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Comment by lordnacho | Hacker News Reader

The 4 equations in the modern form are a wonderful compaction which summarise a whole bunch of different observations:

- How the magnetic field is related to the electric. You can make a magnet with a battery and a coil. - Why there's no "magnetic charge" like there's an electric charge. Why the field lines you see in diagrams always form loops. - How an electric engine works - Why your mobile phone signal drops when you're in a (metal) elevator - How an induction hob works

Etc.

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It’s even better expressed in Geometric Algebra, where Maxwell’s equations become just one single equation: ∇F=J

See e.g. http://ar.newsmth.net/att/26bc57c5677573/imag_numbs.pdf http://www.av8n.com/physics/maxwell-ga.htm http://physics.wooster.edu/Lindner/Texts/Electromagnetism.pd... https://fenix.tecnico.ulisboa.pt/downloadFile/3779571248368/...

First link is "forbidden" - probably requires a university network.

Anyway, thanks for the links! I once tried studying physics and got stuck fairly early on, but I always had an easier time grokking geometry than the other forms of mathematics. I'll try out that second-to-last link, I'm sure it's very tricky and advanced, but maybe it will "click" more than the other mathematics I've encountered.

You might have come across them before, but the Feynman Lectures are a wonderful tour of undergrad-level physics, which combines the math with intuitive narratives. And it's now online: http://www.feynmanlectures.caltech.edu/

Totally forgot about those, thanks for the reminder

Here’s a better link for that one: http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/Im...

Thanks!

If you like visual stuff in math try this exercise before reading anything - pick your favorite software plotting tool - which allows you to plot lines given an equation in terms of x and y and try to plot a wave. Don't use the trig functions available.

Just keep playing with x and y and see what you can come up with.

It can set you off on all sorts of adventures involving waves. Which are quite magical when you start digging :)

I know - I got GeoGebra on my laptop :)

https://www.geogebra.org/

Do you have any tips on the intuition behind the GA product and derivative? I follow the symbols but I can't get any intuition for what it means.

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