Why is Maxwell's theory so hard to understand? (2007) [pdf] • Hacker News Board

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#51

Post by ncmncm » Sun, Jan 06, 2019, 8:35 PM UTC

iorrus wrote: post #36

ncmncm wrote: post #21

It is unfortunate that Dyson neglects the role of Oliver Heaviside, again. This is in a long tradition of English neglect, ultimately traceable to Heaviside's status as a commoner. Heaviside invented the mathematical tools we still use to understand and teach Maxwell, and most of the important consequences of the theory, but Pupin, Hertz, Marconi, and deForest used his methods and took got the credit. Today Heaviside…

Exactly, one of the main reasons why maxwell is so hard to understand is that everything is expressed using quarternions unlike Heaviside who expressed the equations using the vector notation we see them expressed in today. In reality ‘Maxwell’s’ equations are in fact Heaviside’s.

We should not neglect Josiah Willard Gibbs's notational contribution, either.

We otherwise hear of Gibbs mainly when we mention Gibbs free energy.

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#52

Post by aaachilless » Sun, Jan 06, 2019, 8:42 PM UTC

ncmncm wrote: post #21

It is unfortunate that Dyson neglects the role of Oliver Heaviside, again. This is in a long tradition of English neglect, ultimately traceable to Heaviside's status as a commoner. Heaviside invented the mathematical tools we still use to understand and teach Maxwell, and most of the important consequences of the theory, but Pupin, Hertz, Marconi, and deForest used his methods and took got the credit. Today Heaviside…

One of my maths professors was a humorous guy and in his lectures would, as an ongoing joke, only explicitly credit Heaviside and Hungarians.

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#53

Post by gumby » Sun, Jan 06, 2019, 9:18 PM UTC

hopler wrote: post #37

gumby wrote: post #6

I am struck by the clarity and simplicity of Dyson's writing. As to the substance: yes, hiding your work under a bushel does nobody any favor, but it's understandable when it feels like the alternative is the strident trumpeting of trivial "advancements". But also cautionary is the constraints due to the wrong metaphors. We often see this today in linear predictions as to the impact of some new idea. It's easy to moc…

Why would you say Apple, whose main business was an extensive traxk record in creating, promoting, and selling next generation technology, that their major investment in a new field was blind speculation? In contrast to Microsoft whose business was providing stable solutions and extracting monopoly rents.

Not sure I understand your point. Mine was that in science or business we are often held back from understanding by the limitations of our models, even when we ourselves are the inventors.

I thought I used an example well known to HN to make the point. Apple’s stated hope was to eventually have 1% of the market (and they didn’t originally plan for an App Store). Like Maxwell, they didn’t know they had a blockbuster.

Microsoft listened very closely to their customers, who were and are mainly corporate I/T and something like the iphone wasn’t something they said they wanted. In fact it honestly had no affordances that IT wanted.

Maxwell understood the math but his own mechanical metaphor distracted him, and other physicists too, so that they couldn’t really see the larger implications.

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#54

Post by beautifulfreak » Sun, Jan 06, 2019, 9:23 PM UTC

ncmncm wrote: post #21

It is unfortunate that Dyson neglects the role of Oliver Heaviside, again. This is in a long tradition of English neglect, ultimately traceable to Heaviside's status as a commoner. Heaviside invented the mathematical tools we still use to understand and teach Maxwell, and most of the important consequences of the theory, but Pupin, Hertz, Marconi, and deForest used his methods and took got the credit. Today Heaviside…

My thoughts exactly. Heaviside gets a chapter in the book, Strange Brains and Genius, which reveals some of the odder things about him: https://www.amazon.com/Strange-Brains-Genius-Eccentric-Scien...

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#55

Post by Koshkin » Sun, Jan 06, 2019, 9:23 PM UTC

amelius wrote: post #23

Some people hold the view that a better way of teaching electromagnetism is through geometric algebra. See: https://arxiv.org/abs/1010.4947

Also, the approach based on differential forms is very appealing; for a list of various formulations of electromagnetism, see https://en.m.wikipedia.org/wiki/Mathematical_descriptions_of...

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#56

Post by Koshkin » Sun, Jan 06, 2019, 9:35 PM UTC

iorrus wrote: post #38

bsder wrote: post #18

People didn't really get Maxwell because Maxwell's equations don't need a medium aka "aether". Waves propagating without a medium is a shocking message in this time frame. Maxwell published his equations in 1861/1862 in first form. In 1887, the Michelson–Morley experiment gave the first experimental disproof of the "aether". It also doesn't help that you have things like "displacement current" and have to find strang…

Maxwell’s works all assume an ether so it’s not really true to state that the equations don’t need one.

The aether is not required, assumed by or contained in the equations. Its existence was a physical hypothesis which was discarded after Einstein's work on special relativity and a multitude of related experiments.

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#57

Post by killjoywashere » Sun, Jan 06, 2019, 9:37 PM UTC

It's not until now, over 20 years later, that I realize what a magician my E&M prof was. After months of careful development of basic E&M, Maxwell's equations simply fell out. As I recall, it was capacitance that was the impetus. It was as though we had struggled in a dark tunnel for months and suddenly came around a turn and there was light. Not a little, but sheets of daylight and all the equations just fell together, one from the next. All the equations revealed themselves from the middle of one lecture to the middle of the next lecture.

And then, in E&M 2, with a different professor, I spent the entire semester coming to grips with the fact that the implications of these formulas would challenge my grasp on reality for the rest of my life.

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#58

Post by 19f191ty » Sun, Jan 06, 2019, 9:39 PM UTC

Koshkin wrote: post #55

amelius wrote: post #23

Some people hold the view that a better way of teaching electromagnetism is through geometric algebra. See: https://arxiv.org/abs/1010.4947

Also, the approach based on differential forms is very appealing; for a list of various formulations of electromagnetism, see https://en.m.wikipedia.org/wiki/Mathematical_descriptions_of...

Aren't the two very closely related, if not equivalent? Differential forms and Geometric Algebra I mean.

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#59

Post by tntn » Sun, Jan 06, 2019, 9:58 PM UTC

bsder wrote: post #18

People didn't really get Maxwell because Maxwell's equations don't need a medium aka "aether". Waves propagating without a medium is a shocking message in this time frame. Maxwell published his equations in 1861/1862 in first form. In 1887, the Michelson–Morley experiment gave the first experimental disproof of the "aether". It also doesn't help that you have things like "displacement current" and have to find strang…

Could you expand on the problems you have in mind with capacitors and motors? What do you mean by needing to find strange surfaces to "make Maxwell's equations work?" Do you mean find strange surfaces to get useful results, or that the results are wrong if you pick the "wrong" surfaces?

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#60

Post by earthicus » Sun, Jan 06, 2019, 10:08 PM UTC

Koshkin wrote: post #55

amelius wrote: post #23

Some people hold the view that a better way of teaching electromagnetism is through geometric algebra. See: https://arxiv.org/abs/1010.4947

Also, the approach based on differential forms is very appealing; for a list of various formulations of electromagnetism, see https://en.m.wikipedia.org/wiki/Mathematical_descriptions_of...

The differential forms approach also has the advantage over geometric algebra of being widely used by mathematicians and theoretical physicists, and perhaps increasingly used by physicists in general. If you're going to put in the effort to learn geometric algebra, learning differential forms instead would be much much more useful in opening up the literature to you. A 'lightweight' intro is [1].

[1] https://www.amazon.com/Electricity-Magnetism-Mathematicians-...