# Oliver Heaviside

Eyridiki Sellou | Sep 16, 2022

## Table of Content

## Summary

Oliver Heaviside, (London, England, May 18, 1850 - Torquay, England, February 3, 1925) was an English physicist, electrical engineer, radiotelegrapher and mathematician. Heaviside introduced complex numbers into circuit analysis, invented a new technique for solving differential equations (equivalent to the Laplace transform), independently developed vector calculus, and rewrote Maxwell's equations in the format commonly used today. He significantly shaped the way Maxwell's equations were understood and applied in the decades after Maxwell's death. His formulation of the telegraph equations was commercially relevant during his own lifetime, although they went unnoticed for a long time because few were then familiar with his novel methodology. Although his relations with the scientific establishment were complicated for most of his life, Heaviside reshaped the field of telecommunications, mathematics and science.

## Children and Youth

Oliver was the fourth child in the family of Thomas Heaviside and Rachel West. The father was a gifted wood engraver, but his trade was already suffering from the competition of the nascent photographic techniques and the family was always very short of money. The mother set up a sort of small school for young ladies in their rented house in Camden Town to earn more income. The family atmosphere must have been tense and morose. The situation was complicated in Oliver's case because as a child he suffered from scarlet fever, as a result of which he became practically deaf. This made it difficult for him to relate to others, especially the other boys, and probably formed the basis of the sullen and withdrawn character he displayed for the rest of his life, although he recovered much of his hearing later in his adolescence.

A bequest received in 1863 meant a marked financial improvement for the family. The Heavisides moved to better housing in the same neighborhood and Oliver was able to attend school, where he excelled in natural science, winning a medal in the 1865 examinations. But his schooling had to end the following year. The rest of his intellectual formation was self-taught, being apparently an assiduous and avid visitor of public libraries. He was especially attracted to scientific works and thus delved into the treatises of Newton and Laplace.

## Maturity

Unable to attend university, he had to go to work. In 1867 he moved to Newcastle, where he began his working life as a telegrapher. This orientation, so decisive for his later career, was the result of family circumstances. An older sister of his mother, Emma West, had married Charles Wheatstone, co-inventor of a telegraph system with W. F. Cooke, which made him rich and powerful. An older brother of Oliver's, Arthur W. Heaviside, became his uncle's assistant, later going on to run the local telegraph company in Newcastle; he ended up holding an important post in the Post Office. Oliver, for his part, began as his brother's assistant and in the autumn of 1868 was assigned to the running of the new submarine cable laid between Newcastle and Denmark, first as operator and then as electrician, the name then given to specialists in the subject, the newest and most interesting of all electrical engineering. The following years were spent by Oliver in the workshops and on board the ships in charge of the maintenance of the line, privileged places where all aspects of the new phenomena and problems that continually arose were experimented and analyzed. During this time he continued to study physics on his own, both theoretically and experimentally.

In May 1874 he left his job in Newcastle and returned to his parents' home in London, both for health reasons (he suffered from a kind of pseudo-epileptic seizures) and out of a desire to devote himself exclusively to study and research. He never again held a regular paid job, unless one considers as such the sporadic job of columnist, which provided him with a meager return. He rejected all the employment possibilities that his brother and others provided, choosing an extremely austere way of life in exchange for total freedom for his research. "I was born a natural philosopher, not a restless engineer or 'practical man' in the mercantile sense," he characterized himself at the end of his life. Many of his theoretical contributions had important practical applications, but he never attempted to derive economic returns from them (probably following in the footsteps of Faraday, one of his idols), despite the inventive furor and consequent patent applications typical of the time, including the nearby example of his uncle Wheatstone.

## Final years

After 1900 Heaviside's scientific activity declined appreciably in quantity and quality, practically ceasing in 1906, although his last book was published in 1912. One of the fundamental causes was the problems caused by his persistent ill health.

Oliver and his parents went to live in September 1889 with his brother Charles, who had a musical instrument store in Paington (Devonshire), following another of the family operating lines initiated by Wheatstone, who had also invented the concertina. After the death of his parents in 1894 and 1896, Oliver moved in 1897 to a detached house in the countryside near Newton Abbot and not far from Paington, but the experience was not very satisfactory and in 1908 he returned to live as a lodger in Torquay, where he died in 1925, after leading an increasingly solitary and eccentric life.

## Honors and distinctions

Despite his eremitical life, the published work and the activities of his influential friends brought Heaviside numerous recognitions, although he did not seem to appreciate them too much. Of particular note are the following:

The efforts and negotiations of J. Perry, G. F. FitzGerald, O. Lodge and other friends succeeded in obtaining for Heaviside an official pension of 120 pounds per year in 1896 (raised to 220 pounds in 1914), and also in getting him to accept it, since two years earlier he had refused another grant from the Scientific Relief Fund of the Royal Society, managed in the same way, considering it "charity".

