Fun with diﬀerential equations
it comes to diﬀerential equations, things start to get prey 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–Kua 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.
Analogies and analogue computers When faced with a problem to solve, there are two approaches we could take. The first is to recreate a scaled model of the problem to be investigated, based on exactly the same physical principles as the full size version. This is oen done in, for example, structural analysis: Antoní Gaudi first used strings and weights to build a smaller model of his Church of Colònia Güell near Barcelona to help him determine whether it 53
Analogue computers were the workhorses of computing from the 1940s to the mid-1980s.