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 <del>took</del> got the credit.
Today Heaviside's method is taught as Laplace transforms, with Heaviside's name scrubbed off. We only hear of him as an alternative name for the step function, the integral of the Dirac impulse function, and of the "Heaviside layer", the ionosphere that makes transcontinental radio actually possible, but we would have waited decades longer without him.
An excellent reference for the importance of Heaviside in the ultimate success of application if Maxwell's theory is Paul J. Nahin,
"Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age", https://www.amazon.com/Oliver-Heaviside-Electrical-Genius-Vi...
> This is in a long tradition of English neglect, ultimately traceable to Heaviside's status as a commoner
This is unfair on the English. Glancing at their wikipedia entries, Heavyside doesn't seem any more common than [Dirac][1] or [Faraday][2]. If I had to guess at a sociological reason why Heavyside got ignored, it's that he got caught in the transition when people started learning engineering through universities rather than apprenticeships.
Heavyside's uncle Charles Wheatstone was a tradie who never went to unversity, but got knighted for services to electrical engineering. Faraday was another tradie who joined the Royal Society eight years before he got an (honorary) university degree. But in a later age Dirac became a world famous scientist, but would probably have gone nowhere if he hadn't got a scholarship to study electrical engineering at a university.
We can't wag our finger at Victorian English society for a the sin of credentialism when our own society does it much more vigorously. It's especially for our own profession, as programming is much more a craft than a thing you can learn at university.
It's incredible that you can ask a graduating class of EEs if they know of heaviside and only get some mumbling about a step function, given that Heaviside developed the majority of the fundamental ideas still used in EE. Complex impedance, vector calculus, Maxwell's equations, telegrapher's equations, precursors of s-domain methods, inductive loading, many of the names for AC circuit concepts.
I think Hertz acknowledged Heaviside's contributions, though, and didn't intentionally take credit for his work. I could be confused, though.
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.
In university in eng.math, diff.eq, electromagnetism and signals and systems courses, we had a "Heaviside Method" (with this exact name) in deriving the numerator coefficients in partial fraction expansion process of yielding time-domain equivalents of s-domain functions. I specifically remember my professor saying that this method is ascribed to "Heaviside" so much so that I later googled him and read his Wikipedia entry.
E&M is far from "simple". It contains special relativity, for starters. Also it is incompatible with thermodynamics: solving this problem is why Planck invented quantum mechanics. Also point charges have infinite energy: this problem leads to renormalization theory. Also it introduces gauge invariance, an essential but complex part of all modern theories. And lastly, the mathematics of E&M is a big step up from Newtonian theory.
>"E&M is far from "simple". It contains special relativity, for starters."
A theory (which is just a set of assumed first principles and rules of logic) can be simple but allow you to deduce vast complexity from it. In fact, it is ideal for a theory to be as simple as possible.
I can't begin to imagine why this would trigger a downvote. Are there people out there who prefer complex theories that make things more difficult to understand than necessary? Perhaps because it makes them feel smart or something, I don't know.
But that is basically saying you dislike science, because the point of science is to synthesize information into a small set of simple "laws" that allow us to deduce accurate and precise predictions.
E&M is simple in the sense that the equations that govern the relationship between the charge distribution and the electromagnetic field are quite simple. And the equations governing how charges move in an electromagnetic field are quite simple. I think this is what Dyson has in mind. Understanding the implications and limitations of those equations is not simple at all.
An even more blatant difficulty with E&M, related to your third point, is that it is schizophrenic. Given the trajectories of charges it will tell you what the electromagnetic field will be, and given the electromagnetic field it will tell you how charges will move. Unfortunately, these two parts of the theory seem to be incompatible, and the theory will not tell you how fields + charges will evolve in time.
Dyson's statement was about Maxwell's theory, not all of E&M and its interactions with every other physical theory. There are no point charges in Maxwell's theory, for example.
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 mock Ballmer when he laughed at the iphone back in 2007 (back when this essay was written). But his comment made sense for his customer base. He (and nor could Apple) couldn't really see that the game was changing.
