Oliver Heaviside

Oliver Heaviside (18 May 1850 – 3 February 1925) was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations (later found to be equivalent to Laplace transforms), reformulated Maxwell's field equations in terms of electric and magnetic forces and energy flux, and independently co-formulated vector analysis.

• However absurd it may seem, I do in all seriousness hereby declare that I am animated mainly by philanthropic motives. I desire to do good to my fellow creatures, even to the Cui bonos.
  • Electrical Papers (1882), Vol. I; Preface, p. vii; Maxmillan and Co., London and New York. Full Text.

• We do not dwell in the Palace of Truth. But, as was mentioned to me not long since, "There is a time coming when all things shall be found out." I am not so sanguine myself, believing that the well in which Truth is said to reside is really a bottomless pit.
  • Electromagnetic Theory (1893) Vol. 1, p. 1.

• Waves from moving sources: Adagio. Andante. Allegro moderato.
  • Electromagnetic Theory (1912), Volume III; p. 1; "The Electrician" Pub. Co., London. Full Text.

• The following story is true. There was a little boy, and his father said, “Do try to be like other people. Don’t frown.” And he tried and tried, but could not. So his father beat him with a strap; and then he was eaten up by lions.
  Reader, if young, take warning by his sad life and death. For though it may be an honour to be different from other people, if Carlyle’s dictum about the 30 million be still true, yet other people do not like it. So, if you are different, you had better hide it, and pretend to be solemn and wooden-headed. Until you make your fortune. For most wooden-headed people worship money; and, really, I do not see what else they can do. In particular, if you are going to write a book, remember the wooden-headed. So be rigorous; that will cover a multitude of sins. And do not frown.
  • Electromagnetic Theory (1912), Volume III; p. 1; "The Electrician" Pub. Co., London.

• Electric and magnetic forces. May they live for ever, and never be forgot, if only to remind us that the science of electromagnetics, in spite of the abstract nature of its theory, involving quantities whose nature is entirely unknown at the present, is really and truly founded on the observations of real Newtonian forces, electric and magnetic respectively.
  • Electromagnetic Theory (1912), Volume III; p. 1; "The Electrician" Pub. Co., London.

• We do not dwell in the Palace of Truth. But, as was mentioned to me not long since, "There is a time coming when all things shall be found out." I am not so sanguine myself, believing that the well in which Truth is said to reside is really a bottomless pit.
  • Electromagnetic Theory, Volume I; p. 1; "The Electrician" Pub. Co., London.

• More than a third part of a century ago, in the library of an ancient town, a youth might have been seen tasting the sweets of knowledge to see how he liked them. He was of somewhat unprepossessing appearance, carrying on his brow the heavy scowl that the "mostly-fools" consider to mark a scoundrel. In his father's house were not many books, so it was like a journey into strange lands to go book-tasting. Some books were poison; theology and metaphysics in particular they were shut up with a bang. But scientific works were better; there was some sense in seeking the laws of God by observation and experiment, and by reasoning founded thereon. Some very big books bearing stupendous names, such as Newton, Laplace, and so on, attracted his attention. On examination, he concluded that he could understand them if he tried, though the limited capacity of his head made their study undesirable. But what was Quaternions? An extraordinary name! Three books; two very big volumes called Elements, and a smaller fat one called Lectures. What could quaternions be? He took those 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 returned the books. He then died, and was never seen again. He had begun the study of Quaternions too soon.
  • Electromagnetic Theory (1912), Volume III; Appendix K: Vector Analysis, p. 135; "The Electrician" Pub. Co., London.

• My own introduction to quaternionics 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 quaternionics could be employed consistently in vectorial work. But on proceeding to apply quaternionics to the development of electrical theory, I found it very inconvenient. Quaternionics was in its vectorial aspects antiphysical and unnatural, and did not harmonise with common scalar mathematics. So I dropped out the quaternion altogether, and kept to pure scalar and vectors, using a very simple vectorial algebra in my papers from 1883 onward. The paper at the beginning of vol. 2 of my Electrical Papers may be taken as a developed specimen; the earlier work is principally concerned with the vector differentiator ∇ and its applications, and physical interpretations of the various operations. Up to 1888 I imagined that I was the only one doing vectorial work on positive physical principles; but then I received a copy of Prof. Gibbs's Vector Analysis (unpublished, 1881-4).
  • Electromagnetic Theory (1912), Volume III; Appendix K: Vector Analysis, p. 136; "The Electrician" Pub. Co., London.

