Saturday Night Science: The Forgotten Genius of Oliver Heaviside

“The Forgotten Genius of Oliver Heaviside” by Basil MahonAt age eleven, in 1861, young Oliver Heaviside’s family, supported by his father’s irregular income as an engraver of woodblock illustrations for publications (an art beginning to be threatened by the advent of photography) and a day school for girls operated by his mother in the family’s house, received a small legacy which allowed them to move to a better part of London and enroll Oliver in the prestigious Camden House School, where he ranked among the top of his class, taking thirteen subjects including Latin, English, mathematics, French, physics, and chemistry. His independent nature and iconoclastic views had already begun to manifest themselves: despite being an excellent student he dismissed the teaching of Euclid’s geometry in mathematics and English rules of grammar as worthless. He believed that both mathematics and language were best learned, as he wrote decades later, “observationally, descriptively, and experimentally.” These principles would guide his career throughout his life.

At age fifteen he took the College of Perceptors examination, the equivalent of today’s A Levels. He was the youngest of the 538 candidates to take the examination and scored fifth overall and first in the natural sciences. This would easily have qualified him for admission to university, but family finances ruled that out. He decided to study on his own at home for two years and then seek a job, perhaps in the burgeoning telegraph industry. He would receive no further formal education after the age of fifteen.

His mother’s elder sister had married Charles Wheatstone, a successful and wealthy scientist, inventor, and entrepreneur whose inventions include the concertina, the stereoscope, and the Playfair encryption cipher, and who made major contributions to the development of telegraphy. Wheatstone took an interest in his bright nephew, and guided his self-studies after leaving school, encouraging him to master the Morse code and the German and Danish languages. Oliver’s favourite destination was the library, which he later described as “a journey into strange lands to go a book-tasting”. He read the original works of Newton, Laplace, and other “stupendous names” and discovered that with sufficient diligence he could figure them out on his own.

At age eighteen, he took a job as an assistant to his older brother Arthur, well-established as a telegraph engineer in Newcastle. Shortly thereafter, probably on the recommendation of Wheatstone, he was hired by the just-formed Danish-Norwegian-English Telegraph Company as a telegraph operator at a salary of £150 per year (around £12000 in today’s money). The company was about to inaugurate a cable under the North Sea between England and Denmark, and Oliver set off to Jutland to take up his new post. Long distance telegraphy via undersea cables was the technological frontier at the time—the first successful transatlantic cable had only gone into service two years earlier, and connecting the continents into a world-wide web of rapid information transfer was the booming high-technology industry of the age. While the job of telegraph operator might seem a routine clerical task, the élite who operated the undersea cables worked in an environment akin to an electrical research laboratory, trying to wring the best performance (words per minute) from the finicky and unreliable technology.

Heaviside prospered in the new job, and after a merger was promoted to chief operator at a salary of £175 per year and transferred back to England, at Newcastle. At the time, undersea cables were unreliable. It was not uncommon for the signal on a cable to fade and then die completely, most often due to a short circuit caused by failure of the gutta-percha insulation between the copper conductor and the iron sheath surrounding it. When a cable failed, there was no alternative but to send out a ship which would find the cable with a grappling hook, haul it up to the surface, cut it, and test whether the short was to the east or west of the ship’s position (the cable would work in the good direction but fail in that containing the short. Then the cable would be re-spliced, dropped back to the bottom, and the ship would set off in the direction of the short to repeat the exercise over and over until, by a process similar to binary search, the location of the fault was narrowed down and that section of the cable replaced. This was time consuming and potentially hazardous given the North Sea’s propensity for storms, and while the cable remained out of service it made no money for the telegraph company.

Heaviside, who continued his self-study and frequented the library when not at work, realised that knowing the resistance and length of the functioning cable, which could be easily measured, it would be possible to estimate the location of the short simply by measuring the resistance of the cable from each end after the short appeared. He was able to cancel out the resistance of the fault, creating a quadratic equation which could be solved for its location. The first time he applied this technique his bosses were sceptical, but when the ship was sent out to the location he predicted, 114 miles from the English coast, they quickly found the short circuit.

