## Monday, May 18, 2015

### Oliver Heaviside

I’ve written about the brilliance of James Clerk Maxwell, the man who developed a complete set of equations that describe electro-magnetic emissions that we commonly call “radio waves.” His work was one of the key stepping stones to our modern understanding of the universe including the constant speed of light and Einstein’s equations of relativity.

But these advances, key as they are, were more like tiny steps with many minds slowly unraveling the mysteries of creation. Maxwell’s breakthrough was a giant leap, but it was based on the previous insights of others including Michael Faraday, Johann Carl Friedrich Gauss (one of the three greatest mathematicians of all time in addition to a damn good physicist), and André-Marie Ampère. Throw in some important work by Hendrik Antoon Lorentz and Oliver Heaviside and you arrive at the refined version: the four vector equations now commonly known on college campuses as Maxwell’s equations. (I’m sure you’ve seen the tee shirt.)

The Lorentz Force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. The first derivation of the Lorentz force is commonly attributed to Oliver Heaviside in 1889, although other historians suggest an earlier origin in an 1865 paper by James Clerk Maxwell. Hendrik Lorentz derived it a few years after Heaviside.

May 18 is the birthday of Heaviside, who was born in 1850 in London. Heaviside's uncle was Charles Wheatstone, who co-invented one of the first practical telegraph systems. Wheatstone supported his nephew's education and his career in the growing field of telegraphy. By the age of 22, Heaviside had published a paper on the best way to use a Wheatstone bridge.

In 1873, when Heaviside came across James Clerk Maxwell's A Treatise on Electricity and Magnetism, he recognized its revolutionary importance and resolved to study the mathematics needed to understand it. Heaviside went beyond merely understanding the work. Using vector notation, he recast Maxwell's original 20 equations into the four familiar equations that we learn today.

He was a self-taught electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques for 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. Although at odds with the scientific establishment for most of his life, Heaviside changed the face of telecommunications, mathematics, and science for years to come.

He applied the equations to investigate such problems as the behavior of charges moving in electromagnetic fields and to predict the existence of an ionized layer in Earth's upper atmosphere that allows the transmission of radio signals around the planet's curved surface. He also invented and patented the coaxial cable for transmitting radio-frequency electromagnetic signals.

Perhaps he is best known among the general public for an upper layer of the Earth’s atmosphere that carries his name. The Kennelly–Heaviside layer, named after Arthur E. Kennelly and Heaviside, also known as the E region or simply the Heaviside layer, is a layer of ionized gas occurring between roughly 56–93 miles above the ground — one of several layers in the Earth's ionosphere. It reflects medium-frequency radio waves, and because of this reflection, radio waves can be propagated beyond the horizon.

This atmospheric phenomenon has appeared in more than just scientific texts. The Heaviside layer is used as a metaphor for heaven in Andrew Lloyd Webber's musical Cats. This reference is based on a quotation found in a letter written by T. S. Eliot, whose book Old Possum's Book of Practical Cats forms the basis of the musical. In the musical, one cat is chosen each year by Old Deuteronomy to go to the Heaviside Layer and begin a new life. In the song "The Journey to the Heaviside Layer,” it is stated that the Heaviside Layer is "past the Russell Hotel" and "past the Jellicle moon,” indicating that it is very far away and difficult to access. (“Jellicle” is a kind of cat, commonly nocturnal black-and-white cats.)

But I’m just “Ham”-ing it up with that fact.

Happy birthday Oliver.