奥利弗·赫维赛德Oliver Heaviside

奥利弗·赫维赛德的父母是Rachel Elizabeth West和Thomas Heaviside。Thomas是一名木刻师和水彩画家。赫维赛德是其父母四个儿子中最小的一个，出生在Camden Town的King Street 55号。他幼年时患了猩红热，这影响了他的听力。这对他的生活产生了重大影响，使他的童年不快乐，他与其他孩子之间的关系也很困难。然而他的学习成绩相当好，1865年他在500名学生中排名第五。

然而，学科科目似乎对赫维赛德没什么吸引力，16岁时他就离开了学校。也许他对学校比对学习更失望，因为离开学校后他继续学习，特别是他学习了莫尔斯电码，研究了电学，并进一步学习了语言，尤其是丹麦语和德语。他的目标是成为一名报务员，在这方面他得到了叔叔Charles Wheatstone的指导与帮助（被称为Wheatstone bridge的那件电气装置就是以他的名字命名的）。

1868年，赫维赛德前往丹麦，成为一名报务员。他在职业上进步很快，并于1871年返回英格兰，在泰恩河畔纽卡斯尔的大北电报公司办事处任职，该公司处理海外业务。

赫维赛德的听力越来越差，但他继续独自研究电学。在纽卡斯尔担任首席操作员期间，他开始发表关于电学的论文，第一篇发表于1872年，第二篇发表于1873年，引起了詹姆斯·克拉克·麦克斯韦的足够兴趣，以至于他在其Treatise on Electricity and Magnetism第二版中提到了这些结果。詹姆斯·克拉克·麦克斯韦的论著使赫维赛德着迷，他放弃了电报员的工作，将时间投入到这部著作的研究中。他后来写道：-

我看到它是伟大的、更伟大的、最伟大的，其力量中蕴含着惊人的可能性。我决心掌握这本书……我花了好几年才能尽可能多地理解它。然后我把詹姆斯·克拉克·麦克斯韦放在一边，走自己的路。我的进展快得多。

尽管他对这部著作的兴趣和理解很深，赫维赛德对严谨性并不感兴趣。他在学校最差的科目是欧几里得的学习，这个主题强调严格证明，赫维赛德非常不喜欢这个想法，他后来写道：-

令人震惊的是，年轻人竟然为了纯粹的逻辑微妙之处而绞尽脑汁，试图用同样……明显的东西来理解一个明显事实的证明。

尽管厌恶严谨性，赫维赛德还是能够极大地简化詹姆斯·克拉克·麦克斯韦的20个变量中的20个方程，将它们替换为两个变量中的四个方程。今天我们称这些为‘詹姆斯·克拉克·麦克斯韦方程’，忘记了它们实际上是‘赫维赛德方程’。乔治·斐兹杰惹写道：-

麦克斯韦的论著中堆满了他那些辉煌进攻路线、筑垒营地与战役的残骸。赫维赛德清除了这些，开辟了一条直路，筑成了一条宽阔的道路，并勘察了相当长的一段地域。

赫维赛德在电磁学上的成果虽然令人瞩目，却被他在研究中发展出的向量分析的重要方法所掩盖。然而，他在1880年至1887年间发展的运算微积分引起了很大争议。他引入运算微积分是为了求解由电路理论产生的常微分方程。他用变量$p$替换微分算子$\Large\frac{d}{dx}\normalsize$，将微分方程转化为代数方程。代数方程的解可以利用转换表反变换回去，从而给出原微分方程的解。尽管在获得答案方面非常成功，但赫维赛德的运算微积分的正确性直到布罗米奇的工作才得到证明。

威廉·伯恩赛德拒绝了赫维赛德提交给Proceedings of the Royal Society的一篇关于运算微积分的论文，理由是它：-

……包含实质性错误，并且在证明上存在不可弥补的缺陷。

彼得·格思里·泰特支持四元数，反对赫维赛德和约西亚·威拉德·吉布斯的向量方法，并频繁致信Nature攻击赫维赛德的方法。

赫维赛德继续在知识上取得进一步进展，却再次得到少于他应得的回报。1887年，邮政总局技术专家普里斯写了一篇关于清晰电话电路的论文。他的论文有误，赫维赛德在1887年6月3日发表于Electrician的Electromagnetic induction and its propagation中指出了这一点。从不回避争议的赫维赛德写道：-

开尔文爵士的海底电缆理论是一件了不起的事情。……普里斯先生非常值得祝贺，因为他参与了（据他所说）开尔文爵士据以建立其理论的实验，因此他应当对该理论有非同寻常的完整了解。但这位杰出科学家的理论与那位杰出的小科学家（scienticulist）的理论并不相似，只是略有相似而已。

