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Intuitive Guide to Maxwell's Equations

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Re: Intuitive Guide to Maxwell's Equations

#71

Post by rovolo »

BoiledCabbage wrote: post #58
devalgo wrote: post #52

Earlier quoted context omitted.

True generally in Physics as well. What's the point of "understanding" Quantum Mechanics intuitively when you can do computations blindly without it!

I'd even be more ok with that, if mathematicians used more rigor in their notation. Math developed in a time where it was tedious to write this out by hand and a lot was hidden in abbreviations and assumptions. One thing that programming gets very right is that it is way more explicit (although obviously not perfectly) the behavior behind any notation. It's one thing that Structure and Interpretation of Classical Mec…

> Even the description of the Laplacian is wrong. The value isn't the average of the points surrounding it.

The description on page 7 is split into two parts. The first part describes the value of the Laplacian correctly:

> It tells us how the temperature value at the point compares to the average value of its neighboring points.

The second part describes the long-run behavior of the differential equation

> The temperature value that this point takes is the average temperature of the points surrounding it

Re: Intuitive Guide to Maxwell's Equations

#72

Post by muktabh »

This is so well written. I remember being taught these in my first year engineering and I really never understood a lot intuitively. (I could solve numericals and clear the course but I did not get it then. Being a CS student, I never had to care about it ever since). I wonder how the world would have been different if all courses were taught this way.

Re: Intuitive Guide to Maxwell's Equations

#73

Post by SAI_Peregrinus »

photon_lines wrote: post #66
SAI_Peregrinus wrote: post #23

It's also interesting once you understand what Maxwell's equations mean to look at their geometric algebra formulation[1]. In particular it makes their use in special and general relativity somewhat more elegant, since the GA form explicitly includes a spacetime component. Of course that page isn't an elementary introduction, it assumes familiarity with GA and the divergence & curl operators, as well as some concepts…

Actually, at the end of the guide, I tried to include an explanation which states that the magnetic field is just a by-product of relativity, and that the equations really only describe one field. A comment on the other approach: the geometric formulation to me looks interesting, but it's still very information dense and a bit un-intuitive! I'll take a look when I get more time though and see if I can re-formulate th…

That article I linked is definitely not written for beginners, but I do find its notation more intuitive. But that's only because I'm used to working in the notation of geometric algebra, so using it for Maxwell's equations makes sense.

Re: Intuitive Guide to Maxwell's Equations

#74

Post by devalgo »

ArubaJamaica wrote: post #56
devalgo wrote: post #52

Earlier quoted context omitted.

True generally in Physics as well. What's the point of "understanding" Quantum Mechanics intuitively when you can do computations blindly without it!

This statement is misguided. A lot of physical phenomena doesn't lend itself to intuitive understanding. Quantum Mechanics is a great example of this. You cannot expect subatomic particles to behave the same way that macroscopic objects do (and macroscopic behavior is what humans find intuitive because we experience it on a day to day basis). Its the same misguided thinking that leads to the popular PopSci explanatio…

Isn't this just a misunderstanding of what we mean by intuitive? It's possible to have an intuitive understanding of a thing that's not "intuitive" to humans.

Re: Intuitive Guide to Maxwell's Equations

#75

Post by soVeryTired »

QuesnayJr wrote: post #57
soVeryTired wrote: post #46

Earlier quoted context omitted.

I nearly based my Master's dissertation on a topic I discovered on a wikipedia math page when I was looking for something to cover. Turns out that subsection was maintained by the 'inventor' of topic and essentially served as a vanity page. The topic itself had no recognition in the community and if I had forged ahead on it, I would have failed my dissertation pretty hard.

If this is a math topic, you should bring it to the attention of the WikiProject Mathematics talk page: https://en.wikipedia.org/wiki/Wikipedia_talk:WikiProject_Mat... . They might do something about it.

