# Hidden Figure: Review of ‘The Forgotten Genius of Oliver Heaviside’ by Basil Mahon

by Ali Minai

A few years ago, while introducing my class of electrical engineering students to information theory, I said that we lived today in a world created by Faraday, Maxwell, and Shannon. Even as I said this, I was aware that, in my zeal for effect, I was omitting the names of many who had made seminal contributions in the fields of electrical engineering and telecommunications, but one name that did not occur to me then was that of Oliver Heaviside. Basil Mahon’s book, ‘The Forgotten Genius of Oliver Heaviside: A Maverick of Electrical Science’, is a valiant – and, one hopes, successful – attempt to remedy this situation where even those immersed in the field of electrical engineering do not know the achievements of one of its founding figures. To be sure, Heaviside’s name does live on in the simple but surprisingly important Heaviside step function H(x), which takes value 0 if x is less than 0 and 1 if it greater. This function, along with Dirac’s delta function, allows the calculus of discrete variables to be unified with the classical calculus of continuous ones – a fact of great utility in an age where everything is increasingly digital and thus discrete. Forgotten in all this is the fact that Heaviside invented the step function as part of a larger enterprise: An operational calculus that sought to solve the problems of calculus in a purely algebraic form. Though that calculus has left its imprint on many methods used by engineers to solve mathematical problems today, it is not taught explicitly in any curriculum and its name has mostly been forgotten by practitioners – a situation symbolic of the fate that has befallen Oliver Heaviside himself.

A vivid portrait of Heaviside emerges from the book. We see a brilliant and curmudgeonly character – willful but not unkind, except to those who challenge his well-founded theories with half-baked notions. After rather brief coverage of Heaviside’s background and childhood, the book moves to the beginning of his professional career as a technician in the telegraph service. Lacking a formal advanced education, Heaviside was fortunate to get this opportunity, in part through the efforts of his brother, Arthur, who was already employed in the service and – very importantly – the recommendation of the great inventor, Sir Charles Wheatstone, who was Heaviside’s uncle by marriage. For all the struggles that Heaviside had to go through to gain recognition of his genius, he was fortunate in one thing: He got into the field of electrical communication – the telegraph – at exactly the right time for a person of his aptitude. It was then a new technology, but had already established its utility. The desire to connect the world through telegraph was a major effort into which private investors and governments were willing to sink resources. And yet, everything in the field was being done through trial and error, without the benefit of established theory. The field was dominated by technicians rather than scientists, and the leading engineers of the time – such as Heaviside’s nemesis, William Preece – saw theoreticians as little more than ivory tower wonks with little to contribute to engineering practice. Heaviside was the first person to bridge this divide.

He began as a practitioner at the very lowest rung of the ladder, helping to lay cable in the sea and troubleshooting the many practical problems that arose in this great effort. But, with an obviously analytical mind, Heaviside did not remain content simply to discover and apply rules of thumb; he tried to turn them into systematic theories of how current was conducted in cables. To do this, he taught himself mathematics, and – as was the case throughout his life – immediately set out to apply his self-acquired knowledge to a task of extreme complexity: Understanding and organizing James Clerk Maxwell’s newly formulated theory of electromagnetism, which was then understood by few people beside Maxwell himself (who was still alive). Not only did Heaviside understand the theory by reading through Maxwell’s immense treatise on the subject, it was he who first expressed it in the elegant mathematical form that we know today as Maxwell’s Equations. This alone would have been enough to establish him as a great scientist, but it is characteristic of Heaviside’s prodigious genius that this turned out to be only one among his many accomplishments. As the book lays out in well-crafted narrative, Heaviside helped establish the nature of electromagnetic fields, theorized about how the field allowed conductors to carry current, developed vector analysis as a method to describe fields mathematically, defined such fundamental quantities as impedance and inductance, discovered the method for distortion-free communication through cables, took the initial steps towards developing the Lorentz-FitzGerald Equation which is central to Einstein’s theory of special relativity, correctly predicted the existence of a conducting layer in the atmosphere, and laid the groundwork for mathematical methods such as Laplace transforms which remain fundamental to the work of electrical engineers to this day. In a real sense, Oliver Heaviside is the true father of modern electrical engineering with its deep theoretical bent and highly mathematical formulations. That all this could be done by one self-taught individual of very limited means establishes Heaviside as one of the most interesting characters in the annals of science, and the fact that much of this has been forgotten makes him among the most tragic. Mahon’s book attempts to demonstrate the former and mitigate the latter.