At the time, most workers in electricity had little use for mathematics: their trade journal, The Electrician (which would later publish much of Heaviside’s work) wrote in 1861, “In electricity there is seldom any need of mathematical or other abstractions; and although the use of formulæ may in some instances be a convenience, they may for all practical purpose be dispensed with.” Heaviside demurred: while sharing disdain for abstraction for its own sake, he valued mathematics as a powerful tool to understand the behaviour of electricity and attack problems of great practical importance, such as the ability to send multiple messages at once on the same telegraphic line and increase the transmission speed on long undersea cable links (while a skilled telegraph operator could send traffic at thirty words per minute on intercity land lines, the transatlantic cable could run no faster than eight words per minute). He plunged into calculus and differential equations, adding them to his intellectual armamentarium.

He began his own investigations and experiments and began to publish his results, first in English Mechanic, and then, in 1873, the prestigious Philosophical Magazine, where his work drew the attention of two of the most eminent workers in electricity: William Thomson (later Lord Kelvin) and James Clerk Maxwell. Maxwell would go on to cite Heaviside’s paper on the Wheatstone Bridge in the second edition of his Treatise on Electricity and Magnetism, the foundation of the classical theory of electromagnetism, considered by many the greatest work of science since Newton’s Principia, and still in print today. Heady stuff, indeed, for a twenty-two year old telegraph operator who had never set foot inside an institution of higher education.

Heaviside regarded Maxwell’s Treatise as the path to understanding the mysteries of electricity he encountered in his practical work and vowed to master it. It would take him nine years and change his life. He would become one of the first and foremost of the “Maxwellians”, a small group including Heaviside, George FitzGerald, Heinrich Hertz, and Oliver Lodge, who fully grasped Maxwell’s abstract and highly mathematical theory (which, like many subsequent milestones in theoretical physics, predicted the results of experiments without providing a mechanism to explain them, such as earlier concepts like an “electric fluid” or William Thomson’s intricate mechanical models of the “luminiferous ether”) and built upon its foundations to discover and explain phenomena unknown to Maxwell (who would die in 1879 at the age of just 48).

While pursuing his theoretical explorations and publishing papers, Heaviside tackled some of the main practical problems in telegraphy. Foremost among these was “duplex telegraphy”: sending messages in each direction simultaneously on a single telegraph wire. He invented a new technique and was even able to send two messages at the same time in both directions as fast as the operators could send them. This had the potential to boost the revenue from a single installed line by a factor of four. Oliver published his invention, and in doing so made an enemy of William Preece, a senior engineer at the Post Office telegraph department, who had invented and previously published his own duplex system (which would not work), that was not acknowledged in Heaviside’s paper. This would start a feud between Heaviside and Preece which would last the rest of their lives and, on several occasions, thwart Heaviside’s ambition to have his work accepted by mainstream researchers. When he applied to join the Society of Telegraph Engineers, he was rejected on the grounds that membership was not open to “clerks”. He saw the hand of Preece and his cronies at the Post Office behind this and eventually turned to William Thomson to back his membership, which was finally granted.

By 1874, telegraphy had become a big business and the work was increasingly routine. In 1870, the Post Office had taken over all domestic telegraph service in Britain and, as government is wont to do, largely stifled innovation and experimentation. Even at privately-owned international carriers like Oliver’s employer, operators were no longer concerned with the technical aspects of the work but rather tending automated sending and receiving equipment. There was little interest in the kind of work Oliver wanted to do: exploring the new horizons opened up by Maxwell’s work. He decided it was time to move on. So, he quit his job, moved back in with his parents in London, and opted for a life as an independent, unaffiliated researcher, supporting himself purely by payments for his publications.

With the duplex problem solved, the largest problem that remained for telegraphy was the slow transmission speed on long lines, especially submarine cables. The advent of the telephone in the 1870s would increase the need to address this problem. While telegraphic transmission on a long line slowed down the speed at which a message could be sent, with the telephone voice became increasingly distorted the longer the line, to the point where, after around 100 miles, it was incomprehensible. Until this was understood and a solution found, telephone service would be restricted to local areas.

