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Intuitive Guide to Maxwell's Equations

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Re: Intuitive Guide to Maxwell's Equations

#91

Post by fsckboy »

uoaei wrote: post #41
fsckboy wrote: post #34

Earlier quoted context omitted.

just a quibble, if your Calculus 101 covers div and curl, you are going to an intense STEM school and really could be expected to understand the math.

Understanding the math and understanding the importance of the mathematical concept are two different things. Personally, div and curl didn't quite click for me until I took fluid dynamics in my final year. I could do the homework but didn't really get why they were useful until it made sense why "div = 0 always for incompressible fluids".

ok, but my point was that div and curl were taught in 102, not 101 (which you easily could have placed out of). therefore, the reasoning goes, if they were in 101, that must be a hyper 101.

source: went to intense STEM school

Re: Intuitive Guide to Maxwell's Equations

#92

Post by rovolo »

BoiledCabbage wrote: post #79
rovolo wrote: post #71

Earlier quoted context omitted.

> 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…

> 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.

The average of the surrounding points is the attractor temperature for the system. It is an asymptote which the temperature of the point is moving towards. It's like saying an oscillator (such as a spring) wants to be at neutral, even though it never comes to rest at neutral.

I'm not engaging with your larger point, I'm just quibbling with you saying page 7 is wrong. I think that "takes" in the english description says that the temperature approaches the value over time, whereas you interpreted "takes" as referring to the temperature at every point in time.

Re: Intuitive Guide to Maxwell's Equations

#93

Post by BoiledCabbage »

rovolo wrote: post #92
BoiledCabbage wrote: post #79

Earlier quoted context omitted.

> 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…

> 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. The average of the surrounding points is the attractor temperature for the system. It is an asymptote which the temperature of the point is moving towards. It's like saying an…

> I'm not engaging with your larger point, I'm just quibbling with you saying page 7 is wrong. I think that "takes" in the english description says that the temperature approaches the value over time, whereas you interpreted "takes" as referring to the temperature at every point in time.

I hear you, and I think we've probably approaching the end of the productive part of our conversation.

I do want to mention that the quote above, and interpretation of "takes" is exactly my larger point though. These definitions are all sloppy and prone to interpretation. Precise definitions would eliminate the need for all of this.

And since I can't help myself, thinking about this a little more, even your interpretation above is either faulty, or has to change the definition of "surrounding". If I have a point of average temperature, a doughnut or sphere of warmer points a small distance immediately around it and then the majority of all other points around that being colder, then the asymptote is actually towards the average of the of outer colder points, not the surrounding warmer points.

Re: Intuitive Guide to Maxwell's Equations

#94

Post by BoiledCabbage »

kanzenryu2 wrote: post #77
ArubaJamaica wrote: post #56

Earlier quoted context omitted.

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...

Great link - thanks for sharing. Beautiful explanations.

Re: Intuitive Guide to Maxwell's Equations

#95

Post by OscarCunningham »

danharaj wrote: post #31
OscarCunningham wrote: post #12

Earlier quoted context omitted.

You can even write them in terms of the four-vector A rather than F (related by F = dA) to reduce them to d dA = J.

escape your hodge duals fam

Ha that's funny. I'd been copying my notation from the parent post, and I assumed 'd' was just their notation. I didn't realise they meant to say

    *d*
(apparently HN doesn't let you escape asterisks).
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