Dyson points out that Maxwell himself had the same problem.
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.
Interesting. And makes me wonder what else we are missing and misunderstanding, as we waste so much time trying to express the complexity of the world in spoken language rather than math. Not just physics but in sociology, psychology, economics etc.
Faraday purely from experiments 30-40 years before Maxwell, intuitively understood electromagnetism. Nobody serious believed it because he didn't have the training to express it mathematically. Dyson is saying it took Physicists another 20-30 years post Maxwell to get it. So basically ~70 years wasted.
Wasted implies the solution is somehow obvious but that’s hindsite bias. Looking at lotto winners it feels easy. But, the reality is a lot of effort went to things both promising and wacky to get those steps forward. And other less major progress is being glossed over.
> Pupin went first to Cambridge and enrolled as
a student, hoping to learn the theory from
Maxwell himself. He did not know that Maxwe
ll had died four years earlier. After learning
that Maxwell was dead, he stayed on in Cambridge
and was assigned to a college tutor.
It wasn't that people spend all those years actually working on this problem. There wasn't an internet nor modern travel to share/disseminate/argue about these ideas.
In truth, it generally takes significant time to arrive at fundamental theories. Most people don't realize this because in a physics class, at best, you might get taught when so-and-so published an equation.
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.
Yes, but the formulation in that paper is really not the best one. Electromagnetism is best formulated in geometric algebra of 4-space (3 space dimensions + 1 time dimension), not 3-space.
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 strange integration surfaces to make Maxwell's equations work out for things like capacitors or motors. (The Heaviside-Hertz pedagogy that everybody is STILL taught is particularly problematic to use for motors.)
> In 1887, the Michelson–Morley experiment gave the first experimental disproof of the "aether".
In what way is LIGO not a bigger, and successful, version of the Michelson-Morley experiment?
I'm honestly asking, because from my limited understanding, it seems to be.
From Wiki:
> This result is generally considered to be the first strong evidence against the then-prevalent aether theory, and initiated a line of research that eventually led to special relativity, which rules out a stationary aether.
It seems that LIGO merely confirmed properties of an existent aether, not that we no longer believe in one:
> Aether theories (also known as ether theories) in physics propose the existence of a medium, the aether (also spelled ether, from the Greek word (αἰθήρ), meaning "upper air" or "pure, fresh air"[1]), a space-filling substance or field, thought to be necessary as a transmission medium for the propagation of electromagnetic or gravitational forces.
Naively, spacetime and quantum fields are both forms of aether theories.
Maxwell did not use vector calculus, which actually makes it pisser to understand because it bypasses having to convert the vectors to coordinates. I find short hand notion more confusing than writing it all out even if the latter takes more room. I did not understand general relativity at all until I saw an example where everything was written out and then it made much more sense
This is something of a myth. Maxwell actually uses both to ease the mathematical pain for his readers - he writes the equations out coordinate by coordinate, and he also compresses them using Hamilton's (quaternion) model of vectors. In fact Maxwell was the one who introduced the gradient, curl, and divergence (actually he used convergence) operators, and he addressed precisely your concern in his book by giving both formulations!
I have a copy of Maxwell's two volumes on electromagnetism and what makes it difficult to read for me is that his "equations" are actually a long list of disparate equations that describe a unified theory. It's not a simple "answer" such as E=mc^2, it is a series of such descriptor answers.
Mathematically, it is easier for me to focus on one aspect and study that aspect's equations (at a time).
>We still have passionate arguments between believers in various interpretations of quantum mechanics, the
Copenhagen interpretation, the many-worlds interpretation, the decoherence interpretation,
the hidden-variables interpretation, and many others.
The theory is very easy to understand.