Many of the early workers in electricity thought of it as something like a fluid, where current flowed through a wire like water through a pipe. This approximation is more or less correct when current flow is constant, as in a direct current generator powering electric lights, but when current is varying a much more complex set of phenomena become manifest which require Maxwell’s theory to fully describe. Pioneers of telegraphy thought of their wires as sending direct current which was simply switched off and on by the sender’s key, but of course the transmission as a whole was a varying current, jumping back and forth between zero and full current at each make or break of the key contacts. When these transitions are modelled in Maxwell’s theory, one finds that, depending upon the physical properties of the transmission line (its resistance, inductance, capacitance, and leakage between the conductors) different frequencies propagate along the line at different speeds. The sharp on/off transitions in telegraphy can be thought of, by Fourier transform, as the sum of a wide band of frequencies, with the result that, when each propagates at a different speed, a short, sharp pulse sent by the key will, at the other end of the long line, be “smeared out” into an extended bump with a slow rise to a peak and then decay back to zero. Above a certain speed, adjacent dots and dashes will run into one another and the message will be undecipherable at the receiving end. This is why operators on the transatlantic cables had to send at the painfully slow speed of eight words per minute.

In telephony, it’s much worse because human speech is composed of a broad band of frequencies, and the frequencies involved (typically up to around 3400 cycles per second) are much higher than the off/on speeds in telegraphy. The smearing out or dispersion as frequencies are transmitted at different speeds results in distortion which renders the voice signal incomprehensible beyond a certain distance.

In the mid-1850s, during development of the first transatlantic cable, William Thomson had developed a theory called the “KR law” which predicted the transmission speed along a cable based upon its resistance and capacitance. Thomson was aware that other effects existed, but without Maxwell’s theory (which would not be published in its final form until 1873), he lacked the mathematical tools to analyse them. The KR theory, which produced results that predicted the behaviour of the transatlantic cable reasonably well, held out little hope for improvement: decreasing the resistance and capacitance of the cable would dramatically increase its cost per unit length.

Heaviside undertook to analyse what is now called the transmission line problem using the full Maxwell theory and, in 1878, published the general theory of propagation of alternating current through transmission lines, what are now called the telegrapher’s equations. Because he took resistance, capacitance, inductance, and leakage all into account and thus modelled both the electric and magnetic field created around the wire by the changing current, he showed that by balancing these four properties it was possible to design a transmission line which would transmit all frequencies at the same speed. In other words, this balanced transmission line would behave for alternating current (including the range of frequencies in a voice signal) just like a simple wire did for direct current: the signal would be attenuated (reduced in amplitude) with distance but not distorted.

In an 1887 paper, he further showed that existing telegraph and telephone lines could be made nearly distortionless by adding loading coils to increase the inductance at points along the line (as long as the distance between adjacent coils is small compared to the wavelength of the highest frequency carried by the line). This got him into another battle with William Preece, whose incorrect theory attributed distortion to inductance and advocated minimising self-inductance in long lines. Preece moved to block publication of Heaviside’s work, with the result that the paper on distortionless telephony, published in The Electrician, was largely ignored. It was not until 1897 that AT&T in the United States commissioned a study of Heaviside’s work, leading to patents eventually worth millions. The credit, and financial reward, went to Professor Michael Pupin of Columbia University, who became another of Heaviside’s life-long enemies.

You might wonder why what seems such a simple result (which can be written in modern notation as the equation L/R = C/G) which had such immediate technological utlilty eluded so many people for so long (recall that the problem with slow transmission on the transatlantic cable had been observed since the 1850s). The reason is the complexity of Maxwell’s theory and the formidably difficult notation in which it was expressed. Oliver Heaviside spent nine years fully internalising the theory and its implications, and he was one of only a handful of people who had done so and, perhaps, the only one grounded in practical applications such as telegraphy and telephony. Concurrent with his work on transmission line theory, he invented the mathematical field of vector calculus and, in 1884, reformulated Maxwell’s original theory which, written in modern notation less cumbersome than that employed by Maxwell, looks like:

Maxwell's original 20 equations

into the four famous vector equations we today think of as Maxwell’s.

