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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...

⬐ tntn

I'll second that book recommendation.

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.

⬐ ncmncm

It was deForest, particularly, who pretended to originality. I should have written "got".

⬐ iorrus

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.

⬐ wnoise

It was my understanding that the original Maxwell equations used separate letters for each component rather than indices or any modern method of writing down the components as a unified thing (so the four expand to at least 12 separate equations (20, once you factor in constitutive and continuity equations)). Later on, he did use quaternions to organize like quantities, as we would use vectors, but still generally worked component-by-component. But yes, the most common modern versions are effectively due to Heaviside.

⬐ ncmncm

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

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

⬐ srean

Gibbs free energy and the entire body of literature on classical statistical thermodynamics. That alone would have been a enviable legacy to leave behind.

⬐ segfaultbuserr

My realization about Gibbs's contributions was reading an article about Fourier analysis in electronics, the article said when you approximate a square wave by using a series of sine waves, there will be overshoots at the edges, and this problem is called "Gibbs phenomenon".

What, "Gibbs"? Wasn't he the physicist working on the physics behind chemical reactions? So he did some applied mathematics, too? It shouldn't be the same person, is it? Then I've read his Wikipedia article...

And ironically, Gibbs phenomenon was initially discovered by an unnamed mathematician Henry Wilbraham in 1848, not Gibbs, but his paper was ignored and forgotten, like many other important ones in the history of science...

⬐ DoctorOetker

the physics equivalent to vi/emacs flamewars doesn't need any more fuel please...

https://en.wikipedia.org/wiki/Nabla_symbol#History

Also curious, which of Maxwell's texts you are referencing?

⬐ iorrus

“He took these books home and tried to find out. He succeeded after some trouble, but found some of the properties of vectors professedly proved were wholly incomprehensible. How could the square of a vector be negative? And Hamilton was so positive about it. After the deepest research, the youth gave it up [and] died.

My own introduction to quaternions took place in quite a different manner. Maxwell exhibited his main results in quaternionic form in his treatise. I went to Prof. Tait’s treatise to get information, and to learn how to work them. I had the same difficulties as the deceased youth, but by skipping them, was able to see that quaternions could be explored consistently in vectorial form. But on proceeding to apply quaternionics to the development of electrical theory, I found it very inconvenient. ... So I dropped out the quaternions altogether, and kept to pure scalars and vectors....” —Heaviside

⬐ jacobolus

Arguably the reason that generations of STEM students have been horribly confused about 3-dimensional vectors and rotations (including electric/magnetic fields), etc. is that they were reframed in the confused and non-generalizable Gibbs/Heaviside language, instead of in Grassmann/Clifford’s formalism in which vectors and bivectors can be properly described as separate types of objects.

It can be so much nicer. http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf

⬐ MaxBarraclough

Reminds me, I've been meaning to read this [0] blog post for a while now. (See also the HN discussion [1].) My clueless intuition tells me its points may be analogous to your linked document. (It mentions Heaviside, at least.)

[0] https://www.gamedev.net/articles/programming/math-and-physic...

[1] https://news.ycombinator.com/item?id=18365433

⬐ jacobolus

Perhaps start with https://www.shapeoperator.com/2016/12/12/sunset-geometry/ for a concrete example.

⬐ MaxBarraclough

Looks good, thanks.

⬐ iorrus

Wow Thanks for that... fascinating.

⬐ whatshisface

Geometric algebra obscures the point that what really matters is the algebraic structure. There are many ways to construct things that behave the same way (subgroups of matrices, vectors and the cross product, and so on), and while it is nice to invent one construction that gives you everything, you risk loosing sight of the fact that each construction is arbitrary and what really matters is its algebraic structure. That's why it's good to expose students to many partial, fragmented devices, so that they will realize the deeper point that underlies them all. With spin matrices, it is obvious that they are arbitrary manifestations of a group, but if a student were to spend their entire education manipulating blades they might start getting the idea that in some sense the universe was "made out of them."

⬐ aaachilless

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

⬐ ducktective

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.

⬐ beautifulfreak

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...

⬐ adrianratnapala

> 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.

[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.

⬐ eng101

*Heaviside

If you ever used Laplace transforms to solve differential equations, that is Heavisides work too.

Good book: http://www.amazon.com/Oliver-Heaviside-Electrical-Genius-Vic...

⬐ bainsfather

I've read that book, it is very good. A fantastic story/subject, though probably not for a general audience, just those interested in a detailed history of Heaviside and his work. It's nice to see a well-written 'technical' history book - so often such books are written by someone who doesn't really understand the subject - this is an exception.

You are mistaken about Laplace Transforms - Heaviside used a different method which was rather ad-hoc - sometimes it works, sometimes not. For the same problems, we now use Laplace Transforms instead, because they are better/cleaner.

For those interested in the history and mathematical development of Maxwell's Equations as we know them today, Paul J. Nahin's book on Heaviside[1] is a must read.

[1] http://www.amazon.com/Oliver-Heaviside-Electrical-Genius-Vic...

⬐ madengr

Ditto. Good book.

The following two books are a fascinating look at Heaviside's contributions and extraordinary life:

http://www.amazon.com/Maxwellians-Cornell-History-Science/dp...

http://www.amazon.com/Oliver-Heaviside-Electrical-Genius-Vic...