在这篇论文中，赫维赛德首次给出了无失真传输信号所需的条件。他关于用感应线圈来增加感应的想法，在普里斯负责研究提案期间，邮政总局（GPO）从未有可能采纳。赫维赛德放弃了这个想法，但它在1904年在美国获得了专利。哥伦比亚大学的迈克尔·普平（Michael Pupin）和美国电话电报公司（ATT）的乔治·坎贝尔（George Campbell）都读过赫维赛德关于沿电话线每隔一段距离使用感应线圈的论文。坎贝尔和普平都申请了专利，该专利于1904年授予了普平。

然而，并非一切都对赫维赛德不利。开尔文在1889年作为电气工程师学会主席发表就职演说时，称赫维赛德为权威。洛奇写信给Nature，描述赫维赛德是一个这样的人：-

……其对电磁波的深刻研究，其深入程度超出了任何人的理解。

赫维赛德于1891年当选为皇家学会会士，这或许是他获得的最大荣誉。埃德蒙·泰勒·惠特克将赫维赛德的运算微积分评为19世纪晚期三项最重要的发现之一。

1902年，赫维赛德预言大气中存在一个导电层，使无线电波能够沿地球曲率传播。大气中的这一层，即赫维赛德层，以他的名字命名。1923年，当无线电脉冲垂直向上发射并接收到从反射层返回的脉冲时，其存在得到了证明。

如果认为赫维赛德所获得的荣誉给他晚年带来了幸福，那就错了。相反，随着岁月流逝，他似乎变得越来越痛苦。1909年，赫维赛德搬到了托基（Torquay），在那里他表现出越来越多的迫害情结迹象。他的邻居们讲述赫维赛德是一个奇怪而痛苦的隐士，他用……替换了他的家具：-

……光秃秃的房间里四处立着花岗岩石块，仿佛某个新石器时代巨人的家具。他在那些奇异的房间里游荡，变得越来越脏，越来越邋遢——只有一个例外。他的指甲总是修剪得极为精致，涂着闪亮的樱桃粉色。

赫维赛德因安德鲁·劳埃德·韦伯为音乐剧Cats创作的歌曲Journey to the Heaviside Layer而更为人所知，该音乐剧改编自T·S·艾略特的诗作：-

向上 向上 向上 经过罗素酒店
向上 向上 向上 到赫维赛德层

然而，恐怕没有多少人理解这位悲伤的、被误解的天才所取得成就的伟大与意义。正如[3]所述，赫维赛德是：-

一位数学思想家，其工作长期未能获得其才华所应得的认可……

Oliver Heaviside's parents were Rachel Elizabeth West and Thomas Heaviside. Thomas was a wood engraver and water colour artist. Oliver, the youngest of his parents four sons, was born at 55 King Street in Camden Town. He caught scarlet fever when he was a young child and this affected his hearing. This was to have a major effect on his life, making his childhood unhappy with relations between himself and other children difficult. However his school results were rather good and in 1865 he was placed fifth from 500 pupils.

Academic subjects seemed to hold little attraction for Heaviside however and at age 16 he left school. Perhaps he was more disillusioned with school than with learning since he continued to study after leaving school, in particular he learnt Morse code, studied electricity and studied further languages in particular Danish and German. He was aiming at a career as a telegrapher and in this he was advised and helped by his uncle Charles Wheatstone (the piece of electrical apparatus known as the Wheatstone bridge is named after him).

In 1868 Heaviside went to Denmark and became a telegrapher. He progressed quickly in his profession and returned to England in 1871 to take up a post in Newcastle upon Tyne in the office of Great Northern Telegraph Company which dealt with overseas traffic.

Heaviside became increasingly deaf but he worked on his own researches into electricity. While still working as chief operator in Newcastle he began to publish papers on electricity, the first in 1872 and then the second in 1873 was of sufficient interest to Maxwell that he mentioned the results in the second edition of his Treatise on Electricity and Magnetism. Maxwell's treatise fascinated Heaviside and he gave up his job as a telegrapher and devoted his time to the study of the work. He later wrote:-

I saw that it was great, greater, and greatest, with prodigious possibilities in its power. I was determined to master the book... It took me several years before I could understand as much as I possible could. Then I set Maxwell aside and followed my own course. And I progressed much more quickly.

Although his interest and understanding of this work was deep, Heaviside was not interested in rigour. His poorest subject at school had been the study of Euclid, a topic in which the emphasis was on rigorous proof, an idea strongly disliked by Heaviside who later wrote:-

It is shocking that young people should be addling their brains over mere logical subtleties, trying to understand the proof of one obvious fact in terms of something equally ... obvious.

