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Reminds me of 3Blue1Brown "Divergence and curl":

https://www.youtube.com/watch?v=rB83DpBJQsE

Link to 3Blue1Brown video on Divergence and Curl: https://youtu.be/rB83DpBJQsE

His later video where in the outro he mentions about going sponsor-free is the one that made me tear up

https://www.youtube.com/watch?v=rB83DpBJQsE&feature=youtu.be...

Here's a little bit of quote from the video:

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So... typically this is the part where there might be some kind of sponsor message. But one thing I want to do with the channel moving ahead is to stop doing sponsored content, and instead make things just about the direct relationship with the audience.

I mean that not only in the sense of the funding model, with direct support through Patreon, but also in the sense that I think these videos can better accomplish their goal if each one feels like it's just about you and me sharing in a love of math, with no other motive, especially in the cases where viewers are students.

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He's really a good person. I'm glad that now he is able to do this full-time by just the support from his patreon.

⬐ MrQuincle

Yes, right then I finally thought I've to figure out this patreon thing. He deserves it.

⬐ antman

And Maxwell's equations are an artifact of this formulation, whereas in geometric algebra they become one equation. From an older duscussion:

https://news.ycombinator.com/item?id=10232052

⬐ ur-whale

There's also a book on the subject called "Div, Grad, Curl and all that"

https://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161

which I would highly recommend to physics-minded folks, but would not recommend at all to maths-minded folks.

⬐ trendia

> would not recommend at all to maths-minded folks.

Why not?

⬐ ur-whale

I bought the book (a long time ago) thinking I was going to get something exactly like what the OP video is: a mathematical explanation of what the tools do, with some intuitive link between - say - the formula for div and why it measures how much a vector field does indeed "diverge" locally.

Instead, the whole book tries to explain the 3 tools using electrostatics as an intuitive justification for how they behave. Ugh.

To me, the way electromagnetic fields behave is no particularly intuitive or natural, and the way I do - sort of - manage to understand Maxwell's equations is because I have an intuitive feel for what grad, div and curl do to vector fields.

⬐ adamnemecek

...or you can use quaternions (which is what ol’ Maxipad did) and get around all this. You end up with a simple equation https://slehar.wordpress.com/2014/03/18/clifford-algebra-a-v...

⬐ daeken

Quaternions are the subject of the next video going up on the channel. I'd be shocked if he didn't explain the connections to Maxwell's work, since he touched on it in his latest Q&A video.

⬐ mLuby

Amazing link; thanks for the rabbit hole!

⬐ jackylee0424

Here is Maxwell's original (short) paper about Curl and quaternions in his own words.

http://www.clerkmaxwellfoundation.org/MathematicalClassifica...

⬐ Ericson2314

Interesting! The tone is suspect: same cultiness as wildeberger stuff. But hey n-lab covers it, so it must be legit:

https://ncatlab.org/nlab/show/Clifford+algebra