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Intuitive Guide to Maxwell's Equations

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Re: Intuitive Guide to Maxwell's Equations

#51

Post by rusk »

JadeNB wrote: post #10
chronolitus wrote: post #3

These kinds of visual, well thought out explanations of topics which are often taught with terse, obscure and uninviting methods are a gift. On a tangent: I remember asking my Calculus 101 professor what the "intuitive meaning" of divergence and curl was, outside of the formal math and equations. He was shocked that one could ask to sully these perfect mathematical concepts with dirty intuitive reductions. A guide li…

I love explanations of concepts that appeal to people in new and different ways, and I thank anyone clever, patient, and gifted enough to produce them. The world is a better place when more people understand are not afraid of more things. But I think it's important to remember that mathematics is not some evil thing! There are people who train carefully so that the terse mathematical explanations are the intuition. T…

That was beautiful

Re: Intuitive Guide to Maxwell's Equations

#52

Post by devalgo »

ghaff wrote: post #7
chronolitus wrote: post #3

These kinds of visual, well thought out explanations of topics which are often taught with terse, obscure and uninviting methods are a gift. On a tangent: I remember asking my Calculus 101 professor what the "intuitive meaning" of divergence and curl was, outside of the formal math and equations. He was shocked that one could ask to sully these perfect mathematical concepts with dirty intuitive reductions. A guide li…

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.

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

Re: Intuitive Guide to Maxwell's Equations

#53

Post by ericol »

ghaff wrote: post #7
chronolitus wrote: post #3

These kinds of visual, well thought out explanations of topics which are often taught with terse, obscure and uninviting methods are a gift. On a tangent: I remember asking my Calculus 101 professor what the "intuitive meaning" of divergence and curl was, outside of the formal math and equations. He was shocked that one could ask to sully these perfect mathematical concepts with dirty intuitive reductions. A guide li…

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.

This, yes. To this day of the several dozen that I visited, I'm yet to find a math related article that serves the purpose of explaining the concepts laid in it.

Re: Intuitive Guide to Maxwell's Equations

#54

Post by kgwgk »

devalgo wrote: post #52
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.

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

What's the point of "understanding” QM intuitively if it brings confusion rather than understanding?

Re: Intuitive Guide to Maxwell's Equations

#55

Post by devalgo »

kgwgk wrote: post #54
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!

What's the point of "understanding” QM intuitively if it brings confusion rather than understanding?

You literally can't understand something if you are confused by it. Your question makes no sense.

Re: Intuitive Guide to Maxwell's Equations

#56

Post by ArubaJamaica »

devalgo wrote: post #52
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.

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 explanation of electron behavior being both wave and particle like. Why should we try to categorize the behavior a subatomic particle (an entity so distant from our experiential reality) as being analogous to one of two macroscopic entities?

I totally get the desire for intuitive understanding, and it should be encouraged, but sometimes you just have to put intuition aside and come to conclusions with pure mathematical reasoning.

Re: Intuitive Guide to Maxwell's Equations

#57

Post by QuesnayJr »

soVeryTired wrote: post #46
uoaei wrote: post #40

Earlier quoted context omitted.

There are many anecdotal reports of tyrannical Wikipedia editors doing exactly this. They claim dominion over a subset of Wikipedia articles and then manicure them exactly to their own personal tastes. I'm sure the situation you describe happens often in various corners of the website.

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.

Re: Intuitive Guide to Maxwell's Equations

#58

Post by BoiledCabbage »

devalgo wrote: post #52
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.

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 Mechanics (which I haven't read) got really right in concept. It's a shame, that approach hasn't been adopted more widely.

Take for example page 7 of the pdf with the heat equation. Even the description of the Laplacian is wrong. The value isn't the average of the points surrounding it. But if this simple function were written in python as a "update" function over a multi-dim array of temperature values it'd be clear exactly what's happening.

Another example of simple inconsistency in notation: superscript, does that mean squared or not? When writing two terms adjacent is it multiplication or an operator being applied? Where is the behavior of the operator defined that a student and "read the code"?

English is an extremely verbose and imprecise language. Mathematicians replaced a verbose imprecise language with a terse imprecise language. It's about time for rigorous fields to take the last step and introduce precise concepts using a precisely defined language.

Re: Intuitive Guide to Maxwell's Equations

#59

Post by athinggoingon »

ghaff wrote: post #7
chronolitus wrote: post #3

These kinds of visual, well thought out explanations of topics which are often taught with terse, obscure and uninviting methods are a gift. On a tangent: I remember asking my Calculus 101 professor what the "intuitive meaning" of divergence and curl was, outside of the formal math and equations. He was shocked that one could ask to sully these perfect mathematical concepts with dirty intuitive reductions. A guide li…

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.

I wish there was an "intuition" wiki where you can learn the intuition first and then a link at the bottom takes you back to the Wikipedia page where you can stare at the math until you really get it.

Re: Intuitive Guide to Maxwell's Equations

#60

Post by mellosouls »

devalgo wrote: post #55
kgwgk wrote: post #54

Earlier quoted context omitted.

What's the point of "understanding” QM intuitively if it brings confusion rather than understanding?

You literally can't understand something if you are confused by it. Your question makes no sense.

Perhaps the comment was intended to convey the very different potential for intuitive "understanding" between visualisable classical theories and non-visualisable quantum theory.

At a fundamental conceptual level it does not map to anything in our normal experience - attempting to force analogies etc can end up confusing things further.

I agree with your original observation btw, but it's important to recognise the limits we may be bound by in explanation and comparison.

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