Occasionally I get asked what it was that first attracted me to physics. There are many possible answers (If you’re keen, you can find a couple of them here). But part of the answer is definitely something I’d call the ‘economy of solutions’.
What I mean is that when we try to analyse and understand a wide variety of physical systems, the same pieces of mathematics turn up over and over again. This is very economical in terms of brain power. It also means that putting in the effort to understand one particular, perhaps obscure, physical system, often gives you a head start on understanding many others.
Simple harmonic motion is one such ubiquitous piece of maths. ‘Bessel functions’ are another. Bessel functions are named after the Friedrich Wilhelm Bessel (1784 – 1846). He is described on Wikipedia as a ‘German astronomer, mathematician, physicist and geodesist’. Those were the interdisciplinary days.
‘Function’ is a a word we use to describe any equation which tells you how one thing depends on another. For example, if you have lots of squares with sides of different length, the area is always the length squared. That is, Area = length x length. The area is a particular function of the length, in this case its square.
One place Bessel’s eponymous functions arise is when you have some kind of wave (which will be described by an equation of motion) trapped in a circular region. This applies to systems which are, on the face of it, vastly different. From the quantum field of electrons trapped by a ring of iron atoms, to the coffee in a mug, for example. The whole thing is enthusiastically described and demonstrated in this great Sixty Symbols video, by Philip Moriarty:
Coffee is very important in science of course, turning up if anything more often than Bessel functions.
As a struggling guitarist, I also found it very interesting to see how much the neighbouring strings participate when Moriarty plucks a single string. I wonder how much that affects the sound? There’s an equation for that somewhere...
See also Philip Moriarty’s blog about that video here.
Jon Butterworth’s book Smashing Physics is available as “Most Wanted Particle” in Canada & the US. He is also on Twitter.
