Believe it or not, I never leave home without my trusty slide rule in my pocket. In the years before 1970, this would have been totally normal for any engineer, with the slide rule being the archetypal symbol of the engineering profession, much like how the stethoscope remains that of the medical profession. However, with the advent of the pocket calculator, the slide rule has completely vanished from public view and its demise is a wonderful example of a paradigm shift, as described by Thomas S Kuhn in The Structure of Scientific Revolutions.
I often get asked “What are you doing with that thing?” when I grab my slide rule to convert miles to kilometres or, once I’ve finished refuelling, to calculate my fuel economy. Most of my students have never seen a slide rule and are at first quite incredulous when I show them my Faber–Castell 62/82N. Not that I’ve ever managed to convince one of them to switch to a slide rule, but at least I normally manage to instil some interest in them for these mathematical instruments.
When it comes to differential equations, things start to get pretty complicated—or at least that’s what it looks like. When I studied mathematics, lectures on differential equations were considered to be amongst the hardest and most abstract of all and, to be honest, I feared them because they really were incredibly formalistic and dry. This is a pity as differential equations make nature tick and there are few things more fascinating than them.
When asked about solving differential equations, most people tend to think of a plethora of complex numerical techniques, such as Euler’s algorithm, Runge–Kutta or Heun’s method, but few people think of using physical phenomena to tackle them, representing the equation to be solved by interconnecting various mechanical or electrical components in the right way. Before the arrival of high-performance stored-program digital computers, however, this was the main means of solving highly complicated problems and spawned the development of analogue computers.