Oliver Heaviside, Fractional Operators, and the Age of the Earth

Abstract

Oliver Heaviside is today usually remembered by technologists as an eccentric electrical engineer who once had something to do with the ionosphere. Sometimes it is even recalled he had a curious method (called the "operational calculus") for doing his mathematics, and somehow applied it in a strange and mysterious manner to difficult problems. One of these problems was that of calculating the age of the Earth, and it got Heaviside indirectly involved in a controversy that included Lord Kelvin. The new theories of evolution and geology were explicitly tied to the debate. This paper describes the historical context of the controversy, and outlines how Heaviside used his operational methods to demonstrate Kelvin's estimate of the Earth's antiquity to be mathematically simplistic. Heaviside used his "age-of-the-Earth" analyses as the lead to the second volume of his Electromagnetic Theory, partly to demonstrate the power of his operational methods (which he then applied to electrical problems). These methods were the precursor to the now common use of the Laplace transform by electrical engineers.

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