## Friday, March 5, 2010

### Heaviside

I noted this with interest recently, a short biographical essay of Heaviside by a descendant of his. Heaviside's primary contribution to science was simplifying the formalism describing electromagnetism developed by James Maxwell - Heaviside even popularized the term Maxwell's Equations.

Surprisingly to me, Heaviside was a controversial man in his day. His simpler, more beautiful formulation was attacked as being lobotomizing Maxwell. Heaviside was an accomplished engineer before, during and after doing his scientific work and indeed much of his work could be thought of as improving the efficiency of Maxwell's equations to the point that they became useful.

I suppose I should mention what these equations are, and though I am a mathematician I will try to use words in order to increase my audience.

Two of the laws are called both called Gauss's Law, after the genius Carl Gauss. Gauss (and unknown to Gauss, before him Lagrange) showed that the flow going out of a volume is equal to the flow leaving the inside. Gauss's 1st law says that the flow of electricity out of a closed surface is the electric charge inside. Gauss's 2nd law says that magnetism does not flow out of a closed surface.

A few things: 1) if there exist electric monopoles (northern compasses with no south, or vice versa) then Gauss's 2nd law would have to be amended slightly, 2) Gauss's Law is equivalent to Coulomb's inverse square law for electric force even without the other laws and 3) nobody likes that these laws are both called Gauss's Law but nobody does anything about it.

Another of Maxwell's laws is known as Faraday's Law, this time after it's discoverer. It states that electromotive force in a circuit is fixed by the rate of magnetic flow through the circuit. This law was discovered empirically by Michael Faraday who - in addition to being one of the greatest experimentalists of all time - was sufficiently handsome in his younger days to warrant his picture here.The final of the four canonical Maxwell's law's is AmpĂ¨re's Law, which states that a magnetic field can be electrical current or by a changing magnetic field. This second fact was discovered by Maxwell, who used it to show that 1) electricity and magnetism are related and 2) light can be modeled as an electromagnetic wave.

It is too bad that figures as important and stolid as Heaviside are now more obscure than flashier figures such as Tesla. The life of science of their days was a deeply vibrant, if one is interested in such narratives. Faraday, for instance, was a fascinating and practical man, the image of the good scientist in the imagination of the time. His Christmas lectures aimed at young people show his astounding plainness of thought (I mean this as a high compliment, after all is it not often said to seek simplicity in all things?) and his respect for his countrymen.

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