound waves.

One of the rare times that I really felt like the root cause was actually reached when talking about these kinds of deep questions.

Physics and maths rewarding us for respecting symmetries. Always love to see it.

I enjoyed the first two-thirds of the video. Using the idea of oscillation and propagation is a very intuitive way for explaining how waves come about. I especially like the graphics used which pulled a lot of weight but were very very effective in explaining the two concepts. The mass spring chain and energy diagram with the spring was very nice!

I also liked the slight introduction to the idea of a phase space, showing how physical processes can be mathematically abstractified to allow for easier analysis.

Unfortunately, I got lost when symmetry was mentioned. Sure, waves do satisfy the commutative order of operations of spatial translation and time evolution, but a lot of physical processes also satisfy this. Therefore it does not make sense to me to introduce this as if it was a uniquely defining feature of a wave.

Additionally, the section where it immediately jumps from an explanation for linearity towards $f(x+a) = Cf(x)$ came out of nowhere. I understand that said equation leads to the demonstration that waves consist of sines and cosines, but linearity should not lead to the question of “What if we have a function that translating in space multiplies by a constant?”

The unexplained insertion of i into the exponential to fix the “unbounded” exponential behaviour to squeeze our sines and cosines feel very forced. In fact, using the phase space from the beginning to show why sines and cosines come about would have been way better especially for high schoolers. There’s not even a graphic of a circle when i was inserted into the exponential!

Overall, this is still very well made, I love the graphics, and I was very hooked from the beginning!

very healily philosophically charged intro with little to back up some of your claims. “The ocean does not know about differential equation” ? YES IT DOES!

Hey there! Great remarking of the remarkable done in this video, thanks for being genuine, sharing your deep thoughts, reminding everyone not to take physics for granted. As a fellow physicist who loves watching and pondering about ocean waves, this video is dear to my heart, and you’re definitely the kind of classmate I would have liked to have in university :=)

As a lecture or conference I think this video would be brilliant. Great connecting of the math to everyday phenomena we experience, great encouraging for the listeners to think deeper about the concepts being talked about, and great way to break them down into elementary pieces everyone’s familiar with. So I’d say you’re clearly very good at teaching.

With all due respect where I’d say you need to focus more on is the video making aspect of things. If I may, here’s a list of things I think you could improve on:

• ” Hey, I’m Ben” is not a great intro. You have great information being provided within the video, please do it justice in the intro. I personally like to think “How would Veritasium make an intro for this video” - or insert YouTube educator role model of preference there - there should be a high density of things happening of previews of what this video offers to teach, mysteries being built by asking questions or showing phenomenon and asking “but why?”. You should immediately start selling the ideas that you offer; “a deeper understanding of things you may have taken for granted, a connection between different phenomena that reveal a more fundamental underlying truth about the universe, many “aha” moments to come in this video, you should definitely watch it!”. When you say “This video is about a question I’ve had” and then say “so for context”, it’s lost time and viewers, instead start with the context, preview some of the nice animations you’ve made while building the curiosity.

• The story that you use with your galaxy sketch to lead to the main questions about waves is great, I don’t know that the timing of it is quite right. It may have had a better impact with more context about the behavior of waves coming in first, then the philosophical nature of how light moves through time and space could be pointed out as a peculiarity, a segue to think deeper about what is going on, instead of being the leading point into the concept. I understand that you’re opening the path into the ideas you will present by telling this story, but it can seem abstract or unrelated to someone who doesn’t know where it is going. Making that clear first, and using your story to create a compelling path to the rest of the video after will make a viewer more engaged with it from the get go.

• In terms of the animation details, I think you can polish your transitions more, especially some of the fadeouts look a bit glitchy, but these are nitpicks. More importantly, I think you can use the camera frames and angles better, a lot of animations had a lot of unused space on the screen, which can make the animation feel low quality. For a better appreciation of the animations, have more closeups to fill the screen, only zoom out when it is more necessary, in a way that is synced with the educational message at the moment. What I mean by that for example is, when we are looking into the motion of small harmonic oscillators making up the wave, the camera should be zoomed in more. When you want to switch to a “big picture” message, you literally make the picture bigger by zooming out to all of the oscillators coming together, demonstrating the emergence of the wave picture. Leaving the picture to be big like that afterwards can take the edge off that effect. And there’s a bonus effect, having more zoom in/outs makes the animation feel more alive, as if there are more animations than there actually are.

• It’s great that you’re giving lots of real world examples to point out the same phenomenon happening in different places in nature, it is at times difficult to tell where the examples start and end, and whether they are still about the same thing. Jumping between examples and adding extra information in between or to understand that specific can get confusing, I personally had some trouble following the 17-19 minute part, and had to rewind. (Also for that specific case, it might have been better to talk about the prism first, as that’s the easier example to understand, and build up to the earths magnetic field after as a more sophisticated example)

• I think it’s great how you’re building the concepts with animations, and are jumping in with the camera in between to bridge the gap and make the video more interactive. In these on-camera parts I’d advise against reading a script exactly the way it is. When I film these kinds of parts I only script out key things to say and just say them looking directly at the camera. This way you don’t look like you’re reading a script all the time, and also can act more natural, as if you’re teaching a lecture. Allows you to be more “you”. (I think you did really well in the 19:50 scene, it stands out as more natural than the other camera scenes.)

The only critique I’d have about the educational part is this, I agree that the points you discuss yield a rough answer to the philosophical questions you’ve put forth at the start, once meditated upon. But the video can be more satisfying if you put more focus on exactly how they do answer these questions. While it is up to the viewer to make the connection, you can give more support for them to make it. You should also make it more exciting, in the video it felt underwhelming to get to the part you answer the questions, as you move on from it a little too quickly in my opinion. The sudden jump feels a bit like “oh I guess we’re doing symmetry now”, when it could have felt like “that was great, oh and we also get to do symmetry!”

I’d love to see deep and unique content like yours succeed on YouTube. I hope we get to see more. I support and encourage you to keep at it.

All the best!

The coupled springs example was excellent for demonstrating propagation.