• Mathematics is of two kinds, Rigorous and Physical. The former is Narrow: the latter Bold and Broad. To have to stop to formulate rigorous demonstrations would put a stop to most physico-mathematical inquiries. Am I to refuse to eat because I do not fully understand the mechanism of digestion?
  • DA Edge (1983). "Oliver Heaviside (1850-1927) - Physical mathematician". Teaching mathematics and its applications 2: 55-61.
  • This quote cannot be found in Heaviside's corpus, Edge provides no reference, the quote first appears around the 1940s attributed to Heaviside without any references. The quote is actually a composite of a modified sentence from Electromagnetic Theory I (changing 'dinner' to 'eat'), a section header & later sentence from Electromagnetic Theory II, and the paraphrase of Heaviside's views by Carslaw 1928 ("Operational Methods in Mathematical Physics"), respectively:
    • "Nor is the matter an unpractical one. I suppose all workers in mathematical physics have noticed how the mathematics seems made for the physics, the latter suggesting the former, and that practical ways of working arise naturally. This is really the case with resistance operators. It is a fact that their use frequently effects great simplifications, and the avoidance of complicated evaluations of definite integrals. But then the rigorous logic of the matter is not plain! Well, what of that? Shall I refuse my dinner because I do not fully understand the process of digestion? No, not if I am satisfied with the result. Now a physicist may in like manner employ unrigorous processes with satisfaction and usefulness if he, by the application of tests, satisfies himself of the accuracy of his results. At the same time he may be fully aware of his want of infallibility, and that his investigations are largely of an experimental character, and may be repellent to unsympathetically constituted mathematicians accustomed to a different kind of work."
    • "Rigorous Mathematics is Narrow, Physical Mathematics Bold And Broad. § 224. Now, mathematics being fundamentally an experimental science, like any other, it is clear that the Science of Nature might be studied as a whole, the properties of space along with the properties of the matter found moving about therein. This would be very comprehensive, but I do not suppose that it would be generally practicable, though possibly the best course for a large-minded man. Nevertheless, it is greatly to the advantage of a student of physics that he should pick up his mathematics along with his physics, if he can. For then the one will fit the other. This is the natural way, pursued by the creators of analysis. If the student does not pick up so much logical mathematics of a formal kind (commonsense logic is inherited and experiential, as the mind and its ways have grown to harmonise with external Nature), he will, at any rate, get on in a manner suitable for progress in his physical studies. To have to stop to formulate rigorous demonstrations would put a stop to most physico-mathematical inquiries. There is no end to the subtleties involved in rigorous demonstrations, especially, of course, when you go off the beaten track. And the most rigorous demonstration may be found later to contain some flaw, so that exceptions and reservations have to be added. Now, in working out physical problems there should be, in the first place, no pretence of rigorous formalism. The physics will guide the physicist along somehow to useful and important results, by the constant union of physical and geometrical or analytical ideas. The practice of eliminating the physics by reducing a problem to a purely mathematical exercise should be avoided as much as possible. The physics should be carried on right through, to give life and reality to the problem, and to obtain the great assistance which the physics gives to the mathematics. This cannot always be done, especially in details involving much calculation, but the general principle should be carried out as much as possible, with particular attention to dynamical ideas. No mathematical purist could ever do the work involved in Maxwell's treatise. He might have all the mathematics, and much more, but it would be to no purpose, as he could not put it together without the physical guidance. This is in no way to his discredit, but only illustrates different ways of thought."
    • "§ 2. Heaviside himself hardly claimed that he had 'proved' his operational method of solving these partial differential equations to be valid. With him [Cf. loc. cit., p. 4. [Electromagnetic Theory, by Oliver Heaviside, vol. 2, p. 13, 1899.]] mathematics was of two kinds: Rigorous and Physical. The former was Narrow: the latter Bold and Broad. And the thing that mattered was that the Bold and Broad Mathematics got the results. "To have to stop to formulate rigorous demonstrations would put a stop to most physico-mathematical enquiries." Only the purist had to be sure of the validity of the processes employed."

• General circuit theory, the theory of transmission lines and wave propagation, vector analysis, even the four famous Maxwell's equations—all had flowed from the pen of this amazing man.
  • Basil Mahon: The Forgotten Genius of Oliver Heaviside: A Maverick of Electrical Science. Prometheus Books. 2017. p. 11. ISBN 978-1-63388-331-4.  (originally published in 2009)

• ... the present time is the age of communication ... communication engineering began with Gauss, Wheatstone, and the first telegraphers. It received its first reasonably scientific treatment at the hands of Lord Kelvin, after the failure of the first transatlantic cable in the middle of the last century, and from the eighties on, it was perhaps Heaviside who did the most to bring into a modern shape.
  • Norbert Wiener: Cybernetics: Or Control and Communication in the Animal and the Machine (2nd ed.). MIT Press. 1965. p. 39. ISBN 978-0-262-73009-9.  (originally published in 1948)

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Oliver Heaviside

• Many books by Heaviside available online at The Internet Archive