Maxwell's equations: modern vector calculus representation

These are not only simpler, condensing twenty equations to just four, but provide (once you learn the notation and meanings of the variables) an intuitive sense for what is going on. This made, for the first time, Maxwell’s theory accessible to working physicists and engineers interested in getting the answer out rather than spending years studying an arcane theory. (Vector calculus was independently invented at the same time by the American J. Willard Gibbs. Heaviside and Gibbs both acknowledged the work of the other and there was no priority dispute. The notation we use today is that of Gibbs, but the mathematical content of the two formulations is essentially identical.)

And, during the same decade of the 1880s, Heaviside invented the operational calculus, a method of calculation which reduces the solution of complicated problems involving differential equations to simple algebra. Heaviside was able to solve so many problems which others couldn’t because he was using powerful computational tools they had not yet adopted. The situation was similar to that of Isaac Newton who was effortlessly solving problems such as the brachistochrone using the calculus he’d invented while his contemporaries struggled with more cumbersome methods. Some of the things Heaviside did in the operational calculus, such as cancel derivative signs in equations and take the square root of a derivative sign made rigorous mathematicians shudder but, hey, it worked and that was good enough for Heaviside and the many engineers and applied mathematicians who adopted his methods. (In the 1920s, pure mathematicians used the theory of Laplace transforms to reformulate the operational calculus in a rigorous manner, but this was decades after Heaviside’s work and long after engineers were routinely using it in their calculations.)

Heaviside’s intuitive grasp of electromagnetism and powerful computational techniques placed him in the forefront of exploration of the field. He calculated the electric field of a moving charged particle and found it contracted in the direction of motion, foreshadowing the Lorentz-FitzGerald contraction which would figure in Einstein’s special relativity. In 1889 he computed the force on a point charge moving in an electromagnetic field, which is now called the Lorentz force after Hendrik Lorentz who independently discovered it six years later. He predicted that a charge moving faster than the speed of light in a medium (for example, glass or water) would emit a shock wave of electromagnetic radiation; in 1934 Pavel Cherenkov experimentally discovered the phenomenon, now called Cherenkov radiation, for which he won the Nobel Prize in 1958. In 1902, Heaviside applied his theory of transmission lines to the Earth as a whole and explained the propagation of radio waves over intercontinental distances as due to a transmission line formed by conductive seawater and a hypothetical conductive layer in the upper atmosphere dubbed the Heaviside layer. In 1924 Edward V. Appleton confirmed the existence of such a layer, the ionosphere, and won the Nobel prize in 1947 for the discovery.

Oliver Heaviside never won a Nobel Price, although he was nominated for the physics prize in 1912. He shouldn’t have felt too bad, though, as other nominees passed over for the prize that year included Hendrik Lorentz, Ernst Mach, Max Planck, and Albert Einstein. (The winner that year was Gustaf Dalén, “for his invention of automatic regulators for use in conjunction with gas accumulators for illuminating lighthouses and buoys”—oh well.) He did receive Britain’s highest recognition for scientific achievement, being named a Fellow of the Royal Society in 1891. In 1921 he was the first recipient of the Faraday Medal from the Institution of Electrical Engineers.

Having never held a job between 1874 and his death in 1925, Heaviside lived on his irregular income from writing, the generosity of his family, and, from 1896 onward a pension of £120 per year (less than his starting salary as a telegraph operator in 1868) from the Royal Society. He was a proud man and refused several other offers of money which he perceived as charity. He turned down an offer of compensation for his invention of loading coils from AT&T when they refused to acknowledge his sole responsibility for the invention. He never married, and in his elder years became somewhat of a recluse and, although he welcomed visits from other scientists, hardly ever left his home in Torquay in Devon.

His impact on the physics of electromagnetism and the craft of electrical engineering can be seen in the list of terms he coined which are in everyday use: “admittance”, “conductance”, “electret”, “impedance”, “inductance”, “permeability”, “permittance”, “reluctance”, and “susceptance”. His work has never been out of print, and sparkles with his intuition, mathematical prowess, and wicked wit directed at those he considered pompous or lost in needless abstraction and rigor. He never sought the limelight and among those upon whose work much of our present-day technology is founded, he is among the least known. But as long as electronic technology persists, it is a monument to the life and work of Oliver Heaviside.

