[steamer25]

Prior to computer-generated 3D animation, I can imagine it was very difficult to float and spin vector-arrows in mid-air with enough accuracy to show what goes on without having to resort to reams of explanatory paragraphs.

Eugene Khutoryansky is something of a lesser-known 3b1b that's more focused on physics than math. I found his animations very helpful for building intuition around Maxwell's equations:

https://www.youtube.com/watch?v=9Tm2c6NJH4Y

[s1artibartfast]

I wish most explanations wouldn't skip over the fact that field lines arent real, and just a tool to graphically depict what is going on. Statements like the following gets the causality entirely backwards.

>the strength of an electric field depends on the number of electric field lines.

[timeagain]

It’s like saying that rain falls where there are blue regions on the weather map :)

[psuedobrain]

I think the question of whether field lines are real is more of a philosophical (of physics) question so it usually falls outside the scope of introductory material on E&M. However, some texts like Purcell and Morin do kinda take a stance on whether fields are real: "since it works, it doesn’t make any difference."

[gosub100]

isn't that a special case of Plato's argument that "triangles aren't real. show me a perfect triangle...you can't, you can only show representations of a perfect triangle"

Your comment could be reduced to "lines arent real. show me a perfect line"

[rolph]

we can fix that.

the number of electric field lines, depends on the strength of an electric field. ,

[devmor]

Wow this video is actually great at imparting the concepts with animation.

It's a little distracting how it looks like an ad for an adult themed video game, but it's very well thought out.

[Terr_]

> It's a little distracting how it looks like an ad for an adult themed video game

Well-put: Does that demon-squid in the intro look like a Chihuly glass installation to anybody else?

Also I swear I've heard that song long ago on OCRemix.

[lumost]

I suspect something similar happens with manifolds for GR. Riemanian manifolds aren't a big deal when you contrast them to what happens inside of a DNN, but physical analogs for these structures start to break down.

e.g.

Imagine a 4-dimensional hyperbolic surface defined by the lightcone of a particular point in space-time, now imagine that this surface is stretched/compressed by the distortions of gravity. Now let's talk about equations which are only loosely tied to this surface.

vs.

Consider the metric tensor defined by this 4x4 matrix g_xz. Distance is computed as a^x b^z g_xz, now consider all possible walks from point a to c to b. Now let's show the relation between these walks and a quantity we'll call the stress-energy tensor which represents the energy/momentum density at any particular point in space, and it's flux towards any other direction in space.

The latter is a very algebraic description, which does not rely on the audience having to visualize the constructs involved. Practically, even if you get a feel for what a Riemanian manifold looks like in 4-dimensions - you'll struggle to visualize the Riemann tensor, or Christophel symbols.

[jereees]

This video is worth watching for the soundtrack alone. I came across Eugene’s channel before but somehow I missed this gem!

[Ringz]

> … for the soundtrack alone

Did I sense mild sarcasm here?