
Divergence and curl: The language of Maxwell's equations and more [video] - peter_d_sherman
https://www.youtube.com/watch?v=rB83DpBJQsE
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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...](https://slehar.wordpress.com/2014/03/18/clifford-algebra-a-visual-
introduction/)

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mLuby
Amazing link; thanks for the rabbit hole!

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jackylee0424
Here is Maxwell's original (short) paper about Curl and quaternions in his own
words.

[http://www.clerkmaxwellfoundation.org/MathematicalClassifica...](http://www.clerkmaxwellfoundation.org/MathematicalClassificationofPhysicalQuantities_Maxwell.pdf)

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

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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](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.

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

Why not?

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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.