Mahon, Basil. The Forgotten Genius of Oliver Heaviside. Amherst, NY: Prometheus Books, 2017. ISBN 978-1-63388-331-4.

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Author: John Walker

Founder of Ratburger.org, Autodesk, Inc., and Marinchip Systems. Author of The Hacker's Diet. Creator of www.fourmilab.ch.

12 thoughts on “Saturday Night Science: The Forgotten Genius of Oliver Heaviside

  1. I finally was able to read the rest. I see he made enemies that kept him down and was not a self promoter therefore he is little known.

    I think his lack of schooling helped him see things differently. Also working intimately with electricity gave him a feel for its properties. He better than others knew what solving things meant to the operators.

    John, you are really good at explaining things. It amazes me at times.

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  2. MJBubba:
    So, how is the writing?   Does this make a good read for anyone besides nerds?

    This is a scientific biography, like the author’s 2002 biography of James Clerk Maxwell, The Man Who Changed Everything.  Like Maxwell, Heaviside devoted his life pretty much exclusively to his science so, other than anecdotes about scientific feuds with various people, the focus is on his work and how he came to make the discoveries for which he is known.  (When the safety bicycle appeared, he became an ardent bicyclist, but how much can you say about that?)

    The writing is accessible to readers of other popular science works.  The few equations that appear are mostly to illustrate how Heaviside reformulated concepts and notation to make them more accessible to practitioners in the field, not to explain the science.  Those uninterested in the science of electromagnetism and how it came to be understood should probably avoid this book.

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  3. Heaviside’s footprints appear in so many places in 19th century electromagnetic theory that I had omit some in order that the article have finite length.

    One that I left out is the “skin effect”.  With direct current, the current that flows through a conductor is determined purely by its resistance and the voltage applied, given by Ohm’s law: I = V/R.  If you want to transmit more current for a given voltage, you just use a bigger wire, as its cross-section will lower the resistance.

    When experimenters began to work with alternating current, especially at higher frequencies, an odd thing was observed.  Increasing the size of the wire only slowly increased the current, much less than would be expected by Ohm’s law.  This can only be understood through Maxwell’s theory of the propagation of energy by the electromagnetic field surrounding the wire.  The wire can be thought of as a guide directing the energy, but not actually carrying it.  The energy that penetrates the wire flows inward from the field outside radially, and this is what accounts for the resistance of the conductor.  This propagation takes time, and for a high frequency (where the current is reversing rapidly and falling to zero at each reversal) the energy only penetrates the outermost portion of the conductor and never reaches far into its bulk.  As a result, the measured resistance to AC current is more closely proportional to the circumference than the area of a round conductor.

    The skin effect was first described in 1883 by Horace Lamb for the special case of a spherical conductor.  In 1885, Oliver Heaviside published a fully general analysis based on Maxwell’s theory for conductors of any shape (in particular, wires used in electronics), and it is Heaviside’s analysis which is still used today in design of high frequency electronics.

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  4. Heaviside placed great importance on notation and clarity of expression.  His re-formulation of Maxwell’s theory from 20 equations to just four is an example of this.  He also was vexed that the equations of electrodynamics were littered with factors of 4π.  This, in his view, was due to the inverse square law for electromagnetism being formulated based on the obsolete view of “action at a distance”.  In other words, he argued for rewriting the formula for the force between two identically charged particles from F = q²/εr² to be F = q²/4πεr².  By embedding the 4π in the force law, as described by Maxwell’s field view of electromagnetism and rescaling the units accordingly, all of the irritating factors of 4π in the other equations would vanish, making them much more intuitive.

    He published the following argument for the change in 1891, which is a fine example of his acid prose.

    The “brain-wasting perversity” of the British nation in submitting year after year to be ruled by such a heterogeneous and incongruous collection of units such as the yard, foot, inch, mile, knot, pound, ounce, pint, quart, gallon, acre, pole, horse-power, etc., etc., has been repeatedly lamented by would-be reformers, who would introduce the common-sense decimal system; and amongst them have been prominent electricians who hoped to insert the thin end of the wedge by means of the decimal sub-division of the electrical units, and their connection with the meter and gramme, and thus lead to the abolition of the present British system of weights and measures with its absurd and useless arbitrary constants.  But what a satire it is that they should have fallen into the very pit they were professedly avoiding!  The perverse British nation—practically the British engineers—have surely a right to expect that the electricians will first set their own house in order.

