In his book Control System Design, Bernard Friedland writes (section 4.2, page 115):
The roots of the denominator [of a rational function] are called the poles of the transfer function because $H(s)$ becomes infinite at these complex frequencies and a contour map of the complex plane appears as if it has poles sticking up from these points.
Is there any historical legitimacy to this explanation of the origin of the word "pole" to describe a root of the denominator of a rational function?