Oh, I got rid of it years ago. Thanks though. Eventually a big-name mathematician (who some years later won a Fields medal) waded into the discussion and sided with me. I used my real name in that discussion so I won't give more detail than that :)

Re: Intuitive Guide to Maxwell's Equations

#77

Post by kanzenryu2 »

ArubaJamaica wrote: post #56
devalgo wrote: post #52

Earlier quoted context omitted.

True generally in Physics as well. What's the point of "understanding" Quantum Mechanics intuitively when you can do computations blindly without it!

This statement is misguided. A lot of physical phenomena doesn't lend itself to intuitive understanding. Quantum Mechanics is a great example of this. You cannot expect subatomic particles to behave the same way that macroscopic objects do (and macroscopic behavior is what humans find intuitive because we experience it on a day to day basis). Its the same misguided thinking that leads to the popular PopSci explanatio…

https://www.lesswrong.com/posts/apbcLXz5zB7PXfgg2/an-intuiti...

Re: Intuitive Guide to Maxwell's Equations

#78

Post by photon_lines »

Jailbird wrote: post #76

OK since photon_lines is reading, do you want any comments? For instance, right on page 4 of the (not numbered) PDF - I tripped over the word "discreet", where ostensibly you meant "discrete". If not - s'ok. Just askin'

Indeed and thank you!! Yes - if you have any improvement suggestions, or anything which you'd like added, let me know and I'll see what I can do!

I also see that I made a few spelling mistakes, and a few kind folks here have already submitted issues to let me know, so I'll correct them soon! Thank you all for the feedback and for the help and suggestions! I really appreciate it!

Re: Intuitive Guide to Maxwell's Equations

#79

Post by BoiledCabbage »

rovolo wrote: post #71
BoiledCabbage wrote: post #58

Earlier quoted context omitted.

I'd even be more ok with that, if mathematicians used more rigor in their notation. Math developed in a time where it was tedious to write this out by hand and a lot was hidden in abbreviations and assumptions. One thing that programming gets very right is that it is way more explicit (although obviously not perfectly) the behavior behind any notation. It's one thing that Structure and Interpretation of Classical Mec…

> Even the description of the Laplacian is wrong. The value isn't the average of the points surrounding it. The description on page 7 is split into two parts. The first part describes the value of the Laplacian correctly: > It tells us how the temperature value at the point compares to the average value of its neighboring points. The second part describes the long-run behavior of the differential equation > The tempe…

> The second part describes the long-run behavior of the differential equation

> The temperature value that this point takes is the average temperature of the points surrounding it

And this is not correct. Excluding a final state when all temperature values are identical, at no point is the temperature value equal to the average of the surrounding values. You aren't describing and evolution if its inaccurate for all points except a final state.

On top of that, even during the evolution the temperature isn't what's taking on the "average" of surrounding points, it the change in temperature wrt time that's being change by the average of points. And yet again, it's not an average of the surrounding temperatures is and average of the surrounding differences in temperature.

And this interaction we've had highlights exactly my point. English is an impressive language, and Mathematics is full of hand wavy explanations that come with simplicity context that isn't explicity and precisely defined. Mathematicians are used to it, and of course it's learnable like anything. My point is it's not necessary, it evolved in a different time with different constraints. Its a similar example of "the medium is the message" - math evolved when the only way to write was by hand, and duplication of definitions was manually expensive. We don't need these handwavy shortcuts now - we can make it easier for students to learn by being precise and providing definitions for them to see exactly what's happening - not expect them to learn from trying to recall every imagined context. And the fall back of "I had to learn it this way, so they should too", is a horrible excuse.

Re: Intuitive Guide to Maxwell's Equations

#80

Post by machawinka »

lordgrenville wrote: post #70
ghaff wrote: post #7

Earlier quoted context omitted.

Wikipedia is probably the most obvious modern exemplar of this. The editors of most mathematics articles clearly are much fonder of playing with the equations editor than they are of actually explaining things.

A good description I read of Wikipedia maths articles was that they're like the blackboard of a graduate-level class after everyone has left. All the information is there, but if you're not already familiar with the subject there's no way you'll grasp anything.

Great analogy.
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