Just a heads-up because I’m working on a presentation about Heaviside and looking for examples of his operator method, and your site comes up pretty high in the search rankings.

Hi Tom. Thanks for your comment–I had never heard of this concept. I found that chapter of Needham’s book on one of his Visual Complex Analysis pages on the University of San Francisco website at http://usf.usfca.edu/vca//PDF/amplitwist.pdf

To quote slon, above, Heaviside was THE MAN!

Very interesting! I didn’t know that before. Thanks for the pointer. — Ron

Prof. Klein distinguishes three main classes of mathematicians—the intuitionists, the formalists or algorithmists, and the logicians. Now it is intuition that is most useful in physical mathematics, for that means taking a broad view of a question, apart from the narrowness of special mathematics. For what a physicist wants is a good view of the physics itself in its mathematical relations, and it is quite a secondary matter to have logical demonstrations. The mutual consistency of results is more satisfying, and exceptional peculiarities are ignored. It is more useful than exact mathematics.
But when intuition breaks down, something more rudimentary must take its place. This is groping, and it is experimental work, with of course some induction and deduction going along with it. Now, having started on a physical foundation in the treatment of irrational operators, which was successful, in seeking for explanation of some results, I got beyond the physics altogether, and was left without any guidance save that of untrustworthy intuition in the region of pure quantity. But success may come by the study of failures. So I made a detailed study and close examination of some of the obscurities before alluded to, beginning with numerical groping. The result was to clear up most of the obscurities, correct the errors involved, and by their revision to obtain correct formulae and extend results considerably.
Oliver Heaviside, Electromagnetic Theory, April 10, 1899. Vol.II p.460.

Since Laplace transforms are now used in preference to Heaviside’s operators, may I suggest a topic examining the relation between these?

‘The Laplace Transform is one of the many contributions to mathematics and physics of the Marquis Pierre Simon de Laplace (1749-1827), who pointed out the biunique relationship between the two functions and applied the results to the solution of differential equations in a paper published in 1779 with the rather cryptic title “On what follows”. The real value of the Laplace transform seems not to have been appreciated, however, for over a century, until it was essentially rediscovered and popularized by the eccentric British engineer Oliver Heaviside (1850-1925), whose studies had a major impact on many aspects of modern electrical engineering.’

and:

‘The use of impulse functions in science and engineering was popularized by the English physicist P.A.M.Dirac and by Oliver Heaviside long before impulses became “respectable” mathematically. Indeed we continue to use Dirac’s notation, δ(t), and the unit impulse is often called Dirac’s δ-function. Both Dirac and Heaviside stressed the idea that δ(t) was defined in terms of what it “did”. Thus Dirac said, “Whenever an improper function [e.g. impulse] appears it will be something which is to be used ultimately in an integrand—the use of improper functions thus does not involve any lack of rigour in the theory, but is merely a convenient notation, enabling us to express in a concise form certain relations which we could, if necessary, rewrite in a form not involving improper functions, but only in a cumbersome way which would tend to obscure the argument.’ Both quotes from Siebert W.McC. (1986): Circuits, Signals, and Systems; Cambridge, Mass.: MIT Press/ New York: McGraw-Hill. ISBN 0-07-057290-9.

One needs, however, to beware of Stigler’s law:

Stigler’s Law of Eponymy—“No scientific discovery is named after its original discoverer”. The law itself may be construed to contradict Stigler’s eponym. The Gaussian distribution was probably originated by de Moivre. It may also be noted that Laplace used ‘Fourier transforms’ before Fourier’s publication, and that Lagrange used ‘Laplace transforms’ before Laplace began his career. See p278. As Stigler quotes one historian’s view (from an unknown source) ‘Every scientific discovery is named after the last individual too ungenerous to give due credit to his predecessors’.
Stigler S. (1999): Statistics on the Table: the History of Statistical Concepts and Methods; Cambridge: Harvard University Press. ISBN 0-674-83601-4.

Thank you, Scott, I enjoyed reading this! I found your book (An Analog Electronics Companion: Basic Circuit Design for Engineers and Scientists is a link to the US Amazon site) and it looks very interesting, a physicist’s take on analog electronic design—not unlike Heaviside, really. I look forward to reading your book, as I used to be an analog/digital circuit design engineer at one point in my career. Your book looks like a refreshing read on the subject that I would particularly like.

Many moons ago, I had this quotation neatly penned and displayed in my study area. I must have found it in a book or magazine (yeah, those days ;-). Right now, Google only finds it in 3 pages from a couple of sources, apparently in audio electronics circles.

It may be spurious, but it’s at least “bene trovato” … Any confirmation/source gratefully received.

I haven’t heard this quote, but Heaviside was prolific in writing letters as well as articles, so I’m not surprised that he might have written it and not surprised that I haven’t come across it. Sounds just like him, though. If I come across the source of the quote I’ll drop you an email. Thanks for sharing it. — Ron

This was one of my early essays. In later essays I started creating the equations in LaTeX or Word Equation Editor and inserting them as images, which is infinitely better, particularly considering what the Georgia font does to numbers, etc. When I get a chance I’ll redo these. Thanks for the suggestion–I had totally forgotten that this essay had equations rendered in text. Meanwhile, if you click on the link at the bottom of the essay for the printer-friendly PDF version, you will see that the equations are rendered much better in the Times New Roman font of that file.

ps. also what the heck is with that anti-spam thing - do you really expect people to read that they have to add 80?…

The Wordpress Askimet plug-in has caught over 7,000 spam comments submitted to this blog over the last year or so. It was only a matter of time before spam got through their filter. So I started using a Wordpress anti-spam plug-in that required just the simple sum to be calculated, but it only slowed the spam mostly because, I guess, spambots worked around it. By modifying the plug-in code to require adding another value (chosen as 80) written in the text above the box, I’ve really reduced the spam that gets through to the Askimet filter. It’s also true that if an incorrect sum is submitted, a message appears reminding the commenter to add the 80. — Ron

Thank you for your comment, Ed—it makes a nice addendum to the essay! I had seen Mikusinski’s name when I was looking for references on Heaviside, but I didn’t pursue it. It’s also a fact that abstract algebra is not a strong suit of mine. I see that Mikusinski’s “Operational Calculus” is held by a local university library, and now I’m intrigued enough to retrieve the book and have a go at it. We’ll see.