## Home

His first published work dates from July 1872 and appeared in the English Mechanic magazine under the signature "O."; it dealt with a method of comparison of electromotive forces discovered by Heaviside in 1870. In February 1873 he published his first paper in the Philosophical Magazine, the most important physics journal of the time. This time it dealt with the optimization of the Wheatstone bridge, a measuring instrument well known in the practice of telegraphists and physicists, but which until then had not found a rigorous mathematical treatment. This article made him known among the most important scientific personalities of the time, such as Lord Kelvin and Maxwell. Many of Heaviside's intellectual traits are already present in this work, among them the fundamental one of applying powerful mathematical methods to the solution of practical problems (even Kelvin found his algebra difficult, apparently).

During the next forty years Heaviside produced an uninterrupted flow of papers, which were published mainly in periodicals, such as The Electrician, Philosophical Magazine or Nature, until they totaled more than three thousand dense pages. These collaborations were then published regularly in book form, constituting the works reviewed in the bibliography.

## Signal transmission line theory

The fundamental subject of Heaviside's initial investigations was the propagation of signals over telegraph lines, especially the distortion they suffered as they passed through subway or submarine cable lines. The phenomenon had become topical in 1853 when Latimer Clark first observed it on the Anglo-Dutch line, bringing it to the attention of Faraday, who studied it and considered it a proof of his own ideas on the electromagnetic field, specifically on the "transverse effects of currents" (Experimental Researches in Electricity, vol. III, p. 508). All this called into question the very viability of the projected transatlantic cable, of a length hitherto unheard of. Lord Kelvin elaborated in 1855 a theory of the electric telegraph in which he combined Faraday's ideas with Fourier's equations on the diffusion of heat in a solid body, arriving at the conclusion that the delay of the signals was due to the combination of the resistance and capacitance of the cable, growing according to the square of its length. This was thus an unavoidable phenomenon, which limited the speed of transmission, but which could be overcome if due attention was paid both to the electrical characteristics of the cables and to the use of very special apparatus for transmission and reception, together with carefully selected transmission techniques. But these considerations were not initially accepted without reservation (as they would later be) and the cable was laid in 1858. Its initial operation was instead disappointing, becoming unusable after only a month of service and serving only to demonstrate the correctness of the ideas of Kelvin, who was in charge of the design and operation of a new line, completed in 1866 and which was a success.

Heaviside applied Kelvin's theory to his own experiences with the Anglo-Danish cable and published a series of papers on it between 1874 and 1889, which resulted in its extension with two new factors not previously taken into account: the losses of the line (which Heaviside, not at all sparing when creating neologisms, called leakance, which would be translated as leakage or perditance) and above all self-induction. He thus completed and rectified the initial theory, formulating what was known for a long time as "Heaviside's equation" or "telegrapher's equation", which gives the instantaneous value of the voltage (v) at any point (x) of the line as a function of its electrical characteristics resistance (k), capacitance (c) and inductance (s):

When self-induction is taken into account, the electric current no longer simply spreads along the line, as in the previous conception, but causes a series of initial oscillations until a steady state is reached. Signal propagation, even over wires, was thus definitively linked to electromagnetic waves.

In 1887 Heaviside formulated the idea that it was possible to combine the electrical parameters of a signal transmission line in such a way as to eliminate all distortion, i.e., that although the entire signal would be attenuated, all its component frequencies would be attenuated in the same proportion. This was essential for the new telephone communications, even more so than for telegraph communications. Numerous patents were obtained on this basis by others (such as Silvanus P. Thompson, J. S. Stone and A. K. Erlang), but its implementation required considerable additional effort and was not satisfactorily achieved until the contributions of G. A. Campbell and Michael I. Pupin around 1900 (with calls by J. S. Stone and A. K. Erlang). Pupin around 1900 (with the so-called "loading coils").

Although Gustav Kirchhoff had included self-induction in the theory of long lines as early as 1857, his proposal had no repercussions. Heaviside instead became its apostle. "Self-induction is salvation" he said in 1897 (and still in 1904: "If love is what moves the world, self-induction is what moves the waves through it." (Electromagnetic theory, vol. 3, p. 194). This position clashed head-on with that held by the engineer W. H. Preece, who became the supreme head of the British telegraph and telephone service (Post Office), who held to the primitive view that self-induction was always harmful in a communication line and had to be minimized. The confrontation lasted until Preece's death and cost Heaviside no small amount of grief.

## Maxwellianism

The first edition of Maxwell's Treatise on Electricity and Magnetism was published in 1873 and Heaviside studied it immediately, being deeply impressed by its contents, although he did not initially understand its novelty well (like most contemporary readers), especially as it related to electromagnetic waves and their propagation through the medium (the ether as a dielectric). The mathematical apparatus used, based on quaternions, was also beyond his capabilities at the time. For all these reasons he devoted several years to its in-depth study and in 1876 he began to cite it in his own works. Maxwell's early death in 1879 meant a radical change of circumstances, since the master's contributions to a theory in great need of them and of being made known to the public could no longer be expected. Heaviside took upon himself this task and, according to his own confession, consciously began to carry it out as early as 1882. But he did not limit himself to a repetition of the contents of the treatise as a "sacred text" (J. J. Thomson even called Heaviside an "apostate Maxwellian"), but reworked, refined and expanded it, resulting in what is known to science today as Maxwell's theory. Today it is often spoken of as a matter of course as "Maxwell's four equations", but it should be known that the true number of those contained in the Treatise is thirteen. The final synthesis and theoretical clarification represented by the four equations was due to the work, first independently and then jointly, of Heaviside and Hertz.