One of the best features of this book is the insight it provides into the sociology of science. The process is much different today than it was in the 19th century when a few “great men” tended to dominate each field, but the role of human nature – including human failings – in the growth of knowledge is still just as important. Indeed, a study such as this one on Oliver Heaviside provides a clearer view of these processes by focusing in on a very specific topic and on a small dramatis personae – almost like a well-observed laboratory experiment. It certainly helps that educated Victorians were such inveterate writers of letters and keepers of journals, and that the English press, even at that time, was keenly interested in reporting on intellectual matters. Mahon makes extensive use of this source material to create a picture of the times and the heady process of discovery in what was even then becoming the foundation of a whole new technological world. We glimpse the great James Clerk Maxwell in the final years of his all-too-brief and brilliant life. We see the giant figure of William Thomson – Lord Kelvin – looming like a benevolent demigod over the landscape of Victorian science. We encounter Lord Rayliegh contemplating the obstinate Heaviside with bemused exasperation. We look into the mind of William Preece – the doyen of British communication engineers who never reconciled himself to Heaviside’s insights and hounded him through most of his life. Best of all, we get nuanced portraits of “the Maxwellians” – Oliver Lodge, George Francis FitzGerald, and Heinrich Hertz – three distinguished scientists who recognized Heaviside’s genius and participated with him in the great enterprise of establishing a science of electromagnetics, and thus of telecommunications. And at the end, we find G.F.C. Searle, eminent Cambridge physicist and the closest friend Heaviside ever made. Heaviside quarreled all his life with a scientific establishment that repeatedly offered to recognize his contributions at the price of a little formality, which Heaviside invariably refused to provide. That he still became a Fellow of the Royal Society, won the first Faraday Medal, and was short-listed for the Nobel Prize is a testimony more to the sincerity of his admirers than any concession to custom on his own part. And yet one cannot help but admire the strength of character that caused him to refuse almost every honor and monetary reward where he caught the slightest whiff of patronization or pity.

Heaviside’s combative, irreverent, self-confident style is captured well in Mahon’s description (pp. 169-173) of his quarrel with the eminent physicist Peter Guthrie Tait on the matter of quaternions – a generalization of complex numbers invented by the great Irish scientist William Rowan Hamilton, and considered useful in the analysis of mechanical systems. Tait was a close friend of Maxwell’s, and had developed an almost religious zeal for quaternions. Heaviside – ever the practical iconoclast – thought that vector analysis (which he had helped develop) was much more useful than quaternions, and proclaimed this loudly in his writings. Tait took umbrage at this, which prompted Heaviside to label him a “consummately profound metaphysico-mathematician”, and to say that

“Quaternion” was, I think defined by an American schoolgirl to be “an ancient religious ceremony.” This was, however, a complete mistake. The ancients – unlike Prof. Tait – knew not, and did not worship Quaternions.

When Tait responded, with the help of a colleague, Dr. Knott, Heaviside became even more merciless:

The quaternionic calm and peace have been disturbed. There is confusion in the quaternionic citadel; alarms and excursions, and hurling of stones and pouring of boiling water upon the invading host…. It would appear that Prof. Tait, being unable to bring his massive intellect to understand my vectors, or [Josiah Willard] Gibbs’, …. Has delegated to Prof. Knott the task of examining them, apparently just upon the remote chance that there might possibly be something in them that was not utterly despicable.”

This response by Heaviside was published in no less a journal than Nature! This is how he wrote not only his letters and opinions, but also his technical papers, and even his textbooks. It is not surprising that he should have spent his entire professional life at odds with the establishment, and it was only the sheer brilliance of his work that compelled others to return repeatedly with accolades, which he almost always disdained.

In a sense, the real heroes of the book – besides Heaviside, of course – are the editors of The Electrician who continued to publish Heaviside’s prodigious output of technical papers in the face of stern opposition from the establishment and the general incomprehension of their readership. In more than one case, they paid a stiff personal price for this, but without their dedicated promotion of Heaviside’s work, it would probably have been consigned to oblivion, with dramatic consequences for the progress of technology. Indeed, though Oliver Heaviside’s contributions may have largely been “forgotten” today, it is clear from the book that he led a very fortunate life. The main reason why his genius was able to flower at all given his disadvantages of social class and formal education was because, throughout his life, he had remarkably strong support and friendship from so many – including such illustrious figures as Wheatstone, Lord Kelvin, FitzGerald, Hertz, Lodge, Searle, his editors, and many others – and that this support continued in spite of Heaviside’s difficult nature. Even his family, with all their constraints, went far beyond the call of duty to support his unusual and, one is sure, often infuriating lifestyle. Clearly, there was something in the man – perhaps the spark of genius or the fire of intellect – that attracted others to him, and compelled their loyalty even in very trying circumstances. It must also be said that Heaviside did not waste any of this support and affection on frivolities, but used it entirely to do great work that changed the world in profoundly beneficial ways. All in all, it was an excellent bargain on both sides.

The writing in ‘The Forgotten Genius of Oliver Heaviside’ is engaging and skillful. The narrative moves at a rapid pace across the terrain of Heaviside’s life. Some readers may feel a certain lack of ‘storytelling’ because the book does not get too deeply into Heaviside’s personal life. That criticism would be justifiable in a comprehensive biography, but this volume is clearly intended as a history of Oliver Heaviside as a scientist and engineer. His person comes through strongly only because the quirks of his personality were so inextricably intertwined with his professional work, but most of the specific events of his personal life were of little significance, and Mahon has wisely skirted around them. However, even from the material included in the book, it is clear that Oliver Heaviside’s life would make for great storytelling in the hands of a skilled novelist or film-maker. Here is clearly another beautiful mind, or, as his friend Searle said, “A first-rate oddity”.

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"The Forgotten Genius of Oliver Heaviside: A Maverick of Electrical Science" by Basil Mahon has been published in 2017 by Prometheus Books, Amherst, NY. (ISBN 978-1-63388-331-4)

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