    The ohm and the volt, etc., are now legalised, so that, as I am informed, it is too late to alter them.  This is a non seq., however, for the yard and the gallon are legalised; and if it is not too late to alter them, it cannot be too late to put the new fangled ohm and its companions right.  It is never too late to mend.

    Note that 113 word stem-winder of a first sentence.

    In the SI system of units, adopted in 1960, Heaviside’s recommendation was incorporated into its electromagnetic units by defining permeability (μ) to include the factor of 4π.  Heaviside also happens to have coined the word “permeability” in 1885.

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  5. Good thing Heaviside didn’t go to college, it would have just held him back and he’d have driven his professors nuts. (This reminds me of the story of Isaac Newton’s most productive period being the 18 months he spent away from Trinity College while the Great Plague burned itself out in Cambridge.) Also: Oliver Heaviside sounds like a character in a Dickens novel.

     

    PS — AT&T, screwing people over for more than a century.

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  6. Wonderful review of an excellent book. I highly recommend it. The more mathematically inclined might also appreciate Paul Nahin’s biography: Oliver Heaviside – The Life Work and Times of an Electrical Genius of the Victorian Age. He takes a deep dive through Heaviside’s work with extensive quotes from the relevant period literature and works out and presents the relevant math in a particularly clear fashion.

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  7. Heaviside was involved in two areas of mathematics that have bugged me for a long time:

    The link above points to Heaviside’s development of the operational calculus, which boils down to treating d/dt as a linear operator and manipulating differential equations using the techniques of linear algebra.  The cavalier treatment of the differential operator in differential equations interacts in a very queasy way with the formal definitions of the differential using limits, until you learn about the work of Abraham Robinson in the 1960s.

    Robinson extended the real numbers with hyper-reals, which are defined to obey the same arithmetic laws as real numbers but which are all smaller than any real number.  He didn’t run into any contradictions with these postulates and was able to use the hyper-reals to run through all the constructions in calculus, treating the differentials as hyper-real numbers  https://www.youtube.com/watch?v=JEr6sE1C2kc  In Robinson’s work, there is nothing queasy about cancelling and multiplying by differentials.

    Now Calculus can be taught at 3 levels:

    1) Intuitive explanation of differentials, in the way that Newton and Leibnitz started it and in the way they are handled algebraically for differential equations

    2) Traditional limit based analysis, as taught by Spivak

    3) Non-standard analysis, based on the hyper-real number system invented by Robinson and taught to undergraduates in books like this: https://www.math.wisc.edu/~keisler/foundations.html which goes back to treating differentials using the regular techniques of algebra, by extending the real numbers to the hyper-real numbers.

    Heaviside was also involved in the Vector War: https://www.youtube.com/watch?v=_AaOFCl2ihc which sounds like the joke where a bunch of guys with blindfolds all tried to describe an elephant that was perceived only by touch.

    Again in the 1960s, a revision of these mathematical methods started, this time due to the work of David Hestenes, who demonstrated endless applications of the 1860s Clifford Algebra to all aspects of modern physics.  Clifford Algebra (or Geometric Algebra) sets up a kind of place value system for dimensions, where every dimension n has objects in it that can be constructed as sums of objects of every smaller dimension n, n-1, n-2, …, 0.

    So in 3D space, objects can be constructed from volumes, planes, lines and points, just like 3 digit numbers can be put together with hundreds, tens, ones and zero.

    Famously, the techniques of Clifford Algebra allow you to express Maxwell’s laws using just a single equation, instead of the 4 equations that Heaviside came up with.

    In both of these areas of math, intuitive methods such as Heaviside used had a lot of initial success but the fundamental understanding of why the things worked that way was missing. It seems like the insights of Robinson and Clifford are not so hard and are worth learning. (Hestenes even insists Geometric Algebra should be taught to high school students http://geocalc.clas.asu.edu/GA_Primer/GA_Primer/introduction-to-geometric/high-school-geometry-with/index.html)

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