Thanks for watching! Here's a continually updating list of more information, mistakes, & resources to learn more.

1. As many have (correctly) pointed out, a real circuit would actually not settle instantaneously as claimed in the video (at 36:40), as it takes time for information to travel. What I really meant to convey (and how I should've actually worded it) is that typically in a "lumped-element" styled analysis of circuits like this, the modeling assumption used is that everything is small enough for the messages to be passed "instantaneously", instead of modeling it in the "contrived" sort of way I did throughout the video for a fun animation. For more info on the instantaneous modeling assumption which is more typical, see for example the first paragraph in this writeup from an EE course at CMU: https://www.cs.cmu.edu/~tdear/ee/rc_rl.pdf. But anyways, thanks for bringing this to my attention I should've worded it differently!
2. Check out this fascinating article by Jack Copeland (who graciously let me feature his images in the video) for more info & history on Tutte: https://link.springer.com/article/10.1007/s00283-024-10386-7
3. Special thanks to Iain Stratchan for Trinity College 1939 image, and for sharing lots of valuable historical anecdotes!
4. Thanks to Flaming June for the "Unsung Hero" song at the end! https://open.spotify.com/artist/1Y8l8WDlrbz3ymcCz50r3w

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if that's a simple squared rectangle I do NOT want to meet a complicated one!

25:06 "we avoid this problem by ignoring it"

You know a math video is good when the premise seems contrived at the start, but almost trivial at the end

why is it screaming

edit: ok stop

cartel gonna turn you into a simple perfect squared square

The production quality of this video is insane!  All the zooms into the Squared Rectangles like at 13:27 remind me of fractal zooms.

Also I feel like the connections to electric current at 8:35 is the highlight of the video - the realization that squared squares and graphs of wires are connected!

Wow! The quality of the graphics is truly incredible, I’m amazed. I knew a little bit about squared squares before this, but I had NO idea how deep the rabbit hole went. Your presentation style is so good, I can’t wait to see more!!!

Your capturer is the most chill combinatorics professor btw

I'm seeing a trend here
Trapped in a room, making shapes with other shapes

36:50 pretty sure that an electrical network would in fact do that bouncing, just on a timescale too short to notice.

Im sorry you missed the 3b1b competition deadline, but I'm also glad you kept working on it. This turned out fantastic, and I was exposed to multiple aspects of math that were kind of alien to me before the video. I was also reminded, yet again, how systems that look completely different at first are usually just like siblings that dont look alike and lie to you about it until you look closer and see they're related. I loved the references and silly jokes, and I certainly found the video delicious (32:27 reference)😍

2:27 Squared arrangement? More like square derangement!

1:02 is it just me or is the scientist robotnik

Fun fact : In HF electronics design - where we basically cut components as geometric shapes on a sheet of metal - the unit of resistance is ... a square.
It is because a larger track is less resistive in a linear way, and conversely a longer track is more resistive also in a linear way... So the actual resistance (ignoring metal resistivity) is given by the ratio of length/width, which means you can find the resistance of a track by counting how few squares are needed to cover the track end to end. And amazingly, the side length of the squares (which is often the width of the track in an optimal covering) is irrelevant. (see also : wikipedia sheet resistance)

Having watched and rewatched the video, I think this is one of the best math videos I've seen in a few years. Made me remember the spark I felt watching 3b1b all those years ago. The way the squared rectangles link to circuits, and then to polygonal meshes and springs, is just so beautiful and clearly explained. How, as soon as you talked about each node being an average of it's surrounding nodes, it immediately made me realize this is related to the laplacian, and how the end of the video left me hankering for more. The production value of the video is insanely high too, it's honestly amazing how good of a lesson you made here. I hope millions more will be able to enjoy your content as much as I did :)

37:35 idk why but I like that noise

wow. that intro just got crazier and crazier.

Mathematics and horror are like lovers who don't realize they are a perfect match for each other.

And of course there’s a tortured face in it 😭