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Oliver Heaviside (1850-1925)

Oliver Heaviside is someone whom you may not have heard about either. His name

doesnt resonate in the education system as often as Newton, Archimedes, Lorentz, Euler,Poincare`, but it should. He was a remarkable individual and a huge contributor toward

mathematics and physics.

He dropped out of high-school at the tender age of sixteen to pursue an engineering

position at a telegraph cable company and became enthralled with signal processing and electric

measurement. With that, he published a paper in 1873 on a theorem of duplex telegraphy - which

met great success with Maxwell and Thomson who were top electrical scientists at the time. His

paper postulated that more than one signal can be transmitted through the same wire at the same

time. By age 24, he resigned from the cable business and returned home to London to continue

research on signal processing. Not too long after, he had completed his work which was anelaboration on eliminating electromagnetic interference in telegraph wires in a process called

diffusion of voltage and current. He added that signals behaved as oscillatory wavelets.

And if that wasnt innovative enough, the ultimate contribution came from his shortening

of the original 20 Maxwell equations. You have heard there are only 4 of them. Yes, there are,

but not until after Heaviside curtailed the use of quaternions Maxwell had used (Hamiltonians)

into four simple differential equations using vector algebra. He also solved the problem in

Maxwells paper of how energy transfer works in a circuit by a vector component and

divergence theorem ofenergy curl. Unfortunately, John Poynting had submitted the same

postulate shortly before him. Nevertheless, it was conceived before that the electromagneticfields were generated by moving charges, but they found current is what generates them. This is

where the right-hand rule comes in which was developed later on by British physicistcurrent

generates the field perpendicular to it.

Later in his year, after the invention of the telephone, Oliver and his brother discovered

how parallel circuits with the use of inductors diffuse interference and improve signal in

telephones. This was later coined inductive loading. There was a political fiasco that resulted

in this paper, but I will leave that to the reader.

In further contributions to mathematics, Laplace transforms, a hypothetical s-space istransformed into a real space. Oliver invented the step function in Laplace transforms which

describes the activity of current in electrical circuits with respect to time. He did this by

incorporating the Dirac delta function which means the function asymptotically converges to

zero everywhere.

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You can see here in the image below where there is a big jump in current at 0. This is

called a piecewise function (Heaviside step function) and the second is a continuous function.

Piecewise functions are discontinuous as it appears.

Image: Wolframalpha.com

One thing sadly left out in the resource for my paper is that he had also invented thecover-up method of solving unknowns inpartial fractions (a huge headache-saver for me

personally in differential equations).

Oliver Heaviside died in 1925 a rather grumpy and isolated old chap. Although can you

blame him? He was never truly recognized as brilliant in abilities, intelligence and contribution

as the well-known mathematicians and physicists of his time. In fact, a lot of times his work was

unnecessarily shafted in academic journals. It makes me smile a bit whenever I hear a professor

who mentions his name. Its as if to say this is the guy you should be idolizing because he made

many things a hell of a lot easier for us physicists and mathematicians.

That of a Shakespeare or a Newton is stupendous. Such men live the best

parts of their lives after they shuffle off the mortal coil and fall into the

grave. Maxwell was one of those men. His soul will live and grow for

long to come, and, thousands of years hence, it will shine as one of the

bright stars of the past, whose light takes ages to reach us, amongst the

crowd of others, not the least bright.Oliver Heaviside

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