3blue1brown

The coming of ODEs, and some transitive thanks

Added 2019-03-11 20:52:11 +0000 UTC

Hi everyone,

It's been a little while since I've posted a video, and the next video is likely still a couple of weeks out, so I thought I'd give a little update for anyone curious.

Last month I started writing what I hoped would be a small script on the idea of exponentiating a matrix, not in the sense of M^n, but of e^M. Oh, silly me. Drilling in on the questions of "why would you care?" and "what would you need know ahead of time?" has expanded it into several scripts, likely forming the beginning miniseries on differential equations.

In this case, I was actually quite happy let let the scope creep kick in. As I look over content from the past, the work I feel does the most for the world disproportionately includes videos from series. If the next few months of effort can be pointed towards content that builds on itself to give a visual and substantive understanding of ODEs, I'd feel great.

Within the unconquerable mountain of requests, there is a fair number on topics related to differential equations, or which would otherwise benefit from a firm footing in that territory. For example, it opens the door for talking about many interesting ideas from physics not covered in most pop-science outlets, like Hamiltonian mechanics.

Unlike other promised series from the past (*cough* probability *cough*), I have a clear view of what the unifying theme here is where 3b1b-style animations stand to be helpful. It won't be meant as a comprehensive coverage of ODEs by any means, but will instead be a survey of topics which are made clearer when you have a good feel for phase space and phase flow. The two main things I'd like to hit are linearization, with some discussion around the significance of eigenvectors for ODEs, and chaos, with discussion of strange attractors.

Although it's not in that theme, Laplace Transforms are heavily requested enough to potentially include in the sequence as well.

If any of these terms sound unfamiliar, don't worry, the first step here will be an introduction aimed at making everything as accessible as possible.

For the curious $4+ patrons among you, you will likely see animations for this start to populate the folder mentioned here this week.

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Unrelatedly, many people write lovely notes to say thank you for 3blue1brown. More recently I've started including in the site's contact form a little checkbox to ask if people are comfortable with me sharing their thanks with others who help make the channel possible. Obviously you are key to making this happen, so I wanted to share a couple excerpts of my favorites from the last month.

To start, one from a high school student.

“Thanks for your videos! I really appreciate that you explain not just concepts but how to attack difficult problems. I just found out today I was the AMC 12 winner at my school and one of only 2 people to advance to AIME. I was super surprised to hear that I had beaten everyone on the math team since I'm more musically inclined and I kinda just tried the AMC for fun. I am sure the only way I did this was because your videos have changed the way I look at those types of problems.”

Here, one returning to math after high school.

“I always wanted to study engineering as a kid but at school I failed Maths badly and dropped it completely. Over my gap year I started watching your videos and you explained it all in a way that just made sense and it hooked my interest. About a year later I've started my BE and I'm loving it. A Thank you doesn't even come close to how much I appreciate you and your work. But Thank You for making an 9yo's dream come true.”

One step later up the academic ladder...

“I really cannot say how you have inspired me. I am an aerospace engineering graduate, with a fascination towards pure physics. I always never dared to venture the pure side of me, but after your videos something tipped inside me, now i am planning to pursue a full phd in physics...if it weren't for your videos I wouldn't have taken a leap of faith. Now I truly enjoy my learning journey of physics. So thank you for inspiring the physicist in me.”

I guess pulling someone from engineering towards math lands them in physics :)

And finally, one more from a high school student.

“Dutch high schools require pupils from the 11th/12th grade to do research related to one of the subjects they have chosen. I did this with a good friend of mine and we chose the topic of Artificial Intelligence. More specifically, we chose the topic of Voice Recognition (speaker identification) with Neural Networks. We have managed to create a program that identifies a speaker based on a 3 second audio file (using the vowel 'E').

We wanted to thank you for your videos on Neural Networks and the Fourier Transform because these greatly helped us understanding what it was we were using and explaining them in our final paper. We have gotten a 9.7/10 for it and we won the prize of the best paper of our school this year so we would like to thank you again for making such great educational videos on the internet for anyone to access and to understand topics that might not be so straight forward.”

More anecdotally, shifting from students to the working world, I recently paid a visit to OpenAI in SF. I was touched to hear from many people there that they found 3b1b videos meaningful either for how they think about their work, or how they think about communicating it. Of course, they may just have been saying this to be warm and welcoming hosts, but it made me smile nonetheless.

Thank you again for the support, and hopefully see you soon with some new content!

-Grant