A tap dripping into a dirty frying pan may not be as evocative as Newton’s apple but it did get me wondering about mathematics. More particularly I started to think about whether it is possible to appreciate the beauty of maths without the maths.
It was a very prosaic situation. Water dripped slowly from the tap into a dirty frying pan that needed to be washed up. The pan was flat in the sink and filled with water. Each drop from the tap hit the surface off-centre sending out ripples which hit the edge of the pan and bounced back to meet at another point. They then bounced back again (or passed through each other?) to hit the sides of the pan before bouncing inwards to meet at the point where they first hit the surface. The drips from the tap were perfectly timed so that when the surface settled another drop fell to start the cycle over again.
It was all so elegant and simple. There were no equations involved but I could see in the combination of points and circles and movement that something mathematically beautiful was being expressed.
I am not a mathematician but there have been occasions when I have felt the beauty of an equation, not simply knowing what it means but a visceral reaction not unlike listening to music (Elgar’s cello concerto or Barber’s adagio often provides good examples of this sense). When this happens I envy mathematicians who can listen to the music of their numbers.
Watching the circles ripple in the pan I caught a tantalisingly snatch of mathematical music. This was not maths explaining something we already recognise as beautiful. There is not much beauty in a dirty frying pan. The beauty must have been in sensing the maths that gave form to what I watched.
Is it possible to appreciate maths in this way, to see the beauty and hear the music but without actually knowing the maths involved? If this is possible then how might we work with this in public engagement, not just with maths but other aspects of science?
PS. Since writing this post I have found a beautiful example of how to see prime numbers which can be found here.