In his appropriation, reworking and dissemination of the Maxwellian theory, Heaviside had the decisive collaboration of other English physicists, who have been called "the Maxwellians", mainly G. F. FitzGerald and O. Lodge in the early years, and later J. Larmor, although Heaviside's relationship with the latter was less harmonious than with the others.

Despite his involvement in it, Heaviside did not consider the Maxwellian theory to be concluded or to have the last word. He did not even consider the Hertz experiments of 1886-1888 to be irrefutable proof of its correctness. The problems posed by the motion of the ether and its very concept were there to prove it, and a further complication came to signify the growing theoretical role of the electron in the closing years of the nineteenth century together with its experimental confirmations, which forced a modification of the Maxwellian concepts of charge and current. Heaviside actively participated in the extension of the field equations to mobile charges (electrons) and provided some of the first complete solutions.

## Mathematical instruments

The symbolic representation of physical quantities endowed with orientation was a process of slow consolidation, which was carried out throughout the 19th century, starting with complex numbers, applicable to the plane. Their generalization to space was naturally even more difficult. Such was the purpose of W. R. Hamilton's theory of quaternions. In the study of electromagnetism it is essential to have a concise and efficient notation for handling space vectors, and Maxwell had used quaternions, but often in a simplified form. For Heaviside's pedagogical and systematizing purposes this was not enough, so he elaborated vector analysis as an independent algebra, formulated in what is still its present form in Chapter III of Electromagnetic theory. This also contains the reasons for his rejection of quaternionic theory, a matter on which he maintained until the end of his career heated polemics with P. G. Tait, its main expositor and defender. In any case, vector calculus was practically unknown to the engineers and physicists of his time (Heaviside had to teach it to Hertz), which contributed to making Heaviside's writings difficult to understand, in spite of his strenuous pedagogical efforts, to the point that his friend Lodge described them not only as difficult, but even as "eccentric and in some respects repellent".

He was also one of the creators of the calculus by means of operators, operational calculus or operational calculus, so useful later in engineering, to whose elaboration and exposition he dedicated a good part of his activity from 1894 to 1898, collected in the second volume of Electromagnetic theory. Although the method was not generalized until after his death, it has been considered one of the three great mathematical advances of the last quarter of the 19th century.

Heaviside conceived mathematics as an experimental science and despised academic "pure mathematicians". His mathematics was not concerned with demonstrations or existence theorems, but with solving physical problems, whose functional relationships are simple and do not require exhaustive analysis of all abstract possibilities. Needless to say, the opinion of him and his methods among professional mathematicians was correspondingly not very good.

## Sources

- Oliver Heaviside
- Oliver Heaviside
- «Oliver Heaviside; British physicist». Encyclopedia Britannica (en inglés). Consultado el 31 de diciembre de 2019.
- ^ a b Anon (1926). "Obituary Notices of Fellows Deceased: Rudolph Messel, Frederick Thomas Trouton, John Venn, John Young Buchanan, Oliver Heaviside, Andrew Gray". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 110 (756): i–v. Bibcode:1926RSPSA.110D...1.. doi:10.1098/rspa.1926.0036.
- ^ a b Hunt, B. J. (2012). "Oliver Heaviside: A first-rate oddity". Physics Today. 65 (11): 48–54. Bibcode:2012PhT....65k..48H. doi:10.1063/PT.3.1788.
- ^ a b c d Nahin, Paul J. (9 October 2002). Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age. JHU Press. ISBN 978-0-8018-6909-9.
- ^ a b c d Bruce J. Hunt (1991) The Maxwellians, Cornell University Press ISBN 978-0-8014-8234-2
- 2,00 2,01 2,02 2,03 2,04 2,05 2,06 2,07 2,08 2,09 2,10 2,11 2,12 2,13 2,14 «Oxford Dictionary of National Biography» (Αγγλικά) Oxford University Press. Οξφόρδη. 2004.
- (en) Bruce J. Hunt, « Oliver Heaviside: A first-rate oddity », Physics Today, vol. 65, no 11, novembre 2012, p. 48–54 (ISSN 0031-9228 et 1945-0699, DOI 10.1063/PT.3.1788, lire en ligne, consulté le 6 février 2021)
- a et b (en) Nahin, Paul J., Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age., JHU Press, 9 octobre 2002 (ISBN 978-0-8018-6909-9, lire en ligne), p. 13
- a et b (en) Bruce J. Hunt, The Maxwellians, Cornell University Press, 1991 (ISBN 978-0-8014-8234-2), p. 60
- a et b (en) Sarkar, T. K.; Mailloux, Robert; Oliner, Arthur A.; Salazar-Palma, M.; Sengupta, Dipak L., History of Wireless, John Wiley & Sons (ISBN 978-0-471-78301-5, lire en ligne), p. 232