Its the differential notation and manipulation of said notation that is challenging for people who dont math often
Say what? Start with the integral representations of the equations a la Halliday and Resnick. You can do tons of useful problems. Once you understand vector calculus, you will understand the equations as written in differential form. Then, pick up a copy of Purcell to see how magnetism comes out of the Lorentz transformation of electrostatics. If you are mainly interested in applied problems, go through Corson and Lorraine. Finally: 1. Realize that the treatment of ferromagnetism is much too limited in most E&M texts. 2. Optics is also worthless in those books. It is a field unto itself, with theoretical, applied, and quantum parts all handled by different books. 3. You don’t use Feynman’s Lectures to learn anything the first time. You use them to see if you understand physics as well as Feynman (you don’t.). All the problems have to have been done BEFORE this step.
[+] [-] ncmncm|7 years ago|reply
Today Heaviside's method is taught as Laplace transforms, with Heaviside's name scrubbed off. We only hear of him as an alternative name for the step function, the integral of the Dirac impulse function, and of the "Heaviside layer", the ionosphere that makes transcontinental radio actually possible, but we would have waited decades longer without him.
An excellent reference for the importance of Heaviside in the ultimate success of application if Maxwell's theory is Paul J. Nahin, "Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age", https://www.amazon.com/Oliver-Heaviside-Electrical-Genius-Vi...
[+] [-] adrianratnapala|7 years ago|reply
This is unfair on the English. Glancing at their wikipedia entries, Heavyside doesn't seem any more common than [Dirac][1] or [Faraday][2]. If I had to guess at a sociological reason why Heavyside got ignored, it's that he got caught in the transition when people started learning engineering through universities rather than apprenticeships.
[1]: https://en.wikipedia.org/wiki/Paul_Dirac#Early_years [2]: https://en.wikipedia.org/wiki/Michael_Faraday#Early_life
Heavyside's uncle Charles Wheatstone was a tradie who never went to unversity, but got knighted for services to electrical engineering. Faraday was another tradie who joined the Royal Society eight years before he got an (honorary) university degree. But in a later age Dirac became a world famous scientist, but would probably have gone nowhere if he hadn't got a scholarship to study electrical engineering at a university.
We can't wag our finger at Victorian English society for a the sin of credentialism when our own society does it much more vigorously. It's especially for our own profession, as programming is much more a craft than a thing you can learn at university.
[+] [-] tntn|7 years ago|reply
It's incredible that you can ask a graduating class of EEs if they know of heaviside and only get some mumbling about a step function, given that Heaviside developed the majority of the fundamental ideas still used in EE. Complex impedance, vector calculus, Maxwell's equations, telegrapher's equations, precursors of s-domain methods, inductive loading, many of the names for AC circuit concepts.
I think Hertz acknowledged Heaviside's contributions, though, and didn't intentionally take credit for his work. I could be confused, though.
[+] [-] iorrus|7 years ago|reply
[+] [-] aaachilless|7 years ago|reply
[+] [-] ducktective|7 years ago|reply
[+] [-] beautifulfreak|7 years ago|reply
[+] [-] wmnwmn|7 years ago|reply
[+] [-] nonbel|7 years ago|reply
A theory (which is just a set of assumed first principles and rules of logic) can be simple but allow you to deduce vast complexity from it. In fact, it is ideal for a theory to be as simple as possible.
The "game of life" is not really a theory, but it demonstrates that simple rules can lead to surprising complexity: https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life
EDIT:
I can't begin to imagine why this would trigger a downvote. Are there people out there who prefer complex theories that make things more difficult to understand than necessary? Perhaps because it makes them feel smart or something, I don't know.
But that is basically saying you dislike science, because the point of science is to synthesize information into a small set of simple "laws" that allow us to deduce accurate and precise predictions.
[+] [-] jules|7 years ago|reply
An even more blatant difficulty with E&M, related to your third point, is that it is schizophrenic. Given the trajectories of charges it will tell you what the electromagnetic field will be, and given the electromagnetic field it will tell you how charges will move. Unfortunately, these two parts of the theory seem to be incompatible, and the theory will not tell you how fields + charges will evolve in time.