Despite this hatred of rigour, Heaviside was able to greatly simplify Maxwell's 20 equations in 20 variables, replacing them by four equations in two variables. Today we call these 'Maxwell's equations' forgetting that they are in fact 'Heaviside's equations'. FitzGerald wrote:-

Maxwell's treatise is cumbered with the debris of his brilliant lines of assault, of his entrenched camps, of his battles. Oliver Heaviside has cleared these away, has opened up a direct route, has made a broad road, and has explored a considerable trace of country.

Heaviside results on electromagnetism, impressive as they were, were overshadowed by the important methods in vector analysis which he developed in his investigations. His operational calculus, developed between 1880 and 1887, caused much controversy however. He introduced his operational calculus to enable him to solve the ordinary differential equations which came out of the theory of electrical circuits. He replaced the differential operator $\Large\frac{d}{dx}\normalsize$ by a variable $p$ transforming a differential equation into an algebraic equation. The solution of the algebraic equation could be transformed back using conversion tables to give the solution of the original differential equation. Although highly successful in obtaining the answer, the correctness of Heaviside's calculus was not proved until Bromwich's work.

Burnside rejected one of Heaviside's papers on the operational calculus, which he had submitted to the Proceedings of the Royal Society , on the grounds that it:-

... contained errors of substance and had irredeemable inadequacies in proof.

Tait championed quaternions against the vector methods of Heaviside and Gibbs and sent frequent letters to Nature attacking Heaviside's methods.

Heaviside went on to achieved further advances in knowledge, again receiving less than his just deserts. In 1887 Preece, a GPO technical expert, wrote a paper on clear telephone circuits. His paper is in error and Heaviside pointed this out in Electromagnetic induction and its propagation published in the Electrician on 3 June 1887. Heaviside, never one to avoid controversy, wrote:-

Sir W Thomson's theory of the submarine cable is a splendid thing. .. Mr Preece is much to be congratulated upon having assisted at the experiments upon which (so he tells us) Sir W Thomson based his theory, he should therefore have an unusually complete knowledge of it. But the theory of the eminent scientist does not resemble that of the eminent scienticulist, save remotely.

In this paper Heaviside gave, for the first time, the conditions necessary to transmit a signal without distortion. His idea for an induction coil to increase induction was never likely to be taken up by the GPO while Preece was in charge of research proposals. Heaviside dropped the idea but it was patented in 1904 in the United States. Michael Pupin of Columbia University and George Campbell of ATT both read Heaviside's papers about using induction coils at intervals along the telephone line. Both Campbell and Pupin applied for a patent which was awarded to Pupin in 1904.

Not all went badly for Heaviside however. Thomson, giving his inaugural address in 1889 as President of the Institute of Electrical Engineers, described Heaviside as an authority. Lodge wrote to Nature describing Heaviside was a man:-

... whose profound researches into electro-magnetic waves have penetrated further than anyone yet understands.

Heaviside was elected a Fellow of the Royal Society in 1891, perhaps the greatest honour he received. Whittaker rated Heaviside's operational calculus as one of the three most important discoveries of the late 19th Century.

In 1902 Heaviside predicted that there was an conducting layer in the atmosphere which allowed radio waves to follow the Earth's curvature. This layer in the atmosphere, the Heaviside layer, is named after him. Its existence was proved in 1923 when radio pulses were transmitted vertically upward and the returning pulses from the reflecting layer were received.

It would be a mistake to think that the honours that Heaviside received gave him happiness in the last part of his life. On the contrary he seemed to become more and more bitter as the years went by. In 1909 Heaviside moved to Torquay where he showed increasing evidence of a persecution complex. His neighbours related stories of Heaviside as a strange and embittered hermit who replaced his furniture with:-

... granite blocks which stood about in the bare rooms like the furnishings of some Neolithic giant. Through those fantastic rooms he wandered, growing dirtier and dirtier, and more and more unkempt - with one exception. His nails were always exquisitely manicured, and painted a glistening cherry pink.

Perhaps Heaviside has become more widely known due to the Andrew Lloyd Webber song Journey to the Heaviside Layer in the musical Cats , based on the poems of T S Eliot:-

Up up up past the Russell hotel
Up up up to the Heaviside layer

However it is doubtful if many people understand the greatness and significance of the achievements of this sad misunderstood genius. As stated in [3] Heaviside was:-

A mathematical thinker whose work long failed to secure the recognition its brilliance deserved ...