[+] [-] tntn|7 years ago|reply
[+] [-] unknown|7 years ago|reply
[deleted]
[+] [-] weedwarrior|7 years ago|reply
[+] [-] gumby|7 years ago|reply
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 mock Ballmer when he laughed at the iphone back in 2007 (back when this essay was written). But his comment made sense for his customer base. He (and nor could Apple) couldn't really see that the game was changing.
Dyson points out that Maxwell himself had the same problem.
[+] [-] hopler|7 years ago|reply
In contrast to Microsoft whose business was providing stable solutions and extracting monopoly rents.
[+] [-] k9s9|7 years ago|reply
Faraday purely from experiments 30-40 years before Maxwell, intuitively understood electromagnetism. Nobody serious believed it because he didn't have the training to express it mathematically. Dyson is saying it took Physicists another 20-30 years post Maxwell to get it. So basically ~70 years wasted.
[+] [-] tim333|7 years ago|reply
By the way looking at Maxwell's paper it seems awful complicated https://royalsocietypublishing.org/doi/pdf/10.1098/rstl.1865...
compared to the modern form of the equations https://ethw.org/w/images/d/d6/Maxwell_image_02.jpg
[+] [-] Retric|7 years ago|reply
[+] [-] madengr|7 years ago|reply
Hertz proved it experimentally, and Heaviside turned it into an engineering discipline.
[+] [-] pm90|7 years ago|reply
It wasn't that people spend all those years actually working on this problem. There wasn't an internet nor modern travel to share/disseminate/argue about these ideas.
[+] [-] naringas|7 years ago|reply
to call those years wasted implies that we shouldn't have had to wait for them. it suggests that we should look for a way to bypass them.
[+] [-] grigjd3|7 years ago|reply
[+] [-] ncmncm|7 years ago|reply
[+] [-] killjoywashere|7 years ago|reply
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.
[+] [-] amatthew|7 years ago|reply
[+] [-] amelius|7 years ago|reply
[+] [-] Koshkin|7 years ago|reply
[+] [-] jules|7 years ago|reply
[+] [-] bsder|7 years ago|reply
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 strange integration surfaces to make Maxwell's equations work out for things like capacitors or motors. (The Heaviside-Hertz pedagogy that everybody is STILL taught is particularly problematic to use for motors.)
[+] [-] NotAnEconomist|7 years ago|reply
In what way is LIGO not a bigger, and successful, version of the Michelson-Morley experiment?
I'm honestly asking, because from my limited understanding, it seems to be.
From Wiki:
> This result is generally considered to be the first strong evidence against the then-prevalent aether theory, and initiated a line of research that eventually led to special relativity, which rules out a stationary aether.
It seems that LIGO merely confirmed properties of an existent aether, not that we no longer believe in one:
> Aether theories (also known as ether theories) in physics propose the existence of a medium, the aether (also spelled ether, from the Greek word (αἰθήρ), meaning "upper air" or "pure, fresh air"[1]), a space-filling substance or field, thought to be necessary as a transmission medium for the propagation of electromagnetic or gravitational forces.
Naively, spacetime and quantum fields are both forms of aether theories.
[+] [-] paulpauper|7 years ago|reply
[+] [-] earthicus|7 years ago|reply
[+] [-] mikorym|7 years ago|reply
Mathematically, it is easier for me to focus on one aspect and study that aspect's equations (at a time).
[+] [-] UncleSlacky|7 years ago|reply
To me, this just sounds like typical British understatement, which I'm sure the audience at the time would have understood.
[+] [-] unknown|7 years ago|reply
[deleted]
[+] [-] naringas|7 years ago|reply
lukcily there has been slight progress since 2007 https://www.quantamagazine.org/frauchiger-renner-paradox-cla...
[+] [-] almaya|7 years ago|reply
[+] [-] unknown|7 years ago|reply
[deleted]
[+] [-] weedwarrior|7 years ago|reply
[+] [-] aj7|7 years ago|reply
[+] [-] twtw|7 years ago|reply
Dyson describes the theory as "simple and intelligible" once you accept the concept of fields, which was very much foreign in Maxwell's time.